



Produced by Al Haines









  RADIATION

  BY P. PHILLIPS

  D.Sc. (B'HAM), B.Sc. (LONDON), B.A. (CANTAB.)



  LONDON: T. C. & E. C. JACK
  67 LONG ACRE, W.C., AND EDINBURGH
  NEW YORK: DODGE PUBLISHING CO.
  1912




CONTENTS

CHAP.

INTRODUCTION

I. THE NATURE OF RADIANT HEAT AND LIGHT

II. GRAPHIC REPRESENTATION OF WAVES

III. THE MEANING OF THE SPECTRUM

IV. THE LAWS OF RADIATION

V. FULL RADIATION

VI. THE TRANSFORMATION OF ABSORBED RADIATION

VII. PRESSURE OF RADIATION

VIII. THE RELATION BETWEEN RADIANT HEAT AND ELECTRIC WAVES

INDEX




{vii}

INTRODUCTION

We are so familiar with the restlessness of the sea, and with the havoc
which it works on our shipping and our coasts, that we need no
demonstration to convince us that waves can carry energy from one place
to another.  Few of us, however, realise that the energy in the sea is
as nothing compared with that in the space around us, yet such is the
conclusion to which we are led by an enormous amount of experimental
evidence.  The sea waves are only near the surface and the effect of
the wildest storm penetrates but a few yards below the surface, while
the waves which carry light and heat to us from the sun fill the whole
space about us and bring to the earth a continuous stream of energy
year in year out equal to more than 300 million million horsepower.

The most important part of the study of Radiation of energy is the
investigation of the characters of the waves which constitute heat and
light, but there is another method of transference of energy included
in the term Radiation; the source of the energy behaves like a battery
of guns pointing in all directions and pouring out a continuous hail of
bullets, which strike against obstacles and so give up the energy due
to their motion.  This method is relatively unimportant, and is usually
treated of separately when considering the subject of Radioactivity.
We shall therefore not consider it in this book.




{9}

RADIATION



CHAPTER I

THE NATURE OF RADIANT HEAT AND LIGHT

+Similarity of Heat and Light.+--That light and heat have essentially
the same characters is very soon made evident.  Both light and heat
travel to us from the sun across the ninety odd millions of miles of
space unoccupied by any material.

[Illustration: Figure 1]

Both are reflected in the same way from reflecting surfaces.  Thus if
two parabolic mirrors be placed facing each other as in the diagram
(Fig. 1), with a source of light L at the focus of one of them, an
inverted image of the light will be formed at the focus I of the other
one, and may be received on a small screen placed there.  The paths of
two of the rays are shown by the dotted lines.  If L be now replaced by
a heated ball and a[1] blackened thermometer bulb be placed at I, the
thermometer will indicate a sharp rise of temperature, showing that the
rays of heat are focussed there as well as the rays of light.


[1] See page 37.


{10}

Both heat and light behave in the same way in passing from one
transparent substance to another, _e.g._ from air into glass.  This can
be readily shown by forming images of sources of heat and of light by
means of a convex lens, as in the diagram (Fig. 2).

[Illustration: FIG. 2.]

The source of light is represented as an electric light bulb, and two
of the rays going to form the image of the point of the bulb are
represented by the dotted lines.  The image is also dotted and can be
received on a screen placed in that position.

If now the electric light bulb be replaced by a heated ball or some
other source of heat, we find by using a blackened thermometer bulb
again that the rays of heat are brought to a focus at almost the same
position as the rays of light.

The points of similarity between radiant heat and light might be
multiplied indefinitely, but as a number of them will appear in the
course of the book these few fundamental ones will suffice at this
point.

+The Corpuscular Theory.+--A little over a century ago everyone
believed light to consist of almost inconceivably small particles or
corpuscles shooting out at enormous speed from every luminous surface
and causing the sensation of sight when impinging {11} on the retina.
This was the corpuscular theory.  It readily explains why light travels
in straight lines in a homogeneous medium, and it can be made to
explain reflection and refraction.

+Reflection.+--To explain reflection, it is supposed that the reflector
repels the particles as they approach it, and so the path of one
particle would be like that indicated by the dotted line in the diagram
(Fig. 3).

[Illustration: FIG. 3.]

Until reaching the point A we suppose that the particle does not feel
appreciably the repulsion of the surface.  After A the repulsion bends
the path of the particle round until B is reached, and after B the
repulsion becomes inappreciable again.  The effect is the same as a
perfectly elastic ball bouncing on a perfectly smooth surface, and
consequently the angle to the surface at which the corpuscle comes up
is equal to the angle at which it departs.

+Refraction.+--To explain refraction, it is supposed that when the
corpuscle comes very close to the surface of the transparent substance
it is attracted by the denser substance, e.g. glass, more than by the
lighter substance, e.g. air.  Thus a particle moving along the dotted
line in air (Fig. 4) would reach the {12} point A before the attraction
becomes appreciable, and therefore would be moving in a straight line.
Between A and B the attraction of the glass will be felt and will
therefore pull the particle round in the path indicated.  Beyond B, the
attraction again becomes inappreciable, because the glass will attract
the particle equally in all directions, and therefore the path will
again become a straight line.  We notice that by this process the
direction of the path has become more nearly normal to the surface, and
this is as it should be.  Further, by treating the angles between the
two paths and the normal mathematically we may deduce the laws of
refraction which have been obtained experimentally.  One other
important point should be noticed.  Since the surface has been
attracting the particle between A and B the speed of the particle will
be greater in the glass than in the air.

[Illustration: FIG. 4]

+Ejection and Refraction at the same Surface.+--A difficulty very soon
arises from the fact that at nearly all transparent surfaces some light
is reflected and some refracted.  How can the same surface sometimes
repel and sometimes attract a corpuscle?  Newton surmounted this
difficulty by attributing a polarity to each particle, so that one end
was repelled and the other attracted by the reflecting and refracting
{13} surface.  Thus, whether a particle was reflected or refracted
depended simply upon which end happened to be foremost at the time.  By
attributing suitable characteristics to the corpuscles, Newton with his
superhuman ingenuity was able to account for all the known facts, and
as the corpuscles were so small that direct observation was impossible,
and as Newton's authority was so great, there was no one to say him nay.

+Wave Theory.  Rectilinear Propagation.+--True, Huyghens in 1678 had
propounded the theory that light consists of waves of some sort
starting out from the luminous body, and he had shown how readily it
expressed a number of the observed facts; but light travels in straight
lines, or appears to do so, and waves bend round corners and no one at
that time was able to explain the discrepancy.  Thus for nearly a
century the theory which was to be universally accepted remained
lifeless and discredited.  The answer of the wave theory to the
objection now is, that light does bend round corners though only
slightly and that the smallness of the bend is quite simply due to the
extreme shortness of the light waves.  The longer waves are, the more
they bend round corners.  This can be noticed in any harbour with a
tortuous entrance, for the small choppy waves are practically all cut
off whereas a considerable amount of the long swell manages to get into
the harbour.

+Interference of Light.  Illustration by Ripples+.--The revival of the
wave theory dates from the discovery by Dr. Young of the phenomenon of
interference of light.  In order to understand this we will {14}
consider the same effect in the ripples on the surface of mercury.  A
tuning-fork, T (Fig. 5), has two small styles, S S, placed a little
distance apart and dipping into the mercury contained in a large
shallow trough.  When the tuning-fork is set into vibration, the two
styles will move up and down in the mercury at exactly the same time
and each will start a system of ripples exactly similar to the other.
At any instant each system will be a series of concentric circles with
its centre at the style, and the crests of the ripples will be at equal
distance from each other with the troughs half-way between the crests.

[Illustration: FIG. 5.]

The ripples from one style will cross those from the other, and a
curious pattern, something like that in Fig. 6, will be formed on the
mercury.  S S represents the position of the two styles, while the
plain circles denote the positions of the crests and the dotted circles
the positions of the troughs at any instant.  Where two plain circles
cross it is evident that both systems of ripples are producing a crest,
and so the two produce an exaggerated crest.  Similarly where two
dotted circles cross an exaggerated trough is produced.  Thus in the
shaded portions of the diagram we get more violent ripples than those
due to a single style.  Where a plain circle cuts a dotted one,
however, one system of ripples produces a {15} crest and the other a
trough, and between them the mercury is neither depressed below nor
raised above its normal level.  At these points, therefore, the effect
of one series of ripples is just neutralised by the effect of the other
and no ripples are produced at all.  This occurs in the unshaded
regions of the diagram.

The mutual destruction of the effects of the two sets of waves is
"Interference."

[Illustration: FIG. 6.]

Now imagine a row of little floats placed along the line EDCBABCDE.  At
the lettered points the floats will be violently agitated, but at the
points midway between the letters they will be unmoved.  This exactly
represents the effect of two interfering sources of light S, S, sending
light which is received by a screen at the dotted line EDCBABCDE.  The
lettered points will be brightly illuminated while the intermediate
points will be dark.

In practice it is found impossible to make two {16} sources of light
whose vibrations start at exactly the same time and are exactly
similar, but this difficulty is surmounted by using one source of light
and splitting the waves from it into two portions which interfere.

+Young's Experiment.+--Dr. Young's arrangement is diagrammatically
represented in Fig. 7.

Light of a certain wave length is admitted at a narrow slit S, and is
intercepted by a screen in which there are two narrow slits A and B
parallel to the first one.

[Illustration: FIG. 7.]

A screen receives the light emerging from the two slits.  If the old
corpuscular theory were true there would be two bright bands of light,
the one at P and the other at Q, but instead Dr. Young observed a whole
series of parallel bright bands with dark spaces in between them.
Evidently the two small fractions of the original waves which pass
through A and B spread out from A and B and interfere just as if they
were independent sources like the two styles in the mercury ripples
experiment.

{17}

+Speed of Light in Rare and Dense Media.+--The discovery of
interference again brought the wave theory into prominence, and in 1850
the death-blow was given to the corpuscular theory by Foucault, who
showed that light travels more slowly in a dense medium such as glass
or water than in a light medium such as air.  This is what the wave
theory anticipates, while the reverse is anticipated by the corpuscular
theory.

But if light and heat consist of waves, what kind of waves are they and
how are they produced?

+Elastic Solid Theory.+--In the earlier days of the wave theory it was
supposed that the whole of space was filled with something which acted
like an elastic solid material in which the vibrations of the atoms of
a luminous body started waves in all directions, just as the vibrations
of a marble embedded in a jelly would send out waves through the jelly.
These waves are quite easily imagined in the following way.

If one end of an elastic string be made to oscillate to and fro a
series of waves travels along the string.  If a large number of these
strings are attached to an oscillating point and stretch out in all
directions, the waves will travel along each string, and if the strings
are all exactly alike will travel at the same speed along all of them.
Any particular crest of a wave will thus at any instant lie on the
surface of a sphere whose centre is the oscillating point.  If now we
imagine that the strings are so numerous that they fill the whole of
the space we have a conception of the transmission of waves by an
elastic solid.

+Electromagnetic Waves.+--Since Maxwell published {18} his
electromagnetic theory in 1873 it has been universally held that heat
and light consist of electro-magnetic waves.

These are by no means so easy to imagine as the elastic waves, as there
is no actual movement of the medium; an alternating condition of the
medium is carried onward, not an oscillation of position.

When a stick of sealing-wax or ebonite is rubbed with flannel it
becomes possessed of certain properties which it did not have before.
It will attract light pieces of paper or pith that are brought near to
it, it will repel a similar rubbed piece of sealing-wax or ebonite and
will attract a rod of quartz which has been rubbed with silk.

The quartz rod which has been rubbed with silk has the same property of
attracting light bodies which the ebonite and sealing-wax rod has, but
it repels another rubbed quartz rod and attracts a rubbed ebonite or
sealing-wax rod.

+Positive and Negative Electrification.+--The ebonite is said to be
negatively electrified and the quartz positively electrified.

When the two rods, one positively and the other negatively electrified,
are placed near to one another, we may imagine the attraction to be due
to their being joined by stretched strings filling up all the space
around them.  If a very small positively electrified body be placed
between the two it will tend to move from the quartz to the ebonite,
_i.e._ in the direction of the arrows.

[Illustration: FIG. 8.]

+The Electric Field.  Lines of Force.+--The space {19} surrounding the
electrified sticks in which the forces due to them are appreciable is
called the electric field, and the direction in which a small
positively electrified particle tends to move is called the direction
of the field.  The lines along which the small positive charge would
move are called lines of force.

The conception of the electric field as made up of stretched elastic
strings is, of course, a very crude one, but there is evidently some
change in the medium in the electric field which is somewhat analogous
to it.

[Illustration: FIG. 9.]

+Electric Oscillations.+--If the position of the two rods is reversed,
then of course the direction of the field at a point between them is
reversed, and if this reversal is repeated rapidly, we shall have the
direction of the field alternating rapidly.  If these alternations
become sufficiently rapid they are conveyed outwards in much the same
way as the oscillations of position are conveyed in an ordinary ripple.
Thus suppose the two rods are suddenly placed in the position in the
diagram.  The field is not established instantaneously, the lines of
force taking a short time to establish themselves in their ultimate
positions.  During this time the lines of force will be travelling
outwards to A in the direction of the dotted arrow.  {20} Before they
reach A let us suppose that the position of the rods is reversed.  Then
the direction of the lines is reversed and these reversed lines will
travel outwards towards A, following in the track of the original
lines.  Thus a continuous procession of lines of force, first in one
direction and then in the opposite direction, will be moving out
perpendicular to themselves in the direction of the dotted arrow.

This constitutes an electric wave.

+Magnetic Oscillation, Lines of Force, and Field+.--Almost exactly the
same kind of description applies to a magnetic wave.  The space near to
the North and South poles of a magnet is modified in somewhat the same
way as that between the electrified rods, and the magnetic lines of
force are the lines along which a small North magnetic pole would move.
We may imagine a rapid alternation of the magnetic field by the rapid
reversal of the positions of the North and South poles, and we may
imagine the transmission of the alternations by means of the procession
of magnetic lines of force.

+Changes in Magnetic Field.+--But experiment shows that whenever the
magnetic field at any place is changing an electric field is produced
during the alteration, and _vice-versa_.  Electric and magnetic waves
must therefore always accompany one another, and the two sets of waves
together constitute electro-magnetic waves.

These are the waves which a huge amount of experimental evidence leads
us to believe constitute heat, light, the electric waves used in
wireless telegraphy, {21} and the invisible ultraviolet waves which are
so active in inducing chemical action.

+Oscillation of Electric Charges within the Atom.+--We have seen how
these waves might be produced by the oscillation of two electrified
rods, and it is supposed that the light coming from luminous bodies is
produced in a similar way.  There are many reasons for believing that
there exist in the atoms of all substances, minute negatively
electrified particles which may rotate in small orbits or oscillate to
and fro within the atom.  There also exists an equal positive charge
within the atom.  As the negative particles rotate or oscillate in the
atom, it is evident that the field between them and the positively
electrified part of the atom alternates, and so electro-magnetic waves
are sent out.




{22}

CHAPTER II

GRAPHIC REPRESENTATION OF WAVES

A system of ripples on the surface of water appears in vertical section
at any instant somewhat as in Fig. 10.  The dotted line AB represents
the undisturbed surface of the wafer, and the solid line the actual
surface.  If the disturbance which is causing the ripples is an
oscillation of perfectly regular period the individual ripples will be
all alike, except they will get shallower as they become more remote
from the disturbance.

[Illustration: FIG. 10.]

+Wave-length.+--The distance between two successive crests will be the
same everywhere, and this distance or the distance between any two
corresponding points on two successive ripples is called the
wave-length.  Evidently, the wave-length is the distance in which the
whole wave repeats itself.

+Phase.+--The position of a point in the wave is called the phase of
the point.  Thus the difference of phase between the two points A and C
is a quarter {23} of a wave-length.  As the waves move on along the
surface it is evident that each drop of water executes an up and down
oscillation, and at the points C, C the drop has reached its highest
position and at the points T, T its lowest.

+Amplitude.+--The largest displacement of the drop, _i.e._ the distance
from the dotted line to C or to T, is called the amplitude of the wave.
The time taken for a drop to complete one whole oscillation, _i.e._ the
time taken for a wave to travel one whole wave-length forward, is
called the period of the wave.  The number of oscillations in one
second, _i.e._ the number of wave-lengths travelled in one second, is
called the frequency.

[Illustration: FIG. 11.]

Although there is no visible displacement in the waves of light and
heat, yet we may represent them in much the same way.  Thus if AB, Fig.
10, represents the line along which a ray of light is travelling, the
length NP is drawn to scale to represent the value of the electric
field at the point N, and is drawn upwards from the line AB when the
field is in one direction and downwards when it is in the opposite
direction.

Thus the direction of the field at different points in the wave XY,
Fig. 11, is shown by the dotted arrows as if due to electrified rods of
quartz and ebonite placed above and below XY.

In the case of the electromagnetic wave, the {24} amplitude will be the
maximum value to which the electric field attains in either direction,
and the other terms--wave-length, phase, period and frequency--will
have the same meaning as for water ripples.

+Wave Form.+--Waves not only differ in amplitude, wave-length, and
frequency, but also in wave form.  Waves may have any form, _e.g._ Fig
12.  Or we may have a solitary irregular disturbance such as is caused
by the splash of a stone in water.

[Illustration: FIG. 12.]

But there is one form of motion of a particle in a wave which is looked
upon as the simplest and fundamental form.  It is that form which is
executed by the bob of a pendulum, the balance wheel of a watch, the
prong of a tuning-fork, and most other vibrations where the controlling
force is provided by a spring or by some other elastic solid.

It is called "Simple Harmonic Motion" or "Simple Periodic Motion," and
the essential feature of it is that the force restoring the displaced
particle to its undisturbed position is proportional to its
displacement from the undisturbed position.  A wave in which all the
particles execute simple harmonic motion has the form in Fig. 10 or
Fig. 11, which is therefore looked upon as the fundamental wave form or
simple wave form.

Simple waves will vary only in amplitude, wave-length, and frequency,
and the energy in the wave will depend upon these quantities.

{25}

+Energy in a Simple Wave.+--If the velocity is the same for all
wave-lengths, then the frequency will evidently be inversely
proportional to the wave-length and the energy will depend upon the
amplitude and the wave-length.  The kinetic energy of any moving body,
_i.e._ the energy due to its motion, is proportional to the square of
its velocity, and we may apply this to the motion of the particles in a
wave and to show how the energy depends upon the amplitude and
wave-length.

Since the distance travelled by a particle in a single period of the
wave will be equal to four times the amplitude, the velocity at any
point in the wave must be proportional to the amplitude and therefore
the kinetic energy is proportional to the square of the amplitude.

With the same amplitude but with different wave-lengths, we see that
the time in which the oscillation is completed is proportional to the
wave-length and that the velocity is therefore inversely proportional
to the wave-length.  The kinetic energy is therefore inversely
proportional to the square of the wave-length.

+Addition of Waves.+--The superposition of two waves so as to obtain
the effect of both waves at the same place is carried out very simply.
The displacements at any point due to the two waves separately are
algebraically added together, and this sum is the actual displacement.
In Fig. 13 the dotted lines represent two simple waves, one of which
has double the wave-length of the other.  At any point P on the solid
line, the displacement PN is equal to {26} the algebraic sum of the
displacement NQ due to one of the waves and NR due to the other.  The
solid line, therefore, represents the resulting wave.  We may repeat
this process for any number of simple waves, and by suitably choosing
the wave-length and amplitude of the simple waves we may build up any
desired form of wave.  The mathematician Fourier has shown that any
form of wave, even the single irregular disturbance, can thus be
expressed as the sum of a series of simple waves and that the
wave-lengths of these simple waves are equal to the original
wave-length, one-half of it, one-third, one-quarter, one-fifth, and so
on in an infinite series.  Fourier has also shown that only one such
series is possible for any particular form of wave.

[Illustration: FIG. 13.]

The importance of this mathematical expression lies in the fact that in
a number of ways Fourier's series of simple waves is manufactured from
the original wave and the different members of the series become
separated.  Thus the most useful way in which we can represent any wave
is, not to draw the actual form of a wave, but to represent what simple
waves go to form it and to show how much energy there is in each
particular simple wave.

{27}

+Energy--Wave-length Curve.+--This can be done quite simply as in Fig.
14.  The distance PN from the line OA being drawn to scale to represent
the energy in the simple wave whose length is represented by ON.

[Illustration: FIG. 14.]

Thus the simple wave of length OX has the greatest amount of energy in
it.

[Illustration: FIG. 15.]

Fig. 15 wall represent a simple wave of wave-length OX, the energy in
all the other waves being zero.

{28}

The three curves given in Fig. 16 give a comparison of the waves from
the sun, an arc lamp, and an ordinary gas-burner.

[Illustration: FIG. 16.]




{29}

CHAPTER III

THE MEANING OF THE SPECTRUM

+The Spectrum.  Dispersion.+--When a narrow beam of white light is
transmitted through a prism of glass or of any other transparent
substance, it is deflected from its original direction and is at the
same time spread out into a small fan of rays instead of remaining a
single ray.  If a screen is placed in the path of these rays a coloured
band is formed on it, the least deflected part of the band being red
and the colours ranging from red through orange, yellow, green, blue,
and indigo, to violet at the most deflected end of the band.  This band
of colours is called the spectrum of the white light used, and the
spreading out of the rays is called dispersion.

+Newton's Experiment.+--Newton first discovered this fact with an
arrangement like that in Fig. 17.

[Illustration: FIG. 17.]

If by any means the fan of coloured rays be combined again into a
single beam, white light is reformed, and Newton therefore came to the
conclusion that white light was a mixture of the various colours in the
spectrum, and that the only function of the prism was to separate the
constituents.  Of the nature of the constituents Newton had little
knowledge, since he had rejected the wave theory, which could alone
give the clue.

{30}

We now believe that white light is an irregular wave, and that the
prism manufactures from it the Fourier's series of waves to which it is
equivalent.  It is supposed that the manufacture is effected by means
of the principle of resonance.  As an example of resonance let a small
tap be given to a pendulum just as it commences each swing.  Then
because the taps are so timed that each of them increases the swing of
the pendulum by a small amount, they will very soon cause the pendulum
to swing very violently even though the effect of a single tap can
scarcely be detected at all.

Thus when any body which has a free period of vibration is subject to
periodic impulses of the same period as its own, it will vibrate very
vigorously and absorb nearly all the energy of the impulses.

+Electrons and their Vibrations.+--There is conclusive evidence to show
that in the atoms of all substances, and therefore of the glass of
which the prism is composed, there are a number of minute negatively
electrified particles which are called electrons.  These are held in
position by a positive charge on the rest of the {31} atom, and if they
are displaced from their usual positions by any means they will vibrate
about these positions.  The time of vibration of the electron will
depend upon its position in the atom and upon the position of
neighbouring atoms.  In solid or liquid bodies the neighbouring atoms
are so near that they have a considerable influence in modifying the
period of an electron or a system of electrons, and consequently we may
find almost any period of vibration in one or other of these electrons
or systems.

As the wave of light with its alternating electric fields comes up to
the prism, the field will first displace the electrons in one direction
and then in the other, and so on.  If the period of one particular type
of electron happens to coincide with the period of the wave, that
electron will vibrate violently and will in its turn send out a series
of waves in the glass.  If the wave is an irregular one it will start
all the electrons vibrating, but those electrons will vibrate most
violently whose periods are equal to the periods of the Fourier's
constituents which have the greatest energy.  Thus we shall actually
have the Fourier's constituent waves separated into the vibrations of
different electrons.  But the speed with which any simple wave travels
in glass or in any transparent medium, other than a vacuum, is
dependent upon its period.

The shorter the period, _i.e._ the shorter the wave-length, the slower
is the speed in most transparent substances.  But the slower the speed
in the prism the more is the ray deviated, and therefore we conclude
that the violet end of the spectrum consists of the shortest waves
while the red end consists of the {32} longest waves, and that the
different parts of the spectrum are simple waves of different period.

+The Whole Spectrum.+--The visible spectrum is by no means the whole of
the series of Fourier's waves, however.  The eye is sensitive only to a
very small range of period, while there exists in sunlight a range many
times as great.

Those waves of shorter period than the violet end of the visible
spectrum will be deviated even more than the violet, and will therefore
be beyond the violet.  They are called the ultra violet rays, and can
easily be detected by means of their chemical activity.  They cause a
number of substances to glow, and therefore by coating the screen on
which the spectrum is received with one of these substances, the violet
end of the spectrum is extended by this glow.

The waves of longer period than the red rays will be deviated less than
the red, and will therefore lie beyond the red end of the visible
spectrum.  They are called the infra-red rays, and are chiefly
remarkable for their heating effect.

All the rays are absorbed when they fall on to a perfectly dull, black
surface, and their energy is converted into heat.  This heating effect
provides the best way of measuring the energy in the different parts of
the spectrum, and of thus constructing curves similar to those given in
Fig. 16.  The instrument moat commonly used is called Langley's
bolometer.  It consists of a fine strip of blackened platinum, which
can be placed in any part of the spectrum at will and thus absorb the
waves over a very small range of wave-length.  It is heated by {33}
them, and the rise in temperature is found by measuring the electrical
resistance of the strip.  The electrical resistance of all conductors
varies with the temperature, and since resistance can be measured with
extreme accuracy this forms a very sensitive and accurate method.

+Spectrum of an Incandescent Solid or Liquid.+--The spectra given by
different sources of light show certain marked differences.

An incandescent solid or liquid gives a continuous spectrum, _i.e._ all
the different wave-lengths are represented, but the part of the
spectrum which has the greatest energy is different for different
substances and for different temperatures: cf. arc and gas flame in
Fig. 16.  This is quite in keeping with the idea already suggested that
in solids and liquids there are electrons of almost every period of
vibration.  When they are agitated by being heated, a mixture of simple
waves of all periods will be sent out giving a very irregular wave.

Gases may also become incandescent.  Thus when any compound of sodium
is put into a colourless flame the flame becomes coloured an intense
yellow.  This is due to the vapour of sodium, and the agitation of the
electrons in it is probably due to the chemical action in which the
compound is split up into sodium and some other parts.

We may also make the gas incandescent by enclosing it at low pressure
in a vacuum tube and passing an electrical discharge through it.  The
glow in the tube gives the spectrum of the gas.  Incandescent gases
give a very characteristic kind of spectrum.  {34} It consists usually
of a limited number of narrow lines, the rest of the spectrum being
almost perfectly dark.  The light therefore consists of a few simple
waves of perfectly definite period.  This would suggest that in the
atom of a gas there are only a few electrons which are concerned in the
emission of the light waves.

Thus the spectra of gases and of incandescent solids are represented in
character by the curves in Fig. 18.

[Illustration: FIG. 18.]

+Spectrum Analysis.+--The lines in a gas spectrum are so sharply
defined and are so definitely characteristic of the particular gas that
they serve as a delicate method of detecting the presence of some
elements.  These spectra which are emitted by incandescent bodies are
called emission spectra.  But not only do different materials emit
different kinds of light when raised to incandescence, but they also
absorb light differently when it passes through them.

When white light is passed through some transparent solids or liquids
and then through a prism, it is found that whole regions of the
spectrum are absent.  Thus a potassium permanganate solution {35} which
is not too concentrated absorbs the whole of the middle part of the
spectrum, allowing the red and blue rays to pass through.  Since with
solids and liquids the absorbed regions are large and somewhat
ill-defined, the absorption spectra are not of any great use in the
detection of substances.

The absorption spectra of gases show the same sharply defined
characteristics as the emission spectra.  Thus if white light from an
arc lamp passes through a flame coloured yellow with sodium vapour, the
spectrum of the issuing light has two sharply defined narrow dark lines
close together in the yellow part of the spectrum in exactly the same
position as the two bright yellow lines which incandescent sodium
vapour itself gives out.  The flame has therefore absorbed just those
waves which it gives out.  This is perfectly general, and applies to
solids and liquids as well as to gases.  It is perfectly in keeping
with our view of the refraction of light by the resonance of electrons
to the Fourier's constituents which have the same period.  For if the
electrons have a certain period of vibration they will resound to waves
of that period and therefore absorb their energy.

+Spectrum of the Sun.+--One of the most interesting examples of the
absorption by incandescent gases of their own characteristic lines is
provided by the sun.  The spectrum of the sun is crossed by a large
number of fine dark lines which were mapped out by Fraunhöfer and are
therefore called Fraunhöfer lines.  These lines are found to be in the
position of the characteristic lines of a number of known elements,
{36} and therefore we assume that these elements are present in the
sun.  The interior of the sun is liquid or solid owing to the pressure
of the mass round it.  It therefore emits a continuous spectrum.  But
the light has to pass through the outer layers of incandescent vapour,
and these layers absorb from the light their characteristic waves and
so produce the dark lines in the spectrum.

The spectra of stars show similar characters to those of the sun, and
therefore we assume them to be in the same condition as the sun.

The spectra of nebulæ consist only of bright lines, and we therefore
assume that nebulæ consist of incandescent masses of gas which have not
yet cooled enough to have liquid or solid nuclei.




{37}

CHAPTER IV

THE LAWS OF RADIATION

+Absorbing Power.+--A perfectly dull black surface is simply one which
absorbs all the light which is falling on it and reflects or diffuses
none of it back.  If the surface absorbs the heat as well as the light
completely, it is called a perfect or full absorber.  Other surfaces
merely absorb a fraction of the heat and light falling on them, and
this fraction, expressed usually as a percentage, is called the
absorbing power of the surface.  The absorbing powers of different
kinds of surfaces can be measured in a great many ways, but the
following may be taken as fairly typical.  A perfectly steady beam of
heat and light is made to fall on a small metallic disc, and the amount
of heat which is absorbed per second is calculated from the mass of the
metal and the rate at which its temperature rises.  The disc is first
coated with lamp-black, and the rate at which it then receives heat is
taken as the rate at which a full absorber absorbs heat under these
conditions.  The disc is then coated with the surface whose absorbing
power is to be measured, and the experiment is repeated.  Then the rate
at which heat is received in the second case divided by the rate at
which it is received in the first is the absorbing power of the second
surface.  {38} Experiments with a large number of surfaces show that
the lighter in colour and the more polished is the surface, the smaller
is its absorbing power.

+Radiating Power.+--But the character of the surface affects not only
the rate at which heat and light are absorbed, but also the rate at
which they are emitted.  For example, if we heat a fragment of a willow
pattern china plate in a blowpipe flame until it is bright red hot, we
shall notice that the dark pattern now stands out brighter than the
rest.  Thus the dark pattern, which absorbs more of the light which
falls on it when it is cold, emits more light than the rest of the
plate when it is hot.  This is one example of a general rule, for it is
found that the most perfect absorbers are the greatest radiators, and
_vice-versa_.  The perfectly black surface is therefore taken as a
standard in measuring the heat and light emitted by surfaces, in
exactly the same way as for heat and light absorbed.  Thus the emissive
or radiating power of a surface is defined as the quantity of heat
radiated per second by the surface divided by the amount radiated per
second by a perfectly black surface under the same conditions.  As it
is somewhat paradoxical to call a surface a perfectly black surface
when it may even be white hot, the term "a full radiator" has been
suggested as an alternative and will be used in this book.

[Illustration: FIG. 19]

+Relation between Absorbing and Radiating Powers.+--The exact relation
between the absorbing and radiating powers of a surface was first
determined by Ritchie by means of an ingenious experiment.  Two equal
air-tight metal chambers A and B were connected by a glass tube bent
twice at right angles as {39} in Fig. 19.  A drop of mercury in the
horizontal part of this tube acted as an indicator.  When one of the
vessels became hotter than the other, the air in it expanded and the
mercury index moved towards the colder side.  Between the two metal
chambers a third equal one was mounted which could be heated up by
pouring boiling water into it and could thus act as a radiator to the
other two.  One surface of this radiator was coated with lamp-black and
the opposite one with the surface under investigation, _e.g._ cinnabar.
The inner surfaces of the other two vessels were coated in the same
way, the one with lamp-black, the other with cinnabar.  The middle
vessel was first placed so that the lamp-blacked surface was opposite
to a cinnabar one, and _vice-versa_.  In this position, when hot water
was poured into it no movement of the mercury drop was detected, and
therefore the amounts of heat received by the two outer vessels must
have been exactly equal.  On the one side the heat given out by the
cinnabar surface of the middle vessel is only a fraction, equal to its
radiating power, of the heat given out by the black surface.  All the
heat given out by the cinnabar surface to the black surface opposite to
it is absorbed, however, while of the heat given out by the black
surface to the cinnabar surface opposite it only a fraction is absorbed
equal to the absorbing power of the cinnabar surface.  Thus on the one
side only a fraction is sent out but all of it is absorbed, and on the
other side all is sent out and only a fraction absorbed.  Since {40}
the quantities absorbed are exactly equal, it is obvious that the two
fractions must be exactly equal, or the absorbing and radiating powers
of any surface are exactly equal.  This result is known as Kirchoff's
law, and it applies solely to radiation which is caused by temperature.
Later experiments have shown that it applies to each individual
wave-length, _i.e._ to any portion of the spectrum which we isolate, as
well as to the whole radiation.  Thus at any particular temperature let
the dotted line in Fig. 20 represent the wave-length--energy curve for
a full radiator, and let the solid line represent it for the surface
under investigation.  Then for any wave-length, ON, the radiating power
of the surface would be equal to QN divided by PN.

[Illustration: FIG. 20.]

Now a wave-length--energy curve may be as easily constructed for
absorbed as for emitted radiation by means of a Langley's bolometer.
The strip of the bolometer is first coated with lamp-black and the
spectrum of the incident radiation is explored in exactly the same way
as is described in Chapter III.  {41} The strip is then coated with the
surface under investigation and the spectrum is again explored.  Since
the incident radiation is exactly the same in the two experiments, the
differences in the quantities of heat absorbed must be due solely to
the difference in the absorbing powers of the two surfaces.  In Fig. 21
the dotted line represents the wave-length--energy curve for the
radiation absorbed by the blackened bolometer strip, and the solid line
the curve for the strip coated with the surface under investigation.

[Illustration: FIG. 21.]

The actual form of the curves may and probably will be quite different
from the form in Fig. 20, but it will be found for the same wave-length
ON that PN/QN is exactly the same in the two figures.

It has already been mentioned that dull, dark-coloured surfaces radiate
the most heat, and that polished surfaces radiate the least.  A
radiator for heating a room should therefore have a dull, dark surface,
while a vessel which is designed to keep its contents from losing heat
should have a highly polished exterior.

A perfectly transparent substance would radiate no energy, whatever the
temperature to which it is {42} raised, for its absorbing power is zero
and therefore its radiating power is also zero.  No perfectly
transparent substances exist, but some substances are a very near
approach to it.  A fused bead of microcosmic salt heated in a small
loop of platinum wire in a blowpipe flame may be raised to such a
temperature that it is quite painful to look at the platinum wire, yet
the bead itself is scarcely visible at all.  Any speck of metallic dust
on the surface of the bead will at the same time shine out like a
bright star.

+Gases as Radiators.+--Most gases are an even nearer approach to the
perfectly transparent substance, and consequently, with one or two
exceptions, the simple heating of gases causes no appreciable radiation
from them.  Of course, gases do radiate heat and light under some
circumstances, but the radiation seems to be produced either by
chemical action, as in the flames coloured by metallic vapours, or by
electric discharge, as in vacuum tubes, the arc or the electric spark.

The agitation of the electrons is thus produced in a different way in
gases, and we must not apply Kirchoff's law to them, although at first
sight they appear to conform to it.  We have seen that the particular
waves which an incandescent gas radiates are also absorbed by it.  This
we should expect, because the particular electron which has such a
period of vibration that it sends out a certain wave-length will
naturally be in tune to exactly similar waves which fall on it, and
will so resound to them, and absorb their energy.  The quantitative
law, however, that the absorbing power is exactly equal to the
radiating power, is not true for gases.

{43}

+Emission of Polarised Light.+--One very interesting result of
Kirchoff's law is the emission of polarized light by glowing tourmaline
and by one or two other crystal when they are heated to incandescence.
In ordinary light the vibrations are in all directions perpendicular to
the line along winch the light travels, that is, the vibrations at any
point are in a plane perpendicular to this line.  Now any vibration in
a plane may be expressed as the sum of two component vibrations, one
component in one direction and the other in a perpendicular direction.
If we divide up the vibrations all along the wave in this way we shall
have two waves, one of which has its vibrations all in one direction
and the other in a perpendicular direction.  Such waves, in which the
vibrations all lie in one plane, are said to be plane polarised.

Tourmaline is possessed of the curious property of absorbing vibrations
in one direction of the crystal much more rapidly than it does those
vibrations perpendicular to this direction, and therefore light which
passes through it emerges partially, or in some cases wholly, plane
polarised.

Since the absorbing power of tourmaline is different for the two
components, the emissive power should also be different, and that
component which was most absorbed should be radiated most strongly.
This was found to be true by Kirchoff himself, who detected and roughly
measured the polarised light emitted.  Subsequently in 1902, Pflüger
carried out exact experiments which gave a beautiful confirmation of
the law.




{44}

CHAPTER V

FULL RADIATION

+The Full Radiator.+--We have assumed that a lamp-blacked surface is a
perfect absorber, and consequently a full radiator, but although it is
a very near approach to the ideal it is not absolutely perfect.  No
actual surface is a perfectly full radiator, but the exact equivalent
of one has been obtained by an ingenious device.  A hollow vessel which
is blackened on the inside has a small aperture through which the
radiation from the interior of the vessel can escape.  If the vessel is
heated up, therefore, the small aperture may act as a radiator.  The
radiation which emerges through the aperture from any small area on the
interior of the vessel is made up of two parts, one part which it
radiates itself, and the other part which it scatters back from the
radiation which it receives from the other parts of the interior of the
vessel.  These two together are equal to the energy sent out by a full
radiator, and therefore the small aperture acts as a full radiator:
_e.g._ suppose the inner surface has an absorbing power of 90 per
cent., then it radiates 90 per cent. of the full radiation and absorbs
90 per cent. of the radiation coming up to it therefore scattering back
10 per cent.  We have therefore coming from the inner surface 90 per
cent.  {45} radiated and 10 per cent. scattered, and the radiated and
scattered together make 100 per cent.

[Illustration: FIG. 22.]

One form in which such radiators have been used is shown in section in
Fig. 22.  A double walled cylindrical vessel of brass has a small hole,
_a_, in one end.  Steam can be passed through the space between the
double walls, thus keeping the temperature of the inner surface at 100°
C.  A screen with a hole in it just opposite to the hole in the vessel,
or rather several such screens, are placed in front of the vessel in
order to shield any measuring instrument from any radiation except that
emerging through the hole.

+The Full Absorber.+--In an exactly similar way an aperture in a hollow
vessel will act as a full absorber, for the fraction of the incident
radiation which is scattered on the inner surface again impinges on
another portion of the surface and so all is ultimately absorbed except
a minute fraction which is scattered out again through the aperture.

The variation in the heat radiated by a full radiator at different
temperatures forms a very important part of the study of radiation, and
a very large number of experiments and theoretical investigations have
been devoted to it.  These investigations may be divided into two
sections: those concerned with the total quantity of heat radiated at
different temperatures and those concerned with the variation in the
character of the spectrum with varying temperatures.

{46}

The experiments in the first section have been carried out mainly in
two ways.  In the first, the rate of cooling of the full radiator has
been determined, and from the rate of cooling at any temperature the
rate at which heat was lost by radiation was immediately calculated.
Newton was the first to investigate in this way by observing the rate
at which a thermometer bulb cooled down when it was surrounded by an
enclosure which was kept at a uniform temperature.  He found that the
rate of cooling, and therefore the rate at which heat was lost by the
thermometer, was proportional to the difference of temperature between
the thermometer and its surroundings.  This rule is known as Newton's
Law of Cooling, and is still used when it is desired to correct for the
heat lost during an experiment where the temperature differences are
small.  It is only true, however, for very small differences of
temperature between the thermometer and its surroundings, and as early
as 1740 Martine had found that it was only true for a very limited
range of temperature.

+Prévost's Theory of Exchanges.+--In 1792, Prévost of Geneva, when
endeavouring to explain the supposed radiation of cold, introduced the
line of thought, that any body is not to be regarded as radiating heat
only when its temperature is falling, or absorbing heat only when its
temperature is rising, but that both processes are continually and
simultaneously going on.  The amount of heat radiated will depend on
the temperature and character of the body itself, while the amount
absorbed will depend upon the condition of the surroundings as well as
upon the nature {47} of the body.  If the amount of heat radiated is
greater than the amount absorbed the body will fall in temperature, and
_vice-versa_.  This view of Prévost's is called the Theory of
Exchanges, and we can see that it is a necessary consequence of our
ideas as to the production of heat and light waves by the agitation of
electrons in the radiating body.

If the rate of cooling of a body at a certain temperature is measured
when it is placed in an enclosure at a lower temperature, it must be
borne in mind that the rate of loss of heat is equal to the rate at
which heat is radiated minus the rate at which it is absorbed from the
enclosure.

A second way in which the heat lost by a body has been measured at
different temperatures is by heating a conductor such as a thin
platinum strip by means of an electric current, and measuring the
temperature to which the conductor has attained.  When its temperature
is steady, all the energy given to it by the current must be lost as
heat, and therefore the electrical energy, which can very easily be
calculated, must be equal to the heat radiated by the body minus the
heat received from the enclosure.

So many attempts have been made to establish, by one or other of these
two methods, the relation between the quantity of heat radiated and the
temperature, that it is impossible to give even a passing reference to
most of them.  Unfortunately, the results do not show the agreement
with one another which we would like, but probably the most correct
result is that stated by Stefan in 1878, after a close inspection of
the experimental results of Dulong and {48} Petit.  He stated that the
quantity of heat radiated per second by a full radiator is proportional
to the fourth power of its absolute temperature.[1]  Thus the quantity
of heat radiated by one square centimetre of the surface of a full
radiator whose absolute temperature is T, is equal to ET(sup)4, where E
is some constant multiplier which must be determined by experiment and
which is called the radiation constant.  If the absolute temperature of
the enclosure in which the surface is placed is T, then the rate at
which the surface is losing heat will be E(T(sup)4-T(sub)1(sup)4), for
it will receive heat at the rate ET(sub)1(sup)4 and will radiate it at
the rate ET(sup)4.


[1] See page 56.


Stefan's fourth power law has been verified by a number of good
experiments, notably those of Lummer and Pringsheim (_Congrés
International de Physique_, Vol. II. p. 78), so that although some
experiments do not agree with it, we are probably justified in taking
it as correct.

In 1884 Boltzmann added still further evidence in support of this law
by deriving it theoretically.  He applied to a space containing the
waves of full radiation the two known laws which govern the
transformation of energy, by imagining the space to be taken through a
cycle of compressions and expansions in just the same way as a gas is
compressed and expanded in what is known as Carnot's cycle.

+Variation of Spectrum with Temperature.+--The variation of the
character of the spectrum of a full radiator has been determined mainly
by the use of Langley's bolometer, but the general nature of the change
may be readily observed by the eye.

{49}

As the temperature of a full radiator rises it first gives out only
invisible heat waves; as soon as its temperature exceeds about 500° C.
it begins to emit some of the longest visible rays; and as the
temperature rises further, more and more of the visible rays in the
spectrum are emitted until, when the radiator is white hot, the whole
of the visible spectrum.  is produced.  Thus the higher the temperature
of the radiator the more of the shorter waves are produced.

[Illustration: FIG. 23.]

By means of Langley's bolometer the distribution of energy in the
spectrum has been measured accurately, with the results of confirming
and amplifying the general results just stated.  The energy in the
spectrum of even the hottest of terrestrial radiators is mostly in the
longer waves of the infra-red, but the position of the maximum of
energy moves to shorter and shorter wave-lengths as the temperature
rises, and so more of the shorter waves make their appearance.  The sun
is not a full radiator, but is nearly so, and its temperature is so
high that the maximum of energy in its spectrum is in the visible part
near to the red end.

{50}

Fig. 23 shows the results obtained by Lummer and Pringsheim, and brings
out clearly the shift of the maximum with rising temperature and also
the position of the greatest part of the energy in the infrared region.

+Wien's Laws.+--Examination of the results also shows that the
wave-length at which the maximum energy occurs is inversely
proportional to the absolute temperature and that the actual energy at
the maximum point is proportional to the fifth power of the absolute
temperature.  These two results have both been derived theoretically by
Wien[2] in a similar way to that in which Boltzmann derived Stefan's
fourth power law, _i.e._ by imagining a space filled with the radiation
to be taken through a cycle of compressions and rarefactions.


[2] _Wied. Ann._, 46, p. 633; 52, p. 132.


Wien derived an amplification of the last result by showing that if a
wave-length in the spectrum of a full radiator at one temperature and
another wave-length in the spectrum at another temperature are so
related as to be inversely proportional to the two absolute
temperatures, they may be said to correspond to each other, and the
energy in corresponding wave-lengths at different temperatures is
proportional to the fifth power of the absolute temperature.

We see therefore that if the distribution of energy in the spectrum of
the full radiator be known at any one temperature it may be calculated
for any other temperature by applying these two laws of corresponding
wave-lengths and the energy in them.

Neither of them give us any information, however, {51} about the actual
distribution of energy at any one temperature from which we may
calculate that at any other temperature.  For that, some relation must
be found between the energy and the wave-length.  Planck, by reasoning
founded on the electromagnetic character of the waves, derived such a
relation, but both his reasoning and his results are a little too
complicated to be introduced here.  His results have been confirmed in
the most striking manner by experiments carried out by Rubens and
Kurlbaum (_Ann. der Physik_, 4, p. 649, 1901).  They measured the
energy in a particular wave-length (.0051 cms., _i.e._ nearly 100 times
the wave-length of red light) in the radiation of a full radiator from
a temperature of 85° up to 1773° absolute, and their results are given
in the following table:


  Absolute Temperature.    Observed Energy.    Energy calculated from
                                                 Planck's Formula.

         85                    -20.6                    -21.9
        193                    -11.8                    -12
        293                      0                        0
        523                    +31                      +30.4
        773                     64.6                     63.8
       1023                     98.1                     97.2
       1273                    132                      132
       1523                    164                      160
       1773                    196                      200

We have therefore the means of calculating both the total quantity and
the kind of radiation given out by any full radiator at any
temperature, and a number of very interesting problems may be solved by
means of the results.

{52}

+Efficiency in Lighting.+--One very simple problem is concerned with
efficiency in lighting.  We see by reference to Fig. 16, that in the
radiation from the electric arc very little of the energy is in the
visible part of the spectrum even though the temperature in the arc is
the highest yet obtained on the earth, whereas the energy in the
visible part of the spectrum from a gas flame is almost wholly
negligible.  The problem of efficient lighting is to get as big a
proportion as possible of the energy into the visible part of the
spectrum, and therefore the higher the temperature the greater the
efficiency.  This is the reason of the greater efficiency of the
incandescent gas mantle over the ordinary gas burner, for the
introduction of the air into the gas allows the combustion to be much
more complete, and therefore the temperature of the mantle becomes very
much higher than that of the carbon particles in the ordinary flame.
The modern metallic filament electric lamps have filaments made of
metals whose melting point is extremely high, and they may therefore be
raised to a much higher temperature than the older carbon filaments.
The arc is even more efficient than the metallic filament lamps,
because its temperature is higher still; and we must assume that the
temperature of the sun is very much higher even than the arc, since its
maximum of energy lies in the visible spectrum.

+Temperature of the Sun.+--The actual temperature of the sun may be
calculated approximately by means of Stefan's fourth power law.  We
will first assume that the earth and the sun are both full radiators,
and {53} that the earth is a good conductor, so that its temperature is
the same all over.  The first assumption is very nearly true, and we
will make a correction for the small error it introduces; and the
second, although far from true, makes very little difference to the
final result, for it is found that the values obtained on the opposite
assumption that the earth is an absolute non-conductor differ by less
than 2 per cent. from those calculated on the first assumption.  We
will further assume that the heat radiated out by the earth is exactly
equal to the heat which it receives from the sun.  This is scarcely an
assumption, but rather an experimental fact, for experiment shows that
heat is conducted from the interior of the earth to the exterior, and
so is radiated, but at such a small rate that it is perfectly
negligible compared with the rate at which the earth is receiving heat
from the sun.

The sun occupies just about one 94,000th part of the hemisphere of the
heavens or one 188,000th part of the whole sphere.  If the whole sphere
surrounding the earth were of sun brightness, the earth would be in an
enclosure at the temperature of the sun, and would therefore be at that
temperature itself.  The sphere would be sending heat at 188,000 times
the rate at which the sun is sending it, and the earth would be
radiating it at 188,000 times its present rate.  But the rate at which
it radiates is proportional to the fourth power of its absolute
temperature, and therefore its temperature would be the fourth root of
188,000 times its present temperature, _i.e._ 20.8 times.  If the
radiating or absorbing power of the earth's surface be taken as 9/10,
which is somewhere near the mark, {54} the calculation gives the number
21.5 instead of 20.8.  The average temperature of the earth's surface
is probably about 17° C. or 290° absolute, and therefore the
temperature of the sun is 290 x 21.5, _i.e._ about 6200° absolute.

It is easy to see that if we had known the temperature of the sun and
not of the earth, we could have calculated that of the earth by
reversing the process.

By this means we can estimate the temperatures of the other planets, at
any rate of those for which we may make the same assumptions as for the
earth.  Probably those planets which are very much larger than the
earth are still radiating a considerable amount of heat of their own,
and therefore to them the calculation will not apply; but the smaller
planets Mercury, Venus and Mars have probably already radiated nearly
all their own heat and are now radiating only such heat as they receive
from the sun.  The temperatures calculated in this way are--

                           Average
                    Absolute Temperature

  Mercury . . . . . . . . . 467°
  Venus . . . . . . . . . . 342°
  Earth . . . . . . . . . . 290°
  Mars  . . . . . . . . . . 235°

Since the freezing point of water is 273° absolute, we see that the
average temperature of Mars is 38° C. below freezing, and it is almost
certain that no part of Mars ever gets above freezing point.

In a very similar way we may find the temperature to which a
non-conducting surface reaches when it is exposed to full sunlight by
equating the heat absorbed to the heat radiated, and the result comes
{55} to 412° absolute, _i.e._ 139° C., or considerably above boiling
point.  This would be the upper limit to the temperature of the surface
of the moon at a point where the sun is at its zenith.

On the surface of the earth the sunlight has had to pass through the
atmosphere, and in perfectly bright sunshine it is estimated that only
three-fifths of the heat is transmitted.  Any surface is also radiating
out into surroundings which are at about 300° absolute.  Taking into
account these two facts, we find that the upper limit to a
non-conducting surface in full sunshine on the earth is about 365°
absolute, or only a few degrees less than the boiling point of water.

+Effective Temperature of Space.+--The last problem we will attack by
means of the fourth power law is the estimation of the effective
temperature of space, _i.e._ the temperature of a full absorber
shielded from the sun and far away from any planet.

It is estimated by experiment that zenith sun radiation is five million
times the radiation from the stars.  This estimate is only very rough,
as the radiation from the stars is so minute.  As the sun only occupies
one 94,000th part of the heavens, the radiation from a sunbright
hemisphere would be five million times 94,000 times starlight, _i.e._
470,000,000,000 times.  The temperature of the sun is therefore the
fourth root of this quantity times the effective temperature of space,
_i.e._ about 700 times.  Since the temperature of the sun is about
6200°, the temperature of space is a little under 10° absolute; _i.e._
lower than -263° C.

{56}

+Note on Absolute Temperature.+--It is found that, if a gas such as air
has its temperature raised or lowered while its pressure is kept
uniform, for every one degree centigrade rise or fall its volume is
increased or decreased by one two hundred and seventy-third of its
volume at freezing point, _i.e._ at 0° centigrade.  If therefore it
continued in the same way right down to -273° centigrade, its volume
would be reduced to zero at this temperature.  This temperature is
therefore called the absolute zero of temperature, and temperatures
reckoned from it are called absolute temperatures.  To get absolute
temperatures from centigrade temperatures we evidently need to add 273°.




{57}

CHAPTER VI

THE TRANSFORMATION OF ABSORBED RADIATION

No account of radiation would be complete without mentioning what
becomes of the radiation which bodies absorb, but a good deal of the
subject is in so uncertain a state that very little space will be
devoted to it.

+Absorbed Radiation converted into Heat.+--The most common effect of
absorbed radiation is to raise the temperature of the absorbing body,
and so cause it to re-emit long heat-waves.  As the usual arrangement
is for the absorbing body to be at a lower temperature than the
radiating one, the waves given out by the absorber are longer than
those given out by the radiator, and so the net result is the
transformation of shorter waves into longer ones.  But we have seen by
Prévost's theory of exchanges that radiator and absorber are
interchangeable, and therefore we see that those waves which are
emitted by the absorber and absorbed by the radiator are re-emitted by
the latter as shorter waves.

The mechanism by means of which the waves are converted into heat in
the body is still a mystery.  That the waves should cause the electrons
to vibrate is perfectly clear, but how the vibrations of the electrons
are converted into those vibrations of the atoms {58} and molecules
which constitute heat is still unsolved, and the reverse process is, of
course, equally puzzling.

The heating of the body and the consequent re-emission of heat-waves is
not, however, the only process which goes on.  In a large number of
substances, waves are given out under the stimulus of other waves
without any heating of the body at all.  In most of these cases the
emission stops as soon as the stimulating waves are withdrawn, and in
these cases the phenomenon has been called fluorescence.  The name has
been derived from fluor spar, the substance which was first observed to
exhibit this peculiar emission of waves.

A familiar example of fluorescence is provided by paraffin-oil, which
glows with a blue light when it is illuminated with ordinary sunlight
or daylight.  Perhaps the easiest way to view it is to project a narrow
beam of light through the paraffin-oil contained in a glass vessel and
view the oil in a direction perpendicular to the beam.  The latter will
then show up a brilliant blue.

A water solution of sulphate of quinine, made acid by a few drops of
sulphuric acid, also exhibits a blue fluorescence, while a water
solution of æsculin (made by pouring hot water over some scraps of
horse-chestnut bark) shines with a brilliant blue light.

Some lubricating oils fluoresce with a green light, as does also a
solution in water of fluorescene, named thus because of its marked
fluorescence.

A solution of chlorophyll in alcohol, which can be readily prepared by
soaking green leaves in alcohol, shows a red fluorescence; uranium
glass--the canary glass of which small vases are very frequently {59}
made--exhibits a brilliant green fluorescence, as does also crystal
uranium nitrate.

It is found, on observing the spectrum of the fluorescent light, that a
fairly small range of waves is emitted showing a well-marked maximum of
intensity at a wave-length which is characteristic of the particular
fluorescing substance.

There also seems to be a limited range of waves which can induce this
fluorescence, and this range also depends upon the fluorescing
substance.  As a rule, the inducing waves are shorter in length than
the induced fluorescence, but this rule has some very marked exceptions.

The fact that only a limited range of waves produces fluorescence
explains a noticeable characteristic of the phenomenon.  If the
fluorescing solutions are at all strong the fluorescence is confined to
the region close to where the light enters the solution, thus showing
that the rays which are responsible for inducing the glow become
rapidly absorbed, whereas the remainder of the light goes on
practically unabsorbed.

+Phosphorescence.+--Sometimes the emission of the induced light
continues for some time after the inducing waves are withdrawn, and
then the phenomenon is termed phosphorescence, since phosphorus emits a
continuous glow without rise of temperature.

Sometimes the glow will continue for several hours after the exciting
rays have been cut off, a good example of this being provided by
Balmain's luminous paint, which is a sulphide of calcium.  With other
substances the glow will only continue for a very small fraction of a
second, so that it is impossible to {60} say where fluorescence ends
and where phosphorescence begins.

In order to determine the duration of the glow in the case of these
small times, an arrangement consisting of two rotating discs, each of
which have slits in them, is set up.  Through the slits in one of them
the substance is illuminated, and through the slits in the other the
substance is observed while the light is cut off.  By adjusting the
position of the discs with regard to each other the slits may be made
to follow one another after greater or shorter intervals, and so the
time of observation can be made greater or smaller after the
illumination is cut off.

All the bodies which have been observed to exhibit phosphorescence are
solid.

+Theory of Fluorescence.+--It is fairly simple to imagine a mechanism
by which fluorescence might be brought about, as we might assume a
relation between the periods of oscillation of certain types of
electron in the substance and the period of the stimulating waves.
Thus resonance might occur, and the consequent vibrations of the
electrons would start a series of secondary waves.

If, however, we assume resonance, it is difficult to see why there is a
range of wave-lengths produced and another range of wave-lengths which
may produce them.  We should have expected one definite wave-length or
a few definite ones producing one or a few definite wave-lengths in the
glow, while if a whole range of waves will produce the effect it is
difficult to see why all bodies do not exhibit the phenomenon.

But the phenomenon of phosphorescence finally {61} disposes of any such
description, for the two phenomena have no sharp distinction between
them.  Some substances are known in which the phosphorescence lasts for
such an extremely small fraction of a second after the stimulating
waves are withdrawn that it is difficult to know whether to call the
effect fluorescence or phosphorescence.  It is probable, therefore,
that both are due to the same action.  Now a wave of orange light
completes about five hundred million million vibrations in one second,
and therefore if an orange-coloured phosphoresence were to last for
only one five-hundredth of a second it would mean that the electrons
responsible for it vibrate one million million times after the stimulus
is removed.  This is hardly credible, and becomes more credible when we
remember that in some phosphorescent substances the effect lasts for
many hours.

+Chemical Theory of Phosphoresence.+--It is more probable that the
stimulating rays produce an actual chemical change in the
phosphorescent substance.  For instance, it is possible that the
vibrations of a certain type of electron in one kind of atom become so
violent as to detach it from the atom and the temporarily free electron
attaches itself immediately to another kind of atom.

The new arrangement may be quite stable; it is so in the action of
light on a photographic plate, but it may only be stable when the
electrons are being driven out of their original atoms, and in this
case the electrons will begin to return to their old allegiance as soon
as the stimulus is withdrawn.  In the return {62} process the electrons
will naturally be agitated, and will therefore emit waves having their
characteristic period.  The rate at which the return process takes
place will evidently depend upon the stability of the new arrangement.
If it is extremely unstable, the whole return may only occupy a
fraction of a second, but if it is nearly as stable as the original
arrangement the return may be extremely slow.

On this view, then, those substances will phosphoresce which have an
electron which is fairly easily detached from its atom and which will
attach itself to another atom, forming an arrangement which is less
stable than the original.

+Temperature and Phosphorescence.+--A confirmation of this chemical
view is provided by the effect of temperature on phosphorescence.  The
rate of a chemical change is usually very largely increased by rise of
temperature, and further, at very low temperatures a large number of
chemical changes which take place quite readily at ordinary
temperatures do not take place at all.

Similarly at very low temperatures the action of the light may be more
or less stable.  For example, Dewar cooled a fragment of
ammonium-platino-cyanide by means of liquid hydrogen, and exposed it to
a strong light.  After removing the light no phosphorescence was
observed, though at ordinary temperatures a brilliant green
phosphorescence is exhibited, but on allowing the fragment to warm up
it presently glows very brightly.

A partial stability is shown by Balmain's luminous paint, for if it be
kept in the dark until it becomes quite non-luminous it will begin to
glow again for a {63} short time if warmed up in any way.  By means of
this property the infra-red region of the spectrum may be made visible.
For this purpose a screen is coated with the paint, exposed to strong
sunlight, and then placed so as to receive the spectrum.  The first
effect of the invisible heat rays is to make the portions of the screen
on which they fall brighter than their surroundings; but this causes
the phosphorescence to be emitted more rapidly, and soon it is all
emitted, leaving a dark region where the heat has destroyed the
phosphorescence.

On the whole, then, those substances which phosphoresce at ordinary
temperatures do so more rapidly as the temperature rises.

But Dewar has found a number of substances which phosphoresce only at
low temperatures, _e.g._ gelatine, celluloid, paraffin, ivory and horn.
This is not a fatal objection to the idea of chemical change, as some
chemical actions will only take place at low temperatures, but it is an
objection as quite a large number of substances only phosphoresce at
low temperatures, whereas there are not many chemical reactions which
will only take place there.

As a matter of fact, even if the idea of a chemical change be the true
one, it is not a very satisfactory one, as chemical changes are
undoubtedly very complicated ones, and it would be too difficult to
trace the change from the vibration of an electron to the chemical
change, and _vice-versa_.

No satisfactory theory therefore exists to account for the absorption
and the remission of the waves, whether accompanied or unaccompanied by
a rise in temperature of the absorbing body.




{64}

CHAPTER VII

PRESSURE OF RADIATION

+Prediction of Pressure by Maxwell.+--Had the fact that light exerts a
pressure been known in Newton's time there is no doubt that it would
have been hailed as conclusive proof of the superiority of the
corpuscular theory over the wave theory.  Yet, ironically enough, it
was reserved for James Clerk Maxwell to predict its existence and
calculate its value on the assumption of his electromagnetic wave
theory; and further, the measurement of its value has given decisive
evidence in favour of the wave theory, for the value predicted by the
latter is only one-half that predicted by the corpuscular theory, and
the measurements by Nicholls and Hull agree to within 1 per cent. with
the wave theory value.

Maxwell showed that all waves which come up to and are absorbed by a
surface exert a pressure on every square centimetre of the surface
equal to the amount of energy contained in one cubic centimetre of the
beam.

If the surface is a perfect reflector, the reflected waves produce an
equal back pressure, and therefore the pressure is doubled.  As the
waves are reflected back along their original direction, the energy in
the beam will also be doubled, and so {65} the pressure will still be
equal to the energy per cubic centimetre of the beam.

As the energy which is received in one second from the sun on any area
can be measured by measuring the heat absorbed, and since the speed of
light is known, we can calculate the energy contained in one cubic
centimetre of full sunlight, and hence the pressure on one square
centimetre of surface.  For the energy received on one square
centimetre of surface in one second must have been spread originally
over a length of beam equal to the distance which the light has
travelled in one second, _i.e._ over a length equal to the speed of
light.  If we divide that energy, therefore, by the speed of light, we
shall get the energy in a one-centimetre length of the beam, and
therefore in one cubic centimetre.

This turns out to be an extremely small pressure indeed, being only a
little more than the weight of half a milligram, on a square metre of
surface.

Maxwell suggested that a much greater energy of radiation might be
obtained by means of the concentrated rays of an electric lamp.  Such
rays falling on a thin, metallic disc delicately suspended in a vacuum
might perhaps produce an observable mechanical effect.

Nearly thirty years after Maxwell's suggestion it was successfully
carried out by Prof. Lebedew of Moscow, who used precisely the
arrangement which Maxwell had suggested.

+Measurement of the Pressure.+--A beam of light from an arc lamp was
concentrated on to a disc suspended very delicately in an exhausted
glass {66} globe about 8 inches across.  Actually four discs were
suspended, as in Fig. 24, and arrangements were made to concentrate the
beam on to either side of any of the four discs.

[Illustration: FIG. 24.]

The suspension was a very fine quartz fibre _q_.  The discs _d_, _d_,
_d_, _d_, were half a centimetre in diameter and were fixed on two
light arms, so that their centres were one centimetre from the glass
rod, _g_, which carried them.  A mirror, _m_, served to measure the
angle through which the whole system was twisted owing to the pressure
of the beam on one of the discs.  In order to measure the angle a
telescope viewed the reflection of a scale in _m_, and as _m_ turned
different divisions of the scale came into view.

The two discs on the left were polished and therefore the pressure on
them should be about twice that on the blackened discs on the right.

Having measured the angle through which a beam of light has turned the
system, it is a simple matter to measure the force which would cause
this twist in the fibre q.  In order to test whether the pressure
agrees with the calculated value, we must find the energy in the beam
of light.  This was done by receiving the beam on a blackened block of
copper and measuring the rate at which its temperature rose.  From this
rate and the weight of copper it is easy to calculate the amount of
heat received per second, and therefore the amount of energy received
per second on one square {67} centimetre of the area.  Knowing the
speed of the light we can, as suggested above, calculate the energy in
one cubic centimetre of the beam.

Lebedew's result was in very fair accord with the calculated value.
The chief difficulty in the experiment is to eliminate the effects due
to the small amount of gas which remains in the globe.  Each disc is
heated by the beam of light, and the gas in contact with it becomes
heated and causes convection currents in the gas.  At very low
pressures a slightly different action of the gas becomes a disturbing
factor.  This effect is due to the molecules which come up to the disc
becoming heated and rebounding from the disc with a greater velocity
than that with which they approached it.  The rebound of each molecule
causes a backward kick on to the disc, and the continual stream of
molecules causes a steady pressure.

This would be the same on both sides of the disc if both sides were at
the same temperature, but since the beam of light comes up to one side,
that side becomes hotter than the other and there will be an excess of
pressure on that side.  This action is called "radiometer" action,
because it was first made use of by Crookes in detecting radiation.

Between the Scylla of convection currents at higher pressures and the
Charybdis of radiometer action at lower pressures, there seems to be a
channel at a pressure of about two or three centimetres of mercury.
For here the convection currents are small and the radiometer action
has scarcely begun to be appreciable.

By working at this pressure and using one or two {68} other devices for
eliminating and allowing for the gas action, Professors Nicholls and
Hull also measured the pressure of light in an exceedingly careful and
masterly way.  Their results were extremely consistent among
themselves, and agreed with the calculated value to within one per
cent.  Those who know the difficulty of measuring such minute forces,
and the greatness of the disturbing factors, must recognise in this
result one of the finest experimental achievements of our time.

+Effect of Light Pressure in Astronomy.+--Forces due to light pressure
are so small that we should not expect to be able to detect their
effects on astronomical bodies, and certainly we cannot hope to observe
them in the large bodies of our system.

The pressure of the sunlight on the whole surface of the earth is about
75,000 tons weight.  This does not sound small until we compare it with
the pull of the sun for the earth, which is two hundred million million
times as great.

When we consider very small bodies, however, we find that the pressure
of the light may even exceed the gravitational pull, and therefore
these small particles will be driven right away from our system.

In order to show that the light pressure becomes more and more
important, let us imagine two spheres of the same material, one of
which has four times the radius of the other.

Then the weight of the larger one, that is its gravitational pull, will
be sixty-four times as great as that of the smaller one, while the
area, and therefore the light pressure, will be sixteen times as great.

{69}

The light pressure is therefore four times as important in the sphere
of one-quarter the radius.  For a sphere whose radius is one two
hundred million millionth of the radius of the earth and of the same
density, the pressure of the light would equal the pull of the sun, and
therefore such a sphere would not be attracted to the sun at all.

This is an extremely small particle, much smaller than the finest
visible dust, but even for much larger things the light pressure has an
appreciable effect.

Thus for a sphere of one centimetre radius and of the same density as
the earth, the pressure due to the sunlight is one seventy-four
thousandth of the pull due to gravitation.  It therefore need not move
in its orbit with quite such a high speed in order that it may not fall
into the sun, and its year is therefore lengthened by about three
minutes.  The lengthening out of comets' tails as they approach the
sun, and the apparent repulsion of the tail by the sun, has sometimes
been attributed to pressure of sunlight, but it is pretty certain that
the forces called into play are very much greater than can be accounted
for by the light.

+Doppler Effect.+--The Doppler effect also has some influence on the
motion of astronomical bodies.  When a body which is receiving waves
moves towards the source of the waves, it receives the waves more
rapidly than if it were still, and therefore the pressure is greater.
When the body is moving away from the source it receives the waves less
rapidly, and hence the pressure of light on it is less than for a
stationary body.  If a body is moving in an elliptical orbit, it is
moving towards the sun in one part of its orbit and {70} away in
another part; it will therefore be retarded in both parts, and the
ultimate result will be that the orbit will be circular.

The Doppler effect can act in another way.  A body which is receiving
waves from the sun on one side is thereby heated and emits waves in all
directions.  As it is moving in its orbit it will crowd up the waves
which it sends out in front of it and lengthen out those which it sends
out behind it.  But the energy per cubic centimetre will be greater
where the waves are crowded up than where they are drawn out, and
therefore the body will experience a retarding force in its orbit.  As
the body tends to move more slowly it falls in a little towards the
sun, and so approaches the sun in a spiral path.

+Three Effects of Light Pressure.+--We thus have three effects of light
pressure on bodies describing an orbit round the sun.  The first effect
is to lengthen their period of revolution, the second is to make their
orbits more circular, and the third is to make them gradually approach
the sun in a spiral path.  These effects are quite inappreciable for
bodies anything like the size of the earth, but for small bodies of the
order of one centimetre diameter or less the effects would be quite
large.  Our system is full of such bodies, as is evidenced by the
number of them which penetrate our atmosphere and form shooting stars.
The existence of such bodies is somewhat of a problem, as whatever
estimate of the sun's age we accept as correct, he is certainly of such
an age that if these bodies had existed at his beginning they would all
have been drawn in to him long ago.  We must therefore {71} suppose
that they are continually renewed in some way, and since we can see no
sufficient source inside the Solar system, we must come to the
conclusion that they are renewed from outside.  There is every reason
to believe that some of them originate in comets which have become
disintegrated and spread out along their orbits.  These form the
meteoric showers.

Thus the very finest dust is driven by the sun right out of our system,
and all the rest he is gradually drawing in to himself.




{72}

CHAPTER VIII

  THE RELATION BETWEEN RADIANT HEAT
  AND ELECTRIC WAVES

In this concluding chapter it is proposed to show how the wave-lengths
of radiant heat have been determined and to state what range of
wave-lengths has been experimentally observed.  It is then proposed to
show how electromagnetic waves have been produced by straightforward
electrical means and how their wave-lengths have been measured.  The
similarity in properties of the radiant heat and of the electric waves
will be noted, leading to the conclusion that the difference between
the two sets of waves is merely one of wave-length.

+Diffraction Grating.+--The best method of measuring the wave-lengths
of heat and light is by means of the "Diffraction Grating."  This
consists essentially of a large number of fine parallel equidistant
slits placed very close to one another.  For the measurement of the
wave-lengths of light and of the shorter heat waves, it is usually
produced by ruling a large number of very fine close equidistant lines
on a piece of glass or on a polished mirror by means of a diamond
point.  The ruled lines are opaque on the glass and do not reflect on
the mirror, and consequently the spaces in between act as slits.

{73}

+Rowland's Gratings.+--The ruling of these gratings is a very difficult
and tedious business, but the difficulties have been surmounted in a
very remarkable manner by Rowland, so that the gratings ruled on his
machine have become standard instruments throughout the world.  He
succeeded in ruling gratings 6 inches in diameter with 14,000 lines to
the inch, truly a remarkable performance when we remember that if the
diamond point develops the slightest chip in the process, the whole
grating is spoilt.

[Illustration: FIG. 25.]

The action of the grating can be made clear by means of Fig. 25.  Let
A, B, C, D represent the {74} equidistant slits in a grating, and let
the straight lines to the left of the grating represent at any instant
the crests of some simple plane waves coming up to the grating.  The
small fractions of the original waves emerging from the slits A, B, C,
D will spread out from the slits so that the crests of the small
wavelets may at any instant be represented by a series of concentric
circles, starting from each slit as centre.  The series of crests from
each slit are represented in the figure.

Now notice that a line PQ parallel to the original waves lies on one of
the crests from each slit, and therefore the wavelets will make up a
plane wave parallel to the original wave.  This may therefore be
brought to a focus by means of a convex lens just as if the grating
were removed, except that the intensity of the wave is less.  But a
line, LM, also lies on a series of crests, the crest from A being one
wave-length behind that from B, the one from B a wave-length behind
that from C, and so on.  The wavelets will therefore form a plane wave
LM, which will move in the direction perpendicular to itself (_i.e._
the direction DK) and may be brought to a focus in that direction by
means of a lens.

Draw CH and DK perpendicular to LM, and draw CE perpendicular to DK,
_i.e._ parallel to LM.  The difference between CH and DK is evidently
one wave-length, _i.e._ DE is one wave-length.  If [Greek: alpha] is
the angle between the direction of PQ and LM, DE is evidently equal to
CD sin [Greek: alpha] and therefore one wave-length=CD sin [Greek:
alpha].

From the ruling of the grating we know the value {75} of CD, and
therefore by measuring [Greek: alpha] we can calculate the wave-length.

We find that a third line RS also lies on a series of crests, and
therefore a plane wave sets out in the direction perpendicular to RS.
We notice here that the crest from A is two wave-lengths behind that
from B, and so on, and therefore if [Greek: beta] is the angle between
RS and PQ, CD sin [Greek: beta] is equal to two wave-lengths.

Similarly we get another plane wave for a three wave-lengths
difference, and so on.  The intensity of the wavelets falls off fairly
rapidly as they become more oblique to their original direction, and
therefore the intensity of these plane waves also falls off rather
rapidly as they become more oblique to the direction in which PQ goes.

We see that the essential condition for the plane wave to set out in
any direction, is that the difference in the distances of the plane
wave from two successive slits shall be exactly a whole number of
wave-lengths.  Should it depart ever so little from this condition we
should see, on drawing the line, that there lie on the line an equal
number of crests and troughs, and therefore, if a lens focus waves in
this direction, the resulting effect is zero.  The directions of the
waves PQ, LM, RS, &c., will therefore be very sharply defined and will
admit of very accurate determination.

+Dispersion by Grating.+--Evidently the deviations [Greek: alpha],
[Greek: beta] will be greater the greater is DE, _i.e._ the greater the
wave-length, and therefore the light or heat will be "dispersed" into
its different wave-lengths as in the prism; but in this case the
dispersion {76} is opposite to that in the normal prism, the long waves
being dispersed most and the short waves least.

Evidently, too, the smaller the distance CD the greater the angle, and
therefore for the extremely short wave-lengths of light and of
ultraviolet rays we require the distance between successive slits to be
extremely small.

[Illustration: FIG. 26.]

+The Spectrometer.+--The grating is usually used with a spectrometer,
as shown in plan diagrammatically in Fig. 26.  The slit S from which
the waves radiate is placed at the principal focus of the lens L, and
therefore the waves emerge from L as plane waves which come up to the
grating G.  The telescope T is first turned until it views the slit
directly, _i.e._ until the plane waves like PQ in Fig. 25 are brought
to a focus at the principal focus F of the objective of the telescope.
The eyepiece E views the image of the slit S which is formed at F.  The
telescope is then turned through an angle, [Greek: alpha], until it
views the second image of the slit which will be formed by the plane
waves similar to LM in Fig. 25.  The angle [Greek: alpha] is carefully
measured by the graduated circle on the spectrometer, {77} and hence
the wave-length of a particular kind of light, or of a particular part
of the spectrum, is measured.

This spectrometer method is exactly the method used for measuring the
wave-lengths in the visible part of the spectrum.

For the ultraviolet rays, instead of viewing the image of the slit by
means of the eyepiece of the telescope, a photographic plate is placed
at the principal focus F of the objective of the telescope, and serves
to detect the existence and position of these shorter waves.  For the
heat rays a Langley's bolometer strip is placed at F, in fact the
bolometer strip might be used throughout, but it is not quite so
sensitive for the visible and ultraviolet rays as the eye and the
photographic plate.

+Absorption by Glass and Quartz.+--Two main difficulties arise in these
experiments.  The first one is that although glass, or better still
quartz, is extremely transparent to ultraviolet, visible, and the
shorter infra-red waves, yet it absorbs some of the longer heat waves
almost completely.

For these waves, therefore, some arrangement must be devised in which
they are not transmitted through a glass diffraction grating or through
glass or quartz lenses.  To effect this, the convex lenses are replaced
by concave mirrors and the ruled grating is replaced by one which is
made of very fine wires, which are stretched on a frame parallel to and
equidistant from each other.  The wire grating cannot be constructed
with such fine or close slits as the ruled grating, but for the longer
waves this is unnecessary.

{78}

+Reflecting Spectrometer.+--An arrangement used by Rubens is
represented roughly in plan in Fig. 27.  L represents the source of
heat, the rays from which are reflected at the concave mirror M, and
brought to a focus on the slit S.  Emerging from S the rays are
reflected at M(sub)2 and are thereby rendered parallel before passing
through the wire grating G.  After passing through the grating, the
rays are reflected at M(sub)3 and are thereby focussed on to a
bolometer strip placed at B.  Turning the mirror M(sub)3 in this
arrangement is evidently equivalent to turning the telescope in the
ordinary spectrometer arrangement.

[Illustration: FIG. 27.]

+Absorption of Waves by Air.+--By using a spectrometer in an exhausted
vessel Schumann discovered that waves existed in the ultraviolet region
of much smaller wave-length than any previously found, and that these
waves were almost completely absorbed on passing through a few
centimetres of air.  To all longer waves, however, air seems to be
extremely transparent.

The second difficulty arises from the fact, already explained, that a
diffraction grating produces not one, but a number of spectra.  If only
a small range of waves exists, this will lead to no confusion, but if a
large range is being investigated, we may get two or more of these
spectra overlapping.

Suppose, for example, we have some waves of wave-length DE (in Fig.
25), some of wave-length one-half {79} DE and some of one-third DE.
Then in the direction DK we shall get plane waves of each of these
wave-lengths setting out and being brought to a focus in the same
place.  This difficulty can be fairly simply surmounted where the
measurement of wave-length alone is required, by placing in the path of
the rays from the source of light, suitable absorbing screens, which
will only allow a very small range of wave-lengths to pass through
them.  There will then be no overlapping and no confusion.

Where the actual distribution of energy in the spectrum of any source
of heat is to be determined the difficulty becomes more serious, and
probably there is some error in the determinations, especially in the
longest waves, which are masked almost completely by the overlapping
shorter waves.

+Rest-Strahlen or Residual Rays.+--A very beautiful method of isolating
very long heat waves, and so freeing them from the masking effect of
the shorter waves, was devised by Rubens and Nichols.

It is found that when a substance very strongly absorbs any waves that
pass through it, it also strongly reflects at its surface the same
waves.  For example, a sheet of glass used as a fire-screen will cut
off most of the heat coming from the fire, although it is perfectly
transparent to the light.  If, now, it is placed so as to reflect the
light and heat from the fire, it is found to reflect very little light
but a very large proportion of the heat.

Some substances have a well-defined absorption band, _i.e._ they absorb
a particular wave-length very strongly, and these substances will
therefore reflect {80} this same wave-length strongly.  If instead of a
single reflection a number of successive reflections be arranged, at
each reflection the proportion of the strongly reflected wave-length is
increased until ultimately there is practically only this one
wave-length present.  It can therefore be very easily measured.  These
waves resulting from a number of successive reflections, rest-strahlen
or residual rays as they have been named, have been very largely used
for investigating long waves.  Quartz gives rest-strahlen of length
.00085 centimetres and very feeble ones of .0020 centimetres long.
Sylvite gives the longest rays yet isolated, the wave-length being .006
centimetres.

+Range of the Waves.+--The lengths of the waves thus far measured are:--

  Schumann waves . . . . . . . .  .00001 to .00002 cms.
  Ultraviolet  . . . . . . . . .  .00002 to .00004  "
  Violet . . . . . . . . . . . .  .00004            "
  Green  . . . . . . . . . . . .  .00005            "
  Red  . . . . . . . . . . . . .  .00006 to .000075 "
  Infra-red  . . . . . . . . . .  .000075 to about .0001  "
  Rest-strahlen from quartz  . .  .00085 and .0020        "
  Rest-strahlen from Sylvite . .  .0060                   "

Thus the longest waves are six hundred times the length of the shortest.

The corresponding range of wave-lengths of sound would be a little more
than eight octaves, of which the visible part of the spectrum is less
than one.

Electromagnetic Induction.--In the attempt to explain the nature of an
electromagnetic wave (pp. 17-21) it was stated that an electric wave
must always be accompanied by a magnetic wave.  In order to {81}
understand the production of these waves, the relation between electric
and magnetic lines of force must be stated in more detail.  A large
number of quite simple experiments show that whenever the electric
field at any point is changing, _i.e._ whenever the lines of force are
moving perpendicular to themselves, a magnetic field is produced at the
point, and this magnetic field lasts while the change is taking place.
An exactly similar result is observed when the magnetic field at a
point is changing--an electric field is produced which lasts while the
magnetic field is changing.  When the electric field changes,
therefore, there is both an action and a reaction--a magnetic field is
produced and this change in magnetic field produces a corresponding
electric field.  This induced electric field is always of such a kind
as to delay the change in the original electric field; if the original
field is becoming weaker the induced field is in the same direction,
thus delaying the weakening, and if the original field is becoming
stronger the induced field is in the opposite direction, thus delaying
the increase.

+Momentum of Moving Electric Field.+--Imagine now a small portion of an
electric field moving at a steady speed; it will produce, owing to its
motion, a steady magnetic field.  If now the motion be stopped, the
magnetic field will be destroyed, and the change in the magnetic field
will produce an electric field so as to delay the change, _i.e._ so as
to continue the original motion.  The moving electric field thus has
momentum in exactly the same way as a moving mass has.  The parallel
between the two {82} is strictly accurate.  The mass has energy due to
its motion, and in order to stop the mass this energy must be converted
into some other form of energy and work must therefore be done.  The
electric field has energy due to its motion--the energy of the magnetic
field--and therefore to stop the motion of the electric field, the
energy of the magnetic field must be converted into some other form,
and work must therefore be done.  One consequence of the momentum of a
moving mass is well illustrated by the pendulum.  The bob of the
pendulum is in equilibrium when it is at its lowest point, but when it
is displaced from that point and allowed to swing, it does not swing to
its lowest point and stay there, but is carried beyond that point by
its momentum.  The work done in displacing the bob soon brings it to
rest on the other side, and it swings back again only to overshoot the
mark again.  The friction in the support of the pendulum and the
resistance of {83} the air to the motion makes each swing a little
smaller than the one before it, so that ultimately the swing will die
down to zero and the pendulum will come to rest at its lowest point.
The graph of the displacement of the bob at different times will
therefore be something like Fig. 28.  Should the pendulum be put to
swing, not in air, but in some viscous medium like oil, its vibrations
would be damped down very much more rapidly, and if the medium be
viscous enough the vibrations may be suppressed, altogether, the
pendulum merely sinking to its lowest position.

[Illustration: FIG. 28.]

+Electric Oscillation.+--These conditions have their exact counterpart
in the electric field.  To understand them, three properties of lines
of force must be borne in mind: (i.) lines of force act as if in
tension and therefore always tend to shorten as much as possible; (ii.)
the ends of lines of force can move freely on a conductor; (iii.) lines
of force in motion possess momentum.  Now imagine two conducting plates
A and B, Fig. 29, charged positively and negatively, and therefore
connected by lines of force as indicated.  Let the two plates be
suddenly connected by the wire _w_, so that the ends of the lines of
force may freely slide from A to B or _vice-versa_, and therefore all
the lines will slide upwards along A and B, and then towards each other
along _w_, until they shrink to zero {84} somewhere in _w_.  The
condition of equilibrium will evidently be reached when all the lines
have thus shrunk to zero, but the lines which are travelling from A
towards B will have momentum and will therefore overshoot the
equilibrium condition and pass right on to B.  That is, the positive
ends of the lines will travel on to B, and similarly the negative ends
will pass on to A.  The lines of force between A and B will therefore
be reversed.  The tension in the lines will soon bring them to rest,
and they will slide back again, overshoot the mark again, reach a limit
in the original direction and still again slide back.  The field
between A and B will therefore be continually reversed, but each time
its value will be a little less, until ultimately the vibrations will
die down to zero.  Thus if we were to replace the displacement in Fig.
29 by the value of the field between A and B we should have an exactly
similar graph.

[Illustration: FIG. 29.]

The amount by which the oscillations are damped down will depend upon
the character of the wire _w_.  If it is a very poor conductor it will
offer a large resistance to the sliding of the lines along it, and the
vibrations will be quickly damped down or, if the resistance is great
enough, be suppressed altogether.

This rapid alternation of the electric field will send out
electromagnetic waves which die down as the oscillations decrease.

+The Spark Discharge.+--In practice the wire _w_ is not actually used,
but the air itself suddenly becomes a conductor and makes the
connection.  When the electric field at a point in the air exceeds a
certain limiting strength, the air seems to break down and {85}
suddenly become a conductor and remains one for a short time.  This
breaking down is accompanied by light and heat, and is known as the
spark discharge or electric spark.

+Experiments of Hertz.+--In the brilliant experiments carried out by
Hertz at Karlsruhe between 1886 and 1891, he not only demonstrated the
existence of the waves produced in this way, but he showed that they
are reflected and refracted like ordinary light, he measured their
wave-length and roughly measured their speed, this latter being equal
to the speed of light within the errors of experiment.

[Illustration: FIG. 30.]

One arrangement used by Hertz is shown in plan in Fig. 30.  A Ruhmkorff
coil R serves to charge the two conductors A and B until the air breaks
down at the gap G, and a spark passes.  Before the spark is {86}
produced, the lines of force on the lower side of AB will in form be
something like the dotted lines in the figure, but as soon as the air
becomes a conductor, the positive ends of the lines will surge from A
towards B and on to B, and the negative ends will surge on to A.  These
to and fro surgings will continue for a little while, but will
gradually die out.  As the surgings are all up and down AB, the
electric vibrations in the electromagnetic waves sent out {87} will all
be parallel to AB, and therefore they will be polarised.

[Illustration: FIG. 31.]

This is characteristic of all electric waves, as no single sparking
apparatus will produce anything but waves parallel to the spark gap.
The electric vibrations coming up to a conductor placed in the position
of the wire rectangle, M, will cause surging of the lines along it,
and, if these surgings are powerful enough, will cause a spark to pass
across the small gap S.

Such a rectangle was therefore used by Hertz as a detector of the
waves, but since that time many detectors of very much greater
sensitiveness have been devised.

+Reflection.+--In order to show that these waves are reflected in the
same way as light waves, Hertz placed the sparking knobs, G, at the
focus of a large parabolic metallic reflector, and his detector, D, at
the focus of a similar reflector placed as in Fig. 31, but much farther
away (cf. Fig. 1).  In this position sparking at G produced strong
sparking in the detector, although the distance was such that no
sparking was produced without the reflectors.

+Refraction.+--The refraction of the waves was {88} shown by means of a
large prism made of pitch.  This had an angle of 30° and was about 1.5
metres high and 1.2 metres broad.

[Illustration: FIG. 32.]

Setting it up as shown in plan in Fig. 32, strong sparking was produced
in the detector, thus showing that the rays of electric waves were
deflected by 22° on passing through the prism.

Moving the mirror and detector in either direction from the line LM,
made the sparks decrease rapidly in intensity, so that the exact
position of LM can be determined with considerable definiteness.

+Wave-length, by Stationary Waves.+--The wave-lengths of the
oscillations were found by means of what are known as stationary waves.
When two exactly similar sets of waves are travelling in opposite
directions over the same space, they produce no effects at certain
points called nodes.  These nodes are just half a wave-length apart.
Their production can be understood by reference to Fig. 33.  The dotted
lines represent the two waves which are travelling in the direction
indicated by the arrows.  In A the time is chosen when the waves are
exactly superposed, and the resultant displacement will be represented
by the solid line.  The points marked with a cross will be points at
which the displacement is zero.

[Illustration: FIG. 33.]

In B each wave has travelled a distance equal to a quarter of a
wave-length, and it will be seen that the two sets of waves cause equal
and opposite displacements.  The resulting displacement is therefore
zero, as indicated by the solid line.  In C the waves have travelled
another quarter of a wave-length and {89} are superposed again, but in
this case the displacements will be in the opposite directions from
those in A.  In D, still another quarter wave-length has been traversed
by each wave, and another quarter wave-length would bring back the
position A.

In E, we have the successive positions of the wave drawn in one
diagram, and we notice that the points indicated by a cross are always
undisplaced and their distance apart is one-half a wave-length.

Hertz produced these conditions by setting up his coil and sparking
knobs at some distance from a reflecting wall, Fig. 34.  Then the waves
which are coming up to the wall and those which are reflected {90} from
the wall will be travelling in opposite directions over the same space.
True, the reflected waves will be rather weaker than the original ones,
so that there will be a little displacement even at the nodes, but
there will be a well-marked minimum.  Thus when the detector is placed
at A, B, C or D no sparking or very feeble sparking occurs, while
midway between these points the sparking is very vigorous, and the
distance between two successive minima is one-half a wave-length.

[Illustration: FIG. 34.]

The wave-length will depend upon the size, form, &c., of the conductors
between which the sparking occurs, for the time which the lines of
force take to surge backwards and forwards in the conductors will
depend upon these things.  Other things being equal, the smaller the
conductors the smaller the time and therefore the shorter the
wave-length.  The shortest wave which Hertz succeeded in producing was
24 centimetres long, but since then waves as little as 6 millimetres
long have been produced.

{91}

The waves which are produced in a modern wireless telegraphy apparatus
are miles in length.

We thus see that there is rather a large gap between the longest heat
waves which have been isolated, .006 cms., and the shortest electric
waves, .6 cms.  The surprising fact, however, is that this gap is so
small, for the heat waves are produced by vibrations within a molecule,
or at most within a small group of molecules, whereas the electric
surgings, even in the smallest conductors, take place over many many
millions of molecules.

In conclusion, therefore, we see that from the Schumann waves up to the
longest heat waves a little over eight octaves of electromagnetic waves
have been detected, then after a gap of between five and six octaves
the ordinary electrically produced electromagnetic waves begin and
extend on through an almost indefinite number of octaves.




{92}

BOOKS FOR FURTHER READING

J. H. Poynting, _The Pressure of Light_.

E. Edser, _Heat for Advanced Students_: the chapters on Radiation.

E. Edser, _Light for Advanced Students_: the chapters on the Spectrum.

B. W. Wood, _Physical Optics_: the chapters on Fluorescence and
Phosphorescence, Laws of Radiation, Nature of White Light, and
Absorption of Light.




{93}

INDEX

  ABSORBING power, 37
   -- and radiating power, 38
  Absorption, spectra, 34
   -- by glass and quartz, 77
   -- by air, 78
  Addition of waves, 25
  Amplitude, 23


  BALMAIN, luminous paint, 59
  Boltzmann, laws of radiation, 48


  CONVECTION currents, 67
  Corpuscular theory, 10
   -- reflection and refraction by, 11
  Crookes' radiometer, 67


  DEWAR, temperature and phosphorescence, 62
  Diffraction grating, 72
   -- dispersion by, 75
   -- wire grating, 77
  Dispersion, 29, 75
  Doppler effect, 69


  EFFICIENCY in lighting, 52
  Elastic solid theory, 17
  Electric field, 18
  Electric charges within the atom, 21
  Electric oscillations, 19, 83
  Electrification, positive and negative, 18
  Electromagnetic induction, 80
  Electromagnetic waves, 17, 84
  Electrons, 30
  Energy in simple wave, 25
  Energy--wave-length curve, 27


  FLUORESCENCE, 58
   -- theory of, 60
  Foucault, speed of light in different media, 17
  Fourier's series of waves, 26, 30
  Fraunhöfer lines, 35
  Full radiator and absorber, 44, 45


  GASES as radiators, 42


  HUYGHENS' wave theory, 13
  Hertz, experiments on electric waves, 85
   -- reflection, 86
   -- refraction, 87
   -- wave-length by stationary waves, 88


  INFRA-RED rays, 32
  Interference, 13


  KIRCHOFF'S law, 40


  LANGLEY, Bolometer, 32, 48, 49, 77
  Lebedew, pressure of light, 65
  Lummer and Pringsheim, law of radiation, 48, 50


  MAGNETIC oscillations, 20
  Maxwell, electromagnetic theory, 17
   -- pressure of light, 64
  Momentum of moving electric field, 81


  NEWTON, dispersion, 29
   -- corpuscular theory, 12
   -- law of cooling, 46
  Nichols, Rubens and, Rest-strahlen, 79
  Nicholls and Hull, pressure of light, 64, 68


  PFLÜGER, emission from tourmaline, 43
  Phase, 22
  Phosphorescence, 59
   -- chemical theory of, 61
   -- temperature and phosphorescence, 62
  Planck, energy and wave-length, 51
  Polarised light, emission from tourmaline, 42
  Pressure of light, prediction of by Maxwell, 64
   -- measurement by Lebedew, 65
   -- measurement by Nicholls and Hull, 64, 68
   -- on the earth, 68
   -- on fine dust, 69
   -- on comets' tails, 69
   -- three effects of in astronomy, 70
  Prévost, Theory of Exchanges, 46


  RADIATING power, 38
  Radiometer action, 67
  Reflection, corpuscular theory, 11
   -- of electric waves, 87
  Refraction, corpuscular theory, 11
   -- of electric waves, 87
  Resonance, 30
  Rest-strahlen or residual rays, 79
  Ripples on mercury, 13
  Ritchie, radiating and absorbing powers, 38
  Rowland, gratings, 73
  Rubens and Kurlbaum, proof of Planck's law, 51
  Rubens and Nichols, Rest-strahlen, 79


  SCHUMANN waves, 78
  Simple harmonic motion, simple periodic motion, 24
  Spark discharge, 84
  Spectrometer, 76
   -- reflecting, 78
  Spectrum, 29
   -- the whole, 32
   -- incandescent solid or liquid, 33
   -- incandescent gas, 33
   -- analysis, 34
   -- emission and absorption, 34
   -- sun, 35
   -- stars and nebulæ, 36
   -- and temperature, 48
  Stationary waves, 88
  Stefan, law of radiation, 47


  TEMPERATURE, absolute, 56
   -- of planets, 54
   -- of space, 55
   -- of sun, 53


  ULTRAVIOLET rays, 32, 77


  WAVE form, 24
  Wave-length, 22
   -- range of, 80
   -- of electric waves, 90
  Wave theory, rectilinear propagation, 13
  Wien, Law of Radiation, 50


  YOUNG, interference, 16



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  Edinburgh & London




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