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.

+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.

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.

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.

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+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.

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