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Transcriber's Note.

Apparent errors in mathematical expressions have been retained,
although apparent typographical errors elsewhere in the text have been
corrected. Inconsistencies in hyphenation have been retained.

Gesperrt font has been condensed. Small capitals have been replaced by
full capitals. Brackets extending over several columns have been
replaced by columns of standard brackets. Words that are stacked one
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sentence or paragraph includes a word in ordimary font this is also
indicated by _underscores_.

Mathematical variables are usually italicised. In order to avoid an
excessive number of underscores, and where it is possible without
ambiguity, complete mathematical expressions have instead been encased
in underscores. These usually extend over mathematical operators (such
as "+"), or Greek characters, that are not italicised.

The more complex mathematical expressions have been separated out from
the surrounding text. Fifth roots and nth roots are indicated by [⁵√]
and [ⁿ√] respectively.

The decimal point may be indicated by a "." or "," while illustrations
are referred to as a "Plate" or a "Tab."

The Table of Discourses has been amended to include one omitted title
and to correct erroneous page numbers.




[Illustration, probably of Charles II: _M: Vᵉʳ Gucht Sculp:_]




_Miscellanea Curiosa._

CONTAINING A COLLECTION

Of some of the Principal

_PHÆNOMENA_

IN NATURE,

Accounted for by the Greatest Philosophers of this Age;

BEING THE

 Most Valuable DISCOURSES, Read and Delivered to the ROYAL SOCIETY, for
   the Advancement of Physical and Mathematical Knowledge.

 As also a Collection of Curious _Travels_, _Voyages_, _Antiquities_,
   and _Natural Histories_ of Countries; Presented to the same _Society_.

In Three VOLUMES.

 _The Second Edition_; To which is added, A Discourse of the _Influence_
   of the _Sun_ and _Moon_ on _Humane Bodies_, &c. By R. _MEAD_, M. D.
   F. R. S. And also _Fontenelle's Preface_ of the _Usefulness_ of
   _Mathematical Learning_.

VOL. I.

LONDON:

 Printed by _F. M._ for _R. Smith_, at the _Bible_ under the
   _Piazza_ of the _Royal Exchange_ in _Cornhill_. 1708.




TO THE READER.


Some of the Principal Discoveries and Enquiries, both in _Physical_ and
_Mathematical_ Learning, being register'd in the Voluminous Journals of
the _Royal Society_, are amongst a multitude of less useful Matters, so
Obscurely hid, that but very few inquisitive Gentlemen ever so much as
heard of them.

The Design therefore of the ensuing Collection, is to digest in a
convenient Method, all the most curious _Philosophical_ and
_Mathematical_ Discoveries, as they are to be met with, which may any
way tend to the Use of Life or Advancement of Arts and Sciences.

And on this Occasion, it will be convenient to intimate to the Reader;

_First_, That the Theories and Discourses here collected, have already
past the Censure of the _Learned World_: Who have acknowleg'd them the
most satisfactory Accounts of Nature's Proceedings, wherein some of her
greatest Depths are fathom'd, and a Foundation laid for Posterity to
build an infinite _Superstructure_.

_Secondly_, That they are related (_Verbatim_) just as they were
delivered in, or read before the _Royal Society_: For it has been the
Opinion of the most Judicious among those _Honourable Members_, that it
is impossible so to abridge them, (which are but Abridgments themselves)
as not to render them obscure and unintelligible.




A TABLE OF THE

_Discourses_ contain'd in this _Volume_.


 _An Estimate of the Quantity of _Vapours_ raised out of the Sea,
   as derived from Experiment: Together with an Account of the
   _Circulation_ of the wat'ry Vapours of the Sea, and of the Cause of
   _Springs_. Presented to the Royal Society by Mr. _E. Halley_,
   F. R. S._                                                      Pag. 1

 _The True Theory of the _Tides_, extracted from that admired Treatise
   of Mr. _Isaac Newton_, Intituled _Philosophiæ Naturalis Principia
   Mathematica_; being a Discourse presented with that Book to the late
   King _James_, by Mr. _E. Halley_._                                 13

 _A Theory of the _Variation_ of the _Magnetical Compass_, by
   Mr. _E. Halley_._                                                  27

 _An Account of the Cause of the Change of the _Variation_ of the
   _Magnetical Needle_, with an Hypothesis of the Structure of the
   _Internal Parts_ of the _Earth_; as it was presented to the Royal
   Society in one of their late Meetings, by Mr. _E. Halley_._        43

 _An Historical Account of the _Trade-Winds_ and _Monsoons_, observable
   in the Seas between and near the _Tropicks_; with an Attempt to
   assign the Physical Cause of the said Winds, by Mr. _E. Halley_._  61

 _A Discourse of the Rule of the Decrease of the Heighth of the
   _Mercury_ in the _Barometer_, according as Places are elevated above
   the Surface of the _Earth_; with an Attempt to discover the true
   Reason of the rising and falling of the _Mercury_, upon Change of
   Weather, by Mr. _E. Halley_._                                      81

 _A Letter from Mr. _Isaac Newton_, while Professor of the Mathematicks
   in the University of _Cambridge_; containing his new _Theory_ about
   _Light_ and _Colours_: Sent from _Cambridge, Feb. 6. 1671/72._ in
   order to be communicated to the Royal Society._                    97

 _A farther Explanation of the same _Theory_._                       114

 _A Demonstration concerning the _Motion of Light_, communicated from
   _Paris_._                                                         118

 _An Introductory Essay to the Doctrine of _Sounds_, containing some
   Proposals for the Improvement of _Acousticks_; as it was presented to
   the _Dublin_ Society, by the Right Reverend Father in God
   _Narcissus_, Lord Bishop of _Ferns_ and _Leighlin_._              121

 _A Discourse concerning the Modern _Theory_ of _Generation_, by Dr.
   _Geo. Garden_, of _Aberdeen_, being part of a Letter to Dr. _William
   Musgrave_, L. L. D. _Reg. Soc. S._ and by him communicated to the
   Royal Society._                                                   142

 _A short Discourse concerning _Concoction_ Read at a Meeting of the
   _Royal Society_, by _Clopton Havers_, M. D. Fellow of the Royal
   Society._                                                         153

 _A Discourse concerning some Influence of _Respiration_ on
   the Motion of the _Heart_ hitherto unobserved. By _J. Drake_, M. D.
   F. R. S._                                                         171

 _Some Thoughts and Experiments concerning _Vegetation_. By _John
   Woodward_, M. D. of the College of Physicians and Royal Society, and
   Professor of Physick in _Gresham-College_._                       203

 _An Account of the Measure of _Gold_ upon Gilt Wire; together with a
   Demonstration of the exceeding Minuteness of the _Atoms_, or
   constituent Parts of _Gold_; as it was read before the _Royal
   Society_, by Mr. _E. Halley_._                                    243

 _An Account of the several Species of _Infinite Quantity_, and of the
   Proportions they bear one to the other; as it was read before the
   _Royal Society_, by _E. Halley_._                                 246

 _An Account of Dr. _Robert Hook's_ Invention of the _Marine Barometer_,
   with it's Description and Uses. Published by Order of the Royal
   Society by Mr. _E. Halley_._                                      250

 _A Discourse concerning the _Proportional Heat_ of the Sun in all
   _Latitudes_; with the Method of collecting the same, as it was read
   before the _Royal Society_ in one of their late Meetings, by Mr. _E.
   Halley_._                                                         256

 _Concerning the Distance of the _Fixed Stars_, by the Honourable _Fran.
   Roberts_, Esq; F. R. S._                                          265

 _Mr. _Isaac Newton's_ Theory of the _Moon_._                        268

 _An estimate of the Degrees of the Mortality of _Mankind_, drawn from
   Curious Tables of _Births_ and _Funerals_ at the City of _Breslaw_;
   with an Attempt to ascertain the _Price of Annuities_ upon Lives, by
   Mr. _E. Halley_._                                                 280

 _A Discourse concerning _Gravity_, and its Properties, wherein the
   Descent of _Heavy Bodies_, and the Motion of _Projects_ is briefly,
   but fully handled: Together with the Solution of a Problem of great
   Use in _Gunnery_, by Mr. _E. Halley_._                            302

 _A Proposition of General Use in the Art of _Gunnery_, shewing the Rule
   of laying a _Mortar_ to pass, in order to strike any Object above or
   below the Horizon, by Mr. _E. Halley_._                           326

 _A Discourse concerning the Measure of the Air's Resistance to Bodies
   moved in it. By the Learned _John Wallis_, S. T. D. and F. R. S._ 332

 _An Instance of the Excellency of the Modern _Algebra_, in the
   Resolution of the Problem of finding the _Foci_ of Optick Glasses
   universally. By Mr. _E. Halley_, S. R. S._                        348

APPENDIX.

 _An Analytical Resolution of certain Equations of the 3d, 5th, 7th, 9th
   Powers, and so on _ad Infinitum_, in finite Terms, after the manner
   of _Cardan's_ Rules for Cubicks. By Mr. _A. Moivre_, F. R. S._    365

 _A Discourse concerning the Action of the Sun and Moon on Animal
   Bodies; and the Influence which this may have in many Diseases. By
   _Richard Mead_, M. D. F. R. S._                                   371




 _A Translation of Part of Monsieur _Fontenelle's_ Preface to the
   Memoirs of the Royal Academy at _Paris_, in the Year 1699. treating
   of the Usefulness of Mathematical Learning._


But to what purpose should People become fond of the Mathematicks and
Natural Philosophy. Of what use are the Transactions of the Academy?
These are common Questions, which most do not barely propose as
Questions; and it will not be improper to clear them.

People very readily call useless, what they do not understand. It is a
sort of Revenge; and as the Mathematicks and Natural Philosophy are
known but by few, they are generally look'd upon as useless. The reason
of this is; because they are crabbed and not easily learnt.

We have a Moon to light us in the Night; What is it to us, say they,
whether _Jupiter_ hath four? Why so many laborious Observations, so many
tedious Calculations to know exactly their Course? They'll not afford us
the more Light for it; and Nature, which hath plac'd these little
Planets without the reach of our Eyes, doth not seem to have made them
for us. According to this plausible Argument they ought not to have been
observ'd with a Telescope, nor study'd. But it is certain, that we had
been considerable Loosers by it: For those who have some insight into
the Principles of Geography and Navigation know, that since these four
Moons about _Jupiter_ have been discover'd, they have been more useful
to those Sciences than our own Moon; and that they serve, and shall more
and more serve to make new Sea-Charts, infinitely more exact than the
Old; and are likely to save the Lives of a vast many Seamen. Did we reap
no other advantage from Astronomy than this from these Satellites of
_Jupiter_, that wou'd be sufficient to justifie those prodigious
Calculations, those assiduous and nice Observations, this great number
of elaborate Instruments, and this Noble Edifice built only for this
Science. However the greatest part of Mankind know nothing of these
Satellites of _Jupiter_, unless perhaps by hear-say, and that too
confusedly; or else they are ignorant of what Affinity they have with
Navigation, or of the great Improvements which have been lately made in
it.

This is the Fate of Sciences, which are study'd and improv'd by few.
Most People are not sensible of their Progress, and especially when made
in some mean Callings. But what doth it signifie, that we can now more
easily direct the Course of Rivers, cut out Canals, and settle new
Navigations; because our Method of taking the Level and making Sluces is
infinitely better than heretofore? Some Masons and Seamen have thereby
found their Business easier, but they themselves were not sensible of
the Skill of the Geometrician who directed them. They were mov'd, as the
Body by a Soul, it doth not know. Others are yet less sensible of the
Genius that presided over the Undertaking; and the World is the better
for its succeeding well, but not altogether free from Ingratitude.

Anatomy, which is some time since so carefully study'd, can't become
more exact, but Chyrurgical Operations must also be more sure. Surgeons
know this; but those who receive the Benefit of their Art know nothing
of it. And indeed how should they? They would be oblig'd to compare Old
with Modern Surgery; and this wou'd take too much Time, and go against
the Grain: So that since the Operation hath succeeded well, they do not
think it material to know whether it had succeeded as well in another
Century.

It is strange that so many things are before our Eyes, and that we do
not see them. Your Handycraft Shops are full of ingenious Works; but yet
we hardly mind them: And very useful and well contriv'd Instruments and
Experiments want Spectators, who wou'd be wonderfully pleas'd, wou'd
they take the pains to admire them.

If a Learned Society have made some Improvements in Geometry, Anatomy,
Mechanicks, or any other useful Science, it must not be expected, that
the World will go back to so remote a Spring to thank and applaud them
for the Usefulness of their Productions: For it will be more easie to
enjoy the Benefit of their Discoveries and Improvements than to know
them. The Determination of Longitude by the Satellites, the Discovery of
the _Ductus Thoracicus_, a more convenient, and more exact Level, are
not Novelties so fit to make a noise as a pleasant Poem, or a handsome
Piece of Oratory.

Altho' the Usefulness of Mathematicks and Natural Philosophy is obscure,
yet it is real. To consider Mankind in their Natural State, nothing is
more useful to them, than what may preserve their Lives, and produce
those Arts, which are both great Helps and Ornaments to Publick
Societies.

As for what concerns the Preservation of Life, it peculiarly belongs to
Physick; which for that reason is divided in the Academy into three
Branches, which make three different sorts of Members of this Society,
Anatomy, Chymistry, and Botanicks. Every Body knows of what Importance
it is to have an exact Knowledge of Human Body, and of what Medicines
may be extracted from Minerals and Plants.

As for Arts, too tedious to be reckon'd, they depend some upon Natural
Philosophy, others upon Mathematicks.

One wou'd think at first, that if the Mathematicks were to be confin'd
to what is useful in them, they ought only to be improv'd in those
things, which have an immediate and sensible affinity with Arts, and the
rest ought to be neglected as a Vain Theory. But this wou'd be a very
wrong Notion. As for Instance, the Art of Navigation hath a necessary
Connexion with Astronomy, and Astronomy can never be too much improv'd
for the Benefit of Navigation. Astronomy cannot be without Opticks by
reason of Perspective Glasses; and both, as all other Parts of
Mathematicks, are grounded upon Geometry, and to go as far as you can,
even upon Algebra.

Geometry, and especially Algebra, are the Keys of all the Inquiries,
that can be made concerning Magnitude. These Sciences which are only
conversant about abstruse Relations, and simple Ideas, may seem dry and
barren, whilst they keep within the Verge of the Intellectual World; but
mixt Mathematicks, which stoop to Matter, and consider the Motion of the
Stars, the Augmentation of moving Forces, the different Passages of the
Rays of Light through different Mediums; the different Effects of Sound
by the Vibration of Things; to conclude all those Sciences, which
discover the particular Relations of Sensible Magnitudes go on farther
and more securely, when the Art of discovering Relations in General is
more perfect. The Universal Instrument cannot be too extensive, too
handy, or too easily apply'd: It is useful to all the Sciences, and they
cannot be without it: And therefore among the Mathematicians of the
Academy, who are design'd to be useful to the Publick, the Geometricians
and Algebrists make a Class, as well as the Astronomers and Mechanicks.

However, it is certain, that Speculations purely of Geometry, or of
Algebra, are not about useful things: But it is certain too, that those
that are not, either lead or belong to those that are. It is in it self
a very barren thing to know, that in a Parabola a Subtangant is double
the corresponding Abscissæ; but yet it is a Degree of Knowledge
necessary to the Art of throwing Bombs, so exactly as they can do now.
There are not by far so many evident Uses as Propositions or Truths in
the Mathematicks: Yet it is enough if the Concourse of several Truths is
generally of some use.

Farther, a Geometrical Speculation, which was not at first applicable to
any use, becomes so afterwards. When the greatest Geometricians in the
Seventeenth Century set about to study a new Curve, which they call'd a
Cycloide, they only engag'd themselves in a meer Speculation out of
Vanity, striving to outdo one another by the Discovery of difficult
Theorems. They did not even pretend that this was for the Publick Good;
however by diving into the Nature of the Cycloide it was found, that it
was destin'd to make Pendulums as perfect as may be, and carry the
Measure of Time as far as it can go.

It is the same thing with Natural Philosophy as with Geometry. The
Anatomy of Animals seems insignificant; and it only concerns us to know
that of Human Body. But yet some Parts of it, which are of so nice, or
so confus'd a Make, that they are invisible, are sensible and manifest
in the Body of an Animal. Hence it is, that Monsters themselves are not
to be neglected. The Mechanism conceal'd in a particular Kind or in a
common Make, is unfolded in another kind, or in an extraordinary Make;
and one wou'd be almost apt to say, that Nature by multiplying and
varying so much her Works, can't sometimes forbear betraying her
Secrets. All that the Antients knew of the Load-stone, was, that it
attracts Iron. But whether they did not value a Curiosity, which
promis'd them nothing; or that their Genius did not lead them to make
Experiments, they have not examin'd this Stone as carefully as they
might. One Experiment taught them, that it turns of its self towards the
Poles of the World, and did put into their Hands the inestimable
Treasure of the Mariners Compass. They might easily have made this
Discovery important, and yet they did not do it; and if they had spent a
little more time upon a Curiosity which seem'd useless to them, the
Latent use of it had soon appear'd.

Let us always make a Collection of Mathematical and Physical Truths;
happen what it will we can't hazard much by it. It is certain, that they
shall be drawn from Springs, whence a great many useful ones have
already been drawn. We have reason to presume, that we shall draw from
thence, some that shall shine as soon as they are discover'd, and
convince us of their Usefulness. Other Truths shall stay some time till
a piercing Meditation, or some happy Accident discovers their Use. Some
Truths being consider'd by themselves shall be barren, till they are
consider'd with reference to one another. Lastly, let the worse come to
the worse, some shall be eternally useless.

I mean useless with reference to sensible and gross Uses; for otherwise
they shall not be so. An Object upon which alone you cast your Eyes is
the clearer and brighter, when the neighbouring Objects, which however
you do not look upon, are also enlighten'd; because it hath the Benefit
of the Rays, which are reflected from them. Thus those Discoveries,
which are palpably useful, and deserve our chiefest Attention, are in
some measure enlighten'd by those, which may be call'd useless. For all
Truths make one another more lucid.

It is always useful to have right Notions, even of useless Subjects. And
tho' we cou'd reap no benefit by the Knowledge of Numbers and Sines, yet
it wou'd still be the only certain Knowledge granted to our Natural
Light, and they wou'd serve to give our Reason the first Habit of and
Inclination to Truth. They wou'd teach us to operate upon Truths; to
take the Thread of them, which is generally very fine and almost
imperceptible; and to follow it as far as it reaches: In a word, they
wou'd make Truth so familiar, that we might on other Occasions know it
at first sight, and almost by Instinct.

A Geometrical Genius is not so confin'd to Geometry, but that it may be
capable of learning other Sciences. A Tract of Morality, Politicks, or
Criticism, and even a Piece of Oratory, supposing the Author qualify'd
otherwise for those Performances, shall be the better for being compos'd
by a Geometrician. That Order, Perspicuity, _Precision_ and Exactness,
which some time since are found in good Books, may originally proceed
from that Geometrical Genius, which is now more common than ever, and in
some manner is communicated by one Relation to another, nay even to
those that do not understand Geometry. Sometimes a Great Man draws all
his Cotemporaries after him; and he who hath the justest Claim to the
Glory of having settled a new Art of Arguing, was an Excellent
Geometrician.

Lastly, whatever raises us to Great and Noble Reflexions, tho' they be
purely Speculative, afford a Spiritual and Philosophical _Utility_. The
Wants of the Mind are perhaps as many as those of the Body. She desires
to extend her Knowledge: All that can be known, is necessary to her, and
there can be no better Proof than this, that she is design'd for Truth.
Nothing perhaps can redound more to her Glory, than the Pleasure that is
felt sometimes, in spight of ones self, in the dry and crabbed Questions
of Algebra.

But without running counter to the common Notions, and recurring to
Advantages which may seem too far fetch'd and refin'd, it may fairly be
own'd, that the Mathematicks and Natural Philosophy have some things
which are only subservient to Curiosity; and so have those Sciences
which are most generally acknowledg'd to be useful, as History, _&c._

History doth not in every Part of it supply us with Examples of Vertue
and Rules for our Behaviour. For besides these, therein you have a View
of the perpetual Revolutions of Human Affairs, of the Beginning and Fall
of Empires, of Manners, Customs, and Opinions which continually succeed
one another; and in a word, of all that rapid, tho' insensible, Motion
that carries all before it, and incessantly alters the Face of the Earth.

Had we a mind to oppose Curiosity to Curiosity, we shou'd find that
instead of the Motion, which agitates Nations, and gives birth to, and
destroys States; Natural Philosophy considers that Great and Universal
Motion, which hath put the whole Frame of Nature in Order, and suspended
the Cœlestial Bodies in several Spheres, and which illuminates and
extinguishes some Stars; and by following always unalterable Laws,
diversifies its effects _ad infinitum_. If the surprising difference of
Manners and Opinions of Mankind is so entertaining; there is too a great
deal of Pleasure to study the prodigious diversity of the Structure of
the different Species of Animals, with reference to their different
Functions, to the Elements they live in, to the Climates they inhabit,
and the Aliments they are to take, _&c._ The most curious strokes of
History shall hardly be more curious than the _Phosphorus_, the cold
Liquors which being mixt together, break out into a flame; Silver Trees,
the almost Magical Operations of the Load-Stone, and a vast number of
Secrets, which Art hath discover'd by a near and diligent Scrutiny of
Nature.

Lastly, Natural Philosophy doth as much as it is possible unravel the
Footsteps of that Infinite Intellect and Wisdom, who hath made all
things: Whereas the Object of History are the disorderly Effects of the
Passion, and of Humane Caprices; and so odd a Series of Events, that
some formerly fancy'd that a Blind and Senseless Deity had the Direction
of them.

We must not look upon the Sublime Reflexions which Natural Philosophy
leads us to make concerning the Author of the Universe, as meer
Curiosities. For this stupendous Work, which appears always more
wonderful the more we know it, gives us such exalted Notions of its
Maker, that they fill our Minds with Admiration and Respect. But above
all, Astronomy and Anatomy are the two Sciences which more palpably lay
before us two grand Attributes of our Creator; one his Immensity by the
distance, Magnitude and Number of Cœlestial Bodies; the other his
Infinite Knowledge by the Mechanism of Animals. True Natural Philosophy
is a kind of Theology.

The different views of Humane Understanding are almost infinite; and
Nature is really so. So that we may every day expect some Discoveries,
either in Mathematicks or Natural Philosophy, which shall be of a new
sort of Utility or Curiosity. Make a Collection of all the different
Advantages which the Mathematicks afforded a Hundred Years ago, and
you'll find nothing to be compar'd to the Perspective Glasses they have
furnish'd since that time, and which are a new Organ to the Sight, and
cou'd not be expected from Art. How surpriz'd had the Ancients been, if
they had been told that their Posterity, by the help of some
Instruments, shou'd one day see a vast number of Objects which they did
not see; a Heaven that was unknown to them; and Plants and Animals they
did not even suspect it was possible to exist. Naturalists had already a
great many curious Experiments; but within about half a Century, the
Air-Pump hath produced a prodigious quantity of them wholly new, and
which by shewing Bodies in a Space void of Air, shews them as
transported in a World different from ours, where they undergo
Alterations whereof we had no Notion. The Excellency of Geometrical
Methods, which are every day invented and improv'd, may perhaps at last
exhaust Geometry; that is, The Art of making Geometrical Discoveries,
and that is all: Whereas Natural Philosophy, which contemplates an
Object of an unlimited Variety, and _Fæcundity_, shall always find room
for new Observations, and opportunities to increase its vast Stock, and
shall have the Advantage of never being a compleat Science.

There are so many things to be discover'd, whereof a great part, in all
likelyhood shall never be known; that they give an opportunity to those
who will not encounter with the Thorns and Difficulties of Natural
Philosophy, to affect a sort of Discouragement. A great many to vilify
this Natural Science, pretend a mighty veneration for the works of
Nature, and that they are absolutely incomprehensible. However, Nature
is never so admirable, nor so admir'd as when known. True it is, that
what is known is inconsiderable in comparison of what is not yet known.
Nay, Sometimes what is not known, is exactly what seems shou'd be the
soonest known. As for instance, it is not at least certainly known, why
a Stone thrown up into the Air falls down again; but we certainly know
the cause of the Rainbow, why it doth not exceed a certain height; why
its breadth is always the same; why when there are two Rainbows at the
same time, the Colours of the one are overset with reference to the
Colours of the other; and yet the fall of a Stone in the Air appears a
more simple Phænomenon, than the Rainbow. But in a word, altho' we do
not know every thing, we are not neither ignorant of every thing. And
altho' we are ignorant of the most simple Events, yet we have a
knowledge of what seems the most Complex. So that if we have on the one
hand reason to fear, lest our Vanity shou'd flatter us with the hopes of
attaining to the knowledge of things above our reach; on the other we
ought to dread, lest our Slothfulness should also flatter us that we are
condemn'd to a greater degree of Ignorance than really we are.

People may think that the Sciences do not begin to exert themselves,
either because they cou'd be but imperfect among the Ancients; or
because we have almost lost the Footsteps of them during the gloomy
Darkness of Barbarity; or because a better method hath been taken about
100 Years ago. Was the Progress Historically examin'd, they have already
made in so short a time, notwithstanding the strong, but false
Prejudices they had long to encounter with, even sometimes the foreign
Obstacles they have met with from Authority and Power; the want of Zeal
for Sciences so remote from common use, those few who apply'd themselves
to this Work, and the weak Motives which engag'd them in it; a Man would
wonder at the Greatness and Rapidity of the Progress of the Sciences,
and even we might observe some new ones to start out of nothing, and
perhaps be tempted to have too great hopes of future Improvements.

The greater reason we have of future Success, the greater we have to
look upon the Sciences as in their Cradles, at least Natural Philosophy.
And therefore the Academy is only now employ'd to make an ample
Provision of Observations, and Facts well attested, which may one day be
the foundation of a System. For before the Systematical Natural
Philosophy can raise solid Edifices; Experimental Natural Philosophy
must be in a condition to supply it with good Materials.

None but Societies, of those too countenanc'd and encourag'd by the
Prince, can successfully make and prepare this Collection of Materials.
All the Learning, Care, Life and Wealth of one Private Man can never
answer this Design. There are too many different Experiments to be made,
which are to be too much vary'd, and a long time prosecuted with the
same Temper and Mind. The Cause of the least Effect is so wrap'd up,
that unless you very carefully open all the various Foldings, you cannot
come at it.

Hitherto the Academy of Sciences hath consider'd Nature but by parcels:
They have fix'd upon no general System, for fear of falling into the
inconveniency of hasty Systems, which are very grateful to the
impatience of Humane Understanding; and being once settled, are
Obstacles to what Truths are afterwards discover'd. This day we are sure
of a Fact, to morrow we shall be sure of another that hath no relation
with the former. However some Conjectures are ventur'd at upon Causes;
but they are only Conjectures. So that this Collection, which the
Academy gives to the Publick, is compos'd of separate Fragments,
independant of one another; whereof every one who is the Author,
warrants the Facts and Experiments; and whose Arguments are approv'd by
the Academy, but with Restrictions becoming Wise and Wary Scepticks.

Time perhaps will come, when these scatter'd Fragments shall be united
into one regular Body; and if they be such as they are wish'd, they may
of themselves Unite. A great many Truths, when their Numbers is
considerable, shew so near a Relation to, and so mutual a Dependance
upon one another, that it seems, that notwithstanding their violent
Separation, they have a natural Tendency to be re-united.




MISCELLANEA CURIOSA.




 _An Estimate of the Quantity of the Vapours raised out of the Sea
   derived from Experiment: Together with an Account of the Circulation
   of the watry Vapours of the Sea, and of the Cause of Springs,
   presented to the Royal Society. By Mr. _E. Halley, F. R. S.__


That the Quantity of Aqueous Vapours contain'd in the Medium of the Air,
is very considerable, seems most evident from the great Rains and Snows
which are sometimes observ'd to fall, to that degree, that the Water
thus discharg'd out of the Interstices of the Particles of Air, is in
weight a very sensible part of the incumbent Atmosphere: But in what
proportion these Vapours rise, which are the Sources not only of Rains,
but also of Springs or Fountains (as I design to prove) has not, that I
know of, been any where well examin'd, tho' it seem to be one of the
most necessary Ingredients of a Real and Philosophical Meteorology, and,
as such; to deserve the Consideration of this Honourable Society. I
thought it might not be unacceptable to attempt by Experiment to
determine the Quantity of the Evaporations of Water, as far as they
arise from Heat, which upon Trial succeeded as follows.

We took a Pan of Water, about 4 inches deep, and 7 Inches 9/10 Diameter,
in which we placed a Thermometer, and by means of a Pan of Coals, we
brought the Water to the same degree of Heat, which is observed to be
that of the Air in our hottest Summer; the Thermometer nicely shewing
it: This done, we affixed the Pan of Water, with the Thermometer in it,
to one end of the Beam of a Pair of Scales, and exactly counterpois'd it
with weights in the other Scale; and by the application or removal of
the Pan of Coals, we found it very easie to maintain the Water in the
same degree of Heat precisely. Doing thus we found the weight of the
Water sensibly to decrease; and at the end of two hours we observed that
there wanted half an Ounce _Troy_, all but 7 grains, or 233 grains of
Water, which in that time had gone off in Vapour; tho' one could hardly
perceive it smoke, and the Water were not sensibly warm. This Quantity
in so short a time seem'd very considerable, being little less than 6
ounces in 24 hours, from so small a Surface as a Circle of 8 inches
Diameter. To reduce this Experiment to an exact Calculus, and determine
the thickness of the Skin of Water that had so evaporated, I assume the
Experiment alledg'd by Dr. _Edward Bernard_ to have been made in the
_Oxford_ Society, _viz._ That the Cube-foot _English_ of Water weighs
exactly 76 Pounds _Troy_; this divided by 1728, the number of Inches in
a Foot, will give 253⅓ grains, or ½ ounce 13⅓ grains for the
weight of a Cube-inch of Water; wherefore the weight of 233 grains is
233/253 or 35 Parts of 38 of a Cube-inch of Water. Now the Area of the
Circle whose Diameter is 7-9/10 Inches, is 49 square Inches: by which
dividing the Quantity of Water evaporated, _viz._ 35/38 of an Inch, the
Quote 35/1862 or 1/53 shews that the thickness of the Water evaporated
was the 53d part of an Inch; but we will suppose it only the 60th part,
for the Facility of Calculation. If therefore Water as warm as the Air
in Summer, exhales the thickness of a 60th part of an Inch in two hours
from its whole Surface, in 12 hours it will exhale the ⅒ of an Inch;
which Quantity will be found abundantly sufficient to serve for all the
Rains, Springs, and Dews; and account for the _Caspian_ Sea, being
always at a stand, neither wasting nor overflowing; as likewise for the
Current said to set always in at the Streights of _Gibralter_, tho'
those Mediterranean Seas receive so many and so considerable Rivers.

To estimate the Quantity of Water arising in Vapours out of the Sea, I
think I ought to consider it only for the time the Sun is up, for that
the Dews return in the Night, as much if not more Vapours than are then
emitted; and in Summer the Days being no longer than 12 hours, this
Excess is ballanc'd by the weaker Action of the Sun, especially when
rising before the Water be warmed: So that if I allow ⅒ of an Inch of
the Surface of the Sea, to be raised _per diem_ in Vapours, it may not
be an improbable Conjecture.

Upon this Supposition, every 10 square Inches of the Surface of the
Water, yields in Vapour _per diem_ a Cube-inch of Water; and each square
Foot half a Wine-pint; every Space of 4 Foot square, a Gallon; a Mile
square, 6914 Tons; a square Degree suppose of 69 _English_ Miles, will
evaporate 33 Millions of Tons: And if the Mediterranean be estimated at
forty degrees long and four broad, allowances being made for the Places
where it is broader, by those where it is narrower (and I am sure I
guess at the least) there will be 160 Square degrees of Sea; and
consequently, the whole Mediterranean must lose in Vapour, in a Summer's
day, at least 5280 Millions of Tons. And this Quantity of Vapour, tho'
very great, is as little as can be concluded from the Experiment
produced: And yet there remains another Cause, which cannot be reduced
to Rule, I mean the Winds, whereby the Surface of the Water is licked up
some times faster than it exhales by the heat of the Sun; as is well
known to those that have consider'd those drying Winds which blow
sometimes.

To estimate the Quantity of Water, the Mediterranean Sea receives from
the Rivers that fall into it, is a very hard Task, unless one had the
Opportunity to measure their Chanels and Velocity; and therefore we can
only do it by allowing more than enough; that is, by assuming these
Rivers greater than in all probability they be, and then comparing the
Quantity of Water voided by the _Thames_, with that of those Rivers,
whose Waters we desire to compute.

The Mediterranean receives these considerable Rivers; the _Iberus_, the
_Rhone_, the _Tiber_, the _Po_, the _Danube_, the _Neister_, the
_Borystenes_, the _Tanais_, and the _Nile_; all the rest being of no
great Note, and their Quantity of Water inconsiderable: These nine
Rivers, we will suppose each of them to bring down ten times as much
Water as the River _Thames_; not that any of them is great in reality,
but to comprehend with them all the small Rivulets that fall into the
Sea, which otherwise I know not how to allow for.

To calculate the Water of the _Thames_, I assume that at _Kingston_
Bridge where the Flood never reaches, and the Water always runs down,
the breadth of the Chanel is 100 Yards, and its Depth 3, it being
reduced to an Equality (in both which Suppositions I am sure I take with
the most) hence the Profil of the Water in this Place is 300 square
Yards: This multiplied by 48 Miles (which I allow the Water to run in 24
hours, at 2 Miles an hour) or 84480 Yards, gives 25344000 Cubick-yards
of Water to be evacuated every Day; that is, 20300000 Tons _per diem_;
and I doubt not, but in the excess of my Measures of the Chanel of the
River, I have made more than sufficient allowance for the Waters of the
_Brent_, the _Wandel_, the _Lea_, and _Darwent_, which are all worth
notice, that fall into the _Thames_ below _Kingston_.

Now if each of the aforesaid 9 Rivers yield 10 times as much Water as
the _Thames_ doth, 'twill follow that each of them yields but 203
Millions of Ton _per diem_, and the whole 9, but 1827 Millions of Tons
in a day; which is but little more than ⅓ of what is proved to be
raised in vapour out of the Mediterranean in 12 hours time. Now what
becomes of this Vapour when rais'd, and how it comes to pass that the
Current always sets in at the Mouth, of the Streights of _Gibralter_,
shall immediately be shew'd: But first it is necessary to advertise the
Reader, that in making the Experiment herein mention'd, the Water used
had been salted to the same degree as is the common Sea-water, by the
Solution of about a 40th part of Salt.


Having thus shew'd by Experiment the Quantity of Water raised in Vapour
from the Surface of the Sea in a Days time, which was so far approv'd of
by some Honourable Members of this Society, that I receiv'd their
Commands to prosecute these Enquiries; and particularly, in relation to
the Method used by Nature, to return the said Vapours again into the
Sea; which is so justly perform'd, that in many hundred of Years we are
sufficiently assured that the Sea has not sensibly decreased by the loss
in Vapour; nor yet abounded by the immense Quantity of fresh it receives
continually from the Rivers. To demonstrate this Equilibre of Receipt
and Expence in the whole Sea, is a Task too hard for me to undertake,
yet in obedience to those whom I have the Honour to serve, I shall here
offer, what to me has hitherto seem'd the most satisfactory Account of
this grand _Phænomenon_: I have in another place attempted to explain
the manner of the rising of Vapour by Warmth, by shewing, that if an
Atom of Water were expanded into a Shell or Bubble, so as to be ten
times as big in Diameter as when it was Water; such an Atom would become
specifically lighter than Air, and rise so long as that _Flatus_ or warm
Spirit that first separated it from the Mass of Water, shall continue to
distend it to the same Degree; and that Warmth declining, and the Air
growing cooler and also specifically lighter, the Vapours consequently
shall stop at a certain Region of the Air, or else descend, which may
happen upon several accounts, as I shall by and by endeavour to make
out; yet I undertake not that this is the only principal of the rise of
Vapours, and that there may not be a certain sort of Matter, whose
_Conatus_ may be contrary to that of Gravity; as is evident in
Vegetation, where in the Tendency of the Sprouts is directly upwards, or
against the Perpendicular. But what ever is the true Cause, it is in
Fact certain, that warmth does separate the Particles of Water, and emit
them with a greater and greater Velocity, as the heat is more and more
intense; as is evident in the Steam of a boiling Cauldron, wherein
likewise the Velocity of the ascent of the Vapours does visibly decrease
till they disappear, being dispersed into and assimulated with the
Ambient Air. Vapours being thus raised by warmth, let us for a first
Supposition put, that the whole Surface of the Globe were all Water very
deep, or rather that the whole Body of the Earth were Water, and that
the Sun had its diurnal course about it: I take it, that it would
follow, that the Air of it self would imbibe a certain Quantity of
aqueous Vapours, and retain them like Salts dissolved in Water; that the
Sun warming the Air, and raising a more plentiful Vapour from the Water
in the day-time, the Air would sustain a greater proportion of Vapour,
as warm Water will hold more dissolved Salts, which upon the absence of
the Sun in the Nights would be all again discharged in Dews, analogous
to the Precipitation of Salts on the cooling of the Liquors; nor is it
to be believed that in such Case there would be any diversity of
Weather, other than periodically, every Year alike; the mixture of all
terrestrious, saline, heterogenious Vapours being taken away, which as
they are variously compounded and brought by the Winds, seem to be the
Causes of those various Seasons which we now find. In this case the
Aiery Regions every where, at the same height, would be equally
replenished with the Proportion of Water it could contain, regard being
only to be had to the different degree of warmth, from the nearness or
distance of the Sun; and an eternal East-wind would blow all round the
Globe, inclining only to the same side of the _East_, as the Latitude
doth from the Equator; as is observed in the Ocean between the Tropicks.

Next let us suppose this Ocean interspersed with wide and spacious
Tracts of Land, with high Ridges of Mountains, such as the _Pyrenean_,
the _Alps_, the _Apennine_, the _Carpathian_ in _Europe_, _Taurus_,
_Caucasus_, _Imaus_, and several others in _Asia_; _Atlas_ and the
_Montes Lunæ_, with other unknown Ridges in _Africa_, whence came the
_Nile_, the _Nigre_, and the _Zaire_: And in _America_, the _Andes_ and
the _Apalatean_ Mountains; each of which far surpass the usual height to
which the Aqueous Vapours of themselves ascend, and on the tops of which
the Air is so cold and rarified, as to retain but a small part of those
Vapours, that shall be brought thither by Winds. Those Vapours therefore
that are raised copiously in the Sea, and by the Wind, are carried over
the low Land to those Ridges of Mountains, are there compelled by the
Stream of the Air to mount up with it to the tops of the Mountains,
where the Water presently precipitates, gleeting down by the Crannies of
the Stone; and part of the Vapour entering into the Caverns of the
Hills, the Water thereof gathers as in an Alembick into the Basons of
Stone it finds; which being once fill'd, all the overplus of Water that
comes thither runs over by the lowest place, and breaking out by the
sides of the Hills, forms single _Springs_. Many of these running down
by the Valleys or Guts between the Ridges of the Hills, and coming to
unite, form little Rivulets, or Brooks: Many of these again, meeting in
one common Valley and gaining the plain Ground, being grown less rapid,
become a River; and many of these being united in one common Channel,
make such Streams as the _Rhine_, the _Rhone_, the _Danube_; which
latter, one would hardly think the Collection of Water condensed out of
Vapour, unless we consider how vast a Tract of Ground that River drains,
and that it is the Sum of all those Springs which break out on the South
side of the _Carpathian_ Mountains, and on the North side of the immense
Ridge of the _Alps_, which is one continued Chain of Mountains from
_Switzerland_, to the _Black-Sea_. And it may almost pass for a Rule,
that the magnitude of a River, or the quantity of Water it evacuates, is
proportionable to the length and height of the Ridges from whence its
Fountains arise. Now this Theory of _Springs_ is not a bare
_Hypothesis_, but founded on Experience, which it was my luck to gain in
my abode at St. _Helena_, where in the Night-time, on the tops of the
Hills, about 800 Yards above the Sea, there was so strange a
condensation, or rather precipitation of the Vapours, that it was a
great Impediment to my Cœlestial Observations; for in the clear Sky,
the Dew would fall so fast, as to cover, each half quarter of an Hour,
my Glasses with little drops; so that I was necessitated to wipe them so
often, and my Paper on which I wrote my Observations would immediately
be so wet with Dew, that it would not bear Ink: By which it may be
suppos'd how fast the Water gathers in those mighty high Ridges I but
now nam'd.

Thus is one part of the Vapours blown upon the Land return'd by the
Rivers into the Sea, from whence they came; another part by the cool of
the Night falls in Dews, or else in Rains, again into the Sea before it
reaches the Land, which is by much the greatest part of the whole
Vapours, because of the great extent of the Ocean, which the motion of
the Wind does not traverse in a very long space of Time; and this is the
Reason why the Rivers do not return so much into the _Mediterranean_, as
is extracted into Vapour. A third part falls on the Low-Lands, and is
the _Pabulum_ of Plants, where yet it does not rest, but is again
exhaled in Vapour by the action of the Sun, and is either carried by the
Winds to the Sea to fall in Rain or Dew there, or else to the Mountains
to be there turn'd into Springs; and tho' this does not immediately come
to pass, yet after several Vicissitudes of rising in Vapour, and falling
in Rain or Dews, each Particle of the Water is at length return'd to the
Sea from whence it came. Add to this, that the Rain-waters after the
Earth is fully sated with moisture, does, by the Vallies or lower parts
of the Earth, find its way into the Rivers, and so is compendiously sent
back to the Sea. After this manner is the Circulation perform'd, and I
doubt not but this Hypothesis is more reasonable than that of those who
derive all Springs from the Rain-waters, which yet are perpetual and
without diminution, even when no Rain falls for a long space of time; or
that derive them from a Filtration or Percolation of the Sea-waters,
thro' certain imaginary Tubes or Passages within the Earth wherein they
lose their Saltness. This, besides many others, labouring under this
principal Absurdity, that the greatest Rivers have their most copious
Fountains farthest from the Sea, and whether so great quantities of
fresh Water cannot reasonably be deriv'd any other way than in Vapour.
This, if we may allow final Causes, seems to be the design of the Hills,
that their Ridges being plac'd thro' the midst of the Continents, might
serve, as it were, for Alembicks to distil fresh Water for the use of
Man and Beast, and their heights to give a descent to those Streams to
run gently, like so many Veins, of the _Macrocosm_ to be the more
beneficial to the Creation. If the difference between Rain and Dew, and
the cause why sometimes 'tis Cloudy, at other times Serene, be inquir'd,
I can offer nothing like a proper Solution thereof, only with submission
to propose Conjectures, which are the best I can find, _viz._ That the
Air being heaped up by the meeting of two contrary Winds, when the
_Mercury_ is high, the Vapours are the better sustain'd and kept from
Co-agulating or Condensing into Drops, whereby Clouds are not so easily
generated, and the Night the Vapours fall down single, as they rose in
imperceptible Atoms of Water: Whereas, when the _Mercury_ is low, And
the Air rarified by the Exhaustion thereof, by two contrary Winds
blowing from the place; the Atoms of Air keep the Vapours not so well
separated, and they coalesce into visible Drops in the Clouds, and from
thence are easily drawn into greater Drops of Rain; to which 'tis
possible and not improbable, that some sort of Saline or Angular
Particles of Terrestrial Vapour being immix'd with the Aqueous, which I
take to be Bubbles, may cut or break their Skins or Coats, and so
contribute to their more speedy Condensation into Rain.




 _The True Theory of the Tides, extracted from that admired Treatise of
   Mr. _Isaac Newton_, Intitled, _Philosophiæ Naturalis Principia
   Mathematica_; Being a Discourse presented with that Book to the late
   King _James_, by Mr. _Edmund Halley_._


_It may, perhaps, seem strange, that this Paper, being no other than a
particular Account of a Book long since published, should now appear
here; but the Desires of several honourable Persons, which could not be
withstood, have obliged us to insert it here, for the sake of such, who
being less knowing in Mathematical Matters, and therefore not daring to
adventure on the Author himself, are notwithstanding, very curious to be
inform'd of the Causes of Things; particularly of so general and
extraordinary _Phænomena_, as are those of the Tides. Now this Paper
having been drawn up for the late King _James_'s Use, (in whose Reign
the Book was publish'd) and having given good Satisfaction to those that
got Copies of it; it is hoped the Savans of the higher Form will indulge
us this Liberty we take to gratifie their Inferiours in point of
Science; and not be offended, that we here insist more largely upon Mr.
_Newton_'s _Theory of the Tides_, which, how plain and easie soever we
find, is very little understood by the common Reader._


The sole Principle upon which this Author proceeds to explain most of
the great and surprizing Appearances of Nature, is no other than that of
_Gravity_, whereby in the Earth all Bodies have a tendency towards its
Centre; as is most evident: And from undoubted Arguments it's proved,
that there is such a Gravitation towards the Centre of the Sun, Moon,
and all the Planets.

From this Principle, as a necessary Consequence, follows the Sphærical
Figure of the Earth and Sea, and of all the other Cœlestial Bodies:
And tho' the tenacity and firmness of the Solid Parts, support the
Inequalities of the Land above the Level; yet the Fluids, pressing
equally and easily yielding to each other, soon restore the
_Æquilibrium_, if disturbed, and maintain the exact Figure of the Globe.

Now this force of Descent of Bodies towards the Centre, is not in all
places alike, but is still less and less, as the distance from the
Center encreases: And in this Book it is demonstrated, that this Force
decreases as the Square of the distance increases; that is, the weight
of Bodies, and the Force of their Fall is less, in parts more removed
from the Center, in the proportion of the Squares of the Distance. So as
for Example, a Ton weight on the Surface of the Earth, if it were raised
to the height of 4000 Miles, which I suppose the Semidiameter of the
Earth, would weigh but ¼ of a Ton, or 5 Hundred weight: If to 12000
Miles, or 3 Semidiameters from the Surface, that is 4 from the Center,
it would weigh but 1/16 part of the Weight on the Surface, or a Hundred
and Quarter: So that it would be as easie for the Strength of a Man at
that height to carry a Ton weight, as here on the Surface a 100¼. And
in the same Proportion does the Velocities of the fall of Bodies
decrease: For whereas on the Surface of the Earth all things fall 16
Foot in a second; at one Semidiameter above, this fall is but four Foot;
and at three Semidiameters, or four from the Centre, it is but 1/16 of
the Fall at the Surface, or but one Foot in a second: And at greater
Distances both Weight and Fall become very small, but yet at all given
Distances is still some thing, tho' the Effect become insensible. At the
distance of the Moon (which I will suppose 60 Semidiameters of the
Earth) 3600 Pounds weigh but one Pound, and the fall of Bodies is but of
1/3600 a Foot in a second, or 16 Foot in a Minute; that is, a Body so
far off descends in a Minute no more than the same at the Surface of the
Earth would do in a Second of Time.

As was said before, the same force decreasing after the same manner is
evidently found in the Sun, Moon, and all the Planets; but more
especially in the Sun, whose Force is prodigious; becoming sensible even
in the immense distance of _Saturn_: This gives room to suspect, that
the force of Gravity is in the Cœlestial Globes proportional to the
quantity of Matter in each of them: And the Sun being at least ten
Thousand times as big as the Earth, its Gravitation or attracting Force,
is found to be at least ten Thousand times as much as that of the Earth,
acting on Bodies at the same distance.

This Law of the decrease of Gravity being demonstratively proved, and
put past contradiction; the Author with great Sagacity, inquires into
the necessary Consequences of this Supposition; whereby he finds the
genuine Cause of the several Appearances in the Theory of the Moon and
Planets, and discovers the hitherto unknown Laws of the Motion of
Comets, and of the Ebbing and flowing of the Sea. Each of which are
Subjects that have hitherto taken up much larger Volumes; but Truth
being uniform, and always the same, it is admirable to observe how
easily we are enabled to make out very abstruse _and difficult Matters_,
when once true and genuine Principles are obtain'd: And on the other
hand it may be wondred; that, notwithstanding the great facility of
truth, and the perplexity and nonconsequences that always attend
erroneous Suppositions, these great Discoveries should have escaped the
acute Disquisitions of the best Philosophical Heads of all past Ages,
and be reserv'd to these our Times. But that wonder will soon cease, if
it be consider'd how great improvements Geometry has receiv'd in our
Memory, and particularly from the profound Discoveries of our
incomparable Author.

The Theory of the Motion of the primary _Planets_ is here shewn to be
nothing else, but the contemplation of the Curve Lines which Bodies cast
with a given Velocity, in a given Direction, and at the same time drawn
towards the Sun by its gravitating Power, would describe. Or, which is
all one, that the Orbs of the Planets are such Curve Lines as a Shot
from a Gun describes in the Air, being cast according to the direction
of the Piece, but bent in a crooked Line by the supervening Tendency
towards the Earths Centre: And the Planets being supposed to be
projected with a given Force, and attracted towards the Sun, after the
aforesaid manner, are here proved to describe such Figures, as answer
punctually to all that the Industry of this and the last Age has
observed in the Planetary Motions. So that it appears, that there is no
need of solid Orbs and Intelligences, as the Antients imagin'd, nor yet
of _Vortices_ or Whirlpools of the Cœlestial Matter, as _Des Cartes_
supposes; but the whole Affair is simply and mechanically performed,
upon the sole Supposition of a Gravitation towards the Sun; which cannot
be denied.

The Motion of _Comets_ is here shewn to be compounded of the same
Elements, and not to differ from Planets, but in their greater
swiftness, whereby overpowering the Gravity that should hold them to the
Sun, as it doth the Planets, they flie off again, and distance
themselves from the Sun and Earth, so that they soon are out of our
sight. And the imperfect Accounts and Observations Antiquity has left
us, are not sufficient to determine whether the same Comet ever return
again. But this Author has shewn how Geometrically to determine the Orb
of a Comet from Observations, and to find his Distance from the Earth
and Sun, which was never before done.

The third thing here done is the Theory of the Moon, all the
Inequalities of whose Motion are proved to arise from the same
Principles, only here the effect of two Centers operating on, or
attracting a projected Body, comes to be considered; for the Moon,
though principally attracted by the Earth, and moving round it, does
together with the Earth, move round the Sun once a Year, and is,
according as she is nearer or farther from the Sun, drawn by him more or
less than the Center of the Earth, about which she moves; whence arise
several Irregularities in her Motion, of all which, the Author in this
Book, with no less Subtility than Industry, has given a full account.
And though by reason of the great Complication of the Problem, he has
not yet been able to make it purely Geometrical, 'tis to be hoped, that
in some farther Essay he may surmount the difficulty: And having
perfected the Theory of the Moon, the long desir'd Discovery of the
Longitude (which at Sea is only practicable this way) may at length be
brought to light, to the great Honour of your Majesty, and Advantage of
your Subjects.

All the surprising Phænomena of the Flux and Reflux of the Sea, are in
like manner shewn to proceed from the same Principle; which I design
more largely to insist on, since the Matter of Fact is in this Case much
better known to your Majesty than in the foregoing.

If the Earth were alone, that is to say, not affected by the Actions of
the Sun and Moon, it is not to be doubted, but the Ocean, being equally
press'd by the force of Gravity towards the Center, would continue in a
perfect Stagnation, always at the same height, without either Ebbing or
Flowing; but it being here demonstrated, that the Sun and Moon have a
like Principle of Gravitation towards their Centers, and that the Earth
is within the Activity of their Attractions, it will plainly follow,
that the Equality of the pressure of Gravity towards the Center will
thereby be disturb'd; and though the smallness of these Forces, in
respect of the Gravitation towards the Earth's Center, renders them
altogether imperceptible by any Experiments we can devise, yet the Ocean
being fluid and yielding to the least force, by its rising shews where
it is less press'd, and where it is more press'd by its sinking.

Now if we suppose the force of the Moon's Attaction to decrease as the
Square of the Distance from its Center increases (as in the Earth and
other Cœlestial Bodies) we shall find, that where the Moon is
perpendicularly either above or below the Horizon, either in Zenith or
Nadir, there the force of Gravity is most of all diminished, and
consequently that there the Ocean must necessarily swell by the coming
in of the Water from those parts where the Pressure is greatest, _viz._
in those places where the Moon is near the Horizon: But that this may be
the better understood, I thought it needful to add the following Figure,
(_Vide Fig. 1. Plate 1._) where _M_ is the Moon, _E_ the Earth, _C_ its
Center, and _Z_ the place where the Moon is in the Zenith, _N_ where in
the Nadir.

Now by the Hypothesis it is evident, that the Water in _Z_, being
nearer, is more drawn by the Moon, than the Center of the Earth _C_, and
that again more than the Water in _N_; wherefore the Water in _Z_ hath a
tendency towards the Moon, contrary to that of Gravity, being equal to
the excess of the Gravitation in _Z_, above that in _C_: And in the
other case, the Water in _N_, tending less towards the Moon than the
Center _C_, will be less pressed, by as much as is the difference of the
Gravitation towards the Moon in _C_ and _N_. This rightly understood, it
follows plainly, that the Sea, which otherwise would be Spherical, upon
the Pressure of the Moon, must form it self into a Spheroidal or Oval
Figure, whose longest Diameter is where the Moon is vertical, and
shortest where she is in the Horizon; and that the Moon shifting her
Position as she turns round the Earth once a Day, this Oval of Water
shifts with her, occasioning thereby the two Floods and Ebbs observable
in each 25 Hours.

And this may suffice, as to the general Cause of the Tides; it remains
now to shew how naturally this Motion accounts for all the Particulars
that have been observ'd about them; so that there can be no room left to
doubt, but that this is the true cause thereof.

The Spring Tides upon the New and Full Moons, and Neap Tides on the
Quarters, are occasion'd by the attractive Force of the Sun in the New
and Full, conspiring with the Attraction of the Moon, and producing a
Tide by their united Forces: Whereas in the Quarters, the Sun raises the
Water where the Moon depresses it, and the contrary; so as the Tides are
made only by the difference of their Attractions. That the force of the
Sun is no greater in this Case, proceeds from the very small Proportion
the Semi-diameter of the Earth bears to the vast distance of the Sun.

It is also observ'd, that _cæteris paribus_, the Æquinoctial Spring
Tides in _March_ and _September_, or near them, are the Highest, and the
Neap Tides the lowest; which proceeds from the greater Agitations of the
Waters, when the fluid _Spheroid_ revolves about a great Circle of the
Earth, than when it turns about in a lesser Circle; it being plain that
if the Moon were constituted in the Pole, and there stood, that the
_Spheroid_ would have a fix'd Position, and that it would be always high
Water under the Poles, and low Water every where under the Æquinoctial:
And therefore the nearer the Moon approaches the Poles, the less is the
agitation of the Ocean, which is of all the greatest, when the Moon is
in the Æquinoctial, or farthest distant from the Poles. Whence the Sun
and Moon, being either conjoined or opposite in the Æquinoctial, produce
the greatest Spring Tides; and the subsequent Neap Tides, being produc'd
by the Tropical Moon in the Quarters, are always the least Tides;
whereas in _June_ and _December_, the Spring Tides are made by the
Tropical Sun and Moon, and therefore less vigorous; and the Neap Tides
by the Æquinoctial Moon, which therefore are the stronger: Hence it
happens, that the difference between the Spring and Neap Tides in these
Months, is much less considerable than in _March_ and _September_. And
the reason why the very highest Spring Tides are found to be rather
before the Vernal and after the Autumnal Equinox, _viz._ in _February_
and _October_, than precisely upon them, is, because the Sun is nearer
the Earth in the Winter Months, and so comes to have a greater effect in
producing the Tides.

Hitherto we have consider'd such Affections of the Tides as are
Universal, without relation to particular Cases; what follows from the
differing Latitudes of places, will be easily understood by the
following Fig. (_Vide Fig. 2. Plate 1._)

Let _ApEP_ be the Earth cover'd over with very deep Waters, _C_ its
Center, _P_, _p_, its Poles, _AE_ the Æquinoctial, _F_, _f_, the
parallel of Latitude of a Place, _D_, _d_, another Parallel at equal
distance on the other side of the Æquinoctial, _H_, _h_, the two Points
where the Moon is vertical, and let _K_, _k_, be the great Circle,
wherein the Moon appears Horizontal. It is evident, that a Spheroid
describ'd upon _Hh_, and _Kk_, shall nearly represent the Figure of the
Sea, and _Cf_, _CD_, _CF_, _Cd_, shall be the heighths of the Sea in the
places _f_, _D_, _F_, _d_, in all which it is High-water: And seeing
that in twelve Hours time, by the diurnal Rotation of the Earth, the
Point _F_ is transferr'd to _f_, and _d_ to _D_: The height of the Sea
_CF_ will be that of the High-water when the Moon is present, and _Cf_
that of the other High-water, when the Moon is under the Earth: Which in
the case of this Figure is less than the former _CF_. And in the
opposite Parallel _Dd_, the contrary happens. The Rising of the Water
being always alternately greater and less in each place, when it is
produc'd by the Moon declining sensibly from the Æquinoctial; that being
the greatest of the two High-waters in each diurnal Revolution of the
Moon, wherein she approaches nearest either to the Zenith or Nadir of
the place: Whence it is, that the Moon in the Northern Signs, in this
part of the World, makes the greatest Tides when above the Earth, and in
Southern Signs, when under the Earth; the Effect being always the
greatest where the Moon is farthest from the Horizon, either above or
below it. And this alternate Increase and Decrease of the Tides has been
observ'd to hold true on the Coast of _England_, at _Bristol_ by Captain
_Sturmy_, and at _Plymouth_ by Mr. _Colepresse_.

But the Motions hitherto mentioned are somewhat alter'd by the Libration
of the Water, whereby, though the Action of the _Luminaries_ should
cease, the Flux and Reflux of the Sea would for some time continue: This
Conservation of the impress'd Motion diminishes the differences that
otherwise would be between two consequent Tides, and is the reason why
the highest Spring-Tides are not precisely on the New and Full Moons,
nor the Neaps on the Quarters; but generally they are the third Tides
after them, and sometimes later.

All these things would regularly come to pass, if the whole Earth were
cover'd with Sea very deep; but by reason of the shoalness of some
places, and the narrowness of the Streights, by which the Tides are in
many cases propagated, there arises a great diversity in the Effect, and
not to be accounted for, without an exact Knowledge of all the
Circumstances of the Places, as of the Position of the Land, and the
Breadth and Depth of the Channels by which the Tide flows; for a very
slow and imperceptible Motion of the whole Body of the Water, where it
is (for Example) 2 Miles deep, will suffice to raise its Surface 10 or
12 Feet in a Tides time; whereas, if the same quantity of Water were to
be convey'd up a Channel of 40 Fathoms deep, it would require a very
great Stream to effect it, in so large Inlets as are the Channel of
_England_, and the _German_ Ocean; whence the Tide is found to set
strongest in those places where the Sea grows narrowest; the same
quantity of Water being to pass through a smaller Passage: This is most
evident in the _Streights_, between _Portland_ and _Cape de Hague_ in
_Normandy_, where the Tide runs like a Sluce; and would be yet more
between _Dover_ and _Calais_, if the Tide coming about the Island from
the North did not check it. And this force being once impress'd upon the
Water, continues to carry it above the level of the ordinary height in
the Ocean, particularly where the Water meets a direct Obstacle, as it
is at St. _Malo's_; and where it enters into a long Channel, which
running far into the Land, grows very streight at its Extremity; as it
is in the _Severn-Sea_ at _Chepstow_ and _Bristol_.

This shoalness of the Sea, and the intercurrent Continents are the
reason, that in the open Ocean the time of High water is not at the
Moons appulse to the Meridian, but always some Hours after it; as it is
observ'd upon all the West Coast of _Europe_ and _Africa_, from
_Ireland_ to the _Cape of Good Hope_: In all which a S. W. Moon makes
High-water, and the same is reported to be on the West side of
_America_. But it would be endless to account all the particular
Solutions, which are easie Corollaries of this _Hypothesis_; as why the
_Lakes_, such as the _Caspian Sea_, and _Mediterranean Seas_, such as
the _Black Sea_, the _Streights_ and _Baltick_, have no sensible Tides:
For _Lakes_ having no Communication with the Ocean, can neither increase
nor diminish their Water, whereby to rise and fall; and Seas that
communicate by such narrow Inlets, and are of so immense an Extent,
cannot in a few Hours time receive or empty Water enough to raise or
sink their Surface any thing sensibly.

Lastly, to demonstrate the Excellency of this Doctrine, the Example of
the Tides in the Port of _Tunking_ in _China_, which are so
extraordinary, and differing from all others we have yet heard of, may
suffice. In this Port there is but one Flood and Ebb in 24 Hours; and
twice in each Month, _viz._ when the Moon is near the Æquinoctial there
is no Tide at all, but the Water is stagnant; but with the Moons
Declination there begins a Tide, which is greatest when she is in the
Tropical Signs: Only with this difference, that when the Moon is to the
Northward of the Æquinoctial, it Flows when she is above the Earth, and
Ebbs when she is under, so as to make High-water at Moons-setting, and
Low-water at Moons-rising: But on the contrary, the Moon being to the
Southward, makes High-water at rising, and Low-water at setting; it
Ebbing all the time she is above the Horizon. As may be seen more at
large in the _Philosophical Transactions_, Numb. 162.

The Cause of this odd Appearance is propos'd by Mr. _Newton_, to be from
the concurrence of two Tides; the one propagated in six Hours out of the
great _South-Sea_ along the Coast of _China_; the other out of the
_Indian-Sea_, from between the Islands in twelve Hours, along the Coast
of _Malacca_ and _Cambodia_. The one of these Tides, being produc'd in
North Latitude, is, as has been said, greater, when the Moon being to
the North of the Equator is above the Earth, and less when she is under
the Earth. The other of them, which is propagated from the _Indian Sea_,
being raised in South-Latitude, is greater when the Moon declining to
the South, is above the Earth, and less when she is under the Earth: So
that of these Tides alternately greater and lesser, there comes always
successively two of the greater and two of the lesser together every
Day; and the High-water falls always between the times of the arrival of
the two greater Floods; and the Low-water between the arrival of the two
lesser Floods. And the Moon coming to the Æquinoctial, and the alternate
Floods becoming equal, the Tide ceases, and the Water stagnates: But
when she has pass'd to the other side of the Equator, those Floods which
in the former Order were the least, now becoming the greatest, that That
before was the time of High-water, now becomes the Low-water, and the
Converse. So that the whole appearance of these strange Tides, is
without any forcing naturally deduc'd from these Principles, and is a
great Argument of the Certainty of the whole _Theory_.




 _A Theory of the _Variation_ of the _Magnetical Compass_. By Mr. _Ed.
   Halley_, Fellow of the Royal Society._


The Variation of the Compass (by which I mean the Deflection of the
Magnetical Needle from the true Meridian) is of that great Concernment
in the Art of Navigation, that the neglect thereof, does little less
than render useless one of the noblest Inventions Mankind ever yet
attained to. And for this cause all Ships of Consequence (especially
those bound beyond the Equator) carry with them Instruments on purpose
to observe this Variation: That so the Course steer'd by the Compass,
may be reduc'd to the true Course in respect of the Meridian.

Now although the great utility that a perfect Knowledge of the Theory of
the Magnetical Direction would afford to Mankind in general, and
especially to those concern'd in Sea Affairs, seems as sufficient
incitement to all Philosophical and Mathematical Heads, to take under
serious Consideration the several _Phænomena_, and to endeavour to
reconcile them by some general Rule: Yet so it is; that almost all the
Authors, from whom a Discourse of this kind ought to have been expected,
pass by in silence the Difficulties they here Encounter. And those that
mention this Variation: By affirming it to proceed from Causes
altogether uncertain (as are the casual lying of Iron Mines and
Loadstones in the Earth) put a stop to all further Contemplation; and
give discouragement to those that would otherwise undertake this
Enquiry. 'Tis true, that not long since one Mr. _Bond_, an old Teacher
of Navigation, put forth a small Treatise, wherein he pretends to
calculate the Variation: But he limits his Hypothesis to the City of
_London_, affirming himself (as he had a great deal of reason) that the
same _Calculus_ is not sufficient for other Places; whereby it appears
that this Rule is far short of the so much desir'd general one.

Now although (through want of sufficient Observations, and some other
Difficulties, which I shall anon shew) I cannot pretend perfectly to
establish the Numbers and Rules of a _Calculus_, which shall precisely
answer to the Variations of all parts of the World: Yet I suppose it
will not be unacceptable to the Curious to propose something of a Light
into this abstruse Mystery; which, if no other, may have this good
Effect, to stir up the Philosophical _Genii_ of the Age to apply
themselves more attentively to this useful Speculation. But before I
proceed, 'twill be necessary to lay down the Grounds upon which I raise
my Conclusions; and at once to give a Synopsis of those Variations,
which I have reason to look upon as sure, being mostly the Observations
of Persons of good Skill and Integrity.


A TABLE OF VARIATIONS.

        _Names of            | _Longitude |_Latitude._| _Anno | _Variation
         Places._            |  from_ Lon.|           |  Dom._|  Observ'd._
                             |            |           |       |
                             |  _d_ _m_   |  _d_ _m_  |       | _d_ _m_
 _London_                    |   0   0    |  51  32 N |  1580 | 11  15 E
                             |            |           |  1622 |  6   0 E
                             |            |           |  1634 |  4   5 E
                             |            |           |  1672 |  2  30 W
 _Paris_                     |   2  25 E  |  48  51 N |  1683 |  4  30 W
                             |            |           |  1640 |  3  00 E
                             |            |           |  1666 |  0   0
                             |            |           |  1681 |  2  30 W
 _Uraniburg_                 |  13   0 E  |  55  54 N |  1672 |  2  35 W
 ----------------------------+------------+-----------+-------+------------
 _Copenhagen_                |  12  53 E  |  55  41 N |  1649 |  1  30 E
                             |            |           |  1672 |  3  35 W
 _Dantzick_                  |  19   0 E  |  54  23 N |  1679 |  7  00 W
 _Mompelier_                 |   4   0 E  |  43  37 N |  1674 |  1  10 W
 _Brest_                     |   4  25 W  |  48  23 N |  1680 |  1  45 W
 ----------------------------+------------+-----------+-------+------------
 _Rome_                      |  13   0 E  |  41  50 N |  1681 |  5   0 W
 _Bayonne_                   |   1  20 W  |  43  30 N |  1680 |  1  20 W
 _Hudson's_ Bay              |  79  40 W  |  51  00 N |  1668 | 19  15 W
 In _Hud._ Straights         |  57  00 W  |  61  00 N |  1668 | 29  30 W
 In _Baffin's_ Bay at  }     |            |           |       |
   Sir _Thomas Smith's_}     |  80  00 W  |  78  00 N |  1616 | 57  00 W
   Sound               }     |            |           |       |
 ----------------------------+------------+-----------+-------+-----------
 At Sea                      |  50   0 W  |  38  40 N |  1682 |  7  30 W
 At Sea                      |  31  30 W  |  43  50 N |  1682 |  5  30 W
 At Sea                      |  42   0 W  |  21   0 N |  1678 |  0  40 E
 Cape St. _Aug._ of _Brazile_|  35  30 W  |   8   0 S |  1670 |  5  30 E
 Cape _Frio_                 |  41  10 W  |  22  40 S |  1670 | 12  10 E
 ----------------------------+------------+-----------+-------+------------
 At Sea off of the Mou.    } |            |           |       |
 of the River _Plate_      } |  53  00 W  |  39  30 S |  1670 | 20  33 E
 At the East Entrance   }    |            |           |       |
 of _Magellan_ Straits  }    |  68  00 W  |  52  30 S |  1670 | 17  00 E
 At the W. Entrance of     } |            |           |       |
 the _Magellan_ Straits    } |  75  00 W  |  53  00 S |  1670 | 14  10 E
 _Baldivia_                  |  73  00 W  |  40  00 S |  1670 |  8  10 E
 ----------------------------+------------+-----------+-------+------------
 At Cape d'_Agulbas_        |  16  30 E  |  34  50 S |  1622 |  2  00 W
                             |            |           |  1675 |  8  00 W
 At Sea                      |   1   0 E  |  34  30 S |  1675 |  0  00
 At Sea                      |  20   0 W  |  34   0 S |  1675 | 10  30 E
 At Sea                      |  32   0 W  |  24   0 S |  1675 | 10  30 E
 ----------------------------+------------+-----------+-------+------------
 At St. _Helena_             |   6  30 W  |  16  00 S |  1677 |  0  40 E
 At _Ascension_              |  14  30 W  |   7  50 S |  1678 |  1  00 E
 At _Johanna_                |  44  00 E  |  12  15 S |  1675 | 19  30 W
 At _Monbasa_                |  40  00 E  |   4  00 S |  1675 | 16  00 W
 At _Zocatra_                |  56  00 E  |  12  30 N |  1674 | 17  00 W
 ----------------------------+------------+-----------+-------+------------
 At _Aden_, at the Mo.    }  |            |           |       |
 of the _Red Sea_         }  |  47  30 E  |  13  00 N |  1674 | 15  00 W
 At _Diego Roiz_             |  61   0 E  |  20   0 S |  1676 | 20  30 W
 At Sea                      |  64  30 E  |   0   0   |  1676 | 15  30 W
 At Sea                      |  55   0 E  |  27   0 S |  1676 | 24  00 W
 ----------------------------+------------+-----------+-------+------------
 At _Bombay_                 |  72  30 E  |  19   0 N |  1676 | 12  00 W
 At Cape _Comorin_           |  76  00 E  |   8  15 N |  1680 |  8  48 W
 At _Ballafore_              |  87  00 E  |  21  30 N |  1680 |  8  20 W
 At Fort St. _George_        |  80  00 E  |  13  15 N |  1680 |  8  10 W
 At the W. Point of _Java_   | 104  00 E  |   6  40 S |  1676 |  3  10 W
 ----------------------------+------------+-----------+-------+------------
 At Sea                      |  58  00 E  |  39   0 S |  1677 | 27  30 W
 At the Isle of St. _Paul_   |  72   0 E  |  38   0 S |  1677 | 23  30 W
 At _Van Dimen's_ Land       | 142   0 E  |  42  25 S |  1642 |  0   0
 At _New Zealand_            | 170   0 E  |  40  50 S |  1642 |  9   0 E
 At _Three Kings Isle_ in }  |            |           |       |
 _New Zealand_.           }  | 169  30 E  |  34  35 S |  1642 |  8  40 E
 ----------------------------+------------+-----------+-------+------------
 At the Isle _Rotterdam_ }   |            |           |       |
 in the South Sea        }   | 184  00 E  |  20  15 S |  1642 |  6  20 E
 On the Coast of _N. Guin._  | 149  00 E  |   4  30 S |  1643 |  8  45 E
 At the W. P. of _N. Guin._  | 126  00 E  |   0  26 S |  1643 |  5  30 E


Tho' I could wish we could obtain from the _Spaniards_ what Variations
they find in their Voyages from the _Manilhas_ towards _Acapulco_,
through the North part of the South Sea; as likewise what it is at
_Japan_ from the _Dutch_: Yet (considering the number of these
Observations I have collected, and that they are made in parts of the
World so remote from _Europe_, and from one another) I suppose that the
Theory that answers these will scarce fail in those Regions from whence
we have as yet no account. But first we must make some Remarks upon the
foregoing Table: And, First,

That in all _Europe_ the Variation at this time is West, and more in the
Eastern Parts thereof than the Western: As likewise, that it seems
throughout to be upon the increase that way.

Secondly, That on the Coast of _America_, about _Virginia_,
_New-England_ and _New-Foundland_, the Variation is likewise Westerly;
and that it increases all the way as you go Northerly along the Coast,
so as to be above 20 Degrees at _New-Found-Land_, nearly 30 gr. in
_Hudson's Straights_, and not less than 57 Degrees in _Baffin's Bay_;
also, that as you Sail Eastward from this Coast, the Variation
diminishes. From these two it is a Legitimate Corollary: That _Somewhere
between_ Europe, _and the North part of_ America, _there ought to be an
Easterly Variation, or at least no Westerly_. And so I conjecture it is
about the Eastermost of the _Tercera Islands_.

Thirdly, That on the Coast of _Brasile_ there is East Variation, which
increases very notably as you go to the Southward, so as to be 12
Degrees at _Cape Frio_, and over against the River of _Plate_ 20½
Degrees: And from thence Sailing South-Westerly to the Straits of
_Magellan_ it decreases 17 Degrees, and at the West Entrance but 14
Degrees.

Fourthly, That at the Eastward of _Brasile_, properly so call'd, this
Easterly Variation decreases, so as to be very little at St. _Helena_
and _Ascension_, and to be quite gone, and the Compass Point true about
18 Degrees of Longitude West from the Cape of _Good-hope_.

Fifthly, That to the Eastward of the aforesaid Places a Westward
Variation begins, which Reigns in the whole _Indian_ Sea, and arises to
no less than Eighteen Degrees under the Equator it self, about the
Meridian of the Northern part of _Madagascar_; and near the same
Meridian, but in 39 Degrees South Latitude it is found full 27½
Degrees: From thence Easterly the West Variation decreases, so as to be
little more than eight Degrees at _Cape Comorin_, and than three Degrees
upon the Coast of _Java_; and to be quite extinct about the _Molucca
Islands_, as also a little to the Westwards of _Van Diemens_ Land found
out by the _Dutch_ in 1642.

Sixthly, That to the Eastward of the _Molucca's_ and _Van Diemens_ Land
in South Latitude there arises another Easterly Variation, which seems
not so great as the former, nor of so large Extent; for that at the
Island _Rotterdam_ it is sensibly less than upon the East Coast of _New
Guinea_; and, at the rate it decreases, it may well be suppos'd, that
about 20 Degrees farther East, or 225 Degrees East Longitude from
_London_, in the Latitude of 20 Degrees South, a Westerly Variation
begins.

Seventhly, That the Variations observ'd by the Honourable Sir _John
Norborough_ at _Baldivia_, and at the West Entrance of the _Straights_
of _Magellan_ do plainly shew, that That East Variation, noted in our
third Remark, is decreasing apace; and that it cannot reasonably extend
many Degrees into the South Sea from the Coast of _Peru_ and _Chili_,
leaving room for a small Westerly Variation, in that Tract of the
unknown World that lies in the mid-way between _Chili_ and
_New-Zealand_, and between _Hounds-Island_ and _Peru_.

Eighthly, That in Sailing North-West from St. _Helena_ by _Ascension_,
as far as the Equator, the Variation continues very small East, and as
it were constantly the same: So that in this part of the World the
Course, wherein there is no Variation, is evidently no Meridian, but
rather North-West.

Ninthly, That the Entrance of _Hudson's Straights_, and the Mouth of the
River of _Plate_, being nearly under the same Meridian, at the one place
the Needle varies 29½ Degrees to the _West_; at the other 20½
Degrees to the _East_. This plainly demonstrates the impossibility of
reconciling these Variations by the Theory of _Bond_; _which is by two
Magnetical Poles and an Axis, inclin'd to the Axis of the Earth_; from
whence it would follow, That _under the same Meridian the Variation
should be in all places the same way_.


These things being premised may serve as a sure Foundation to raise the
Superstructure of a Theory upon. But first it would not be amiss to shew
hereby the mistake of _Gilbert_ and _Des Cartes_: The first whereof
supposes, that _the Earth it self being in all its parts Magnetical, and
the Water not; wheresoever the Land is, thither also should the Needle
turn, as to the greater quantity of Magnetical Matter_. But this in many
Instances is not true; but most remarkably upon the Coast of _Brazile_,
where the Needle is so far from being attracted by the Land, that it
turns the quite contrary way, leaving the Meridian to lye N b E, which
is just along the Coast. As to the Position of _Des Cartes_, _that the
Iron and Loadstones hid in the Bowels of the Earth and the Bottom of the
Sea, may be the Causes that the Needle varies_; if we consider for how
great a part of the Earths Surface, _ex. gr._ in the whole _Indian_ Sea,
the Needle declines the same way, and that regularly, 'twill follow that
the attracting Substance that occasions it, must be very far distant.
Now by Experience we find the little force that Iron Guns have upon the
Compass in Ships (their Vertue, though they be Demiculverin, or greater
Cannon, being not perceptible at four or five Yards distance) and the
Experiments now before the _Royal Society_ do plainly shew, how little a
Magnetism there is in most crude Iron Oars: What quantity thereof must
be then suppos'd to make so powerful a Diversion at two or three
Thousand Miles distance? Yet I cannot deny that in some places near the
Shoar, or in Shoal-Water, the Needle may be irregularly directed from
the aforesaid Causes, and that not a little, as _Gassendus_ gives a
notable instance of the Island _Elba_ in the Mediterranean Sea: But
these differences from the general Direction are always signs of the
nearness of those Magnetical Substances, for the Production whereof that
Island _Elba_ has been famous from all Antiquity. Besides, against both
_Des Cartes_ and _Gilbert_, the change of the Variation, which has been
within these Hundred Years last past more than 15 gr. at _London_, is an
entire Demonstration; tho' _Des Cartes_ does not stick to say, that the
transportation of Iron from place to place, and the growth of new Iron
within the Earth, where there was none before, may be the cause thereof.
The same holds likewise against the _Hypothesis_ of _Magnetical Fibres_,
which _Kircher_ maintains.

Now to propose something that may answer the several appearances, and
introduce nothing strange in Philosophy, after a great many close
Thoughts, I can come to no other Conclusion than that, _The whole Globe
of the Earth is one great Magnet, having four Magnetical Poles, or
Points of Attraction, near each Pole of the Equator. Two; and that, in
those parts of the World which lie near adjacent to any one of those
Magnetical Poles, the Needle is govern'd thereby, the nearest Pole being
always predominant over the more remote_. The parts of the Earth wherein
these Magnetical _Poles_ lie, cannot as yet be exactly determin'd for
want of sufficient _Data_ to proceed Geometrically; but, as near as
Conjecture can reach, I reckon that the _Pole_, which is at present
nearest to us, lies in or near the Meridian of the Lands-end of
_England_, and not above seven Degrees from the Pole Arctick; by this
_Pole_ the Variations in all _Europe_ and _Tartary_, and the _North Sea_
are principally govern'd, though with regard to the other Northern Pole,
whose situation is in a _Meridian_ passing about the middle of
_California_, and about 15 gr. from the North Pole of the World; to this
the Needle has chiefly respect in all the North _America_, and in the
two Oceans on either side thereof, from the _Azores_ Westward to
_Japan_, and farther. The two Southern Poles are rather farther distant
from the South Pole of the World: The one about sixteen Degrees
therefrom, is in a Meridian, some twenty Degrees to the Westward of
_Magellan Straights_, or ninety five Degrees West from _London_: This
commands the Needle in all the _South-America_, in the _Pacifick Sea_,
and the greatest part of the _Ethiopick_ Ocean. The Fourth and last
_Pole_ seems to have the greatest Power, and largest Dominions of all,
as it is the most remote from the _Pole_ of the World, being little less
than 20 Degrees distant therefrom in the Meridian, which passes through
_Hollandia Nova_, and the Island _Celebes_ about one hundred and twenty
Degrees East from _London_; this Pole is predominant in the South part
of _Africa_, in _Arabia_ and the _Red Sea_, in _Persia_, _India_, and
its Islands, and all over the _Indian Sea_, from the Cape of _Good-Hope_
Eastwards to the middle of the great South Sea, that divides _Asia_ from
_America_. This seems to be the present Disposition of the Magnetical
Vertue throughout the whole Globe of the Earth; it remains to shew how
this Hypothesis makes out all the Variations that have been observ'd of
late; and how it answers to our several Remarks drawn from the Table.
And first it is plain, that (our _European_ North _Pole_ being in the
Meridian of the Lands-end of _England_) all places more Easterly than
that will have it on the West side of their Meridian, and consequently
the Needle, respecting it with its Northern Point, will have a Westerly
Variation, which will still be greater as you go to the Eastwards, till
you come to some Meridian of _Russia_, where 'twill be greatest, and
from thence decrease again. Thus at _Brest_ the Variation is but 1¾
Degrees, at _London_ 4½ Degrees; but at _Dantzick_ seven Degrees
West. To the Westward of the Meridian of the Lands-end, the Needle ought
to have an Easterly Variation; were it not that (by approaching the
_American_ Northern _Pole_, which lies on the West side of the Meridian,
and seems to be of greater force than this other) the Needle is drawn
thereby Westwards, so as to counterballance the Direction given by the
_European Pole_, and to make a small West Variation in the Meridian of
the Lands-end it self. Yet I suppose that about the Meridian of the Isle
_Tercera_, our nearest _Pole_ may so far prevail as to give the Needle a
little turn to the East, though but for a very small space: The
Counterballance of those two _Poles_ permitting no considerable
Variation in all the Eastern Parts of the _Atlantick_ Ocean; nor upon
the West Coasts of _England_ and _Ireland_, _France_, _Spain_ and
_Barbary_. But to the Westwards of the _Azores_ the Power of the
_American_ Pole overcoming that of the _European_, the Needle has
chiefly respect thereto, and turns still more and more towards it as you
approach it. Whence it comes to pass, that on the Coast of _Virginia_,
_New-England_, _New-found-Land_, and in _Hudson's-Straights_ the
Variation is Westward; that it decreases as you go from thence towards
_Europe_, and that it is less in _Virginia_ and _New-England_, than in
_New-found-Land_, and _Hudson's-Straights_. This Westerly Variation
again decreases, as you pass over the _North America_; and about the
Meridian of the middle of _California_ the Needle again points due
North; and from thence Westward to _Yedzo_ and _Japan_, I make no doubt
but the Variation is Easterly, and half the Sea over no less than
fifteen Degrees, if there be any truth in this Hypothesis of mine.
Therefore I propose this as a Trial, that the whole may be scann'd
thereby; and I conceive it will not be hard to know of the _Spaniards_
how it is, who so frequently sail through that Ocean, in their return
from the _Manilha_ Isles. This East Variation extends over _Japan_,
_Yedzo_, _East-Tartary_, and part of _China_, till it meet with the
Westerly, which is govern'd by the _European_ North Pole, and which I
said was greatest some where in _Russia_.

Towards the Southern Pole the effect is much the same, only that here
the South Point of the Needle is attracted. Hence it will follow, that
the Variation on the Coast of _Brazile_, at the River of _Plate_, and so
on to the Straights of _Magellan_, should be Easterly (as in our third
Remark); if we suppose a Magnetical Pole situate about twenty Degrees
more Westerly than the Straights of _Magellan_. And this Easterly
Variation doth extend Eastward over the greatest part of the _Ethiopick_
Sea, till it be counterpoised by the Vertue of the other Southern
_Pole_; as it is about mid-way between the Cape of _Good-Hope_, and the
Isles of _Tristan d' Acuntia_. From thence Eastwards, the _Asian_ South
Pole (as I must take the liberty to call it) becoming prevalent, and the
South point of the Needle being attracted thereby, there arises a West
Variation, very great in quantity and extent, because of the great
distance of this Magnetical Pole of the World. Hence it is, that in all
the _Indian_ Sea as far as _Hollandia Nova_, and farther, there is
constantly West Variation; at that under the Equator it self it arises
to no less than eighteen Degrees, where 'tis most. About the Meridian of
the Island _Celebes_, being likewise that of this Pole, this Westerly
Variation ceases, and an Easterly begins; which reaches, according to my
Hypothesis, to the middle of the _South-Sea_, between _Zelandia Nova_,
and _Chili_, leaving room for a small _West Variation_ govern'd by the
_American_ South Pole, which I shew'd to be in the _Pacifick Sea_, in
the sixth and seventh Remark.

What I have now said, does plainly shew the sufficiency of this
Hypothesis for solving the Variations that are at this time observ'd in
the temperate and frigid _Zones_, where the Direction of the Needle
chiefly depends upon the Counterpoise of the forces of two Magnetical
Poles of the same Nature; and I suppose I have shewn how it comes to
pass, that under the same Meridian the Variation should be in one place
29½ West, and another 20½ East; as I have noted in my ninth Remark.

In the _Torrid Zone_, and particularly under the Equinoctial, respect
must be had to all four Poles, and their Positions well consider'd,
otherwise it will not be easie to determine what the Variations shall
be; the nearest _Pole_ being always the strongest; yet not so, as not to
be counterballanc'd sometimes by the united forces of two more remote; a
notable Instance whereof is in our eighth Remark, where I took notice,
that in sailing from St. _Helena_ by the Isle of _Ascension_, to the
Equator, on a N. W. Course, the Variation is very little Easterly, and
in that whole Tract unalterable; for which I give this Reason, That the
South _American_ Pole (which is considerably the nearest in the
aforesaid Places) requiring a great Easterly Variation, is counterpoised
by the contrary Attraction of the _North-American_ and the
_Asian-South-Pole_; each whereof singly are in these Parts, weaker than
the _American-South-Pole_; and upon the North West Course, the Distance
from this latter is very little varied; and as you recede from the
_Asian-South-Pole_, the Ballance is still preserv'd by the access
towards the _North-American-Pole_. I mention not in this Case the
_European-North-Pole_, its Meridian being little remov'd from those of
these places; and of it self requiring the same Variations we here find.
After the same manner we might proceed to conclude the Variations in
other places under and near the Equator; but I purposely leave it for an
Exercise to the Thoughts of the serious Reader, who is desir'd to help
his Imagination, by having before him a Map or Globe of the Earth: And
to mark thereon the Magnetical _Poles_ in the _Longitudes_ and
_Latitudes_ I assign them. (_Vide Plate 2._)

Thus, I hope, I have not lost my Pains and Study in this difficult
Subject; believing that I have put it past doubt, _That there are in the
Earth four such Magnetical Points or Poles, which occasion the great
variety and seeming irregularity which is observed in the Variations of
the Compass_. But to calculate exactly what it is, in any place
assign'd, is what I dare not yet pretend to, though I could wish it were
my happiness to be able to oblige the World with so useful a piece of
Knowledge; there are Difficulties that occur, that render the thing as
yet not feasible; for first there are a great many Observations
requisite, which ought to be made at the same time; not at Sea, but
ashore, with greater Care and Attention than the generality of Sailors
apply. And besides, it remains undetermin'd in what proportion the
attractive Power decreases, as you remove from the _Pole_ of a Magnet,
without which it were a vain attempt to go about to calculate. There is
yet a further Difficulty, which is the Change of the Variation, one of
the Discoveries of this last Century; which shews, that it will require
some hundreds of Years to establish a compleat Doctrine of the
Magnetical System. From the foregoing Table it should seem, that all the
Magnetical _Poles_ had a motion Westward: But if it be so, 'tis evident,
that it is not a Rotation about the Axis of the Earth; for then the
Variations would continue the same, in the same parallel of _Latitude_
(the _Longitude_ only chang'd) as much as is the motion of the
Magnetical _Poles_, but the contrary is found by Experience; for there
is no where in the Latitude of 15½ North between _England_ and
_America_, a Variation of eleven Degrees East at this time; as it was
once here at _London_; it seems therefore, that our _European_ Pole is
grown nearer the Pole _Arctick_ than it was heretofore, or else that it
has lost part of its Vertue. But whether these Magnetical Poles move
altogether with one motion, or with several; whether equally or
unequally; whether Circular or Libratory: If Circular, about what
Center; if Libratory, after what manner; are Secrets as yet utterly
unknown to Mankind, and are reserv'd for the Industry of future Ages.




 _An Account of the Cause of the Change of the Variation of the
   Magnetical Needle, with an Hypothesis of the Structure of the
   Internal Parts of the Earth; as it was proposed to the _Royal
   Society_ in one of their late Meetings. By Mr. _Edmund Halley_._


Having in the precedent Discourse delivered a Theory of the Variation of
the Magnetical Compass, wherein I did collect as many Observations as at
that time I could procure, and having carefully compar'd them together,
I came at length to this general conclusion, _That the Globe of the
Earth might be supposed to be one great Magnet, having four Magnetical
Poles or Points of Attraction, near each Pole of the Equator two; and
that in those parts of the World which lie near adjacent to any one of
those Magnetical Poles, the Needle is chiefly govern'd thereby; the
nearest Pole being always predominant ever the more remote_. And I there
have endeavour'd to state and limit the present Position of those Poles
in the Surface of our Globe, which the Reader pleasing to consult, will
save us the pains of repeating. But after all, tho' that Discourse was
favourably receiv'd both at home and abroad, as seeming to render a
tolerable account of the observ'd Variations, yet I found two
Difficulties not easie to surmount; the one was, that no Magnet I had
ever seen or heard of, had more than two opposite _Poles_, whereas the
Earth had visibly four, and perhaps more. And secondly, it was plain
that these _Poles_ were not, at least all of them, fixt in the Earth,
but shifted from place to place, as appear'd by the great Changes in the
Needles Direction within this last Century of Years, not only at
_London_, (where this great Discovery was first made) but almost all
over the Globe of Earth; whereas it is not known or observ'd that the
_Poles_ of a Load-stone ever shifted their place in the Stone, nor
(considering the compact hardness of that Substance) can it easily be
suppos'd; though the Matter of Fact be too notorious and universal, not
to be accounted for.

These Difficulties had wholly made me despond, and I had long since
given over an Inquiry I had so little hopes of, when in accidental
Discourse, and least expecting it, I stumbl'd on the following
Hypothesis; in delivering whereof, if I shall seem to advance any thing
that looks like Extravagant or Romantick, the Reader is desir'd to
suspend his Censure, till he have consider'd the force and number of the
many Arguments which concur to make good so new and so bold a
Supposition.

Though it be sufficiently known and allow'd, that the Needles Variation
changes, it will be necessary however to give a few Instances, whereby
it may appear that this Change is gradual and universal, and the effect
of a great and permanent motion: For which take the following Examples.

At _London_, in the Year 1580, the Variation was observ'd by Mr.
_Burrows_ to be 11° 15' East. In _Anno_ 1622, the same was found by Mr.
_Gunter_ to be but 6° 0' East. In the Year 1634, Mr. _Gellibrand_ found
it 4° 5' East. In 1657, Mr. _Bond_ observ'd that there was no Variation
at _London_. _Anno_ 1672, my self observ'd it 2° 30' to the West; and in
the Year 1692, I again found it 6° 00' West. So that in 112 Years the
Direction of the Needle has chang'd no less than seventeen Degrees.

At _Paris_, _Orontius Finæus_ about the Year 1550, did account it about
eight or nine Degrees East Variation. _Anno_ 1640, it was found three
Degrees East. _Anno_ 1660, there was no Variation there, and _Anno_
1681, I found it to be 2° 30' to the West.

At _Cape d' Agulhas_, the most Southerly Promontary of _Africa_, about
the Year 1600, the Needle pointed due North and South without Variation,
whence the _Portugueze_ gave its name. _Anno_ 1622, there was two
Degrees West Variation. _Anno_ 1675, it was 8° 50' West; and in the Year
1691, it was curiously observ'd not less than eleven Degrees West.

At St. _Helena_, about the Year 1600, the Needle declin'd eight Degrees
to the East. _Anno_ 1623, it was but 6° 0' East. _Anno_ 1677, when I was
there, I observ'd it accurately on Shoar to be 0° 40' East; and in 1692
it was found about 1° to the Westward of the North.

At _Cape Comorine_ in _India_, in the Year 1620, there was 14° 20' West
Variation. In the Year 1680, there was 8° 48', but now lately in the
Year 1688, it was no more than 7° 30', so that here the Needle has
return'd to the East about seven Degrees in seventy Years.

In all the other Examples the Needle has gradually mov'd towards the
West, and the places are too far asunder to be influenc'd by the removal
of any Magnetical Matter, which may by accident be transplac'd within
the Bowels, or on the Surface of the Earth. If more Examples are
desir'd, the Reader may be furnished with them in the _Portugueze
Routier_ of _Aleixo de Motta_ (written about the Year 1600) and in the
Voyage of _Beaulieu_, both publish'd in Mr. _Thevenot_'s first
Collection of curious Voyages, Printed at _Paris_, _Anno_ 1663; which he
is to compare with the Journals of our late _East India_ Voyagers, and I
am assur'd, that it will be thereby evident, that the Direction of the
Needle is in no place fix'd and constant, tho' in some it change faster
than in others: And where for a long time it has continu'd as it were
unalter'd, it is there to be understood, that the Needle has its
greatest Deflection, and is become Stationary in order to return, like
the Sun, in the Tropick. This, at present, is in the _Indian Sea_, about
the Island _Mauritius_, where is the highest West Variation, and in a
Tract tending from thence into the N. N. W. towards the _Red-Sea_ and
_Egypt_. And in all Places to the Westward of this Tract, all over
_Africa_ and the Seas adjoining, the West Variation will be found to
have encreas'd; and to the Eastwards thereof as in the Example of _Cape
Comorine_, to have decreased, _viz._ all over the _East-Indies_, and the
Islands near it.

After the like manner in that Space of East Variation, which, beginning
near St. _Helena_, is found all over the South _America_, and which at
present is highest about the Mouth of _Rio de la Plata_, it has been
observ'd, that in the Eastern Parts thereof, the Variation of the Needle
gradually decreases; but whether on the contrary it increases in those
places which lie more Westerly than that Tract wherein the highest East
Variation is found; or how it may be in the vast _Pacifick Sea_, we have
not Experience enough to ascertain, only we may by Analogy infer, that
both the East and West Variations therein do gradually increase and
decrease after the same Rule.

These _Phænomena_ being well understood and duly consider'd, do
sufficiently evince, That the whole Magnetical System is by one, or
perhaps more motions translated, whether Eastwards or Westwards, I shall
anon discuss; that this moving thing is very great, as extending its
effects from Pole to Pole, and that the motion thereof is not _per
saltum_, but a gradual and regular motion.

Now considering the Structure of our _Terraqueous_ Globe, it cannot be
well suppos'd that a very great part thereof can move within it, without
notably changing its Center of Gravity and the Equilibre of its Parts,
which would produce very wonderful Effects in changing the Axis of
diurnal Rotation, and occasion strange alteration in the Seas Surface,
by Inundations and Recesses thereof, such as History never yet
mention'd. Besides, the solid parts of the Earth are not to be granted
permeably by any other than fluid Substances, of which we know none that
are any ways Magnetical. So that the only way to render this motion
intelligible and possible, is to suppose it to turn about the Center of
the Globe, having its Center of Gravity fix'd and immoveable in the same
common Center of the Earth: And there is yet requir'd, that this moving
internal Substance be loose and detached from the external Parts of the
Earth whereon we live; for otherwise, were it affix'd thereto, the whole
must necessarily move together.

So then the External Parts of the Globe may well be reckon'd as the
Shell, and the Internal as a _Nucleus_ or inner Globe, included within
ours, with a fluid Medium between, which having the same Common Center
and Axis of diurnal Rotation, may turn about with our Earth each twenty
four Hours; only this outer Sphere having its turbinating motion some
small matter either swifter or slower than the internal Ball: And a very
minute Difference in length of time, by many Repetitions becoming
sensible, the Internal Parts will by degrees recede from the External,
and not keeping pace with one another, will appear gradually to move
either Eastwards or Westwards by the difference of their motions.

Now supposing such an Internal Sphere having such a motion, we shall
solve the two great Difficulties we encounter'd in my former Hypothesis:
For if this exteriour Shell of Earth be a Magnet, having its Poles at a
distance from the Poles of diurnal Rotation; and if the Internal
_Nucleus_ be likewise a Magnet, having its Poles in two other places,
distant also from the Axis; and these latter by a gradual and slow
motion change their place in respect of the External; we may then give a
reasonable account of the four Magnetical Poles I presume to have
demonstrated before; as likewise of the Changes of the Needles
Variations, which till now hath been unattempted.

The Period of this Motion being wonderful great, and there being hardly
an hundred Years since these Variations have been duly observ'd, it will
be very hard to bring this Hypothesis to a Calculus, especially since,
though the Variations do increase and decrease regularly in the same
place, yet in differing places, at no great distance, there are found
such casual Changes thereof as can no ways be accounted for by a regular
Hypothesis; as depending upon the unequal and irregular distribution of
the Magnetical Matter within the Substance of the External Shell or Coat
of the Earth, which deflect the Needle from the Position it would
acquire from the effect of the general Magnetism of the whole. Of this
the Variations at _London_ and _Paris_ give a notable Instance, for the
Needle has been constantly about 1°½ more Easterly at _Paris_ than at
_London_; though it be certain that according to the general effect, the
Difference ought to be the contrary way: Notwithstanding which, the
Variations in both places do change alike.

Hence, and from some other of like Nature, I conclude, That the two
Poles of the External Globe are fixt in the Earth, and that if the
Needle were wholly govern'd by them, the Variations thereof would be
always the same, with some little Irregularities upon the account I but
just now mention'd: But the Internal Sphere having such a gradual
translation of its Poles, does influence the Needle, and direct it
variously, according to the result of the attractive or directive Power
of each Pole; and consequently there must be a Period of the Revolution
of this Internal Ball, after which the Variations will return again as
before. But if it shall in future Ages be observ'd otherwise, we must
then conclude that there are more of these Internal Spheres, and more
Magnetical Poles than Four, which at present we have not a sufficient
number of Observations to determine, and particularly in that vast _Mar
del Zur_, which occupies so great a part of the whole Surface of the
Earth.

If then two of the Poles be fixt and two moveable, it remains to
ascertain which they are that keep their place; and though I could wish
we had the Experience of another Century of Years to found our
Conclusions upon, yet I think we may safely determine, That our
_European North Pole_ (which in the precedent Discourse I suppos'd near
the Meridian of the Lands-end of _England_, and about seven Degrees
therefrom) is that That is moveable of the two Northern Poles, and that
That has chiefly influenc'd the Variations in these parts of the World:
For in _Hudson_'s Bay, which is under the Direction of the _American_
Pole, the Change is not observ'd to be near so fast as in these parts of
_Europe_, though that Pole be much farther remov'd from the Axis.

As to the South Poles, I take the _Asian_ Pole, which I place about the
Meridian of the Island _Celebes_ to be the fixt, and consequently the
_American_ Pole to move; from the like Observation of the slow Decrease
of the Variation on the Coast of _Java_, and near the Meridian of the
_Asian_ Pole; though I must confess to have no account of the effects of
the other beyond _Magellan_'s Streights.

If this be allow'd me, 'tis plain that the fixt Poles are the Poles of
this External Shell or Cortex of the _Earth_, and the other two the
Poles of a Magnetical _Nucleus_ included and moveable within the other.
It likewise follows, that this Motion is Westwards, and by consequence
that the aforesaid _Nucleus_ has not precisely attained the same degree
of Velocity with the exteriour Parts in their diurnal Revolution; but so
very nearly equals it, that in 365 Revolves the difference is scarce
sensible. This I conceive to arise from the Impulse whereby this diurnal
Motion was imprest on the Earth, being given to the External Parts, and
from thence in time communicated to the Internal; but not so as
perfectly to equal the Velocity of the first Motion impress'd on, and
still conserv'd by the superficial Parts of the Globe.

As to the quantity of this Motion it is almost impossible to define it,
both from the Nature of this kind of Observation, which cannot be very
accurately perform'd, as also from the small time these Variations have
been observ'd, and their Change discover'd. It appears by all
Circumstances, that its Period is of many Centuries of Years, and as far
as may be collected from the Change of the Place, where there was no
Variation, by reason of the Equilibre of the two Southern Magnetical
Poles, _viz._ from _Cape d' Agulhas_ to the Meridian of St. _Helena_
(which is about 23 _degr._ in about ninety Years) and of the place where
the Westerly Variation is in its ἀκμὴ or greatest Deflection, being
about half so much, _viz._ from the Isle of _Diego Roiz_ to the South
West Parts of _Madagascar_. We may with some Reason conjecture, that the
_American_ Pole has mov'd Westwards forty six Degrees in that time, and
that the whole Period thereof is perform'd in seven hundred Years, or
thereabouts; so that the nice Determination of this, and of several
other Particulars in the Magnetick System is reserv'd for remote
Posterity; all that we can hope to do, is to leave behind us
Observations that may be confided in, and to propose an Hypothesis which
after Ages may examine, amend or refute. Only here I must take leave to
recommend to all Masters of Ships, and all others, Lovers of Natural
Truths, that they use their utmost Diligence to make, or procure to be
made, Observations of these Variations in all parts of the World, as
well in the North as South Latitude (after the laudable Custom of our
_East India_ Commanders) and that they please to communicate them to the
_Royal Society_, in order to leave as compleat a History as may be to
those that are hereafter to compare all together, and to compleat and
perfect this abstruse Theory.

And by the way it will not be amiss to amend a receiv'd Error in the
Practice of observing the Variation, which is, to take it by the
Amplitude of the Rising and Setting Sun, when his Center appears in the
visible Horizon; whereas he ought to be observ'd when his under Limb is
still above the Horizon about ⅔ of his Diameter, or twenty Minutes,
upon the score of the Refraction, and the height of the Eye of the
Observer above the Surface of the Sea: Or else they are to work the
Amplitudes as they do the Azimuth, reckoning the Suns Distance from the
Zenith 90° 36': This, though it be of little consequence near the
Æquinoctial, will make a great Error in high Latitudes, where the Sun
rises and sets obliquely.

But to return to our Hypothesis, In order to explain the Change of the
Variations, we have adventur'd to make the Earth hollow, and to place
another Globe within it; and I doubt not but this will find Opposers
enough. I know 'twill be Objected, That there is no Instance in Nature
of the like thing; that if there was such a middle Globe it would not
keep its place in the Center, but be apt to deviate therefrom, and might
possibly chock against the Concave Shell, to the ruin, or at least
endammaging thereof; That the Water of the Sea would perpetually leak
through, unless we suppose the Cavity full of Water; That were it
possible, yet it does not appear of what use such an inward Sphere can
be of, being shut up in Eternal Darkness, and therefore unfit for the
Production of Animals or Plants; with many more Objections, according to
the Fate of all such new Propositions.

To these, and all other that I can foresee, I briefly Answer, That the
Ring environing the Globe of _Saturn_ is a notable Instance of this
kind, as having the same common Center, and moving along with the
Planet, without sensibly approaching him on one side more than the
other. And if this Ring were turn'd on one of its Diameters, it would
then describe such a Concave Sphere as I suppose our External one to be.
And since the Ring, in any Position given, would, in the same manner,
keep the Centre of _Saturn_ in its own, it follows, that such a Concave
Sphere may move with another included in it, having the same common
Centre. Nor can it well be suppos'd otherwise, considering the Nature of
Gravity; for should these Globes be adjusted once to the same common
Centre, the Gravity of the parts of the Concave would press equally
towards the Centre of the inner Ball, which equality must necessarily
continue till some External Force disturb it, which is not easie to
imagine in our Case. This perhaps I might more intelligibly express, by
saying that the inner Globe being posited in the Centre of the
Exteriour, must necessarily ascend which way soever it move; that is, it
must overcome the force of Gravity pressing towards the common Centre,
by an impulse it must receive from some outward Agent; but all outward
Efforts being sufficiently fenc'd against by the Shell that surrounds
it, it follows, that this _Nucleus_ being once fixt in the common
Centre, must always there remain.

As to the leaking of the Water through this Shell, when once a passage
shall be found for it to run through, I must confess it is an Objection
seemingly of weight; but when we consider how tightly great Beds of
Chalk or Clay, and much more Stone do hold Water, and even Caves arch'd
with Sand; no Man can doubt but the Wisdom of the Creator has provided
for the Macrocosm by many more ways than I can either imagine or
express, especially since we see the admirable and innumerable
Contrivances wherewith each worthless Individual is furnish'd both to
defend it self, and propagate its Species. What Curiosity in the
Structure, what Accuracy in the Mixture and Composition of the parts,
ought not we to expect in the Fabrick of this Globe, made to be the
lasting Habitation of so many various Species of Animals, in each of
which there want not many Instances that manifest the boundless Power
and Goodness of their Divine Author; and can we then think it a hard
Supposition, that the Internal Parts of this Bubble of Earth should be
replete with such Saline and Vitriolick Particles as may contribute to
Petrefaction, and dispose the transuding Water to shoot and coagulate
into Stone, so as continually to fortifie, and, if need were, to
consolidate any breach or flaw in the Concave Surface of the Shell.

And this perhaps may not without Reason be suppos'd to be the final
Cause of the admixture of the Magnetical Matter in the Mass of the
Terrestrial parts of our Globe, _viz._ To make good and maintain the
Concave Arch of this Shell: For by what the Excellent Mr. _Newton_ has
shewn in his _Principia Philosophiæ_, it will follow, that according to
the general Principle of Gravity, visible throughout the whole Universe,
all those Particles that by length of time, or otherwise, shall moulder
away, or become loose on the Concave Surface of the External Sphere,
would fall in, and with great force descend on the Internal, unless
those Particles were of another sort of Matter capable by their stronger
tendency to each other, to suspend the force of Gravity; but we know no
other Substances capable of supporting each other by their mutual
Attraction but the Magnetical, and these we see miraculously to perform
that Office, even where the Power of Gravity has its full effect, much
more within the Globe where it is weaker. Why then may we not suppose
these said Arches to be lin'd throughout with a Magnetical Matter, or
rather to be one great Concave Magnet, whose two Poles are the Poles we
have before observ'd to be fixt in the Surface of our Globe.

Another Argument, favouring this Hypothesis, is drawn from a Proposition
of the same Mr. _Newton_, where he determines the force wherewith the
_Moon_ moves the _Sea_ in producing the _Tides_: His Words are,
_Densitas Lunæ est ad densitatem Terra ut 680 ad 387 seu 9 ad 5
quamproximé. Est igitur corpus Lunæ densius ac magis terrestre quam
Terra nostra_, p. 466. Now if the Moon be more solid than the Earth, as
9 to 5, why may we not reasonably suppose the Moon, being a small Body,
and a secondary Planet, to be solid Earth, Water, Stone, and this Globe
to consist of the same Materials, only four Ninths thereof to be Cavity,
within and between the Internal Spheres; which I would render not
improbable.

To those that shall enquire of what use these included Globes can be, it
must be allow'd, that they can be of very little service to the
Inhabitants of this outward World, nor can the Sun be serviceable to
them, either with his Light or Heat. But since it is now taken for
granted, that the Earth is one of the Planets, and they all are with
Reason suppos'd Habitable, though we are not able to define by what sort
of Animals; and since we see all the parts of the Creation abound with
Animate Beings, as the Air with Birds and Flies, the Water with the
numerous varieties of Fish, and the very Earth with Reptiles of so many
sorts; all whose ways of Living would be to us incredible did not daily
Experience teach us. Why then should we think it strange that the
prodigious Mass of Matter, whereof this Globe does consist, should be
capable of some other improvement than barely to serve to support its
Surface? Why may not we rather suppose that the exceeding small quantity
of solid Matter, in respect of the fluid Æther, is so dispos'd by the
Almighty Wisdom, as to yield as great a Surface for the use of living
Creatures, as can consist with the conveniency and security of the
whole? We our selves, in Cities where we are pressed for Room, commonly
build many Stories one over the other, and thereby accommodate a much
greater multitude of Inhabitants.

But still it will be said, That without Light there can be no living,
and therefore all this _apparatus_ of our inward Globes must be useless:
To this I Answer, That there are many ways of producing Light which we
are wholly ignorant of; the Medium it self may be always luminous after
the manner of our _Ignes fatui_. The Concave Arches may in several
places shine with such a Substance as invests the Surface of the Sun;
nor can we, without a boldness unbecoming a Philosopher, adventure to
assert the impossibility of peculiar Luminaries below, of which we have
no sort of _Idea_. I am sure the Poets _Virgil_ and _Claudian_ have gone
before me in this Thought, inlightning their _Elysian Fields_ with Sun
and Stars proper to those infernal, or rather internal Regions. _Virg.
Æneid. 6._

  _Largior hic compos Æther & lumine vestit
  Purpureo; Solemque suum sua Sidera norunt._

And _Claudian lib 2. De Raptu Proserpinæ._

  _Amissum ne crede diem, sunt altera nobis
  Sidera, sunt orbes alii, luménque videbis
  Purius, Elysiumque magis mirabere Solem._

And though this be not to be esteem'd as an Argument, yet I may take the
liberty I see others do, to quote the Poets when it makes for my purpose.

Lastly, To explain yet farther what I mean, I have adventur'd to adjoin
the following Scheme, (_Tab. 1. Fig. 3_) wherein the Earth is
represented by the outward Circle, and the three inward Circles are made
nearly proportionable to the Magnitudes of the Planets _Venus_, _Mars_
and _Mercury_, all which may be included within the Globe of Earth, and
all the Arches more than sufficiently strong to bear their weight. The
Concave of each Arch, which is shaded differently from the rest, I
suppose to be made up of Magnetical Matter; and the whole to turn about
the same common Axis _pp_, only with this difference, that the Outer
Sphere still moves somewhat faster than the Inner. Thus the Diameter of
the Earth being about eight thousand _English_ Miles, I allow five
hundred Miles for the thickness of its Shell, and another space of five
hundred Miles for a Medium between, capable of an immense Atmosphere for
the use of the Globe of _Venus_: _Venus_ again I give a Shell of the
same thickness, and leave as great a space between her Concave and
_Mars_; so likewise from _Mars_ to _Mercury_, which latter Ball we will
suppose solid, and about two thousand Miles Diameter. Thus I have shew'd
a possibility of a much more ample Creation, than has hitherto been
imagin'd; and if this seem strange to those that are unacquainted with
the Magnetical System, it is hop'd that all such will endeavour, first,
to inform themselves of the Matter of Fact, and then try if they can
find out a more simple Hypothesis, at least a less absurd, even in their
own Opinions. And whereas I have adventur'd to make these Subterraneous
Orbs capable of being Inhabited, 'twas done designedly for the sake of
those who will be apt to ask _cui bono_, and with whom Arguments drawn
from _Final Causes_ prevail much. If this short Essay shall find a kind
Acceptance, I shall be encourag'd to enquire farther, and to Polish this
rough Draft of a Notion till hitherto not so much as started in the
World, and of which we could have no Intimation from any other of the
_Phænomena_ of Nature.

Since this was written, a Discovery I have made in the Cœlestial
Motions, seems to render a farther Account of the Use of the Cavity of
the Earth, _viz._ To diminish the Specifick Gravity thereof, in respect
of the Moon; for I think I can demonstrate that the Opposition of the
Æther to the Motions of the Planets in long time becomes sensible; and
consequently the greater Body must receive a less Opposition than the
smaller, unless the Specifick Gravity of the smaller do proportionably
exceed that of the greater, in which case only they can move together;
so that the Cavity I assign in the Earth, may well serve to adjust its
weight to that of the Moon, for otherwise the Earth would leave the Moon
behind it, and she become another Primary Planet.




 _An Historical Account of the _Trade Winds_ and _Monsoons_, observable
   in the Seas between and near the _Tropicks_, with an attempt to
   assign the Physical Cause of the said Winds, by Mr. _Ed. Halley_._


An exact Relation of the constant and periodical Winds, observable in
several Tracts of the Ocean, is a part of Natural History not less
desireable and useful, than it is difficult to obtain, and its
_Phænomena_ hard to explicate: I am not ignorant that several Writers
have undertaken this Subject, and although _Varenius_ (_Lib. 1. Chap.
21. Geo. Gen._) seems to have endeavour'd after the best information
from _Voyagers_, yet cannot his Accounts be admitted for accurate, by
those that shall attentively consider and compare them together, and
some of them are most evident Mistakes; which, as near as I can, I shall
attempt to rectify, having had the opportunity of conversing with
Navigators, acquainted with all parts of _India_, and having liv'd a
considerable time between the _Tropicks_, and there made my own Remarks.

The Substance of what I have collected is briefly as follows.

The Universal _Ocean_ may most properly be divided into three Parts,
_viz._ 1. The _Atlantick_ and _Æthiopick-Sea_. 2. The _Indian Ocean_.
3. The Great _South Sea_, or the _Pacifick Ocean_; and though these Seas
do all communicate by the South, yet as to our present purpose of the
_Trade Winds_, they are sufficiently separated by the interposition of
great Tracts of _Land_; the first lying between _Africa_ and _America_,
the second between _Africa_ and the _Indian Islands_, and _Hollandia
Nova_; and the last between the _Phillipine Isles_, _China_, _Japan_ and
_Hollandia Nova_ on the _West_, and the Coast of _America_ on the
_East_. Now following this natural division of the Seas, so will we
divide our History into three parts in the same order.


I. In the _Atlantick_ and _Æthiopick_ Seas between the _Tropicks_, there
is a general _Easterly Wind_ all the Year long, without any considerable
Variation, excepting that it is subject to be deflected therefrom, some
few Points of the Compass towards the _North_ or _South_, according to
the Position of the place. The Observations which have been made of
these Deflections, are the following.

1. That near the Coast of _Africa_, as soon as you have pass'd the
_Canary Isles_, you are sure to meet a fresh Gale of _North East_ Wind,
about the Latitude of 28 Degrees _North_, which seldom comes to the
_Eastwards_ of the _East North-East_, or passes the _North North-East_.
This Wind accompanies those bound to the Southward, to the Latitude of
ten North, and about a hundred Leagues from the _Guinea_ Coast, where,
till the fourth Degree of North Latitude, they fall into the Calms and
Tornadoes; of which more hereafter.

2. That those bound to the _Caribbee Isles_, find, as they approach the
_American_ side, that the aforesaid _North-East_ Wind becomes still more
and more Easterly, so as sometimes to be _East_, sometimes _East_ by
_South_, but yet most commonly to the _Northward_ of the _East_ a Point
or two, seldom more. 'Tis likewise observ'd, that the strength of these
Winds does gradually decrease, as you sail to the _Westwards_.

3. That the limits of the Trade and variable Winds, in this Ocean, are
farther extended on the _American_ side than the _African_; for whereas
you meet not with this certain Wind till after you have pass'd the
Latitude of twenty eight Degrees on this side; on the _American_ side it
commonly holds to thirty, thirty one, or thirty two Degrees of Latitude;
and this is verified likewise to the Southwards of the Æquinoctial, for
near the _Cape_ of _Good-Hope_ the limits of the Trade Winds, are three
or four Degrees nearer the Line, than on the Coast of _Brazile_.

4. That from the Latitude of four Degrees _North_, to the aforesaid
Limits on the _South_ of the Æquator, the Winds are generally and
perpetually between the _South_ and _East_, and most commonly between
the _South-East_ and _East_, observing always this Rule, That on the
_African_ side they are more _Southerly_, on the _Brazilian_ more
_Easterly_, so as to become almost due _East_, the little deflection
they have being still to the _Southwards_. In this part of the Ocean it
has been my fortune to pass a full Year, in an Employment that oblig'd
me to regard more than ordinary the Weather, and I found the Winds
constantly about the _South-East_, the most usual Point _S E b E_; when
it was Easterly, it generally blew hard, and was gloomy, dark, and
sometimes rainy Weather; if it came to the Southwards it was generally
Serene, and a small Gale next to a Calm, but this not very common. But I
never saw it to the Westwards of the South, or Northwards of the East.

5. That the Season of the Year has some small effect on these Trade
Winds, for that when the Sun is considerable to the Northwards of the
Æquator, the South-East Winds, especially in the Straight of this Ocean
(if I may so call it) between _Brazile_ and the Coast of _Guinea_, do
vary a Point or two to the Southwards, and the North-East become more
Easterly; and on the contrary, when the Sun is towards the Tropick of
_Capricorn_ the South-Easterly Winds become more Easterly, and the
North-Easterly Winds on this side the Line veere more to the Northwards.

6. That as there is no general Rule that admits not of some Exception,
so there is in this Ocean a Tract of Sea wherein the Southerly and
South-West Winds are perpetual, _viz._ all along the Coast of _Guinea_,
for above five hundred Leagues together, from _Sierra Leona_ to the Isle
of St. _Thomas_; for the South-East Trade Wind having pass'd the Line,
and approaching the Coast of _Guinea_ within eighty or 100 Leagues,
inclines towards the Shore, and becomes S. S. E. and by Degrees, as you
come nearer, it veeres about to South, S. S. W. and in with the Land
South-West, and sometimes West South-West; which Variation is better
express'd in the Mapp hereto annexed, (_Vide Plate 2_) than it can well
be in Words. These are the Winds which are observ'd on this Coast when
it blows true, but there are frequent Calms, violent sudden Gusts call'd
_Tornado's_, from all Points of the Compass, and sometimes unwholsome
foggy Easterly Winds, call'd _Hermitaa_ by the Natives, which too often
infest the Navigation of these parts.

7. That to the Northwards of the Line, between four and ten Degrees of
Latitude, and between the Meridians of _Cape Virde_, and of the
Eastermost Islands that bear that Name, there is a Tract of Sea wherein
it were improper to say there is any Trade Wind, or yet a Variable; for
it seems condemn'd to perpetual Calms, attended with terrible Thunder
and Lightning, and Rains so frequent, that our Navigators from thence
call this part of the Sea the _Rains_; the little Winds that are, be
only some sudden uncertain Gusts, of very little Continuance and less
Extent; so that sometimes each Hour you shall have a different Gale,
which dies away into a Calm before another succeed, and in a Fleet of
Ships in sight of one another, each shall have the Wind from a several
Point of the Compass; with these weak _Breezes_ Ships are oblig'd to
make the best of their way to the Southward through the aforesaid six
Degrees, wherein 'tis reported some have been detain'd whole Months for
want of Wind.

From the three last Observables is shewn the Reason of two notable
Occurents in the _East-India_ and _Guinea_ Navigations: The one is, why,
notwithstanding the narrowest part of the Sea between _Guinea_ and
_Brazile_ be about five hundred Leagues over, yet Ships bound to the
Southward, sometimes, especially in the Months of _July_ and _August_,
find a great difficulty to pass it. This happens because of the
South-East Winds, at that time of the Year commonly extending some
Degrees beyond the ordinary limit of four Degrees North Latitude, and
withal they come so much Southerly, as to be sometimes South, sometimes
a Point or two to the West; there remains then only to ply to Windward,
and if on the one side they stand away W. S. W. they gain the Wind still
more and more Easterly; but there is danger of not weathering the
_Brazilian_ Shoar, or at least the Shoals upon that Coast. But if upon
the other Tack they go away E. S. E. they fall into the Neighbourhood of
the Coast of _Guinea_, from which there is no departing without running
Easterly, as far as the Isle of St. _Thomas_, which is the constant
practice of all the _Guinea_ Ships, and which may seem very strange,
without the consideration of the sixth Remark, which shews the Reason of
it: For being in with the Coast, the Wind blows generally at S. W. and
W. S. W. with which Winds they cannot go to the Northward for the Land;
and on the other Tack they can lie no nearer the Wind than S. S. E. or
South; with these Courses they run off the Shoar, but in so doing they
always find the Winds more and more contrary; so that when near the
Shoar they could lie South, at a greater distance they can make their
way no better than S. E. and afterwards E. S. E. with which Courses they
fetch commonly the Isle of St. _Thomas_ and Cape _Lopez_, where finding
the Winds to the Eastward of the South, they keep them favourable, by
running away to the Westward in the South Latitude, of three or four
Degrees, where the S. E. Winds are perpetual.

For the sake of these general Winds, all those that use the
_West-Indian_ Trade, even those bound to _Virginia_, count it their best
Course to get as soon as they can to the Southwards, that so they may be
certain of a fair and fresh Gale to run before it to the Westwards; and
for the same Reason those homewards bound from _America_, endeavour to
gain the Latitude of thirty Degrees, as soon as possible, where they
first find the Winds begin to be variable; tho' the most ordinary Winds
in the Northern part of the _Atlantick_ Ocean come from between the
South and West.

As to those furious Storms call'd _Hurricanes_, which are, as it were,
peculiar to the _Caribbee_ Isles; and which so dreadfully afflict them
in the Month of _August_, or not much before or after, they do not so
properly belong to this place, both by Reason of their small continuance
and extent, as likewise because they are not Anniversary, some Years
having more than one, and sometimes for several Years together there
being none at all. But their Violence is so unconceivable, and their
other _Phænomena_ so surprising, that they merit well to be consider'd
apart.

What is here said, is to be understood of the Sea Winds at some distance
from the Land; for upon and near the Shoars, the Land and Sea Breezes
are almost every where sensible; and the great Variety which happens in
their Periods, Force and Direction, from the situation of the Mountains,
Vallies and Woods, and from the various Texture of the Soil, more or
less capable of retaining and reflecting Heat, and of exhaling or
condensing Vapours, is such, that it were an endless task, to endeavour
to account for them.


II. In the _Indian_ Ocean, the Winds are partly general, as in the
_Æthiopick_ Ocean, partly Periodical; that is, half the Year they blow
one way, and the other half near upon the opposite Points; and these
Points and Times of shifting are different in different parts of this
Ocean; the limits of each Tract of Sea, subject to the same Change or
_Monsoon_, are certainly very hard to determine, but the diligence I
have used to be rightly inform'd, and the care I have taken therein,
has, in a great measure, surmounted that Difficulty; and I am perswaded
that the following Particulars may be relied upon.

1. That between the Latitudes of ten Degrees and thirty Degrees South,
between _Madagascar_ and _Hollandia Nova_, the general Trade Wind about
the S. E. by E. is found to blow all the Year long, to all Intents and
Purposes after the same manner as in the same Latitudes in the
_Æthiopick_ Ocean, as it is describ'd in the fourth _Remark_ aforegoing.

2. That the aforesaid S. E. Winds extend to within two Degrees of the
_Æquator_, during the Months of _June_, _July_, _August_, &c. to
_November_; at which time between the _South Latitudes_ of three and ten
Degrees, being near the Meridian of the North end of _Madagascar_, and
between two and twelve South Latitude, being near _Sumatra_ and _Java_,
the contrary Winds from the N. W. or between the North and West, set in
and blow for half the Year, _viz._ from the beginning of _December_ till
_May_; and this _Monsoon_ is observ'd as far as the _Molucca_ Isles, of
which more anon.

3. That to the Northward of three Degrees South Latitude, over the whole
_Arabian_ or _Indian-Sea_ and Gulph of _Bengall_, from _Sumatra_ to the
Coast of _Africa_, there is another _Monsoon_, blowing from _October_ to
_April_ upon the North East Points; but in the other half Year, from
_April_ to _October_, upon the opposite Points of S. W. and W. S. W. and
that with rather more force than the other, accompanied with dark rainy
Weather, whereas the N. E. blows clear; 'tis likewise to be noted, that
the Winds are not so constant, either in strength or point in the Gulph
of _Bengall_, as they are in the _Indian-Sea_, where a certain and
steady Gale scarce ever fails. 'Tis also remarkable, that the S. W.
Winds in these Seas are generally more Southerly on the _African_ side,
more Westerly on the _Indian_.

4. That as an _Appendix_ to the last describ'd _Monsoon_, there is a
Tract of Sea to the Southwards of the Æquator, subject to the same
Changes of the Winds, _viz._ near the _African_ Coast, between it and
the Island _Madagascar_ or St. _Lawrence_, and from thence Northwards as
far as the Line; wherein from _April_ to _October_ there is found a
constant fresh S. S. W. Wind, which, as you go more Northerly, becomes
still more and more Westerly, so as to fall in with the W. S. W. Winds,
mention'd before, in those Months of the Year to be certain to the
Northward of the Æquator: What Winds blow in these Seas, for the other
half Year, from _October_ to _April_, I have not yet been able to obtain
to my full satisfaction, for that our Navigators always return from
_India_ without _Madagascar_, and so are little acquainted in this
Matter; the Account that has been given me is only this, that the Winds
are much Easterly hereabouts, and as often to the North of the true East
as to the Southwards thereof.

5. That to the Eastward of _Sumatra_ and _Malacca_, to the Northwards of
the Line, and along the Coast of _Cambodia_ and _China_, the _Monsoons_
blow North and South, that is to say, the N. E. Winds are much
Northerly, and the S. W. much Southerly: This Constitution reaches to
the Eastwards of the _Philippine_ Isles, and as far Northerly as
_Japan_. The Northern _Monsoon_ setting in, in these Seas, in _October_
or _November_, and the Southern in _May_, blowing all the Summer Months:
Here it is to be noted, That the Points of the Compass, from whence the
Wind comes in these Parts of the World, are not so fixt as in those
lately describ'd; for the Southerly will frequently pass a Point or two
to the Eastwards of the South, and the Northerly as much to the
Westwards of the North, which seems occasion'd by the great quantity of
Land, which is interspers'd in these Seas.

6. That in the same _Meridians_, but to the Southwards of the Æquator,
being that Tract lying between _Sumatra_ and _Java_ to the West, and
_New Guinea_ to the East, the same Northerly _Monsoons_ are observ'd,
but with this difference, that the inclination of the Northerly is
towards the N. West, and of the Southerly towards the S. E. but the
_plagæ venti_ are not more constant here than in the former, _viz._
variable five or six Points; besides the times of the Change of these
Winds, are not the same as in the _Chinese_ Seas, but about a Month or
six Weeks later.

7. That these contrary Winds do not shift all at once, but in some
places the time of the Change is attended with Calms, in others with
variable Winds; and it is particularly remarkable, that the end of the
Westerly _Monsoon_ on the Coast of _Coromandel_, and the two last Months
of the Southerly _Monsoon_ in the Seas of _China_, are very subject to
be tempestuous: The violence of these Storms is such, that they seem to
be of the Nature of the _West-India Hurricanes_, and render the
Navigation of these parts very unsafe about that time of the Year. These
Tempests are by our Seamen usually term'd, _The breaking up of the
Monsoons_.

By reason of the shifting of these Winds, all those that sail in these
Seas, are oblig'd to observe the Seasons proper for their Voyages, and
so doing they fail not of a fair Wind and speedy Passage; but if so be
they chance to out-stay their time, till the contrary _Monsoon_ sets in,
as it frequently happens, they are forc'd to give over the hopes of
accomplishing their intended Voyages, and either return to the Port from
whence they came, or else put in to some other Harbour, there to spend
the time till the Winds shall come favourable.


III. The third Ocean call'd _Mare Pacificum_, whose Extent is equal to
that of the other two (it being from the West Coast of _America_ to the
_Philippine_ Islands, not less than 150 Degrees of Longitude) is that
which is least known to our own or the Neighbour Nations; that
Navigation that there is on it, is by the _Spaniards_, who go Yearly
from the Coast of _New Spain_ to the _Manilha's_, but that but by one
beaten track; so that I cannot be so particular here as in the other
two. What the _Spanish_ Authors say of the Winds they find in their
Courses, and what is confirm'd by the old Accounts of _Drake_ and
_Cavendish_; and since by _Schooten_, who sail'd the whole breadth of
this Sea in the Southern Latitude of fifteen or sixteen Degrees, is,
that there is a great conformity between the Winds of this Sea, and
those of the _Atlantick_ and _Æthiopick_; that is to say, that to the
Northwards of the Æquator, the predominant Wind is between the East and
North-East; and to the Southwards thereof there is a constant steady
Gale between the East and South-East, and that on both sides the Line
with so much constancy, that they scarce ever need to attend the Sails,
and Strength, that it is rare to fail of crossing this vast Ocean in ten
Weeks time, which is about 130 Miles _per diem_; besides, 'tis said that
Storms and Tempests are never known in these parts: So that here is the
very best of Sailing; no want of a fresh fair Wind, and yet no danger of
having too much: Wherefore some have thought it might be as short a
Voyage to _Japan_ and _China_, to go by the Streights of _Magellan_, as
by the _Cape_ of _Good Hope_.

The Limits of these general Winds are also much the same as in the
_Atlantick_ Sea, _viz._ about the thirtieth Degree of Latitude on both
sides; for the _Spaniards_ homewards bound from the _Manilha's_, always
take the advantage of the Southerly _Monsoon_, blowing there in the
Summer Months, and run up to the Northwards of that Latitude, as high as
_Japan_, before they meet with variable Winds, to shape their Course to
the Eastwards. And _Schooten_ and others that have gone about by the
_Magellan_ Streights, have found the Limits of S. E. Winds, much about
the same Latitude to the Southwards; besides a farther _Analogy_ between
the Winds of this Ocean, and the _Æthiopick_, appears in that, upon the
Coast of _Peru_, they are always much Southerly, like as they are found
near the Shoars of _Angola_.

Thus far Matter of Fact, wherein if the information I have receiv'd be
not in all parts Accurate, it has not been for want of inquiry from
those I conceiv'd best able to instruct me; and I shall take it for a
very great Kindness if any Master of a Ship, or other Person, well
inform'd of the Nature of the Winds, in any of the aforemention'd parts
of the World, shall please to communicate their Observations thereupon;
so that what I have here Collected may be either confirm'd or amended,
or by the addition of some material Circumstances enlarg'd. It is not
the work of one, nor of few, but of a multitude of Observers, to bring
together the Experience requisite to compose a perfect and compleat
History of these Winds; however I am not much doubtful that I have err'd
in, or omitted any of the principal Observables, whatever lesser
Particulars may have escaped my Knowledge.

To help the Conception of the Reader in a manner of so much difficulty,
I believ'd it necessary to adjoin a Scheme, (_Plate 2._) shewing at one
view all the various Tracts and Courses of these Winds; whereby 'tis
possible the thing may be better understood, than by any verbal
Description whatsoever.

The Limits of these several Tracts are design'd every where by prickt
Lines, as well in the _Atlantick_ and _Æthiopick_, where they are the
boundaries of the Trade and variable Winds, as in the _Indian_ Ocean,
where they also shew the Extent of the several _Monsoons_. I could think
of no better way to design the Course of the Winds on the Map, than by
drawing rows of stroaks in the same Line that a Ship would move going
always before it; the sharp end of each little stroak pointing out that
part of the Horizon, from whence the Wind continually comes; and where
there are _Monsoons_, the rows of the stroaks run alternately backwards
and forwards, by which means they are thicker there than elsewhere. As
to the great South Sea, considering its vast Extent, and the little
Variety there is in its Winds, and the great _Analogy_ between them, and
those of the _Atlantick_ and _Æthiopick_ Oceans; besides, that the
greatest part thereof is wholly unknown to us; I thought it unnecessary
to lengthen the Map therewith.

In the foregoing History are contained several Problems, that merit well
the Consideration of our acutest Naturalists, both by reason of the
constancy of the Effect, and of the immense Extent thereof; near half
the Surface of the Globe being concerned. The chief of these Problems
are, 1. Why these Winds are perpetually from the East in the _Atlantic_
and _Æthiopick_; as likewise in the _Pacifick_ Ocean, between the
Latitudes of 30 North and South? 2. Why the said Winds extend no farther
with constancy than to the Latitude of 30 Degrees? 3. Why there should
be a constant South-Westerly Wind upon and near the Coast of _Guinea_?
4. Why in the North part of the _Indian_ Ocean, the Winds, which for one
half Year do agree with those of the other two Oceans, should change in
other half Year, and blow from the opposite Points; whilst the Southern
part of that Ocean follows the General Rule, and has perpetual Winds
about S. E? 5. Why in these General Trade-Winds it should be always
true, that to the Northward of the _Æquator_ it is inclin'd to the
Northwards of the East; and in South Latitudes, to the Southward
thereof? 6. Why in these Seas of _China_ there should be so great an
Inclination from the East to the North, more than elsewhere? with many
more, which it would be much easier to propose than answer.

But lest I should seem to propose to others, Difficulties which I have
not thought worth my own Time and Pains, take here the result of an
earnest Endeavour after the true reason of the aforesaid _Phænomena_;
wherein if I am not able to account for all Particulars, yet 'tis hoped
the Thoughts I have spent thereon, will not be judged wholly lost, by
the Curious in Natural Enquiries.

Wind is most properly defined to be the Stream or Current of the Air,
and where such a Current is perpetual and fixt in its Course, 'tis
necessary that it proceed from a permanent un-intermitting Cause.
Wherefore some have been inclin'd to propose the diurnal _Rotation_ of
the Earth upon its _Axis_, by which, as the _Globe_ turns Eastwards, the
loose and _fluid_ Particles of the Air, being so exceeding light as they
be, are left behind, so that in respect of the Earths _Surface_ they
move Westwards, and become a constant Easterly Wind. This Opinion seems
confirm'd, for that these Winds are found only near the _Æquinoctial_,
in those Parallels of Latitude where the diurnal Motion is swiftest; and
I should readily assent to it, if the constant Calms in the _Atlantick_
Sea, near the _Æquator_, the Westerly Winds near the Coast of _Guinea_;
and the _Periodical_ Westerly _Monsoons_ under the _Æquator_ in the
_Indian_ Seas, did not declare the insufficency of that _Hypothesis_.
Besides the Air being kept to the Earth by the Principle of _Gravity_,
would acquire the same degree of _Velocity_ that the Earths _Surface_
moves with, as well in respect of the diurnal _Rotation_, as of the
Annual about the Sun, which is about thirty times swifter.

It remains therefore to substitute some other Cause, capable of
producing a like constant Effect, not liable to the same Objections, but
agreeable to the known Properties of the Elements of Air and Water, and
the Laws of the Motion of fluid Bodies. Such an one is, I conceive, the
Action of the Sun Beams upon the Air and Water, as he passes every Day
over the Oceans, consider'd together with the Nature of the Soil, and
Situation of the adjoining Continents: I say therefore, first, that
according to the Laws of _Staticks_, the Air which is less rarified or
expanded by heat, and consequently more ponderous, must have a Motion
towards those parts thereof, which are more rarified, and less
ponderous, to bring it to an _Æquilibrium_; and secondly, That the
Presence of the Sun continually shifting to the Westwards, that part
towards which the Air tends, by reason of the Rarifaction made by his
greatest _Meridian_ Heat, is with him carried Westward, and consequently
the tendency of the whole Body of the lower Air is that way.

Thus a general Easterly Wind is formed, which being impressed upon all
the Air of a vast Ocean, the Parts impel one the other, and so keep
moving till the next return of the Sun, whereby so much of the Motion as
was lost, is again restored, and thus the Westerly Wind is made
perpetual.

From the same Principle it follows, that this Easterly Wind should on
the North side of the _Æquator_, be to the Northwards of the East, and
in South Latitudes to the Southwards thereof; for near the _Line_, the
Air is much more rarified, than at a greater distance from it; because
of the Sun twice in a Year Vertical, and at no time distant above 23
Degr. and a half; at which distance the Heat, being as the Sine of the
Angle of Incidence, is but little short of that of the perpendicular
Ray. Whereas under the Tropicks, though the Sun stay long Vertical, yet
he is as long 47 Degr. off; which is a kind of Winter, wherein the Air
so cools, as that the Summer-heat cannot warm it to the same degree with
that under the Æquator. Wherefore the Air to the Northwards and
Southwards, being less rarified than that in the middle, it follows,
that from both sides it ought to tend towards the Æquator: This Motion
compounded with the former Easterly Wind, answers all the _Phænomena_ of
the general Trade-winds; which, if the whole Surface of the Globe were
Sea, would undoubtedly blow all round the World, as they are found to do
in the _Atlantick_, and _Æthiopick_ Oceans.

But seeing that so great Continents do interpose, and break the
continuity of the Oceans, regard must be had to the Nature of the Soil,
and the Position of the high Mountains, which I suppose the two
principal Causes of the several Variations of the Winds, from the former
general Rule: For if a Country lying near the Sun, prove to be flat,
sandy, low Land, such as the Desarts of _Lybia_ are usually reported to
be, the Heat occasion'd by the Reflection of the Suns Beams, and the
retention thereof in the Sand, is incredible to those that have not felt
it; whereby the Air being exceedingly rarified, it is necessary that the
cooler and more dense Air should run thitherwards to restore the
_Æquilibrium_: This I take to be the cause, why near the Coast of
_Guinea_ the Wind always sets in upon the Land, blowing Westerly instead
of Easterly, there being sufficient Reason to believe, that the Inland
Parts of _Africa_ are prodigiously hot, since the Northern Borders
thereof were so intemperate, as to give the Ancients cause to conclude,
that all beyond the _Tropick_, was made uninhabitable by excess of Heat:
From the same Cause it happens, that there are so constant Calms in that
part of the Ocean, called the _Rains_, (described in the 7th Remark on
the _Atlantick_ Sea) for this Tract being placed in the middle, between
the Westerly Winds blowing on the Coast of _Guinea_, and the Easterly
Trade-winds, blowing to the Westwards thereof, the tendency of the Air
here, is indifferent to either, and so stands in _Æquilibrio_ between
both; and the weight of the incumbent Atmosphere being diminished by the
continual contrary Winds blowing from hence, is the reason that the Air
here holds not the copious Vapour it receives, but lets it fall into
frequent Rains.

But as the cool and dense Air, by reason of its greater Gravity, presses
upon the hot and rarified, 'tis demonstrative that this latter must
ascend in a continued Stream as fast it rarifies; and that being
ascended, it must disperse it self to preserve the _Æquilibrium_: that
is, by a contrary Current, the upper Air must move from those Parts
where the greatest Heat is: So by a kind of Circulation, the North-East
Trade-Wind below, will be attended with a South-Westerly above, and the
South-Easterly with a North-West Wind above; that this is more than a
bare Conjecture, the almost instantaneous Change of the Wind to the
opposite Point, which is frequently found in passing the limits of the
Trade-winds, seems to assure us; but that which above all confirms this
_Hypothesis_ is the _Phænomenon_ of the _Monsoons_, by this means most
easily solved, and without it hardly explicable.

Supposing therefore such a Circulation, as above, 'tis to be considered
that to the Northward of the _Indian_ Ocean there is every where Land
within the usual limit of the Latitude of 30, _viz._ _Arabia_, _Persia_,
_India_, _&c._ which for the same reason as the _Mediterranean_ Parts of
_Africa_, are subject to unsufferable Heats when the Sun is to the
North, passing nearly Vertical; but yet are temperate enough when the
Sun is removed towards the other _Tropick_; because of a ridge of
Mountains at some distance within the Land, said to be frequently in
Winter cover'd with Snow, over which the Air, as it passes, must needs
be much chill'd. Hence it comes to pass, that the Air coming according
to the general Rule, out of the N. E. in the _Indian_ Seas, is sometimes
hotter, sometimes colder, than that which by this Circulation is
return'd out of the S. W. and by consequence, sometimes the under
Current or Wind, is from the N. E. sometimes from the S. W.

That this has no other Cause, is clear from the times wherein these
Winds set in, _viz._ in _April_, when the Sun begins to warm those
Countries to the North, the S. W. _Monsoon_ begins, and blows during the
Heats till _October_; when the Sun being retir'd, and all things growing
cooler Northward, and the Heat increasing to the South, the North-East
Winds enter and blow all the Winter till _April_ again. And it is
undoubtedly from the same Principle that to the Southwards of the
Æquator, in part of the _Indian_ Ocean, the North-West Winds succeed to
the South-East, when the Sun draws near the _Tropick_ of _Capricorn_;
but I must confess, that in this latter occurs a difficulty, not well to
be accounted for, which is, why this Change of the _Monsoons_ should be
any more in this Ocean, than in the same Latitudes in the _Æthopick_,
where there is nothing more certain than a S. E. Wind all the Year.

'Tis likewise very hard to conceive why the limits of the Trade-wind
should be fixt, about the thirtieth Degree of Latitude all round the
Globe; and that they should so seldom transgress or fall short of those
bounds; as also that in the _Indian_ Sea, only the Northern Part should
be subject to the changeable _Monsoons_, and in the Southern there be a
constant S. E.

These are Particulars that merit to be consider'd more at large, and
furnish a sufficient Subject for a just Volume, which will be a very
commendable Task for such, who being us'd to Philosophick Contemplation,
shall have leisure to apply their serious Thoughts about it.

[Illustration: _Plate 2 pag. 80_

 A new & Correct SEA CHART
 of the
 WHOLE WORLD
 _Shewing the _Variations_ of yᵉ
 _COMPASS_
 as they were found Año 1700
 with a View of the Generall
 and Coasting _Trade Winds_
 and _Monsoons_ or shifting
 _Trade Winds_
 by the Direction of
 _Capᵗ. Edm. Halley_._]




 _A Discourse of the Rule of the Decrease of the height of the _Mercury_
   in the Barometer, according as Places are elevated above the Surface
   of the Earth; with an Attempt to discover the true Reason of the
   Rising and Falling of the _Mercury_, upon Change of Weather. By _Edm.
   Halley_._


The Elastick Property of the Air has been long since made out, by
Experiments before the _Royal Society_, and elsewhere; and the
Resistance of its Spring is found to be nearly equal to the Weight or
Force that compresses it; as also, that the Spaces the same Air
occupies, under differing Pressures, are reciprocally as those
Pressures: It has been shewn likewise by undoubted Experiment, that the
specifick Gravity of the Air, near the Earth's Surface to that of Water,
was once as 1 to 840; again as 1 to 852; and a third time, in a very
large Vessel holding 10 Gallons, as 1 to 860; all which, considering the
Difficulty of the Experiment, agree well enough, the Mercury standing at
all those times about 29 Inches ¾: But by Reason 'twas Summer-weather,
and consequently the Air rarified, when all these were tried, we may
without sensible Error say in round numbers, that the Barometer standing
at 30 Inches, and in a mean State of Heat and Cold, the specifick
Gravity of the Air to Water, is as 1 to 800. By the like Trials the
weight of Mercury to Water, is as 13½ to 1, or very near it; so that
the weight of Mercury to Air, is as 10800 to 1; and a Cylinder of Air of
10800 Inches or 900 Feet, is equal to an Inch of Mercury; and were the
Air of an equal density like Water, the whole Atmosphere would be no
more than 5,1 Miles high, and in the Ascent of every 900 Feet the
Barometer would sink an Inch. But the Expansion of the Air increasing in
the same proportion as the incumbent weight of the Atmosphere decreases;
that is, as the Mercury in the Barometer sinks; the upper Parts of the
Air are much more rarified than the lower, and each Space answering to
an Inch of Quicksilver, grows greater and greater; so that the
Atmosphere must be extended to a much greater height. Now, upon these
Principles, to determine the height of the Mercury at any assigned
height in the Air; and _è contra_, having the height of the _Mercury_
given, to find the height of the Place where the Barometer stands, are
Problems not more difficult than curious; and which I thus resolve.

The Expansions of the Air being reciprocally as the heights of the
Mercury, it is evident, that by the help of the Curve of the _Hyperbola_
and its _Asymptotes_, the said Expansions may be expounded to any given
height of the _Mercury_: For by the 65th _Prop. lib. 2. Conic.
Mydorgii_, _the Rectangles_, _ABCE_, _AKGE_, _ALDE_, _&c._ (in _Plate 1.
Fig. 4._) are always equal, and consequently the sides, _CB_, _GK_,
_LD_, &c. are reciprocally as the sides _AB_, _AK_, _AL_, &c. If then
the Lines _AB_, _AK_, _AL_, be supposed equal to the heights of the
_Mercury_, or the pressures of the Atmosphere, the Lines _CB_, _GK_,
_LD_, answering thereto, will be as the Expansions of the Air under
those Pressures, or the Bulks that the same quantity of Air will occupy;
which Expansions being taken infinitely many, and infinitely little,
(according to the Method of Indivisibles) their Summ will give the
Spaces of Air between the several heights of the _Barometer_; that is to
say, the Summ of all the Lines between _CB_ and _KG_, or the _Area_
_CBKG_, will be proportioned to the Distance or Space intercepted
between the Levels of two Places in the Air, where the _Mercury_ would
stand at the heights represented by the Lines _AB_, _AK_; so then the
Spaces of Air answering to equal Parts of _Mercury_ in the _Barometer_,
are as the _Area's_ _CBKG_, _GKLD_, _DLFM_, &c. These _Area's_ again
are, by the Demonstration of _Gregory_ of St. _Vincent_, proportionate
to the _Logarithms_ of the Numbers expressing the _Rationes_ of _AK_ to
_AB_, of _AL_ to _AK_, of _AM_ to _AL_, &c. So then by the common Table
of _Logarithms_, the height of any Place in the _Atmosphere_, having any
assign'd height of the _Mercury_, may most easily be found: For the Line
_CB_ in the _Hyperbola_, whereof the _Area's_ design the _Tabular
Logarithms_, being 0,0144765; 'twill be, as 0,0144765, to the difference
of the _Logarithms_ of 30, or any other lesser Number, for 900 Feet, or
the Space answering to an Inch of _Mercury_, if the Air were equally
prest with 30 Inches of _Mercury_, and every where alike, to the height
of the _Barometer_ in the Air, where it will stand at that lesser number
of Inches: And by the Converse of this Proportion may the height of the
_Mercury_ be found, having the Altitude of the Place given. From these
Rules I deriv'd the following Tables.

 _A Table shewing the Altitude,
 to given heights of the _Mercury_._

 Inch.               Feet.

 30                      0
 29                    915
 28                   1862
 27                   2844
 26                   3863
 25                   4922
 20                  10947
 15                  18715
 10                  29662
  5                  48378
  1                  91831
  0.5               110547
  0.25              129262
  0.1    29 mil. or 154000
  0.01   41 m.   or 216169
  0.001  53 m.      278338

 _A Table shewing the heights of the
 _Mercury_, at given Altitudes._

 Feet.           Inch.

    0           30  00
 1000           28  91
 2000           27  86
 3000           26  85
 4000           35  87
 5000 feet      24  93
    1 mile      24  67
    2           20  29
    3           16  68
    4           13  72
    5           11  28
   10            4  24
   15            1  60
   20            0  95
   25            0  23
   30            0  08
   40            0  012

Upon these Suppositions it appears, that at the height of 41 Miles the
Air is so rarified, as to take up 3000 times the Space it occupies here,
and at 53 Miles high it would be expanded above 30000 times; but it's
probable that the utmost Power of its Spring cannot exert it self, to so
great an Extension, and that no part of the _Atmosphere_ reaches above
45 Miles from the Surface of the Earth.

This seems confirm'd from the Observations of the _Crepusculum_, which
is observ'd commonly to begin and end when the Sun is about 18 Degrees
below the Horizon; for supposing the Air to reflect light from its most
rarified Parts, and that as long as the Sun illuminates any of its
_Atoms_, they are visible to an Eye not intercepted by the Curvity of
the Earth, it will follow from _Fig. 5. Plate 1._ that the proportion of
the height of the whole Air, to the Semi-diameter of the Earth, is much
about, as 1 to 90, or as the excess of the _Secant_ of about 8½
Degrees to the _Radius_. For if _E_ be the Eye of the Observer, _S_ a
Place where the Sun sets at the end of Twilight in _E_, and the Arch
_ECS_, or _TCA_, be found 18 Degrees, the excess of the _Secant_ of half
thereof _ECH_, would be the height of the Air, _viz._ _GH_: But the Beam
of the Sun _ASH_, and the Visual Ray _EH_, do each of them suffer a
Refraction of about 32 or 33 Minutes, whereby being bent inwards from
_H_ towards _G_, the height of the Air need not be so great as if they
went streight; and having from the Angle _ECS_ taken the double
Refraction of the _Horizontal Ray_, the half of the Remainder will be
8½ Degrees _circiter_, whose _Secant_ being 10,111, it follows, that
as 10000 to 111, so the Semi-diameter of the Earth supposed 4000 Miles,
to 44,4 Miles; which will be the height of the whole Air, if the Places
_E_, _S_, whose visible Portions of the _Atmosphere_ _ERZH_, and _SHKB_,
just touch one the other, be 18 Degrees asunder.

At this height the Air is expanded into above 3000 times the space it
occupies here, and we have seen the Experience of condensing it into the
60th part of the same Space, so that it should seem, that the Air is a
Substance capable of being compressed into the 180000th part of the
Space it would naturally take up, when free from pressure. Now what
Texture or Composition of Parts shall be capable of this great Expansion
and Contraction, seems a very hard Question; and which, I suppose, is
scarce sufficiently accounted for, by comparing it to Wool, Cotten, and
the like springy Bodies.

Hitherto I have only consider'd the _Air_ and _Atmosphere_, as one
unalter'd Body, as having constantly at the Earth's Surface the 800th
part of the weight of Water, and being capable of Rarifaction and
Condensation _in infinitum_; neither of which _Hypotheses_ are rigidly
true: For here in _England_ it is notoriously known, that the weight of
the whole _Atmosphere_ is various, being counterpoised sometimes by
28½ Inches of _Mercury_, and at other times by no less than 30½;
so that the under parts being pressed by about a 15th part, less weight,
the _specifick_ Gravity of the Air upon that score will sometimes be a
15th part lighter than another; besides Heat and Cold, does very
considerably dilate and contract the Air, and consequently alter its
Gravity; to which add the mixture of _Effluvia_, or steams arising from
almost all Bodies, which assimulating into the Form of Air, are kept
suspended therein, as Salts dissolv'd in Liquors, or Metals in corroding
_Menstrua_; which Bodies being all of them very much heavier than Air,
their Particles by their Admixture must needs encrease the weight of
that Air they lie incorporated withal, after the same manner as melted
Salts do augment the specifick Gravity of Water. The other Consideration
is, that the Rarifaction and Condensation of the Air is not precisely
according to the proportion here laid down; for the Experiment very
nearly agrees thereto, as may be seen in the 58th Chapter of Mr.
_Hook's_ _Micrography_; yet are the Condensations not possible beyond
certain degrees: For being compressed into an 800th part of the Space it
takes up here, its consistence would be equally dense with that of
Water; which yields not to any force whatsoever, as hath been found by
several Experiments tried here, and at _Florence_, by the _Academia del
Cimento_. Nor can the Rarifaction proceed _in infinitum_; for supposing
the Spring whereby it dilates it self, occasion'd by what Texture of
Parts you please, yet must there be a determinate Magnitude of the
natural State of each Particle, as we see it is in Wool, and the like,
whose Bodies being compressable into a very small Space, have yet a
determinate bulk which they cannot exceed, when free'd from all manner
of Pressure.

These Objections being true, do disturb the Geometrical Accuracy of
these Conclusions, drawn from the specifick Gravity of the Air observ'd
at any time; but the Method here shewn will compute by a like
Calculation, the heights of the Quick-silver, and the Rarifactions of
the Air from any assign'd height of the _Barometer_ at the Earth's
Surface, and any specifick Gravity given. As to the Condensation and
Rarifaction by Heat and Cold, and the various mixture of Aqueous and
other Vapours, these two Objections seem generally to compensate each
other; for when the Air is rarified by Heat, they are raised most
copiously; so that though the Air properly so call'd, be expanded, and
consequently lighter, yet the _Interstices_ thereof being crouded full
of Vapours of much heavier Matters, bulk for bulk, the weight of the
_Compositum_ may continue much the same, at least a most curious
Experiment made by the Ingenious Mr. _John Caswell_, of _Oxford_, upon
the top of _Snowdon_ Hill, in _Carnarvanshire_, seems to prove, that the
first Inches of _Mercury_ have their Portions of Air near enough to what
I now determine: For the height of the Hill being 1240 Yards, or very
near it, he found the _Mercury_ to have subsided to 25,6 Inches, or 4
inches below the mean Altitude thereof at the Level of the Sea, (which
is a greater difference than has been found in any of our former
Experiments,) and the Space answering to 4 Inches, by my Calculation,
should be 1288 Yards; and it agrees as well with the Observations in the
Appendix to Mr. _Pascall_'s Book, _del Equilibre des Liqueurs_, made on
the high Hill in _Auvergne_, call'd _le puy de Domme_. So that the
Rarifaction and Vapours seem not to have alter'd considerably, the
Gravity of the under Parts of the _Air_; and much above the height where
these Experiments were made, do few Vapours ascend, and the Cold is such
that the Snow lies continually, so that for the more elevated Parts of
the Sphere of _Air_, there is much less Reason to doubt.

But now we have had occasion to mention the difference there is between
the height of the _Mercury_ at one time, from the height thereof at
another, it may not be unacceptable to offer at some Reasons for the
said difference; which, at least to my self, seem to have some
appearance of Truth. _First_, Then it's undoubtedly demonstrable, that
the height of the Cylinder of _Mercury_ is equal to the weight of the
whole incumbent Air, and consequently that that whole is sometimes a
fifteenth more than at other times; which cannot otherwise be, but by
the access of new Matter when 'tis heavy, and its diminution when 'tis
light; that _Hypothesis_ therefore that shews how the Air shall be
encreased or diminished, in any particular place, will give a Reason for
the greater and lesser height of the _Mercury_ in the _Baroscope_: But
to direct us in the choice of the several Causes, which may be assign'd
for the Increase and Decrease of the Air, 'twill not be unnecessary to
enumerate some of the principal Observations made upon the _Barometer_,
most whereof are sufficiently known already to all those that are
curious in these Matters.

The _First_ is, That in calm Weather, when the Air is inclin'd to Rain,
the _Mercury_ is commonly low.

2. That in serene good settled Weather, the _Mercury_ is generally high.

3. That upon very great Winds, though they be not accompanied with Rain,
the _Mercury_ sinks lowest of all, with relation to the Point of the
Compass the Wind blows upon.

4. That _cæteris paribus_ the greatest heights of the _Mercury_ are
found upon Easterly and North-Easterly Winds.

5. That in calm frosty Weather the _Mercury_ generally stands high.

6. That after very great Storms of Wind, when the _Quicksilver_ has been
low, it generally rises again very fast.

7. That the more Northerly places have greater Alterations of the
_Baroscope_, than the more Southerly.

8. That within the _Tropicks_ and near them, those Accounts I have had
from others, and my own Observation at St. _Helena_, make very little or
no Variation of the height of the _Mercury_ in all Weathers.


Now that Theory that can well account for all these appearances, will,
in all probability, approach nearer the true cause of the _Barometers_
Variations, than any thing hitherto afforded; and such an one I am bound
to believe, is that which I here lay down with submission to better
Judgments.

I conceive that the principal Cause of the rise and fall of the
_Mercury_, is from the variable Winds, which are found in the _Temperate
Zones_, and whose great unconstancy here in _England_ is most notorious.
I shall not at present inquire into the Cause of its uncertainty, but
the Matter of Fact being most undoubted, the Legitimate Consequences
thereof must be allow'd me, let it proceed from what it will.

A second Cause is the uncertain Exhalation and Præcipitation of the
Vapours lodging in the Air, whereby it comes to be at one time much more
crowded than at another, and consequently heavier; but this latter in a
great measure depends upon the former. Now from these Principles I shall
endeavour to explicate the several _Phænomena_ of the _Barometer_,
taking them in the same order I laid them down.

1. _Why in calm Weather the Air being inclin'd to Rain, the _Mercury_ is
commonly low?_ I Answer, That the _Mercury_'s being low, inclines it to
Rain; for the Air being light, the Vapours are no longer supported
thereby, being become specifically heavier than the Medium wherein they
floated; so that they descend towards the Earth, and in their fall
meeting with other aqueous Particles, they incorporate together, and
form little drops of Rain; but the _Mercury_'s being at one time lower
than another, is the effect of two contrary Winds blowing from the place
whence the _Barometer_ stands; whereby the Air of that place is carried
both ways from it, and consequently the incumbent Cylinder of Air is
diminished, and accordingly the _Mercury_ sinks; as for Instance, if in
the _German Ocean_ it should blow a Gale of Westerly Wind, and at the
same time an Easterly Wind in the _Irish Sea_; or if in _France_ it
should blow a Southerly Wind, and in _Scotland_ a Northern; it must be
granted me, that That part of the _Atmosphere_ impendent over _England_,
would thereby be exhausted and attenuated, and the _Mercury_ would
subside, and the Vapours which before floated in those parts of the
_Air_ of equal Gravity with themselves, would sink to the Earth.

2. _Why in serene good settled weather the _Mercury_ is generally high?_
To this I Answer, That the greater height of the _Barometer_, is
occasion'd by two contrary Winds blowing towards the place of
Observation, whereby the Air of other places is brought thither and
accumulated; so that the incumbent Cylinder of Air being encreas'd both
in height and weight, the _Mercury_ press'd thereby must needs rise and
stand high, as long as the Winds continue so to blow; and then the Air
being specifically heavier, the Vapours are better kept suspended, so
that they have no inclination to Præcipitate and fall down in Drops,
which is the reason of the serene good Weather, which attends the
greater heights of the _Mercury_.

3. _Why upon very great Winds or Storms, tho' accompanied with no Rain,
the _Mercury_ sinks lowest of all, with relation to the Point of the
Compass upon which the Wind blows?_ This is caus'd by the very rapid
Motion of the Air in these Storms; for the Tract or Region of the Earths
Surface, wherein these Winds rage, not extending all round the Globe,
that stagnant Air which is left behind, as likewise that on the sides,
cannot come in so fast as to supply the Evacuation made by so swift a
Current; so that the Air must necessarily be attenuated, when and where
the said Winds continue to blow, and that more or less, according to
their Violence; add to which, that the _Horizontal_ Motion of the Air
being so quick as it is, may in all probability take off some part of
the perpendicular pressure thereof; and the great Agitation of its
Particles, is the Reason why the Vapours are dissipated, and do not
condense into Drops, so as to form Rain, otherwise the natural
Consequence of the Airs Rarifaction.

4. _Why _cæteris paribus_ the _Mercury_ stands highest upon an Easterly
or North-Easterly Wind?_ This happens because that in the great
_Atlantick Ocean_, on this side the thirty fifth Degree of North
Latitude, the Westerly and South-Westerly Trade-Winds blow almost
always; so that whenever here the Wind comes up at East and North-East,
'tis sure to be checked by a contrary Gale, as soon as it reaches the
Ocean; wherefore, according to what is made out in our second Remark,
the Air must needs be heaped over this Island; and consequently the
_Mercury_ must stand high, as often as these Winds blow. This holds true
in this Country, but is not a general Rule for others, where the Winds
are under different Circumstances; and I have sometimes seen the
_Mercury_ here as low as twenty nine Inches, upon an Easterly Wind, but
then it blows exceeding hard, and so comes to be accounted for by what
was observ'd upon the third Remark.

5. _Why in calm Weather the _Mercury_ generally stands high?_ The cause
hereof is, as I conceive, that it seldom freezes but when the Winds come
out of the Northern and North-Eastern Quarters, or at least unless those
Winds blow at no great distance off; for the Northern Parts of
_Germany_, _Denmark_, _Sweden_, _Norway_, and all that Tract from whence
North-Eastern Winds come, are subject to almost continual Frost all the
Winter; and thereby the lower Air is very much condens'd, and in that
State is brought hitherwards by these Winds, and being accumulated by
the opposition of the Westerly Wind blowing in the Ocean, the _Mercury_
must needs be prest to a more than ordinary height, and as a concurring
Cause, the shrinking of the lower parts of the Air into lesser room by
cold, must needs cause a descent of the upper parts of the Atmosphere,
to reduce the Cavity made by this contraction to an _Æquilibrium_.

6. _Why after very great Storms of Wind, when the _Mercury_ has been
very low, it generally rises again very fast?_ This I have frequently
observed, and once found it risen an Inch and a half in less than six
Hours, after a long continu'd Storm of South-West Wind. This seems to be
occasion'd by the sudden Accession of new Air to supply the great
Evacuation which such continu'd Storms make thereof, in those places
whence they happen (as in the third Remark) and by the Recoile of the
Air, after the force ceases that impelled it; and the Reason why the
_Mercury_ rises so fast, is because the Air being very much rarify'd
beyond its mean density, the Neighbouring Air runs in the more swiftly
to bring it to an _Æquilibration_, as we see Water runs the faster for
having a great declivity.

7. _Why in more Northerly places the Variations of the _Baroscope_ are
greater than in the Southerly?_ The truth of the Matter of Fact is
prov'd from Observations made at _Clermont_ and _Paris_, compar'd with
others, made at _Stockholm_, as may be seen in the Appendix to Mr.
_Pascal_'s Book before-cited. The Reason I conjecture to be, that the
more Northerly Parts have usually greater Storms of Wind than the more
Southerly, whereby the _Mercury_ should sink lower in that Extream; and
then the Northerly Winds bringing the condens'd and ponderous Air from
the Neighbourhood of the Pole, and that again being check'd by a
Southerly Wind, at no great distance, and so heaped, must of necessity
make the _Mercury_ in such case stand higher in the other Extream.

8. And Lastly, _Why near the _Æquinoctial_, as at _Barbadoes_ and St.
_Helena_, there is very little or no Variation of the height of the
Barometer?_ This Remark, above all others, confirms the Hypothesis of
the variable Winds, being the cause of these Variations of the height of
the _Mercury_; for in the Places above-named, there is always an easie
Gale of Wind blowing nearly upon the same Point, _viz._ E. N. E. at
_Barbadoes_, and E. S. E. at St. _Helena_; so that there being no
contrary Currents of the Air, to exhaust or accumulate it, the
Atmosphere continues much in the same State. However, upon Hurricanes,
the most violent of Storms, the _Mercury_ has been observ'd very low,
but this is but for once in two or three Years, and it soon recovers its
settled state of about 29½ Inches. I doubt not but the same thing is
in the East Coast of _Africa_, and in _India_, where the Monsoons or
Trade-Winds are for half the Year one way, and half the Year another;
only it's probable, that there may something worth noting happen, about
the times of the change or shifting of the Winds, which might be
obtain'd, if any Body had the Curiosity to keep the _Barometer_ at our
Factories in _India_.


I doubt not but this Doctrine will find some Opposers, and that one
principal Objection will be, that I suppose the Air sometimes to move
from those Parts where it is already evacuated below the _Æquilibrium_,
and sometimes again towards those parts, where it is condens'd and
crouded above the mean State, which may be thought contradictory to the
Laws of Staticks and the Rules of the _Æquilibrium_ of Fluids. But those
that shall consider how, when once an impetus is given to a Fluid Body,
it is capable of mounting above its Level, and checking others that have
a contrary tendency to descent by their own Gravity, will no longer
regard this as a material Obstacle, but will rather conclude, that the
great _Analogy_ there is between the rising and falling of the Water
upon the Flux and Reflux of the Sea, and this of the accumulating and
extenuating the Air, is a great Argument for the Truth of this
Hypothesis: For as the Sea over against the Coast of _Essex_, rises and
swells by the meeting of the two contrary Tides of Flood, (whereof the
one comes from the S. W. along the Channel of _England_, and the other
from the North); and on the contrary sinks below its Level upon the
retreat of the Water both ways in the Tide of Ebb; so it is very
probable that the Air may Ebb and Flow, after the same manner; but by
reason of the diversity of Causes, whereby the Air may be set in moving,
the times of these Fluxes and Refluxes thereof, are purely Casual, and
not reducible to any Rule, as are the Motions of the Sea, depending
wholly upon the regular Course of the Moon.

[Illustration: _Plate 1. pag. 97_]




 _A Letter of Mr. _Isaac Newton_, Professor of the Mathematicks in the
   University of _Cambridge_; containing his New Theory about _Light_
   and _Colours_: Sent by the Author to the Publisher from _Cambridge_,
   Feb. 6. 1671/2; in order to be communicated to the _Royal Society_._


_SIR_,

To perform my late promise to you, I shall without further Ceremony
acquaint you, That in the beginning of the Year 1666 (at which time I
apply'd my self to the grinding of Optick-glasses of other Figures than
_Spherical_,) I procur'd me a Triangular Glass-Prism, to try therewith
the celebrated _Phænomena_ of _Colours_. And in order thereto, having
darken'd my Chamber, and made a small hole in my Window-shuts, to let in
a convenient quantity of the Sun's Light, I plac'd my Prism at his
entrance, that it might be thereby refracted to the opposite Wall. It
was at first a very pleasing Divertisement, to view the vivid and
intense Colours produced thereby; but after a while applying my self to
consider them more circumspectly, I became surpriz'd to see them in an
_oblong_ Form; which, according to the received Laws of Rarefraction, I
expected should have been _Circular_.

They were terminated at the sides with streight Lines, but at the ends,
the decay of Light was so gradual, that it was difficult to determine
justly, what was their Figure; yet they seem'd _Semicircular_.

Comparing the length of this colour'd _Spectrum_ with its breadth, I
found it about five times greater; a disproportion so extravagant, that
it excited me to a more than ordinary Curiosity of examining, from
whence it might proceed. I could scarce think, that the various
thickness of the Glass, or the termination with shadow or darkness,
could have any Influence on Light to produce such an effect; yet I
thought it not amiss, first to examine those Circumstances, and so try'd
what would happen by transmitting Light through parts of the Glass of
divers thicknesses, or through holes in the Window of divers bignesses,
or by setting the Prism without, so that the Light might pass through
it, and be refracted before it was terminated by the hole: But I found
none of those Circumstances material. The fashion of the Colours was, in
all these Cases, the same.

Then I suspected, whether by any unevenness in the Glass, or other
contingent Irregularity, these Colours might be thus dilated. And to try
this, I took another Prism like the former, and so plac'd it, that the
Light passing through them both, might be refracted contrary ways, and
so by the latter return'd into that Course, from which the former had
diverted it. For, by this means, I thought the _regular_ effects of the
first Prism would be destroy'd by the second Prism, but the _irregular_
ones more augmented by the multiplicity of Refractions. The Event was,
that the Light, which by the first Prism was diffused into an _oblong_
Form, was, by the second, reduc'd into an _orbicular_ one, with as much
regularity, as when it did not at all pass through them. So that
whatever was the cause of that length, 'twas not any contingent
Irregularity.

I then proceeded to examine more critically, what might be effected by
the difference of the incidence of Rays coming from divers parts of the
Sun; and to that end, measur'd the several Lines and Angles belonging to
the Image. Its distance from the Hole or Prism was twenty two Foot; its
utmost length 13¼ Inches; its breadth 2⅝; the Diameter of the Hole
¼ of an Inch; the Angle, with the Rays, tending towards the middle of
the Image, made with those Lines, in which they would have proceeded
without Refraction, was 44° 56'. And the Vertical Angle of the Prism,
63° 12'. Also the Refractions on both sides the Prism, that is, of the
Incident, and Emergent Rays, were as near, as I could make them, equal,
and consequently about 54° 4'. And the Rays fell perpendicularly upon
the Wall. Now subducting the Diameter of the Hole from the length and
breadth of the Image, there remains 13 Inches the length, and 2⅜ the
breadth, comprehended by those Rays, which passed thro' the Center of
the said Hole, and consequently the Angle of the Hole, which that
breadth subtended, was about 31', answerable to the Sun's Diameter; but
the Angle, which its length subtended, was more than five such
Diameters, namely 2° 49'.

Having made these Observations, I first computed from them the
refractive Power of that Glass, and found it measur'd by the _ratio_ of
the Sines, twenty to thirty one. And then, by that _ratio_, I computed
the Refractions of two Rays flowing from opposite parts of the Sun's
_discus_, so as to differ 31' in their obliquity of Incidence, and found
that the emergent Rays should have comprehended an Angle of about 31',
as they did, before they were incident.

But because this Computation was founded on the Hypothesis of the
proportionality of the Sines of Incidence and Refraction, which, tho' by
my own Experience I could not imagine to be so erroneous as to make that
Angle but 31', which in reality was 2° 49'; yet my Curiosity caus'd me
again to take my Prism. And having plac'd it at my Window, as before, I
observ'd, that by turning it a little about its _Axis_ to and fro, so as
to vary its obliquity to the light, more than an Angle of four or five
Degrees, the Colours were not thereby sensibly translated from their
place on the Wall, and consequently by that Variation of Incidence, the
quantity of Refraction was not sensibly varied. By this Experiment
therefore, as well as by the former Computation, it was evident, that
the difference of the Incidence of Rays, flowing from divers parts of
the Sun could not make them, after decussation, diverge at a sensibly
greater Angle, than that at which they before converged; which being, at
most, but about thirty one or thirty two Minutes, there still remain'd
some other cause to be found out, from whence it could be two Deg. 49
Min.

Then I began to suspect, whether the Rays, after their Trajection
through the Prism, did not move in curve Lines, and according to their
more or less Curvity, tend to divers parts of the Wall. And it increas'd
my suspicion, when I remember'd that I had often seen a Tennis-Ball,
struck with an oblique Racket, describe such a curve Line. For a
Circular as well as a Progressive Motion being communicated to it by
that stroak, its parts on that side, where the Motions conspire, must
press and beat the contiguous Air more violently than on the other, and
there excite a Reluctancy and Reaction of the Air proportionably
greater. And for the same Reason, if the Rays of Light should possibly
be globular Bodies, and by their oblique Passage out of one Medium into
another, acquire a circulating Motion, they ought to feel the greater
resistance from the ambient Æther, on that side, where this Motion
conspires, and thence be continually bowed to the other. But
notwithstanding this plausible ground of suspicion, when I came to
examine it, I could observe no such Curvity in them. And besides (which
was enough for my purpose) I observ'd, that the difference 'twixt the
length of the Image, and Diameter of the Hole, through which the Light
was transmitted, was proportionable to their distance.

The gradual removal of these suspicions, at length led me to the
_Experimentum Crucis_, which was this; I took two Boards, and plac'd one
of them close behind the Prism at the Window, so that the light might
pass through a small hole, made in it for the purpose, and fall on the
other Board, which I plac'd at about twelve Feet distance, having first
made a small hole in it also, for some of that incident Light to pass
through. Then I plac'd another Prism behind this second Board, so that
the Light, trajected through both the Boards, might pass thro' that
also, and be again refracted before it arrived at the Wall. This done, I
took the first Prism in my Hand, and turn'd it to and fro slowly about
its _Axis_, so much as to make the several parts of the Image, cast on
the second Board, successively pass through the hole in it, that I might
observe to what places on the Wall the second Prism would refract them.
And I saw by the Variation of those places, that the Light, tending to
that end of the Image, towards which the Refraction of the first Prism
was made, did, in the second Prism, suffer a Refraction considerably
greater than the Light tending to the other end. And so the true cause
of the length of that Image was detected to be no other, than that
_Light_ consists of _Rays differently refrangible_, which, without any
respect to a difference in their incidence, were, according to their
degrees of Refrangibility, transmitted towards divers parts of the Wall.

When I understood this, I left off my aforesaid Glass Works; for I saw,
that the perfection of Telescopes was hitherto limited, not so much for
want of Glasses truly figur'd, according to the prescriptions of Optick
Authors (which all Men have hitherto imagin'd), as because that Light it
self is a _Heterogeneous mixture of differently refrangible Rays_. So
that, were a Glass so exactly figur'd, so as to collect any one sort of
Rays into one Point, it could not collect those also into the same
Point, which having the same Incidence upon the same Medium, are apt to
suffer a different Refraction. Nay, I wonder'd, that seeing the
difference of Refrangibility was so great, as I found it, Telescopes
should arrive to that perfection they are now at. For, measuring the
Refractions in one of my Prisms, I found, that, supposing the common
Sine of Incidence upon one of its plains, was forty four Parts, the Sine
of Refraction of the utmost Rays on the red end of the Colours, made out
of the Glass into the Air, would be sixty eight parts, and the Sine of
Refraction of the utmost Rays on the other end, sixty nine parts; so
that the difference is about a twenty fourth or twenty fifth part of the
whole Refraction. And consequently the Object glass of any Telescope
cannot collect all the Rays, which come from one point of an Object, so
as to make them convene at its _Focus_ in less room than in a Circular
space, whose Diameter is the fiftieth part of the Diameter of its
Aperture; which is an irregularity, some hundred of times greater, than
a circularly figur'd _Lens_, of so small a section as the Object-glasses
of long Telescopes are, would cause by the unfitness of its Figure, were
Light _uniform_.

This made me take _Reflections_ into Consideration, and finding them
regular, so that the Angle of Reflection of all sorts of Rays was equal
to their Angle of Incidence; I understood, that by their mediation,
Optick Instruments might be brought to any degree of Perfection
imaginable, provided a _Reflecting_ Substance could be found, which
would polish as finely as Glass, and _reflect_ as much Light as Glass
_transmits_; and the art of communicating to it a _Parabolick_ Figure be
also attain'd. But there seem'd very great Difficulties, and I have
almost thought them insuperable, when I further consider'd, that every
Irregularity in a reflecting Superficies makes the Rays stray five or
six times more out of their due course, than the like Irregularities in
a refracting one; So that a much greater Curiosity would be here
requisite, than in Figuring Glasses for Refraction.

Amidst these Thoughts I was forc'd from _Cambridge_ by the Intervening
Plague, and it was more than two Years before I proceeded further. But
then having thought on a tender way of polishing, proper for Metal,
whereby, as I imagin'd, the Figure also would be corrected to the last;
I began to try what might be effected in this kind, and by degrees so
far perfected an Instrument (in the essential parts of it like that I
sent to _London_,) by which I could discern _Jupiter_'s four
Concomitants, and shew'd them divers times to two others of my
Acquaintance. I could also discern the Moon-like Phase of _Venus_, but
not very distinctly, nor without some niceness in disposing the
Instrument.

From that time I was interrupted, till this last Autumn, when I made the
other. And as that was sensibly better than the first (especially for
Day-Objects,) so I doubt not but they will be still brought to a much
greater perfection by their Endeavours, who, as you inform me, are
taking care about it at _London_.

I have sometimes thought to make a _Microscope_, which in like manner
should have, instead of an Object-glass, a reflecting piece of Metal.
And this I hope they will also take into Consideration: For those
Instruments seem as capable of improvement as _Telescopes_, and perhaps
more, because but one reflective piece of Metal is requisite in them, as
you may perceive in _Plate 3. Fig. 1._ where _AB_ representeth the
Object Metal, _CD_ the Eye-glass, _F_ their common Focus, and _O_ the
other Focus of the Metal, in which the Object is placed.

But to return from this digression, I told you, that Light is not
similar, or homogeneal, but consists of _difform_ Rays, some of which
are more refrangible than others: So that of those, which are alike
incident on the same Medium, some shall be more refracted than others,
and that not by any virtue of the Glass, or other external Cause, but
from a predisposition, which every particular Ray hath to suffer a
particular degree of Refraction.

I shall now proceed to acquaint you with another more notable deformity
in its Rays, wherein the _Origin of Colours_ is unfolded: Concerning
which I shall lay down the _Doctrine_ first, and then, for its
Examination, give you an Instance or two of the _Experiments_, as a
Specimen of the rest.

The Doctrine you will find comprehended and illustrated in the following
Propositions.

1. As the Rays of Light differ in degrees of Refrangibility, so they
also differ in their disposition to exhibit this or that particular
Colour. Colours are not _Qualifications of Light_, derived from
Refractions, or Reflections of natural Bodies, (as 'tis generally
believed) but _Original_ and _connate Properties_, which in divers Rays
are divers. Some Rays are disposed to exhibit a red Colour and no other;
some a yellow and no other, some a green and no other, and so of the
rest. Nor are there only Rays proper and particular to the more eminent
Colours, but even to all their intermediate Gradations.

2. To the same degree of Refrangibility ever belongs the same Colour,
and to the same Colour ever belongs the same degree of Refrangibility.
The _least Refrangible_ Rays are all disposed to exhibit a _Red_ Colour,
and contrarily those Rays, which are disposed to exhibit a _Red_ Colour,
are all the least Refrangible: So the _most Refrangible_ Rays are all
disposed to exhibit a deep _Violet Colour_, and contrarily those which
are apt to exhibit such a _Violet Colour_, are all the most Refrangible.
And so to all the intermediate Colours in a continued Series belong
intermediate degrees of Refrangibility. And this Analogy 'twixt Colours,
and Refrangibility, is very precise and strict; the Rays always either
exactly agreeing in both, or proportionally disagreeing in both.

3. The Species of Colour, and Degree of Refrangibility proper to any
particular sort of Rays, is not mutable by Refraction, nor by Reflection
from Natural Bodies, nor by any other Cause, that I could yet observe.
When any one sort of Rays hath been well parted from those of other
kinds, it hath afterwards obstinately retain'd its Colour,
notwithstanding my utmost Endeavours to change it. I have refracted it
with Prisms, and reflected it with Bodies, which in Day-light were of
other Colours; I have intercepted it with the colour'd Film of Air
interceding two compressed Plates of Glass; transmitted it through
colour'd Mediums, and through Mediums irradiated with other sorts of
Rays, and diversly terminated it, and yet could never produce any new
Colour out of it. It would by contracting and dilating become more
brisk, or faint, and by the loss of many Rays in some Cases very obscure
and dark; but I could never see it chang'd _in specie_.

4. Yet seeming Transmutations of Colours may be made, where there is any
mixture of divers sorts of Rays. For in such mixtures, the component
Colours appear not, but by their mutual allaying each other, constitute
a midling Colour. And therefore, if by Refraction, or any other of the
aforesaid Causes, the difform Rays, latent in such a mixture, be
separated, there shall emerge Colours different from the colour of the
Composition. Which Colours are not new generated, but only made apparent
by being parted; for if they be again intirely mix'd and blended
together, they will again compose that Colour, which they did before
separation. And for the same reason, Transmutations made by the
convening of divers Colours are not real; for when the difform Rays are
again severed, they will exhibit the very same Colours, which they did
before they entered the Composition; as you see, _Blue_ and _Yellow_
Powders, when finely mixed, appear to the naked Eye _Green_, and yet the
Colours of the component Corpuscles are not thereby really transmuted,
but only blended. For, when viewed with a good Microscope, they still
appear _Blue_ and _Yellow_ interspersedly.

5. There are therefore two sorts of Colours. The one Original and
Simple, the other compounded of these. The Original or Primary Colours
are, _Red_, _Yellow_, _Green_, _Blue_, and a _Violet-purple_, together
with Orange, Indico, and an indefinite variety of intermediate
Gradations.

6. The same Colours in _Specie_ with these primary Ones, may be also
produced by Composition: For, a mixture of _Yellow_ and _Blue_ makes
_Green_; of _Red_ and _Yellow_, makes _Orange_; of _Orange_ and
_Yellowish Green_, makes _Yellow_. And in general, if any two Colours be
mix'd, which in the Series of those, generated by the Prism, are not too
far distant one from another, they by their mutual Alloy compound that
Colour, which in the said Series appeareth in the mid-way between them.
But those, which are situated at too great a distance, do not so.
_Orange_ and _Indico_ produce not the intermediate _Green_, nor
_Scarlet_ and _Green_ the intermediate _Yellow_.

7. But the most surprizing and wonderful Composition was that of
_Whiteness_. There is no one sort of Rays which alone can exhibit this.
'Tis ever compounded, and to its Composition are requisite all the
aforesaid primary Colours, mix'd in a due proportion. I have often with
admiration beheld, that all the Colours of the Prism being made to
converge, and thereby to be again mixed as they were in the light before
it was incident upon the Prism, reproduced light, intirely and perfectly
white, and not at all sensibly differing from a _direct_ light of the
Sun, unless when the Glasses, I used, were not sufficiently clear; for
then they would a little incline it to _their_ Colour.

8. Hence therefore it comes to pass, that _Whiteness_ is the usual
Colour of _Light_; for Light is a confused aggregate of Rays, indued
with all sorts of Colours, as they are promiscuously darted from the
various parts of luminous Bodies. And of such a confused aggregate, as I
said, is generated Whiteness, if there be a due proportion of the
Ingredients; but if any one predominate, the Light must incline to that
Colour; as it happens in the blue Flame of Brimstone, the yellow Flame
of a Candle, and the various Colours of the fixed Stars.

9. These things consider'd, the _manner_, how Colours are produced by
the Prism, is evident. For, of the Rays, constituting the incident
Light, since those which differ in Colour proportionally differ in
Refrangibility, _they_ by their unequal Refractions must be severed and
dispersed into an oblong Form, in an orderly succession, from the least
refracted Scarlet to the most refracted Violet. And for the same reason
it is, that Objects, when look'd upon through a Prism, appear coloured.
For the difform Rays, by their unequal Refractions, are made to diverge
towards several parts of the _Retina_, and there express the Images of
things coloured, as in the former case they did the Sun's Image upon a
Wall. And by this inequality of Refractions, they become not only
coloured, but also very confused and indistinct.

10. Why the Colours of the _Rainbow_ appear in falling drops of Rain, is
also from hence evident. For those drops, which refract the Rays,
disposed to appear Purple, in greatest quantity to the Spectator's Eye,
refract the Rays of other sorts so much less, as to make them pass
beside it; and such are the drops on the inside of the _Primary_ Bow,
and on the outside of the _Secondary_ or Exteriour one. So those drops,
which refract in greatest plenty the Rays, apt to appear red, toward the
Spectator's Eye, refract those of other sorts so much more, as to make
them pass beside it; and such are the drops on the Exteriour part of the
_Primary_, and Interiour part of the _Secondary_ Bow.

11. The odd Phænomena of an infusion of _Lignum Nephriticum_,
_Leaf-gold_, _Fragments of colour'd Glass_, and some other transparently
coloured Bodies, appearing in one Position of one Colour, and of another
in another, are on these grounds no longer Riddles. For those are
Substances apt to reflect one sort of Light, and transmit another; as
may be seen in a dark Room, by illuminating them with similar or
uncompounded Light. For then they appear of that Colour only, with which
they are illuminated; but yet in one Position more vivid and luminous
than in another, accordingly as they are disposed more or less to
reflect or transmit the incident Colour.

12. From hence also is manifest the reason of an unexpected Experiment,
which Mr. _Hook_, somewhere in his _Micrography_, relates to have made
with two wedge-like transparent Vessels fill'd, the one with a red, the
other with a blue Liquor; namely, that though they were severally
transparent enough, yet both together became opake: For, if one
transmitted only red, and the other only blue, no Rays could pass
through both.

13. I might add more Instances of this Nature; but I shall conclude with
this general one, that the Colours of all natural Bodies have no other
Origin than this, that they are variously qualified to reflect one sort
of Light in greater plenty than another. And this I have experimented in
a dark Room, by illuminating those Bodies with uncompounded Light of
divers Colours. For by that means any body may be made to appear of any
Colour. They have there no appropriate Colour, but ever appear of the
Colour of the Light cast upon them; but yet with this difference,
that they are most brisk and vivid in the Light of their own
day-light-colour. _Minium_ appeareth there of any Colour indifferently,
with which 'tis illustrated, but yet most luminous in red; and so _Bise_
appeareth indifferently of any Colour with which 'tis illustrated, but
yet most luminous in blue. And therefore _Minium_ reflecteth Rays of any
Colour, but most copiously those endu'd with red, and consequently when
illustrated with day-light, that is, with all sorts of Rays
promiscuously blended, those qualified with red, shall abound most in
the reflected Light, and by their prevalence cause it to appear of that
Colour. And for the same reason _Bise_, reflecting blue most copiously,
shall appear blue by the excess of those Rays in its reflected Light;
and the like of other Bodies. And that this is the intire and adequate
cause of their Colours, is manifest, because they have no power to
change or alter the Colours of any sort of Rays incident apart, but put
on all Colours indifferently, with which they are enlightned.

These things being so, it can be no longer disputed, whether there be
Colours in the dark, nor whether they be the Qualities of the Objects we
see, no nor perhaps, whether Light be a Body. For, since Colours are the
_Qualities_ of Light, having its Rays for their intire and immediate
Subject, how can we think those Rays _Qualities_ also, unless one
Quality may be the Subject of and sustain another; which in effect is to
call it _Substance_? We should not know Bodies for Substances, were it
not for their sensible Qualities; and the principal of those being now
found due to something else, we have as good reason to believe that to
be a Substance also.

Besides, whoever thought any Quality to be a _heterogeneous_ Aggregate,
such as Light is discovered to be? But to determine more absolutely,
what Light is, after what manner refracted, and by what Modes or Actions
it produceth in our Minds the Phantasms of Colours, is not so easie. And
I shall not mingle Conjectures with Certainties.

Reviewing what I have written, I see the Discourse it self will lead to
divers Experiments sufficient for its Examination; and therefore I shall
not trouble you farther, than to describe one of those, which I have
already insinuated.

In a darkned Room, make a hole in the shut of a Window, whose Diameter
may conveniently be about a third part of an Inch, to admit a convenient
quantity of the Sun's Light. And there place a clear and colourless
Prism, to refract the entring Light towards the farther part of the
Room; which, as I said, will thereby be diffused into an oblong coloured
Image. Then place a _Lens_ of about three Foot Radius (suppose a broad
Object-glass of a three Foot Telescope,) at the distance of about four
or five Foot from thence, through which all those Colours may at once be
transmitted, and made by its Refraction to convene at a farther distance
of about ten or twelve Feet. If at that distance you intercept this
Light with a Sheet of white Paper, you will see the Colours converted
into whiteness again by being mingled. But it is requisite, that the
_Prism_ and _Lens_ be placed steady, and that the Paper, on which the
Colours are cast, be moved to and fro; for, by such motion, you will not
only find at what distance the whiteness is most perfect, but also see
how the Colours gradually convene, and vanish into whiteness; and
afterwards, having crossed one another in that place where they compound
whiteness, are again dissipated and severed, and in an inverted order
retain the same Colours, which they had before they entred the
Composition. You may also see, that, if any of the Colours at the _Lens_
be intercepted, the whiteness will be changed into the other Colours.
And therefore, that the Composition of whiteness be perfect, care must
be taken that none of the Colours fall besides the _Lens_.

In the annexed Design, _Tab. 3. Fig. 2._ of this Experiment, _ABC_
expresseth the Prism set end-wise to sight, close by the hole _F_ of the
Window _EG_. Its vertical Angle _ABC_ may conveniently be about 60
Degrees: _MN_ designeth the _Lens_. Its breadth 2½ or 3 Inches. _SF_
one of the streight Lines, in which difform Rays may be conceived to
flow successively from the Sun. _FP_, and _FR_ two of those Rays
unequally refracted, which the _Lens_ makes to converge towards _Q_, and
after decussation to diverge again. And _HI_ the Paper, at divers
distances, on which the Colours are projected, which in _Q_ constitute
_Whiteness_, but are _Red_ and _Yellow_ in _R_, _r_, and ρ, and _Blue_
and _Purple_ in _P_, _p_, and π.

If you proceed further to try the impossibility of changing any
uncompounded Colour (which I have asserted in the third and thirteenth
Propositions,) 'tis requisite that the Room may be very dark, lest any
scattering light, mixing with the Colour, disturb and allay it, and
render it compound, contrary to the design of the Experiment. 'Tis also
requisite, that there be a perfecter separation of the Colours, than,
after the manner above described, can be made by the Refraction of one
single Prism; and how to make such farther separations, will scarce be
difficult to them, that consider the discovered Laws of Refractions. But
if trial shall be made with Colours not throughly separated, there must
be allowed changes proportionable to the mixture. Thus if compound
Yellow Light fall upon blue _Bise_, the Bise will not appear perfectly
yellow, but rather green, because there are in the yellow mixture many
Rays indued with green, and green being less remote from the usual blue
Colour of Bise than yellow, is the more copiously reflected by it.

In like manner, if any one of the Prismatick Colours, suppose red, be
intercepted, on design to try the asserted impossibility of reproducing
that Colour out of the others which are pretermitted; 'tis necessary,
either that the Colours be very well parted before the red be
intercepted; or that, together with the red, the neighbouring Colours,
into which any red is secretly dispersed, (that is, the yellow, and
perhaps green too) be intercepted; or else, that allowance be made for
the emerging of so much red out of the yellow green, as may possibly
have been diffused, and scatteringly blended in those Colours. And if
these things be observed, the new Production of red, or any intercepted
Colour, will be found impossible.

This, I conceive, is enough for an Introduction to Experiments of this
kind; which if any of the _Royal Society_ shall be so curious as to
prosecute, I should be very glad to be informed with what success: That,
if any thing seem to be defective, or to thwart this Relation, I may
have an opportunity of giving farther Direction about it, or of
acknowledging my Errors, if I have committed any.




 _Since the Publication of this Theory, some Misunderstandings happening
   between a _French_ Philosopher at _Paris_ and Mr. _Newton_, he has
   endeavour'd to explain himself a little further in these Things,
   according to the following Method._


_DEFINITIONS._

1. I call that Light Homogeneal, Similar, or Uniform, whose Rays are
equally refrangible.

2. And that Heterogeneal, whose Rays are unequally refrangible.

_Note_, There are but three Affections of Light in which I have observ'd
its Rays to differ; _viz._ Refrangibility, Reflexibility, and Colour;
and those Rays which agree in Refrangibility, agree also in the other
two, and therefore may well be defined Homogeneal; especially since Men
usually call those things Homogeneal, which are so in all Qualities that
come under their Knowledge, tho' in other Qualities, that their
Knowledge extends not to, there may possibly be some Heterogeneity.

3. Those Colours I call Simple or Homogeneal, which are exhibited by
Homogeneal Light.

4. And those Compound or Heterogeneal, which are exhibited by
Heterogeneal Light.

5. Different Colours, I call, not only the more eminent Species, Red,
Yellow, Green, Blue, Purple, but all other the minutest Gradations; much
after the same manner, that not only the more eminent Degrees in Musick,
but all the lead Gradations, are esteem'd different Sounds.


_PROPOSITIONS._

1. The Sun's Light consists of Rays differing by indefinite Degrees of
Refrangibility.

2. Rays which differ in Refrangibility, when parted from one another, do
proportionally differ in the Colours which they exhibit. These Two
Propositions are Matter of Fact.

3. There are as many Simple or Homogeneal Colours, as Degrees of
Refrangibility. For to every Degree of Refrangibility belongs a
different Colour, by _Prop._ 2. and that Colour is Simple, by _Def._ 1,
and 3.

4. Whiteness, in all respects like that of the Sun's immediate Light,
and of all the usual Objects of our Senses, cannot be compounded of two
Simple Colours alone. For such a Composition must be made by Rays that
have only two Degrees of Refrangibility, by _Def._ 1 and 3. and
therefore it cannot be like that of the Sun's Light. by _Prop._ 1. nor,
for the same Reason, like that of ordinary white Objects.

5. Whiteness, in all respects, like that of the Sun's immediate Light,
cannot be compounded of Simple Colours without an indefinite Variety of
them. For to such a Composition, there are requisite Rays endu'd with
all the indefinite Degrees of Refrangibility, by _Prop._ 1. And those
infer as many Simple Colours, by _Def._ 1 and 3. and _Prop._ 2 and 3.

To make these a little plainer, I have added also the Propositions that
follow.

6. The Rays of Light do not act on one another, in passing through the
same Medium.

7. The Rays of Light suffer not any change of their Qualities from
Refraction.

8. Nor afterwards from the adjacent quiet _Medium_: These two
Propositions are manifest _de Facto_ in Homogeneal Light, whose Colour
and Refrangibility is not at all changeable, either by Refraction, or by
the Contermination of a quiet _Medium_. And as for Heterogeneal Light,
it is but an Aggregate of several sorts of Homogeneal Light, no one sort
of which suffers any more alteration than if it were alone; because the
Rays act not on one another, by _Prop._ 6. and therefore the Aggregate
can suffer none. These two Propositions also might be further proved
apart, by Experiments too long to be here described.

9. There can no Homogeneal Colours be reduced out of Light by
Refraction, which were not commixt in it before. Because by _Prop._ 7.
and 8. Refraction changeth not the Qualities of the Rays, but only
separates those which have divers Qualities, by means of their different
Refrangibility.

10. The Sun's Light is an Aggregate of an indefinite variety of
Homogeneal Colours, by _Prop._ 1, 3, and 9. And hence it is, that I call
Homogeneal Colours also Primitive or Original. And thus much concerning
Colours.


 _For a further Illustration of this Doctrine, Mr. _Newton_, in his Book
   of Opticks lately published, has by undeniable Experiments explained
   most of the Principal Phænomena of Light and Colours: To which we
   refer the Reader._




 _A Demonstration concerning the Motion of Light, communicated from
   _Paris_._


Philosophers have been labouring for many Years to decide by some
Experiment, whether the Action of Light be conveyed in an instant to
distant Places, or whether it requireth time. M. _Romer_, of the _Royal
Academy_ of Sciences, hath devised a way taken from the Observations of
the first Satellit of _Jupiter_, by which he demonstrates, that for the
distance of about 3000 Leagues, such as is very near the bigness of the
Diameter of the Earth, Light needs not one Second of Time.

Let (in _Fig. 3. Plate 3._) _A_ be the _Sun_, _B_ _Jupiter_, _C_ the
first Satellit of _Jupiter_, which enters into the shadow of _Jupiter_,
to come out at _D_, and let _EFGHKL_ be the _Earth_, placed at divers
distances from _Jupiter_.

Now suppose the _Earth_, being in _L_, towards the second Quadrature of
_Jupiter_, hath seen the first Satellit, at the time of its emersion, or
issuing out of the shadow at _D_, and that about 42½ Hours after
(_viz._ after one Revolution of this _Satellit_) the _Earth_ being in
_K_, do see it return'd in _D_: It is manifest, that if the Light
require time to traverse the Interval _LK_, the _Satellit_ will be seen
return'd later in _D_, than it would have been if the _Earth_ had
remained in _L_. So that the Revolution of the _Satellit_ being thus
observ'd by the Emersions, will be retarded by so much time, as the
Light shall have taken in passing from _L_ to _K_; and that on the
contrary, in the other Quadrature _FG_, where the _Earth_ by approaching
goes to meet the Light, the Revolutions of the Emersions will appear to
be shortned, by so much as those of the Emersions had appear'd to be
lengthned. And because 42½ Hours, which this _Satellit_ very near
takes to make one Revolution, the distance between the _Earth_ and
_Jupiter_, in both the Quadratures, varies at least 210 Diameters of the
_Earth_: It follows, that if for the Account of every Diameter of the
_Earth_ there were required a Second of Time, the Light would take 3½
Minutes for each of the Intervals _GF_, _KL_; which would cause near
half a quarter of an Hour between two Revolutions of the first
_Satellit_, one observ'd in _FG_, and the other in _KL_, whereas there
is not observed any sensible difference.

Yet doth it not follow hence, that Light demands no time. For after M.
_Romer_ had examin'd the thing more nearly, he found that what was not
sensible in two Revolutions, became very considerable in many being
taken together; and that, for Example, forty Revolutions observed on the
side _F_, might be sensibly shorter, than forty others observ'd in any
place of the _Zodiack_ where _Jupiter_ may be met with; and that in
proportion of Twenty two for the whole Interval of _HE_, which is the
double of the Interval that is from hence to the Sun.

The necessity of this new Equation of the Retardment of Light, is
establish'd by all the Observations that have been made in the _Royal
Academy_, and in the _Observatory_, for the space of eight Years; and it
hath been lately confirmed by the Emersion of the first _Satellit_
observ'd at _Paris_, the _9th_ of _November_ last, at 5 a-clock 35' 45"
at Night, 10 Minutes later than it was to be expected, by deducting it
from those that had been observ'd in the Month of _August_, when the
_Earth_ was much nearer to _Jupiter_; which M. _Romer_ had predicted to
the said Academy from the beginning of _September_.

But to remove all doubt, that this Inequality is caused by the
Retardment of the Light, he demonstrates, that it cannot come from any
Excentricity, or other Cause of those that are commonly alledged to
explicate the Irregularities of the _Moon_, and the other Planets;
though he be well aware, that the first _Satellit_ of _Jupiter_ was
Excentrick; and that, besides his Revolutions were advanced or retarded,
according as _Jupiter_ did approach to or recede from the Sun; as also,
that the Revolutions of the _Primum Mobile_ were unequal: Yet, saith he,
these three last Causes of Inequality do not hinder the first from being
manifest.




 _An introductory _Essay_ to the Doctrine of _Sounds_, containing some
   Proposals for the improvement of _Acousticks_; As it was presented to
   the _Dublin Society_, Nov. 12. 1683, by the Right Reverend Father in
   God _Narcissus_ Lord Bishop of _Ferns_ and _Leighlin_._


Being to treat of the Doctrine of _Sounds_, I hold it convenient to
premise something in the general, concerning this Theory; which may
serve at once to ingage your Attention, and excuse my Pains, when I
shall have recommended them, as bestow'd on a Subject not altogether
useless and unfruitful.

And for this purpose I shall omit to speak any thing of the _Excellency_
of the Matter in Hand; though it might be celebrated by Arguments drawn
from several Topicks, and particularly from this, that new Discoveries
and Improvements may be made, both as to the _Generation_, _Propagation_
and _Reception_ of Sounds into the Sense; which, in a peculiar manner
agrees to this, above the Object of any other Sense whatsoever. I shall,
I say, omit these things, and apply my self wholly to the _Usefulness_
of the Theory, that we are now falling upon, which I think cannot better
be discovered, than by making a comparison 'twixt the Senses of _Seeing_
and _Hearing_, as to their Improvements. I mean, by shewing, that this
latter of _Hearing_ is capable of all those improvements which the Sense
of _Seeing_ has receiv'd from Art, besides many more advantages that the
_Ear_ may enjoy, by the help of our Doctrine, above the _Eye_; all which
moreover will be of as great benefit to Mankind, as any thing that
_Opticks_ have yet discover'd, if not of greater; which, with some other
pre-eminencies that it has upon another Score, will happily render
_Acousticks_ the nobler Science of the two.

In order to the making good what I but now premised of the Comparison of
these two Faculties of _Seeing_ and _Hearing_, as to their Improvements,
I observe;

That _Vision_ is threefold, _Direct_, _Refracted_, and _Reflex'd_;
answerable whereunto we have _Opticks_, _Dioptricks_, and _Catoptricks_.

In like manner _Hearing_ may be divided into _Direct_, _Refracted_ and
_Reflex'd_; whereto answer three parts of our Doctrine of _Acousticks_,
which are yet nameless, unless we call them _Acousticks_, _Diacousticks_,
and _Catacousticks_, or (in another Sense, but to as good Purpose)
_Phonicks_, _Diaphonicks_, and _Cataphonicks_.


I. Direct Vision has been improv'd two ways, _ex parte_ Objecti, and _ex
parte_ Organi _vel_ Medii.

1. _Ex parte Objecti_, Direct Vision has receiv'd advantages by the Arts
of _Producing_, _Conserving_ and _Imitating Light_ and _Colours_, which
are the Objects of Vision.

1. For the Art of _Producing Light_, we have the Frication of all hard
Bodies that beget Fire; especially of the Flint and Steel; and instead
of the Flint, most hard Stones (as well as the Cane) may be us'd to the
same effect, as upon trial I have found. Add hereto the lately invented
_Phosphorus_, which is a new and admirable way of producing a _Lucid
Substance_ by Art, out of a Body in itself not _Lucid_; and therefore
may not unfitly be term'd an _Artificial production_ of _Light_.

And then of the Art of _Conserving Light_, the _Lapis Bononiensis_ is a
notable Instance; and so happily were the _Sepulchral Lamps_ of the
Ancients.

2. As to _Colours_, 'tis the greatest part of the Art of _Dying_ to be
able to make and fix (that is preserve) them; and the _Painters_ and
_Limners_ will own it to be no small part of their Skill to be able well
to _Mix_ (that is, in effect, to _Generate_) _Colours_.

3. For _Imitation of Light_ and _Colours_, 'tis well known how far
_Perspective_ with the Art of _Limning_ and _Shadowing_ have gone
therein, which all tend some way to the Advance or Improvement of
_Direct Vision_.

Add to all these, That _a due Application of Light to the Object_
renders it Visible, if it were not so before; as appears from a dark
Room illuminated; or else makes it better and more truly discernable by
the Sense of _Seeing_, if before it might have been discern'd.

Hence the same _Colour_, in a diverse Light, will appear different, and
no _Picture_ can well be discern'd or judg'd of but by its true Light.
Besides, the _Limner_ will assure you, that he can hardly make true
Work, or hit the Air of a Face exactly, unless he draw by a
_North-Light_, by reason of the steadiness of that, and the uncertainty
of all other Lights whatsoever. Which things shew, that the _Art of duly
applying Light to the Object_ does very much help and improve Vision. So
also does the due placing of the _Object_, as to _Height_ and
_Distance_. But to enumerate all things that help _Direct Vision_, would
be infinite.

2. _Ex parte Organi vel Medii_, Direct Vision has been improv'd by
making use of a _Tube_, without Glasses, or a Man's clos'd Hand, to look
thro'; which admitting into the _Eye_ only the principal Rays, that come
directly from the Object, do very much strengthen and clear the Sight,
by excluding all the Collateral Rays, that crouding into the Eye,
together with the direct ones, would confound and disturb it, partly by
mixing and interfering with the direct Rays, and partly (or rather
chiefly) by too much enlightning the fund of the Eye, wherein Vision is
truly (tho' then imperfectly) made.

On this is founded the Art of making _Spectacles_ without Glasses; (as
well as _Tubes_) which is done by putting into the Glass-holes (instead
of Glasses) two short _Tubes_ of between three and four Inches long (for
their length is to be vary'd according to the Age or Eye of the
Beholder, and so also is the Diameter of the extream ends) which _Tubes_
being made of _Spanish Leather_ (or Past-board, or some such like
Matter) and black'd on the inside, are so to be placed, as that the
visual Rays, receiv'd thro' them, may meet in one point (or rather issue
out from one Point) of the Object standing at such a due distance, as
the Person may clearly and distinctly see it, or according to his length
of Sight (as ABC, in the 4th _Fig. Tab._ 3.)

And these _Spectacles_ may be suppos'd better for preserving the Sight,
than the ordinary ones with Glasses, because they represent the Object
more naturally, and withal more clearly and distinctly to the Eye, than
the other, whose refracted Rays being collected together with the right
ones in the Glasses, do somewhat confound good Vision, as before:
Especially if the visive Power be strong enough to be sufficiently
determin'd by the right Rays alone.

For I speak now of preserving a good Eye by these Spectacles, which
holds in proportion true also of a bad one. Because those Rays (both
right and refracted) being collected and brought so near the Eye
(whether good or bad) as the Spectacles are usually plac'd, do too much
affect it, both by their own brightness, and also by the brightness of
the Colours of the Object (when they are bright) which is brought very
near also; whereby the Eye is dazl'd and confounded, unless there be a
strong attention and _conatus_ of the Spirits, whereto the bright Rays
do certainly engage them, which of necessity weakens Vision, especially
if these Glass-spectacles be much us'd.

Wherefore the now describ'd new Tube-spectacles, contributing so much to
the help and preservation of Sight, may well be counted an improvement
of _Direct Vision_, because they convey the Rays to the Eye without any
kind of Refraction whatsoever. Seeing the same Object also through
various holes, plac'd at certain distances, does somewhat alter Vision;
but of this perhaps more hereafter.

Now as _Direct Vision_ has thus been improved, so likewise _Direct
Hearing_ partly has already receiv'd, and partly may by the Doctrine
whereof we are treating, (if well cultivated) farther receive as great
and notable Improvements, both _ex parte_ Objecti, and _ex parte_ Organi
_vel_ Medii.

1. As to the _Object_ of Hearing, which is Sound, improvement has been
and may be made, both as to the _Begetting_, and as to the _Conveying_
and _Propagating_ (which is a kind of _Conserving_) of Sounds.

1. As to the _Begetting_ of Sounds. The Art of imitating any Sound,
whether by _Speaking_ (that is pronouncing) any kind of Language, (which
really is an Art, and the _Art of Speaking_, perhaps one of the
greatest) or by _Whistling_, or by _Singing_ (which are allow'd Arts) or
by _Hollowing_ or _Luring_ (which the Huntsman or Faulkner would have to
be an Art also) or by imitating with the Mouth (or otherwise) the Voice
of any Animal, as of _Quails_, _Cats_, and the like; or by
_representing_ any Sound begotten by the Collision of Solid Bodies, or
after any other manner; these are all _Improvements_ of _Direct
Hearing_, and may be improv'd.

Moreover the Skill to make all sorts of _Musical Instruments_, both
Ancient and Modern, whether _Wind_ Instruments or _String'd_, or of any
other sort, whereof there are very many (as _Drums_, _Bells_, the
_Systrum_ of the _Egyptians_, and the like) that beget (and not only
propagate) Sounds; the Skill of making these, I say, is an Art, that has
as much improv'd _Direct Hearing_, as an Harmonious Sound exceeds a
single and rude one, that is, an immusical _Tone_; which Art is yet
capable of farther improvement. And I do hope, that by the Rules, which
may happily be laid down concerning the _Nature_, _Propagation_ and
_Proportion_, or _Adapting_ of Sounds, a way may be found out, both to
improve _Musical Instruments_ already in use, and to invent new ones,
that shall be more sweet and luscious, than any yet known. Besides that,
by the same means _Instruments_ may be made, that shall imitate any
Sound in Nature, that is not Articulate, be it of Bird, Beast, or what
thing else soever.

2. The _Conveying_ and _Propagating_ (which is a kind of _Conserving_)
of Sounds, is much help'd by _duly placing the Sonorous Body_, and also
by the _Medium_.

For if the Medium be _Thin_ and _Quiescent_, and the Sounding Body
_plac'd conveniently_, the Sound will be easily and regularly
propagated, and mightily conserv'd. I say,

1. If the _Medium be Thin and Quiescent_, because it otherwise causes a
_Refracted Sound_, of which afterwards. Hence in a _still Evening_, or
the _dead of the Night_ (when the Wind ceases) a Sound is better sent
out, and to a greater distance than otherwise, tho' much of this may be
ascrib'd to its _Refraction_ also.

2. I say, that the _Sonorous Body must be plac'd conveniently_, near a
_Smooth Wall_, near _Water_, or _a Plain_, whose Surface is even.

1. Near a _Smooth Wall_, either Plain or Arch'd (Cycloidically or
Elliptically, rather than otherwise, tho' a Circular or any Arch will
do, but not so well.)

Hence in a Church, the nearer the Preacher stands to the Wall (and
certainly 'tis much the best way to place Pulpits near the Wall) the
better is he heard, especially by those who stand near the Wall also,
though at a greater distance from the Pulpit; those at the remotest end
of the Church, by laying their Ears somewhat close to the Wall, may hear
him easier than those in the middle.

Hence also do arise _Whispering Places_. For the Voice being apply'd to
one end of an Arch, easily rowls to the other. And indeed were the
_Motion_ and _Propagation_ of Sounds but rightly understood, 'twould be
no hard matter to contrive _Whispering Places_ of infinite variety and
use. And perhaps there could be no better or more pleasant hearing a
_Consort of Musick_ than at such a place as this, where the Sounds
rowling along together, before they come to the Ear, must needs
consolidate and imbody into one; which becomes a true composition of
Sounds, and is the very Life and Soul of Consort.

2. If the Sonorous Body be plac'd near _Water_, the Sound will easily be
convey'd, yet mollified; as Experience teacheth us from a Ring of
_Bells_ near a River, and a great _Gun_ shot off at Sea, which yet
differ much in the strength, and softness and continuance, or
propagation of their Sounds, from the same at Land, where the Sound is
more harsh and more perishing, or much sooner decays.

3. In a _Plain_ a Voice may be heard at a far greater distance than in
uneven Ground.

The _Reason_ of all which last nam'd _Phænomena_ is the same; because
the Sonorous Air meeting with little or no resistance upon a _Plane_
(much less upon an Arch'd) smooth Superficies, easily rowls along it,
without being let or hinder'd in its Motion, and consequently without
having its parts disfigured, and put into another kind of Revolution,
than what they had at the first begetting of the Sound. Which is the
true cause of its _Preservation_ or _Progression_, and fails much when
the Air passes over an uneven Surface, according to the degrees of its
inequality, and somewhat also, when it passes over the plain Superficies
of a Body that is hard and resisting.

Wherefore the smooth Top of the Water (by reason of its yielding to the
Arch'd Air, and gently arising again with a kind of Resurge, like to
_Elasticity_, tho' it be not so, by which Resurge it quickens and
hastens the motion of the Air rowling over it, and by its yielding
preserves it in its Arch'd Cycloidical or Elliptical Figure) the smooth
Top of the Water, I say, for these Reasons, and by these Means, conveys
a Sound more entire, and to a greater distance than the plain Surface of
a piece of Ground, a Wall, or any other Solid Body whatever, can do.

As for the _Speaking Trumpet_, by which a Voice may be convey'd to a
considerable distance, I refer its consideration to that of _Refracted
Sounds_, or _Refracted Audition_.

Thus much of the Improvements of Hearing, that respect its _Object_,
which is _Sound_.

2. The _Organ_ and _Medium_ are to be consider'd. And, 1. The _Organ_,
which is the _Ear_, is helpt much by placing it near a Wall (especially
at one end of an Arch, the Sound being begotten at the other) or near
the Surface of Water, or of the Earth, along which the Sounds are most
easily and naturally convey'd, as was before declar'd. And 'tis
incredible how far a Sound made upon the Earth (by the trampling of a
Troop of Horses, for Example) may be heard in a still Night, if a Man
lays his Ear close to the Ground in a large Plain.

_Otacousticks_ here come in for helping the _Ear_; which may be so
contriv'd (by a right understanding the _Progression of Sounds_, which
is the principal thing to be known for the due regulating all such kinds
of Instruments) as that the Sound might enter the Ear without any
Refraction, but as now they are generally made I refer them to
_Refracted Audition_.

2. As to the _Medium_, I know not how that, by any contrivance of Art,
can advantage _Direct Hearing_, otherwise than I have declar'd already
in the propagation or conveyance of Sounds, though to the Refracting or
Reflecting of them it may very much conduce; of which presently.

And so I have done with the first part of my present undertaking, which
is the _Comparison of Direct Vision and Audition_, as to their
Improvements from Art. The rest follow. Wherefore,


II. Concerning _Refracted Vision_ and its Comparison, I observe, That
_Refracted Vision_ is always made _Ex parte Medii_, as _Reflected_ is
_ex parte Objecti_. And therefore, though _Direct Vision_ may be help'd
_ex parte Objecti, Medii vel Organi_, yet _Refracted_ can be
improv'd only _ex parte Medii_, and _Reflected_ _ex parte Corporis
oppositi_ alone. Unless it be in a mixt or compound Vision, that is
_Refracto-Reflext_, when the reflext Rays pass to the Eye through a
refracting Medium, such as the _Medium Internum_, contain'd in the Body
of the Eye, always is. So that in truth, all Vision is _Refracted_ by an
internal Refraction made in _ipso Oculo_.

And all that I have spoken of _Vision_ holds true of _Hearing_ also,
both _Refracted_ and _Reflext_, and therefore need not be repeated.

_Refracted Vision_ arises from the different _Density_, _Figure_, and
_Magnitude_ of the Medium, which is somewhat alter'd also by the diverse
incidence of the visible Rays. And so it is in _Refracted Hearing_, all
these Causes concur to its Production, and some others to be hereafter
consider'd.

Now as any Object (a Man for example) seen through a thicken'd Air, by
_Refraction_ appears greater than really he is: So likewise a _Sound_,
heard through the same thicken'd part of the _Atmosphere_, will be
considerably vary'd from what it would seem to be, if heard through a
thinner Medium.

And this I call a _Refracted Sound_: But what this Refraction of Sound
is, and how caus'd, may hereafter be discuss'd, when the Nature, and
Motion, or Progression of Sounds are well stated.

For the Improvement of _Refracted Vision_ artificial Instruments have
been made, by grinding or blowing Glasses, into a certain Figure, and
placing them at due distances, whereby the Object may be (as 'twere)
enabled to send forth its Rays more vigorously, and the Visive Faculty
impower'd the better to receive them. And thus also Instruments may be
contriv'd for the assisting both the _Sonorous Body_, to send forth its
Sound more strongly, and the _Acoustick Faculty_, to receive and discern
it more easily and clearly. _For_,

1. As a fine _Glass Bubble_, fill'd with clear Water, and placed before
a burning Candle or Lamp, does help it to dart forth its Rays to a
prodigious Length and Brightness: So an _Instrument_ may be invented,
that apply'd to the Mouth (or any Sonorous Body) shall send forth the
Voice distinctly to as prodigious a Distance and Loudness.

For if the _Stentoro-phonecon_ (which is but a rude and unartificial
Instrument) does such great feats, what might be done with one compos'd
according to the Rules of Art? whose make should comply with the Laws of
_Sonorous Motion_ (which that does not) and therefore not so much
_Refract_, as to alter and confound the _Tone_ of the _Voice_ and Words
(as that somewhat does.)

Now of what use such an Instrument might be for speaking clearly and
articulately at a distance (and that without altering the Tone of the
Voice) whether it be at Sea or at Land (but especially at Sea in
tempestuous Weather and in the Night) is obvious to any Man to conceive.

2. As Instruments have been invented to help the Eye, So likewise are
there some, and more such there may be, for the Ear.

_For_,

1. As _Spectacles_ and other _Glasses_ are made to help the _Purblind_
and weak _Eyes_, to see at any competent distance: So there are
_Otacousticks_ (and better may be made) to help weak _Ears_ to hear at a
reasonable distance also. Which would be as great a help to the
infirmity of Old Age, as the other invention of Spectacles is, and
perhaps greater; forasmuch as the Hearing what's spoken is of more daily
use and concern to such Men, then to be able to _read Books_ or to _view
Pictures_.

2. As _Perspective-Glasses_ and Telescopes help the Eye to see Objects
at a very great distance, which otherwise would not be discernable; in
like manner may a sort of _Otacousticks_ be so contriv'd, as that they
shall receive in _Sounds_ made at a very great distance also, but with
so much advantage, that the Ear shall be able to hear them, which
otherwise would have been _inaudible_.

And these _Otacousticks_ in some respects would be of greater use than
_Perspectives_. For whereas at Land _Perspectives_ are many times
render'd almost useless, by the interposition of Woods and Mountains,
which hinder the Sight from reaching very far: Our _Otacousticks_ would,
notwithstanding these Obstacles, take in a Sound made some Leagues off.
Which might be of notable use in the time of War, for discovering the
Enemy at a good distance, when he marches or lyes incamp'd behind a
Mountain or Wood, or any such place of shelter.

Yea, even at Sea also, where _Perspectives_ are of most use, by reason
of the plainess of the Surface of the Water; yet sometimes there
_Otacousticks_ may be of more benefit, when in dark hazy Weather the Air
is too thick, or in Stormy Tempestuous Weather the Waves arise too high
for the _Perspective_ to be made use of.

But, whether at Sea or Land, _Perspectives_ become altogether
insignificant in the Night-time (unless it be for viewing the Stars)
which is the chief time for using _Otacousticks_; as it is generally,
for Soldiers to take their March, when they would surprise their Enemies.

And therefore this sort of _Otacousticks_ have then their chief use,
when _Perspectives_ are of no use at all; besides that they may be
imploy'd in the Day-time, as well as _Perspectives_, whence they may
(not unfitly) be term'd _the most useful Instrument_ of the two.

3. As _Microscopes_ or _Magnifying-Glasses_ help the Eye to see near
Objects, that by reason of their smallness were _Invisible_ before;
which Objects they Magnify to a strange greatness: So _Microphones_ or
_Micracousticks_, that is Magnifying Ear Instruments, may be contriv'd
after that manner, that they shall render the most minute Sound in
nature distinctly audible, by Magnifying it to an unconceivable loudness.

By the help hereof we may hear the different Cries and Tones, as well as
by _Microscopes_ see the divers Shapes and Figures of the smallest
Animals.

4. As by _Polyscopes_ or _Multiplying-Glasses_, one thing is represented
to the Eye as many, whether in the same or different Shapes (for so
Multiplying-Glasses may be contriv'd:) So by a _Polyphone_ or
_Polyacoustick_ well order'd, one _Sound_ may be heard as many, either
of the same or a different Note. Insomuch, that who uses this
Instrument, he shall, at the Sound of a single Viol, seem to hear a
whole Consort and all true Harmony. By which means this Instrument has
much the advantage of the _Polyscope_.

And thus much may suffice for comparing the Improvements made upon
_Refracted Seeing and Hearing_; I call it _Refracted Hearing_, because
made through a _Medium_, viz. thick Air, or an Instrument, through which
the Sound passing is broken or refracted.


III. _Reflected Vision_ has been improv'd by the Invention of
_Looking-glasses_ and _Polished Metals_, whether _Plane_, _Concave_, or
_Convex_; and these two last, either _Spherical_, _Oval_, _Cylindrical_,
_Conical_, _Hyperbolical_, or of several other shapes; all which cause a
different Reflection, and vary the _Phænomena_.

Thus also _Reflext Audition_, made by _Ecchoes_, may be improv'd, by
contriving several sorts of _Artificial Ecchoes_; as 'tis no hard matter
to do in almost any place.

For (speaking in the general) _Any Sound, falling directly or obliquely
upon any dense Body, of a smooth (whether Plane or Arch'd) Superficies,
is beat back again and reflected, or does eccho more or less_.

I say (1.) _falling directly or obliquely_; because, if the Sound be
sent out and propagated parallel to the Surface of the _Dense Body_, or
be made so _far off_ and so _weak_, that it cannot reach it, there will
be no Reflection of Sound, no _Eccho_.

I say (2.) _upon a Body of a smooth Superficies_; because if the Surface
of the _Corpus Obstans_ be uneven, the Air by reverberation will be put
out of its regular Motion, and the Sound thereby broken and
extinguish'd: So that tho' in this case also the Air be beaten back
again, yet Sound is not reflected, nor is there any Eccho.

I say (3.) _it does eccho more or less_, to shew, that when all things
are, as is before describ'd, there is still an Ecchoing, though it be
not always heard; either because the _direct Sound_ is too weak to be
beaten quite back again to him that made it; or that it does return home
to him, but so weak, that without the help of a good _Otacoustick_, it
cannot be discern'd; or that he stands in a wrong place, to receive the
reflected Sound, which passes over his head, under his Feet, or to one
side of him; which therefore may be heard by a Man standing in that
place, where the reflected Sound will come, provided no interpos'd Body
does intercept it; but not by him, that first made it.

I shall further make out the comparison 'twixt _Reflex'd Vision_ and
_Audition_, by these following _Propositions_.

1. As a _Plain Speculum_ reflects the _Object_ in its due _Dimensions_
and _Colours_; allowing for their difference of appearance, according to
their distance: So a _Plane Corpus Obstans_ reflects the _Sound_ back in
its due _Tone_ and _Loudness_; if allowance be likewise made for the
proportionable decrease of the Sound, according to its distance.

2. As a _Convex Speculum_ reflects the _Object less_, but somewhat
_brighter_ or clearer: So a _Convex Corpus Obstans_ repels the Sound
(insensibly) _smaller_; but somewhat _quicker_ (though _weaker_) than
otherwise it would be.

3. As a _Concave Speculum_ reflects the Object _bigger_, more obscure
and _Inverted_: So a _Concave Corpus Obstans_ ecchoes back the Sound
(insensibly) _bigger_, _slower_ (though _stronger_) and also _inverted_;
but never according to the order of Words. Nor do I think it possible
for the Art of Man to contrive a _Single Eccho_, that shall invert the
Sound, and repeat backwards; because then the Words last spoken, that
is, which do last occur to the _Corpus Obstans_, must first be repell'd;
which cannot be: For where, in the mean time, should the first Words
hang, and be conceal'd, or lie dormant? Or how, after such a pause, be
reviv'd and animated again into Motion? Yet in complicated or _Compound
Ecchoes_, where many receive from one another, I know not whether
something that way may not be done.

From the determinate _Concavity_ or _Archedness_ of these reflecting
Bodies, it comes to pass, that some of them, from a certain distance or
posture, will eccho back but one determinate Note, and from no other
place will they reverberate any; because of the undue Position of the
sounding Body. Such an one (as I remember) is the Vault in _Merton_
College in _Oxford_.

4. As a _Speculum_ takes in and reflects more of its Object, when plac'd
at a great distance from it, than when nearer; because it reflects
according to the apparent Magnitude of the Body at such a distance,
which is less: So also the _Ecchoing Body_, being remov'd farther off,
reflects more of the Sound, than when nearer. And this is the reason,
why some Ecchoes repeat but one Syllable, some one Word, and some many.

5. As _Specula's_ may be so plac'd, that reflecting one upon or into the
other, either directly or obliquely, one Object shall appear many; as in
Sir _Samuel Moreland_'s Glass-room: After the same manner _Ecchoing
Bodies_ may be so contriv'd and plac'd, as that reflecting the Sound
from one to the other, either directly and mutually, or obliquely and by
Succession, out of one Sound shall many Ecchoes be begotten; which in
the first case will be all together, and somewhat involv'd or swallow'd
up of each other, and thereby confus'd (as a Face in Looking-glasses
obverted) in the other they will be distinct, separate, and succeeding
one another; as most _multiple Ecchoes_ do.

Moreover a _Multiple-Eccho_ may be made, by so placing the _Ecchoing
Bodies_, at unequal distances, that they reflect all one way, and not
one on the other; by which means a manifold successive Sound will be
heard (not without astonishment) one Clap of the hands like many, one
Ha, like a laughter, one single Word like many of the same Tone and
Accent, and so one Viol like many of the same kind imitating each other.

Furthermore, as _Specula's_ may be so order'd, that by Reflection they
shall make one single thing appear many different things; as one single
Man to seem many Men, differing as to Shape and Complexion (or a company
of Men) which I think Sir _Samuel Moreland_'s Contrivance does not: So
may _Ecchoing Bodies_ also be order'd, that from any one Sound given,
they shall produce many Ecchoes, different both as to their _Tone_ and
_Intension_. (The ground whereof has elsewhere been laid down in a
Treatise concerning the _Sympathy of Lute-strings_.)

By this means a _Musical Room_ may be so contriv'd, that not only one
Instrument, play'd on in it shall seem many of the same _sort_ and
_size_; but even a Consort of (somewhat) different ones; only by placing
certain _Ecchoing Bodies_ so, as that any Note (play'd) shall be
return'd by them in 3_ds_, 5_ths_, and 8_ths_, which is possible to be
done otherwise than was mention'd before in _Refracted Audition_.

I have now done with my _Comparison_ of the two Noblest _Senses_, and
_Sciences_, as to their _Improvements_; wherein I have been thus large,
that I might give you a little prospect into the _Excellency_ and
_Usefulness_ of _Acousticks_; and that thereby I might excite all that
hear me, to bend their Thoughts towards the making of Experiments for
the compleating this (yet very imperfect, tho' noble) Science; a
_Specimen_ whereof I will give you in three _Problems_, and then present
you with the _Semiplane_ of an _Acoustick or Phonical Sphere_, as an
Attempt to explicate the great _Principle_ in this Science, which is
_The Progression of Sounds_.


_The Problems are these:_

1. _Sonum intendere quousque velis_; or, _Datum sonum ad datum gradum
intendere_.

2. _Sonum extendere quousque velis_; or, _Datum sonum ad datum
distantiam extendere seu propagare_.

3. _Sonum transire ab extremo ad extremum_ & _non per Medium_.

1. The first is, _To make the least Sound_ (by the help of Instruments)
_as loud as the greatest_; a whisper to become as loud as the shot of a
Cannon.

By the help of this _Problem_, the most minute Sounds in Nature may be
clearly and distinctly heard.

2. The second is, _To propagate any_ (the least) _Sound to the greatest
distance_.

By the help hereof any Sound may be convey'd to any, and therefore heard
at any distance, (I must add, within a certain, tho' very large Sphere.)

Moreover, by this means, a _Weather-cock_ may be so contriv'd, as that
with an ordinary blast of Wind it shall cry (or whistle) loud enough to
be heard many Leagues: Which happily may be found of some use, not only
for _Pilots_ in mighty tempestuous Weather, when _light Houses_ are
render'd almost useless, but also for the measuring the strength of
Winds, if allowance be made for their different moisture. For I
conceive, that the more dry any Wind is, the louder it will whistle
_cæteris paribus_; I say, _cæteris paribus_, because, besides the
strength and dryness of Winds or Breath, there are a great many other
things (hereafter to be considered) that concur to the increase or
magnifying of Sounds, begotten by them in an Instrument exposed to their
Violence, or blown into.

3. The third _Problem_, is, _That a Sound may be convey'd from one
extreme to the other_ (or from one distant place to another) _so as not
to be heard in the middle_.

By the help of this _Problem_ a Man may talk to his Friend at a very
considerable distance, so that those in the middle space shall hear
nothing of what passed betwixt them.

FIG. V. TAB. III.

_Semiplanum Sphæræ Phonicæ seu Acousticæ._

You are to conceive that (rude) _Semiplane_, as parallel to the
_Horizon_: For if it be perpendicular thereunto, I suppose the upper
extremity will be no longer _Circular_, but _Hyperbolical_, and the
lower part of it suited to a greater Circle of the Earth. So that the
whole _Phonical_ Sphere (if I may so call it) will be a solid
_Hyperbola_, standing upon a _Concave Spherical_ Base. I speak this
concerning _Sounds_ made (as usually they are) nigh the Earth, and whose
Sonorous _Medium_ has a free passage every way. For if they are
generated high in the Air, or directed one way, the case will be
different; which is partly design'd in the inequality of that Draught.




 _A Discourse concerning the Modern _Theory_ of _Generation_, by Dr.
   _George Garden_ of _Aberdeen_, being part of a Letter to Dr. _William
   Musgrave_, L. L. D. Reg. Soc. S. and by him communicated the Royal
   Society._


The Subject I pitch upon, is that of the Formation of Animals, You know
how wide and unsatisfying Men's Conjectures were upon this Head, until
this Age, in which first the deservedly Famous Dr. _Harvey_ discovered
the proper place of the Formation of the Chick in the _Cicatricula_ of
the Egg, and the Formation of the Parts so far as was discernable by the
naked Eye; and after him _Malpighius_, by the help of exact Glasses,
observ'd the first Rudiments of it there, both before and after
Incubation: And _R. de Graef_, and others, having upon many Observations
concluded, that the _Testes Fœminei_ were the Ovaries of Females, and
consequently that all Animals were _ex ovo_; they began from hence to
infer, that the Rudiments of each Animal were originally in the
respective Females, and that the Male contributed only to give a new
Ferment to the Mass of the Blood and Spirits, by which means a
spirituous Liquor (which the Blood in its ordinary Ferment could not
produce) did insinuate it self into the same Ducts and Pores of the
Rudiments of those Animals, which were in greatest forwardness in the
Ovary, and so extend and enlarge all their Parts, and at last bring them
to perfection, as Mr. _Perrault_ does ingeniously discourse in the third
Part of his _Essais de Physique_; till now at last _Leowenhoek_ has
discover'd an infinite number of _Animalcula in semine marium_ of all
kinds, which has made him condemn the former Opinions about the
Propagation of all Animals _ex Ovo_.

Now upon comparing the Observations and Discoveries which have been made
with one another, these three things seem to me very probable. 1. That
Animals are _ex Animalculo_. 2. That these Animalcles are originally _in
semine Marium_ & _non in Fœminis_. 3. That they can never come
forward, nor be formed into Animals of the respective kind, without the
_Ova in Fœminis_.

The first of these seems probable from these three Observations. 1. That
some such thing has been so often observ'd by _Malpighius_, in the
_Cicatricula_ of an Egg before Incubation, as the Rudiments of an Animal
in the shape of a Tadpole, as may be seen in his first, and in his
repeated Observations _de formatione Pulli in Ovo_. 2. The sudden
appearance and displaying of all the Parts after Incubation, makes it
probable, that they are not then actually formed out of a fluid, but
that the _Stamina_ of them have been formerly there existent, and are
now expanded. The first Part of the Chick which is discovered with the
naked Eye, is, you know, the _Punctum saliens_, and that not till three
days and nights of Incubation be past; and then, on the fifth day, the
Rudiments of the Head and Body do appear. This made Dr. _Harvey_
conclude, that the Blood had a being before any other Part of the Body;
and that from it, all the Organs of the _Fœtus_ were both form'd and
nourished: But by _Malpighius_'s Observations we find that the Parts are
then only so far extended, as to be made visible to the naked Eye, and
that they were actually existent before, and discernable by Glasses.
After an Incubation of thirty hours, are to be seen the Head, the Eyes,
and the _Carina_ with the _Vertebræ_, distinct, and the Heart. After
forty hours its Pulse is visible, and all the other Parts more distinct,
which cannot be discerned by the naked Eye before the beginning of the
fifth day; from whence it seems probable, that even the so early
discovery of those Parts of the _Fœtus_ by the Microscope, is not the
discerning of Parts newly formed, but only more dilated and extended by
receiving of Nutriment from the _Colliquamentum_; so that they seem all
to have been actually existent before the Incubation of the Hen. And
what _Swammerdam_ has discovered in the transformation of Insects, gives
no small light to this; whilst he makes appear in the Explanation of the
13th Table of the General History of Insects, that in those large
_Eruca's_ which feed upon Cabbage, if they be taken about the time they
retire to be transformed into _Aurelia's_, and plung'd often in warm
Water to make a Rupture of the outer Skin, you will discern through the
transparency of their second Membrane, all the Parts of the Butterfly,
the Trunk, Wings, Feelers, _&c._ folded up. But that after the _Eruca_
is chang'd into an _Aurelia_, none of these Parts can be discern'd, they
are so drencht with moisture, tho' they be there actually form'd.
Another Consideration is from the Analogy, which we may suppose between
Plants and Animals. All Vegetables we do see proceed _ex Plantula_, the
Seeds of Vegetables being nothing else but little Plants of the same
kind folded up in Coats and Membranes; and from hence we may probably
conjecture, that so curiously an organized Creature as an Animal, is not
the sudden Product of a Fluid or _Colliquamentum_, but does much rather
proceed from an Animalcle of the same kind, and has all its little
Members folded up according to their several Joints and Plicatures,
which are afterwards enlarged and distended, as we see in Plants. Now
tho' this Consideration alone may seem not to bear much weight; yet
being join'd to the two former, they do mutually strengthen each other.
And indeed all the Laws of Motion, which are as yet discovered, can give
but a very lame account of the forming of a Plant or Animal. We see how
wretchedly _Des Cartes_ came off when he began to apply them to this
Subject; they are formed by Laws yet unknown to Mankind; and it seems
most probable, that the _Stamina_ of all the Plants and Animals that
have been, or ever shall be in the World, have been form'd, _ab Origine
Mundi_, by the Almighty Creator within the first of each respective
kind. And he who considers the Nature of Vision, that it does not give
us the true magnitude, but the proportion of things; and that what seems
to our naked Eye but a Point, may truly be made up of as many Parts as
seem to us to be in the whole visible World, will not think this an
absurd or impossible thing.

But the second thing which later Discoveries have made probable, is,
that these Animalcles are originally _in Semine Marium_ & _non in
Fœminis_. And this I collect from these Considerations: 1. That there
are innumerable _Animalcula_ discover'd _in Semine Masculo omnium
Animalium_. Mr. _Leewenhoeck_ has made this so evident by so many
Observations, that I do not in the least question the truth of the
thing. The reason of their Multitude, and some of the Difficulties which
arise thereupon, he has cleared to very good Purpose, so that I shall
not repeat them. 2. The observing the Rudiments of the _Fœtus_ in
Eggs, which have been fecundated by the Male, and the seeing no such
thing in those which are not fecundated, as appears from _Malpighius_
his Observations, make it very probable that these Rudiments proceed
originally from the Male, and not from the Female. 3. The resemblance
between the Rudiments of the _Fœtus in Ovo_, both before and after
Incubation, and the _Animalcle_, makes it very probable, that they are
one and the same. The same Shape and Figure which Mr. _Leewenhoeck_
gives us of the _Animalcle_, _Malpighius_ likewise gives of the
Rudiments of the _Fœtus_, both before and after Incubation; yea, and
even the _Fœtus's_ of Animals do appear so at first to the naked Eye,
so that Dr. _Harvey_ does acknowledge that all Animals, even the most
perfect, are begotten of a Worm, _De Gen. Anim. Ex._ 18. 4. This gives a
rational account of many _Fœtus's_ at one Birth, especially that of
the Countess of _Holland_, and how at least a whole Cluster of Eggs in a
Hen are fecundated by one Coition of the Male. 5. This gives a new
light, as it were, to the first Prophecy concerning the _Messiah_, that
the Seed of the Woman shall bruise the Head of the Serpent, all the rest
of Mankind being thus most properly and truly the Seed of the Man.
6. The Analogy I have already mentioned, which we may rationally suppose
between the manner of the propagation of Plants and Animals, does
likewise make this probable. Every Herb and Tree bears its Seed after
its kind; which Seed is nothing else but a little Plant of the same
kind, which being thrown into the Earth, as into its _Uterus_, spreads
forth its Roots, and receives its Nourishment, but has its form within
its self, and we may rationally conjecture some such Analogy in the
Propagation of Animals.

The third Particular which later Discoveries make probable, is, that
Animals cannot be formed of these _Animalcula_ without the _Ova in
fœminis_, which are necessary for supplying of them with proper
Nutriment: And this these Considerations seem to evince. 1. It is
probable that an _Animalcle_ cannot come forward, if it do not fall into
a proper _Nidus_. This we see is the _Cicatricula_ in Eggs; and tho' a
Million of them should fall into an Egg, none of them would come
forward, but what were in the Center of the _Cicatricula_; and perhaps
the _Nidus_ necessary for their formation is so proportion'd to their
bulk, that it can hardly contain more than one _Animalcle_; and this may
be the reason why there are so few Monsters. This we see is absolutely
necessary in _Oviparis_; and the only difference which seems to be
between them and the _Vivipara_, in this matter, is in this, that in the
latter the _Ova_ are properly nothing more but the _Cicatricula_, with
its _Colliquamentum_, so that the _Fœtus_ must spread forth its Roots
into the _Uterus_ to receive its nourishment; but the Eggs in _Oviparis_
may be properly term'd an _Uterus_, in relation to the _Fœtus_; for
they contain not only the _Cicatricula_, with its _Amnion_ and the
_Colliquamentum_, which is the immediate nourishment of the _Fœtus_,
but also the materials which are to be converted into that
_Colliquamentum_; so that the _Fœtus_ spreads forth its Roots no
farther than into the White and Yolk of the Egg, from whence it derives
all its nourishment. Now that an Animalcle cannot come forward without
some such proper _Nidus_, Mr. _Leewenhoeck_ will not readily deny; for
if there were nothing needful, but their being thrown into the _Uterus_,
I do not see why many hundreds of them should not come forward at once;
for as to what Mr. _Leewenhoeck_ says, that one of them would be-dwarf
and choak the rest; this might fall out in process of time: But at first
I do not see why many of them should not grow together, whilst scatter'd
in so large a Field (and yet no such thing is observed) if there were
not an absolute necessity of a _Cicatricula_ for their growth and
thriving. Now, 2. That this _Cicatricula_ is not originally in _Utero_,
seems evident from the frequent Conceptions which have been found _extra
Uterum_: Such as the Child which continued Twenty six Years in the Woman
of _Tholouse_'s Belly, mention'd _Numb._ 139. of the _Philos. Trans._
And the little _Fœtus_ found in the _Abdomen de St. Mere_, together
with the Testicle torn and full of clotted Blood, recorded _Numb._ 150.
both taken out of the Journals _des Savans_: Such also seem to be the
_Fœtus_ in the _Abdomen_ of the Woman of _Copenhagen_, mention'd in
the _Nouvelles des Lettres_, for _Sept._ 85. _pag._ 996. all the Members
of which were easily to be felt through the Skin of the Belly, and which
she had carried in her Belly for four Years; and the seven Years
Gravidation, related by Dr. _Cole_, _Numb._ 172. of the _Transact._ That
these two were undoubtedly _extra Uterum_, is uncertain, because the
last was not open'd after her death, and the former may be yet still
alive. Now granting once the necessity of a proper _Nidus_, for the
formation of an Animalcle into the Animal of its respective kind; these
Observations make it probable, that the _Testes_ are the _Ovaria_
appropriated for this use; for tho' the Animalcles coming thither in
such Cases may seem to be extraordinary, and that usually the
Impregnation is in _Utero_; yet it may be collected from hence, that the
_Cicatriculæ_ or _Ova_ to be impregnated, are in _Testibus fœmineis_;
for if it were not so, the accidental coming of Animalcles thither could
not make them come forward more than in any other part of the Body,
since they cannot be formed and nourished without a proper _Nidus_. But
3. It is acknowledg'd by all, that the _Fœtus in Utero_, for some
considerable time after Conception, has no connexion with the Womb, that
it sits wholly loose to it, and is perfectly a little round Egg with the
_Fœtus_ in the midst, which sends forth its Umbilical Vessels by
degrees, and at last lays hold on the _Uterus_. Now from hence it seems
evident, that the _Cicatricula_, which is the Fountain of the Animalcles
nourishment, does not sprout from the _Uterus_, but has its _Origin_
elsewhere, and falls in thither as into a fit Soil, from whence it may
draw Nutriment for the growth of the _Fœtus_, else it cannot be
easily imagin'd, how it should not have an immediate Connexion with the
_Uterus_ from the time of Conception. If you join all these three
Considerations together, _viz._ that an _Animalcle_ cannot come forward
without a proper _Nidus_ or _Cicatricula_; that there have been frequent
_Fœtus's extra Uterum_; and that they have no _Adhæsion_ to the
_Uterus_, for a considerable time after Conception, they seem to make it
evident, that Animals cannot be form'd _ex Animalculis_ without the _Ova
in Fœminis_. To all these I shall subjoin the Proposal of an
_Experimentum Crucis_, which may seem to determine, whether the _Testes
Fœmineæ_ be truly the _Ovaria_, _viz._ Open the _Abdomen_ of the
Females of some kinds, and cut out these Testicles, and this will
determine, whether they be absolutely necessary for the formation of
Animals.

There are some Difficulties proposed against this Conjecture, which I
think may be easily resolved. Some object the distance between the
_Tubæ_ or _Cornua Uteri_, and the Testicles; but to this is opposed by
_Swammerdam_, and others, the like distance between the _Infundibulum_,
in Hens and Frogs, and the Ovary; and yet it cannot be denied that the
Eggs are transmitted thro' this into the _Uterus_: And besides _R. de
Graef_, and others, have by repeated Observations found that the _Cornua
Uteri_ do at certain times after Conception, embrace the _Testes_ on
both sides the _Uterus_. They object in the second place the great
disproportion between the pretended Eggs in the _Ovary_, and the
Aperture of the _Tubæ_ or _Cornua Uteri_, the former being a great deal
bigger than the latter: But both _R. de Graef_ and _Malpighius_ have
clear'd that Matter, by making appear, that these Bladders in the Ovary
are not the _Ova_, but serve to form the _Glandules_ within which the
_Ova_ are formed, which break through a small _Papilla_ opening in the
_Glandule_, which bears a proportion to the Aperture of the Tube. They
object 3, The difficulty to conceive how these Eggs should be
impregnated _per semen Maris_, both because there is no Connexion
between the _Tubæ_ and the _Ovary_ for its transmission, and for that
Dr. _Harvey_ could never discover any thing of it _in Utero_. As to the
last, Mr. _Leewenhoeck_ has cleared that difficulty, by the discovery of
innumerable _Animalcula Seminis Maris in Cornubus Uteri_, and those
living a considerable time after Coition. _Numb._ 174. of the
_Transact._ And as to the former, we may either suppose that there is
such an Inflation of the _Tubæ_ or _Cornua Uteri tempore Coitionis_, as
makes them embrace the _Ovaria_, and such an approach of the _Uterus_
and its _Cornua_, as that I may easily transmit the Seed into the
_Ovary_; or else, that the _Ova_ are impregnated by the Animalcles after
they descend into the _Uterus_, and not in the _Ovary_; the former seems
probable for this Reason, that at least a whole Cluster of Eggs in a Hen
will be fecundated by one Tread of the Cock: Now this Fecundation seems
to be in the Vitellary, and not in the _Uterus_, as the Eggs pass along
from day to day; for it can hardly be supposed that the Animalcles
should subsist so long, being scattered loosely in the _Uterus_, as to
wait there for many days for the Fecundation of the Eggs as they pass
along. The latter Conjecture has this to strengthen it, that the
Animalcles are found to live a considerable time in the _Uterus_; and
that if they should impregnate the _Ova_ in the Ovary it self, the
_Fœtus_ would increase so fast, that the _Ova_ could not pass through
the _Tubæ Uteri_, but would either burst the Ovary, or fall down into
the Abdomen from the Orifices of the _Tubæ_; and that from hence proceed
those extraordinary Conceptions in _Abdomine extra Uterum_. But, 4. Mr.
_Leewehoeck_, _Numb._ 147. of the _Transact._ to weaken the third
Consideration about the Conceptions, being like unto an _Ovum_ in the
Womb, proposes a Parallel between these Animalcles and Insects; and
insinuates, that as the latter cast their Skins, and appear of another
Shape, so the other which at first seem like Tadpoles, may cast their
outer Skin, and then be round; and that this may be the occasion of the
round Figure of the Conception in the Womb. To this it may be replied,
that according to Mr. _Leewenhoeck_'s own Sentiment, the Animalcles
cannot come forward, if they do not find the _Punctum_ or proper place
for their Nourishment, to which it seems they must have some _Adhæsion_.
Now the Conception in _Viviparis_ is not fastned unto the Womb for many
days, nor does adhere to any point of it; so that it seems this roundish
Body is not the Animalcle thus chang'd after having cast an outer Skin,
but is rather the _Cicatricula_ or little Egg, into which the Animalcle
has entred as its _Punctum_ or place of nourishment; else I do not see
why they should not be adhering to the Womb from the first Conception,
or why (as I have said) many hundreds of them are not conceiv'd and
formed together, _&c._




 _A short Discourse concerning Concoction: Read at a Meeting of the Royal
   Society, _May ... 1699_, by _Clopton Havers_, M. D. Fellow of the
   Royal Society._


The manner in which the Digestion of the Aliment is performed, is a
thing not very easie to be understood and explained. However, it has not
escap'd the Conjectures of some Philosophical Men, who having curiously
observ'd the _Phænomena_ of Nature, and enquired into their Causes,
have, amongst other things, endeavour'd to account for this. But their
Sentiments about it have been various, and the Hypothesis, by which they
have studied to explain it, very different. Some have thought the
Concoction of the Food to be a kind of Elixation; and that the grosser
and more solid Parts being, as it were, boil'd in the Liquid by the Heat
of the Stomach, and the Parts adjacent to it, as the Liver, Spleen, and
Omentum, are by a long and continued Elixation, first render'd more
tender, and then colliquated, and dissolved into minuter Particles, so
as to mix more equally with the Fluid, and with that to make one
Pulpament, or chylous Mass. And _Hippocrates_, tho' he does not plainly
call it an Elixation, yet seems to attribute the Concoction of the Food
to the Heat of the Stomach, as the Cause of it, _Sect. 4. Libro de
salubri victus ratione_. So where he takes notice of the voiding of such
Fæces, as appear to be like the Food that has been eaten; he adds,
_Constat enim, sane ventriculum, ciborum copiam, ut concoquat,
calefacere non posse_. And there are other Passages in the same Book,
from which we may conclude, that he suppos'd the Heat of the Stomach to
be the great Cause of the Digestion of the Food.

There are others that make the Stomach itself to be the great Instrument
of Digestion, but in a different manner: And they suppose it to be
perform'd by an Attrition, as if the Stomach, by those repeated Motions,
which are the necessary Effects of Respiration, when it is distended by
the Aliment, did both rub or grind off some minuter Particles from the
grosser Parts; and by continually agitating the Mass of Food, make those
Parts, which are not contiguous to the Stomach, strike one against
another, and break one another in pieces, until they are all attenuated.
It is evident enough, that the sides of the Stomach do in Expiration
press upon the _Contenta_, so as to oblige, at least some Parts of them,
every time the Muscles of the Abdomen are contracted, to move and shift
their places. So in Inspiration, when the Diaphragm and Liver press upon
the upper part of the Stomach, the Aliment must be moved again. So that
by these reciprocal Motions, that part of the Food which is contiguous
to the Stomach, and moves in a Line parallel to it, must rub against it;
and all the other Parts being moved by such a Compression, as gives them
a different Tendency, it is certain they must be continually striking
one against another. And for Bread, and such things as are made of
Flower, that will be softned and dissolv'd with any common Liquid, that
Agitation of the Stomach which moves them in Respiration, might seem
sufficient to break and dissolve them, when they are sufficiently
moisten'd with a Fluid. Yet this cannot be thought enough to break and
digest Flesh-meat, Fruits, or any other thing that will not be softned
and dissolv'd in Water, or some such Liquid. But although this Motion of
the Aliment, caused by Respiration, does not actually digest it, yet it
has a great and necessary Use in Concoction, and makes all the grosser
Parts, as they are attenuated, mix equally with the Fluid.

Some think that the Bilious Juice; others, that the Spirits are chiefly
concern'd in this Affair. _Galen_, in his Book _de Neutralibus
Facultatibus_, makes it to be the Effect, not of one, but of several
Causes; as a pituitous Juice in the Stomach, the Bile, _&c._ which
appears from what he has said, and the Translator thus render'd: '_Verum
quanto ii (cibi) qui mansi sunt, iis, qui inhæserunt, magis sunt
alterati; tanto etiam his magis ii, qui devorati sunt. Siquidem
incomparabilis erit horum alterationis excessus, si & quæ in ventre est
Pituita & Bilis, & Spiritus, & Calor, & tota Ventris substantia,
æstimentur._'

Some there are that will have the Food to be dissolv'd by a Menstruum,
which is supply'd from the Glands of the Stomach, or some other way: But
those that do so far agree in the General, as to think Concoction is
perform'd by a Dissolvent, do differ in their Notions of the Nature of
the Menstruum: For there are some that suppose it to be an Acid, which
does erode the grosser parts of the Food, and dissolves them in the same
manner as Vinegar, Spirit of Vitriol, or any such-like Acid, will
dissolve even so solid a Body as Iron. And it cannot be deny'd, but that
Oil of Vitriol will dissolve Flesh-meat, and reduce it to a Pulp; but it
is not to be suppos'd, that the Fibres of the Stomach can admit any such
strong and corroding Acid, without something to correct it, but it must
be injur'd in its Tone, and labour under great and extraordinary Pains.
Neither does such a Menstruum, tho' it will digest some things, seem
capable of dissolving so great a Variety of Things as we eat, especially
when a great many of them are of a contrary Nature. Some will have the
Menstruum to be a _nitro-aerius_ Spirit, that is, quick, and very
penetrating, and included in its proper Vehicle; which, being in its own
Nature apt to penetrate the Mass of the Aliment, does diffuse it self
through the Whole, and breaking the Vinculum of the more solid Parts,
does dissolve their Compages. By others, it is thought to be some saline
Juice in the Stomach, by which the Parts of the Aliment are divided and
dissolved, and those which are fit for Nourishment, are volatiliz'd.

_Lastly_, There are some others who reject the Opinions I have already
mention'd, and suppose the Digestion of the Food to be perform'd by the
Benefit of a Ferment; which, when it is mixed with the Aliment, excites
in the Mass an intestine motion; and the different and contrary motions
and tendency of the Parts, making some kind of Collision, gradually
break off Particles from the grosser, and more solid Parts, till they
are so attenuated as to be apt to mix more equally with the Fluid, and
with them to make one soft or chylous Substance. But yet there is not
amongst them an universal Consent, either about the Nature of this
Ferment, or the manner how it is supply'd. For first, some think it to
be the Remains of the Food that was last digested; which having lain
some time in the Stomach, after the rest is carried down into the
Intestines, contracts an Acid, or some other Quality, and is so alter'd,
as to partake of the Nature of a Leaven. And this Leaven being a part of
the Food, which has been already digested, is so soft and liquid as to
be capable of mixing with the Aliment, which is next taken into the
Stomach; and being agitated with it by the repeated Pressures of the
Diaphragm, Liver, and Abdominal Muscles upon the Stomach in Respiration,
does diffuse it self through the whole Mass; and being mixed with it,
like Leaven, or Yest added to new Wort, _&c._ puts it into a State of
Fermentation; and by this Fermentation, or the Expansion of the Ferment,
and the more tenuious Parts, which are first put into motion by it,
those which are more solid, and with which they are intermixed, are
rent, and divided, and so attenuated, as to become a soft and pulpous
matter. And altho' the greatest part of the Food, that is thus broken
and concocted, is by the Contraction of the Fibres of the Stomach
press'd into the Duodenum; yet they do not contract themselves so as to
force out all the Aliment, but leave between the _Rugæ_ or Folds, on the
inside of the Stomach, a sufficient Quantity to be a Leaven to the next
Meal; and so from time to time.

Some have a Notion, That this Ferment, or Principle of Fermentation, is
in the Aliment it self; which being a Congeries of Matter, consisting of
various Parts of a different Nature, is no sooner enclosed in the
Stomach, and digested in the Heat of that, and the adjacent Parts, but
the more spirituous and subtil Particles are put into motion both from
that Warmth, and the difference of their Natures, and enter upon a
Fermentation. And so by their intestine Commotion, and the Violence they
offer to those Parts which oppose the tendency of any of them, they
break and dissolve what is more solid.

Again: Some suppose, that this Ferment is supply'd from the Glands of
the Stomach.

And Lastly, Others, and perhaps with much better Reason, contend for the
Saliva, and make that to be the Ferment, which serves principally for
the Digestion of the Food; which in Mastication being mix'd with our
Aliment, is with that carried down into the Stomach, where the Parts of
it being put into motion by a kindly and agreeable Heat, they do ferment
with, and exagitate first those Parts of the Food which are most apt to
ferment with it, and then both conspire to break and dissolve the
grosser and more stubborn Parts. And _Galen_, in the Book I have
before-mention'd, plainly allows that the _Saliva_ is concern'd in the
business of Concoction, tho' he supposes the Alteration, which is
produc'd by this Juice, to be made in the Mouth, as appears from these
Words: _Quæ (alteratio) in ore agitur mutat quidem id (nutrimentum) in
alteram speciem manifestè, non tamen ad perfectionem transmutat--Qui
mansi sunt cibi primum quidem hac Pituita (oris) imbuunter, & cum ea
miscentur----Itaque majorem mutationem consecuti sunt, quam ii, qui in
vacuis dentium intervallis fuere impacti_.

Now I have given this short Account of the various Opinions of some
Ingenious Men, concerning the manner how Concoction is perform'd; I come
now to propose my own Hypothesis, by which I shall endeavour to explain
it.


In order to the more easie and effectual Digestion of the Food, Nature
has appointed some Parts for the breaking our Aliment, and reducing
whatever is gross into smaller Parts, before it is put upon Digestion:
Others to supply the Ferment, by which it is to be dissolv'd and
concocted, and which, before it comes to be included in the Stomach,
does moisten, and make it more soft, that it may more easily be
penetrated, and broken by those Parts which serve to divide every Morsel
into smaller Pieces, and prevents the Inconvenience and Trouble which
would arise from the Nourishment sticking about or between them, when it
is dry or viscous.

For the breaking of that part of our Food, which is not liquid, Nature
has furnish'd us with Teeth, and those of two sorts: For some are
ordain'd to divide and break off smaller Morsels from a larger Mass;
others are made for the grinding those Morsels into much smaller parts.
The Teeth, which serve to break off Pieces of a convenient Magnitude
from a larger Mass, are of two sorts, accommodated to the Nature of the
Substance which we eat. These are the _Incisores_, and the _Dentes
Canini_. If the Substance, which we have to eat, be not hard, but more
easily penetrated and divided, then the _Incisores_ are capable of
making an Impression upon it, and fix'd firmly enough in the Jaws to
break off that part which they take hold of. But if it be more solid,
and not easily penetrated, nor any Piece without difficulty to be
separated from that Body, whereof it is a part; then we apply the
_Dentes Canini_, or Eye-Teeth, to it, which are not spread, nor have
such an edge as the _Incisores_, but are sharp and pointed like an Awl,
and so do more readily penetrate a Substance that is hard, and which the
_Incisores_ can scarcely make any Impression upon. And as the Parts of a
more solid Body are commonly with more difficulty separated, and there
must be a greater stress put upon those Teeth which pull it into pieces;
so these Teeth are much more firmly fixed in the Jaws than the
_Incisores_, tho' they have but one single Root. Besides, the Position
of all these Teeth is accommodated to their use, as being planted
opposite to the Aperture of the Mouth; so that they may be conveniently
apply'd to the Substance which we have to eat, before it is broken, and
when it is too large to be admitted within the Mouth.

The Teeth which do by a Compression and Attrition reduce the little
Morsels to smaller Parts, are from the manner in which they break the
Aliment, called _Dentes Molares_, because they do, like so many
Mill-stones, grind the Food between them. And that they might be
render'd fit for this purpose, they are made broad at that Extremity,
which stands out of the Gums, by which means they retain some Quantity
of the Food between them every time the lower Jaw is pulled up and
forc'd against the _Maxilla superior_. And as they are broad, so they
are formed with Inequalities and Protuberances; and by the motion of the
lower Jaw, from one side towards the other, they grind what they have
between them into pieces. The Position of these Teeth too is as
convenient as that of the _Incisores_, and the _Dentes Canini_: For
being design'd to break those pieces of our solid Food, which are taken
into the Mouth, and these pieces, when they are compress'd, and mov'd by
the _Dentes Molares_, being apt to fly out of the Mouth, if there were
no Contrivance to prevent it, they are placed beyond the Aperture of the
Mouth, and opposite to the Cheeks, which keep the Food within that
Cavity, and not only so, but press it in between the _Dentes Molares_ on
one side, as the Tongue does on the other, until they have sufficiently
broken and divided it.

At the same time, whilst the _Dentes Molares_ are breaking the Food,
there flows into the Mouth a Salival Juice, which mixes with it, and not
only serves to moisten it, and to render it more apt and easie to be
divided, but seems to be the Ferment, by the Benefit of which the Food
is dissolved and digested. And therefore it is intimately mixed with it,
by the Teeth agitating or stirring them together in Mastication.

This Liquor, which we commonly call the _Saliva_, or Spittle, seems to
be a Composition made of two several Juices, very different in their
Nature: And therefore the several Parts of it are separated by their
proper Glands, and Nature has planted no fewer than four Pair about the
Mouth, which supply the Juices that make the _Saliva_; to wit, the
_Parotides_, and the _Glandulæ Nuckianæ_, the _Glandulæ Maxillares
internæ_, and _Sublinguales_. Whereas if the _Saliva_ were but one more
simple Liquor, a less number of Glands might have been sufficient. At
least there appears no Reason why one of every Pair should disembogue
itself into the Mouth so very near to the Orifice, by which a Gland of
some other Pair throws in its Juice; and they are not rather all planted
at more equal distances from one another, so to flow in upon every part
of the Aliment at the same time.

Not that I suppose, as there are four Pair of salivatory Glands, so
there are four sorts of Juices supply'd from them, to make the _Saliva_;
but, as I hinted before, that there are only two different Juices that
constitute it. And these are not only sufficient, but more proper to
excite and secure that Fermentation, which is necessary to Concoction.
For we find that most of those Fermentations, which arise upon Mixtures
made for Experiments, are produced from the mixture of two things; and
it is not so easie to find out three or four such Liquors of a different
Nature, as will, upon the mixtion of them all, produce a Fermentation,
and from the omission of any one of them discover no Discord or
Disposition to ferment: Besides, it is certain that two do better secure
the End, which Nature designs. For, if there were three or four
different Juices, of which the _Saliva_ naturally consists, these must
all have their proper Qualities preserved to them, or else the
Fermentation, which should arise between them, will not necessarily
follow upon their mixture; and it is certain, that there would be more
Danger, that one of three or four should be deprived of its Natural
Quality, than one of two.

What Nature these two Juices are of, I do not pretend positively to
determine; but so far as I have been able to make my Conjectures about
it from Experiments, I do think one of them to be an acid Juice; the
other an oleaginous Liquor, something like Oil of Turpentine. For
amongst the many Experiments I have made, there was no one that gave me
so much Satisfaction, as that which I made with Oil of Turpentine, and
Oil of Vitriol, though I try'd several other things, that will produce a
Fermentation upon their Mixture. And it was for this Reason, that I made
the Experiment with Oil of Turpentine and the other Oil.

I took a piece of raw Flesh, and having cut it into pieces, but much
larger than what our more solid Food is reduc'd to by due Mastication, I
mix'd some Crums of Bread with it, then I pour'd in the Oil of
Turpentine to them, and upon that the Oil of Vitriol; and having shak'd
them together, I digested them about four Hours in _Balneo Mariæ_, and
then shaking them again in the Glass, I found the Meat dissolv'd, and
they all became a thickish Pulp. I could not but take notice, that Oil
of Camphire (though it does not otherwise seem much different in its
Nature from Oil of Turpentine) and Oil of Vitriol, which upon mixture
will produce an Effervescence as well as the Oil of Turpentine and Oil
of Vitriol, yet did not touch the Meat, upon which I poured them, so as
in the least to dissolve them. I cannot deny but that an Acid, and a
Solution of Salt of Tartar, did dissolve some part of the Flesh-meat,
which I mix'd them with, but yet neither so soon, nor so perfectly as
the two forementioned Oils. And I do the rather think one of those
Juices, which constitute the _Saliva_, to be of the Nature of Oil of
Turpentine, than of a fix'd Salt, because it will correct and temper
even Oil of Vitriol, so as to render it more tolerable to the Fibres of
the Stomach. Not that I suppose the acid part of the _Saliva_ to come
near to the Acidity of Oil of Vitriol. For though, when they are mix'd,
they will make a Liquor that may not be injurious to the Stomach; yet
the acid Juice, if it were so corrosive as Oil of Vitriol, would
certainly be injurious and painful to the Salivatory Ducts, which convey
it to the Mouth before it is mix'd with the oleaginous Liquor. But I
only say it is an Acid, and in some degree approaches to the Nature of
that Oil. And Nature, which can much better adapt several Causes for the
Production of such an Effect than Art, may attain her End by a more
temperate Acid; though, at the same time, we may be able to make some
probable and true Conjectures about the Nature of those Causes from
Experiments.

It being most reasonable to suppose, that there are but two sorts of
Juices, of a different Quality, that make the _Saliva_, I do conceive,
that four of the eight Salivatory Glands, or two Pair of the four, do
supply one of these Juices, and the other four Glands the other. And
this seems to be a very good Reason, why they are so planted, and the
Orifice of their Ducts so order'd, that the Juice, which is supply'd by
one Gland, is discharg'd into the Mouth, very near to the Orifice, by
which the Juice of a different Nature is transmitted from another, so
that they must necessarily meet and mix together. Thus the _Glandulæ
Nuckianæ_, and _Parotides_, throw in two different Juices by Orifices,
which open into the Mouth very near to one another; and the _Glandulæ
Maxillares internæ_, and _Sublinguales_, do below supply the same kind
of Juices by Orifices, that open so near to one another as to secure the
mixture of the two different Juices.

These Glands, I say, do between them afford two divers sorts of Liquors,
of such a Nature as are apt to ferment upon their first Mixture, but
perhaps more considerably when they come to be digested by the Heat of
the Stomach. So that the Colluctation, or Fermentation, which attenuates
and concocts the Food in the Stomach, does not ordinarily arise between
the Aliment and the _Saliva_, but between the several Parts of the
_Saliva_ it self. And indeed, if the _Saliva_ did not consist of two
Juices, whose Nature is in such a manner different, as to render them
apt to ferment upon their mixture, it would be very hard to conceive how
it should so readily and indifferently serve for the Digestion of all
Eatables; how it should ferment with, and dissolve so great a variety of
Things, not only of a different, but of a contrary Nature; how it should
ferment with Acids as well as Alkalies, digest things that are cold, as
well as hot or temperate; some things that are salt, others that are
insipid, bitter and sweet, mucilaginous, oily, _&c._ But if we suppose,
that the Fermentation, which serves for the Digestion of the Food,
arises from a peculiar difference in the Nature of two Juices, which
constitute the _Saliva_, it will be easie to give a rational Account of
our Concoction of innumerable things of a different Nature. And this
seems to be as effectual, and a more certain way to attenuate and
dissolve the grosser Parts of our Food, than if the Fermentation were
made only between the _Saliva_ and the Aliment: Besides, the _Saliva_
seems to discover a Fermentation upon the mixture of its constituent
Juices, even at those times when we do not actually eat; for it is
always attended with Bubbles, and a Froth, when it has not been at all
agitated in the Mouth, and many of those Bubbles will remain for some
considerable time after we have spit it out.

Nature therefore having appointed the _Saliva_ for the digestion of the
Food, has taken care that it shall be thrown in upon the Aliment on
every side. Thus the _Glandulæ Nuckianæ_, and the _Parotides_, supply
their Juices to that part of the Food, which lies on the outside of the
Gums, between the Cheeks and the Teeth, and the _Glandulæ Maxillares
internæ_, and _Sublinguales_, do bestow their Liquor upon the Meat,
which is within the Teeth and Gums. Neither has she had a Regard only to
that Supply, which is due to all the parts of our Food, but likewise to
the mixture of the two different Juices of the _Saliva_, which is
necessary to its Fermentation. And therefore, as I have already
observ'd, the Orifices of the Ducts, which belong to one sort of Glands,
are placed near the Aperture of a Duct, which conveys a Juice from one
of the other Glands. So the Ducts of the _Glandulæ Nuckianæ_, and the
_Ductus Stenoniani_, do on each side open into the Mouth, near one
another; and the salivatory Ducts of the _Glandulæ Sublinguales_, and
the _Maxillares internæ_, though they have distinct Orifices, empty
themselves under the same _Papillæ_, and the Juices, which are supply'd
by them, meet there, and flow into the Mouth together.

The several Parts of the _Saliva_ being discharg'd into the Mouth in
such a manner as to meet and begin a Fermentation, the _Saliva_ does,
partly as it is agitated, with the Food by the Teeth, and some other
parts of the Mouth; partly by its own Fluidity, insinuate it self into,
and mixes with the Food, and not only moistens and softens it, but
excites the Fermentation, which is to dissolve it. And when the Aliment
is thus mix'd with the _Saliva_, which serves to ferment the whole Mass,
it is then to be convey'd into the Stomach, that great digestive Vessel
of the Body, where the Fermentation is not only continued, but improved.

The Nourishment being convey'd into the Cavity of the Stomach, is there
kept for some time in a digestive Heat, all which time it is under a
Fermentation, produc'd by the different Parts or Juices of the _Saliva_,
which are mix'd with it; which Fermentation does first agitate the more
tenuious or subtil parts of the Food, and puts them into motion, and so
with the Fermentation of its own, and those Alimentary Parts, which it
first communicates a Motion to, improved by the Heat of the Stomach, the
_Saliva_ must necessarily act upon the grosser Parts. For the intestine
Motion, which is excited in the Mass, does not give the Particles, which
are fermented, the same Tendency, but what is so various and confus'd,
that they must inevitably strike not only one against another, but
against those which are more gross, so as to attenuate them, sometimes
by a Collision, which strikes off smaller Particles from the larger
Parts; sometimes by a Compression, when the Particles which are in
Motion, happen to strike directly against any grosser Part, on every
side of it, sometimes by a kind of Explosion. For without doubt the
_Saliva_, which is fluid, insinuates it self into the Interstices of the
more crass Parts of the Aliment, and whatever is agitated and expanded
in those Interstices, requiring a larger space for the Freedom of its
Motion, and offering a Violence to every thing that opposes its
Tendency, will, like Gun-powder included in a Shell, force its way out,
and tear to pieces that Matter, which does endeavour to confine it.

Thus the grosser Parts are broken and divided, until they are at last so
far attenuated as to mix more equally with the Fluid, and with them to
make one Pulp or Chylous Mass. And although I do not apprehend how the
Stomach should by its reciprocal Motions in Inspiration and Expiration,
be able to break and attenuate any Matter, that will not be softned and
dissolved by Agitation in a Liquid; yet it is certain that these
Motions, caused by the Diaphragm and Abdominal Muscles in Respiration,
do make those Parts, which are broken off, as they are dissolv'd, mix
intimately with the more Liquid; as the Meat which I digested with Oil
of Turpentine, and Oil of Vitriol, did by Agitation mix more equally
with the Oils, and became a Pulpament.

As the Juices, which constitute the _Saliva_, do ferment upon their
mixture, so it is probable, that from their Mixture and Fermentation
there results such a _Tertium quid_, as is apt to ferment with the Bile.
And therefore, when the Aliment has been under the Fermentation, excited
by the _Saliva_, a sufficient time, it is then thrown into the
_Duodenum_, where it meets with the bilious Juice, which flows into that
Intestine from the Liver, from which a new Fermentation seems to begin;
and the Commotion of the Parts of the Aliment being still continued,
does carry on the Business of Digestion until the Food is perfectly
concocted: Though it is probable, that this new Fermentation serves not
only for the more perfect Digestion of the Food, but likewise for the
Separation of the Chyle from the feculent Parts.

Neither do I by a random Guess, and an ungrounded Conjecture, suppose
that from the Mixture and Fermentation of the two Juices, which
constitute the _Saliva_, there results a Matter, which is apt to ferment
with the Bile. But to me the Notion seem'd to be confirmed by an
Experiment that I made. For considering with my self, that the Bile is
generally allow'd to have much of a saponary Nature, I made a Solution
of Soap in fair Water, and mix'd it with the Oils of Turpentine and
Vitriol first put together, and from their Mixture I observ'd a very
easie and gentle Fermentation, which continued for a considerable time.




 _A Discourse concerning some Influence of _Respiration_ on the _Motion_
   of the _Heart_, hitherto unobserved. By _J. Drake_, M. D. F. R. S._


Tho' divers accurate Treatises of the _Heart_, and its Action, have been
written by Learned Men of several Nations, especially by two of our own
Country; the Great Dr. _Harvey_, to whose happy Sagacity this Nation
owes the Glory of the Invention of the _Circulation_ of the _Blood_; and
the incomparable Dr. _Lower_, to whom we are beholden for a compleat
Display of the _Mechanical Structure_ of the _Heart_, and a most
ingenious Rationale of its Action. Yet there remain several Doubts and
Difficulties about it (in my Opinion) not sufficiently accounted for;
towards the resolving some of which, I shall offer what my own Thoughts
have suggested to me, and leave it to the Consideration of the Reader.

The Learned Dr. _Lower_ (whose accurate Piece on this Argument will
insure his Reputation so long as Physical Knowledge shall last in
esteem) has so well accounted for the _Systole_, or Contraction of the
Heart, from the _Mechanical_ Structure of it, that he seems almost to
have exhausted the Subject; and had he been as happy in discovering the
true cause of the _Diastole_, he had left little room for the Industry
and Sagacity of others about this _Viscus_.

But having judiciously and solidly explain'd the _Systole_, he contents
himself to ascribe the _Diastole_ to a motion of _Restitution_, which
account gives me no Satisfaction: Because the _Systole_ being the
proper, and (as himself confesses) the only motion of the Heart, a State
of _Contraction_ seems to be the natural State, and consequently without
External Violence, it shou'd have no _Diastole_ at all.

This will appear more plain, if we consider the Circumstances of it, and
its Motion, as a Muscle, with respect to other Muscles. That Contraction
is the proper Action, and State of all Muscles, is evident from
Experience of Fact, as well as Reason. For, if any Muscle be freed from
the power of its _Antagonist_, it is immediately _contracted_, and is
not by any Action of the Will, or Spirits, to be reduced to a State of
_Dilatation_. Thus, if the _Musculi Flexores_ of any Joint be divided,
the _Extensores_ of that Joint being by that means free'd from the
contrary Action of their _Antagonists_, that Joint is immediately
extended without any consent of the Will, and in that State it remains;
and so _Vice versa_, if the _Extensores_ be divided. From whence it is
plain, that the Muscles have no restitutive Motion, but what they derive
from the Action of their _Antagonists_, by which they are balanc'd. Thus
likewise the _Sphincters_ of the _Gula_, _Anus_ and _Vesica_, having no
proper _Antagonists_, are always in a State of Contraction, and suffer
nothing to pass them, but what is forced through them by the contrary
Action of some stronger Muscles, which, though not properly to be call'd
_Antagonists_, yet on all necessary Occasions perform the Office of such.

That the Heart is a Muscle, furnish'd and instructed for Motion like
other Muscles, is (in my Opinion at least) demonstrated beyond
Contradiction by Dr. _Lower_ and others. And, as it is a _Solitary_
Muscle without any proper _Antagonist_, and not directly under the power
of the Will, nor exercising _Voluntary_ Motion, it approaches nearest to
the _Sphincter_ kind, which only has these Conditions in common with it.
But in constant and regular Alternations of Contraction and Dilatation,
it differs exceedingly from all the Muscles of the Body.

This _reciprocal Æstus_ of the Heart has given the Learned abundance of
trouble; who, finding nothing peculiar in the Structure, which shou'd
necessarily occasion it, nor any _Antagonist_, whose re-action should
produce it, have been extreamly perplex'd to find out the cause of it.

But passing over the various Opinions of Authors, to avoid being
tedious, I shall take notice here only of the very Learned Dr.
_Lower_'s, in whose Account of the _Systole_, however solid and
ingenious, I observe something deficient, and whose _Hypothesis_ of the
_Diastole_ I think to be precarious and false.

This Excellent Author, having by sound Arguments drawn from the
Structure and Mechanism of the Heart, establish'd the Certainty of its
_Muscular Motion_, rests satisfied, without taking notice of any
Assistance, that the Heart receives from any other Part, except from the
Brain, by the means of the eight pair of Nerves.

[Sidenote: _Part_ 2_d_. _Prop._ 67. _Prop._ 73.]

[Sidenote: _Prop._ 76.]

The Accurate _Borellus_, in his _Oeconomia Animalis_, computes the
_Motive_ Power of the _Machine_ of the Heart to be equal to, or to
surmount that of a Weight of 3000_l._ The _Obstacles_ to the Motion of
the Blood thro' the _Arteries_ he esteems equivalent to 180,000_l._
which is 60 times as much as he rates the Force of the Heart at. Then
deducting 45,000_l._ for the adventitious Help of the _Muscular Elastic
Coat_ of the _Arteries_, he leaves the Heart with a Force of 3,000_l._
to overcome a resistance of 135,000_l._ that is, with 1, to remove 45.

This stupendous Effect he contents himself to ascribe to the _Energy_ of
_Percussion_. But, had he proceeded in his Calculation to the Veins,
which he allows to contain constantly a quantity of Blood, quadruple to
the Contents of the Arteries, and to which this _Energy_ of _Percussion_
does either not reach at all, or but very languidly, he might probably
have seen a necessity for some other Expedient to remove so insuperable
a Difficulty.

But not to insist rigorously on the Exactness of this Calculation,
(though the great Abilities of the Author in this way, and his Ingenuity
and Modesty, are a sufficient Warrant for the Accuracy of his
Computations, and the Fidelity of his Accounts) we may allow a much
greater Deduction, than would be justifiable, without lessening the
Difficulty. But this Account I have taken notice of purely for the sake
of the Calculation, which may be of use in the Sequel; the account it
self being in other respects more defective than Dr. _Lower_'s, to which
we will return.

The Doctor, notwithstanding his great Sagacity, appears (to me) to have
overlook'd something of very great moment, and importance in the
explication of the Action of the Heart. For, tho' it should be granted,
that the _Muscular Fibres_ of the Heart acted by the Nerves, are the
immediate Instruments of its _Constriction_ or _Systole_, yet it must
not be denied, that the _Intercostal_ Muscles and _Diaphragm_ are of
great service to aid and facilitate this Contraction, by opening a
Passage for the Blood through the Lungs, which denied would be an
invincible Obstacle.

Neither do they promote it that way only. The manner how they farther
assist the Heart in its Contraction, will appear manifestly, if we
consider the different Posture, Situation, and Capacity of the
Blood-Vessels of the Lungs in the several times of _Elevation_ and
_Depression_ of the _Costæ_.

The _Pulmonary_ Artery rises from the _right_ Ventricle of the Heart,
and runs in one Trunk, till it comes to the _Aspera Arteria_, where it
is divided, and sends a Branch along with each Division of the _Aspera
Arteria_, according to all the minutest Subdivisions, of which it is
likewise subdivided, accompanying all the _Bronchi_, in their whole
progress through the Lungs.

The _Pulmonary_ Vein, which empties itself into the _Left_ Ventricle of
the Heart, spreads it self on the _Aspera Arteria_ and _Bronchi_, in the
same manner that the Artery does.

The necessary confluence of this Disposition if, that this Artery and
Vein being co-extended with, and fasten'd to the _Bronchi_, must needs
suffer such alteration of _Superficial_ Dimensions, as the _Bronchi_ do
in the _Elevation_ or _Depression_ of the _Costæ_.

While the Ribs are in a State of _Depression_ (whether before Commerce
with the External Air or after) the _Annular Cartilages_ of the
_Bronchi_ shrink one into another, and by that means their _Dimensions_
are exceedingly contracted. In conformity to this condition of the
_Bronchi_, the _Pulmonary_ Artery and Vein must likewise, either by
means of their _Muscular_ Coats, contract themselves to the same
_Dimensions_, or lye in _Folds_ or _Corrugations_, which is less
probable.

On the other hand, when the Ribs are elevated, and the _Diaphragm_ bears
downward, the Air rushing into the Lungs, shoots out the _Cartilaginous_
Rings, and _divaricates_ the Branches of the _Trachea_, and by them
extends and divaricates the several Divisions of the _Pulmonary_ Artery
and Veins, and thereby lengthens and enlarges their Cavities.

This enlargement of their Cavities is very considerable, not only upon
the score of the addition, which they receive in length thereby, but
also upon the account of their _Divarication_. For whereas, when the
Ribs are depress'd, and the Lungs subside, the Blood-vessels are not
only contracted, (as I have already observ'd) but their Branches,
which are exceeding numerous, approach one another, and lie in
_juxta-position_, by which their Cavities are very much compress'd and
streighten'd: When the Ribs are elevated, and the Lungs turgid with Air,
not only the Fibres, by which their Coats in the opposite state were
contracted, are extended; but those innumerable Vessels, which lying
before in lines almost parallel upon one another, compress'd one
another, making an _acute_ Angle at their Junctures, are divaricated and
separated from each other, and make an _obtuse_, whereby their Channels
are widened.

Thus a passage is open'd to the Blood, from the _Right_ Ventricle of the
Heart to the _Left_, through the Lungs, to which it could not otherwise
pass; and the opposition, which the Blood contain'd in that Ventricle,
must otherwise necessarily have made to its Constriction, is taken off,
and the _Systole_ thereby facilitated.

Nor is that all. For the _Diastole_ being caus'd (as I shall in the
Sequel shew) by the force of the Blood rushing into the Ventricles, this
Ampliation and Extension of the _Pulmonary_ Artery is a sort of _Check_
or _Counterpoise_ to it, and prevents an endeavour towards two contrary
Actions at once, which must necessarily frustrate both. For the Heart
being a _Springy_, _Compressible_ Body, whose proper Action, which is
Contraction, depends on the influx of certain Fluids into its Fibers, or
Substance; and containing besides a Fluid in its _Ventricles_, or great
Cavities, in one of which is the Mouth of this Artery, the action of
this Vessel must in great measure resemble that of a _Syringe_, whose
extremity is immers'd in Water, the Enlargement or Expansion of the
Chanels of the Artery answering the drawing of the _Embolum_, as the
constrictive motion of the Muscle of the Heart does the pressure of the
_Atmosphere_ upon the _Surface_ of the Water, the one making way for the
fluid, and the other forcing it to follow, where the resistance is
least. In this Sense we may allow a sort of Attraction to the
_Pulmonary_-Artery, depending wholly upon the Action of the
_Intercostal_ Muscles and _Diaphragm_, which we must therefore confess
to be very serviceable and instrumental in promoting the _Systole_ of
the Heart.

But if the Learned Author be deficient in his Account of the _Systole_;
that is, if he has not observ'd all the Mechanism and Contrivance of
Nature for the Contraction of the Heart; much less sufficiently has he
accounted for the _Diastole_, or Dilatation of it, which he ascribes to
a motion of _Restitution_ of the over-strain'd Fibres, which yet he
confesses are made for _Constriction_ only. 'Tis true, he immediately
after joins the _Influx_ of the _Blood_ as a concurrent Cause; but from
the slight notice that he takes of it, 'tis plain, that he did not so
much as dream of any great share it had in that Action. His Words are
these:

[Sidenote: _De Corde, Pag. 75._]

_Quin & (ut obiter hoc moneam) omnis motus contractione perficiatur, &
Cordis Fibræ ad constrictionem solum factæ sint, apparet quoque Cordis
motum _totum_ in _Systole_ positum esse; cumque Fibræ ultra tonum suum
in omni constrictione eius tendantur, idcirco ubi nixus iste absolvitur,
motu quasi _restitutionis_ Cor iterum relaxatur, & sanguine à Venis
_influente_ rursus distenditur; à _nullo_ enim cordis motu, nisi
_tensionem suam remittente_, & ab _irruente_ sanguine _Diastole_ ejus
libratis adeo viribus succedit._

I have transcrib'd the intire Paragraph, because it contains his whole
_Hypothesis_ of the _Diastole_, and all the notice that he takes of it
through his whole Work. But how slender soever this may prove, it is the
most substantial that I have any where met with, except a late one of
Mr. _Cowper_, which is properly an Improvement of this, and shall be
consider'd in the Sequel.

But if Contraction be the sole Action of these Fibres (as this Great Man
confesses it to be) and as indeed it is of all _Muscular_ Fibres, I
wonder how so judicious a Writer came to slip into such an Absurdity, as
to call their Distention (vulgarly but improperly call'd Relaxation) a
Motion of _Restitution_. For from the Nature of those Fibres, and their
disposition in the Structure of the Heart, the natural State of the
Heart appears manifestly to be _Tonical_, and its Dilatation a State of
Violence; and consequently, the Constriction is the _true_ motion of
_Restitution_, and the State to which it will _spontaneously_ return,
when the Force is taken off, which is the work of the _Intercostal_
Muscles and _Diaphragm_.

Thus we are left still to seek for the true Cause of the _Diastole_,
which seems to me to be the main and most difficult _Phænomenon_,
relating to the Heart and the Circulation of the Blood. But in Mr.
_Cowper_'s ingenious _Introduction_ to his _Anatomy of Humane Bodies_, I
find the Share which Dr. _Lower_ hints the Blood to have in that Action,
further prosecuted, and improved into the main Instrument of the
Dilatation of the Heart, wherein I agree intirely with him. But as to
the manner, and reasons of its being so very instrumental, I can't be so
perfectly of his mind.

_The Heart (_says this accurate Anatomist_) of an Animal bears a great
Analogy to the Pendulums of those Artificial Automata, Clocks and
Watches, whilst its motion is performed like that of other Muscles, the
Blood doing the Office of a _Pondus_._

This Explication, being but a Simile without a distinct application to
Particulars, is beside so very short, that I can at best but give a
conjecture at the meaning; which if I mistake, I shall deserve to be
excused, and expect to be better inform'd.

By the _Bloods_ doing the Office of a _Pondus_, I suppose he means, that
the Blood contributes in the same manner to the motion of the Heart, as
the _Weights_ do to that of the _Pendulum_ of a _Clock_. If so, the
Blood, according to him, must be the Instrument of _Constriction_; and
_Dilatation_ must be the _Natural_ State, or _Spontaneous_ Motion, to
which it wou'd, when under no violence, return; the contrary of which, I
presume, will appear e're I have done.

But if he means, that the _Blood_ in its reflux, by _gravitating_ on the
_Auricles_ and _Ventricles_, dilates and expands 'em, acting therein as
a _Counterpoise_ to its contractions as a Muscle, I cou'd wish his
Design had not bound him up to so narrow a compass, and that he had
given us an explication at large of so abstruse and so important a
_Phænomenon_: Because the _Specifick Gravity_ of the Blood seems to me a
cause by no means alone adequate to the effect, which it is here
suppos'd to produce.

For, if the Blood acts only as a _weight_ by meer _gravitation_, then
that part of it only which descends from the Parts above the Heart can
be employ'd in that Action. This at the largest computation can't amount
to Five pound weight, and must, according to the computation of
_Borellus_, force a Machine, that is able to overcome a resistance of
135,000_l._ I leave every Man to deduct what he shall upon examination
find reasonably to be deducted, and yet shall rest secure, that it is
not to be effected in the least with so small a Weight.

But neither does the _Refluent_ Blood gravitate in any such proportion,
as I have here assign'd. For to make a true estimate of its
_Gravitation_, we must consider the Circumstances of the Liquor suppos'd
to gravitate; in which it very much resembles Water inclos'd in a
recurve Tube, of which, if the length of the two Legs be equal, it may
be suspended in the Air full of Water, with the Extremities downwards,
without losing a drop, although the _Diameter_ of those Legs should be
very unequal. The Case of the Arteries and Veins is pretty near a
parallel to a Tube, so fill'd and inverted. For, if the Arteries and
Veins be continued Tubes, (as by the Microscope they are made to appear)
then supposing their contents to have no other determination of motion,
than their own weight wou'd give them, the contain'd Fluids must be
Counterpoises to each other. For the Veins and Arteries being join'd at
the smaller Extremities, and the larger of both terminating in the
same parallel Line, it is impossible, according to the Laws of
_Hydrostaticks_, that the contents of either shou'd overbalance t'other.
How far then must it fall short of forcing the natural Power and
Resistance of so strong a Muscle as the Heart, by meer Gravitation?

The Blood indeed has a _Progressive_ Motion through its Vessels, wherein
it differs from Water, in a recurve Tube, in the Experiment
above-stated. But, if the natural Gravitation of the Blood contributes
nothing to the Dilatation of the Heart, this progressive Motion will not
be found much more sufficient. For, as this Motion is deriv'd intirely
from the Heart's Constriction (as all Accounts hitherto derive it) cou'd
the Blood be suppos'd to re-act upon it by the Heart, with all the force
first impress'd upon it by the Heart, it would be insufficient, unless
we will suppose the _Force communicated_ to be superiour to the _Power
Communicant_, which is absurd.

But when the just and necessary Deductions for the Impediments, which
the Blood meets with in its Progress through the Vessels, shall be made,
the remaining Force will be found so exceeding weak, that to prop the
Blood through the Veins may be a task alone too great for so small a
Power, without charging it with the additional difficulty of forcing the
Muscle of the Heart.

_Alphonsus Borellus_, after a great deal of solemn pains taken to shew
his Care and Exactness, and to possess his Reader of the Truth of his
Calculations, casts up the force of the Heart, and the _Muscular_ Coat
of the Arteries, to be together equal to a weight of 3,750_l._ and
allots them a Resistance equal to 180,000_l._ to overcome which is 45 to
1. To make up for a disproportion, by his own confession, incredible to
those who have not consider'd the Matter as he had done, he flings into
the Scale the additional _Force of Percussion_, which he leaves
_indefinite_, and thinks sufficient to _force any quiescent finite
Resistance whatsoever_.

But as this Account and _Hypothesis_ are part of a Posthumous Work (if a
liberty of Conjecture may be allow'd in so uncertain a Matter,) I shou'd
suspect, that these Papers were left unfinish'd by _Borellus_; or at
least, that in many places the last Hand was never put to them. For
neither in this Place, nor any other of this Work, does he account for
any more than the _Systole_ of the Heart, and the resistance which is
made to the progressive motion of the Blood in the Arteries only. This
alone he found to exceed the Power of the Heart so prodigiously, that he
seems to shuffle it off his Hands with a general and precarious
Solution, as a difficulty that he was desirous to be rid of. For, having
ascrib'd this _stupendous_ (as he himself calls it) effect to the
_Energy of Percussion_, he takes no care to satisfie his Reader any
farther about it, or to refer him, or give him the expectation of
Satisfaction any where else; although he has an express Treatise on the
_Force of Percussion_, which was written preparatory to this, and to
which he frequently refers in other Places of this Work. But what
confirms my suspicion, that this part was intended for a farther Revise
by the Author, is, that he has left the Progress of the Blood through
the Veins, and the _Diastole_ of the Heart, absolutely untouch'd, tho'
they are Difficulties of a much greater magnitude than this, which he
has attempted to account so slightly for: For, in these he is excluded
the benefit of _Percussion_, and has yet a greater resistance to
overcome without it. Omissions of this kind are so unusual with this
Author, where-ever he knows himself to go upon sure grounds, that it is
to me an Argument, that he doubted the sufficience of his _Percussion_,
and reserv'd these important _Phænomena_ for farther Consideration,
without plunging himself into such an Absurdity, as to ascribe to
_Percussion_ any such _Energy_ as to be able (so broken as it returns to
the Heart) by its re-action to force that Power, from whence only it was
at first deriv'd.

Dr. _Lower_, and Mr. _Cowper_, deliver their Opinions of the Cause of
the Dilatation of the Heart so very short, and without any Arguments to
support them, that by exposing them naked, they seem rather to discourse
of it transiently, as Men oblig'd by the Nature of their Subjects to say
something of it, than solicitous to give any full or satisfactory
Account; and therefore I shall proceed no farther upon them here.

But though the _Hypothesis_ of _Borellus_ may, in this Case, be found
precarious or insufficient (a Misfortune that has befallen him in divers
other Particulars) his _Theory_ holds still good. At least it ought to
be allow'd, in justice to his great Abilities and Exactness, till some
Body convicts him of some material Error in his Calculations, which has
not as yet been done by any Body, that I know of.

Supposing then the force of the Heart, and of the _Muscular_ Coat of the
Arteries, as likewise of the resistance, which they must overcome, to be
computed with any degree of accuracy, there remains yet such a
prodigious disproportion to be accounted for, as requires some more
powerful Agent, than any yet assign'd, to make up the deficiency.

What assistance the Heart receives from the action of the _Thorax_
towards the facilitating its Contraction, without which assistance there
cou'd have been no _Systole_, has been already shewn. But neither the
_Intercostal_ Muscles, or _Diaphragm_, which are so instrumental in that
part of its action, can contribute any thing to the _Diastole_; because
they serve only to enlarge the Cavity of the _Thorax_, and thereby to
open a passage to the Blood from the Heart, and promote its Constriction.

Whatever therefore the force is, that dilates the Heart, and is the
cause of the _Diastole_, it must be equal to that of the Heart, the
_Intercostal_ Muscles and _Diaphragm_; to all which it acts as an
Antagonist. I take no notice of the _Serratus Major Anticus_, and other
Muscles; which have an obscure share in the _Elevation_ of the _Costæ_,
because as much may reasonably be deducted upon the account of the
_Obliquus externus Abdominis_, and other Muscles; which having their
Insertions on some of the lower _Ribs_ are as instrumental towards the
_Depression_ of them, and so balance the Account. But the chief use of
these is in violent Respiration: In ordinary Respiration their share is
small.

Such a real Power (which may in the least be suspected of any share in
this Action) is hard, perhaps impossible to be found in the _Machine_ of
any _Animal_ Body; and yet without some such Antagonist, it is as
impossible the Circulation of the Blood should be maintain'd. All the
Engines yet discover'd within the Body, conspire towards the
_Constriction_ of the Heart, which is the _State_ of _Quiescence_, to
which it naturally tends. Yet we find it alternately in a _State_ of
_Violence_, that is, of _Dilatation_; and this upon necessity, because
upon this _Alternation_ depends all Animal Life.

Some sufficient Cause External must therefore be found, to produce this
great _Phænomenon_; which Cause must be either in the _Air_, or
_Atmosphere_, because we have no constant and immediate Commerce with
any other _Mediums_.

Some great Physicians observing this, and that depriv'd by whatsoever
means of Communication with the _external_ Air, we became instantly
extinct, have imagin'd, that in the Act of Inspiration certain purer
parts of the Air, mixed with the Blood in the Lungs, and was convey'd
with it to the Heart, where it nourish'd a sort of _Vital Flame_, which
was the Cause of this reciprocal _Æstus_ of the Heart. Others not quite
so gross, rejecting an _Actual Flame_, have fancied, that these fine
Parts of Air mixing with the Blood in the Ventricles of the Heart,
produc'd an _Effervescence_ which dilated it. But these Fancies have
been long since exploded and condemn'd upon ample Conviction; and 'tis a
Point yet undetermin'd, whether any Air does mix with the Blood at all
in the Lungs, or not.

But supposing, that some Air may insinuate it self into the _Pulmonary_
Vein, it can no other way dilate the Heart than by an Effervescence in
the Left Ventricle, which wou'd not dilate the Right. But this Opinion
is contradicted by _Autopsie_, and too laboriously confuted by others,
to be brought upon the Stage again here.

There remains therefore only the _gross Body_ of the _Atmosphere_ to be
considered, which is undoubtedly the _true Antagonist_ to all those
Muscles, which serve for ordinary Inspiration, and the Constriction of
the Heart. This will appear more evidently, if we consider not only the
Power, but the Necessity of its Action upon _Animal_ Bodies, as well as
the want of other sufficient Agents.

The Heart is a _Solitary_ Muscle of very great strength, and the
_Intercostal_ Muscles and Diaphragm, which likewise have no
_Antagonists_, are a vast additional Force, which must be balanc'd by
the contrary Action of some equivalent Power or other. For, tho' the
Action of the _Intercostal_ Muscles be voluntary, that does not exempt
them from the condition of all other Muscles serving for _voluntary_
motion, which wou'd be in a State of perpetual Contraction,
notwithstanding any Influence of the Will, were it not for the Libration
of _Antagonist_ Muscles. This Libration between other Muscles, is
answer'd by the _Weight_ of the incumbent _Atmosphere_, which presses
upon the _Thorax_ and other parts of the Body. And, as in all other
voluntary Motions the influence of the Will only gives a prevalence to
one of its two Powers before equilibrated, so here it serves to enable
those Muscles to lift up a weight too ponderous for their strength not
so assisted; and therefore as soon as that assistance is withdrawn, the
_Costæ_ are again depress'd by the meer _Gravitation_ of the
_Atmosphere_, which wou'd otherwise remain elevated through the natural
Tendency of those Muscles to Contraction.

This is evidently prov'd from the _Torricellian_ Experiments, and those
made upon Animals in Mr. _Boyle_'s Engine; where, as soon as the Air is
withdrawn, and the _pressure_ thereby taken off, the Intercostal Muscles
and Diaphragm are contracted, and the Ribs elevated in an instant, and
can't by any Power of the Will be made to subside, till the Air is again
let in to bear them forcibly down.

[Sidenote: _De Respirationis Organis & Usu._]

It were scarce worth while to take notice here of a Mistake of the
Learned Dr. _Willis_, were it not for the great Authority of the Man,
which is almost sufficient to keep Error in countenance. The Doctor
having observ'd, that the Fibres of the _External_ and _Internal
Intercostal_ Muscles ran in a contrary order, as it were, decussating
each other, takes occasion from thence to fansie, that there was an
opposition in their Office; and that as the _External_ serv'd to raise
up the Ribs, the _Internal_ drew them down again, forgetting at that
time, That, when a contractile Body is fasten'd at the several ends to
Points unequally moveable, let the Contraction happen in what part or
manner soever, the more moveable Point must be drawn towards the less
moveable: By which Rule, whether _External_ or _Internal Intercostals_
be contracted, the lower Ribs will be forc'd to approach the upper, that
is, be rais'd up.

As in the Elevation of the _Costæ_, the Blood, by the passage that is
open'd for it, is in a manner solicited into the Lungs; so in the
Depression of them, by the subsidence of the Lungs, and the Contraction
of the Blood-Vessels, both which are consequent thereof, the Blood is
forcibly driven, as it were with an _Embolum_, through the Pulmonary
Vein into the Left Ventricle of the Heart. And this, together with the
_general Compression_ of the _Body_ by the _weight_ of the _Atmosphere_,
which surrounds and presses upon the whole Surface of it, is that Power
which causes the Blood to mount in the Veins, after the force impress'd
upon it by the Heart is broken and spent, and which is sufficient to
force the Heart from its natural State to Dilatation.

He that is able to compute the weight of a Column of Air, equal to the
Surface of the whole Body, will readily grant it a power sufficient for
the Effects, which are here ascrib'd to it. And when he considers, that
the Bodies of Animals are compressible Machines, he will find that it
must of necessity affect them in the manner here laid down. But though
our Bodies be entirely compos'd of _Tubuli_, or Vessels fill'd with
Fluids; yet this pressure, how great soever, being equal, cou'd have no
effect upon them, if the superficial Dimensions were not easily
variable; because being compress'd on all parts with the same degree of
Force, the contain'd Fluids cou'd not any where begin to recede, and
make way for the rest to follow, but wou'd remain as fix'd and
immoveable as if they were actually solid. But by the Dilatation of the
_Thorax_, room is made for the Fluids to move, and by the Coarctation of
it, fresh motion is imprest, which is the main Spring whereby the
Circulation is set and kept going.

This reciprocal Dilatation and Contraction of the superficial Dimensions
of the Body, seems so necessary to Animal Life, that there is not any
Animal so imperfect as to want it, at least none to the inward
Structure, of which our Anatomical Discoveries have yet reach'd. For,
tho' most kinds of _Fish_ and _Insects_, want both _moveable_ Ribs and
Lungs, and consequently have no dilatable _Thorax_, yet that want is
made up to 'em by an _Analogous_ Mechanism, answering sufficiently the
Necessities of their Life.

Those Fishes which have no Lungs, have _Gills_, which do the _Office_ of
Lungs, receiving and expelling alternately the Water, whereby the
_Blood-Vessels_ suffer the same alteration of Dimensions, that they do
in the Lungs of more perfect Animals.

The Lungs or _Air-Vessels_ of Insects, are yet exceedingly more
different in Structure, Distribution, and Situation from those of
perfect Animals, than those of Fishes are, and yet in their Use and
Action agree perfectly with both; that is, _receiving_ and _expelling_
the Air, and _varying_ the _Dimensions_ and _Capacities_ of the
_Blood-Vessels_. These having no _Thorax_, or separate Cavity for the
Heart and Air-Vessels, have the latter distributed through the whole
Trunk of their Bodies, by which they communicate with the _External_ Air
through several _Spiracula_ or _Vent-holes_, to which are fasten'd so
many little _Tracheæ_, or Wind-pipes, which thence send their Branches
to all the Muscles and _Viscera_, and seem to accompany the
Blood-Vessels all over the Body, as they do in the Lungs only of perfect
Animals. By this disposition in every _Inspiration_, the whole Body of
these little Animals is inflated, and in every _Expiration_ compress'd;
and consequently the Blood-Vessels must suffer a _Vicissitude_ of
Extension and Contraction, and a greater motion must thereby be
impress'd upon the Fluids contain'd in them, than the Heart, which does
not in those Creatures appear to be Muscular, seems capable of giving.

The only Animal that is exempted from this necessary condition of
_Breathing_, or _receiving_ and _expelling alternately some Fluid_ into
and out of the Body, is a _Fœtus_. But this, while included in the
Womb, has little more than a _vegetative_ Life, and ought scarce to be
reckon'd among the number of _Animals_. For, were it not for that small
share of _Muscular_ Motion, which it exercises in the Womb, it might
without absurdity be accounted for as a Graft upon, or Branch of the
Mother.

[Sidenote: Boyle _of the Elasticity of Air. Pechlinus de Aeris &
Alimenti defectu._]

Concerning the immediate Matter, and Means of Life, and Nutrition,
Authors are not agreed, nor is it the business of this place to
reconcile, or decide their Differences, but to account for the Motion of
the Blood through the Vessels only. In order to this, it will be
necessary to observe, that the Pulsation of the Heart in a _Fœtus_ is
so very weak and obscure, and the Motion of the Blood so extream slow
and languid, as to be scarce, if at all perceivable, as has been
experienced in the Dissection of Puppies before Respiration had. To
produce such a feeble Palpitation, and creeping Motion, no greater force
seems to be required, than may be deriv'd from the Communication between
the Vessels of the Mother and _Fœtus_ in the _Placenta_. I am not
ignorant, that divers very Learned Anatomists (whom the Crowd have
implicitly follow'd) have absolutely rejected all Communication between
these Vessels. But, with submission to Great Authorities, I think they
have acted arbitrarily, and without sufficient Warrant from Reason or
Experiment: For neither are the Arguments which they bring against it
conclusive, nor the Office which they assign to the Umbilical Vessels in
lieu of it, proper, or natural to those Vessels, or the reality of the
Fact made out by any substantial Reasons. Those that reject this
Communication usually do it in favour of one or both of these Opinions,
that the Arteries of the _Uterus_ do deposite a Nutritive Juice, or a
Juice impregnate _with Air_ in the _Placenta_, which is suck'd in by the
_Umbilical_ Vein, and convey'd to the _Fœtus_, for the necessary Uses
of Nutrition and Life. Now those that patronize either of these
Opinions, lead Nature an unnecessary Dance. For if the _Maternal_ Blood
does really contain any such _Nutritious_, or any such necessary _Aerial
Particles_, why shou'd they be separated and extravasated, to be with
difficulty receiv'd into the _Umbilical_ Vein, and again mixt with the
Blood, when they might more easily have been imparted by the plain
simple way of Transfusion from the Arteries of the _Mother_ to the Veins
of the _Fœtus_. And, that this is the course which Nature takes in
this Case, I am perswaded from the easiness and simplicity of the
Method, which readily performs what might be perhaps in vain expected
from the other, and wou'd over and above find them, what they seem to
grope so blindly about for, a first Mover of the Blood in a _Fœtus_.

Those that contend for the conveyance of the _Nutricious_ Juice, through
the _Umbilical_ Vein from the _Placenta_, are forc'd upon two
Difficulties next to Absurdities. For first they are oblig'd to make
this Vein, which, as all other Veins, seems dedicated to the
Re-conveyance of Blood only, the proper and immediate Chanel, thro'
which a very different Liquour is to be carried; and next, to give a
Power of Attraction or Suction to it; because the _Nutricious_ Juice,
which it is thus destin'd to carry, is both viscous and stagnant, and
has neither force to drive, nor subtilty to penetrate, or insinuate it
self into the Capillary Veins; and therefore must be drawn or suck'd as
_Milk_ is from the _Breast_, to which the _Placenta_ and its
_Nutricious_ Juice are by the Favourers of them expresly compar'd. But
if this were the sole use of the _Placenta_, and _Umbilical Vessels_,
why were the Umbilical _Arteries_ sent along with the Vein? Their
business is not to bring any thing back to the _Fœtus_, nor can they
contribute any thing to the benefit of the _Mother_; for the _Uterine_
Arteries bring all to the _Placenta_, the Umbilical Vein carries it to
the _Fœtus_, and the _Uterine_ Veins convey back again the Surcharge
of the _Mother_'s Blood; the Umbilical _Arteries_ only, have nothing to
do, and are superfluous and impertinent, which is contrary to the
constant Practice of Nature. Yet if _Autopsie_ did in the least
countenance this Hypothesis, some Defence might still be made; but we
find in the Umbilical _Vein_ of a _Fœtus_ nothing but _Florid_ Blood,
such as in all probability it received immediately from the _Arteries_
of the _Mother_ without any mixture. And therefore I can't help
concluding, that this Opinion engages its Favourers in some Absurdity,
without Necessity and without Proof.

They that from the _Placenta_ supply the Body of the _Fœtus_ with
_Air_, are as much distress'd as t'other; for they are forc'd to beg the
Question twice, which, even when granted, will not answer their Ends.
First, they suppose, that an intimate mixture or confusion of _Air_ with
the _Blood_, is necessary for the support of Animal Life, a
_Postulatum_, which perhaps the former part of this Discourse may have
render'd unnecessary; and next, that the _Fœtus_ is supply'd with
_Air_ from, and its _Blood_ mix'd with it in the _Placenta_.

But here again they fetch a Compass without necessity or proof. For if a
mixture of _Air_ were necessary to a _Fœtus_, why should it be
separated from the _Mother_'s Blood, and not rather both communicated
together, since it is so much more easie and commodious? But neither
does the _Placenta_ seem to be instructed and provided for the
separation of _Air_, but of a much _grosser Fluid_, destin'd to some
other use, which _Autopsie_ confirms: Yet, were both these Opinions
true, they are however defective, and the Circular Motion of the Blood
unprovided for.

By the way of _Transfusion_, this great Phænomenon is naturally
accounted for, and the Ends, for which the other two Hypotheses were
devis'd, might both be answer'd with more ease. For the _Hysterick_
Arteries transmitting their Blood immediately to the _Umbilical_ Vein,
may very easily transmit such _Nutricious_ Juices or _Aerìal_ Particles,
as are contain'd in the Blood, along with it, without depositing them by
the way. By this means so much of the Impulse of the Mother's Blood is
preserv'd, as suffices to maintain that languid Circulation which a
_Fœtus_ enjoys. For the Blood being driven through the _Arteries_ of
the _Uterus_ into the _Umbilical Vein_, is convey'd directly to the
_Sinus_ of the _Porta_, and thence by a short and direct Passage through
the _Cava_ to the Heart; where passing through the _Foramen Ovale_ to
the _Left_ Ventricle, and through the _Canalis Arteriosus_ from the
_Right_ and _Pulmonary_ Artery, it is all deliver'd without coming at
the _Lungs_ to the _Aorta_, and from thence again by the _Umbilical
Arteries_ to the _Veins_ of the _Uterus_, making a sort of _Epicycle_ to
the main Circulation in the Mother.

As this Opinion is Favour'd by the Structure and Disposition of the
Blood-Vessels on both Parts, so there is nothing in it difficult to be
conceiv'd, or repugnant to Experience. Late Discoveries have made it
appear, that the Arteries and Veins are continu'd Tubes, and that the
latter contain nothing but what they receive from the former, and no
Reason appears why we shou'd think this Method to be varied in the
_Placenta_. On the other hand, if the Arteries of the _Uterus_ were
continued to the Veins of the _same_ part, and those of the _Fœtus_
in like manner, without communicating with each other, their Confluence
in the _Placenta_ seems to be altogether impertinent, and of no use, and
the _Umbilical_ Arteries and Vein fram'd for no other Service or
Purpose, than to give the Blood room for an idle Sally.

Thus the Reasonableness of this old Opinion may be vindicated, but the
Certainty of it rests upon stronger Proof. Mr. _Cowper_, to whose happy
Industry we owe the Confirmation of many ancient Discoveries, and the
Benefit of some new ones, has the Honour to re-establish this old, but
long exploded Truth. For by pouring _Mercury_ into a Branch of the
_Uterine Arterie_ of a _Cow_, that went into one of the _Cotyledones_ of
the _Uterus_, he fill'd those Branches of the _Umbilical_ Veins, which
went from that _Cotyledon_ to the _Navel_ of the _Fœtus_; which, with
a part of the _Uterus_, he keeps prepared by him.

It would be a weak Objection, to alledge, That the Observation and
Experiment being made on the _Uterus_ of a _Cow_, the Inference would
not hold from thence to a _Woman_, the one being _Glanduliferous_, and
the other _Placentiferous_; since every one of these _Cotyledones_, or
_Uterine Glandules_, is in all respects a little _Placenta_, and all the
difference between them is in number, name, and magnitude. Why
_Ruminants_ differ in this Particular from other _Viviparous_ Animals,
is beside the Subject of our present Enquiry. But the great Flux of
Blood, which constantly follows upon drawing the _Placenta_ from Women
(which is frequently so great as to cost them their Lives) is as plain a
demonstration to Reason of the _Continuity_ of the Vessels, as Mr.
_Cowper_'s Experiments is to the Eye.

I have heard it objected by very Learned Men, that if there were such a
_Continuity_ of Vessels, and such _Transfusion_ of Blood, the _Fœtus_
must necessarily perish through loss of Blood, upon the separation of
the _Placenta_ from the _Uterus_; but that, on the contrary, no visible
Flux of Blood does follow while the _Fœtus_ continues wrapt in the
Membrane, in which Condition it may be kept alive some Hours. To this it
may be answer'd, that the Circulation in the _Fœtus_, being deriv'd
from the Mother, may be suppos'd wholly to cease upon the cutting off
the Communication between them, till it is again renew'd more forcibly
by _Respiration_. But if we allow the motion already impress'd upon the
Blood to be sufficient to keep it going a little while; yet it must
needs be so exceeding languid, that the meer resistance of the External
Air must be more than enough to hinder any Efflux of Blood from a
_Fœtus_ before Respiration. How long Life may be preserv'd without an
_actual_ Circulation of the Blood, is a Question not of this place. But
we have been convinc'd by many and notorious Observations and
Experiments, that Life has been recover'd a long time after all tokens
of Respiration, Circulation, or even Life it self, have disappear'd; so
that we can't think the first Solution either impossible or improbable.

I expect to be told, that in the early Days of _Gestation_ in
_Viviparous_ Animals, there is no _Placenta_, or any Adhesion of the
_Umbilical_ Vessels to any part of the _Mother_, and consequently no
such _Transfusion_; and that in _Oviparous_ there is no _continuity_, or
_communication_ of Vessels of any kind, during the whole time of
_Incubation_.

But these Objections carry neither the Weight nor Difficulty along with
them, that they may be suppos'd to do; for in those Days there is
neither _Blood_ or _Blood-Vessels_, and consequently there can be no
_Circulation_ of the _Blood_; and the _Embryo_, of what Species soever,
is no more than a _Vegetable_ at that time; nor does the _Fœtus_ of
any _Viviparous_ Creature enjoy any _Circulation_, or shew any signs of
Animal Life, till after those Vessels, as well as others requisite to
the Circulation, are compleated.

It must be confess'd, that _Oviparous_ Animals are denied the benefit of
this Communication; but that want is sufficiently compensated by a
peculiar Mechanism, which directly answers the ends of _Respiration_,
and the _pressure_ of the _Atmosphere_ upon the _Fœtus_. There is at
the _obtuse_ end of an Egg a small Cavity fill'd with Air, which is the
succedaneous Instrument to the _Respiratory_ Organs. For as soon as the
Contents begin to be warm'd by the _Incubation_ of the Hen, or _any
analogous_ Heat of _Furnace_ or _Dunghill_, the several Humours of the
Egg require a _fermentative_ motion, and the _Air_ contain'd in the
_Cavity_ or _Vesicle_, at the _obtuse_ end of the Egg, is rarefied, and
the Vesicle extended and enlarg'd, and consequently the other Contents
are comprest; to which the _fermentative_ motion naturally resists. But
both Bodies being as well _compressible_ as _dilatable_, and both having
an _expansive_ motion imprest upon them by _Incubation_, the Compression
and Renitency will be mutual, but varied in degree, according as either,
through the variation of Circumstances, shall prevail. By this means, an
Alternation of Compression and Dilatation will be produc'd in both,
answering the _respiratory_ motion, by which a motion will be
communicated, which, as soon as the Organs by which it should be
regulated are compleated, will in the Body of the _Pullus_ be _regular_
and _circulatory_.

_Fabricius_ ab _Aquapendente_, and after him, our Great Dr. _Harvey_,
have assign'd divers Uses to this Cavity or Air Vesicle, the
Extravagance of which have perhaps deterr'd others from enquiring so
much into the Use, as the Importance of it requir'd. But though I can't
agree to that _Perspiration_, _Refrigeration_, and _Respiration_, which
they make it the Instrument of; yet perhaps the _Air_, that was inclos'd
in that _Cavity_, may through the Augmentation of the Body of the
_Pullus_, and its own _Rarefaction_ (which is at last so great as to
occupy half the Shell) break the _Membrane_, which separated it from the
_Pullus_, and thereby give so much _Respiration_ as to form the
_chirping Voice_, which is often heard before the breaking of the Shell,
and with it give an addition of Strength to enable it to break the
Shell. But how it should respire sooner, is to me inconceivable.

There are many Problems of great seeming Difficulty, the Solutions of
which flow naturally from what has been laid down here: But intending to
prosecute this Subject farther, and to treat of the Impediments of
Respiration, and the Consequences of Respiration obstructed or
intermitted, I shall reserve them for that Opportunity, and content my
self here to attempt the _Harveyan_ Problem only, which has given
abundance of Authors so much perplexity.

That incomparable Philosopher enquires, _Why a _Fœtus_, taken out of
the _Uterus_ with the _Membranes_ intire, shall live in Water some Hours
without communication with the _External Air_; whereas if it be taken
out and suffer'd once to breath, it can't afterwards survive a Moment
without the benefit of _Respiration_._

Granting the Fact to be as he has deliver'd it, which yet is not so in
all Cases, the main Difficulty is grounded on a Mistake, which from the
stating of the Question I find this Great Man to have slipt into. For he
thinks, that a _Fœtus_ is sooner suffocated after having once
breath'd, than if it had not breath'd at all, and that by breathing it
had contracted something which render'd it more perishable. _Idem tamen
secundis exutus, (_says he_) si semel _aerem_ intra _Pulmones_
attraxerit, postea ne momentum quidem temporis absque eo durare possit,
sed confestim moriatur._ And presently after, _Siquidem constat,
fœtum, postquam _eum semel_ hauserit, _citius_ suffocari; quam cum ab
_illo prorsus_ accebatur._ The Doctor observing a _Fœtus_ to live
longer without Respiration, and to dispence better with the want of Air
while included in the Membranes intire, than it cou'd afterwards; infers
thence, that the Air does in the first Act of Inspiration impress upon
the Lungs some quality, which renders it ever after more indispensably
necessary. But allowing his Observation, I must yet deny his Inference
to be good: For deprive a _Fœtus_ of means of respiring, and then
take it out of the Membranes, and it shall be as soon suffocated, as if
it had respired before. This proves, that this necessity of intercourse
with the Air, by way of the Lungs, is not the Offspring, but the Parent
of Respiration, and that, that Learned Man was drawn into a Fallacy of
_Non causa pro causa_.

The Reason of this Necessity is the pressure of the External Air upon
the Surface of the Body, from which it was defended by the Interposition
of the Membranes, and the Humours contain'd, which are not so
compressible as the Body of the _Fœtus_ it self. So soon therefore as
the _Fœtus_ is excluded, and expos'd to the immediate contact of the
ambient Atmosphere, the Vessels and all the Cavities of the Body must
necessarily be so compress'd, that the Fluids can't have room for
motion, and consequently the _Fœtus_ could have no Life, if Nature
had not contriv'd by the motion of the _Thorax_ to remove and admit that
pressure alternately, and thereby to impress a motion on the Fluids,
which is the Spring of Life. But this motion of the _Thorax_ being any
way suppress'd, the equal pressure of the Atmosphere on all parts,
occasions a total Cessation of motion, which is Death.

I shall prosecute this Subject no farther now, nor trouble the Reader
with any Apology, for dissenting from those Great Men herein named;
because, I hope, I have done it with Modesty, and all the Respect due to
so great Authorities, and have assign'd nothing which is not Matter of
Fact uncontroverted, or deduc'd from it by plain Mechanical Necessity.




 _Some Thoughts and Experiments concerning _Vegetation_. By _John
   Woodward_, M. D. of the College of Physicians, and R. S. and
   Professor of Physick in _Gresham College_._


The _Ancients_ generally intitled the _Earth_ to the Production of the
_Animals_, _Vegetables_, and _other Bodies_ upon and about it; and that
for that Reason 'twas, that they gave it so frequently the Epithets of
_Parent_ and _Mother_[1]. They were of opinion, that it furnished forth
the _Matter_ whereof _those Bodies_ consist; and receiv'd it all back
again at their Dissolution for the Composure of _others_. Even those who
asserted _four Elements_, supposed that the _Earth_ was the _Matter_
that _constituted_ those Bodies; and that _Water_ and the _rest_, serv'd
only for the _Conveyance_ and _Distribution_ of that _Matter_, in order
to the _forming_ and _composition_ of them. 'Tis true, _Thales_, a
Philosopher of the first Rank in those early Ages, has been thought to
have Sentiments very different from these; but that without just
Grounds, as I think I have sufficiently prov'd in another Paper, which I
am ready to produce.

But though _Antiquity_ thus gave its _Vote_ for _Terrestrial Matter_,
several of the _Moderns_, and some of very _great Name_ too, both _here_
and _abroad_, have gone quite counter, and given _theirs_ in behalf of
_Water_. The _Dignity_ of the _Persons_ that have espoused it, as well
as their _Numbers_, renders this Doctrine very considerable, and well
worth our enquiring into. The great Restorer of _Philosophy_ in this
last Age, my Lord _Bacon_, is of Opinion, _That for Nourishment of
_Vegetables_, the Water is almost all in all; and that the Earth doth
but keep the Plant upright, and save it from over-heat, and
over-cold[2]._ Others there are who are still more express; and assert
Water to be the only Principle or Ingredient of all Natural Things. They
suppose that, I cannot tell by what Process of Nature, Water is
_transmuted_ into _Stones_, into _Plants_, and in brief, all other
Substances whatever. _Helmont_,[3] particularly, and his _Followers_,
are very positive in this; and offer some _Experiments_ to render it
credible. Nay, a very _Extraordinary Person_ of our own _Nation_[4]
tries those _Experiments_ over again; and discovers a great Propensity
to the same Thoughts and Opinion they had; declaring for this
_Transmutation of Water_ into _Plants_ and _other Bodies_, though with
great Modesty and Deference, which was his usual manner.

The _Experiments_ they insist upon are chiefly _two_; the _first_ is,
that _Mint_, and several _other_ _Plants_ prosper and thrive very
greatly in _Water_. The _other_ is this; they take a certain quantity of
_Earth_, and _bake_ it in an _Oven_; then they weigh it, and put it into
an _Earthen Pot_. Having well water'd this _Earth_, they make choice of
some fit _Plant_, which, being first carefully _weigh'd_, they _set_ in
it. There they let it grow, continuing to _water it_ for some time, till
'tis much advanced in _bigness_: Then they take it up; and though the
_Bulk_ and _Weight_ of the _Plant_ be much greater than when _first
set_, yet upon _baking_ the _Earth_, and _weighing_ it, as at first,
they find it little or not at all diminished in _weight_; and therefore
conclude, 'tis not the _Earth_ but _Water_, that nourishes and is
_turn'd_ into the Substance of the _Plant_.

I must confess I cannot see how _this Experiment_ can ever be made with
the _nicety_ and _justness_ that is requisite, in order to _build_ upon
it so _much_ as _these Gentlemen_ do. 'Tis hard to weigh _Earth_ in that
_quantity_, or _Plants_ of the _size_ of those they mention, with any
great _exactness_; or to _bake_ the Earth with that _accuracy_, as to
reduce it _twice_ to just the _same Driness_. But I may wave all this;
for though the _Experiment_ be never so easily practicable, and all the
Accidents of it exactly as they set forth, yet nothing like what they
_infer_ can possibly be concluded from it; unless _Water_, which they so
plentifully bestow upon the _Plant_ in _this Experiment_, be _pure_,
_homogeneous_, and not charged with any _terrestrial Mixture_; for if it
be, the Plant after all may owe its _Growth_ and _Encrease_ intirely to
_that_.

Some _Waters_ are indeed so very _clear_ and _transparent_, that one
would not easily suspect any _terrestrial Matter_ were latent in them;
but they may be _highly saturated_ with such _Matter_, though the Eye be
not presently able to descry or discern it. 'Tis true, _Earth_ is an
_Opake Body_; but it may be so far dissolved, reduced to so extreme
small Particles, and these so _diffused_ through the _watry Mass_, as
not sensibly to impede _Vision_, or render the Water much the less
_diaphanous_. _Silver_ is an _Opake_, and indeed a very _dense Body_;
and yet, if perfectly _dissolved_ in _Spirit_ of _Nitre_, or _Aqua
Fortis_, that is _rectified_ and thorowly _fine_, it does not _darken_
the _Menstruum_, or render it less _pellucid_ than before[5]. And other
Instances there are, that oftentimes _great quantities_ of _Opake
Matter_ are sustain'd in _Fluids_, without considerably striking the
_Eye_, or being perceiv'd by it. So that were there _Water_ any where
found so _pure_, that the quickest Eye could discover in it no
_terrestrial Intermixture_; that would be far short of a _Proof_, that
in reality there was _none_.

But after all, even the _clearest Water_ is very far from being _pure_
and wholly _defecate_, in any part of the World that I can learn. For
ours here, I have had an Opportunity of examining it over a good part of
_England_; and cannot say I ever met with any, that, however fresh and
newly taken out of the Spring, did not exhibit, even to the naked Eye,
great numbers of exceeding small terrestrial Particles disseminated
through all parts of it. Thicker and crasser Water exhibits them in
still greater Plenty.

These are of two general kinds. The one a vegetable terrestrial Matter,
consisting of very different Corpuscles; some whereof are proper for the
formation and increment of one sort of Plant, and some of another; as
also some for the Nourishment of one part of the same Plant, and some of
another. The other kind of Particles sustain'd in Water are of a Mineral
Nature. These likewise are of different sorts. In some Springs we find
common Salt, in others _Vitriol_, in others _Alum_, _Nitre_, _Sparr_,
_Ochre_, &c. nay, frequently several of these, or other Minerals, all in
the same Spring; the Water as it drains and passes thorough the _Strata_
of Stone, Earth, and the like, taking up and bearing along such loose
Mineral Corpuscles, as it meets with in the Pores and Interstices of
those _Strata_, and bringing them on with it quite to the Spring. All
Water whatever is much charg'd with the Vegetable Matter, this being
fine, light, and easily moveable. For the Mineral, the Water of Springs
contains more of it than that of Rivers, especially when at distance
from their Sources; and that of Rivers more than the Water that falls in
Rain. This I have learn'd from several Trials, which I must not give
Account of here; my Drift in this place being only to evince the
Existence of Terrestrial Matter in Water.

Any one who desires farther Satisfaction in this, may easily obtain it,
if he only put Water into a clear Glass Viol, stopping it close, to keep
Dust and other exterior Matter out, and letting it stand, without
stirring it for some Days: He will then find a considerable Quantity of
terrestrial Matter in the Water, however pure and free it might appear
when first put into the Viol. He will in a very short time observe, as I
have frequently done, the Corpuscles that were at first, while the Water
was agitated and kept in motion, separate, and hardly visible[6], by
degrees, as the Water permits, by its becoming more still and at rest,
assembling and combining together; by that means forming somewhat larger
and more conspicuous _Moleculæ_. Afterwards he may behold these joining
and fixing each to other, by that means forming large thin Masses,
appearing like _Nubeculæ_, or Clouds in the Water; which grow more thick
and opake, by the continual appulse and accretion of fresh Matter. If
the said Matter be chiefly of the Vegetable kind, it will be sustain'd
in the Water; and discover at length a green Colour, becoming still more
and more of that Colour, I mean an higher and more saturate Green, as
the Matter thickens and encreases. That this _Matter_ inclines so much
to that _Colour_, is the less strange, since we see so large a share of
it, when constituting Vegetables wearing the same Colour in them. But if
there be any considerable quantity of meer Mineral Matter in the Water,
this, being of a greater specifick Gravity than the Vegetable, as the
Particles of it unite and combine in such Number, till they form a
_Molecula_, the Impetus of whose Gravity surpasses that of the
Resistance of the Water, subsides a great deal of it to the _bottom_.
Nor does it only fall down it self, but frequently entangling with the
_Vegetable Nubeculæ_, forces them down along with it.

The Reason why Bodies, when dissolved and reduced to extreme small
Parts, are sustain'd in Liquors that are of less specifick Gravity than
those Bodies are, hath been pointed at by a late ingenious Member of
this Society[7]. He is indeed far from having adjusted all the _Momenta_
of this Affair; however it must be admitted, that, in the _dividing_ or
_solution_ of Bodies, their Surfaces do not decrease in the same
Proportion that their Bulk does. Now the Gravity of a Body, which is the
Cause of its sinking or tendency downwards, is commensurate to its Bulk;
but the resistance that the Liquor makes, is proportion'd, not to the
Bulk, but to the Extent of the Surface of the Body immersed in it.
Whence 'tis plain, a Body may be so far divided, that its Parts may be
sustain'd in a Fluid, whose specifick Gravity is less than that of the
said Body. Nay, 'tis Matter of Fact, that they frequently are so; and we
daily see _Menstrua_ supporting the Parts of _Metals_, and other Bodies,
that are of six, ten, nay, almost twenty times the specifick Gravity of
those _Menstrua_. And as the Parts of Bodies when divided, are thus
supported in a Fluid; so when they occur and unite again, they must sink
of course, and fall to the Bottom.

Upon the whole, 'tis palpable and beyond reasonable Contest, that
_Water_ contains in it a very considerable Quantity of terrestrial
Matter. Now the Question is, to which of these, the Water, or the
Earthly Matter sustain'd in it, Vegetables owe their Growth and Augment:
For deciding of which, I conceive the following Experiments may afford
some Light; and I can safely say, they were made with due Care and
Exactness.


_Anno_ 1691.

I chose several _Glass Vials_, that were all, as near as possible, of
the same shape and bigness. After I had put what Water I thought fit
into every one of them, and taken an Account of the weight of it, I
strain'd and ty'd over the Orifice of each Vial, a Piece of Parchment,
having an hole in the middle of it, large enough to admit the Stem of
the Plant I design'd to set in the Vial, without confining or
streightning it, so as to impede its _Growth_. My Intention in this, was
to prevent the inclosed Water from evaporating, or ascending any other
way than only through the Plant to be set therein. Then I made choice of
several Sprigs of Mint, and other Plants, that were, as near as I could
possibly judge, alike fresh, sound, and lively. Having taken the weight
of each, I placed it in a Vial, order'd as above; and as the Plant
imbib'd and drew off the Water, I took care to add more of the same from
time to time, keeping an Account of the weight of all I added. Each of
the Glasses were, for better distinction, and the more easie keeping a
Register of all Circumstances, noted with a different Mark or _Letter_,
_A_, _B_, _C_, _&c._ and all set in a Row in the same Window, in such
manner that all might partake alike of _Air_, _Light_, and _Sun_. Thus
they continued from _July_ the Twentieth, to _October_ the Fifth, which
was just Seventy Seven Days. Then I took them out, weigh'd the Water in
each Vial, and the Plant likewise, adding to its weight that of all the
Leaves that had fallen off during the time it stood thus. And Lastly, I
computed how much each Plant had gain'd; and how much Water was spent
upon it. The Particulars are as follow.

 (A.) _Common Spear-Mint_, set in _Spring-Water_. The Planted weighed
 when put in, _July_ 20. just 27 Grains; when taken forth, _October_ 5.
 42 Grains: So that in this space of 77 Days, it had gained in weight
 15 Grains.

 The whole Quantity of Water expended, during these 77 Days, amounted to
 2558 Grains. Consequently the weight of the Water taken up, was
 170-8/15 times as much as the Plant had got in weight.

 (B.) _Common Spear-Mint_, _Rain-Water_. The Mint weigh'd, when put in,
 Gr. 28¼; when taken out Gr. 45¾, having gain'd in 77 Days Gr.
 17½.

 The Dispendium of the Water Gr. 3004, which was 171-22/35 times as much
 as the Plant had received in weight.

 (C.) _Common Spear-Mint_, _Thames-water_. The Plant when put in, Gr.
 28, when taken forth, Gr. 54. So that in 77 Days it had gained Gr. 26.

 The Water expended, amounted to Gr. 2493. which was 95-23/26 times as
 much as the additional weight of the Mint.

 (D.) _Common Solanum_, or _Night-shade_: _Spring-water_. The Plant
 weigh'd, when put in, Gr. 49; when taken out, 106; having gain'd in 77
 Days 57 Gr.

 The Water expended during the said time, was 3708 Gr. which was 65-3/57
 times as much as the Augment of the Plant.

 _This Specimen_ had several _Buds_ upon it, when first set in the
 Water. _These_ in some Days became fair _Flowers_, which were at length
 succeeded by _Berries_.

 (E.) _Lathyris seu Cataputia Gerh._ _Spring-Water._ It weigh'd, when
 put in, Gr. 98. when taken forth, Gr. 101½. The additional weight
 for the whole 77 Days, being but Gr. 3½.

 The Quantity of Water spent upon it during that time, Gr. 2501. which
 is 714-4/7 times as much as the Plant was augmented.

  _Several _other Plants_ were try'd, that did _not thrive_ in _Water_,
  or succeed any better than the _Cataputia_ foregoing:_ _But 'tis
  besides my purpose to give a particular _Account_ of them here._

(F, G.) _These Two Vials_ were fill'd, the former (F) with _Rain_, the
other with _Spring-water_, at the same time as those above-mention'd
were; and stood as long as they did. But they had neither of them any
Plant; my Design in these being only to inform my self, whether any
Water exhaled out of the Glasses, otherwise than _thorow_ the Bodies of
the Plants. The Orifices of these two Glasses were cover'd with
Parchment; each piece of it being perforated with an hole of the same
bigness with those of the Vials above. In this I suspended a bit of
Stick, about the thickness of the Stem of one of the aforesaid Plants,
but not reaching down to the Surface of the included Water. I put them
in thus, that the Water in these might not have more Scope to evaporate
than that in the other Vials. Thus they stood the whole 77 Days in the
same Window with the rest; when, upon Examination, I found none of the
Water in these wasted or gone off. Tho' I observed both in these, and
the rest, especially after hot Weather, small Drops of Water, not unlike
Dew, adhering to the Insides of the Glasses, that Part of them, I mean,
that was above the Surface of the enclosed Water.

The Water in these two Glasses that had no Plants in them, at the end of
the Experiment, exhibited a larger Quantity of Terrestrial Matter than
that in any of those that had the Plants in them did. The Sediment at
the bottom of the Vials was greater; and the _Nubeculæ_, diffus'd
through the Body of the Water, thicker. And of that which was in the
others, some of it proceeded from certain small Leaves that had fallen
from that part of the Stems of the Plants that was within the Water,
wherein they rotted and dissolved. The Terrestrial Matter in the
Rain-water was finer than that in the Spring-water.


_Anno 1692._

The Glasses made use of in this, were of the same sort with those in the
former Experiment; and cover'd over with Parchment in like manner. The
Plants here were all _Spear-Mint_; the most kindly, fresh, sprightly
Shoots I could chuse. The Water, and the Plants were weigh'd as above;
and the Vials set in a Line, in a South Window: where they stood from
_June_ the 2d to _July_ 28. which was just 56 Days.

 (H.) _Hyde-Park Conduit Water_, alone. The _Mint_ weighed, when put in,
 127 Gr. when taken out, 255 Gr. The whole Quantity of Water expended
 upon this Plant, amounted to 14190 Gr.

 This was all along a very kindly Plant; and had run up to above two
 Foot in height. It had shot but one considerable collateral Branch; but
 had sent forth many and long Roots, from which sprung very numerous,
 though small and short, lesser Fibres. These lesser Roots came out of
 the larger on two opposite sides, for the most part; so that each Root,
 with its _Fibrillæ_, appear'd not unlike a small Feather. To these
 _Fibrillæ_ adher'd pretty must Terrestrial Matter. In the Water, which
 was at last thick and turbid, was a green Substance, resembling a fine
 thin _Conserva_.

 (I.) The _same Water_, alone. The _Mint_ weigh'd, when put in, 110 Gr.
 when taken out, 249. Water expended, 13140 Gr.

 This Plant was as kindly as the former, but had shot no collateral
 Branches. Its Roots, the Water, and the green Substance, all much as in
 the former.

 (K.) _Hyde-Park Conduit-water_, in which was dissolved an Ounce and
 half of _Common Garden-earth_. The _Mint_ weigh'd, when put in, 76 Gr.
 when taken out, 244 Gr. Water expended, Gr. 10731.

 This Plant, though it had the Misfortune to be annoy'd with many small
 Insects that hapn'd to fix upon it; yet had shot very considerable
 collateral Branches; and at least as many Roots as either that in H or
 I; which had a much greater Quantity of Terrestrial Matter adhering to
 the Extremities of them. The same green Substance here, that was in the
 two preceding.

 (L.) _Hyde-Park Water_, with the same Quantity of _Garden-mould_ as in
 the former. The _Mint_ weigh'd, when put in, 92 Gr. when taken out, 376
 Gr. The Water expended 14950 Gr.

 This Plant was far more flourishing than any of the precedent; had
 several very considerable collateral Branches, and very numerous Roots,
 to which Terrestrial Matter adhered very copiously.

 The Earth in both these Glasses was very sensibly and considerably
 wasted, and less than when first put in. The same sort of green
 Substance here as in those above.

 (M.) _Hyde-Park Water_, distilled off with a gentle Still. The _Mint_
 weigh'd, when put in, 114 Gr. when taken out 155. The Water expended,
 8803 Gr.

 This Plant was pretty kindly; had two small collateral Branches, and
 several Roots, though not so many as that in H or I, but as much
 Terrestrial Matter adhering to them as those had. The Water was pretty
 thick; having very numerous small Terrestrial Particles swimming in it,
 and some Sediment at the bottom of the Glass. This Glass had none of
 the green Matter above mentioned, in it.

 (N.) The Residue of the Water, which remain'd in the _Still_ after that
 in M, was distill'd off. It was very turbid, and as high-colour'd
 (reddish) as ordinary Beer. The _Mint_ weigh'd, when put in, 81 Gr.
 when taken out, 175 Gr. Water expended, 4344 Gr. This Plant was very
 lively; and had sent out six collateral Branches, and several Roots.

(O.) _Hyde-Park Conduit-water_, in which was dissolved a Drachm of
Nitre. The Mint set in this suddenly began to wither and decay; and died
in a few Days: As likewise did two more Sprigs, that were set in it,
successively. In another Glass I dissolv'd an Ounce of good
Garden-mould, and a Drachm of Nitre, and in a third, half an Ounce of
Wood ashes, and a Drachm of Nitre; but the Plants in these succeeded no
better than in the former. In other Glasses I dissolved several other
sorts of Earths, Clays, Marles, and variety of Manures, _&c._ I set Mint
in distill'd Mint-water; and other Experiments I made, of several kinds,
in order to get Light and Information, what hastened or retarded,
promoted or impeded Vegetation; but these do not belong to the Head I am
now upon.

(P.) _Hyde-Park Conduit-water._ In this I fix'd a Glass-Tube about ten
Inches long, the Bore about one sixth of an Inch in Diameter, fill'd
with very fine and white Sand, which I kept from falling down out of the
Tube into the Vial, by tying a thin piece of Silk over that end of the
Tube that was downwards. Upon Immersion of the lower end of it into the
Water, this by little and little ascended quite to the upper Orifice of
the Tube. And yet, in all the fifty six Days which it stood thus, a very
inconsiderable Quantity of Water had gone off, _viz._ scarce twenty
Grains; though the Sand continued moist up to the top till the very
last. The Water had imparted a green Tincture to the Sand, quite to the
very top of the Tube. And, in the Vial, it had precipitated a greenish
Sediment, mix'd with black. To the bottom and sides of the Tube, as far
as 'twas immers'd in the Water, adher'd pretty much of the green
Substance describ'd above. Other like Tubes I fill'd with Cotton, Lint,
Pith of Elder, and several other porous Vegetable Substances; setting
some of them in clear Water; others in Water tinged with Saffron,
Cochinele, _&c._ And several other Trials were made, in order to give a
mechanical Representation of the motion and distribution of the Juices
in Plants; and of some other _Phænomena_ observable in Vegetation, which
I shall not give the Particulars of here, as being not of use to my
present design.

(Q, R, S, _&c._) Several Plants set in Vials, ordered in like manner as
those above, in _October_, and the following colder Months. These throve
not near so much; nor did the Water ascend in nigh the quantity it did
in the better Seasons, in which the before recited Trials were made.


_Some Reflections upon the foregoing Experiments._

1. _In Plants of the same kind, the less they are in Bulk, the smaller
the Quantity of the fluid Mass, in which they are set, is drawn off; the
Dispendium of it, where the Mass is of equal thickness, being pretty
nearly proportion'd to the Bulk, of the Plant._ Thus that in the Glass
mark'd A, which weigh'd only 27 Grains, drew off but 2558 Grains of the
Fluid; and that in B, which weigh'd only 28¼, took up but 3004
Grains; whereas that in H, which weigh'd 127 Grains, spent 14190 Grains
of the Liquid Mass.

The Water seems to ascend up the _Vessels_ of Plants, in much the same
manner as up a Filtre; and 'tis no great wonder that a larger Filtre
should draw off more Water than a lesser; or that a Plant that has more
and larger Vessels, should take up a greater share of the Fluid in which
it is set, than one that has fewer and smaller ones can. Nor do I note
this as a thing very considerable in it self, but chiefly in regard to
what I am about to offer beneath; and that it may be seen that, in my
other Collations of Things, I made due Allowance for this Difference.

2. _The much greatest part of the fluid Mass, that is thus drawn off and
convey'd into the Plants, does not settle or abide there; but passes
through the pores of them, and exhales up into the Atmosphere._ That the
Water in these Experiments ascended only through the Vessel of the
Plants, is certain. The _Glasses_ F and G, that had no Plants in them,
though disposed of in like manner as the rest, remain'd at the End of
the Experiment, as at first; and none of the Water was gone off. And
that the greatest part of it flies off from the Plant into the
Atmosphere, is as certain. The least Proportion of the Water expended,
was to the Augment of the Plant, as 46 or 50 to 1. And in some the
weight of the Water drawn off, was 100, 200, nay, in one above 700 times
as much as the Plant had received of Addition.

This so continual an Emission and Detachment of Water, in so great
Plenty from the Parts of Plants, affords us a manifest Reason why
Countries that abound with Trees, and the larger Vegetables especially,
should be very obnoxious to Damps, great Humidity in the Air, and more
frequent Rains, than others that are more open and free. The great
Moisture in the Air, was a mighty inconvenience and annoyance to those
who first settled in _America_; which at that time was much overgrown
with Woods and Groves. But as these were burnt and destroy'd, to make
way for Habitation and Culture of the Earth, the Air mended and clear'd
up apace, changing into a Temper much more dry and serene than before.

Nor does this Humidity go off pure and alone; but usually bears forth
with it many Parts of the same Nature with those whereof the Plant,
through which it passes, consists. The _Crasser_ indeed are not so
easily born up into the Atmosphere; but are usually deposited on the
Surface of the Flowers, Leaves, and other Parts of the Plants: Hence
comes our Manna's, our Honeys, and other Gummous Exsudations of
Vegetables. But the finer and lighter Parts are with greater ease sent
up into the Atmosphere. Thence they are conveyed to our Organs of Smell,
by the Air we draw in Respiration; and are pleasant or offensive,
beneficent or injurious to us, according to the Nature of the Plants
from whence they arise. And since these owe their Rise to the Water,
that ascends out of the Earth through the Bodies of Plants, we cannot be
far to seek for the Cause why they are more numerous in the Air, and we
find a greater quantity of Odors exhaling from Vegetables, in warm,
humid Seasons, than in any other whatever.

3. _A great part of the Terrestrial Matter that is mix'd with the Water,
ascends up into the Plant as well as the Water._ There was much more
Terrestrial Matter at the end of the Experiment, in the Water of the
Glasses F and G, that had no Plants in them, than in those that had
Plants. The _Garden-mould_ dissolved in the Glasses K and L, was
considerably diminished, and carried off. Nay, the Terrestrial and
Vegetable Matter was born up in the Tubes fill'd with Sand, Cotton,
_&c._ in that Quantity, as to be evident even to Sense. And the Bodies
in the Cavities of the other Tubes, that had their lower Ends immers'd
in Water, wherein Saffron, Cochinele, _&c._ had been infused, were
tinged with Yellow, Purple, _&c._

If I may be permitted to look abroad a while, towards our Shores and
Parts within the Verge of the Sea, these will present us with a large
Scene of Plants, that, along with the Vegetable, take up into them meer
mineral Matter also in great abundance. Such are our Sea-Purslains, the
several sorts of _Alga's_, of Sampires, and other marine Plants. These
contain common Sea-salt, which is all one with the _Fossil_, in such
plenty, as not only to be plainly distinguish'd on the Palate, but may
be drawn forth of them in considerable Quantity. Nay, there want not
those who affirm, there are Plants found that will yield _Nitre_, and
other mineral Salts; of which indeed I am not so far satisfied, that I
can depend on the Thing, and therefore give this only as an hint for
Enquiry.

To go on with the Vegetable Matter, how apt and how much disposed this,
being so very fine and light, is to attend Water in all its Motions, and
follow it into each of its Recesses, is manifest, not only from the
Instances above alledg'd, but many others. Percolate it withal the Care
imaginable: Filter it with never so many Filtrations, yet some
Terrestrial Matter will remain. 'Tis true, the Fluid will be thinner
every time than other, and more disingaged of the said Matter; but never
wholly free and clear. I have filtred Water thorough several wholly free
and clear Sheets of thick Paper; and, after that, through very close
fine Cloth twelve times doubled. Nay, I have done this over and over;
and yet a considerable quantity of this Matter discover'd it self in the
Water after all. Now if it thus pass Interstices, that are so very small
and fine along with the Water, 'tis the less strange it should attend it
in its passage through the Ducts and Vessels of Plants. 'Tis true,
filtering and distilling of Water intercepts and makes it quit some of
the Earthy Matter it was before impregnated withal: But then that which
continues with the Water after this, is fine and light; and such
consequently, as is in a peculiar manner fit for the Growth and
Nourishment of Vegetables. And this is the Case of Rain-water. The
Quantity of Terrestrial Matter it bears up into the Atmosphere, is not
great. But that which it does bear up, is mainly of that light kind of
Vegetable Matter; and that too perfectly dissolved, and reduced to
single Corpuscles, all fit to enter the Tubules and Vessels of Plants:
On which Account 'tis, that this Water is so very fertile and prolifick.

The Reason, why in this Proposition, I say, only a great part of the
Terrestrial Matter that is mix'd with the Water, ascends up with it into
the Plant, is, because all of it cannot. The Mineral Matter is a great
deal of it, not only gross and ponderous, but scabrous and inflexible;
and so not disposed to enter the Pores of the Roots. And a great many of
the simple Vegetable Particles by degrees unite, and form some of them
small Clods or _Moleculæ_; such as those mention'd in H, K, and L,
sticking to the Extremities of the Roots of those Plants. Others of them
intangle in a looser manner; and form the _Nubeculæ_, and green Bodies,
so commonly observ'd in stagnant Water. These, when thus conjoin'd, are
too big to enter the Pores, or ascend up the Vessels of Plants, which
singly they might have done. They who are conversant in Agriculture,
will easily subscribe to this. They are well aware that, be their Earth
never so rich, so good, and so fit for the production of Corn or other
Vegetables, little will come of it, unless the Parts of it be separated
and loose. 'Tis on this Account they bestow the Pains they do in Culture
of it, in Digging, Plowing, Harrowing, and Breaking of the Clodded Lumps
of Earth. 'Tis the same way that Sea-salt, Nitre, and other Salts,
promote Vegetation. I am sorry I cannot subscribe to the Opinion of
those Learned Gentlemen, who imagine Nitre to be essential to Plants;
and that nothing in the Vegetable Kingdom is transacted without it. By
all the Trials I have been able to make, the thing is quite otherwise;
and when contiguous to the Plant, it rather destroys than nourishes it.
But this Nitre and other Salts certainly do; they loosen the Earth, and
separate the concreted Parts of it; by that means fitting and disposing
them to be assumed by the Water, and carried up into the Seed or Plant,
for its Formation and Augment. There's no Man but must observe, how apt
all sorts of Salts are to be wrought upon by Moisture; how easily they
liquate and run with it; and when these are drawn off, and have deserted
the Lumps wherewith they were incorporated, those must moulder
immediately, and fall asunder of Course. The hardest Stone we meet with,
if it happen, as frequently it does, to have any sort of Salt intermix'd
with the Sand, of which it consists, upon being expos'd to an humid Air,
in a short time dissolves and crumbles all to pieces; and much more will
clodded Earth or Clay, which is not of near so compact and solid a
Constitution as Stone is. The same way likewise is Lime serviceable in
this Affair. The Husbandmen say of it, that it does not fatten, but only
mellows the Ground: By which they mean, that it does not contain any
thing in it self that is of the same Nature with the Vegetable Mould, or
afford any Matter fit for the Formation of Plants; but meerly softens
and relaxes the Earth; by that means rendering it more capable of
entering the Seeds and Vegetables set in it, in order to their
Nourishment, than otherwise it would have been. The Properties of Lime
are well known; and how apt 'tis to be put into Ferment and Commotion by
Water. Nor can such Commotion ever happen when Lime is mix'd with Earth,
however hard and clodded that may be, without opening and loosening of
it.

4. _The Plant is more or less nourish'd and augmented, in Proportion as
the Water, in which it stands, contains a greater or smaller Quantity of
proper terrestrial Matter in it._ The Truth of this Proportion is so
eminently discernable through the whole Process of these Trials, that I
think no doubt can be made of it. The _Mint_ in the Glass C, was of much
the same Bulk and Weight with those in A and B. But the Water, in which
that was, being River-water, which was apparently stored more copiously
with terrestrial Matter, than the Spring or Rain-water, wherein they
stood, were; it had thriven to almost double the Bulk that either of
them had, and with a less Expence of Water too. So likewise the Mint in
L, in whose Water was dissolved a small quantity of good Garden-mould,
though it had the disadvantage[8] to be less, when first set, than
either of the Mints in H or I, whose Water was the very same with this
in L, but had none of that Earth mix'd with it; yet, in a short time the
Plant not only overtook, but much out-strip'd those and at the end of
the Experiment was very considerably bigger and heavier than either of
them. In like manner the _Mint_ in N, though less at the beginning than
that in M, being set in that thick, turbid, feculent Water, that
remained behind, after that wherein M was placed, was still'd off, had
in fine more than double its original weight and bulk; and receiv'd
above twice the additional Encrease, than that in M, which stood in the
thinner distill'd Water, had done. And, which is not less considerable,
had not drawn off half the Quantity of Water that that had.

Why, in the beginning of this Article, I limit the Proportion of the
Augment of the Plant to the Quantity of proper Terrestrial Matter in the
Water, is, because all, even the Vegetable Matter, to say nothing of the
Mineral, is not proper for the Nourishment of every Plant. There may be,
and doubtless are, some Parts in different Species of Plants, that may
be much alike, and so owe their Supply to the same common Matter; but
'tis plain all cannot. And there are other Parts so differing, that 'tis
no ways credible they should be formed all out of the same sort of
Corpuscles. So far from it, that there want not good Indications, as we
shall see by and by, that every kind of Vegetable requires a peculiar
and specifick Matter for its Formation and Nourishment. Yea, each Part
of the same Vegetable does so; and there are very many and different
Ingredients go to the Composition of the same individual Plant. If
therefore the Soil, wherein any Vegetable or Seed is planted, contains
all or most of these ingredients, and those in due quantity, it will
grow and thrive there; otherwise 'twill not. If there be not as many
sorts of Corpuscles as are requisite for the Constitution of the main
and more essential Parts of the Plant, 'twill not prosper at all. If
there be these, and not in sufficient Plenty, 'twill starve, and never
arrive to its natural Stature: Or if there be any the less necessary and
essential Corpuscles wanting, there will be some failure in the Plant;
'twill be defective in Taste, in Smell, in Colour, or some other way.
But though a Tract of Land may happen not to contain Matter proper for
the Constitution of some one peculiar kind of Plant; yet it may for
several others, and those much differing among themselves. The
Vegetative Particles are commix'd and blended in the Earth, with all the
diversity and variety, as well as all the uncertainty, conceivable. I
have given some intimations of this elsewhere[9], and shall not repeat
them here, but hope in due time to put them into a much better Light
than that they there stand in.

It is not possible to imagine, how one uniform, homogeneous Matter,
having its Principles or Original Parts all of the same Substance,
Constitution, Magnitude, Figure, and Gravity, should ever constitute
Bodies so egregiously unlike, in all those respects, as Vegetables of
different kinds are; nay, even as the different Parts of the same
Vegetable. That one should carry a resinous, another a milky, a third a
yellow, a fourth a red Juice, in its Veins; one afford a fragrant,
another an offensive Smell; one be sweet to the Taste, another bitter,
acid, acerbe, austere, &c. that one should be nourishing, another
poisonous, one purging, another astringent: In brief, that there should
be that vast difference in them, in their several Constitutions, Makes,
Properties, and Effects, and yet all arise from the very same sort of
Matter, would be very strange. And, to note by the by, this Argument
makes equally strong against those, who suppose meer Water the Matter,
out of which all Bodies are form'd.

The _Cataputia_ in the Glass E, received but very little Encrease, only
three Grains and an half all the while it stood, though 2501 Grains of
Water were spent upon it. I will not say the Reason was, because that
Water did not contain in it Matter fit and proper for the Nourishment of
that peculiar and remarkable Plant. No, it may be the Water was not a
proper _Medium_ for it to grow in; and we know there are very many
Plants that will not thrive in it. Too much of that Liquor, in some
Plants, may probably hurry the Terrestrial Matter thorough their Vessels
too fast for them to arrest and lay hold of it. Be that as it will, 'tis
most certain there are peculiar Soils that suit particular Plants. In
_England_, Cherries are observ'd to succeed best in _Kent_; Apples in
_Herefordshire_; Saffron in _Cambridgeshire_; Wood in two or three of
our _Midland Counties_; and Teazles in _Somersetshire_. This is an
Observation that hath held in all Parts, and indeed in all Ages of the
World. The most ancient Writers of Husbandry[10] took notice of it; and
are not wanting in their Rules for making choice of Soils suited to the
Nature of each kind of Vegetable they thought valuable, or worth
propagating.

But, which is a further Proof of what I am here endeavouring to advance,
that Soil that is once proper and fit for the Production of some one
sort of Vegetable, does not ever continue to be so. No, in Tract of time
it loses that Property; but sooner in some Lands, and later in others:
This is what all who are conversant in these things know very well. If
Wheat, for Example, be sown upon a Tract of Land that is proper for that
Grain, the first Crop will succeed very well; and perhaps the second,
and the third, as long as the Ground is in Heart, as the Farmers speak;
but in a few Years 'twill produce no more, if sowed with that Corn: Some
other Grain indeed it may, as Barley. And after this has been sown so
often, that the Land can bring forth no more of the same, it may
afterwards yield good Oats; and, perhaps, Pease after them. At length
'twill become barren; the Vegetative Matter, that at first it abounded
withal, being educed forth of it by those successive Crops, and most of
it born off. Each sort of Grain takes forth that peculiar Matter that is
proper for its own Nourishment. First, the Wheat draws off those
Particles that suit the Body of that Plant; the rest lying all quiet and
undisturbed the while. And when the Earth has yielded up all them, those
that are proper for Barley, a different Grain, remain still behind, till
the successive Crops of that Corn fetch them forth too. And so the Oats
and Pease, in their Turn; till in fine all is carried off, and the Earth
in great measure drain'd of that sort of Matter.

After all which, that very Tract of Land may be brought to produce
another Series of the same Vegetables; but never till 'tis supplied with
a new Fund of Matter, of like sort with that it at first contain'd. This
Supply is made several ways: By the Grounds lying fallow for some time,
till the Rain has pour'd down a fresh Stock upon it: _Or_, by the
Tiller's Care in manuring of it. And for farther Evidence that this
Supply is in reality of like sort, we need only reflect a while upon
those Manures that are found by constant Experience best to promote
Vegetation, and the Fruitfulness of the Earth. These are chiefly either
parts of Vegetables, or of Animals; which indeed either derive their own
Nourishment immediately from Vegetable Bodies, or from other Animals
that do so. In particular, the Blood, Urine, and Excrements of Animals;
Shavings of Horns, and of Hoofs; Hair, Wool, Feathers; calcin'd Shells;
Lees of Wine, and of Beer; Ashes of all sorts of Vegetable Bodies;
Leaves, Straw, Roots, and Stubble, turn'd into the Earth by Plowing or
otherwise to rot and dissolve there: These, I say, are our best Manures;
and, being Vegetable Substances, when refunded back again into the
Earth, serve for the Formation of other like Bodies.

Not wholly to confine our Thoughts to the Fields, let us look a while
into our Gardens; where we shall meet with still further Confirmations
of the same thing. The Trees, Shrubs, and Herbs cultivated in these,
after they have continued in one Station, till they have derived thence
the greater part of the Matter fit for their Augment, will decay and
degenerate, unless either fresh Earth, or some fit Manure, be applied
unto them. 'Tis true, they may maintain themselves there for some time,
by sending forth Roots further and further to a great Extent all round,
to fetch in more remote Provision; but at last all will fail; and they
must either have a fresh Supply brought to them, or they themselves be
removed and transplanted to some Place better furnished with Matter for
their Subsistence. And accordingly _Gardiners_ observe, that Plants that
have stood a great while in a Place, have longer Roots than usual; part
of which they cut off, when they transplant them to a fresh Soil, as now
not of any further use to them. All these Instances, to pass over a
great many others that might be alledg'd, point forth a particular
Terrestrial Matter, and not Water, for the Subject to which Plants owe
their Increase. Were it Water only, there would be no need of Manures;
or of transplanting them from place to place. The Rain falls in all
Places alike; in this Field and in that indifferently; in one side of an
Orchard or Garden, as well as another. Nor could there be any Reason,
why a Tract of Land should yield Wheat one Year, and not the next; since
the Rain showers down alike in each. But I am sensible I have carried on
this Article to too great a length; which yet on so ample and extensive
a Subject, 'twas not easie to avoid.

5. _Vegetables are not form'd of Water; but of a certain peculiar
Terrestrial Matter._ It hath been shewn, that there is a considerable
Quantity of this Matter contain'd both in Rain, Spring, and River-water:
That the much greatest part of the fluid Mass that ascends up into
Plants, does not settle or abide there, but passes through the Pores of
them, and _exhales_ up into the Atmosphere; That a great part of the
Terrestrial Matter, mix'd with the Water, passes up into the Plant along
with it; and that the Plant is more or less augmented in proportion, as
the Water contains a greater or smaller Quantity of that Matter. From
all which we may very reasonably infer, that _Earth, and not Water, is
the Matter that constitutes Vegetables_. The Plant in E, drew up into it
2501 Grains of the fluid Mass; and yet had received but Grains 3 and a
half of Increase from all that. The Mint in L, though it had at first
the disadvantage to be much less than that in I; yet being set in Water
wherewith Earth was plentifully mix'd, and _that_ in I, _only in Water_
without any such additional Earth, it had vastly outgrown the other,
weighing at last 145 Grains more than that did, and so having gain'd
about twice as much as that had. In like manner that in K, though 'twas
a great deal less when put in than that in I, and also was impair'd and
offended by Insects; yet being planted in Water wherein Earth was
dissolved, whereas the Water in which it stood had none, it not only
over-took, but considerably surpass'd the other; weighing at last 29
Grains more than that in I, and yet had not expended so much Water as
that, by above 2400 Grains. The Plant in N, tho' at first a great deal
less than that in M; yet being set in the foul crass Water that was left
in the Still, after that, in which M was set, was drawn off, in
Conclusion had gain'd in weight above double what that in the finer and
thinner Water had. The Proportion of the Augment of that Plant that
throve most was, to the fluid Mass spent upon it, but as 1 to 46. In
others, 'twas but as 1 to 60, 100, 200; nay, in the _Cataputia_, 'twas
but as 1 to 714. The Mint in B took up 39 Grains of Water a-day, one day
with another; which was much more than the whole weight of the Plant
originally; and yet, with all this, it gain'd not one fourth of a Grain
a-day in weight. Nay, that in H took up 253 Grains a day of the Fluid:
Which was near twice as much as its original Weight, it weighing, when
first set in the Water, but 127 Grains. And, after all, the daily
Encrease of the Plant was no more than Grains 2-15/56.

6. _Spring, and Rain-water, contain pretty near an equal Charge of
Vegetable Matter_; _River-water more than either of them._ The Plants in
the Glasses A, B, and C, were at first of much the same size and weight.
At the End of the Experiment, the Mint in A had gain'd 15 Grains out of
2558 Grains of Spring-water; that in B, Grains 17 and an half, out of
3004 Grains of Rain-water; but that in C had got 26 Grains out of only
2493 Grains of River-water. I do not found this Proposition solely upon
these Trials; having made some more, which I do not relate here, that
agree well enough with these. So that the Proportions here deliver'd,
will hold for the main; but a strict and just Comparison is hardly to be
expected. So far from it, that I make no doubt, but the Water that falls
in Rain, at some times, contains a greater share of Terrestrial Matter
than that which falls at others. A more powerful and intense Heat must
needs hurry up a larger quantity of that Matter along with the humid
Vapours that form Rain, than one more feeble and remiss ever possibly
can. The Water of one Spring may flow forth with an higher Charge of
this Matter, than that of another; this depending partly upon the
quickness of the Ebullition of the Water, and partly upon the Quantity
of that Matter latent in the _Strata_, through which the Fluid passes,
and the greater or less laxity of those _Strata_. For the same Reason,
the Water of one River may abound with it more than that of another.
Nay, the same River, when much agitated, and in commotion, must bear up
more of it, than when it moves with less rapidity and violence. That
there is a great Quantity of this Matter in Rivers; and that it
contributes vastly to the ordinary Fertility of the Earth, we have an
illustrious Instance in the _Nile_, the _Ganges_, and other Rivers that
yearly overflow the neighbouring Plains. Their Banks shew the fairest
and largest Crops of any in the whole World. They are even loaded with
the multitude of their Productions; and those who have not seen them,
will hardly be induced to believe the mighty Returns those Tracts make
in comparison of others, that have not the Benefit of like Inundations.

7. _Water serves only for a Vehicle to the Terrestrial Matter, which
forms Vegetables; and does not it self make any addition unto them._
Where the proper Terrestrial Matter is wanting, the Plant is not
augmented, though never so much Water ascend into it. The _Cataputia_ in
E, took up more Water than the Mint in C, and yet had grown but very
little, having received only three Grains and an half of additional
weight; whereas the other had received no less than twenty six Grains.
The Mint in I, was planted in the same sort of Water as that in K, was;
only the latter had Earth dissolved in the Water; and yet that drew off
13140 Grains of the Water, gaining it self no more than 139 Grains in
weight; whereas the other took up but 10731 Grains of the Water, and was
augmented 168 Grains in weight. Consequently that spent 2409 Grains more
of the Water than this in K, did, and yet was not so much encreased in
weight as this by 29 Grains. The Mint in M, stood in the very same kind
of Water as that in N, did. But the Water in M, having much less
Terrestrial Matter in it than that in N had, the Plant bore up 8803
Grains of it, gaining it self only 41 Grains the while; whereas that in
N drew off no more than 4344 Grains, and yet was augmented 94 Grains. So
that it spent 4459 Grains of Water more than that did; and yet was not
it self so much increased in weight, as that was, by 53 Grains. This is
both a very fair, and a very conclusive Instance; on which Account 'tis
that I make oftner use of it. Indeed they are all so; and to add any
thing further on this Head, will not be needful.

'Tis evident therefore Water is not the Matter that composes Vegetable
Bodies. 'Tis only the Agent that conveys that Matter to them; that
introduces and distributes it to their several Parts for their
Nourishment. That Matter is sluggish and unactive, and would lie
eternally confin'd to its Beds of Earth, without ever advancing up into
Plants, did not Water, or some like Instrument, fetch it forth and carry
it unto them. That therefore there is that plentiful Provision, and vast
Abundance of it supplied to all Parts of the Earth, is a mark of a
natural Providence superintending over the Globe we inhabit; and
ordaining a due Dispensation of that Fluid, without the Ministry of
which the Noble Succession of Bodies we behold, _Animals_, _Vegetables_,
and _Minerals_, would be all at a stand[11]. But to keep to Plants, 'tis
manifest Water, as well on this, as upon the other Hypothesis, is
absolutely necessary in the Affair of Vegetation; and it will not
succeed without it: Which indeed gave occasion to the Opinion, that
Water it self nourished, and was changed into Vegetable Bodies. They
saw, though these were planted in a Soil never so rich, so happy, so
advantageous, nothing came of it unless there was Water too in a
considerable quantity. And it must be allow'd Vegetables will not come
on or prosper where that is wanting: But yet what those Gentlemen
inferr'd thence, was not, we see, well grounded.

This Fluid is capacitated for the Office here assign'd it several ways:
By the Figure of its Parts, which, as appears from many Experiments, is
exactly and mathematically Spherical; their Surfaces being perfectly
polite, and without any the least Inequalities. 'Tis evident, Corpuscles
of such a Figure are easily susceptible of Motion, yea, far above any
others whatever; and consequently the most capable of moving and
conveying other Matter, that is not so active and voluble. Then the
Intervals of Bodies of that Figure are, with respect to their Bulk, of
all others the largest; and so the most fitted to receive and entertain
foreign Matter in them. Besides, as far as the Trials hitherto made
inform us, the constituent Corpuscles of Water are, each singly
consider'd, absolutely solid; and do not yield to the greatest External
Force. This secures their Figure against any Alteration; and the
Intervals of the Corpuscles must be always alike. By the latter, 'twill
be ever disposed to receive Matter into it; and by the former, when once
received, to bear it on along with it. Water is further capacitated to
be a Vehicle to this Matter, by the tenuity and fineness of the
Corpuscles of which it consists. We hardly know any Fluid in all Nature,
except Fire, whose constituent Parts are so exceeding subtle and small
as those of Water are. They'll pass Pores and Interstices, that neither
Air nor any other Fluid will. This enables them to enter the finest
Tubes and Vessels of Plants, and to introduce the Terrestrial Matter,
conveying it to all Parts of them; whilst each, by means of Organs 'tis
endowed with for the Purpose, intercepts and assumes into it self such
Particles as are suitable to its own Nature, letting the rest pass on
through the common Ducts. Nay, we have almost every where Mechanical
Instances of much the same Tenor. 'Tis obvious to every one, how easily
and suddenly Humidity, or the Corpuscles of Water sustained in the Air,
pervade and insinuate themselves into Cords, however tightly twisted,
into Leather, Parchment, Vegetable Bodies, Wood, and the like. This it
is that fits them for _Hygrometers_; and to measure and determine the
different quantities of Moisture in the Air, in different Places and
Seasons. How freely Water passes and carries with it Terrestrial Matter,
through Filtres, Colatures, Distillations, _&c._ hath been intimated
already.

8. _Water is not capable of performing this Office to Plants, unless
assisted by a due Quantity of Heat; and this must concur, or Vegetation
will not succeed._ The Plants that were set in the Glasses Q, R, S,
_&c._ in _October_, and the following colder Months, had not near the
quantity of Water sent up into them, or so great an additional Encrease
by much, as those that were set in _June_, _July_, and the hotter. 'Tis
plain Water has no power of moving it self; or rising to the vast height
it does in the more tall and lofty Plants. So far from this, that it
does not appear from any Discovery yet made, that even its own Fluidity
consists in the intestine Motion of its Parts; whatever some, otherwise
very learned and knowing, Persons may have thought. There is no need of
any thing more, for solving all the _Phænomena_ of Fluidity, than such a
Figure and Disposition of the Parts, as Water has. Corpuscles of that
make, and that are all absolutely Spherical, must stand so very tickle
and nicely upon each other, as to be susceptible of every Impression;
and though not perpetually in Motion, yet must be ever ready and liable
to be put into it, by any the slightest Force imaginable. It is true,
the Parts of Fire or Heat are not capable of moving themselves any more
than those of Water; but they are more subtil, light, and active, than
those are, and so more easily put into Motion. In fine, 'tis evident and
matter of Fact, that Heat does operate upon, and move the Water, in
order to its carrying on the Work of Vegetation: But how 'tis agitated
it self, and where the Motion first begins, this is no fit Place to
enquire.

That the Concourse of Heat in this Work is really necessary, appears,
not only from the Experiments before us, but from all Nature; from our
Fields and Forests, our Gardens and our Orchards. We see in _Autumn_, as
the Sun's Power grows gradually less and less, so its Effects on Plants
is remitted, and their Vegetation slackens by little and little. Its
Failure is first discernible in Trees. These are raised highest above
the Earth; and require a more intense Heat to elevate the Water, charged
with their Nourishment, to the Tops and Extremities of them. So that for
want of fresh Support and Nutriment, they shed their Leaves, unless
secur'd by a very firm and hardy Constitution indeed, as our
_ever-Greens_ are. Next the Shrubs part with theirs; and then the Herbs
and lower Tribes; the Heat being at length not sufficient to supply even
these, though so near the Earth, the Fund of their Nourishment. As the
Heat returns the succeeding Spring, they all recruit again; and are
furnish'd with fresh Supplies and Verdure: But first, those which are
lowest and nearest the Earth, Herbs, and they that require a lesser
degree of Heat to raise the Water with its Earthy Charge into them: Then
the Shrubs and higher Vegetables in their Turns; and lastly, the Trees.
As the Heat increases, it grows too powerful, and hurries the Matter
with too great Rapidity thorough the finer and more tender Plants: These
therefore go off, and decay; and others that are more hardy and
vigorous, and require a greater share of Heat, succeed in their Order.
By which Mechanism, provident Nature furnishes us with a very various
and differing Entertainment; and what is best suited to each Season, all
the Year round.

As the Heat of the several Seasons affords us a different Face of
Things; so the several distant Climates shew different Scenes of Nature,
and Productions of the Earth[12]. The Hotter Countries yield ordinarily
the largest and tallest Trees; and those in too much greater variety
than the colder ever do. Even those Plants which are common to both,
attain to a much greater Bulk in the Southern than in the Northern
Climes. Nay, there are some Regions so bleak and chill, that they raise
no Vegetables at all to any considerable Size. This we learn from
_Greenland_, from _Iseland_, and other Places of like cold Site and
Condition. In these no Tree ever appears; and the very Shrubs they
afford, are few, little, and low.

Again, in the warmer Climates, and such as do furnish forth Trees and
the larger Vegetables, if there happen a remission or diminution of the
usual Heat, their Productions will be impeded and diminished in
proportion. Our late Colder Summers have given us proof enough of this.
For though the Heat we have had, was sufficient to raise the Vegetative
Matter into the lower Plants, into our Corns, our Wheat, Barley, Pease
and the like; and we have had plenty of Straw-berries, Ras-berries,
Currans, Goosberries, and the Fruits of such other Vegetables as are low
and near the Earth: Yea, and a moderate store of Cherries, Mulberries,
Plumbs, Filberts, and some others that grow somewhat at a greater
Height; yet our Apples, our Pears, Walnuts, and the Productions of the
taller[13] Trees have been fewer, and those not so kindly, so thoroughly
ripen'd, and brought to that Perfection they were in the former more
benign and their warm Seasons. Nay, even the lower Fruits and Grains
have had some share in the common Calamity; and fallen short both in
Number and Goodness of what the hotter and kinder Seasons were wont to
shew us. As to our Grapes, Abricots, Peaches, Nectarens, and Figs, being
transplanted hither out of hotter Climes, 'tis the less wonder we have
of late had so general a Failure of them.

Nor is it the Sun, or the ordinary emission of the Subterranean Heat
only, that promotes Vegetation; but any other indifferently, according
to its Power and Degree: This we are taught by our Stoves, hot Beds, and
the like. All Heat is of like kind; and where-ever is the same Cause,
there will be constantly the same Effect. There's a Procedure in every
part of Nature, that is perfectly regular and geometrical, if we can but
find it out; and the further our Searches carry us, the more shall we
have occasion to admire this, and the better 'twill compensate our
Industry.

[1] _Terra Parens._ Γῆη μὴτηρ πάντων. _Terra Matter._

[2] _Nat. History, Cent._ 5. §. 411.

[3] _Complexionum atque Mistion. Element. Figm._

[4] Mr. _Boyle_, _Scept. Chym. par. 2._

[5] _Provided the _Silver_ be _pure_ and absolutely _refin'd_: For the
least admixture of _Copper_ will produce _a blue Tincture_ in the
_Menstruum_; as _that_ of some _other Bodies_, one _different_._

[6] _To say nothing of those that were not discernible._

[7] Mr. _W. Molineux_, _Philosophical Trans. No. 181_.

[8] _Confer. Prop. 1. supra._

[9] _Nat. Hist. Earth_, p. 228. & seq.

[10] _Vid. Varronem, Columellam, & reliquos Rei Rusticæ Scriptores._

[11] _Conf. Nat. Hist. Earth_, p. 47. & seq. uti & p. 128, _&c._

[12] _Conf. Nat. Hist. Earth_, Pag. 267. & seq.

[13] _The Dwarf Apple and Pear trees have succeeded better. And indeed
in Trees of the same kind, those that keep closest to the Earth always
produce the most and best Fruit. For which Reason 'tis that the
Gardiners check and restrain the Growth of better Fruit-trees, and
prevent their running up to too great a Height._




 _An Account of the Measure of the thickness of Gold upon Gilt Wire;
   together with Demonstration of the exceeding Minuteness of the Atoms
   or constituent Particles of Gold; as it was read before the _Royal
   Society_, by _E. Halley_._


What are the constituent Parts of Matter, and how there comes to be so
great a diversity in the weight of Bodies, to all appearance equally
solid and dense, such as are Gold and Glass, (whose specifick Gravities
are nearly as 7 to 1) seems a very hard Question to those that shall
rightly consider it: For from undoubted Experiment, Gravity is in all
Bodies proportionable to the Quantity of Matter in each; and there is no
such thing as a Propension of some more, others less, towards the
Earth's Center; since the Impediment of the Air being removed, all
Bodies descend, be they never so loose or compact in Texture, with equal
Velocity. It follows therefore, That there is 7 times as much Matter in
Gold, as in a piece of Glass of the same Magnitude; and consequently,
that at least six parts of seven in the Bulk of Glass, must be Pore or
Vacuity: This some Favourers of the Atomical Philosophy have endeavoured
to solve, by supposing the primary or constituent Atoms of Gold to be
much larger than those of other Bodies, and consequently the Pores
fewer; whereas in other Bodies, the great multitude of the interspersed
Vacuities does diminish their Weights.

Being desirous to examine this Notion of the Magnitude of Atoms of Gold,
I bethought my self of the extreme Ductility of that Metal, which is
seen in the beating of it into Leaf, and above all in the drawing fine
Gilt-wire, by means whereof, I believed I might most exactly obtain the
true thickness of the Coat of Gold, that appears, even with the
Microscope, so well to represent Gold it self, that not the least point
of Silver appears through it. In order to this, I inform'd my self among
the Wire-drawers, what Gold they us'd to their Silver; and they told me,
That the very best double Gilt Wire was made out of Cylindrick Ingots, 4
Inches in Circumference, and 28 Inches long, which weigh 16 Pounds Troy;
on these they bestow 4 Ounces of Gold, that is, to every 48 Ounces of
Silver one of Gold; and that two Yards of the super-fine Wire weighs a
Grain. Hence at first sight it appear'd, that the length of 98 Yards is
in weight 49 Grains, and that a single Grain of Gold covers the said 98
Yards, and that the 10000th part of a Grain is above ⅓ of an Inch
long; which yet may be actually divided into 10, and so the 100000th
part of a Grain of Gold be visible without a Microscope. But being
desirous to compute the thickness of the Skin of Gold, by means of the
specifick Gravities of the Metals, viz. Silver 10⅓, and Gold 18⅔,
I found the Diameter of such Wire the 1/386 part of an Inch, and its
Circumference the 1/123 part; but the Gold in thickness not to exceed
the 1/134500 part of an Inch; whence it may be concluded, that the Cube
of the hundredth part of an Inch would contain above 2433000000, (or the
Cube of 1345) of such Atoms. And it may likewise be marvelled at, that
Gold being stretcht to so great a degree, as is here demonstrated,
should yet shew it self of so even and united a Texture, as not to let
the white Colour of the Silver under it appear through any the least
Pores; which argues, that even in this exceeding thinness very many of
those Atoms may still lie one over the other: Which is a Consideration
may merit the Thoughts of this Honourable Society, as tending to examine
that renowned Atomical Doctrine, which has of late much obtain'd among
the Learned.




 _An Account of the several Species of _Infinite Quantity_, and of the
   Proportions they bear one to the other; as it was read before the
   _Royal Society_, by _E. Halley_._


That all Magnitudes infinitely great, or such as exceed any assignable
Quantity, are equal among themselves, though it be vulgarly received for
a Maxim, is not yet so common as it is erroneous; and the Reason of the
mistake seems to be, That the Mind of Man, coming to contemplate the
Extensions of what exceeds the bounds of its Capacity, and of which the
very Idea does include a Negation of Limits; it comes to pass that we
acquiesce generally, and it suffices to say such a Quantity is infinite.

But if we come more nearly to examine this Notion, we shall find, that
there are really besides infinite _Length_ and infinite _Area_, no less
than three several sorts of infinite Solidity; all of which are
_Quantitates sui generis_, having no more relation or proportion the one
to the other, than a Line to a Plane, or a Plane to a Solid, or a Finite
to an Infinite. But that among themselves, each of those Species of
Infinites are in given Proportions, is what I now intend to make plain,
if possible.

But first, infinite Length, or a Line infinitely long, is to be
considered either as beginning at a Point, and so infinitely extended
one way, or else both ways from the same Point; in which case the one,
which is a beginning infinity, is the one half of the whole, which is
the Summ of the beginning and ceasing Infinity; or, as I may say, of
Infinity, _à parte ante_, and _à parte post_: Which is analogous to
Eternity in Time or Duration, in which there is always as much to follow
as is past, from any point or moment of Time: Nor doth the Addition or
Subduction of finite Length or Space of time alter the case either in
Infinity or Eternity, since both the one or the other cannot be any part
of the whole.

As to infinite _Surface_ or _Area_, any right Line, infinitely extended
both ways on an infinite Plane, does divide that infinite Plane into
equal Parts; the one to the right, and the other to the left of the said
Line: But if from any Point in such a Plane, two right Lines be
infinitely extended, so as to make an Angle, the infinite Area,
intercepted between those infinite right Lines, is to the whole infinite
Plane, as the Arch of a Circle, on the Point of Concourse of those
Lines, as a Centre, intercepted between the said Lines, is to the
Circumference of the Circle; or as the Degrees of the Angle to the 360
Degrees of a Circle. For Example, two right Lines meeting at a right
Angle do include, on an infinite Plane, a quarter part of the whole
infinite Area of such a Plane.

But if so be, two parallel infinite Lines be supposed drawn on such an
infinite Plane, the Area intercepted between them will be likewise
infinite; but at the same time will be infinitely less, than that Space
which is intercepted between two infinite Lines that are inclined,
though with never so small an Angle; for that in the one Case, the given
finite distance of the parallel Lines diminishes the Infinity in one
Degree of Dimension; whereas in a Sector, there is Infinity in both
Dimensions; and consequently, the Quantities are the one infinitely
greater than the other, and there is no proportion between them.

From the same Consideration arise the Three several Species of infinite
Space or Solidity, as has been said; for a Parallelepipede, or a
Cylinder, infinitely long, is greater than any finite Magnitude how
great soever; and all such Solids, supposed to be formed on given Bases,
are as those Bases, in proportion to one another. But if two of these
three Dimensions are wanting, as in the Space intercepted between two
parallel Planes infinitely extended, and at a finite distance; or with
infinite Length and Breadth, with a finite Thickness; All such Solids
shall be as the given finite distances one to another: But these
Quantities, though infinitely greater than the other, are yet infinitely
less than any of those, wherein all the three Dimensions are infinite.
Such are the Spaces intercepted between two inclined Planes infinitely
extended; the Space intercepted by the Surface of a Cone, or the sides
of a Pyramid likewise infinitely continued, _&c._ of all which
notwithstanding, the Proportions one to another, and to the τὸ πᾶν, or
vast Abyss of infinite Space (wherein is the _Locus_ of all things that
are or can be; or to the Solid of infinite Length, Breadth, and
Thickness, taken all manner of ways) are easily assignable. For the
Space between two Planes, is to the whole, as the Angle of those Planes
to the 360 Degrees of the Circle. As for Cones and Pyramids, they are as
the Spherical Surface, intercepted by them, is to the Surface of the
Sphere; and therefore Cones are as the versed Sines of half their
Angles, to the Diameter of the Circle: These three sorts of infinite
Quantity are analogous to a Line, Surface and Solid, and after the same
manner cannot be compared, or have any proportion the one to the other.

Besides these, there are several other Species of infinite Quantity,
arising from the Contemplation of Curves, and their Asymptotes; which,
by reason of the difficulty of the Subject, cannot be made so plain to
most Readers: But what has been already said, may be sufficient to
evince what we undertook to explain.




 _An Account of Dr. _Robert Hook_'s Invention of the Marine Barometer,
   with its Description and Uses; published by order of the Royal
   Society, by _E. Halley_, R. S. S._


Since it was found that the _Torricellian Tube_, commonly call'd the
_Mercurial Barometer_, by the rising and falling of the _Quick-silver_
therein, doth presage the Changes of the Air, in relation to fair and
foul Weather; upon several Years Observation of it, it has been proved
and adjusted for that purpose by Dr. _Robert Hook_; and there have been
by him many attempts to improve the Instrument, and render the Minute
Divisions on the Scale thereof more sensible. He also judging that it
might be of great use at Sea, contrived several ways to make it
serviceable on Board of Ship; one of which he explain'd to the _Royal
Society_ at their Weekly Meeting in _Gresham College_, _January 2.
1667/8_. Since which time he hath further cultivated the Invention, and
some Years ago produced before the said _Society_, the Instrument I am
now to describe, which for its subtilty and usefulness, seemeth to
surpass all other performances of the like Nature.

'Till such time as the Author's present Indisposition will give him
leave to bestow freely his Thoughts on this Subject upon the Publick, it
is the Opinion of the Society, that such an Account be given of this
Contrivance, as may render it known, and recommend it to the Mariners
use, for which it was principally intended.

The _Mercurial Barometer_ requiring a perpendicular Posture, and the
_Quick-silver_ vibrating therein with great Violence upon any Agitation,
is therefore uncapable of being used at Sea (tho' it hath lately been
contrived to be made portable), so it remain'd to find out some other
Principle, wherein the Position of the Instrument was not so
indispensably necessary: For this, all those that use the Sea are
obliged to the great facility Dr. _Hook_ has always shewn, in applying
Philosophical Experiments to their proper uses.

It is about forty Years since, that the _Thermometers_ of _Robert de
Fluctibus_, depending on the Dilatation and Contraction of included Air
by Heat and Cold, have been disused, upon discovery that the Airs
pressure is unequal; that inequality mixing it self with the Effects of
the warmth of the Air in that Instrument. And instead thereof was
substituted the seal'd _Thermometer_, including Spirit of Wine (first
brought into _England_, out of _Italy_, by Sir _Robert Southwell_) as a
proper Standard of the temper of the Air, in relation to Heat and Cold;
that Ætherial Spirit being of all the known Liquors the most susceptible
of Dilatation and Contraction, especially with a moderate degree of
either Heat or Cold. Now this being allow'd as a Standard, and the other
_Thermometer_ that includes Air, being graduated with the same
Divisions, so as at the time when the Air was included, to agree with
the Spirit-_Thermometer_ in all the degrees of Heat and Cold, noting at
the same time the precise height of the _Mercury_ in the common
Barometers: It will readily be understood, that whensoever these two
_Thermometers_ shall agree, the pressure of the Air is the same it was,
when the Air was included, and the Instrument graduated: That if in the
Air-_Thermometer_ the Liquor stand higher than the Division marked
thereon, corresponding with that on the Spirit-glass, it is an
indication that there is a greater pressure of the Air at that time,
than when the Instrument was graduated. And the contrary is to be
concluded, when the Air-glass stands lower than the Spirit, _viz._ that
then the Air is so much lighter, and the _Quick silver_, in the ordinary
Barometer lower than at the said time of Graduation.

And the Spaces answering to an Inch of _Mercury_, will be more or less,
according to the quantity of Air so included, and the smallness of the
Glass Cane, in which the Liquor rises and falls, and may be augmented
almost in any proportion, under that of the Specifick Gravity of the
Liquor of the _Thermometer_ to _Mercury_. So as to have a Foot or more
for an Inch of _Mercury_, which is another great convenience.

It has been observed by some, that in long keeping this Instrument, the
Air included either finds a means to escape, or deposites some Vapours
mixt with it, or else for some other cause becomes less Elastick,
whereby, in process of time, it gives the height of the _Mercury_
somewhat greater than it ought; but this, if it should happen in some of
them, hinders not the usefulness thereof, for that it may at any time
very easily be corrected by Experiment, and the rising and falling
thereof are the things chiefly remarkable in it, the just height being
barely a Curiosity.

In these Parts of the World, long Experience has told us, that the
rising of the _Mercury_ forebodes fair Weather after foul, and an
Easterly or Northerly Wind; and that the falling thereof, on the
contrary, signifies Southerly or Westerly Winds, with Rain, or stormy
Winds, or both; which latter it is of much more consequence to provide
against at Sea than at Land; and in a Storm, the _Mercury_ beginning to
rise is a sure sign that it begins to abate, as has been experienced in
high Latitudes, both to the Northwards and Southwards of the Æquator.

The Form of this Instrument is shown in the Cut, by Tab. 4. Fig. 1.
wherein,

AB represents the Spirit-_Thermometer_, graduated from 0, or the
freezing Point, through all the possible degrees of the Heat or Cold of
the Air, at least in these Climates.

CD, is the Air-_Thermometer_, graduated after the same manner with the
like Degrees.

EF, is a Plate applied to the side of the _Thermometer_ CD, graduated
into Spaces answering to Inches and parts of an Inch of _Mercury_, in
the common Barometers.

G, a Hand standing on the Plate at the height of the _Mercury_ thereon,
as it was when the Instrument was graduated, as suppose here at 29½
Inches.

LM, a Wire on which the Plate EF, slips up and down, parallel to the
Cane of the _Thermometer_ CD.

K, any Point at which the Spirit stands at the time of Observation;
suppose at 38 on the Spirit-_Thermometer_; Slide the Plate EF till the
Hand G stand at 38 on the Air-_Thermometer_, and if the Liquor therein
stand at 38 likewise, then is the pressure of the Air the same as at the
time of Graduation, _viz._ 29,5; but if it stand higher, as at 30, at I;
then is the pressure of the Air greater; and the division on the sliding
Plate against the Liquor, shews the present height of the _Mercury_ to
be twenty nine Inches seven Tenths. And this may suffice as to the
manner of using it.

I had one of these Barometers with me in my late Southern Voyage, and it
never failed to prognostick and give early notice of all the bad Weather
we had, so that I depended thereon, and made provision accordingly; and
from my own Experience I conclude that a more useful Contrivance hath
not for this long time been offer for the benefit of Navigation.

These Instruments are made according to the Direction of Dr. _Hook_, by
Mr. _Henry Hunt_, Operator to the Royal Society, who will furnish any
Gentlemen with them, and give them Directions how to use them.




 _A Discourse concerning the Proportional Heat of the Sun in all
   Latitudes, with the Method of collecting the same; as it was read
   before the Royal Society, in one of their late Meetings. By _E.
   Halley_._


There having lately arisen some Discourse about that part of the Heat of
Weather, simply produced by the Action of the Sun; and I having
affirmed, that if that were considered, as the only Cause of the Heat of
the Weather, I saw no Reason, but that under the Pole the solstitical
Day ought to be as hot as it is under the Æquinoctial, when the Sun
comes vertical, or over the Zenith: For this Reason, that for all the 24
Hours of that Day under the Pole, the Sun's Beams are inclined to the
Horizon, with an Angle of 23½ Degrees; and under the Æquinoctial,
though he come vertical, yet he shines no more than 12 Hours, and is
again 12 Hours absent; and that for 3 Hours 8 Minutes of that 12 Hours,
he is not so much elevated as under the Pole; so that he is not 9 of the
whole 24, higher than 'tis there, and is 15 Hours lower. Now the simple
Action of the Sun is, as all other Impulses or Stroaks, more or less
forceable, according to the _Sinus_ of the Angle of Incidence, or to the
Perpendicular let fall on the Plain, whence the vertical Ray (being that
of the greatest Heat,) being put _Radius_, the force of the Sun on the
Horizontal Surface of the Earth will be to that, as the _Sinus_ of the
Sun's Altitude at any other time. This being allow'd for true, it will
then follow, that the time of the continuance of the Sun's shining being
taken for a _Basis_, and the _Sines_ of the Sun's Altitudes erected
thereon as Perpendiculars, and a Curve drawn through the Extremities of
those Perpendiculars, the _Area_ comprehended shall be proportionate to
the Collection of the Heat of all the Beams of the Sun in that space of
time. Hence it will follow, that under the Pole the Collection of all
the Heat of a tropical Day, is proportionate to a Rectangle of the
_Sine_ of 23½ _gr._ into 24 Hours, or the Circumference of a Circle;
that is, the _Sine_ of 23½ _gr._ being nearly 4 Tenths of _Radius_;
as 3/10 into 12 Hours. Or the Polar Heat is equal to that of the Sun
containing 12 Hours above the Horizon, at 53 _gr._ height, than which
the Sun is not 5 Hours more elevated under the Æquinoctial.

But that this Matter may the better be understood, I have exemplified it
by a Scheme, (_Tab. 4. Fig. 2_) wherein the _Area ZGHH_, is equal to the
_Area_ of all the _Sines_ of the Sun's Altitude under the Æquinoctial,
erected on the respective Hours from Sun-rise to the Zenith; and
the _Area ♋HH♋_ is in the same proportion to the Heat of the
same 6 Hours under the Pole on the Topical Day; and _⨀HHQ_, is
proportional to the collected Heat of 12 Hours, or half a Day under the
Pole, which space _⨀HHQ_, is visibly greater than the other _Area
HZGH_, by as much as the _Area HGQ_ is greater than the _Area ZG⨀_;
which, that it is so, is visible to sight, by a great excess; and so
much in proportion does the Heat of the 24 Hours Sun-shine under the
Pole, exceed that of the 12 Hours under the Æquinoctial: Whence,
_Cæteris paribus_, it is reasonable to conclude, that were the Sun
perpetually under the Tropick, the Pole would be at least as warm, as it
is now under the Line it self.

But whereas the Nature of Heat is to remain in the Subject, after the
Cause that heated is removed, and particularly in the Air; under the
Æquinoctial, the 12 Hours absence of the Sun does very little still the
Motion impressed by the part Action of his Rays, wherein Heat consists,
before he arise again: But under the Pole the long absence of the Sun
for 6 Months, wherein the extremity of Cold does obtain, has so chill'd
the Air, that it is as it were frozen, and cannot, before the Sun has
got far towards it, be any way sensible of his presence, his Beams being
obstructed by thick Clouds, and perpetual Fogs and Mists, and by that
Atmosphere of Cold, as the late Honourable Mr. _Boyle_ was pleased to
term it, proceeding from the everlasting Ice, which in immense
Quantities does chill the Neighbouring Air, and which the too soon
retreat of the Sun leaves unthawed, to encrease again, during the long
Winter that follows this short interval of Summer. But the differing
Degrees of Heat and Cold, in differing Places, depend in great measure
upon the Accidents of the Neighbourhood of high Mountains, whose height
exceedingly chills the Air brought by the Winds over them; and of the
Nature of the Soil, which variously retains the Heat, particularly the
Sandy, which in _Africa_, _Arabia_, and generally where such Sandy
Desarts are found, do make the Heat of the Summer incredible to those
that have not felt it.

In the prosecution of this first Thought, I have solved the Problem
generally, _viz._ to give the proportional Degree of Heat, or the Sum of
all the _Sines_ of the Sun's Altitude, while he is above the Horizon in
any oblique Sphere, by reducing it to the finding of the Curve Surface
of a Cylindrick Hoof, or of a given part thereof.

Now this Problem is not of that difficulty as appears at first sight,
for in _Tab. 4. Fig. 3._ let the Cylinder ABCD be cut obliquely with the
Ellipse BKDI, and by the Center thereof H, describe the Circle IKLM; I
say, the Curve Surface IKLB is equal to the Rectangle of IK and BL, or
of HK and 2 BL or BC: And if there be supposed another Circle, as NQPO,
cutting the said Ellipse in the Points P, Q; draw PS, QR, parallel to
the Cylinders Axe, till they meet with the aforesaid Circle IKLM in the
Points R, S, and draw the Lines RTS, QVP bisected in T and V. I say
again, that the Curve Surface RMSQDP is equal to the Rectangle of BL or
MD and RS, or of 2 BL or AD and ST or VP; and the Curve Surface QNPD is
equal to RS × MD----the Arch RMS × SP, or the Arch MS × 2 SP: Or it is
equal to the Surface RMSQDP, substracting the Surface RMSQNP. So
likewise the Curve Surface QBPO is equal to the Sum of the Surface
RMSQDP, or RS × MD, and of the Surface RLSQOP, or the Arch LS × 2 SP.

This is the most easily demonstrated from the Consideration, That the
Cylindrick Surface IKLB is to the inscrib'd Spherical Surface IKLE,
either in the whole, or in its Analogous Parts, as the tangent BL is to
the Arch EL, and from the Demonstrations of _Archimedes de Sphæra &
Cylindro, Lib. I. Prop._ XXX, and XXXVII, XXXIIX. which I shall not
repeat here, but leave the Reader the pleasure of examining it himself;
nor will it be amiss to consult Dr. _Barrow_'s Learned Lectures on that
Book, Publish'd at _London_, _Anno 1684_, _viz._ _Probl._ IX. and the
Corollaries thereof.

Now to reduce our Case of the Sum of all the _Sines_ of the Sun's
Altitude in a given Declination and Latitude to the aforesaid Problem,
let us consider (_Tab. 4. Fig. 4._) which is the _Analemma_ projected on
the Plain of the _Meridian_, Z the Zenith, P the Pole, HH the Horizon,
ææ the Æquinoctial, ♋♋, ♑♑ the two Tropicks, ♋1 the _Sine_ of the
Meridian Altitude in ♋; and equal thereto, but perpendicular to the
Tropick, erect ♋I, and draw the Line TI intersecting the Horizon in T,
and the Hour Circle of 6, in the Point 4, and 64 shall be equal to 6R,
or to the Sine of the Altitude at 6: And the like for any other Point in
the Tropick, erecting a Perpendicular thereat, terminated by the Line T
I: Through the Point 4 draw the Line 4, 5, 7 parallel to the Tropick,
and representing a Circle equal thereto; then shall the Tropick ♋♋ in
_Fig. 4._ answer to the Circle NOPQ, in _Fig. 3._ the Circle 457 shall
answer the Circle IKLM, T4I shall answer to the Elliptick Segment QIBKP,
6R or 64 shall answer to SP, and 5I to BL, and the Arch ♋T, to the Arch
LS, being the semidiurnal Arch in that Latitude and Declination; the
_Sine_ whereof, tho' not expressible in _Fig. 4._ must be conceived as
Analogous to the Line TS or UP in _Fig. 3._

The Relation between these two Figures being well understood, it will
follow from what precedes, That, _the sum of the _Sines_ of the Meridian
Altitudes of the Sun in the two Tropicks, (and the like for any two
opposite Parallels) being multiplied by the _Sine_ of the semidiurnal
Arch, will give an _Area_ Analogous to the Curve Surface RIMSQDP; and
thereto adding in Summer, or substracting in Winter, the Product of the
length of the semidiurnal Arch, (taken according to _Van Ceulen_'s
Numbers) into the difference of the above-said _Sines_ of the Meridian
Altitude: The sum in one case, and difference in another, shall be as
the Aggregate of all the _Sines_ of the Sun's Altitude, during his
appearance above the Horizon; and consequently of all his Heat and
Action on the Plain of the Horizon in the proposed Day_. And this may
also be extended to the parts of the same Day; for if the aforesaid Sum
of the _Sines_ of the Meridian Altitudes, be multiplied by half the Sum
of the _Sines_ of the Sun's Horary distance from Noon, when the Times
are before and after Noon; or by half their difference, when both are on
the same side of the Meridian; and thereto in Summer, or therefrom in
Winter, be added or substracted the Product of half the Arch answerable
to the proposed interval of Time, into the difference of the _Sines_ of
Meridian Altitudes, the Sum in one case and Difference in the other,
shall be proportional to all the Action of the Sun during that space of
time.

I fore-see it will be Objected, that I take the _Radius_ of my Circle on
which I erect my Perpendiculars always the same, whereas the Parallels
of Declination are unequal; but to this I answer, That our said Circular
Bases ought not to be Analogous to the Parallels, but to the Times of
Revolution, which are equal in all of them.

It may perhaps be useful to give an Example of the Computation of this
Rule, which may seem difficult to some. Let the Solstitical Heat in
♋ and ♑ be required at _London_, _Lat._ 51° 32'.

 380-2'8 _Co-Lat._
 23 -30  _Decl. ⨀_
 ------
 61 -58               _Sinus_ = ,882674
 14 -58               _Sinus_ = ,258257
                                 ------
                      _Summa_  1,140931
                       _Diff._  ,624417

 _Diff. Ascen._      3300-1'1.
 _Arch. Semid. æstiv._ 123-11.

 _Ar. Sem. hyb. 56-49. S._      ,638923
 _Arch. æstiv. mensura_        2,149955
 _Arc. hyb. mensura_            ,991683

 Then 1,140931 in ,836923, + 624417 in 2,149955 = 2,29734.
 And 1,140931 in 836929 - ,624417 in ,991638 = 33895.

So that 2,29734 will be as the Tropical Summers Day Heat, and 0,33895 as
the Action of the Sun in the Day of the Winter Solstice.

After this manner I computed the following Table for every tenth Degree
of Latitude, to the Æquinoctial and Tropical Sun, by which an Estimate
may be made of the intermediate Degrees.

 +------+--------------+--------------+--------------+
 |      |    Sun in    |    Sun in    |    Sun in    |
 | Lat. |     ♈ ♎      |      ♋       |      ♑       |
 +------+--------------+--------------+--------------+
 |  0   |    20000     |    18341     |    18341     |
 |  10  |    19696     |    20290     |    15834     |
 |  20  |    18794     |    21737     |    13166     |
 |  30  |    17321     |    22651     |    10124     |
 |  40  |    15321     |    23048     |     6944     |
 +------+--------------+--------------+--------------+
 |  50  |    12855     |    22991     |     3798     |
 |  60  |    10000     |    22773     |     1075     |
 |  70  |     6840     |    23543     |      000     |
 |  80  |     3473     |    24673     |      000     |
 |  90  |     0000     |    25055     |      000     |
 +------+--------------+--------------+--------------+

Those that desire more of the Nature of this Problem, as to the Geometry
thereof, would do well to compare the XIII. _Prop. Cap. V._ of the
Learned Treatise, _De Calculo Centri Gravitatis_, by the Reverend Dr.
_Wallis_, Published _Anno 1670_.

From this Rule there follow several Corollaries worth Note: As I. That
the Æquinoctial Heat, when the Sun comes Vertical, is as twice the
Square of _Radius_, which may be proposed as a Standard to compare with,
in all other Cases. II. That under the Æquinoctial, the Heat is as the
_Sine_ of the Sun's Declination. III. That in the Frigid Zones when the
Sun sets not, the Heat is as the Circumference of a Circle into the
_Sine_ of the Altitude at 6. And consequently, that in the same Latitude
these Aggregates of Warmth, are as the _Sines_ of the Sun's
Declinations; and in the same Declination of _Sol_, they are as the
_Sines_ of the Latitude, and generally they are as the _Sines_ of the
Latitude into the _Sines_ of Declination. IV. That the Æquinoctial Days
Heat is every where as the Co-sine of the Latitude. V. In all places
where the Sun sets, the difference between the Summer and Winter Heats,
when the Declinations are contrary, is equal to a Circle into the _Sine_
of the Altitude at six in the Summer Parallel, and consequently those
differences are as the _Sines_ of Latitude into, or multiplied by the
_Sines_ of Declination. VI. From the Table I have added, it appears,
that the Tropical Sun under the Æquinoctial, has, of all others, the
least Force. Under the Pole it is greater than any other Days Heat
whatsoever, being to that of the Æquinoctial as 5 to 4.

From the Table and these Corollaries may a general _Idea_ be conceived
of the Sum of all the Actions of the Sun in the whole Year, and that
part of the Heat that arises simply from the Presence of the Sun be
brought to a Geometrical Certainty: And if the like could be performed
for Cold; which is something else than the bare Absence of the Sun, as
appears by many Instances, we might hope to bring what relates to this
part of _Meteorology_ to a perfect Theory.




 _Concerning the Distance of the Fix'd Stars. By the Honourable _Francis
   Roberts_, Esq; S. R. S._


The Ancient Astronomers, who had no other way of computing the Distances
of the Heavenly Bodies, but by their Parallax to the Semi-diameter of
the Earth; and being never able to discover any in the fix'd Stars, did
from thence rightly enough infer, that their Distance was very great,
and much exceeding that of the Planets, but could go no farther
otherwise than by uncertain guess.

Since the _Pythagorean_ System of the World has been reviv'd by
_Copernicus_, (and now by all Mathematicians accepted for the true one)
there seem'd Ground to imagine that the Diameter of the Earth's Annual
Course (which, according to our best Astronomers, is at least 40000
times bigger than the Semi-diameter of the Earth) might give a sensible
Parallax to the fix'd Stars, though the other could not, and thereby
determine their Distance more precisely.

But though we have a Foundation to build on so vastly exceeding that of
the Ancients, there are some Considerations may make us suspect that
even this is not large enough for our purpose.

Monsieur _Hugens_ (who is very exact in his Astronomical Observations)
tells us, he could never discover any visible Magnitude in the fix'd
Stars, though he used Glasses which magnified the apparent Diameter
above 100 times.

Now, since in all likelyhood the fix'd Stars are Suns, (perhaps of a
different Magnitude) we may as a reasonable _Medium_ presume they are
generally about the bigness of the Sun.

Let us then (for Example) suppose the Dog-Star to be so. The Distance
from us to the Sun being about 100 times the Sun's Diameter (as is
demonstrable from the Sun's Diameter being 32 Minutes) it is evident,
that the Angle under which the Dog-Star is seen in Mr. _Hugens_'s
Telescope, must be near the same with the Angle of its Parallax to the
Sun's Distance, or Semi-diameter of the Earth's Annual Course; so that
the Parallax to the whole Diameter, can be but double such a quantity,
as even to Mr. _Hugens_'s nice Observation is altogether insensible.

The Distance therefore of the fix'd Stars seems hardly within the reach
of any of our Methods to determine; but from what has been laid down, we
may draw some Conclusions that will much illustrate the prodigious
vastness of it.

1. That the Diameter of the Earth's Annual Orb (which contains at least
160 Millions of Miles) is but as a Point in comparison of it; at least
it must be above 6000 times the Distance of the Sun. For if a Star
should appear thro' the aforesaid Telescope half a Minute broad (which
is a pretty sensible Magnitude) the true apparent Diameter would not
exceed 18 3d Minutes, which is less than the 6000th part of the apparent
Diameter of the Sun, and consequently the Sun's Distance not the 6000th
part of the Distance of the Star.

2. That could we advance towards the Stars 99 Parts of the whole
Distance, and have only 1/100 Part remaining, the Stars would appear
little bigger to us than they do here; for they would shew no otherwise
than they do through a Telescope, which magnifies an Hundred-fold.

3. That at least Nine Parts in Ten of the Space between us and the fix'd
Stars, can receive no greater Light from the Sun, or any of the Stars,
than what we have from the Stars in a clear Night.

4. That Light takes up more time in travelling from the Stars to us,
than we in making a _West-India_ Voyage (which is ordinarily perform'd
in six Weeks.) That a Sound would not arrive to us from thence in 50000
Years, nor a Cannon-bullet in a much longer time. This is easily
computed, by allowing (according to Mr. _Newton_) Ten Minutes for the
Journey of Light from the Sun hither, and that a Sound moves about 1300
Foot in a Second.




 _The Famous Mr. _Isaac Newton_'s Theory of the _Moon_._


This _Theory_ which hath been long expected by all the true Lovers of
_Astronomy_, was communicated from Mr. _Newton_ to Dr. _Gregory_,
_Astronomy_ Professor at _Oxford_, and by him published in his _Astron.
Elem. Philos._ and _Geomet._ p. 336. From whence, as it was lately
translated into _English_, I thought fit to insert it here.

By this Theory, what by all Astronomers was thought most difficult and
almost impossible to be done, the Excellent Mr. _Newton_ hath now
effected; _viz._ to determine the Moon's Place even in her Quadratures,
and all other Parts of her Orbit, besides the Syzygys, so accurately by
Calculation, that the Difference between that and her true Place in the
Heavens, shall scarce be above two minutes in her Syzygys, or above
three in her Quadratures, and is usually so small, that it may well
enough be reckon'd only as a Defect in the Observation. And this Mr.
_Newton_ experienced, by comparing it with very many Places of the Moon,
observ'd by Mr. _Flamsteed_, and communicated to him.

The Royal Observatory at _Greenwich_, is to the West of the Meridian of
_Paris_, 2 degrees, 19 minutes. Of _Uraniburgh_, 12 degrees, 51 minutes,
30 seconds. And of _Gedanum_, 18 degrees, 48 minutes.

The mean Motions of the Sun and Moon, accounted from the Vernal Æquinox
at the Meridian of _Greenwich_, I make to be as followeth.

The last Day of _December 1680_, at Noon (_Old Stile_) the mean Motion
of the Sun was 9 Signs, 20 degrees, 34 minutes, 46 seconds. Of the Sun's
Apogæum, was 3 S. 7 deg. 23 min. 30 seconds.

That the mean Motion of the Moon at that time, was 6 S. 1 degree, 45
minutes, 45 seconds. And of her Apogee, 8 S. 4 degrees, 28 minutes, 5
seconds. Of the ascending Node of the Moon's Orbit, 5 S. 24 deg. 14 min.
35 seconds, _&c._

And on the last Day of _December, 1700_, at Noon, the mean Motion of the
Sun was 9 S. 20 degrees, 43 minutes, 50 seconds. Of the Sun's Apogee,
3 S. 7 degrees, 44 minutes, 30 seconds. The mean Motion of the Moon was
10 S. 15 degrees, 19 minutes, 50 seconds. Of the Moon's Apogee, 11 S. 8
degrees, 18 minutes, 20 seconds. And of her ascending Node, 4 S. 27
degrees, 24 minutes, 20 seconds. For in 20 _Julian_ Years, or 7305 Days,
the Sun's Motion is 20 Revol. 0 S. 0 degrees, 9 minutes, 4 seconds. And
the Motion of the Sun's Apogee, 21 minutes, 0 seconds.

The Motion of the Moon in the same time, is 267 Revol. 4 S. 13 degrees,
34 minutes, 5 seconds. And the Motion of the Lunar Apogee, is 2 Revol.
3 S. 3 degrees, 50 minutes, 15 seconds. And the Motion of her Node, 1
Revol. 0 S, 26 degrees, 50 minutes, 15 seconds.

All which Motions are accounted from the Vernal Æquinox: Wherefore if
from them there be subtracted the Recession or Motion of the Æquinoctial
Point, in _Antecedentia_, during that space, which is 16 minutes, 40
seconds, there will remain the Motions in reference to the fix'd Stars
in 20 _Julian_ Years; _viz._ the Sun's 19 Revol. 11 S. 29 degrees, 52
minutes, 24 seconds. Of his Apogee, 4 minutes, 20 seconds. And the
Moon's 267 Revol. 4 S. 13 degrees, 17 minutes, 25 seconds. Of her
Apogee, 2 Revol. 3 S. 3 degrees, 33 minutes, 35 seconds. And of the Node
of the Moon, 1 Revol. 0 S. 27 degrees, 6 minutes, 55 seconds.

According to this Computation, the _Tropical Year_ is 365 Days, 5 Hours,
48 Minutes, 57 Seconds. And the _Sydereal Year_ is 365 Days, 6 Hours, 9
Minutes, 14 Seconds.

These mean Motions of the Luminaries are affected with various
Inequalities: Of which,

1. There are the Annual Equations of the aforesaid mean Motions of the
Sun and Moon, and of the Apogee and Node of the Moon.

The Annual Equation of the mean Motion of the Sun, depends on the
Eccentricity of the Earth's Orbit round the Sun, which is 16-11/12 of
such Parts, as that the Earth's mean Distance from the Sun shall be
1000: Whence 'tis call'd the _Equation of the Centre_; and is, when
greatest, 1 degree, 56 minutes, 20 seconds.

The greatest Annual Equation of the Moon's mean Motion, is 11 degrees,
49 seconds; of her Apogee, 20 minutes, and of her Node, 9 minutes, 30
seconds.

And these four Annual Equations are always mutually proportional one to
another: Wherefore when any of them is at the greatest, the other three
will also be greatest; and when any one lessens, the other three will
also be diminished in the same Ratio.

The Annual Equation of the Sun's Centre being given, the three other
corresponding Annual Equations will be also given; and therefore a Table
of that will serve for all. For if the Annual Equation of the Sun's
Centre be taken from thence, for any Time, and be call'd P, and let
1/10P = Q, Q + 1/60Q = R, 1/6P = D, D + 1/30D = E, and D - 1/50D = 2F;
then shall the Annual Equation of the Moon's mean Motion for that time
be R, that of the Apogee of the Moon will be E, and that of the Node F.

Only observe here, That if the Equation of the Sun's Centre be required
to be added; then the Equation of the Moon's mean Motion must be
subtracted, that of her Apogee must be added, and that of the Node
subducted, And on the contrary, if the Equation of the Sun's Centre were
to be subducted, the Moon's Equation must be added, the Equation of her
Apogee subducted, and that of her Node added.

There is also an _Equation of the Moon's mean Motion_, depending on the
situation of her Apogee, in respect of the Sun; which is greatest when
the Moon's Apogee is in an Octant with the Sun, and is nothing at all
when it is in the Quadratures or Syzygys. This Equation, when greatest,
and the Sun in _Perigæo_, is 3 Minutes, 56 Seconds. But if the Sun be in
_Apogæo_, it will never be above 3 Minutes, 34 Seconds. At other
Distances of the Sun from the Earth, this Equation, when greatest, is
reciprocally as the Cube of such Distance. But when the Moon's Apogee is
any where but in the _Octants_, this Equation grows less, and is mostly
at the same distance between the Earth and Sun, as the Sine of the
double Distance of the Moon's Apogee, from the next Quadrature or
Syzygy, to the Radius.

This is to be added to the Moon's Motion, while her Apogee passes from a
Quadrature with the Sun to a Syzygy; but this is to be subtracted from
it, while the Apogee moves from the Syzygy to the Quadrature.

There is moreover another _Equation of the Moon's Motion_, which depends
on the Aspect of the Nodes of the Moon's Orbit with the Sun: And this is
greatest, when her Nodes are in _Octants_ to the Sun, and vanishes
quite, when they come to their Quadratures or Syzygys. This Equation is
proportional to the Sine of the double Distance of the Node from the
next Syzygy, or Quadrature; and at greatest, is but 47 seconds. This
must be added to the Moon's mean Motion, while the Nodes are passing
from their Syzygys with the Sun, to their Quadratures with him; but
subtracted while they pass from the Quadratures to the Syzygys.

From the Sun's true Place, take the equated mean Motion of the Lunar
Apogee, as was above shew'd, the Remainder will be the Annual Argument
of the said Apogee. From whence the _Eccentricity of the Moon_, and the
_second Equation_ of her Apogee may be computed after the manner of the
following (_which takes place also in the Computation of any other
intermediate Equations_).

Tab. 3. Fig. 6. Let T represent the Earth, TS, a Right Line joining the
Earth and Sun, TACB, a Right Line drawn from the Earth to the middle or
mean Place of the Moon's Apogee, equated, as above: Let the Angle STA be
the Annual Argument of the aforesaid Apogee, TA the least Eccentricity
of the Moon's Orbit, TB the greatest. Bissect AB in G; and on the Centre
C, with the Distance AC describe a Circle AFB, and make the Angle BCF =
to the double of the Annual Argument. Draw the Right Line TF, that shall
be the Eccentricity of the Moon's Orbit; and the Angle BTF, is the
second Equation of the Moon's Apogee required.

In order to whose Determination, let the mean Distance of the Earth from
the Moon, or the Semi-diameter of the Moon's Orbit, be 100000; then
shall its greatest Eccentricity TB be 66782 such Parts; and the least
TA, 43319. So that the greatest Equation of the Orbit, _viz._ when the
Apogee is in the Syzygys, will be 7 degrees, 39 minutes, 30 seconds, or
perhaps 7 degrees, 40 minutes, (for I suspect there will be some
Alteration, according to the Position of the Apogee in _Cancer_ and
_Capricorn_.) But when it is Quadrate to the Sun, the greatest Equation
aforesaid will be 4 degrees, 57 minutes, 56 seconds; and the greatest
Equation of the Apogee, 12 degrees, 15 minutes, 4 seconds.

Having from these Principles made a Table of the Equation of the Moon's
Apogee, and of the Eccentricities of her Orbit to each degree of the
Annual Argument, from whence the Eccentricity TF, and the Angle BTF
(_viz._ the second and the principal Equation of the Apogee) may easily
be had for any Time required; let the Equation thus found be added to
the first Equated Place of the Moon's Apogee, if the Annual Argument be
less than 90 degrees, or greater than 180 degrees, and less than 270;
otherwise it must be subducted from it; and the Sum or Difference shall
be the Place of the Lunar Apogee secondarily equated; which being taken
from the Moon's Place equated a third time, shall leave the mean Anomaly
of the Moon corresponding to any given Time. Moreover, from this mean
Anomaly of the Moon, and the before-found Eccentricity of her Orbit, may
be found (by means of a Table of Equations of the Moon's Centre made to
every degree of the mean Anomaly, and some Eccentricities, _viz._ 45000,
50000, 55000, 60000, and 65000) the _Prostaphæresis_, or Equation of the
Moon's Centre, as in the common way: And this being taken from the
former Semi-circle of the middle Anomaly, and added in the latter to the
Moon's Place thus thrice equated, will produce the Place of the Moon a
fourth time equated.

The greatest Variation of the Moon (_viz._ that which happens when the
Moon is in an Octant with the Sun) is nearly, reciprocally as the Cube
of the Distance of the Sun from the Earth. Let that be taken 37 minutes,
25 seconds, when the Sun is _in Perigæo_, and 33 minutes, 40 seconds,
when he is _in Apogæo_: And let the Differences of this Variation in the
Octants be made reciprocally, as the Cubes of the Distances of the Sun
from the Earth; and so let a Table be made of the aforesaid Variation of
the Moon in her Octants (or its Logarithms) to every Tenth, Sixth, or
Fifth Degree of the mean Anomaly: And for the Variation out of the
Octants, make, as Radius to the Sine of the double Distance of the Moon
from the next Syzygy, or Quadrature :: so let the afore-found Variation
in the Octant be to the Variation congruous to any other Aspect; and
this added to the Moon's Place before found in the first and third
Quadrant (accounting from the Sun) or subducted from it in the second
and fourth, will give the Moon's Place equated a fifth time.

Again, as Radius to the Sine of the Summ of the Distances of the Moon
from the Sun, and of her Apogee from the Sun's Apogee (or the Sine of
the Excess of that Summ above 360 degrees,) :: so is 2 minutes, 10
seconds, to a sixth Equation of the Moon's Place, which must be
subtracted, if the aforesaid Summ or Excess be less than a Semi-circle;
but added, if it be greater. Let it be made also, as Radius to the Sine
of the Moon's distance from the Sun :: so 2 degrees, 20 secants, to a
seventh Equation; which when the Moon's Light is increasing, add; but
when decreasing, subtract; and the Moon's Place will be equated a
seventh time, and this is her Place _in her proper Orbit_.

Note here, the Equation thus produced by the mean Quantity 2 degrees, 20
seconds, is not always of the same magnitude; but is increased and
diminished, according to the Position of the Lunar Apogee. For if the
Moon's Apogee be in Conjunction with the Sun's, the aforesaid Equation
is about 54 seconds greater: But when the Apogees are in Opposition,
'tis about as much less; and it librates between its greatest Quantity 3
minutes, 14 seconds, and its least, 1 minute, 26 seconds. And this is,
when the Lunar Apogee is in Conjunction, or Opposition with the Sun's:
But in the Quadratures, the aforesaid Equation is to be lessen'd about
50 seconds, or 1 minute, when the Apogees of the Sun and Moon are in
Conjunction; but if they are in Opposition, for want of a sufficient
number of Observations, I cannot determine, whether it is to be lessen'd
or increas'd. And even as to the Argument or Decrement of the Equation,
2 minutes, 20 seconds, above mentioned, I dare determine nothing
certain, for the same Reason, _viz._ the want of Observations accurately
made.

If the sixth and seventh Equations are augmented or diminished in a
reciprocal _Ratio_ of the distance of the Moon from the Earth; _i. e._
in a direct _Ratio_ of the Moon's Horizontal Parallax, they will become
more accurate: And this may be readily done, if Tables are first made to
each minute of the said Parallax, and to every sixth or fifth degree of
the Argument of the sixth Equation for the Sixth, as of the distance of
the Moon from the Sun, for the Seventh Equation.

From the Sun's Place, take the mean motion of the Moon's ascending Node,
equated as above; the Remainder shall be the Annual Argument of the
Node, whence its second Equation may be computed after the following
manner in the preceding Figure.

Let T, as before, represent the Earth; TS a Right Line, conjoining the
Earth and Sun: Let also the Line TACB, be drawn to the Place of the
ascending Node of the Moon, as above equated; and let STA be the Annual
Argument of the Node. Take TA from a Scale, and let it be to AB :: as 56
to 3, or as 11⅔ to 1. Then bissect BA in C, and on C as a Centre,
with the Distance CA, describe a Circle, as AFB, and make the Angle BCF,
equal to double the Annual Argument of the Node before-found: So shall
the Angle BTF, be the second Equation of the ascending Node; which must
be added, when the Node is passing from the Quadrature to a Syzygy with
the Sun; and subducted, when the Node moves from a Syzygy towards a
Quadrature. By which means, the true Place of the Node of the Lunar
Orbit will be gained: Whence from Tables made after the common way, the
_Moon's Latitude, and the Reduction of her Orbit to the Ecliptick_, may
be computed, supposing the Inclination of the Moon's Orbit to the
Ecliptick, to be 4 degrees, 59 minutes, 35 seconds, when the Nodes are
in Quadrature with the Sun; and 5 degrees, 17 minutes, 20 seconds, when
they are in the Syzygys.

And from the Longitude and Latitude thus found, and the given Obliquity
of the Ecliptick, 23 degrees, 29 minutes, the Right Ascension and
Declination of the Moon will be found.

The Horizontal Parallax of the Moon, when she is in the Syzygys, at a
mean distance from the Earth, I make to be 57 minutes, 30 seconds; and
her Horary Motion, 33 minutes, 32 seconds, 32 thirds; and her apparent
Diameter 31 minutes, 30 seconds. But in her Quadratures at a mean
Distance from the Earth, I make the Horizontal Parallax of the Moon to
be 59 minutes, 40 seconds, her Horary Motion 32 minutes, 12 seconds, 2
thirds, and her apparent Diameter, 31 minutes, 3 seconds. The Moon in an
Octant to the Sun, and at a mean distance, hath her Centre distant from
the Centre of the Earth about 60-2/9 of the Earth's Semi-diameters.

The Sun's Horizontal Parallax I make to be 10 seconds, and its apparent
Diameter at a mean distance from the Earth, I make 32 minutes, 15
seconds.

The Atmosphere of the Earth, by dispersing and refracting the Sun's
Light, casts a Shadow, as if it were an Opake Body, at least to the
height of 40 or 50 Geographical Miles (by a Geographical Mile, I mean
the sixtieth part of a Degree of a great Circle, on the Earth's
Surface.) This Shadow falling upon the Moon in a Lunar Eclipse, makes
the Earth's Shadow be the larger or broader. And to each Mile of the
Earth's Atmosphere, is correspondent a Second in the Moon's Disk, so
that the Semi-diameter of the Earth's shadow projected upon the Disk of
the Moon, is to be increased about 50 seconds: Or, which is all one, in
a Lunar Eclipse, the Horizontal Parallax of the Moon is to be increased
in the Ratio of about 70 to 69.

Thus far the Theory of this Incomparable Mathematician. And if we had
many Places of the Moon accurately observ'd, especially about her
Quadratures, and these well compar'd with her Places, at the same time
calculated according to this Theory; it would then appear, whether there
yet remain any other sensible Equations; which when accounted for, might
serve to improve and enlarge this Theory.




 _An Estimate of the Degrees of the _Mortality_ of Mankind, drawn from
   curious _Tables_ of the _Births_ and _Funerals_ at the City of
   _Breslaw_; with an Attempt to ascertain the Price of _Annuities_ upon
   _Lives_. By Mr. _E. Halley_, R. S. S._


The Contemplation of the _Mortality_ of _Mankind_, has besides the
_Moral_, its _Physical_ and _Political_ Uses, both which have been some
Years since most judiciously consider'd by the Curious Sir _William
Petty_, in his _Natural_ and _Political_ Observations on the Bills of
_Mortality_ of _London_, own'd by Captain _John Graunt_: And since in a
like Treatise on the Bills of _Mortality_ of _Dublin_. But the Deduction
from those Bills of _Mortality_ seemed even to their Authors to be
defective: First, In that the _Number_ of the People was wanting.
Secondly, That the _Ages_ of the People dying was not to be had. And
Lastly, That both _London_ and _Dublin_, by reason of the great and
casual Accession of _Strangers_ who die therein, (as appeared in both,
by the great Excess of the _Funerals_ above the _Births_) rendred them
incapable of being Standards for this purpose; which requires, if it
were possible, that the People we treat of, should not at all be
changed, but die where they were born, without any adventitious Increase
from Abroad, or Decay by Migration elsewhere.

[Illustration: _Plate 3. pag. 280._]

This _Defect_ seems in a great measure to be satisfied by the late
curious Tables of the Bills of _Mortality_ at the City of _Breslaw_,
lately communicated to this Honourable Society by Mr. _Justell_, wherein
both the Ages and Sexes of all that die, are Monthly delivered, and
compared with the number of the _Births_, for Five Years last past,
_viz._ 1687, 88, 89, 90, 91, seeming to be done with all the Exactness
and Sincerity possible.

This City of _Breslaw_ is the Capital City of the Province of _Silesia_;
or, as the _Germans_ call it, _Schlesia_, and is situated on the Western
Bank of the River _Oder_, anciently call'd _Viadrus_, near the Confines
of _Germany_ and _Poland_, and very nigh the Latitude of _London_. It is
very far from the Sea, and as much a _Mediterranean_ Place as can be
desired, whence the Confluence of Strangers is but small, and the
Manufacture of Linnen employs chiefly the poor People of the Place, as
well as of the Country round about; whence comes that sort of Linnen we
usually call your _Sclesiæ Linnen_; which is the chief, if not the only
Merchandize of the Place. For these Reasons, the People of this City
seem most proper for a _Standard_; and the rather, for that the _Births_
do a small matter exceed the Funerals. The only thing wanting, is the
Number of the whole People, which in some measure I have endeavour'd to
supply, by the comparison of the _Mortality_ of the People of all Ages,
which I shall from the said Bills trace out with all the Accuracy
possible.

It appears that in the Five Years mentioned, _viz._ from 87 to 91
inclusive, there were born 6193 Persons, and buried 5869; that is, born
_per Annum_ 1238, and buried 1174; whence an _Increase_ of the People
may be argued of 64 _per Annum_, or of about a 20th part, which may
perhaps be balanc'd by the Levies for the _Emperor_'s Service in his
Wars. But this being contingent, and the Births certain, I will suppose
the People of _Breslaw_ to be increased by 1238 _Births_ annually. Of
these it appears by the same Tables, that 348 do die _yearly_ in the
_first Year_ of their _Age_, and that but 890 do arrive at a full
_Year's Age_; and likewise, that 198 do die in the _Five Years_ between
1 and 6 compleat, taken at a _Medium_; so that but 692 of the Persons
_born_ do survive _Six_ whole _Years_. From this _Age_ the Infants being
arrived at some degree of Firmness, grow less and less _Mortal_; and it
appears, that of the whole People of _Breslaw_ there die _yearly_, as in
the following Table, wherein the upper Line shews the _Age_, and the
next under it, the _Number_ of Persons of that Age _dying yearly_.

  7   8  9      14     18     21     27  28    35
 11  11  6  5½   2  3½  5  6  4½  6½  9   8  7  7

 36     42    45     39  54  55  56      63
  8  9½  8  9  7  7  10  11   9   9  10  12

     70  71  72     77    81    84    90  91
 9½  14   9  11  9½  6  7  3  4  2  1  1   1

 98   99   100
  0    ⅕     ⅗

And where no Figure is placed over, it is to be understood of those that
die between the Ages of the precedent and consequent _Column_.

From this Table it is evident, that from the Age of 9 to about 25, there
does not die above 6 _per Annum_ of each Age, which is much about 1 _per
Cent._ of those that are of those _Ages_: And whereas in the 14, 15, 16,
17 _Years_, there appear to die much fewer, as 2 and 3½; yet that
seems rather to be attributed to Chance, as are the other Irregularities
in the Series of Ages, which would rectifie themselves, were the number
of Years much more considerable, as 20 instead of 5. And by our own
Experience in _Christ-Church Hospital_, I am inform'd there die of the
_Young Lads_, much about 1 _per Cent. per Annum_, they being of the
aforesaid _Ages_. From 25 to 50, there seem to die from 7 to 8 and 9
_per Annum_ of each Age; and after that to 70, they growing more
_crasie_, though the number be much diminished, yet the _Mortality
increases_, and there are found to die 10 or 11 of each Age _per Annum_:
From thence the number of the Living being grown very small, they
gradually decline till there be none left to _die_; as may be seen at
one View in the Table.

From these Considerations I have form'd the _adjoined Table_, whose Uses
are manifold, and give a more just _Idea_ of the _State_ and _Condition_
of _Mankind_, than any thing yet extant that I know of. It exhibits the
_Number_ of _People_ in the City of _Breslaw_ of all Ages, from the
_Birth_ to extreme _Old Age_, and thereby shews the Chances of
_Mortality_ at all _Ages_, and likewise how to make a certain Estimate
of the Value of _Annuities_ for _Lives_, which hitherto has been only
done by an imaginary _Valuation_: Also the _Chances_ that there are that
a _Person_ of any _Age_ proposed does live to any other _Age_ given;
with many more, as I shall hereafter shew. This _Table_ does shew the
_Number_ of Persons that are living in the _Age_ current annexed
thereto, as follows:

 +------+---------+------+---------+------+---------+
 | Age. | Persons.| Age. | Persons.| Age. | Persons.|
 | Curt.|         | Curt.|         | Curt.|         |
 +------+---------+------+---------+------+---------+
 |   1  |  1000   |   8  |   680   |  15  |   628   |
 |   2  |   855   |   9  |   670   |  16  |   622   |
 |   3  |   798   |  10  |   661   |  17  |   616   |
 |   4  |   760   |  11  |   653   |  18  |   610   |
 |   5  |   732   |  12  |   646   |  19  |   604   |
 |   6  |   710   |  13  |   640   |  20  |   598   |
 |   7  |   692   |  14  |   634   |  21  |   592   |
 +------+---------+------+---------+------+---------+
 |  22  |   586   |  29  |   539   |  36  |   481   |
 |  23  |   579   |  30  |   531   |  37  |   472   |
 |  24  |   573   |  31  |   523   |  38  |   463   |
 |  25  |   567   |  32  |   515   |  39  |   454   |
 |  26  |   560   |  33  |   507   |  40  |   445   |
 |  27  |   553   |  34  |   499   |  41  |   436   |
 |  28  |   546   |  35  |   490   |  42  |   427   |
 +------+---------+------+---------+------+---------+
 |  43  |   417   |  50  |   346   |  57  |   272   |
 |  44  |   407   |  51  |   335   |  58  |   262   |
 |  45  |   397   |  52  |   324   |  59  |   252   |
 |  46  |   387   |  53  |   313   |  60  |   242   |
 |  47  |   377   |  54  |   302   |  61  |   232   |
 |  48  |   367   |  55  |   292   |  62  |   222   |
 |  49  |   357   |  56  |   282   |  63  |   212   |
 +------+---------+------+---------+------+---------+
 |  64  |   202   |  71  |   131   |  78  |    58   |
 |  65  |   192   |  72  |   120   |  79  |    49   |
 |  66  |   182   |  73  |   109   |  80  |    41   |
 |  67  |   172   |  74  |    98   |  81  |    34   |
 |  68  |   162   |  75  |    88   |  82  |    28   |
 |  69  |   152   |  76  |    78   |  83  |    23   |
 |  79  |   142   |  77  |    68   |  84  |    20   |
 +------+---------+------+---------+------+---------+

 Age. Persons.

   7    5547
  14    4584
  21    4270
  28    3964
  35    3604
  42    3708
  49    2709
  56    2194
  63    1694
  70    1204
  77     692
  84     253
 100     107
 -----------
       34000
 -----------
  Sum Total.

Thus it appears, that the whole People of _Breslaw_ does consist of
34000 _Souls_, being the Sum _Total_ of the Persons of all Ages in the
_Table_: The first use hereof is to shew the Proportion of _Men_ able to
bear _Arms_ in any _Multitude_, which are those between 18 and 56,
rather than 16 and 60; the one being generally too weak to bear the
_Fatigues_ of _War_, and the Weight of _Arms_; and the other too crasie
and infirm from _Age_, notwithstanding particular Instances to the
contrary. Under 18 from the _Table_, are found in this City 11997
Persons, 3950 above 56, which together make 15947, so that the Residue
to 34000 being 18053, are Persons between those _Ages_. At least one
half thereof are Males, or 9027: So that the whole Force this City can
raise of _Fencible Men_, as the _Scotch_ call them, is about 9000, or
9/34, or somewhat more than a quarter of the _Number_ of _Souls_; which
may parhaps pass for a Rule for all other places.

The _Second Use_ of this _Table_, is, to shew the differing degrees of
_Mortality_, or rather _Vitality_, in all _Ages_; for if the Number of
Persons of any _Age_ remaining after one Year, be divided by the
difference between that and the number of the _Age_ proposed, it shews
the _Odds_ that there is, that a Person of that _Age_ does not die in a
_Year_. As for Instance, a Person of 25 _Years_ of _Age_ has the Odds of
560 to 7, or 80 to 1, that he does not _die_ in a _Year_: Because that
of 567, living of 25 _Years_ of _Age_, there do die no more than 7 in a
_Year_, leaving 560 of 26 Years old.

So likewise for the _Odds_, that any Person does not die before he
attain any proposed _Age_: Take the _number_ of the remaining Persons of
the _Age_ proposed, and divide it by the difference between it and the
number of those of the _Age_ of the Party proposed; and that shews the
_Odds_ there is between the Chances of the Party's living or dying. As
for Instance; What is the _Odds_ that a Man of 40 lives 7 Years: Take
the number of Persons of 47 Years, which in the Table is 377, and
subtract it from the number of Persons of 40 Years, which is 445, and
the _difference_ is 68: Which shews that the _Persons dying_ in that 7
Years, are 68, and that it is 377 to 68, or 5½ to 1, that a Man of 40
does live 7 Years. And the like for any other _number_ of _Years_.

_Use_ III. But if it be enquired at what number of _Years_, it is an
even Lay that a Person of any _Age_ shall die, this Table readily
performs it; For if the _number_ of Persons _living_ of the _Age_
proposed, be _halfed_, it will be found by the _Table_ at what Year the
said _Number_ is reduced to half by _Mortality_; and that is the _Age_,
to which it is an even Wager, that a Person of the _Age_ proposed shall
arrive before he _die_. As for Instance; A Person of 30 Years of _Age_
is proposed, the number of that _Age_ is 531, the half thereof is 265,
which number I find to be between 57 and 58 Years; so that a Man of 30
may reasonably expect to live between 27 and 28 Years.

_Use_ IV. By what has been said, the _Price_ of _Insurance_ upon Lives
ought to be regulated, and the difference is discovered between the
_Price_ of insuring the _Life_ of a _Man_ of 20 and 50. For Example; It
being 100 to 1, that a Man of 20 dies not in a Year, and but 38 to 1,
for a Man of 50 Years of Age.

_Use_ V. On this depends the Valuation of _Annuities_ upon _Lives_; for
it is plain, that the _Purchaser_ ought to pay for only such a part of
the Value of the _Annuity_, as he has Chances that he is living; and
this ought to be computed yearly, and the Sum of all those yearly Values
being added together, will amount to the Value of the _Annuity_ for the
_Life_ of the Person proposed. Now the present Value of Money payable
after a Term of Years, at any given Rate of Interest, either may be had
from Tables already computed; or almost as compendiously, by the Table
of Logarithms: For the Arithmetical Complement of the Logarithm of
Unity, and its yearly Interest, (that is, of 1,06 for Six _per Cent._
being 9,974694.) being multiplied by the number of Years proposed, gives
the present Value of One Pound payable after the end of so many Years.
Then by the foregoing Proposition, it will be as the number of Persons
living after that Term of Years, to the number dead; so are the Odds
that any one Person is alive or dead. And by consequence, as the Sum of
both, or the number of Persons living of the _Age_ first proposed, to
the number remaining after so many Years, (both given by the Table) so
the present Value of the yearly Sum payable after the Term proposed, to
the Sum which ought to be paid for the Chance the Person has to enjoy
such an _Annuity_ after so many Years. And this being repeated for every
Year of the Person's Life, the Sum of all the present Values of those
Chances is the true Value of the Annuity. This will without doubt appear
to be a most laborious Calculation; but it being one of the principal
Uses of this Speculation, and having found some _Compendia_ for the
Work, I took the pains to compute the following Table, being the short
Result of a not ordinary number of Arithmetical Operations: It shews the
Value of Annuities for every Fifth Year of Age, to the Seventieth, as
follows.

 +------+------------+------+------------+------+------------+
 | Age. | Years Pur. | Age. | Years Pur. | Age. | Years Pur. |
 +------+------------+------+------------+------+------------+
 |   1  |   10,28    |  25  |   12,27    |  50  |    9,21    |
 |   5  |   13,40    |  30  |   11,72    |  55  |    8,51    |
 |  10  |   13,44    |  35  |   11,12    |  60  |    7,60    |
 |  15  |   13,33    |  40  |   10,57    |  65  |    6,54    |
 |  20  |   12,78    |  45  |    9,91    |  70  |    5,32    |
 +------+------------+------+------------+------+------------+

This shews the great Advantage of putting Money into the present _Fund_
lately granted to Their Majesties, giving 14 _per Cent. per Annum_, or
at the Rate of 7 Years Purchase for a Life; when young Lives, at the
usual Rate of Interest, are worth above 13 Years Purchase. It shews
likewise the Advantage of young Lives over those in Years; a Life of Ten
Years being almost worth 13½ Years Purchase, whereas one of 36 is
worth but 11.

_Use_ VI. Two Lives are likewise valuable by the same Rule; for the
number of Chances of each single Life, found in the Table, being
multiplied together, become the Chances of the Two Lives. And after any
certain Term of Years, the Product of the two remaining Sums is the
Chances that both the Persons are living. The Product of the two
Differences, being the numbers of the Dead of both Ages, are the Chances
that both the Persons are dead. And the two Products of the remaining
Sums of the one Age multiplied by those dead of the other, shew the
Chances that there are, that each Party survives the other: Whence is
derived the Rule to estimate the Value of the Remainder of one Life
after another. Now as the Product of the Two Numbers in the Table for
the Two Ages proposed, is to the difference between that Product, and
the Product of the two numbers of Persons deceased in any space of time;
so is the Value of a Sum of Money to be paid after so much time, to the
Value thereof under the Contingency of Mortality. And as the aforesaid
Product of the two Numbers answering to the Ages proposed, to the
Product of the Deceased of one Age multiplied by those remaining alive
of the other; so the Value of a Sum of Money to be paid after any time
proposed, to the Value of the Chances, that the one Party has that he
survives the other, whose number of Deceased you made use of, in the
second Term of the Proportion. This perhaps may be better understood, by
putting _N_ for the number of the younger Age, and _n_ for that of the
Elder; _Y_, _y_ the Deceased of both Ages respectively, and _R_, _r_ for
the Remainders; and _R + Y_ = _N_, and _r + y_ = _n_. Then shall _Nn_ be
the whole Number of Chances; _Nn - Yy_ be the Chances that one of the
two Persons is living, _Yy_ the Chances that they are both dead; _Ry_
the Chances that the elder Person is dead, and the younger living; and
_rY_ the Chances, that the elder is living, and the younger dead. Thus
two Persons of 18 and 35 are proposed, and after 8 Years these Chances
are required. The Numbers for 18 and 35, are 610 and 490; and there are
50 of the First Age dead in 8 Years, and 73 of the Elder Age. There are
in all 610 × 490, or 298900 Chances; of these there are 50 × 73, or
3650, that they are both dead. And as 298900, to 298900 - 3650, or
295250: So is the present Value of a Sum of Money to be paid after 8
Years, to the present Value of a Sum to be paid, if either of the two
live. And as 560 × 73, so are the Chances that the Elder is dead,
leaving the Younger; and as 417 × 50, so are the Chances that the
Younger is dead, leaving the Elder. Wherefore as 610 × 490 to 560 × 73,
so is the present Value of a Sum to be paid at 8 Years end, to the Sum
to be paid for the Chance of the Younger's Survivance; and as 610 × 490
to 417 × 50, so is the same present Value to the Sum to be paid for the
Chance of the Elder's Survivance.

This possibly may be yet better explained, by expounding these Products
by Rectangular Parallelograms, as in _Fig. 7._ wherein _AB_ or _CD_
represents the number of Persons of the younger Age, and _DE_, _BH_
those remaining alive after a certain Term of Years; whence _CE_ will
answer the number of those dead in that time: So _AC_, _BD_ may
represent the number of the elder Age; _AF_, _BI_ the Survivors after
the same Term; and _CF_, _DI_, those of that Age that are dead at that
time. Then shall the whole Parallelogram _ABCD_ be _Nn_, or the Product
of the two Numbers of Persons, representing such a number of Persons of
the two Ages given; and by what was said before, after the Term
proposed, the Rectangle _HD_ shall be as the number of Persons of the
younger Age that survive, and the Rectangle _AE_ as the number of those
that die. So likewise the Rectangles _AI_, _FD_ shall be as the Numbers,
living and dead, of the other Age. Hence the Rectangle _HI_ shall be as
an equal number of both Ages surviving. The Rectangle _FE_ being the
Product of the Deceased, or _Yy_, an equal number of both dead. The
Rectangle _GD_ or _Ry_, a number living of the younger Age, and dead of
the elder: And the Rectangle _AG_ or _rY_ a number living of the elder
Age, but dead of the younger. This being understood, it is obvious, that
as the whole Rectangle _AD_ or _Nn_ is to the _Gnomon FABDEG_ or
_Nn - Yy_, so is the whole number of Persons or Chances, to the number of
Chances that one of the two Persons is living: And as _AD_ or _Nn_ is to
_FE_ or _Yy_, so are all the Chances, to the Chances that both are dead;
whereby may be computed the Value of the Reversion after both Lives. And
as _AD_ to _GD_ or _Ry_, so the whole number of Chances, to the Chances
that the younger is living, and the other dead; whereby may be cast up
what Value ought to be paid for the Reversion of one Life after another,
as in the Case of providing for Clergy-men's Widows, and others, by such
Reversions. And as _AD_ to _AG_, or _rY_, so are all the Chances, to
those that the elder survives the younger. I have been the more
particular, and perhaps tedious, in this Matter, because it is the Key
to the Case of Three Lives, which of it self would not have been so
easie to comprehend.

VII. If Three Lives are proposed, to find the Value of an Annuity during
the continuance of any of those three Lives; the Rule is, _As the
Product of the continual Multiplication of the Three Numbers, in the
Table, answering to the Ages proposed, is to the difference of that
Product, and of the Product of the Three Numbers of the Deceased of
those Ages, in any given Term of Years: So is the present Value of a Sum
of Money, to be paid certainly after so many Years, to the present Value
of the same Sum to be paid, provided one of those Three Persons be
living at the Expiration of that Term._ Which Proportion being yearly
repeated, the Sum of all those present Values will be the Value of an
Annuity granted for three such Lives. But to explain this, together with
all the Cases of Survivance in Three Lives: Let _N_ be the Number in the
Table for the younger Age, _n_ for the second, and ν for the elder
Age; let _Y_ be those dead of the younger Age in the Term proposed, _y_
those dead of the second Age, and υ those of the elder Age; and let
_R_ be the Remainder of the younger Age, _r_ that of the middle Age, and
ρ the Remainder of the elder Age. Then shall _R + Y_ be equal to _N_,
_r + y_ to _n_, and ρ + υ to ν, and the continual Product of the
three Numbers _N_, _n_, ν, shall be equal to the continual Product of
_R + Y × r + y × ρ + υ_, which being the whole Number of Chances for
three Lives, is compounded of the eight Products following. (1) _Rrρ_,
which is the Number of Chances that all three of the Persons are living.
(2) _rρY_, which is the Number of Chances that the two elder Persons
are living, and the younger dead. (3) _Rρy_ the Number of Chances that
the middle Age is dead, and the younger and elder living. (4) _Rrυ_
being the Chances that the two younger are living, and the elder dead.
(5) _ρYy_ the Chances that the two younger are dead, and the elder
living. (6) _rYυ_ the Chances that the younger and elder are dead, and
the middle Age living. (7) _Ryυ_, which are the Chances that the
younger is living, and the two other dead. And Lastly and Eighthly,
_Yyυ_, which are the Chances that all three are dead. Which latter
subtracted from the whole Number of Chances _Nnν_, leaves _Nnν -
Yyυ_ the Sum of all the other seven Products; in all of which one or
more of the three Persons are surviving.

To make this yet more evident, I have added _Fig. 8._ wherein these
eight several Products are at one view exhibited. Let the rectangled
Parallelepipedon _ABCDEFGH_ be constituted of the sides _AB_, _GH_,
_&c._ proportional to _N_ the Number of the younger Age; _AC_, _BD_,
_&c._ proportional to _n_; and _AG_, _CE_, _&c._ proportional to the
Number of the elder, or ν. And the whole Parallelepipedon shall be as
the Product _Nnν_, or our whole Number of Chances. Let _BP_ be as _R_,
and _AP_ as _Y_; let _CL_ be as _r_, and _Ln_ as _y_; and _GN_ as ρ,
and _NA_ as υ; and let the Plain _PRea_ be made parallel to the Plain
_ACGE_; the Plain _NVbY_ parallel to _ABCD_; and the Plain _LXTQ_
parallel to the Plain _ABGH_. And our first Product _Rrρ_ shall be as
the Solid _STWIFZeb_. The Second, or _rρY_ will be as the Solid
_EYZeQSMI_. The Third, _Rρy_, as the Solid _RHOVWIST_. And the Fourth,
_Rrυ_, as the Solid _ZabDWXIK_. Fifthly, _ρYy_, as the Solid
_GQRSIMNO_. Sixthly, _rYυ_, as _IKLMGYZA_. Seventhly, _Ryυ_, as the
Solid _IKPOBXVW_. And Lastly, _AIKLMNOP_ will be as the Product of the 3
Numbers of Persons dead, or _Yyυ_. I shall not apply this in all the
Cases thereof, for brevity sake; only to shew in one how all the rest
may be performed, let it be demanded what is the Value of the Reversion
of the younger Life after the two elder proposed. The proportion is as
the whole Number of Chances, or _Nnν_ to the Product _Ryυ_; so is
the certain present Value of the Sum payable after any Term proposed, to
the Value due to such Chances as the younger Person has to bury both the
elder, by the Term proposed; which therefore he is to pay for. Here it
is to be noted, that the first Term of all these Proportions is the same
throughout, _viz._ _Nnν_. The second changing yearly according to the
Decrease of _R_, _r_, _ρ_, and Increase of _Y_, _y_, _υ_. And the
third are successively the present Values of Money payable after one,
two, three, _&c._ years, according to the Rate of Interest agreed on.
These Numbers, which are in all Cases of Annuities of necessary Use, I
have put into the following Table, they being Decimal Values of one
Pound payable after the Number of Years in the Margent, at the Rate of 6
_per Cent._

 +--------+-------------+--------+-------------+--------+-------------+
 | Years. | Pres. Value | Years. | Pres. Value | Years. | Pres. Value |
 |        |  of 1 _l._  |        |  of 1 _l._  |        |  of 1 _l._  |
 +--------+-------------+--------+-------------+--------+-------------+
 |    1   |   0,9434    |   19   |   0,3305    |   37   |   0,1158    |
 |    2   |   0,8900    |   20   |   0,3118    |   38   |   0,1092    |
 |    3   |   0,8396    |   21   |   0,2941    |   39   |   0,1031    |
 |    4   |   0,7921    |   22   |   0,2775    |   40   |   0,0972    |
 |    5   |   0,7473    |   23   |   0,2618    |   45   |   0,0726    |
 |    6   |   0,7050    |   24   |   0,2470    |   50   |   0,0543    |
 +--------+-------------+--------+-------------+--------+-------------+
 |    7   |   0,6650    |   25   |   0,2330    |   55   |   0,0406    |
 |    8   |   0,6274    |   26   |   0,2198    |   60   |   0,0303    |
 |    9   |   0,5919    |   27   |   0,2074    |   65   |   0,0227    |
 |   10   |   0,5584    |   28   |   0,1956    |   70   |   0,0169    |
 |   11   |   0,5268    |   29   |   0,1845    |   75   |   0,0126    |
 |   12   |   0,4970    |   30   |   0,1741    |   80   |   0,0094    |
 +--------+-------------+--------+-------------+--------+-------------+
 |   13   |   0,4688    |   31   |   0,1643    |   85   |   0,0071    |
 |   14   |   0,4423    |   32   |   0,1550    |   90   |   0,0053    |
 |   15   |   0,4173    |   33   |   0,1462    |   95   |   0,0039    |
 |   16   |   0,3936    |   34   |   0,1379    |  100   |   0,0029    |
 |   17   |   0,3714    |   35   |   0,1301    |        |             |
 |   18   |   0,3503    |   36   |   0,1227    |        |             |
 +--------+-------------+--------+-------------+--------+-------------+

It were needless to advertise, that the great trouble of working so many
Proportions will be very much alleviated by using Logarithms; and that
instead of using _Nnν - Yyυ_ for the second Term of the Proportion
in finding the Value of Three Lives, it may suffice to use only _Yyυ_,
and then deducting the fourth Term so found out of the third, the
Remainder shall be the present Value sought; or all these fourth Terms
being added together, and deducted out of the Value of the certain
Annuity for so many Years, will leave the Value of the contingent
Annuity upon the Chance of Mortality of all those Three Lives. For
Example; Let there be Three Lives of 10, 30, and 40 Years of Age
proposed, and the Proportions will be thus;

 As 661 in 531 in 445 or 156190995, or _Nnν_
 to 8 in 8 in 9, or 576, or _Yyυ_ for the first
 Year, so 0,9434. to 0,00000348.

 To 15 in 16 in 18, or 4320, for the second
 Year, so 0,8900. to 0,00002462.

 To 21 in 24 in 28, or 14112 for the third
 Year, so 0,8396. to 0,00008128.

 To 27 in 32 in 38, for the fourth Year, so
 0,7921. to 0,00016650.

 To 33 in 41 in 48, for the fifth Year, so
 0,7473. to 0,00031071.

 To 39 in 50 in 58, for the sixth Year, so
 0,7050. to 0,00051051.

And so forth to the 60th Year, when we suppose the elder Life of Forty
certainly to be expired; from whence till Seventy we must compute for
the First and Second only, and from thence to Ninety for the single
youngest Life. Then the Sum Total of all these Fourth Proportionals
being taken out of the Value of a certain Annuity for 90 Years, being
16,58 Years Purchase, shall leave the just Value to be paid for an
Annuity during the whole Term of the Lives of Three Persons of the Ages
proposed. And note, that it will not be necessary to compute for every
Year singly; but that in most Cases every 4th or 5th Year may suffice,
interpoling for the intermediate Years _seceundum artem_.

It may be objected, that the different _Salubrity_ of Places does hinder
this Proposal from being _universal_; nor can it be denied. But by the
Number that die, being 1174. _per Annum_ in 34000, it does appear that
about a 30th part die yearly, as Sir _William Petty_ has computed for
_London_; and the Number that die in Infancy, is a good Argument that
the Air is but indifferently salubrious. So that by what I can learn,
there cannot perhaps be one better Place proposed for a Standard. At
least 'tis desired, that in Imitation hereof the Curious in other Cities
would attempt something of the same Nature, than which nothing perhaps
can be more useful.

Were this _Calculus_ founded on the Experience of a very great number of
Years, it would be very well worth the while to think of Methods for
facilitating the Computation of the Value of two, three, or more Lives;
which, as proposed in my former, seems (as I am inform'd) a Work of too
much Difficulty for the ordinary Arithmetician to undertake.

I have sought, If it were possible, to find a Theorem that might be more
concise than the Rules there laid down, but in vain; for all that can be
done to expedite it, is, by Tables of Logarithms ready computed, to
exhibit the _Rationes_ of _N_ to _Y_ in each single Life, for every
third, fourth, or fifth Year of Age, as occasion shall require; and
these Logarithms being added to the Logarithms of the present Value of
Money payable after so many Years, will give a Series of Numbers, the
Sum of which will shew the Value of the Annuity sought. However, for
each Number of this Series, two Logarithms for a single Life, three for
two Lives, and four for three Lives, must necessarily be added together.
If you think the Matter, under the Uncertainties I have mentioned, to
deserve it, I shall shortly give you such a Table of Logarithms, as I
speak of, and an Example or two of the use thereof: But by Vulgar
Arithmetick, the Labour of these Numbers were immense; and nothing will
more recommend the useful Invention of Logarithms to all Lovers of
Numbers, than the advantage of Dispatch in this and such like
Computations.

Besides the Uses mentioned, it may perhaps not be an unacceptable thing
to infer from the same Tables, how unjustly we repine at the shortness
of our Lives, and think our selves wronged if we attain not old Age;
whereas it appears hereby, that the one half of those that are born are
dead in Seventeen Years time, 1238 being in that time reduced to 616. So
that instead of murmuring at what we call an untimely Death, we ought
with Patience and Unconcern to submit to that Dissolution which is the
necessary Condition of our perishable Materials, and of our nice and
frail Structure and Composition: And to account it as a Blessing that we
have survived, perhaps by many Years, that Period of Life, whereat the
one half of the whole Race of Mankind does not arrive.

A second Observation I make upon the said Table, is that the Growth and
Increase of Mankind is not so much stinted by any thing in the Nature of
the _Species_, as it is from the cautious difficulty most People make to
adventure on the State of _Marriage_, from the Prospect of the Trouble
and Charge of providing for a Family. Nor are the poorer sort of People
herein to be blamed, since their difficulty of subsisting is occasion'd
by the unequal Distribution of Possessions, all being necessarily fed
from the Earth, of which yet so few are Masters. So that besides
themselves and Families, they are yet to work for those who own the
Ground that feeds them: And of such does by very much the greater part
of Mankind consist; otherwise it is plain, that there might well be four
times as many Births as we now find. For by Computation from the Table,
I find that there are nearly 15000 Persons above 16, and under 45, of
which at least 7000 are Women capable to bear Children. Of these
notwithstanding there are but 1238 born yearly, which is but little more
than a sixth part: So that about one in six of these Women do breed
yearly; whereas were they all married, it would not appear strange or
unlikely, that four of six should bring a Child every Year. The
Political Consequences hereof I shall not insist on; only the Strength
and Glory of a King being in the multitude of his Subjects, I shall only
hint, that above all things, Celibacy ought to be discouraged, as, by
extraordinary Taxing and Military Service: And those who have numerous
Families of Children to be countenanced and encouraged by such Laws as
the _Jus trium Liberorum_ among the _Romans_. But especially, by an
effectual Care to provide for the Subsistence of the Poor, by finding
them Employments, whereby they may earn their Bread, without being
chargeable to the Publick.




 _A Discourse concerning _Gravity_, and its Properties, wherein the
   Descent of _Heavy Bodies_, and the Motion of _Projects_ is briefly,
   but fully handled: Together with the _Solution_ of a _Problem_ of
   great Use in _Gunnery_. By _E. Halley_._


Nature, amidst the great Variety of _Problems_, wherewith She exercises
the Wits of Philosophical Men, scarce affords any one wherein the Effect
is more visible, and the Cause more concealed, than in those of the
_Phænomena_ of _Gravity_. Before we can go alone, we must learn to
defend our selves from the Violence of its Impulse, by not trusting the
_Center_ of _Gravity_ of our Bodies beyond our reach; and yet the
acutest Philosophers, and the subtilest Enquirers into the Original of
this Motion, have been so far from satisfying their Readers, that they
themselves seem little to have understood the Consequences of their own
_Hypotheses_.

_Des Cartes_ his Notion, I must needs confess to be to me incomprehensible,
while he will have the Particles of his _Cœlestial Matter_, by being
reflected on the Surface of the _Earth_, and so ascending therefrom, to
drive down into their Places those _Terrestrial Bodies_ they find above
them: This is, as near as I can gather, the Scope of the 20, 21, 22, and
23 _Sections_ of the last Book of his _Principia Philosophiæ_; yet
neither he, nor any of his Followers, can shew how a Body suspended in
_Libero Æthere_, shall be carried downwards by a continual Impulse
tending upwards, and acting upon all its Parts equally: And besides the
Obscurity wherewith he expresses himself, particularly, _Sect. 23._ does
sufficiently argue according to his own Rules, the confused _Idea_ he
had of the thing he wrote.

Others, and among them Dr. _Vossius_, assert the Cause of the _Descent_
of _heavy Bodies_, to be the _Diurnal Rotation_ of the _Earth_ upon its
_Axis_, without considering, that according to the Doctrine of Motion
fortified with Demonstration, all Bodies moved _in Circulo_, would
recede from the Center of their Motion; whereby the contrary to
_Gravity_ would follow, and all loose Bodies would be cast into the Air
in a _Tangent_ to the _Parallel_ of _Latitude_, without the intervention
of some other Principle to keep them fast, such as is that of _Gravity_.
Besides, the Effect of this Principle is throughout the whole Surface of
the Globe found nearly equal; and certain Experiments have proved it
rather less near the _Æquinoctial_, than towards the _Poles_; which
could not be by any means, if the _Diurnal Rotation_ of the _Earth_ upon
its _Axis_ were the Cause of _Gravity_; for where the Motion was
swiftest, the Effect would be most considerable.

Others assign the Pressure of the _Atmosphere_, to be the Cause of this
Tendency towards the Center of the Earth; but unhappily they have
mistaken the Cause for the Effect; it being from undoubted Principles
plain, that the _Atmosphere_ has no other Pressure but what it derives
from its _Gravity_; and that the Weight of the upper Parts of the _Air_,
pressing on the lower Parts thereof, do so far bend the Springs of that
_Elastick_ Body, as to give it a Force equal to the Weight that
compress'd it, having of it self no force at all: And supposing it had,
it will be very hard to explain the _Modus_, how that Pressure should
occasion the Descent of a Body circumscribed by it, and pressed equally
above and below, without some other Force to draw, or thrust it
downwards. But to demonstrate the contrary of this Opinion, an
_Experiment_ was long since shewn before the _Royal Society_, whereby it
appeared, that the _Atmosphere_ was so far from being the Cause of
_Gravity_, that the Effects thereof were much more vigorous, where the
Pressure of the _Atmosphere_ was taken off; for a long _Glass-Receiver_
having a light Down-feather included, being evacuated of Air, the
Feather, which in the Air would hardly sink, did _in vacuo_ descend with
nearly the same _Velocity_, as if it had been a Stone.

Some think to illustrate this Descent of Heavy Bodies, by comparing it
with the Vertue of the _Loadstone_; but setting aside the difference
there is in the manner of their Attractions, the _Loadstone_ drawing
only in and about its Poles, and the Earth near equally in all Parts of
its Surface, this Comparison avails no more than to explain _ignotum per
æque ignotum_.

Others assign a certain _Sympæthetical Attraction_ between the Earth and
its Parts, whereby they have, as it were, a desire to be united, to be
the Cause we enquire after: But this is so far from explaining the
_Modus_, that it is little more, than to tell us in other Terms, that
Heavy Bodies descend, because they descend.

This, I say, not that I can pretend to substitute any Solution of this
Important Philosophical Problem, that shall more happily explicate the
Appearances of Gravity; only it may be serviceable to those with whom
the Credit of great Authors sways much, and who too readily assent _in
Verba Magistri_, to let them see that their Books are not always
infallible: Besides, the detection of Errors is the first and surest
Step towards the discovery of Truth.

Though the efficient Cause of _Gravity_ be so obscure, yet the final
Cause thereof is clear enough; for it is by this single _Principle_,
that the _Earth_ and all the _Cœlestial Bodies_ are kept from
_Dissolution_; the least of their _Particles_ not being suffer'd to
recede far from their _Surfaces_, without being immediately brought down
again by Virtue of this _Natural Tendency_; which, for their
Preservation, the Infinite Wisdom of their _Creator_ has ordained to be
towards each of their _Centers_; nor can the _Globes_ of the _Sun_ and
_Planets_ otherwise be destroy'd, but by taking from them this Power of
keeping their Parts united.

The Affections or Properties of _Gravity_, and its manner of acting upon
_Bodies falling_, have been in a great measure discovered, and most of
them made out by _Mathematical Demonstration_ in this our _Century_, by
the accurate diligence of _Galilæus_, _Torricellius_, _Hugenius_, and
others, and now lately by our worthy Countryman, Mr. _Isaac Newton_,
which Properties it may be very material here to enumerate, that they
may serve for a Foundation to all those that shall be willing to spend
their Thoughts in search of the true Cause of this _Descent of Bodies_.

The first Property is, That by this Principle of _Gravitation_, all
Bodies do descend towards a Point, which either is, or else is very near
to the Center of Magnitude of the Earth and Sea, about which the Sea
forms it self exactly into a _Spherical Surface_, and the _Prominences_
of the Land, considering the Bulk of the whole, differ but insensibly
therefrom.

_Secondly_, That this Point or Center of _Gravitation_, is fix'd within
the _Earth_, or at least has been so, ever since we have any _Authentick
History_: For a Consequence of its Change, though never so little, would
be the over-flowing of the low Lands on that side of the _Globe_ towards
which it approached, and the leaving new Islands bare on the opposite
side, from which it receded; but for this Two Thousand Years it appears,
that the low Islands of the _Mediterranean Sea_ (near to which the
ancientest Writers liv'd) have continued much at the same height above
the Water, as they now are found; and no _Inundations_ or _Recesses_ of
the _Sea_ arguing any such Change, are recorded in History; excepting
the _Universal Deluge_, which can no better way be accounted for, than
by supposing this Center of _Gravitation_ removed for a time, towards
the middle of the then inhabited Parts of the World; and a change of its
Place, but the Two Thousandth Part of the _Radius_ of this _Globe_, were
sufficient to bury the Tops of the highest Hills under Water.

_Thirdly_, That in all Parts of the _Surface_ of the _Earth_, or rather
in all Points equidistant from its _Center_, the Force of _Gravity_ is
nearly equal; so that the length of the _Pendulum_ vibrating _Seconds of
Time_, is found in all Parts of the World to be very near the same. 'Tis
true at St. _Helena_, in the _Latitude_ of 16 Degrees _South_, I found
that the _Pendulum_ of my Clock, which vibrated _Seconds_, needed to be
made shorter than it had been in _England_, by a very sensible Space
(but which at that time I neglected to observe accurately) before it
would keep time; and since the like Observations have been made by the
_French Observers_, near the _Æquinoctial_: Yet I dare not affirm, that
in mine it proceeded from any other Cause, than the great Height of my
Place of Observation above the _Surface_ of the _Sea_, whereby the
_Gravity_ being diminished, the length of the _Pendulum_ vibrating
_Seconds_, is proportionably short'ned.

_Fourthly_, That _Gravity_ does equally affect all _Bodies_, without
regard either to their _Matter_, _Bulk_, or _Figure_; so that the
Impediment of the _Medium_ being removed, the most compact and most
loose, the greatest and smallest _Bodies_ would descend the same
_Spaces_ in equal Times; the Truth thereof will appear from the
Experiment I before-cited. In these two last Particulars, is shewn the
great difference between _Gravity_ and _Magnetism_, the one affecting
only _Iron_, and that towards its _Poles_, the other all _Bodies_ alike
in every part. As a _Corollary_, from hence it will follow, that there
is no such thing as _positive Levity_, those things that appear light,
being only comparatively so; and whereas several things rise and swim in
_Fluids_, 'tis because, Bulk for Bulk, they are not so heavy as those
_Fluids_; nor is there any Reason why _Cork_, for Instance, should be
said to be light, because it swims on Water, any more than _Iron_,
because it swims on _Mercury_.

_Fifthly_, That this Power increases as you descend, and decreases as
you ascend from the Center, and that in the Proportion of the Squares of
the _Distances_ therefrom _reciprocally_, so as at a double Distance to
have but a quarter of the Force; this Property is the Principle on which
Mr. _Newton_ has made out all the _Phænomena_ of the _Cœlestial
Motions_, so easily and naturally, that its Truth is past Dispute.
Besides that, it is highly rational, that the _attractive_ or
_gravitating_ Power should exert it self more vigorously in a small
Sphere, and weaker in a greater, in proportion as it is contracted or
expanded; and if so, seeing that the _Surfaces_ of _Spheres_ are as the
_Squares_ of their _Radii_, this Power, at several Distances, will be as
the _Squares_ of those _Distances reciprocally_; and then its whole
Action upon each _Spherical Surface_, be it great or small, will be
always equal. And this is evidently the Rule of _Gravitation_ towards
the _Centers_ of the _Sun_, _Jupiter_, _Saturn_ and the _Earth_, and
thence is reasonably inferred, to be the general Principle observed by
_Nature_, in all the rest of the _Cœlestial Bodies_.

These are the principal Affections of _Gravity_, from which the Rules of
the _Fall_ of _Bodies_, and the _Motion_ of _Projects_ are
_Mathematically_ deducible. Mr. _Isaac Newton_ has shew'd how to define
the Spaces of the _Descent_ of a _Body_, let fall from any given height,
down to the _Center_, supposing the _Gravitation_ to increase, as in the
fifth Property; but considering the smallness of heighth, to which any
_Project_ can be made ascend, and over how little an _Arch_ of the
_Globe_ it can be cast by any of our _Engines_, we may well enough
suppose the _Gravity_ equal throughout, and the Descents of _Projects_
in parallel Lines, which in Truth are towards the _Center_, the
difference being so small as by no means to be discovered in _Practice_.
The _Opposition_ of the _Air_, 'tis true, is considerable against all
light Bodies moving through it, as likewise against small ones (of which
more hereafter) but in great and ponderous Shot, this Impediment is
found by _Experience_ but very small, and may safely be neglected.


_Propositions concerning the Descent of Heavy Bodies, and the Motion of
_Projects_._

_Prop. I._ The _Velocities_ of _Falling Bodies_, are proportionate to
the Times from the beginning of their _Falls_.

This follows, for that the Action of _Gravity_ being _continual_, in
every Space of Time, the falling Body receives a new Impulse, equal to
what it had before, in the same Space of Time, received from the same
Power: For Instance, in the first Second of Time, the falling Body has
acquired a _Velocity_, which in that time would carry it to a certain
Distance, suppose 32 Foot, and were there no new Force, would descend at
that rate with an _equable Motion_: But in the next Second of Time, the
same Power of _Gravity_ continually acting thereon, superadds a new
_Velocity_ equal to the former; so that at the end of two Seconds, the
_Velocity_ is double to what it was at the end of the first, and after
the same manner may it be proved to be triple, at the end of the third
Second, and so on. Wherefore the _Velocities_ of _falling Bodies_, are
proportionate to the Time of their _Falls_, _Q. E. D._

[Illustration: _Plate 4. pag. 310_]


_Prop. II._ The _Spaces_ described by the Fall of a Body, are as the
_Squares_ of the Times, from the beginning of the _Fall_.

_Demonstration._ Let AB (_Fig. 9. Tab. 4._) represent the _Time_ of the
_Fall_ of a _Body_, BC perpendicular to AB, the _Velocity_ acquired at
the end of the _Fall_, and draw the Line AC; then divide the Line AB
representing the Time, into as many equal Parts as you please, as b, b,
b, b, _&c._ and through these Points draw the Lines bc, bc, bc, bc,
_&c._ parallel to BC, 'tis manifest that the several Lines, bc,
represent the several _Velocities_ of the falling Body, in such Parts of
the _Time_ as Ab is of AB, by the former Proposition. It is evident
likewise, that the _Area_ ABC is the Sum of all the Lines bc being
taken, according to the Method of _Indivisibles_, infinitely many; so
that the _Area_ ABC represents the Sum of all the _Velocities_, between
none and BC supposed infinitely many; which Sum is as the Space
descended in the Time represented by AB. And by the same Reason the
_Areas_ Abc, will represent the Spaces descended in the Times Ab; so
then the Spaces descended in the Times AB, Ab, are as the _Areas_ of the
_Triangles_ ABC, Abc, which by the 20th of the 6 of _Euclid_, are as the
_Squares_ of their _Homologous Sides_ AB, Ab, that is to say, of the
_Times_: Wherefore the Descents of _falling Bodies_, are as the
_Squares_ of the Times of their _Fall_, _Q. E. D._


_Prop. III._ The _Velocity_ which a _falling Body_ acquires in any Space
of time, is double to that, wherewith it would have moved the Space,
descended by an equable Motion, in the same _time_.

_Demonstration._ Draw the Line EC parallel to AB, and AE parallel to BC
in the same _Fig. 9._ and compleat the _Parallelogram_ ABCE, it is
evident that the _Area_ thereof may represent the Space, a _Body_ moved
equably with the _Velocity_ BC would describe in the Time AB, and the
_Triangle_ ABC represents the _Space_ describ'd by the _Fall_ of a
_Body_, in the same Time AB, by the second Proposition. Now the
_Triangle_ ABC is half of the _Parallelogram_ ABCE, and consequently the
Space described by the _Fall_, is half what would have been described by
an _equable Motion_ with the _Velocity_ BC, in the same Time; wherefore
the _Velocity_ BC at the end of the _Fall_, is double to that
_Velocity_, which in the Time AB, would have described the _Space
fallen_, represented by the _Triangle_ ABC with an _equable Motion_, _Q.
E. D._


_Prop. IV._ All _Bodies_ on or near the Surface of the _Earth_, in their
_Fall_, descend so, as at the end of the first Second of Time, they have
described 16 Feet, 1 Inch, _London Measure_, and acquired the _Velocity_
of 32 Feet, 2 Inches, in a Second.

This is made out from the 25th Proposition of the second Part of that
excellent Treatise of Mr. _Hugenius de Horologio Oscillatorio_; wherein
he demonstrates the time of the least _Vibrations_ of a _Pendulum_, to
be to the Time of the _Fall_ of a _Body_, from the heighth of half the
length of the _Pendulum_, as the _Circumference_ of a _Circle_ to its
_Diameter_; whence, as a _Corollary_, it follows, That as the _Square_
of the _Diameter_ to the _Square_ of the _Circumference_, so half the
length of the _Pendulum_ vibrating _Seconds_, to the _Space_ described
by the _Fall_ of a _Body_ in a _Second_ of _Time_: And the Length of the
_Pendulum_ vibrating _Seconds_, being found 39, 125, or ⅛ Inches, the
_Descent_ in a _Second_ will be found by the aforesaid _Analogy_ 16 Foot
and 1 Inch; and, by the third Proposition, the _Velocity_ will be double
thereto; and near to this it hath been found by several Experiments,
which by reason of the _swiftness_ of the _Fall_, cannot so exactly
determine its _Quantity_. The Demonstration of _Hugenius_ being the
Conclusion of a long Train of _Consequences_, I shall for brevity sake
omit; and refer you to his Book, where these things are more amply
treated of.

From these Four _Propositions_, all _Questions_ concerning the
_Perpendicular Fall of Bodies_, are easily _solved_, and either _Time_,
_Height_, or _Velocity_ being assign'd, one may readily find the other
two. From them likewise is the Doctrine of _Projects_ deducible,
assuming the two following _Axioms_; _viz._ That a _Body_ set a moving,
will move on continually in a right _Line_ with an _equable Motion_,
unless some other Force or Impediment intervene, whereby it is
accelerated, or retarded, or deflected.

_Secondly_, That a _Body_ being agitated by two _Motions_ at a time,
does by their _compounded Forces_ pass through the same _Points_, as it
would do, were the two _Motions divided_ and acted _successively_. As
for Instance, Suppose a _Body_ moved in the Line GF, (_Fig. 1. Tab. 5._)
from G to R, and there stopping, by another _Impulse_, suppose it moved
in a _Space_ of _Time_ equal to the former, from R towards K, to V. I
say, the _Body_ shall pass through the Point to V, though these two
_several Forces_ acted both in the _same time_.


_Prop._ V. The _Motion_ of all _Projects_ is in the _Curve_ of a
_Parabola_: Let the _Line_ GRF (in _Fig._ 1.) be the _Line_ in which the
_Project_ is directed, and in which by the first _Axiom_ it would move
equal _Spaces_ in equal _Times_, were it not deflected downwards by the
Force of _Gravity_. Let GB be the _Horizontal Line_, and GC a
_Perpendicular_ thereto. Then the _Line_ GRF being divided into equal
Parts, answering to equal _Spaces_ of _Time_, let the _Descents_ of the
_Project_ be laid down in _Lines parallel_ to GC, proportioned as the
_Squares_ of the _Lines_ GS, GR, GL, GF, or as the _Squares_ of the
_Times_, from S to T, from R to V, from L to X, and from F to B, and
draw the _Lines_ TH, VD, XY, BC parallel to GF; I say, the Points T, V,
X, B, are Points in the _Curve_ described by the _Project_, and that
that _Curve_ is a _Parabola_. By the second _Axiom_, they are Points in
the _Curve_; and the Parts of the _Descent_ GH, GD, GY, GC, = to ST, RV,
LX, FB, being as the _Squares_ of the _Times_ (by the _Second
Proposition_) that is, as the _Squares_ of the _Ordinates_, HT, DU, YX,
BC, equal to GS, GR, GL, GF, the _Spaces_ measured in those Times; and
there being no other _Curve_ but the _Parabola_, whose Parts of the
_Diameter_ are as the _Squares_ of the _Ordinates_, it follows that the
_Curve_ describ'd by a _Project_, can be no other than a _Parabola_: And
saying, as RU the _Descent_ in any _time_, to GR or UD the _direct
Motion_ in the same _time_, so is UD to a _third_ proportional; that
_third_ will be the _Line_ call'd by all Writers of _Conicks_, the
_Parameter_ of the _Parabola_ to the _Diameter_ GC, which is always the
same in _Projects_ cast with the same _Velocity_: And the _Velocity_
being defined by the Number of _Feet_ moved in a _Second_ of Time, the
_Parameter_ will be found by dividing the _Square_ of the _Velocity_, by
16 _Feet_, 1 _Inch_, the _Fall_ of a _Body_ in the same _Time_.

_Lemma._

The _Sine_ of the double of any _Arch_, is equal to twice the _Sine_ of
that _Arch_ into its _Co-sine_, divided by _Radius_; and the _versed
Sine_ of the _double_ of any _Arch_ is equal to twice the _Square_ of
the _Sine_ thereof divided by _Radius_.

Let the _Arch_ BC (in _Fig. 2. Tab. 5._) be double the _Arch_ BF, and A
the _Center_; draw the _Radii_ AB, AF, AC, and the _Chord_ BDC, and let
fall BE perpendicular to AC, and the _Angle_ EBC, will be equal to the
_Angle_ ABD, and the _Triangle_ BCE, will be like to the _Triangle_ BDA;
wherefore it will be as AB to AD, so BC or twice BD, to BE; that is, as
_Radius_ to _Co-sine_, so twice _Sine_ to _Sine_ of the double _Arch_.
And as AB to BD, so twice BD or BC to EC, that is, as _Radius_ to
_Sine_, so twice that _Sine_, to the _Versed Sine_ of the double _Arch_;
which two _Analogies_ resolved into _Equations_, are the _Propositions_
contained in the _Lemma_ to be proved.


_Prop._ VI. The _Horizontal_ Distances of _Projections_ made with the
same _Velocity_, at several _Elevations_ of the _Line_ of Direction, are
as the _Sines_ of the doubled _Angles_ of _Elevation_.

Let GB (_Fig._ 1) the _Horizontal_ Distance be = _z_, the _Sine_ of the
_Angle_ of _Elevation_, FGB, be = _s_, its _Co-sine_ = _c_, _Radius_ =
_r_, and the _Parameter_ = _p_. It will be as _c_ to _s_; so _z_ to
_sz_/_c_ = FB = GC, and by reason of the _Parabola_ _psz_/_c_ = to the
_Square_ of CB, or GF; Now as _c_ to _r_, so is _z_ to _zr_/_c_ = GF,
and its _Square_ _zzrr_/_cc_ will be therefore = to _psz_/_c_: Which
_Equation_ reduced will be _psc_/_rr_ = _z_. But by the former _Lemma_
2_sc_/_r_ is equal to the _Sine_ of the double _Angle_, whereof _s_ is
the _Sine_: Wherefore 'twill be as _Radius_ to _Sine_ of double the
_Angle_ FGB, so is half the _Parameter_, to the _Horizontal Range_ or
_Distance_ sought; and at the several _Elevations_, the _Ranges_ are as
the _Sines_ of the double _Angles_ of _Elevation_, _Q. E. D._

_Corollary._

Hence it follows, that half the _Parameter_ is the greatest _Randon_,
and that that happens at the _Elevation_ of 45 Degrees, the _Sine_ of
whose double is _Radius_. Likewise that the _Ranges_ equally distant
above and below 45 are equal, as are the _Sines_ of all double _Arches_,
to the _Sines_ of their doubled _Complements_.


_Prop._ VII. The _Altitudes_ of _Projections_ made with the same
_Velocity_, at several _Elevations_, are as the _versed Sines_ of the
doubled _Angles_ of _Elevation_: As _c_ is to _s_; so is _psc/rr_ = GB
to _pss/rr_ = BF: and UK = RU = BF/4, the _Altitude_ of the _Projection_
= _psc/4rr_. Now by the foregoing _Lemma_ _2ss/r_ = to the _versed Sine_
of the double _Angle_, and therefore it will be as _Radius_, to _versed
Sine_ of double the _Angle_ FGB, so an 8th of the _Parameter_ to the
height of the _Projection_ VK; and so these heights at several
_Elevations_, are as the said _versed Sines_, _Q. E. D._

_Corollary._

From hence it is plain, that the greatest _Altitude_ of the
perpendicular _Projection_ is a 4th of _Parameter_, or half the greatest
_Horizontal Range_; the _versed Sine_ of 180 Degrees being = _2r_.


_Prop._ VIII. The _Lines_ GF, or Times of the Flight of a _Project_ cast
with the same Degree of _Velocity_ at different _Elevations_, are as the
_Sines_ of the _Elevations_.

As _c_ is to _r_; so is _psc/rr_ = GB by the 6 Prop. to _ps/r_ GF; that
is, as _Radius_ to _Sine_ of _Elevation_, so the _Parameter_ to the
_Line_ GF; so the _Lines_ GF are as the _Sines_ of _Elevation_, and the
_Times_ are proportional to those _Lines_; wherefore the _Times_ are as
the _Sines_ of _Elevation_: _Ergo constat propositio_.


_Prop._ IX. Problem. A _Projection_ being made as you please, having the
Distance and Altitude, or Descent, of an Object, through which the
Project passes, together with the _Angle_ of _Elevation_ of the _Line_
of _Direction_; to find the _Parameter_ and _Velocity_, that is (in
_Fig._ 1.) having the _Angle_ FGB, GM, and MX.

_Solution._ As _Radius_ to _Secant_ of FGB, so GM the _Distance_ given
to GL; and as _Radius_ to _Tangent_ of FGB, so GM to LM. Then LM - MX in
_Heights_, or + MX in _Descents_; or else MX - ML, if the _Direction_ be
below the _Horizontal Line_, is the _Fall_ in the _Time_ that the direct
_Impulse_ given in G would have carried the Project from G to L = LX =
GY; then by Reason of the _Parabola_, as LX or GY, is to GL or YX, so is
GL to the _Parameter_ sought. To find the _Velocity_ of the _Impulse_:
by Prop. 2, and 4, find the Time in Seconds that a Body would fall the
Space LX; and by that dividing the Line GL, the _Quote_ will be the
_Velocity_, or Space moved in a Second sought, which is always a mean
Proportional between the _Parameter_, and 16 Feet, 1 Inch.


_Prop_. X. Problem 2. Having the _Parameter_, Horizontal Distance, and
Height or Descent of an _Object_, to find the Elevations of the Line of
Direction necessary to hit the given _Object_; that is, having GM, MX,
and the greatest _Randon_ equal to half the _Parameter_; to find the
_Angles_ FGB.

Let the _Tangent_ of the _Angle_ sought be = _t_, the _Horizontal
Distance_ GM = _b_, the Altitude of the _Object_ MX = _h_, the
_Parameter_ = _p_, and _Radius_ = _r_, and it will be,

 As _r_ to _t_, so _b_ to _tb/r_ = ML and
 _tb/r ∓ h_ {in ascents|in descents} = LX, and
 _ptb/r ∓ ph_ = GL _quad._ = XY _quad. ratione Parabolæ_; but
 _bb ∓ ttbb/rr_ = GL _quad._ 47. 1. _Euclid_. Wherefore
 _ptb/r ∓ ph_ = _bb ∓ ttbb/rr_ which Equation transposed, is
 _ttbb/rr_ = _ptb/r ∓ ph - bb_, divided by _bb_ is
 _tt/rr_ = _pt/br ∓ ph/bb_ - 1.

this Equation shews the Question to have 2 Answers, and the Roots
thereof are

 _t/r_ = _p/2h_ ∓ √((_pp ∓ 4ph_)/_4bb_) - 1;

from which I derive the following Rule.

Divide half the _Parameter_ by the Horizontal distance, and keep the
Quote; _viz._ _p/2b_ then say, as _square_ of the _distance_ given to
the half _Parameter_, so half _Parameter_ ∓ double {height|descent} to
the _square_ of a _Secant_ = (_pp ∓ 4ph_)/(_4bb_). The _Tangent_
answering to that _Secant_, will be

 √((_pp ∓ 4ph_)/4_bb_) - 1 or Square of Radius,

so then the sum and difference of the afore-found _Quote_, and this
_Tangent_ will be the Roots of the _Equation_, and the _Tangents_ of the
_Elevations_ sought.

Note here, that in _Descents_, if the _Tangent_ exceed the _Quote_, as
it does when _ph_ is more than _bb_, the _direction_ of the lower
_Elevation_ will be below the _Horizon_, and if _ph_ = _bb_, it must be
directed _Horizontal_, and the _Tangent_ of the upper _Elevation_ will
be _pr/b_: Note likewise, that if _4bb + 4ph_ in _Ascents_, or _4bb -
4ph_ in _Descents_, be equal to _pp_, there is but one _Elevation_ that
can hit the _Object_, and its _Tangent_ is _pr/2b_. And if _4bb + 4ph_
in _Ascents_, or _4bb - 4ph_ in _descents_, do exceed _pp_, the _Object_
is without the reach of a _Project_ cast with that _Velocity_, and so
the thing impossible.

From this _Equation_ _4bb ∓ 4ph_ = _pp_ are determined the utmost
limits of the reach of any _Project_, and the Figure assigned, wherein
are all the _heights_ upon each _Horizontal distance_ beyond which it
cannot pass; for by reduction of that _Equation_, _h_ will be found =
_¼p_ - _bb/p_ in _heights_, and _bb/p_ - _¼p_ in _descents_; from
whence it follows, that all the Points _h_ are in the _Curve_ of the
_Parabola_, whose _Focus_ is the Point from whence the _Project_ is
cast, and whose _Latus rectum_, or _Parameter ad Axem_ is = _p_.
Likewise from the same _Equation_ may the least _Parameter_ or
_Velocity_ be found capable to reach the _Object_ proposed; for _bb_ =
_¼pp_ ∓ _ph_ being reduced, _½p_ will be = √(_bb + hh_) ± _h_
{in ascents|in descents} which is the _Horizontal Range_ at 45 degrees,
of a Project cast with the least Velocity that would just reach the
_Object_, and the _Elevation_ requisite will be easily had; for dividing
the so found _Semi-parameter_ by the _Horizontal distance_ given _b_,
the _Quote_ into _Radius_ will be the _Tangent_ of the _Elevation_
sought. This Rule may be of good use to all _Bombardiers_ and _Gunners_,
not only that they may use no more Powder than is necessary, to cast
their _Bombs_ into the place assigned, but that they may shoot with much
more certainty, for that a small Error committed in the _Elevation_ of
the _Piece_, will produce no sensible Difference in the fall of the
Shot: For which Reasons the _French_ Engineers in their late Sieges have
used Mortar-pieces inclin'd constantly to the _Elevation_ of 45,
proportioning their Charge of Pouder according to the distance of the
_Object_ they intend to strike on the Horizon.

And this is all that need to be said concerning this _Problem_ of
shooting upon _Heights_ and _Descents_. But if a _Geometrical_
Construction thereof be required; I think I have one that is as easy as
can be expected, which I deduce from the foregoing _Analytical
Solution_, _viz._

 _t/r_ = _p/2b_ ± √((_¼pp ± ph - bb_)/_bb_),

and 'tis this, having made the right Angle GDF, (_Tab. 5. Fig. 3._) make
DF = _½p_, or greatest Range, and GD = _b_ the Horizontal Distance,
and DB = _h_ the perpendicular heighth of the Object; to be laid upwards
from D, if the Object be above the Horizon, or downwards if below it.
Parallel to GD draw FA, and make it equal to GB the Hypothenusal
Distance of the Object; and with the Center A and Radius FB = _½p ±
h_, sweep an Arch, which shall if the thing be possible, intersect the
indeterminate Perpendicular DF in two Points K and L, to which draw the
Lines, GL, GK; I say, the Angles DGK, DGL, are the Elevations requisite
to strike the Object B.

_Demonstration._ The Square of FK or FL, is equal to FB_q_ - GB_q_: or
(_½p ± h_)² - _bb_ - _hh_ or _¼pp ± ph - bb_, and therefore
√(_¼pp ± ph - bb_) is = FK = FL, and by Consequence DK, DL =
_½p_ ± √(_½pp ± ph - bb_). And as DG: DK and DL :: Radius:
Tangents sought, which coincides with our Algebraical Expression thereof.


_Prop._ XI. To determine the Force or _Velocity_ of a _Project_, in
every Point of the _Curve_ it describes.

To do this we need no other _Præcognita_, but only the third
Proposition, _viz._ That the _Velocity_ of _falling Bodies_, is double
to that which in the same time, would have described the Space _fallen_
by an equable Motion: For the _Velocity_ of a Project, is compounded of
the constant equal _Velocity_ of the impressed Motion, and the
_Velocity_ of the _Fall_, under a given _Angle_, _viz._ the Complement
of the _Elevation_: For Instance, in _Fig. 2._ in the time wherein a
Project would move from G to L, it descends from L to X, and by the
third _Proposition_ has acquired a _Velocity_, which in that time would
have carried it by an equable Motion from L to Z, or twice the Descent
LX; and drawing the Line GZ, I say, the _Velocity_ in the Point X,
compounded of the _Velocities_ GL and LZ under the Angle GLZ, is to the
_Velocity_ impress'd in the Point G, as GZ is to GL; this follows from
our second _Axiom_, and by the 20 and 21 _Prop. lib. 1. conic.
Midorgii_, XO parallel and equal to GZ shall touch the _Parabola_ in the
Point X. So that the _Velocities_ in the several Points, are as the
lengths of the _Tangents_ to the _Parabola_ in those Points, intercepted
between any two _Diameters_: And these again are as the _Secants_ of the
_Angles_, which those _Tangents_ continued make with the _Horizontal_
Line GB. From what is here laid down, may the comparative Force of a
_Shot_ in any two Points of the _Curve_, be either _Geometrically_ or
_Arithmetically_ discover'd.

_Corollary._

From hence it follows, that the force of a Shot is always least at U, or
the _Vertex_ of the _Parabola_, and that at equal distances therefrom,
as at T and X, G and B its force is always equal, and that the least
force in U is to that in G and B, as _Radius_ to the Secant of the
_Angle_ of _Elevation_ FGB.

These _Propositions_ considered, there is no question relating to
_Projects_, which, by the help of them, may not easily be Solved; and
tho' it be true that most of them are to be met withal, in _Galileus_,
_Torricellius_ and others, who have taken them from those Authors, yet
their Books being Foreign, and not easy to come by, and their
_Demonstrations_ long and difficult, I thought it not amiss to give the
whole _Doctrine_ here in _English_, with such short _Analytical_ Proof
of my own, as might be sufficient to evince their Truth.

The Tenth _Proposition_ contains a _Problem_, untouch'd by _Torricellius_,
which is of the greatest use in _Gunnery_, and for the sake of which
this _Discourse_ was principally intended: It was first Solved by Mr.
_Anderson_, in his Book of the Genuine Use and Effects of the _Gun_,
Printed in the Year 1674; but his Solution required so much Calculation,
that it put me upon search, whether it might not be done more easily,
and thereupon in the Year 1678 I found out the Rule I now Publish, and
from it the _Geometrical_ Construction: Since which time there has a
large _Treatise_ of this Subject, Intituled, _L'Art dejetter les
Bombes_, been Published by _Monsieur Blondel_, wherein he gives the
Solutions of this _Problem_ by _Messieurs Buot_, _Romer_ and _de la
Hire_: But none of them being the same with Mine, or, in my Opinion,
more easy, and most of them more Operose, and besides mine finding the
_Tangent_, which generally determines the _Angle_ better than its
_Sine_, I thought my self obliged to Print it for the use of all such,
as desire to be informed in the _Mathematical_ part of the Art of
_Gunnery_.

Now these Rules were rigidly true, were it not, as I said before, for
the Opposition of the Medium, whereby not only the direct imprest Motion
is continually retarded, but likewise the increase of the _Velocity_ of
the _Fall_, so that the Spaces described thereby, are not exactly as the
Squares of the Times: But what this Opposition of the _Air_ is, against
several _Velocities_, _Bulks_, and _Weights_, is not so easie to
determine. 'Tis certain that the weight of _Air_ to that of _Water_, is
nearly as 1 to 800, whence the weight thereof, to that of any _Project_
is given; 'tis very likely, that to the same _Velocity_ and _Magnitude_,
but of different Matter, the _Opposition_ should be _reciprocally_ as
the weights of the Shot; as likewise that to Shot of the same _Velocity_
and Matter, but of different _Sizes_, it should be as the _Diameters
reciprocally_: Whence generally the _Opposition_ to Shot with the same
_Velocity_, but of differing _Diameters_, and _Materials_, should be as
their _Specifick Gravities_ into their _Diameters reciprocally_; but
whether the _Opposition_, to differing _Velocities_ of the same Shot, be
as the _Squares_ of those _Velocities_, or as the _Velocities_
themselves, or otherwise, is yet a harder Question. However it be, 'tis
certain, that in large Shot of _Metal_, whose weight many Thousand times
surpasses that of the _Air_, and whose force is very great, in
proportion to the _Surface_ wherewith they press thereon; this
_Opposition_ is scarce discernable; For by several _Experiments_ made
with all Care and Circumspection with a _Mortarpiece_, Extraordinary
well fix'd to the Earth on purpose, which carried a solid Brass Shot of
four Inches and a half _Diameter_, and of about fourteen Pound Weight,
the _Ranges_ above and below forty five _Degrees_ were found nearly
equal; if there were any difference, the under _Ranges_ went rather the
farthest, but those differences were usually less than the Errors
committed in ordinary Practice, by the unequal Goodness and Dryness of
the same sort of Powder, by the Unfitness of the Shot to the Bore, and
by the Loosness of the Carriage.

In a smaller Brass-Shot of about an Inch and half Diameter, cast by a
Cross-Bow which ranged it, at most about four Hundred Foot, the Force
being much more equal than in the Mortarpiece, this difference was found
more Curiously: and Constantly and most Evidently, the under Ranges
out-went the upper. From which Trials I conclude, that although in small
and light Shot, the Opposition of the Air, ought and must be accounted
for; yet in Shooting of great and weighty Bombs, there need be very
little or no allowance made; and so these Rules may be put in practice
to all Intents and Purposes, as if this Impediment were absolutely
remov'd.


_A Proposition of general Use in the Art of Gunnery, shewing the Rule of
laying a Mortar to pass, in order to strike an Object above or below the
Horizon._

It was formerly the Opinion of those concerned in Artillery, that there
was a certain requisite of Powder for each Gun, and that in Mortars,
where the distance was to be varied, it must be done by giving a greater
or lesser Elevation to the Piece. But now our later Experience has
taught us that the same thing may be more certainly and readily
performed by increasing and diminishing the quantity of Powder, whether
regard be had to the Execution to be done, or to the Charge of doing it.
For when Bombs are discharged with great Elevations of the Mortar, they
fall too Perpendicular, and bury themselves too deep in the Ground, to
do all that damage they might, if they came more Oblique, and broke upon
or near the Surface of the Earth; which is a thing acknowledg'd by the
Besieged in all Towns, who unpave their Streets, to let the Bombs bury
themselves, and thereby stifle the force of their Splinters. A Second
Convenience is, that at the extream Elevation, the Gunner is not obliged
to be so curious in the direction of his Piece, but it will suffice to
be within a Degree or two of the Truth; whereas in the other Method of
Shooting he ought to be very curious. But a Third, and no less
considerable Advantage is, in the saving the Prince's Powder, which in
so great and so numerous Discharges, as we have lately seen, must needs
amount to a considerable Value. And for Sea-Mortars, it is scarce
practicable otherwise to use them, where the agitation of the Sea
continually changes the Direction of the Mortar, and would render the
Shot very uncertain, were it not that they are placed about 45 Degrees
Elevation, where several Degrees above or under, make very little
difference in the Effect.

In the precedent Discourse, I considered all the Propositions relating
to the Motion of Projectiles, and gave a Solution to this Problem;
_viz._ _To hit an Object above or below the Horizontal Line with the
greatest Certainty and least Force._ That is, that the Horizontal
distance of the Object being put = _b_, and the Perpendicular Heighth =
_b_, the Charge requisite to strike the Object with the greatest
Advantage, was that which with an Elevation of 45° would cast the Shot
on the Horizontal Line, to the distance of √(_bb +hh_), when the
Object was above the Horizon; or if it were below it, the Charge must be
lesser, so as to reach on the Horizon, at 45° Elevation, no greater a
Distance than √(_bb + hh_) - _h_; that is, in the one Case, the Sum
of the Hypothenusal Distance of the Object from the Gun, and the
Perpendicular Heighth thereof above the Gun; and in the other Case, when
the Object is below the Horizon, the difference of the same _per_ 47. I
_Eucl._ And I then shew'd how to find the Elevation proper for the Gun
so charged, _viz._ As the Horizontal Distance of the Object, to the Sum
or Difference of the Hypothenusal Distance and Perpendicular Height: So
Radius to the Tangent of the Elevation sought. But I was not at that
time aware that the aforesaid Elevation did constantly bisect the Angle
between the Perpendicular and the Object, as is demonstrated from the
Difference and Sum of the _Tangent_ and _Secant_ of any Arch being
always equal to the _Tangent_ and _Cotangent_ of the half Complement
thereof to a Quadrant. Having discovered this, I think nothing can be
more compendious, or bids fairer to compleat the Art of Gunnery, it
being as easie to shoot with a Mortar at any Object on demand, as if it
were on the Level; neither is there need of any Computation, but only
simply laying the Gun to pass, in the middle Line between the Zenith and
the Object, and giving it its due Charge. Nor is there any great need of
Instruments for this purpose: For if the Muzzle of the Mortar be turned
truly Square to the Bore of the Piece, as it usually is or ought to be,
a piece of Looking-glass Plate applied parallel to the Muzzle, will by
its Reflection give the true Position of the Piece, the Bombardeer
having no more to do, but to look perpendicularly down on the
Looking-glass, along a small Thread with a Plumbet, and to raise or
depress the Elevation of the Piece, till the Object appear reflected on
the same Point of the _Speculum_, on which the Plumbet falls; for the
Angle of Incidence and Reflection being equal, in this Case a Line at
Right Angles to the _Speculum_, as is the _Axis_ of the Chase of the
Piece, will bisect the Angle between the Perpendicular and the Object,
according as our Proposition requires. So that it only remains by good
and valid Experiments to be assured of the Force of Gunpowder, how to
make and conserve it equal, and to know the Effect thereof in each
Piece; that is, how far differing Charges will cast the same Shot out of
it; which may most conveniently be engraven on the outside thereof, as a
standing Direction to all Gunners, who shall from thence forward have
occasion to use that Piece: And were this Matter well ascertained, it
might be worth the while to make all Mortars of the like Diameter as
near as may he, alike in length of Chase, Weight, Chamber, and all other
Circumstances.

This Discovery that the utmost Range on an inclined Plane, is, when the
_Axis_ of the Piece makes equal Angles with the Perpendicular and the
Object; compared with what I have demonstrated of the same Problem in
the aforesaid Discourse does lead to and discover two very ready
Theorems; the one, to find the greatest Horizontal Range at 45°
Elevation, by any Shot made upon any inclined Plane, with any Elevation
of the Piece whatsoever: And the other to find the Elevations proper to
strike a given Object, with any Force greater than what suffices to
reach it with the aforesaid middle Elevation. Both which being performed
by one single Proportion, may be very serviceable to such as are
concerned in the Practice of Gunnery, but are unwilling to trouble
themselves with tedious and difficult Rules. The two Propositions are
these.


_PROP. I._

A Shot being made on an inclined Plane, having the Horizontal Distance
of the Object it strikes, with the Elevation of the Piece, and the Angle
at the Gun between the Object and the Perpendicular; to find the
greatest Horizontal Range of that Piece, laden with the same Charge;
that is, half the _Latus rectum_ of all the _Parabolæ_ made with the
same _Impetus_.

_RULE._

Take half the Distance of the Object from the _Nadir_, and take the
Difference of the given Elevation from that half; the Versed Sine of
twice that Difference subtract from the Versed Sine of the Distance of
the Object from the _Zenith_: Then shall the Difference of those Versed
Sines be to the Sine of the Distance of the Object from the _Zenith_, as
the Horizontal Distance of the Object strook, to the greatest Horizontal
Range at 45°.

_PROP. II._

Having the greatest Horizontal Range of a Gun, the Horizontal Distance
and Angle of Inclination of an Object to the Perpendicular, to find the
two Elevations necessary to strike that Object.

_RULE._

Halve the Distance of the Object from the _Nadir_; this half is always
equal to the half Sum of the two Elevations we seek. Then say, _As the
greatest Horizontal Range is to the Horizontal Distance of the Object:
So is the Sine of the Angle of Inclination or Distance of the Object
from the Perpendicular, to a fourth Proportional; which fourth being
subtracted from the Versed Sine of the Distance of the Object from the
_Zenith_, leaves the Versed Sine of the Difference of the Elevations
sought; which Elevations are therefore had by adding and subtracting the
half Difference to and from the aforesaid half Sum._

I shall not need to speak of the Facility of these Solutions, I shall
only observe that they are both General, without Exception or Caution,
and derived from the Knowledge that these two Elevations are equidistant
above and below the Line, bisecting the Angle between the Object and the
_Zenith_.




 _A Discourse concerning the Measure of the Airs Resistance to Bodies
   moved in it. By the Learned _John Wallis_, S. T. D. and R. S. S._


1. That the Air (and the like of any other _Medium_) doth considerably
give Resistance to Bodies moved in it; and doth thereby abate their
Celerity and Force; is generally admitted. And Experience doth attest
it: For otherwise, a Cannon Bullet projected Horizontally, should
(supposing the Celerity and Force undiminished) strike as hard against a
Perpendicular Wall, erected at a great distance, as near at hand; which
we find it doth not.

2. But at what Rate, or in what Proportion, such Resistance is; and
(consequently, at what Rate the Celerity and Force is continually
diminished) seems not to have been so well examined. Whence it is, that
the Motion of a Project (secluding this Consideration) is commonly
reputed to describe a Parabolick Line; as arising from an Uniform or
equal Celerity in the Line of Projection, and a Celerity uniformly
accelerated in the Line of Descent; which two so compounded, do create a
Parabola.

3. In order to the Computation hereof, I first premise this _Lemma_, (as
the most rational that doth occur for my first footing,) That (supposing
other things equal) the Resistance is proportional to the Celerity. For
in a double Celerity, there is to be removed (in the same time) twice as
much Air, (which is a double Impediment) in a treble, thrice as much;
and so in other Proportions.

4. Suppose we then the Force impressed (and consequently the Celerity,
if there were no Resistance) as 1; the Resistance as _r_. (which must be
less than the Force, or else the Force would not prevail over the
Impediment, to create a Motion.) And therefore the effective Force at a
first Moment, is to be reputed as 1 - _r_: That is, so much as the Force
impressed, is more than the Impediment or Resistance.

5. Be it as 1 - _r_ to 1; so one to _m_. (which _m_ is therefore greater
than 1.)

6. And therefore the effective Force (and consequently the Celerity) as
to a first Moment, is to be 1/_m_ of what it would be, had there been no
Resistance.

7. This 1/_m_ is also the remaining Force after such first Moment; and
this remaining Force is (for the same Reason) to be proportionally
abated as to a second Moment; that is, we are to take 1/_m_ thereof,
that is 1/_mm_ of the impressed Force. And for a third Moment (at equal
distance of time) 1/_mmm_; for a fourth 1/_m_⁴; and so onward
infinitely.

8. Because the length dispatched (in equal times) is proportional to the
Celerities; the Lines of Motion (answering to those equal Times) are to
be as 1/_m_, 1/_m_², 1/_m_³, 1/_m_⁴, _&c._ of what they would have
been, in the same Times, had there been no Resistance.

9. This therefore is a Geometrical Progression; and (because of _m_
greater than 1) continually decreasing.

10. This decreasing Progression infinitely continued (determining in the
same Point of Rest, where the Motion is supposed to expire) is yet of a
finite Magnitude; and equal to 1/(_m_ - 1), of what it would have been
in so much Time, if there had been no Resistance. As is demonstrated in
my Algebra, _Chap._ 95. _Prop._ 8. For (as I have elsewhere
demonstrated) the Sum or Aggregate of a Geometrical Progression is (_VR
- A_)/(_R_ - 1) (supposing _V_ the greatest Term, _A_ the least, and _R_
the common Multiplier.) That is _VR_/(_R_ - 1) - _A_/(_R_ - 1). Now in
the present Case, (supposing the Progression infinitely continued) the
least Term _A_, becomes infinitely small, or = 0. And consequently
_A_/(_R_ - 1) doth also vanish, and thereby the Aggregate becomes =
_VR_/(_R_ - 1). That is (as will appear by dividing _VR_ by _R_ - 1;) _V
+ V/R + V/RR + V/R³ + &c._ = _VR_/(_R_ - 1);[14] (supposing the
Progression to begin at _V_ = 1.) That is (dividing all by _R_, that so
the Progression may begin at _V/R_ = 1/_m_:) _V_/(_R_ - 1) = _V/R + V/RR
+ V/R³ + &c._,  That is, in our present Case (because of _V_ = 1, &
_R_ = _m_:) 1/_m_ + 1/_mm_ + 1/_m_³ &c. = 1/(_m_ - 1). That is,
(putting _n_ = _m_ - 1) 1/_n_ of what it would have been if there had
been no Resistance.

11. This infinite Progression is fitly expressed by an Ordinate in the
Exterior Hyperbola, parallel to one of the Asymptotes; and the several
Members of that, by the several Members of this, cut in continual
Proportion. As is there demonstrated at _Prop._ 15. For let _SH_,
(_vid._ Fig. 4. Tab. 5.) be an Hyperbola between the Asymptotes _AB_,
_AF_: And let the Ordinate _DH_ (in the Exterior Hyperbola, parallel to
_AF_,) represent the impressed Force undiminished; or the Line to be
described in such time, by a Celerity answerable to such undiminished
Force. And let _BS_ (a like Ordinate) be 1/_m_ thereof; which therefore,
being less than _DH_ (as being equal to a Part of it) will be farther
than it from _AF_. In _AB_ (which I put = 1) let _Bd_ be such a Part
thereof, as is _BS_ of _DH_. Now because (as is, well known) all the
inscribed Parallelograms, in the Exterior Hyperbola, _AS_, _AH_, _&c._
are equal; and therefore their sides reciprocal: Therefore as _Ad_ = 1 -
1/_m_ (supposing _Bd_ to be taken, from _B_ towards _A_,) to _AB_ = 1,
or as _m_ - 1 to _m_: so is _BS_ = (1/_m_)_DH_, to _dh_, which is
therefore equal to 1/(_m_ - 1) of _DH_; that is (as will appear by
dividing 1, by _m_ - 1,) to 1/_m_ + 1/_mm_ + 1/_m_³, _&c._ of _DH_.[15]

Or if _Bd_ be taken beyond _B_; then as _Ad_ = 1 + 1/_m_ to _AB_ = 1, or
as _m_ + 1 to _m_, so is (1/_m_)_DH_ to _dh_, which is therefore equal
to 1/(_m_ + 1)DH; that is (as will appear by like dividing of 1 by _m_ +
1;) = to 1/_m_ - 1/_mm_ + 1/_m_³ - _&c._ of _DH_.

12. Let such ordinate _dh_, or (equal to it in the Asymptote) _AF_, be
so divided in _L_, _M_, _N_, _&c._ (by Perpendiculars cutting the
Hyperbola in _l_, _m_, _n_, _&c._) as that _FL_, _LM_, _MN_, be as
1/_m_, 1/_mm_, 1/_m_³, _&c._ That is, so continually decreasing as that
each Antecedent be to its Consequent, as 1 to 1/_m_, or as _m_ to 1. See
_Fig. 5. Tab. 5._

13. This is done by taking _AF_, _AL_, _AN_, _&c._ in such proportion.
For, of continual Proportionals, the Differences are also continually
proportional, and in the same proportion. For let _A_, _B_, _C_, _D_,
_&c._ be such Proportionals, and their Differences _a_, _b_, _c_, _&c._
That is, _A_ - _B_ = _a_, _B_ - _C_ = _b_, _C_ - _D_ = _c_, _&c._

 Then, because A, B, C, D, _&c._ are in continual proportion,
 That is, A. B :: B. C :: C. D :: _&c._
 And dividing (A - B). B :: (B - C). C :: (C - D). D :: _&c._
 That is, _a_. B :: _b_. C :: _d_. D :: _&c._
 And alternly _a. b. c._ _&c._ :: B. C. D. _&c._ :: A. B. C. _&c._
 That is, in continual proportion as A to B, or as _m_ to 1.

14. This being done; the Hyperbolick Spaces _Fl_, _Lm_, _Mn_, &c. are
equal. As is demonstrated by _Gregory San-Vincent_; and as such is
commonly admitted.

15. So that _Fl_, _Lm_, _Mn_, _&c._ may fitly represent equal Times, in
which are dispatched unequal Lengths, represented by _FL_, _LM_, _MN_,
_&c._

16. And because they are in Number infinite (though equal to a finite
Magnitude) the Duration is infinite: And consequently the impressed
Force, and Motion thence arising, never to be wholly extinguished
(without some further Impediment) but perpetually approaching to _A_, in
the Nature of Asymptotes.

17. The Spaces _Fl_, _Fm_, _Fn_, &c. are therefore as Logarithms (in
Arithmetical Progression increasing) answering to the Lines _AF_, _AL_,
_AM_, &c. or to _FL_, _LM_, _MN_, &c. in Geometrical Progression
decreasing.

18. Because _FL_, _LM_, _MN_, &c. are as 1/_m_, 1/_mm_, 1/_m_³, &c.
(infinitely) terminated at _A_; therefore (by ¶ 10) their Aggregate _FA_
or _dh_, is to _DH_, (so much Length as would have been dispatched, in
the same time, by such impressed Force undiminished) as 1 to _m_ - 1 =
_n_.

19. If therefore we take, as 1 to _n_, so _AF_ to _DH_; this will
represent the Length to be dispatched, in the same time, by such
undiminished Force.

20. And if such _DH_ be supposed to be divided into equal Parts
innumerable (and therefore infinitely small;) these answer to those (as
many) Parts unequal in _FA_, or _hd_.

21. But, what is the Proportion of _r_ to 1, or (which depends on it) of
1 - _r_ to 1, or 1 to _m_; remains to be inquired by Experiment?

22. If the Progression be not infinitely continued; but end (suppose) at
_N_, and its least Term be _A_ = _MN_; then, out of

 _V_/(_R_ - 1) = 1/_m_ + 1/_mm_ + 1/_m_³, _&c._

is to be subducted _A_/(_R_ - 1) (as at ¶ 10.) that is (as by Division
will appear)

 _A_/_R_ + _A_/_R_² + _A_/_R_³ &c.

That is (in our present Case)

 _a_/_m_ + _a_/_mm_ + _a_/_m_³ &c.

And so the Aggregate will be

 (1-_a_)/_m_ + (1-_a_)/_mm_ + (1-_a_)/_m_³ &c. = (1-_a_)/_n_.

And thus as to the Line of Projection, in which (secluding the
Resistance) the Motion is reputed uniform; dispatching equal Lengths in
equal Times. Consider we next the Line of Descent.

23. In the Descent of Heavy Bodies, it is supposed that to each Moment
of Time, there is superadded a new Impulse of Gravity to what was
before: And each of these, secluding the Consideration of the Air's
Resistance, to proceed equally (from their several beginnings) through
the succeeding Moments. As (in the erect Lines) 1 1 1 1, _&c._ 1 1 1,
_&c._ 1 1, _&c._ 1, _&c._ and so continually, as in the Line of
Projection.[16]

24. Hence ariseth (in the transverse Lines) for the first Moment 1, for
the second 1 + 1, for the third 1 + 1 + 1, and so forth, in Arithmetical
Progression: As are the Ordinates in a Triangle, at equal distance.

25. And such are the continual Increments of the Diameter, or of the
Ordinates in the exterior Parabola, answering to the interior Ordinates,
or Segments of the Tangent, equally increasing; as is known, and
commonly admitted.

26. If we take in the Consideration of the Air's Resistance; we are
then, for each of these equal Progressions, to substitute a decreasing
Progression Geometrical; in like manner (and for the same Reasons) as in
the Line of Projection.

27. Hence ariseth, for the first Moment 1/_m_; for the second 1/_m_ +
1/_m_²; for the third 1/_m_ + 1/_m_² + 1/_m_³, _&c._[17] And such is
therefore the Descent of a heavy Body falling by its own weight. The
several Impulses of Gravity being supposed equal.

28. That is (in the Figure of ¶ 12) as _FL_, _FM_, _FN_, &c. in the Line
of Descent, answering to _FL_, _LM_, _MN_, &c. in the Line of Projection.

29. But though the Progressions for the Line of Projection, are like to
each of those many in the Line of Descent; it is not to be thence
inferred, that therefore 1/_m_ in the one, is equal to 1/_m_ in the
other: But in the Line of Projection (suppose) (1/_m_)_f_ (such a Part
of the Force impressed, and a Celerity answerable:) in the Line of
Descent, (1/_m_)_g_ such a Part of the Impulse of Gravity.

30. Those for the Line of Descent (of the some Body) are all equal, each
to other: Because _g_ (the new Impulse of Gravity) in each Moment is
supposed to be the same.

31. But what is the Proportion of _f_ to _g_ (that of the Force
impressed, to the Impulse of Gravity in each Body) remains to be
inquired by Experiment.

32. This Proportion being found as to one known Force; the same is
thence known as to any other Force (whose Proportion to this is given)
in the same uniform _Medium_.

33. And this being known, as to one _Medium_; the same is thence known
as to any other _Medium_, the Proportion of whose Resistance to that of
this is known.

34. If a heavy Body be projected downward in a perpendicular Line; it
descends therefore at the Rate 1/_m_, 1/_mm_, 1/_m_³, _&c._ of _f_,
(the impressed Force) increased by 1/_m_, 1/_m_ + 1/_m_², 1/_m_ +
1/_m_² + 1/_m_³, _&c._ of _g_ the impulse of Gravity, (by ¶ 7, and ¶
27) Because both Forces are here united.

35. If in a perpendicular Projection upwards; it ascends in the rate of
the former, abated by that of the latter. Because here the impulse of
Gravity is contrary to the Force impressed.

36. When therefore this latter (continually increasing) becomes equal to
that former (continually decreasing) it then ceaseth to ascend; and doth
thenceforth descend at the rate wherein the latter continually exceeds
the former.

37. In an Horizontal, or Oblique Projection: If to a Tangent, whose
Increments are as _FL_, _LM_, _MN_, &c. that is as (1/_m_)_f_, &c. be
fitted Ordinates (at a given Angle) whose Increments are as _FL_, _FM_,
_FN_, &c. that is, as (1/_m_)_g_, &c. The Curve answering to the
Compound of these Motions, is that wherein the Project is to move.

38. This Curve (being hitherto without a Name) may be call'd _Linea
Projectorum_; the Line of Projects, or things projected; which resembles
a Parabola deform'd.

39. The Celerity and Tendency, as to each Point of this Line, is
determined by a Tangent at that Point.

40. And that against which it makes the greatest Stroke or Percussion,
is that which (at that Point) is at right Angles to that Tangent.

41. If the Projection (at ¶ 27) be not infinitely continued, but
terminate (suppose) at _N_, so that the last Term in the first Column or
Series erect be _a_; and consequently in the second, _ma_; in the third,
_mma_, &c. (each Series having one Term fewer than that before it:) Then
(for the same Reasons, as at ¶ 22) the Aggregates of the several Columns
(or erect Series) will be (1 - _a_)/_n_, (1 - _ma_)/_n_, (1 - _mma_)/_n_,
and so forth, till (the Multiple of _a_ becoming = 1) the Progression
expire.

42. Now all the Abatements here, _a_, _ma_, _mma_, &c. are the same with
the Terms of the first Column taken backward. For _a_ is the last, _ma_
the next before it; and so of the rest.

43. And the Aggregate of all the Numerators is so many times 1, as is
the Number of Terms (suppose _t_,) wanting the first Column; that is

 _t_ - (1 - _a_)/_n_, or (_nt_ - 1 + _a_)/_n_;

and this again divided by the common Denominator _n_, becomes

 (_nt_ - 1 + _a_)/_nn_.

And therefore ((_nt_ - 1 + _a_)/_nn_)_g_, is the Line of Descent by its
own Gravity.

44. If therefore this be added to a projecting Force downward in a
Perpendicular; or subducted from such projecting Force upward; that is,
to or from ((1 - _a_)/_n_)_f_: The Descent in the first Case will be

 ((1 - _a_)/_n_)_f_ + ((_nt - 1 + a_)/_nn_)_g_;

and the Ascent in the other Case

 ((1 - _a_)/_n_)_f_ - ((_nt - 1 + a_)/_nn_)_g_.

And in this latter Case, when the ablative Part becomes equal to the
positive Part, the Ascent is at the highest; and thenceforth (the
ablative Part exceeding the positive) will descend.

45. In an Horizontal or Oblique Projection, having taken

 ((1 - _a_)/_n_)_f_,

in the Line of Projection, and thence (at the Angle given)

 ((_nt_ - 1 + _a_)/_nn_)_g_,

in the Line of Descent; the Point in the Curve answering to these, is
the Place of the Project answering to that Moment.

46. I am aware of some Objections to be made, whether to some Points of
the Process, or to some of the Suppositions. But I saw not well how to
wave it, without making the Computation much more perplex'd. And in a
Matter so nice, and which must depend upon Physical Observations, 'twill
be hard to attain such Accuracy, as not to stand in need of some
Allowances.

47. Somewhat might have been farther added to direct the Experiments
suggested at ¶ 21, and 31. But that may be done at leisure, after
deliberation had, which way to attempt the Experiment.

48. The like is to be said of the different resistance which different
Bodies may meet with in the same _Medium_, according to their different
Gravities (extensively or intensively consider'd) and their different
Figures and Positions in Motion. Whereof we have hitherto taken no
account; but supposed them, as to all these, to be alike and equal.


_POSTSCRIPT._

49. The Computation in ¶ 41, 42, 43, may (if that be also desired) be
thus represented by Lines and Spaces. The Ablatives _a_, _ma_, _mma_,
&c. (being the same with the first Column taken backward) are fitly
represented by the Segments of _NF_ (beginning at _N_) in Figure 5 and
6, and therefore by Parallelograms on these Bases, assuming the common
height of _Fh_, or _NQ_; the Aggregate of which is _Nh_, or _FQ_. And,
so many times 1, by so many equal Spaces, on the same Bases, between the
same Parallels, terminated at the Hyperbola: The Aggregate of which is
_hFNQn_. From whence if we subduct the Aggregate of Ablatives _FY_; the
remaining Trilinear _hQn_, represents the Descent.

50. If to this of Gravity, be joined a projecting Force; which is to the
Impulse of Gravity as _hK_ to _hF_ (be it greater, less, or equal) taken
in the same Line; the same Parallels determine proportional
Parallelograms, whose Aggregate is _KQ_.

51. And therefore if this be a perpendicular Projection downwards; then
_hKkn_ (the Sum of this with the former) represents the Descent.

52. If it be a Perpendicular upwards; then the difference of these two
represents the Motion; which so long as _KQ_ is the greater, is
Ascendent; but Descendent, when _hQn_ becomes greater; and it is then at
the highest when they be equal.

53. If the Projection be not in the same Perpendicular, (but Horizontal,
or Oblique) then _KQ_ represents the Tangent of the Curve; and _hQn_ the
Ordinates to that Tangent, at the given Angle.

54. But the Computation before given, I take to be of better use than
this Representation in Figure. Because in such Mathematical Enquiries, I
choose to separate (as much as may be) what purely concerns Proportions;
and consider it abstractly from Lines, or other Matter wherewith it is
incumbred.

As to the Question proposed; whether the resistance of the _Medium_ do
not always take off such a proportional part of the Force moving through
it, as is the specifick Gravity of the _Medium_ to that of the Body
moved in it: (For, if so, it will save us the trouble of Observation.)

I think this can by no means be admitted. For there be many other things
of Consideration herein, beside the intensive Gravity (or, as some call
it, the specifick Gravity) of the _Medium_.

A viscous _Medium_ shall more resist, than one more fluid, though of
like intensive Gravity.

And a sharp Arrow shall bore his way more easily through the _Medium_,
than a blunt-headed Bolt, though of equal Weight, and like intensive
Gravity.

And the same Pyramid with the Point, than with the Base forward.

And many other like Varieties, intended in my ¶ 48.

But this I think may be admitted, namely, That different _Mediums_,
equally liquid, (and other Circumstances alike,) do in such proportion
resist, as is their intensive Gravity. Because there is, in such
proportion, a heavier Object to be removed, by the same Force. Which is
one of the things to which ¶ 33 refers.

And again: The heavier Project once in Motion, (being equally swift, and
all other Circumstances alike) moves through the same _Medium_ in such
proportion more strongly, as is its intensive Gravity. For now the Force
is in such proportion greater, for the removal of the same resistance.
And this Part of what my ¶ 32, insinuates.

But where there is a Complication of these Considerations one with
another, and with many other Circumstances, whereof each is severally to
be considered; there must be respect had to all of them.

[14]
 R - 1_V_) _R_ (_V_ + _V/R_, _V/RR_, &c.
                _VR_ - V
                --------
                     + V
                      + V/VR
                     -------
                      + V/R
                     + VV/RRR
                     --------
                      + V/RR
                         _&c_.

[15]
 _m_ - 1) 1 (1/_m_ + 1/_mm_ + 1/_m_³ + &c.
          1 - 1/_m_
           -------
           + 1/_m_
           + 1/_m_ - 1/_mm_
             --------------
                + 1/_mm_
                + 1/_mm_ - 1/_mmm_
                  ----------------
                          + 1/_mmm_
                   &c.

[16]
 1
 1 1
 1 1 1
 1 1 1 1
 _&c._

[17]
   1
  ---
  _m_

   1    1
 ----- ---
 _m_² _m_

   1     1    1
 ----- ----- ---
 _m_³ _m_² _m_

   1     1     1    1
 ----- ----- ----- ---
 _m_⁴ _m_³ _m_² _m_




 _An Instance of the Excellence of the _Modern Algebra_, in the
   Resolution of the Problem of finding the _Foci_ of Optick Glasses
   Universally. By _E. Halley_, S. R. S._


The Excellence of the _Modern Geometry_ is in nothing more evident, than
in those full and adequate Solutions it gives to Problems; representing
all the possible Cases at one view, and in one general Theorem, many
times comprehending whole Sciences; which deduced at length into
Propositions, and demonstrated after the manner of the _Ancients_, might
well become the Subjects of large Treatises: For whatsoever Theorem
solves the most complicated Problem of the kind, does with a due
Reduction reach all the subordinate Cases. Of this I now design to give
a notable Instance in the Doctrine of _Dioptricks_.

This Dioptrick Problem is that of finding the _Focus_ of any sort of
_Lens_, exposed either to converging, diverging, or parallel Rays of
Light, proceeding from, or tending to a given Point in the _Axis_ of the
_Lens_, be the _Ratio_ of _Refraction_ what it will, according to the
Nature of the transparent Material whereof the _Lens_ is formed, and
also with allowance for the thickness of the _Lens_ between the
_Vertices_ of the two Spherical Segments. This Problem being solved in
one Case, _mutatis mutandis_, will exhibit Theorems for all the possible
Cases, whether the _Lens_ be _Double-Convex_ or _Double-Concave_,
_Plano-Convex_, or _Plano-Concave_, or _Convexo-Concave_, which sort are
usually call'd _Menisci_. But this only to be understood of those Beams
which are nearest to the _Axis_ of the _Lens_, so as to occasion no
sensible difference by their Inclination thereto; and the _Focus_ here
formed, is by _Dioptrick Writers_ commonly call'd the principal _Focus_,
being that of use in _Telescopes_ and _Microscopes_.

Let then (in _Fig. 7. Tab. 5._) BEβ be a double Convex _Lens_, C the
Center of the Segment EB, and K the Center of the Segment Eβ, Bβ the
thickness of the _Lens_, D a Point in the _Axis_ of the _Lens_; and it
is required to find the Point F, at which the Beams proceeding from the
Point D, are collected therein, the _Ratio_ of Refraction being as _m_
to _n_. Let the distance of the Object DB = DA = _d_ (the Point A being
supposed the same with B, but taken at a distance therefrom, to prevent
the coincidence of so many Lines) the _Radius_ of the Segment towards
the Object CB or CA = _r_, and the _Radius_ of the Segment from the
Object Kβ or K = ρ; and let Bβ the thickness of the _Lens_ be =
_t_, and then let the Sine of the Angle of Incidence DAG be to the Sine
of the refracted Angle HAG or CAφ as _m_ to _n_: And in very small
Angles, the Angles themselves will be in the same proportion; whence it
will follow that,

As _d_ to _r_, so the Angle at C to the Angle at D, and _d + r_ will be
as the Angle of Incidence GAD; and again as _m_ to _n_, so _d + r_ to
(_dn + rn_)/_m_, which will be as the Angle GAH = CAφ; This being
taken from ACD which is as _d_, will leave (_m - nd - nr_)/_m_ analogous
to the Angle AφD; and the Sides being in this Case proportional to
the Angles they subtend, it will follow, that as the Angle AφD is to
the Angle ADφ, so is the Side AD or BD to Aφ or Bφ: That is,
Bφ will be = _mdr_/(_m - nd - nr_), which shews in what Point the
Beams proceeding from D, would be collected by means of the first
Refraction; but if _nr_ cannot be subtracted from _m - nd_, it follows
that the Beams after Refraction do still pass on diverging, and the
Point φ is on the same side of the _Lens_ beyond D. But if _nr_ be
equal to _m - nd_, then they proceed parallel to the _Axis_, and the
Point φ is infinitely distant.

The Point φ being found as before, and Bφ - Bβ being given,
which we will call δ, it follows by a Process like the former, that
βF, or the focal Distance sought, is equal to

 _δρn_/(_m - δ + mρ_) = _f_.

And in the room of δ substituting

 Bφ - Bβ = _mdr_/(_m - nd - nr_) - _t_,

putting _p_ for _n_/(_m - n_), after due Reduction this following
Equation will arise,

 (_mpdrρ - ndρt + nprρt_)/(_mdr + mdρ - mprρ - m - ndt + nrt_)
 = _f_.

Which Theorem, however it may seem operose, is not so, considering the
great Number of _Data_ that enter the Question; and that one half of the
Terms arise from our taking in the thickness of the _Lens_, which in
most Cases can produce no great Effect; however it was necessary to
consider it, to make our Rule perfect. If therefore the _Lens_ consist
of _Glass_, whose Refraction is as 3 to 2 'twill be

 (_6drρ - 2dρt + 4rρt_)/(_3dr + 3dρ - 6rρ - dt + 2rt_) = _f_.

If of _Water_, whose Refraction is as 4 to 3, the Theorem will stand thus

 (_12drρ - 3dρt + 9rρt_)/(_4dr + 4dρ - 12rρ - dt + 3rt_) = _f_.

If it could be made of _Diamant_, whose Refraction is as 5 to 2, it
would be

 (_(10/3)drρ - 2dρt + (4/3)rρt_)/(_5dr + 5dρ - (10/3)rρ - 3dt
 + 2rt_) = _f_.

And this is the universal Rule for the _Foci_ of double Convex Glasses
exposed to diverging Rays. But if the thickness of the _Lens_ be
rejected, as not sensible, the Rule will be much shorter, _viz._

 _pdrρ_/(_dr + dρ - prt_) = _f_,

or in Glass

 _2drρ_/(_dr + dρ - 2rρ_) = _f_,

all the Terms wherein _t_ is found being omitted, as equal to nothing.
In this Case, if _d_ be so small, as that _2rρ_ exceed _dr + dρ_,
then will it be - _f_, or the _Focus_ will be Negative, which shews that
the Beams after both Refractions still proceed diverging.

To bring this to the other Cases, as of converging Beams, or of Concave
Glasses, the Rule is ever composed of the same Terms, only changing the
Signs of + and -; for the distance of the Point of Concourse of
converging Beams, from the Point B, or the first Surface of the _Lens_,
I call a negative Distance or - _d_; and the Radius of a Concave _Lens_
I call a negative Radius, or - _r_ if it be the first Surface, and - ρ
if it be the second Surface. Let then converging Beams fall on a double
Convex of Glass, and the Theorem will stand thus

 - _2drρ_/(- _dr - dρ - 2rt_) = + _f_,

which shews that in this Case the _Focus_ is always affirmative.

If the _Lens_ were a _Meniscus_ of Glass, exposed to diverging Beams,
the Rule is

 - _2drρ_/(- _dr + dρ + 2rρ_) = _f_,

which is affirmative when _2rρ_ is less than _dr - dρ_ otherwise
negative: But in the Case of converging Beams falling on the same
_Meniscus_, 'twill be

 + _2drρ_/(+ _dr - dρ + 2rp_) = _f_,

and it will be + _f_, whilst _dρ - dr_ is less than _2rρ_; but if it
be greater than _2rρ_, it will always be found negative or - _f_. If
the _Lens_ be double Concave, the _Focus_ of converging Beams is
negative, where it was affirmative in the Case of diverging Beams on a
double Convex, _viz._

 - _2drρ_/(+ _dr + dρ - 2rρ_) = _f_,

which is affirmative only when _2rρ_ exceeds _dr + dρ_: But
diverging Beams passing a double Concave, have always a negative
_Focus_, _viz._

 - _2drρ_/(+ _dr + dρ + 2rρ_) = - _f_.

The Theorems for converging Beams, are principally of use to determine
the _Focus_ resulting from any sort of _Lens_ placed in a Telescope,
between the _Focus_ of the Object-Glass and the Glass it self; the
distance between the said _Focus_ of the Object-Glass, and the
interposed _Lens_ being made = - _d_.

I here suppose my Reader acquainted with the Rules of Analytical
Multiplication and Division, as that + multiplied by + makes the Product
+, + by - makes -, and - by - makes +; so dividing + by + makes the
Quote +, + by - makes -, and - by - makes +; which will be necessary to
be understood in the preceding Examples.

In case the Beams are parallel, as coming from an infinite distance,
(which is supposed in the Case of Telescopes) then will _d_ be supposed
Infinite, and in the Theorem

 _pdρr_/(_dr + dρ - prρ_)

the Term _prρ_ vanishes, as being finite, which is no part of the
other infinite Terms; and dividing the Remainder by the infinite Part
_d_, the Theorem will stand thus _pρr_/(_r + ρ_) = _f_, or in Glass,
_2rρ_/(_r + ρ_) = _f_.

In case the _Lens_ were _Plano-Convex_ exposed to diverging Beams,
instead of _pdρr_/(_dr + dρ - prρ_), _r_ being infinite, it will
be _pdρ_/(_d - pρ_) = _f_, or _2dρ_/(_d - 2ρ_) if the _Lens_ be
Glass.

If the _Lens_ be Double-Convex, and _r_ be equal to ρ, as being formed
of Segments of equal Spheres, then will (_pdρr_)/(_dr + dρ - prρ_)
be reduced to (_pdr_/(_2d - pr_))_f_; and in case _d_ be infinite, then
it will yet be farther contracted to ½_pr_, and _p_ being = _n_/(_m
- n_), the focal distance in Glass will be = _r_, in Water 1½_r_,
but in Diamant ⅓_r_.

I am sensible that these Examples are too much for the compleat Analyst,
though I fear too little for the less Skilful; it being very hard, if
possible, in such Matters, so to write, as to give satisfaction to both;
or to please the one, and instruct the other. But this may suffice to
shew the extent of our Theorem, and how easie a Reduction adapts any one
case to all the rest.

Nor is this only useful to discover the _Focus_ from the other proposed
_data_, but from the _Focus_ given, we may thereby determine the
distance of the Object; or from the _Focus_ and Distance given, we may
find of what Sphere it is requisite to take another Segment, to make any
given Segment of another Sphere cast the Beams from the distance _d_ to
the _Focus_ _f_. As likewise from the _Lens_, _Focus_, and Distance
given, to find the _Ratio_ of Refraction, or of _m_ to _n_, requisite to
answer those _Data_. All which it is obvious, are fully determined from
the Equation we have hitherto used, _viz._

 _pdρr_ = _drf + dρf - prρf_,

for to find _d_ the Theorem is (_prρf_)/(_rf + ρf - pρr_) = _d_,
the distance of the Object.

For ρ the Rule is

 _drf_/(_pdr + df + prf_) = ρ.

But for _p_ will be

 (_drf + dρf_)/(_dρr + fρr_) = _p_,

which latter determines the _Ratio_ of Refraction, _m_ being to _n_, as
1 + _p_ to _p_.

I shall not expatiate on these Particulars, but leave them for the
Exercise of those that are desirous to be informed in Optical Matters,
which I am bold to say are comprehended in these three Rules, as fully
as the most Inquisitive can desire them, and in all possible Cases;
regard being had to the Signs + and -, as in the former Cases of finding
the _Focus_. I shall only shew two considerable Uses of them; the one to
find the distance whereat an Object being plac'd, shall by a given
_Lens_ be represented in a _Species_ as large as the Object it self,
which may be of singular Use in drawing Faces and other things in their
true Magnitude, by transmitting the _Species_ by a Glass into a dark
Room, which will not only give the true Figure and Shades, but even the
Colours themselves, almost as vivid as the Life. In this Case _d_ is
equal to _f_, and substituting _d_ for _f_ in the Equation, we shall have

 _pdrρ_ = _ddr + ddρ - dpρr_,

and dividing all by _dprρ_ = _dr + dρ - prρ_, that is, _2prρ_/(_r + ρ_)
= _d_; but if the two Convexities be of the same Sphere so as _r_ = ρ,
then will the distance be = _pr_; that is, if the _Lens_ be Glass =
_2r_, so that if an Object be placed at the Diameter of the Sphere
distant, in this Case the _Focus_ will be as far within as the Object is
without, and the _Species_ represented thereby will be as big as the
Life; but if it were a _Plano-Convex_, the same distance will be =
_2pr_, or in Glass to four times the _Radius_ of the Convexity; but of
this Method I may entertain the Curious at some other Time, and shew how
to magnifie or diminish an Object in any proportion assign'd, (which yet
will be obvious enough from what is here deliver'd) as likewise how to
erect the Object which in this Method is represented inverted.

A Second Use is to find what Convexity or Concavity is required, to make
a vastly distant Object be represented at a given _Focus_, after the one
Surface of the _Lens_ is formed; which is but a Corollary of our Theorem
for finding ρ, having _p_, _d_, _r_ and _f_ given; for _d_ being
infinite, that Rule becomes

 _rf_/(_pr - f_) = ρ,

that is in Glass _rf_/(_2r - f_) = ρ, whence if _f_ be greater than
_2r_, ρ becomes Negative, and _rf_/(_f - 2r_) is the _Radius_ of the
Concave sought.

Those that are wholly to begin with this Dioptrical Science, cannot do
better than to read with Attention a late Treatise of Dioptricks,
published by _W. Molineux_, Esq, R. S. S. who has at large shewn the
Nature of Optick Glasses, and the Construction and Use of Microscopes
and Telescopes; and though some nicely Critical have endeavour'd to spy
Faults, and to traduce the Book; yet having long since examin'd it with
Care, I affirm, that if I can judge, it hath but two things that with
any Colour may be call'd Faults; the one, an over-careful acknowledgment
of every Trifle the Author had receiv'd from others; and the other that
he labours to make easie this curious Subject, so little understood by
most, in a manner perhaps too familiar for the _Learned Critick_, and
which demonstrates that it was writ _cum animo docendi_, both which
require but very little Friendship or good Nature in the Reader, to pass
for Vertues in an Author.

[Illustration: _Tab. 5. pag. 359_]

But to return to our first Theorem, which accounting for the thickness
of the _Lens_, we will here again resume, _viz._

 (_mpdrρ - ndρt + nprρt_)/(_mdr + mdρ - mprρ - m - ndt + nrt_)
 = _f_.

And let it be required to find the _Focus_ where a whole Sphere will
collect the Beams proceeding from an Object at the distance _d_: Here
_t_ is equal to _2r_, and _r_ equal to ρ. And after due Reduction, the
Theorem will stand thus,

 (_mpdr - 2ndr + 2nprr_)/(_2nd + 2nr - mpr_) = _f_;

but if _d_ be Infinite, it is contracted to

 _mpr_/_2n_ - _r_ = ((_2n - m_)/(_2m - 2n_))_r_ = _f_,

wherefore a Sphere of Glass collects the Sun-Beams at half the
Semi-diameter of the Sphere without it, and a Sphere of Water at a whole
Semi-diameter. But if the _Ratio_ of Refraction _m_ to _n_ be as 2 to 1,
the _Focus_ falls on the opposite Surface of the Sphere; but if it be of
greater Inequality it falls within.

Another Example shall be when a Hemisphere is exposed to parallel Rays,
that is, _d_ and ρ being infinite, and _t_ = _r_, and after due
Reduction the Theorem results

 (_nn_/(_mm - mn_))_r_ = _f_.

That is, in Glass it is at 4/3_r_, in Water at 9/4_r_; but if the
Hemisphere were Diamant, it would collect the Beams at 1-4/15 of the
_Radius_ beyond the Center.

_Lastly_, As to the Effect of turning the two sides of a _Lens_ towards
an Object; it is evident, that if the thickness of the _Lens_ be very
small, so as that you neglect it, or account _t_ = 0; then in all Cases
the _Focus_ of the same _Lens_, to whatsoever Beams, will be the same,
without any difference upon the turning the _Lens_: But if you are so
curious as to consider the thickness, (which is seldom worth accounting
for) in the Case of parallel Rays falling on a _Plano-Convex_ of Glass,
if the plain side be towards the Object, _t_ does occasion no
difference, but the focal distance _f_ = 2_r_. But when the Convex-side
is towards the Object, it is contracted to _2r - ⅔t_, so that the
_Focus_ is nearer by ⅔_t_. If the _Lens_ be double Convex, the
difference is less; if a _Meniscus_, greater. If the Convexity on both
sides be equal, the focal length is about ⅙_t_ shorter than when _t_ = 0.
In a _Meniscus_ the Concave-side towards the Object increases the
focal Length, but the Convex towards the Object diminishes it. A General
Rule for the difference arising on turning the _Lens_, where the _Focus_
is Affirmative, is this

 (_2rt - 2ρt_)/(_3r + 3ρ - t_),

for double Convexes of differing Spheres. But for _Menisci_ the same
difference becomes

 (_2rt + 2ρt_)/(_3r - 3ρ + t_);

of which I need give no other Demonstration, but that by a due Reduction
it will so follow from what is premised, as will the Theorems for all
sorts of Problems relating to the _Foci_ of Optick-Glasses.




APPENDIX.




 _An Analytical Resolution of certain Equations of the Third, Fifth,
   Seventh, Ninth Powers, and so on _ad Infinitum_, in finite Terms,
   after the manner of _Cardan_'s Rules for Cubicks. By Mr. _A. Moivre_,
   Transact. _Nᵒ 309_._


Let (_n_) be any Number, (_y_) an unknown Quantity, or Root of the
Equation, (_a_) a Quantity altogether known, or what they call
_Homogeneum Comparationis_: And let the Relation of these Quantities to
each other be exprest by the Equation.

 _ny_ + ((_nn_ - 1)/(2 × 3))_ny_³ + ((_nn_ - 1)/(2 × 3)) ×
 ((_nn_ - 9)/(4 × 5))_ny_⁵ + ((_nn_ - 1)/(2 × 3)) ×
 ((_nn_ - 9)/(4 × 5)) × ((_nn_ - 25)/(6 × 7))_ny_⁷, _&c._ = _a_.

Its plain from the Nature of this Series, that if _n_ be any odd Number
(that is an Integer, it matters not whether Affirmative or Negative)
then the Series will Terminate, and the Equation arising will be one of
the above defin'd, whose Root is

 (1) _y_ = ½[ⁿ√](√(1 + _aa_) + _a_) -
           ½/[ⁿ√](√(1 + _aa_) + _a_) or,

 (2) _y_ = ½[ⁿ√](√(1 + _aa_) + _a_) -
           ½[ⁿ√](√(1 + _aa_) - _a_) or,

 (3) _y_ = ½/[ⁿ√](√(1 + _aa_) - _a_) -
           ½[ⁿ√](√(1 + _aa_) - _a_) or,

 (4) _y_ = ½/[ⁿ√](√(1 + _aa_) - _a_) -
           ½/[ⁿ√](√(1 + _aa_) + _a_)

For Example, Let the Root of this Equation of the Fifth Power be required

 5_y_ + 20_y_³ + 16_y_⁵ = 4

in which case _n_ is = 5, and _a_ = 4, and the Root, according to the
first Form, is

 _y_ = ½[⁵√](√(17 + 4)) - ½/[⁵√](√(17 + 4))

which is Expeditiously resolved into Numbers after this manner.

√17 + 4 is equal to 8.1231, whose Logarithm is 0,9097164, and the
fifth part of it is 0,1819433, the Number answering it

 1.5203 = [⁵√](√17 + 4).

But the Arithmetical Complement of 0.6577 is 9.8180567, the Number
answering is

 0.1819433 = 1/[⁵√](√17 + 4)

and the half difference of these Numbers is 0,4313 = _y_.

Here we may observe, that in the Room of the general Root, we may
advantageously take

 _y_ = ½√(_2a_) - ½/[ⁿ√](_2a_)

if the quantity _a_ be pretty large in respect of Unity. As if the
Equation were

 5_y_ + 20_y_³ + 16_y_⁵ = 682,

the Logarithm of _2a_ = 3.1348143 whose Fifth part is 0.6269628, the
Number answering is 4.236, and the Number answering the Arithmetical
Complement 9.3730372 is 0.236, the half difference of these Numbers is 2
= _y_.

But if in the aforegoing Equation the Signs are alternately Affirmative
and Negative; or which is the same thing if the Series be after this
manner,

 _ny_ + ((1 - _nn_)/(2 × 3))_ny_³ + ((1 - _nn_)/(2 × 3)) ×
 ((9 - _nn_)/(4 × 5))_ny_⁵ + ((1 - _nn_)/(2 × 3)) ×
 ((9 - _nn_)/(4 × 5)) × ((25 - _nn_)/(6 × 7))_ny_⁷ + _&c._ = _a_.

The Root of it will be equal to

 (1) _y_ = ½[ⁿ√](_a_ + √(_aa_ - 1)) +
           ½/[ⁿ√](_a_ + √(_aa_ - 1)), or

 (2) _y_ = ½[ⁿ√](_a_ + √(_aa_ - 1)) +
           ½[ⁿ√](_a_ - √(_aa_ - 1)), or

 (3) _y_ = ½/[ⁿ√](_a_ - √(_aa_ - 1)) +
           ½[ⁿ√](_a_ - √(_aa_ - 1)), or

 (4) _y_ = ½/[ⁿ√](_a_ - √(_aa_ - 1)) +
           ½/[ⁿ√](_a_ + √(_aa_ - 1)).

Here it is to be noted, that if (_n_ - 1)/2 be an odd Number, the Sign
of the Root found must be contrary to it.

Let an Equation be propos'd

 5_y_ - 20_y_³ + 16_y_⁵ = 6,

whence _n_ = 5, and _a_ = 6, and the Root will be =

 ½[⁵√](6 + √(35)) + ½/[⁵√](6 + √(35))

or because 6 + √35 = 11.916 whose Logarithm is 1.0761304, and its
Fifth part is 0.2152561, whose Arithmetical Complement is 9.7847439. The
Numbers belonging to these Logarithms are 1.6415 and 0.6091, whose half
Sum is 1.1253 = _y_.

But if it happen that _a_ is less than Unity then the Second Form, as
being more convenient, ought to be pitch'd on. So if the Equation had
been

 5_y_ - 20_y_³ + 16_y_⁵ = 61/64,

then _y_ will be =

 ½[⁵√](61/64 + √(-375/4096)) +
 ½[⁵√](61/64 - √(-375/4096))

and if the Root of the Fifth Power can by any means be Extracted the
true and possible Root of the Equation, will thence Emerge, tho' the
Expression seems to insinuate an Impossibility. But the Root of the
Fifth Power of the Binomial

 61/64 + √(-375/4096) is
 ¼ + ¼√(-15)

and so the same Root of the Binomial

 61/64 + √(-375/4096) is
 ¼ - ¼√(-15)

the half Sum of which Roots is = ¼ = _y_.

But if that Extraction can not be perform'd, or may seem too difficult,
the thing may be solv'd by the help of a Table of Natural Sines, after
the following manner;

To the Radius 1 let _a_ = 61/64 = 0,95112 the Sine of some Arch which is
therefore 72° 23', whose Fifth part (because _n_ is equal to 5) is 14°
28' the Sine of it is 0.24981 = ¼ nearly.

The same is the Method of proceeding in Equations of higher Dimensions.




 _A Discourse concerning the Action of the Sun and Moon on Animal
   Bodies; and the Influence which This may have in many Diseases. By
   _Richard Mead_, M. D. F. R. S._


PART I.

That some Diseases are properly the Effects of the Influence of the
Heavenly Bodies, and that others do vary their Periods and Symptoms
according to the different Positions of one or other of those Luminous
Globes, is a very ancient and certain Observation. Upon this score
_Hippocrates_[18] advises his Son _Thessalus_ to the study of Geometry
and Numbers, because _the Knowledge of the Stars is of very great use in
Physick_[19]. And the earliest Histories of Epidemic Distempers,
particularly do all turn upon the alterations made in our Bodies by the
Heavens.

But when in later Times Medicine came to be accommodated to the
Reasonings of Philosophers; no body being able to account for the manner
of this Celestial Action, It was allowed no farther share in affecting
our Health, than what might be imputed to the changes in the manifest
Constitution of the Air, excepting perhaps something of Truth which
still remains disguised and blended with the Jargon of Judiciary
Astrology.

In order therefore to set this Matter in a little clearer light, I shall
in the first place shew, That the Sun and Moon regarding their Nearness
and Direction to the Earth only, besides the Effects of Heat, Moisture,
_&c._ thereby caused in our Atmosphere, must at certain times make some
Alterations in all Animal Bodies; then enumerate some Histories and
Observations of such Changes, and enquire of what Use such Thoughts as
these may be in the Practice of Physick.

It is a constant Observation of those who write the History of the
_Winds_, That the most Windy Seasons of the Year, are the Time about the
Vernal and Autumnal Equinox; for be the Air never so calm before or
after, we never fail of having Winds at that Juncture. Every body
likewise knows, that in the most quiet Weather we are sure of some
Breeze at Mid-day and Mid-night, as also at Full Sea, _i.e._ always
about the time the Sun or Moon arrive at the Meridian. Seamen and
Country People reckon upon This, and order their Affairs accordingly.
And the changes of the Weather as to Winds or Calms especially about the
New and Full Moon, are too well known to require any Authority to
confirm such Remarks. Those who desire a fuller account of these
Observations, may see it in _De Chales_'s Navigation, _Gassendus_'s
Natural Philosophy, and _J. Goad_, his _Astro-Meteoro-Logica_.

These things being Matters of Fact, and in a manner Regular and
Universal, it may very well seem strange that Philosophers have not been
more accurate in their Enquiries into the Reason of such Appearances.
True indeed it is, that the Origin of Winds is various and uncertain,
but however, so constant and uniform an Effect must undoubtedly be owing
to one necessary Cause.

It has bin, now a considerable time since, sufficiently made out, that
our Atmosphere is a thin Elastic Fluid, one part of which gravitates
upon another, and whose Pressure is communicated every way in a Sphere
to any given Part thereof. From hence it follows, That if by any
external Cause the Gravity of any one part shou'd be taken off or
diminished, that from all sides around this part, the more heavy Air
would rush in to restore the Equilibrium which must of necessity be
preserved in all Fluids. Now this violent running in of the heavier Air
would certainly produce a Wind, which is no more than a strong Motion of
the Air in some determined Direction. If therefore we can find any
outward Cause that would at these stated Seasons we have mentioned,
diminish the Weight or Pressure of the Atmosphere; we shall have the
genuine Reason of these Periodical Winds, and the necessary Consequences
thereof.

The Flux and Reflux of the Sea was a Phænomenon too visible, and too
much conducing to the Subsistance of Mankind, and all other Animals, to
be neglected by those who applyed themselves to the Study of Nature;
however all their Attempts to explain this Admirable Contrivance of
infinite Wisdom were unsuccessfull, till Sir _Isaac Newton_ reveal'd to
the World juster Principles, and by a truer Philosophy than was formerly
known, shew'd us how by the United or Divided Forces of the Sun and
Moon, which are encreased and lessened by several Circumstances, all the
Varieties of the Tides are to be accounted for. And since all the
Changes we have enumerated in the Atmosphere do fall out at the same
times when those happen in the Ocean; and likewise whereas both the
Waters of the Sea and the Air of our Earth, are Fluids subject, in a
great Measure, to the same Laws of Motion; it is plain, that the Rule of
our great Philosopher takes place here, _viz._ _That Natural Effects of
the same kind are owing to the same Causes_.[20]

What difference that known Property of the Air, which is not in Water,
makes in the Case, I shall shew anon; setting aside the Consideration of
that for the present; It is certain, That as the Sea is, so must our
Air, twice every 25 Hours, be rais'd upwards to a considerable height,
by the Attraction of the Moon coming to the Meridian; so that instead of
a _Spherical_, it must form it self into a _Spheroidal_, or _Oval_
Figure, whose longest Diameter being produced, would pass thro' the
Moon. That the like Raising must follow as often as the Sun is in the
Meridian of any Place, either above or below the Horizon. Moreover, That
this Elevation is _greatest_ upon the New and Full Moons, because both
Sun and Moon do then conspire in their Attraction; _least_ on the
Quarters, in that they then drawing different ways, 'tis only the
Difference of their Actions produces the Effect. Lastly, That this
Intumescence will be of a _middle degree_, at the time between the
Quarters, and New and Full Moon.

From the same Principles, The Motion upwards of the Air will be
strongest of all about the Equinoxes; the Equinoctial Line being over
that Circle of the Globe, which has the greatest Diameter, either of the
Luminaries when in that are nearer, and the Agitation of the Fluid
Spheroid revolving about a greater Circle, is greater; besides, the
Centrifugal Force (arising from the Diurnal Rotation) is there greatest
of all. This will still be more considerable about the New and Full
Moons happening at these times, for the Reasons just now mentioned. And
the least Attraction will be about the Quadratures of these Lunar
Months, because the Declination of the Moon from the Equator is then
greatest. The different distances of the Moon in her Perigæum and
Apogæum, are the Reason that these full changes fall out a little before
the Vernal, and after the Autumnal Equinox. Now the Inverse of all this
happens when the Luminaries are in the Solstitial Circles. Lastly, In
the same Parallel, when the Moon's Declination is towards the Elevated
Pole, the Attraction is strongest when the Moon is in that Places
Meridian, and weakest when she is in the Opposite Places Meridian: The
contrary happens in the Opposite Parallel; by reason of the Spheroidal
Figure of the Earth and its Atmosphere.

Whatever has been said on this Head, is no more that applying what Sir
_Isaac Newton_ has Demonstrated of the Sea to our Atmosphere; and it is
needless to shew how necessarily those Appearances, just now mentioned,
of _Winds_, at the Stated Times, _&c._ must happen hereupon. It will be
of more use to consider the Proportion of the Forces of the two
Luminaries upon the _Air_, to that which they have upon the Water of our
Globe; that it may the more plainly appear what Influence the
Alterations hereby made, must have upon the Animal Body.

Sir _Isaac Newton_ has demonstrated[21] That the Force of the Sun to
move the Sea, is to the Force of Gravity, as 1 to 12868200. Let that be

 S. G :: 1. _n_. Hence, S = G/_n_.

And that the Force of the Moon to raise the Sea is to Gravity, as 1 to
2031821. Let this be

 L. G :: 1. _s_. Hence, L = G/_s_.

And since the Centrifugal force of the Parts of the Earth arising from
its Diurnal Motion is to Gravity, as 1 to 291. Let this be

 C. G :: 1. C. Then C = G/_e_. Hence,

 (S + L). C :: (G/_n_ + G/_s_). G/_e_ ::
 (1/_n_ + 1/_s_). 1/_e_ ::
 1. _sn_/((_s + n_) × _e_) :: 1. 6031.

The same Philosopher has taught us[22] that the Centrifugal force raises
the Water at the Equator above the Water at the Poles, to the height of
85200 Feet. Wherefore if that Force which is as 6031, raise the Ocean to
85200 Feet, the United forces of the Sun and Moon, which are as 1. will
raise the same to 14 Feet, for 85200/6031 = 14. _Proximé_.

Now we know that the more easily the Waters can obey the Attraction,
with the more Force are the Tides moved; but since, as Mr. _Halley_ has
determin'd it,[23] our Atmosphere is extended to 45 Miles, whereas the
middle depth of the Ocean is but about half a Mile; it is plain, that
the Air revolving in a Sphere about 100 times larger than that of the
Ocean, will have a proportionably greater Agitation.

Besides, Rocks, Shelves, and the inequality of Shoars are a great stop
to the Access and Recess of the Sea: But nothing repels the rising Air,
which is also of such thinness and fluidity, that it is easily driven,
and runs every way.

Nor ought we to omit, that it is the universal Law of Bodies Attracted,
that the Force of Attraction is reciprocally as the Squares of their
Distances; so that the Action of the Sun and Moon will be greater upon
the Air than upon the Water, upon the Account of its Nearness.

But the Consideration of the Elasticity is still of greater Moment here,
of which this is the nature, that it is reciprocally as the Pressure, so
that the incumbent Weight being diminished by the Attraction, the Air
underneath will upon this score be mightily expanded.

These and such like Causes will make the Tides in the Air to be much
greater than those of the Ocean; nor is it necessary to our purpose to
determine, by nice Calculations, their particular Forces; it is
sufficient to have proved that these Motions must both be Universal, and
also return at certain Intervals.

Now since the raising of the Water of the Ocean 14 Feet, produces
Torrents of such a prodigious Force, we may easily conceive what
Tempests of Winds (if not otherwise check'd) the Elevation of the Air
much higher (perhaps above a Mile) will necessarily cause. And there is
no doubt to be made, but that the same infinitely Wise Being, who
contrived the Flux and Reflux of the Sea, to secure that vast Collection
of Waters from Stagnation and Corruption (which would inevitably destroy
all the Animals and Vegetables on this Globe) has ordered this Ebb and
Flood of the Air of our Atmosphere, with the like good design, that is
to preserve (in Case all other Causes should fail, as they may, and at
times do in some Countries) the sweet Freshness, and brisk Temper of
this Fluid, so necessary to Life, and keep it, by a kind of continual
Circulation, from Deadness and Stinking.

This Reasoning is liable to only one Objection that I know of, and that
is this: That the Appearances we have mention'd cannot be owing to the
Causes now assigned; since by Calculation from them, the Mercury must at
New and Full Moon subside in the Barometer to a certain degree, which
yet we do not observe to happen.

In answer to which, (besides that there have been some Observations made
of the sinking of the Mercury at those times; and it may perhaps be the
fault of the Observers that these have not been reduced to any Rule) We
are to Consider, That altho' Winds and Alterations in the Pressure of
the Atmosphere, are the necessary consequents of the Lunar Attraction,
and true Causes of the different Rise of the Mercury in the Barometer;
yet these may be produced many others ways too, and therefore tho'
regularly the Mercury would always fall at the New and Full Moon, those
other Causes may be strong enough, even to raise it at those Seasons; in
as much as two contrary Winds, for instance, blowing towards the Place
of Observation, may accumulate the Air there, so as to increase both the
height and weight of the incumbent Cylinder; in like manner, the
Direction of two Winds may be such, as meeting at certain Angle they may
keep the Gravity of the Air in the middle place unaltered; and a
Thousand such Varieties there may be, by which the Regularity of
Appearances of this nature may be hindered. Now the other Springs, from
which such Changes in the Air may arise, are these.

1. Elastic Vapours forc'd from the Bowels of the Earth, by Subterraneous
Heats, and condensed by whatever cause in the Atmosphere.

2. A mixture of Effluvia of different qualities in the Air, may by
Rarefactions, Fermentations, _&c._ produce Winds and other Effects like
those resulting from the Combination of some Chymical Liquors; and that
such things happen, we are assured from the Nature of Thunder,
Lightning, and Meteors.

3. From the Eruptions of Vulcanoes and Earthquakes in distant Places,
Winds may be propagated to remoter Countries.

4. The divided or United Forces of the other Planets and of Comets, may
variously disturb the influence of the Sun and Moon, _&c._ We know that
there happen violent Tempests in the upper Regions of the Air, while we
below enjoy a Calm; and how many Ridges of Mountains there are on our
Globe, which interrupt and check the Propagation of the Winds; so that
it is no wonder that the Phænomena we have ascribed to the Action of the
Sun and Moon, are not always constant and uniform, and that every Effect
does not hereupon follow; which, were there no other Powers in Nature
able to alter the influence of this, might in a very regular and uniform
manner be expected from it.


These things being premised, it will not be difficult to shew (as was
proposed in the first Place) that these Changes in our Atmosphere at
High Water, New and Full Moon, the Æquinoxes, _&c._ must occasion some
Alterations in all Animal Bodies; and that from the following
Considerations.

1. All living Creatures require Air of a determined Gravity to perform
Respiration easily, and with Advantage; for it is by its weight that
this Fluid insinuates it self into the Cavity of the Breast and Lungs.
Now the Gravity, as we have proved, being lessened at these Seasons, a
smaller quantity only will insinuate it self, and this must be of
smaller force to comminute the Blood, and forward its Passage into the
left Ventricle of the Heart, whence a slower Circulation insues, and the
Secretion of Spirits is diminished.

2. This Effect will be the more sure, in that the Elasticity of the
Atmosphere is likewise diminished. Animals want Air as heavy so Elastic
to a certain degree; For as this is by its weight forced into the Cavity
of the _Thorax_ in Inspiration, so the Muscles of the _Abdomen_ press it
into the _Bronchi_ in Expiration, where the bending force being somewhat
taken off, and Springy Bodies when unbended, exerting their Power every
way, in Proportion to their Pressures, the Parts of the Air push against
all the sides of the _Vesiculæ_, and promote the Passage of the Blood.

We have a convincing Instance of all this, in those who go to the top of
high Mountains, for the Air is there so pure (as they call it) that is,
wants so much of its Gravity and Elasticity, that they Breathe with very
great difficulty.

3. All the Fluids in Animals have in them a mixture of Elastic _Aura_,
which when set at liberty, shews its Energy, and causes those
Fermentations we observe in the Blood and Spirits: Now when the Pressure
of the Atmosphere, upon the Surface of our Body is diminished, the
inward Air in the Vessels must necessarily be inabled to exert its
Force, in Proportion to the lessening the Gravity and Elasticity of the
outward; hereupon the Juices begin to ferment, change the Union and
Cohæsion of their Parts, break their Canals, _&c._


This is very plain in living Creatures put into the Receiver, exhausted
by the Air-Pump, which always swell as the Air is more and more drawn
out; their Lungs at the same time contracting themselves, and falling so
together as to be hardly discernible.[24]

E're we proceed to Matters of Fact, it may be worth the while to take
Notice, That Effects depending on such Causes as these, must of
necessity be most visible in Weak Bodies and Morbid Constitutions, when
other Circumstances concur to their taking Place. For this reason,
whatever Mischiefs do hence follow, cannot in the least disparage the
Wise Contrivance of Infinite Power in ordering these Tides of our
Atmosphere. The Author of Nature, we know, has made all things to the
greatest Advantage that could be, for the whole System of Animals on our
Globe, but it was impossible that such a disposition shou'd not in some
Cases be prejudicial to a Few. The Position and Distance of the Sun are
so adjusted, as to give in the most beneficial manner possible, Heat and
Light to the Earth; yet this notwithstanding, some Places may be too hot
for some weakly Bodies; some Autumns too sultry to agree with some
Animals, and some Winters too cold to be endured by some tender
Creatures: The whole however we must own, is most carefully provided
for. Besides, as most of these last mentioned Inconveniencies are by
easy shifts to be avoided; so there are such Powerful Checks put to this
Aereal Flux and Reflux, so many ways of abating the Damages accruing
from it now and then; that these are of no account in comparison of the
mighty Benefits hence arising, in which the Race of Mankind does
universally share.

[18] _Epist. ad Thessalum Filium._

[19] Ὀυκ ἐλαχίστον μέρος συμβάλλεται Ἀστρονομίη εἰς Ἰητρικήν. De Aere
Aquis & Locis.

[20] Newton, _Princip._ p. 402.

[21] _Princip. Lib._ 3. _Prop._ 36.

[22] _Ibid. Lib._ 3. _Prop._ 37.

[23] _Philos. Trans._ Nᵒ 181.

[24] _Esperienze dell' Academia del Cimento_, p.m. 113.


PART II.

There are no Historys in Physick which we may more safely take upon the
Credit of the Authors who relate 'em, than such as we are now going to
mention. In some Cases a Point may perhaps be strained to serve a
darling Hypothesis which the Writer has taken up, but here we are much
more likely to have pure Matter of Fact, because hitherto no one has
pretended the Appearances of this kind to be within the Reach of any
Scheme of Philosophy.

Epileptical Diseases besides the other Difficultys with which they are
attended, have this also surprizing, that in some the Fits do constantly
return every New and Full Moon; _the Moon_ (says Galen[25]) _governs the
Periods of Epileptic Cases_. Upon this score, They who were thus
affected were called Σεληνιακοὶ[26] and in the Historys of the Gospel
Σεληνιαζόμενοι[27] by some of the Latins afterwards, _Lunatici_[28].
_Bartholin_[29] tells a Story of one Epileptic who had apparent Spots in
her Face, which according to the Time of the Moon, varyed both their
Colour and Magnitude.

But no greater Consent in such Cases was perhaps ever Observed than what
I saw some time since in a Child about 5 years old, in which the
Convulsions were so strong and frequent, that life was almost despair'd
of, and by Evacuations and other Medicines very difficultly saved. The
Girl, who was of a lusty full habit of Body, continued well for a few
days, but was at Full Moon again seized with a most violent Fit, after
which, the Disease kept its Periods constant and regular with the Tides;
She lay always Speechless during the whole time of Flood, and Recovered
upon the Ebb. The Father who lives by the _Thames_ side, and does
business upon the River, observed these Returns to be so punctual, that
not only coming home He knew how the Child was before he saw it, but in
the night has risen to his Employ, being warned by Cries when coming out
of her Fit, of the turning of the Water. This continued 14 days, that
is, to the next great Change of the Moon, and then a dry Scab on the
Crown of the Head, (the effect of an Epispastic Plaister, with which I
had covered the whole _Occiput_ in the beginning of the Illness) broke,
and from the Sore, tho' there had been no sensible Discharge this way
for above a Fortnight, ran a considerable quantity of limpid Serum; upon
which, the Fits returning no more, I took great care to promote this new
Evacuation by proper Applications, with desired Success, for some time;
and when it ceased, besides two or three Purges with _Mercurius Dulcis_,
&c. ordered an Issue in the Neck, which being thought troublesome, was
made in the Arm; the Patient however has never since felt any Attacks of
those frightful Symptoms.

Whether or no it be thro' want of due Heed and Enquiry that we have not
in all the Collections of Histories and Cases, any Instance of the like
Nature so particular as this is, I know not; this is certain, that as
the _Vertigo_ is a Disease nearly related to the _Epilepsy_, and the
_Hysterical Symptoms_ do partake of the same Nature; so both one and the
other are frequently observed to obey the Lunar Influence. In like
manner, the raving Fits of Mad People, which keep Lunar Periods, are
generally in some degree Epileptic too.

_Tulpius_[30] and _Piso_[31] afford us remarkable Instances of
Periodical _Palseys_.

Every one knows how great a share the Moon has in forwarding those
Evacuations of the weaker Sex, which have their Name from the constant
Regularity they keep in their Returns; and there is no question to be
made, but the Correspondency we here observe, would be greater still,
and even Universal, did not many Accidents, and the infinite Varieties
in particular Constitutions one way or other concur to make a
difference. It is very observable that in Countries nearest to the
Æquator, where we have proved the Lunar Action to be strongest; these
Monthly Secretions are in much greater quantity than in those near the
Poles, where this force is weakest. This _Hippocrates_[32] takes notice
of, and gives it as one Reason why the Women in _Scythia_ are not very
fruitful.

The Case being thus with Females, it is no wonder if we sometimes meet
with Periodical Hæmorrhages answering to the times of the Moon in Males
also. For as a greater quantity of Blood in proportion to the bulk in
_one_ Sex, is the reason of its discharging it self thro' proper Ducts,
at certain Intervals, when the pressure of the external Air being
diminish'd, the internal _Aura_ can exert its Elasticity; so in the
_other_, if at any time there happens to be a Superabundancy of the same
Fluid, together with a weak Tone of the Fibres; it is plain that the
Vessels will be most easily burst, when the Resistance of the Atmosphere
is least. And this more especially, if any accidental hurt, or rarefying
Force has first given occasion to the other Causes to take effect.

I know a Gentleman of a tender frame of Body, who having once, by over
reaching, strained the parts about the Breast; fell thereupon into a
spitting of Blood, which for a Year and half constantly return'd every
New Moon, and decreasing gradually, continued always 4 or 5 days. The
Fits being more or less considerable, according as his management about
that time, contributed to a greater or lesser fullness of the Vessels.

We have two notable Instances of the like nature in our Philosophical
Transactions; the one[33] of a Person, who from his Infancy to the 24th
Year of his Age, had every full Moon an Eruption of Blood on the right
side of the Nail of his left Thumb, at first to 3 or 4 Ounces, and after
his sixteenth Year, to half a Pound each time; which when by searing the
part with a hot Iron, he stopp'd, he fell into a _Sputum Sanguinis_, and
by frequent Bleeding, _&c._ was very difficultly saved from a
Consumption. The other[34] is a Story of an _Inn-Keeper_ in _Ireland_,
who from the 43rd Year of his Life, to the 55th (in which it killed him)
suffered a Periodical Evacuation at the point of the Fore-Finger of his
Right-hand; and altho the Fits here kept not their returns so certain as
in the forementioned Case, (it may be either from the irregular way of
living of the Patient, or the mighty change every Effusion made in his
habit of Body, the quantity seldom amounting to less than four Pounds at
a time) yet there is this remarkable Circumstance in the Relation, that
the first beginning of this _Hæmorrhage_ was at _Easter_, that is, the
next Full Moon after the Vernal Equinox, which is one of the two Seasons
of the Year, at which we have proved the attraction of the Air, or
lessening of its Pressure, to be greater than at any other time
whatsoever.

But we are besides this to consider, That the Static Chair, and nice
Observation taught _Sanctorius_,[35] That _Men do increase a Pound or
two in their weight every Month, which overplus is discharged at the
Months end, by a Crisis of copious, or thick turbid Urine_.

It is not therefore at all strange that we should once a Month be liable
to the returns of such Distempers as depend upon a Fullness of the
Vessels, that these should take place at those times especially, when
the ambient Air is least able to repress the Turgency; and that tho' New
and Full Moon are both of equal Force, yet that sometimes one, and
sometimes the other only should Influence the Periods, according as this
or that happens to fall in with the inward Repletion.

The Afflux of Humours to Ulcers is sometimes manifestly altered by this
Power; [36] _Baglivi_ was acquainted with a Learned Young Man at _Rome_,
who labour'd under a _Fistula_ in the _Abdomen_, penetrating to the
_Colon_, which discharged so plentifully in the Increase, and so
sparingly in the Decrease of the Moon, that he could make a very true
judgment of the Periods and Quadratures of the Planet, from the
different quantity of the _Matter_ that came from Him.

_Nephritic_ Paroxysms have frequently been observed to obey the Lunar
Attraction: _Tulpius_[37] relates the Case of Mr. _Ainsworth_, an
_English_ Minister at _Amsterdam_, who had a Fit of the Gravel and
suppression of Urine every Full Moon, of which he found no relief till
the Moon decreased, unless by Bleeding at the Arm. After his death two
large Stones were taken out of his Bladder, and the _Pelvis_ of the left
Kidney was enlarged to that degree by the quantity of Urine so often
stopt there, as to contain almost as much as the Bladder it self.

I was present, not long since, at the Dissection of a Child about 5 or 6
Year old, who dyed of the frequent returns of _Nephritic_ Fits, attended
with Vomitings and a _Diarrhæa_. The Kidneys and Ureters were quite
stuffed with a slimy calculous Matter, and it was very instructive to
see the different degrees of Concretion in the several parts of it, from
a clear limpid Water, to a hard friable Substance. Dr. _Groenvelt_, who
had tended the Boy in his Illness, observed him to be seized with his
Pains at every Full Moon for several Months together, which generally
ended with the voiding of a Stone.

What Influence the Moon has in _Asthma's_,[38] _van Helmont_ takes
Notice, _Exacerbatur Paroxysmus_ (says he) _Lunæ Stationibus, & ævi
tempestatibus quas ideo præsentit & præsagit_.[39] And Sir _John
Floyer_, who has given us a more particular History of this Disease than
any Author, observes, that _The Fits usually return once in a Fortnight,
and frequently happen near the Change of the Moon_.

'Tis a more uncommon Effect of this Attractive Power that is related by
the Learned _Kerckringius_.[40] He knew a Young Gentlewoman, whose
Beauty depended upon the Lunar Force, insomuch that at Full Moon she was
Plump and very Handsome, but in the decrease of the Planet so Wan and
ill Favoured, that she was asham'd to go abroad till the return of the
New Moon gave _Fullness_ to her Face, and _Attraction_ to her Charms.

Tho' this is indeed no more than an Influence of the same kind, with
that the Moon has always been observed to have upon Shell-Fish, and some
other living Creatures. For as the old _Latin_ Poet _Lucilius_ says,[41]

  _Luna alit Ostrea & implet Echinos, Muribu' fibras
  Et Pecui addit---- ---- ----_

And after him _Manilius_[42]

  _Sic submersa fretris concharum & Carcere clausa,
  Ad Lunæ motum variant animalia corpus._

It is very well worth the pains to enquire what share such an Alteration
in the Weight and Pressure of the Atmosphere may have in the _Crises_ or
Changes of Acute Diseases. The Ancients made great Account of _Critical_
Days, and regulated their Practice according to the Expectation they had
from them; This Part of Physick is grown now into disuse, quite
slighted, and even ridiculed; and that I suppose chiefly for these two
reasons. In the first place, because the earliest Observations of this
kind, which were drawn into Rules being made in _Eastern_ Countries,
when these came to be applied to the Distempers of _Northern_ Regions,
without allowance given for the difference of the Climate, they were
oftentimes found not to answer. And secondly, Fevers of old were treated
with few or no Medicines, the Motions of Nature were carefully watched,
and no Violence offer'd to interrupt her Work. The Histories therefore
of _Crises_, tho' of great Use, and certainty under such Management as
this, were at length unavoidably set aside and lost; when Acute Cases
came to be Cured, according to this or that Hypothesis, not only by
Evacuations, but hot or cold Alteratives too; there being no longer any
room for those Laws of Practice which supposed a regular and uniform
Progress of the Distemper.

Wherefore, in order to understand a little both what might Induce the
first Masters of our Profession to so nice and strict an Observance in
this point; and what grounds there may be now, for a more due regard to
their Precepts, even upon the score of the Lunar Attraction only, I
propose the following Remarks.

1. All Epidemic Diseases do in their regular course require a stated
time, in which they come to their height, decline, and leave the Body
free.

This is so constant and certain, that when a Fever of any _Constitution_
which is _continual_ in one Subject, happens from some other cause, in
another to be _intermitting_, the Paroxysms do always return so often as
all together to make up just as many days of Illness as he suffers,
whose Distemper goes on from beginning to end, without any abatement.

Dr. _Sydenham_, a sworn Enemy to all Theories, learn'd thus much from
downright Observation; and gives this reason why Autumnal Quartans hold
six Months, because by computation the Fits of so long a time amount to
336 hours, or 14 days, the period of a continual Fever of the same
Season.[43]

So _Galen_ takes notice that when an Exquisite Tertian is terminated in
seven Paroxysms, a true Continual at the same time has its Crisis in
seven days; that is, the Fever lasts as long in one as in the other, in
as much (says he) as _a Fit in an Intermitting Feaver answers to a day
in a Continual_[44]. Now this so comes to pass, because

2. In these Cases there is always a Fermentation in the Blood, which
goes not off till the active Particles are thrown out by those Organs of
Secretion, which, according to the Laws of Motion, are most fitted to
separate 'em. And

3. As different Liquors put upon a Ferment, are depurated in different
times, so the Arterial Fluid takes up a determined Period, of which it
is discharged of an induced Effervescence.

4. The Symptoms, during this Ebullition, do not proceed all along in the
same Tenour; but on some days particularly, they give such evident Marks
of their good or bad Quality, that the nature of the ensuing _Solution_
may very well be guess'd at, and foretold by 'em.


Things being thus, Those days on which the Disease was so evidently
terminated one way or other, might very justly be call'd the days of
_Crisis_; and those upon which the tendency of Illness was discovered by
most visible Tokens, the _Indices_ of the _Critical Days_.

And thus far the Foundation was good, but when a false Theory happen'd
unluckily to be joined to true Observations, this did a little puzzle
the Cause. _Hippocrates_, it is plain, knew not to what to ascribe that
remarkable regularity with which he saw the Periods of Feavers were
ended on the _Seventh_, _Fourteenth_, _One and Twentieth_ day, _&c._
_Pythagoras_ his Philosophy was in those Ages very Famous, of which
_Harmony_ and the _Mysteries of Numbers_ made a considerable part, _Odd_
were more Powerful than _Even_, and _Seven_ was the most perfect of all.
Our great Physician espoused these Notions,[45] and confined the Stages
of acute Distempers to a _Septenary_ Progression[46], upon which this
Inconvenience follow'd, that when a Crisis fell out a day sooner or
later than this Computation required, his Measures were quite broken;
and that this must necessarily oftentimes happen, will appear by and by.

Upon this score _Asclepiades_ rejected this whole Doctrine as vain,[47]
and _Celsus_ finding it to be too nice and scrupulous, observes that the
_Pythagorean Numbers led the Ancients into the Error_.[48]

_Galen_ being aware of this, succeeded much better in his reasoning upon
the Matter, and very happily imputed the Critical Changes not to the
Power of Numbers, but to the Influence of the Moon; which he observes,
_has a mighty Action upon our Earth, exceeding the other Planets, not in
Energy, but in Nearness_[49]. So that according to him, the Septenary
Periods in Diseases are owing to the _Quarterly Lunar Phases, which are
the times of the greatest Force, and which return in about seven
days_.[50]

The result of the whole Affair, in short is this, A _Crisis_ is no more
than the Expulsion of the Morbific Matter out of the Body, thro' some or
other of the Secretory Organs; in order to which, it is necessary that
this should be prepar'd and comminuted to such a degree, as is required
to make it pass into the Orifices of the respective Glands; and
therefore _as_ the most _perfect Crisis_ is by _Sweat_, (both by reason
that the Subcutaneous Glands do naturally discharge more than all the
other put together, and also that their Ducts being the smallest of any,
whatsoever comes this way is certainly wery well divided and broken)
_so_ the most _imperfect_ is an _Hæmorrhage_, because This is an
Argument that what Offends is not fit to be cast off in any Part, and
consequently breaks the Vessels by the Effervescence of the Blood. An
_Abscess_ in those Organs which separate thick, slimy Juices is of a
middle nature betwixt these two.

Now it is very plain, That if the time, in which either the Peccant
Humour is prepar'd for Secretion, or the Fermentation of the Blood is
come to its height, falls in with those Changes in the Atmosphere which
diminish its pressure; the _Crisis_ will then be more compleat and
large. And also, that this Work may be forwarded or delay'd a day, upon
the account of such an Alteration in the Air; the Distention of the
Vessels upon which it depends, being hereby made more easie, and a weak
Habit of Body in some Cases standing in need of this outward Assistance.
Thus a Fever which requires about a Week to its Period, may sometimes,
as _Hippocrates_ observed, have a good Crisis on the sixth, and
sometimes not till the eighth day.

In Order therefore to make true Observations of this kind, the time of
Invasion is to be considered, The genuine course of the Distemper must
first be watched, which is not to be interrupted by any violent Methods:
The strength of Nature in the Patient is to be considered, and by what
Secretions the Crisis is most likely to be performed; and it will then
be found, that not only the _New_ and _Full_ Moons, but even the
_Southings_, whether visible or latent, of the Planet, are here of
considerable Moment.

For Confirmation of which, we need only to reflect on what Mr. _Paschal_
has remark'd, _concerning the Motions of Diseases and Births and
Deaths_[51]. Dividing the Νυχθήμερον into Four Senaries of Hours,
the first consists of three hours before the Southing of the Moon, and
three after; the second of the six hours following, and the third and
fourth of the remaining Quarters of the natural day; He takes notice
that none are born, or die a natural Death in the first and third
Senaries, which he calls first and second Tides, but all either in the
second or fourth Senaries, which he calls first and second Ebbs. In like
manner, that in Agues, the tumult of the Fits generally lasts all the
Tiding time, and then goes off in kindly Sweats in the Ebbs. From whence
he very rationally concludes, that Motion, Vigour, Action, Strength,
_&c._ appear most, and do best in the _Tiding Senaries_; and that Rest,
Relaxation, Decay, Dissolution, _&c._ belong to the _Ebbing Senaries_.

[25] Τας τῶν ἐπιλήπτων τηρεῖ περιόδους. _De Dieb. Critic. lib._ 3.

[26] _Alexand. Trallian._ lib. 1. c. 15.

[27] Matth. c. 17. v. 15.

[28] _Apuleius de Virtutib. Herbar._ cap. 6. & 95.

[29] _Anatom. Centur._ 2. H. 72.

[30] _Observ. Med._ lib. 1. cap. 12.

[31] _De Morb. à serosâ Colluvie_, Obs. 28.

[32] _De Aere Aquis & Locis._

[33] Nᵒ 272.

[34] _Philos. Trans._ Nᵒ 171.

[35] _Medicin. Static._ Sect. 1. Aph. 65.

[36] _De Experiment. circa Sanguin._ p. m. 341.

[37] _Observat._ Lib. 2. c. 43. _vid. etiam Observ._ 52.

[38] _Asthma & Tuss._ § 22.

[39] _Treatise of the Asthma_, p. 17.

[40] _Observat. Anatomic._ 92.

[41] _Apud_ A. Gellium, lib. 20. c. 8.

[42] _Astronomic._ lib. 2.

[43] _De Feber. Intermit._ Ann. 1661. pag. _m._ 65.

[44] _Comment. in Aphor._ 59. lib. 4. & _de Crisib._ lib. 2. c. 6.

[45] _Epidem._ lib. 1. Sect. 3.

[46] αἱ μὲν οὖν ἡμέραι ἐπισημόταταί εἰσιν ἐν τοῖς πλείστοις αἵτε πρῶται
καὶ ἑβδομιαῖαι, πολλαὶ μὲν περὶ νούσων, πολλαὶ δὲ καὶ τοῖς ἐμβρύοις.
_de Septimestri Partu._

[47] _Vid. Celsum_ lib. 3. c. 4.

[48] _Ibid._

[49] _De diebus Decretor._ lib. 3.

[50] _Ibid._

[51] _Philos. Transact._ Nᵒ 202.


A COROLLARY.

It having bin explained in the Beginning of this Discourse, how those
Influences of the Heavens, which favour the _Returns_ of _Diseases_, may
likewise raise _Winds_ at the same times; and that We feel the different
Effects of _These_ according as other Causes do concurr to the Motion of
the Air; it will not be amiss, to shew in one Instance or two, how much
Natural History confirms this Reasoning.

There happened on the 26th of _November_, 1703. a little before
Midnight, a most terrible _Storm_ of _Wind_, the Fury of it is still
fresh in every ones Mind, which lasted above six Hours.

It is not to the present purpose to relate its History and Causes; What
we observe is, That the Moon was at that time _in Perigæo_, and just
upon the change to _New_. Upon both which accounts its Action in raising
the Atmosphere must be great; And hence indeed the _Tides_ which
followed were also very great, and the _Mercury_ in the _Barometer_, at
least, in most places, fell very low.

This Influence was, without all doubt, assisted by some such other
Causes of _Winds_, as we have mentioned; These we can't know, but may
however take notice how much the manifest State of the Air contributed
to this Calamity.

After a greater quantity of Rains than ordinary had fallen in the Summer
and Autumn, in those places where the Storm was felt, the Winter came on
much warmer than usual; so that the Liquor in a Thermometer, of which
the 84th Degree notes Frost, never fell below the 100th.[52]

Hence we may very well believe, that the Atmosphere was at that time
fill'd with Atoms of _Salts_ and _Sulphur_, out of the Vapours raised by
the Heat from the moist Earth, which being variously combined and
agitated, gave that deadly force to the Motion of the Air.

A Proof of this we have not only from the frequent _Flashes_ of
_Lightning_, observed a little before the Storm, but also from what the
Country People took notice of the next day, that the Grass and Twiggs of
the Trees, in Fields remote from the Sea, tasted very salt, so that the
Cattle wou'd not feed on them.

Our Histories mention another Storm, which if not equal to this last in
Violence, is however thought the greatest that had then ever been known
and memorable from the time at which it happened, _viz._ on the 3d of
_September_, 1658. the day on which the Usurper _O. Cromwel_ died.

No _Ephemerides_ that I know of relate the Condition of the Air that
Year, but it is sufficient to remark, That whatever other Causes
concurr'd, their force was accompanied with a _Full Moon_, just before
the time of the _Atumnal Equinox_.

Upon the same score it comes to pass, That in those Countries which are
Subject to frequent _Inundations_, these Calamities are observed to
happen at the times of the _Moon_'s greatest Influence, so that the
Learned _Baccius_[53] has rightly enough laid the Cause of such
Mischiefs upon immoderate _Tides of the Ocean_, being unhappily
accompanied with the _attractive Force_ of some or other _Stars_.

Dr. _Childrey_ in his _Britannia Baconica_[54] has from several
Instances shewn the _Lunar_ Action in Damages of this kind.

Such and the like _Natural_ Causes have _Storms_ and _Tempests_; for as
to the Question of Divine Power, whether or no Calamities of this kind
do not sometimes, by the Anger of Heaven, happen out of the Course of
Nature, it is not my Business to Dispute, nor would I by any means
indeavour to absolve Mens Minds from the Bands of Religion. For although
we must allow all the Parts of the Machine of this World to be framed
and moved by Established Laws, and that the same Disposition of its
Fabrick, which is most beneficial to the Whole, must of necessity, in
some few Places now and then occasion Hurts and Mischiefs; it is however
most highly reasonable, that we should yield to the Supreme Creator an
absolute Power over all his Works; Concluding withal, that it was
perhaps agreeable to Divine Wisdom, to order the Make of the World after
such a manner as might sometimes bring Mischiefs and Calamities upon
Mankind, whom it was necessary by the Frights of _Storms_, _Thunder_ and
_Lightning_ to keep in a continual Sence of their Duty.

[52] _Vid._ Philos. Transact. N 289.

[53] _Del_ Tevere, lib. 3. p. 228.

[54] Pag. 97.


_The End._





End of Project Gutenberg's Miscellanea Curiosa, Vol 1, by Edmond Halley

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