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diff --git a/49467-0.txt b/49467-0.txt new file mode 100644 index 0000000..2f1bd8e --- /dev/null +++ b/49467-0.txt @@ -0,0 +1,2507 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 49467 *** + + 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 + + + + Printed by BALLANTYNE, HANSON & CO. + Edinburgh & London + + + + +/tb + + + + +THE PEOPLE'S BOOKS + + "A wonderful enterprise, admirably planned, and + deserving the highest success."--_The Nation_. + +THE FIRST DOZEN VOLUMES + + +5. +BOTANY: THE MODERN STUDY OF PLANTS+. + +By M. C. STOPES, D.Sc., Ph.D., F.L.S. + +"A wonderful 'multum in parvo,' and cannot fail, by its lucidity and +pleasant method of exposition, to give the reader not only a clear +conception of the science of botany as a whole, but also a desire for +fuller knowledge of plant life."--_Notes and Queries_. + + +10. +HEREDITY+. By J. A. S. WATSON, B.Sc. + +"Accurate, and written in a simple manner which will stimulate those +who are interested to wider reading."--_Athenæum_. + + +12. +ORGANIC CHEMISTRY+. + +By Professor J. B. COHEN, B.Sc., F.R.S. + +"An excellently clear and efficient treatise on a subject not easily +confined within a short or untechnical discourse."--_The Manchester +Guardian_. + + +13. +THE PRINCIPLES OF ELECTRICITY+. By NORMAN R. CAMPBELL, M.A. + +"As for Mr. Norman Campbell's treatise 'in petto' I cannot but think it +a model of its kind. He takes next to nothing for granted."--_Sunday +Times_. + + +15. +THE SCIENCE OF THE STARS+. By E. W. MAUNDER, F.R.A.S., of the +Royal Observatory, Greenwich. + +"Will convey to the attentive reader an enormous amount of information +in a small space, being clear and abreast of current knowledge."--_The +Athenæum_. + + +26. +HENRI BERGSON: THE PHILOSOPHY OF CHANGE+. By H. WILDON CARR. + +"The fact that M. Bergson has read the proof-sheets of Mr. Carr's +admirable survey will give it a certain authoritativeness for the +general reader."--_Daily News_. + + +32. +ROMAN CATHOLICISM+. By H. B. COXON. Preface, Mgr. R. H. BENSON. + +"This small book is one which cannot fail to be of use to those who +desire to know what Catholics do, and do not, believe."--_The Catholic +Chronicle_. + + +39. +MARY QUEEN OF SCOTS+. By E. O'NEILL, M.A. + +"Mrs. O'Neill, on 'Mary Queen of Scots,' is splendid; it is an attempt +to give the very truth about a subject on which all feel interest and +most lie freely."--_Daily Express_. + + +47. +WOMEN'S SUFFRAGE+. By M. G. FAWCETT, LL.D. + +"Mrs. Fawcett's admirably concise and fair-minded historical sketch of +the women's suffrage movement. We could hardly ask for a better +summary of events and prospects."--_Daily News_. + + +51. +SHAKESPEARE+. By Professor C. H. HERFORD, Litt.D. + +"Well worth a place alongside Professor Raleigh's book in the 'English +Men of Letters.' ... Sets a high note and retains it without +effort."--_Observer_. + + +53. +PURE GOLD--A CHOICE OF LYRICS AND SONNETS+. By H. C. O'NEILL. + +"An anthology of good poetry such as we might expect from a man of +taste."--_Daily News_. + + +57. _DANTE_. By A. G. FERRERS HOWELL. + +"It is a fine piece of scholarship, and should be read by any one who +is beginning the study of Dante, or indeed any one who is interested +generally in the early process of European literature, for the process +is here admirably analysed."--_The Manchester Guardian_. + + + +THE SECOND DOZEN VOLUMES (Ready) + +1. +THE FOUNDATIONS OF SCIENCE+. By W. C. D. WHETHAM, M.A., F.R.S. + +11. +INORGANIC CHEMISTRY+. By Professor K. C. C. BALY, F.R.S. + +14. +RADIATION+. By P. PHILLIPS, D.Sc. + +22. +LORD KELVIN+. By A. RUSSELL, M.A., D.Sc., M.I.E.E. + +23. +HUXLEY+. By Professor G. LEIGHTON, M.D. + +36. +THE GROWTH OF FREEDOM+. By H. W. NEVINSON. + +41. +JULIUS CAESAR: SOLDIER, STATESMAN, EMPEROR+. By HILARY HARDINGE. + +43. +ENGLAND IN THE MIDDLE AGES+. By Mrs. E. O'NEILL, M.A. + +54. +FRANCIS BACON+. By Professor A. R. SKEMP, M.A. + +55. +THE BRONTËS+. By Miss FLORA MASSON. + +60. +A DICTIONARY OF SYNONYMS+. By AUSTIN K. GRAY, B.A. + +61. +HOME RULE+. By L. G. REDMOND HOWARD. + + +_List of other Volumes in Preparation may be had_. + + + LONDON AND EDINBURGH: T. C. & E. C. JACK + NEW YORK: DODGE PUBLISHING CO. + + + + + + + + + + + +End of the Project Gutenberg EBook of Radiation, by P. Phillips + +*** END OF THE PROJECT GUTENBERG EBOOK 49467 *** |