1902 Encyclopedia > Radiation


RADIATION AND CONVECTION. 1. When a red-hot cannon ball is taken out of a furnace and suspended in the air it is observed to cool, i.e., to part with heat, and it continues to do so at a gradually diminishing rate till it finally reaches the temperature of the room. But the pro-cess by which this effect is produced is a very complex one. If the hand be held at a distance of a few inches from the hot ball on either side of it or below it, the feeling of warmth experienced is considerable; but it becomes intolerable when the hand is held at the same distance above the ball. Even this rude form of experiment is sufficient to show that two processes of cooling are simul-taneously at work,—one which apparently leads to the loss of heat in all directions indifferently, another which leads to a special loss in a vertical direction upwards. If the ex-periment is made in a dark room, into which a ray of sun-light is admitted so as to throw a shadow of the ball on a screen, we see that the column of air above the ball also casts a distinct shadow. It is, in fact, a column of air very irregularly heated by contact with the ball, and rising, in obedience to hydrostatic laws, in the colder and denser air around it. This conveyance of heat by the motion of the heated body itself is called convection; the process by which heat is lost indifferently in all directions is called radiation. These two processes are entirely different in their nature, laws, and mechanism; but we have to treat of both in the present article.

2. To illustrate how the third method by which heat can be transferred, viz., conduction (see HEAT, vol. xi. p. 577), is involved in this process, let the cannon ball (which for this purpose should be a large one) be again heated and at once immersed in water until it just ceases to be luminous in the dark, and then be immediately hung up in the air. After a short period it again becomes red-hot all over, and the phenomenon then proceeds precisely as before, except that the surface of the ball does not become so hot as it was before being plunged in the water. This form of experiment, which requires that the interior shall be very considerably cooled before the surface ceases to be self-luminous, does not succeed nearly so well with a copper ball as with an iron one, on account of the comparatively high conductivity of copper. In fact, even when its surface is covered with lamp-black, to make the loss by radiation as great as possible, the difference of temperature between the centre and the surface of a very hot copper ball—which is only an inch or two in diameter—is in-considerable.

3. In conduction there is passage of heat from hotter to colder parts of the same body; in convection an irregularly heated fluid becomes hydrostatically unstable, and each part carries its heat with it to its new position. In both processes heat is conveyed from place to place. But it is quite otherwise with radiation. That a body cools in con-sequence of radiation is certain; that other bodies which absorb the radiation are thereby heated is also certain; but it does not at all follow that what passes in the radiant form is heat. To return for a moment to the red-hot cannon ball. If, while the hand is held below it, a thick but dry plate of rock-salt is interposed between the ball and the hand there is no perceptible diminution of warmth, and the temperature of the salt is not perceptibly raised by the radiation which passes through it. When a piece of clear ice is cut into the form of a large burning-glass it can be employed to inflame tinder by concentrating the sun's rays, and the lens does the work nearly as rapidly as if it had been made of glass. It is certainly not what we ordinarily call "heat " which can be transmitted under conditions like these. Radiation is undoubtedly a trans-ference of energy, which was in the form commonly called heat in the radiating body, and becomes heat in a body which absorbs it; but it is transformed as it leaves the first body, and retransformed when it is absorbed by the second. Until the comparatively recent full recognition of the con-servation and transformation of energy it was almost im-possible to form precise ideas on matters like this ; and, consequently, we find in the writings even of men like Prévost and Sir J. Leslie notions of the wildest character as to the mechanism of radiation. Leslie, strangely, re-garded it as a species of "pulsation" in the air, in some respects analogous to sound, and propagated with the same speed as sound. Prévost, on the other hand, says, " Le calorique est un fluide discret ; chaque élément de calorique suit constamment la même ligne droite, tant qu'aucun obstacle ne l'arrête. Dans un espace chaud, chaque point est traversé sans cesse en tout sens par des filets de calorique."

4. The more intensely the cannon ball is heated the more luminous does it become, and also the more nearly white is the light which it gives out. So well is this known that in almost all forms of civilized speech there are terms corresponding to our "red-hot," "white-hot," &c. As another instance, suppose a powerful electric current is made to pass through a stout iron wire. The wire becomes gradually hotter, up to a certain point, at which the loss by radiation and convection just balances the gain of heat by electric resistance. And as it becomes hotter the amount of its radiation increases, till at a definite temperature it becomes just visible in the dark by red rays of low refrangibility. As it becomes still hotter the whole radiation increases ; the red rays formerly given off become more luminous, and are joined by others of higher refrangibility. This process goes on, the whole amount of radiation still increasing, each kind of visible light becoming more intense, and new rays of light of higher refrangibility coming in, until the whole becomes white, i.e., gives off all the more efficient kinds of visible light in much the same relative proportion as that in which they exist in sunlight. When the circuit is broken, exactly the same phenomena occur in the reverse order, the various kinds of light disappearing later as their refrangibility is less. But the radiation continues, grow-ing weaker every instant, even after the whole is dark. This simple observation irresistibly points to the con-clusion that the so-called "radiant heat" is precisely the same phenomenon as " light," only the invisible rays are still less refrangible than the lowest red, and that our sense of sight is confined to rays of a certain definite range of refrangibility, while the sense of touch comes in where sight fails us. Sir W. Herschel in 1798, by placing the bulb of a thermometer in the solar spectrum formed by a flint-glass prism, found that the highest temperature was in the dark region outside the lowest visible red,—a result amply verified at the time by others, though warmly contested by Leslie.

5. This striking conclusion is not without close analogies in connexion with the other senses, especially that of hearing. Thus it has long been known that the " range of hearing" differs considerably in different individuals, seme, for instance, being painfully affected by the chirp of a cricket, which is inaudible to others whose general hearing is quite as good. Extremely low notes, on the other hand, of whose existence we have ample dynamical evidence, are not heard by any one; when perceived at all they are felt.

6. We may now rapidly run over the principal facts characteristic cf the behaviour of visible rays (see LIGHT), and point out how far each has been found to characterize that of so-called " radiant heat" under similar conditions.

(a) Rectilinear propagation : an opaque screen which is placed so as to intercept the sun's light intercepts its heat also, whether it be close to the observer, at a few miles from him (as a cloud or a mountain), or 240,000 miles off (as the moon in a total eclipse), (b) Speed of propagation : this must be of the same order of magni-tude, at least, for both phenomena, i.e., 186,000 miles or so per second; for the sun's heat ceases to be percep-tible the moment an eclipse becomes total, and is perceived again the instant the edge of the sun's disk is visible, (c) Reflexion: the law must be exactly the same, for the heat-producing rays from a star are concentrated by Lord Rosse's great reflector along with its light, (d) Refraction : when a lens is not achromatic its principal focus for red rays is farther off than that for blue rays ; that for dark heat is still farther off. Herschel's determination of the warmest region of the spectrum (§ 4 above) is another case in point, (e) Oblique radiation : an illumi-nated or a self-luminous surface appears equally bright however it is inclined to the line of sight. The radiation of heat from a hot blackened surface (through an aperture which it appears to fill) is sensibly the same however it be inclined (Leslie, Fourier, Melloni). (/) Intensity: when there is no absorption by the way the intensity of the light received from a luminous point-source is inversely as the square of the distance. The same is true of dark heat. But this is not a new analogy ; it is a mere conse ^uence of (a) rectilinear propagation, (cr) Selective absorption: light which has been sifted by passing through one plate of blue glass passes in much greater percentage through a second plate of the same glass, and in still greater percentage through a third. The same is true of radiant heat, even when the experiment is made with uncoloured glass; for clear glass absorbs certain colours of dark heat more than others (De Laroche, Melloni). (h) Interference bands, whether produced by two mirrors or by gratings, characterize dark heat as well as light; only they indicate longer waves (Fizeau and Foucault). (i) Polarization and double refraction: with special apparatus, such as plates of mica split by heat into numerous parallel films, the polarization of dark heat is easily established. When two of these bundles are so placed as to intercept the heat, an unsplit film of mica interposed between them allows the heat to pass, or arrests it, as it is made to rotate in its own plane (Forbes). (,/) By proper chemical adjustments photographs of a region of the solar spectrum beyond the visible red have been obtained (Abney). We might mention more, but those given above, when considered together, are conclusive. In fact (b) or (i) alone would almost settle the question.

7. But there is a superior as well as an inferior limit of visible rays. Light whose period of vibration is too small to produce any impression on the optic nerve can be degraded by fluorescence (see LIGHT) into visible rays, and can also be detected by its energetic action on various photographic chemicals. In fact photographic portraits can be taken in a room which appears absolutely dark to the keenest eyesight. By one or other of these processes the solar spectrum with its dark lines and the electric arc with its bright lines have been delineated to many times the length of their visible ranges. The electric arc especially gives (in either of these ways) a spectrum of extraordinary length ; for we can examine it, as we can not examine sunlight, before it has suffered any sensible absorption.

8. Thus radiation is one phenomenon, and (as we shall find) the spectrum of a black body (a conception roughly-realized in the carbon poles of an electric lamp) is continu-ous from the longest possible wave-length to the shortest which it is hot enough to emit. These various groups of rays, however, are perceived by us in very different ways, whether by direct impressions of sense or by the different modes in which they effect physical changes or transformations. The only way as yet known to us of treating them all alike is to convert their energy into the heat-form and measure it as such. This we can do in a satisfactory manner by the thermo-electric pile and galvanometer.

9. Of the history of the gradual development of the theory of radiation we can give only the main features. The apparent concentration of cold by a concave mirror, which had been long before observed by Porta, was redis-covered by Pictet, and led to the extremely important enunciation of the Law of Exchanges by Prévost in 1791. As we have already seen, Prévost's idea of the nature of radiation was a corpuscular one, no doubt greatly influenced in this direction by the speculations of Lesage (see ATOM). But the value of his theory as a concise statement of facts and a mode of co-ordinating them is not thereby materially lessened. We give his own statements in the following close paraphrase, in which the italics are re-tained, from sect. ix. of his Du Calorique Rayonnant (Geneva, 1809).

"1. Free calorie is a radiant fluid. And because caloric becomes free at the surfaces of bodies every point of the surface of a body is a centre, towards and from which filaments (filets) of caloric move in all directions.

" 2. Heat equilibrium between two neighbouring free spaces consists in equality of exchange.

' ' 3. When equilibrium is interfered with it is re-established by inequalities of exchange. And, in a medium of constant temper-ature, a hotter or a colder body reaches this temperature according to the law that difference of temperature diminislies in geometrical progression in successive equal intervals of time.

"4. If into a locality at uniform temperature a, reflecting or refracting surface is introduced, it has no effect in the way of changing the temperature at any point in that locality.

"5. If into a locality otherwise at uniform temperature there is introduced a warmer or a colder body, and next a reflecting or refract-ing surface, the points on which the rays emanating from the body are thrown by these surfaces will be affected, in the sense of being warmed if the body is warmer, and cooled if it is colder.

" 6. A reflecting body, heated or cooled in its interior, will acquire the surrounding temperature more slowly than would a non-reflector.

"7. A reflecting body, heated or cooled in its interior, will less affect (in the way of heating or cooling it) another body placed at a little distance than would a non-reflecting body under the same circumstances.

" All these consequences have been verified by experiment, except that which regards the refraction of cold. This experiment remains to be made, and I confidently predict the result, at least if the refraction of cold can be accurately observed. This result is indi-cated in the fourth and fifth consequences [above], and they might thus be subjected to a new test. It is scarcely necessary to point out here the precautions requisite to guard against illusory results of all kinds in this matter."

10. There the matter rested, so far as theory is concerned, for more than half a century. Leslie and, after him, many others added fact by fact, up to the time of De la Provostaye and Desains, whose experiments pointed to a real improvement of the theory in the form of specialization. But, though such experiments indicated, on the whole, a proportionality between the radiating and absorbing powers of bodies and a diminution of both in the case of highly reflecting surfaces, the anomalies frequently met with (depending on the then unrecognized colour-differences of various radiations) prevented any grand generalization.

The first real step of the general theory, in advance of what Prévost had achieved, and it was one of immense import, was made by Balfour Stewart in 1858. Before we take it up, however, we may briefly consider Prévost's statements, putting aside his erroneous views as to the nature of heat ; and we must also introduce some results of the splendid investigations of Sadi Carnot (1824), which cast an entirely new light on the whole subject of heat.

11. Prévost's leading idea was that all bodies, whether cold or hot, are constantly radiating heat. This of itself was a very great step. It is distinctly enunciated in the term " exchange " which he employs. And from the way in which he introduces it it is obvious that he means (though he does not expressly say so) that the radiation from a body depends on its own nature and temperature alone, and is independent altogether of the nature and temperature of any adjacent body. This also was a step in advance, and of the utmost value. It will be seen later that Prévost was altogether wrong in his assumption of the geometrical rate of adjustment of differences of temperature,—a statement originally made by Newton, but true only approximately, and even so for very small temperature differences alone. Newton in the Queries to the third book of his Optics distinctly recognizes the pro-pagation of heat from a hot body to a cold one by the vibrations of an intervening medium. But he says nothing as to bodies of the same temperature.

12. To Carnot we owe the proposition that the thermal motivity of a system cannot be increased by internal actions. A system in which all the parts are at the same tempera-ture has no thermal motivity, for bodies at different temperatures are required in order to work a heat-engine, so as to convert part of their heat into work. Hence, if the contents of an enclosure which is impervious to heat are at any instant at one and the same temperature, no changes of temperature can take place among them. This is certainly true so far as our modes of measurement are concerned, because the particles of matter (those of a gas, for instance) are excessively small in comparison with the dimensions of any of our forms of apparatus for mea-suring temperatures. Something akin to this statement has often been assumed as a direct result of experiment : a number of bodies (of any kinds) within the same imper-vious enclosure, which contains no source of heat, will ulti-mately acquire the same temperature. This form is more general than that above, inasmuch as it involves considerations of dissipation of energy. Either of them, were it strictly true, would suffice for our present purpose. But neither statement can be considered as rigorously true. We may employ them, however, in our reasoning as true in the statistical sense ; but we must not be surprised if we should find that the assumption of their rigorous truth may in some special cases lead us to theoretical results which are inconsistent with experimental facts,—i.e., if we should find that deviations from an average, which are on far too minute a scale to be directly detected by any of our most delicate instruments, may be seized upon and converted into observable phenomena by some of the almost incomparably more delicate systems which we call individual particles of matter.

13. The next great advance was made by. Balfour Stewart.1 The grand novelty which he introduced, and from which all his varied results follow almost intuitively, is the idea of the absolute uniformity (qualitative as well as quantitative) of the radiation at all points, and in all direc-tions, within an enclosure impervious to heat, when thermal equilibrium has once been arrived at. (So strongly does he insist on this point that he even states that, whatever be the nature of the bodies in the enclosure, the radiation there will, when equilibrium is established, be that of a black body at the same temperature. He does not expressly say that the proposition will still be true even if the bodies can radiate, and therefore absorb, one definite wave-length only ; but this is a legitimate deduction from his statements. To this we will recur.) His desire to escape the difficulties of surface-reflexion led him to consider the radia-tion inside an imperfectly transparent body in the enclo-sure above spoken of. He thus arrived at an immediate proof of the existence of internal radiation, which recruits the stream of radiant heat in any direction step by step precisely to the amount by which it has been weakened by absorption. Thus the radiation and absorption rigorously compensate one another, not merely in quantity but in quality also, so that a body which is specially absorptive of one particular ray is in the same proportion specially radiative of the same ray, its temperature being the same in both cases. To complete the statement, all that is necessary is to show how one ray may differ from another, viz., in intensity, wave-length, and polarization.

14. The illustrations which Stewart brought forward in support of his theory are of the two following kinds. (1) He experimentally verified the existence of internal radiation, to which his theory had led him. This he did by show-ing that a thick j>late of rock-salt (chosen on account of its comparative transparency to heat-radiations) radiates more than a thin one at the same temperature,—surrounding bodies being in this case of course at a lower temperature, so that the effect should not be masked by transmission. The' same was found true of mica and of glass. (2) He showed that each of these bodies is more opaque to radia-tions from a portion of its own substance than to radiation in general. Then comes his conclusion, based, it will be observed, on his fundamental assumption as to the nature of the equilibrium radiation in an enclosure. It is merely a detailed explanation that, once equilibrium has been arrived at, the consequent uniformity of radiation throughout the interior of a body requires the step-by-step compensation already mentioned. And thus he finally arrives at the state-ment that at any temperature a body's radiation is exactly the same both as to quality and quantity as that of its absorption from the radiation of a black body at the same temperature. In symbolical language Stewart's proposi-tion (extended in virtue of a principle always assumed) amounts to this :—at any one temperature let R be the radiation of a black body, and eR (where e is never greater than 1) that of any other substance, both for the same definite wave-length; then the substance will, while at that temperature, absorb the fraction e of radiation of that wave-length, whatever be the source from which it comes. The last clause contains the plausible assumption already referred to. Stewart proceeds to show, in a very original and ingenious way, that his result is compatible with the known facts of reflexion, refraction, &c, and arrives at the conclusion that for internal radiation parallel to a plane the amount is (in isotropic bodies) proportional to the refractive index. Of course, when the restriction of parallelism to a plane is removed the internal radiation is found to be proportional to the square of the refractive index. This obvious completion of the statement was first given by Stewart himself at a somewhat later date.

15. So far Stewart had restricted his work to " dark heat," as it was then called; and he says that he did so expressly in order to confine himself to rays " which were universally acknowledged to produce heat by their absorp-tion." But he soon proceeded to apply himself to luminous radiations. And here he brought forward the extremely important fact that " coloured glasses invariably lose their colour in the fire " when exactly at the temperature of the coals behind them, i.e., they compensate exactly for their absorption by their radiation. But a red glass when colder than the coals behind appears red, while if it be hotter than they are it appears green. He also showed that a piece of china or earthenware with a dark pattern on a light ground appears to have a light pattern on a dark ground when it is taken out ot tne fire and examined in a dark room. Hence he concluded that his extension of Prevost's theory was true for luminous rays also.

16. In this part of the subject he had been anticipated, for Fraunhofer had long ago shown that the flame of a candle when examined by a prism gives bright lines (i.e., maxima of intensity of radiation) in the position of the constituents of a remarkable double dark line (i.e., minima of radiation) in the solar spectrum, which he called D. Hallows Miller had afterwards more rigorously verified the exact coincidence of these bright and dark lines. But Foucault went very much farther, and proved that the electric arc, which shows these lines bright in its spectrum, not only intensifies their blackness in the spectrum of sunlight transmitted through it, but produces them as dark lines in the otherwise continuous spectrum of the light from one of the carbon points, when that light is made by" reflexion to pass through the arc. Stokes about 1850 pointed out the true nature of the connexion of these phenomena, and illustrated it by a dynamical analogy drawn from sound. He stated his conclusions to Sir W. Thomson, who (from 1852 at least) gave them regularly in his public lectures, always pointing out that one con-stituent of the solar atmosphere is certainly sodium, and that others are to be discovered by the coincidences of solar dark lines with bright lines given by terrestrial sub-stances rendered incandescent in the state of vapour. Stokes's analogy is based on the fact of synchronism (long ago discussed by Hooke and others), viz., that a musical string is set in vibration when the note to which it is tuned is sounded in its neighbourhood. Hence we have only to imagine a space containing a great number of such strings, all tuned to the same note. Such an arrangement would form, as it were, a medium which, when agitated, would give that note, but which would be set in vibration by, and therefore diminish the intensity of, that particular note in any mixed sound which passed through it.

17. Late in 1859 appeared Kirchhoff's first paper on the subject. He supplied one important omission in Stewart's development of the theory by showing why it is necessary to use as an absorbing body one colder than the source in order to produce reversal of spectral lines. This we will presently consider. Kirchhoff's proof of the equality of radiating and absorbing powers is an elaborate but unnecessary piece of mathematics, called for in con-sequence of his mode of attacking the question. He chose to limit his reasoning to special wave-lengths by introduc-ing the complex mechanism of the colours of thin plates (LIGHT, vol. xiv. p. 608), and a consequent appeal to Fourier's theorem (HARMONIC ANALYSIS, vol. xi. p. 481), instead of to the obviously permissible assumption of a sub-stance imperfectly transparent for one special wave-length, but perfectly transparent for all others; and he did not, as Stewart had done, carry his reasoning into the interior of the body. With all its elaboration, his mode of attack-ing the question leads us no farther than could Stewart's. Both are ultimately based on the final equilibrium of tem-perature in an enclosure required by Carnot's principle, and both are, as a consequence, equally inapplicable to exceptional cases, such as the behaviour of fluorescent or phosphorescent substances. In fact (see THERMODYNAMICS) Carnot's principle is established only on a statistical basis of averages, and is not necessarily true when we are deal-ing with portions of space, which, though of essentially finite dimensions, are extremely small in comparison with the sentient part of even the tiniest instrument for measur-ing temperature.

24. For this would lead to the result that, as soon as either of the bodies has cooled, ever so slightly, the radia-tion in the enclosure should become that belonging to a black body of a slightly higher temperature than before, and thus the plates would be furnished with radiation which they could at once absorb, and be gradually heated to their former temperature.

18. A very recent speculation, founded by Boltzmann upon some ideas due to Bartoli, is closely connected in principle with that just mentioned. This speculation is highly interesting, because it leads to an expression for the amount of the whole radiation from a black body in terms of its absolute temperature. Boltzmann's investigation may be put, as follows, in an exceedingly simple form. It was pointed out by Clerk Maxwell, as a result of his electro-magnetic theory of light, that radiation falling on the surface of a body must produce a certain pressure. It is easy to see (most simply by the analogy of the virial Kirchhoff's addition to Stewart's result may be given as follows. Let radiation r, of the same particular wave-length as that spoken of in § 14, fall on the substance; er of it will be absorbed, and (1 - e)r transmitted. This will be recruited by the radiation of the substance itself, so that the whole amount for that particular wave-length becomes (1 - e)r + eli, or r - e(r - li). Thus the radiation is weakened only when H<r, a condition which requires that the source (even if it be a black body) should be at a higher temperature than the absorbing substance (§ 4, above). But the converse is, of course, not necessarily true. This part of the subject, as well as the special work of Kirchhoff and of Bunsen, belongs properly to spectrum analysis (see SPECTROSCOPY).

19. From the extension of Prevost's theory, obtained in either of the ways just explained, we see at once how the constancy of the radiation in an enclosure is maintained. In the neighbourhood of and perpendicular to the surfaces of a black body it is wholly due to radiation, near a transparent body wholly to transmission. A body which reflects must to the same extent be deficient in its radia-tion and transmission; thus a perfect reflector can neither radiate nor transmit. And a body which polarizes by reflexion must supply by radiation what is requisite to render the whole radiation unpolarized. A body, such as a plate of tourmaline, which polarizes transmitted light, must radiate light polarized in the same plane as that which it absorbs. Kirchhoff and Stewart independently gave this beautiful application.

20. Empirical formulae representing more or less closely the law of cooling of bodies, whether by radiation alone or by simultaneous radiation and convection, have at least an historic interest. What is called Newton's Law of Cooling was employed by Fourier in his Theorie Analytique de la Chaleur. Here the rate of surface-loss was taken as proportional to the excess of temperature over surrounding bodies. For small differences of temperature it is accurate enough in its applications, such as to the corrections for loss of heat in experimental determinations of specific heat, &c, but it was soon found to give results much below the truth, even when the excess of temperature was only 10° C.

21. Dulong and Petit, by carefully noting the rate of cooling of the bulb of a large thermometer enclosed in a metallic vessel with blackened walls, from which the air had been as far as possible extracted and which was main-tained at a constant temperature, were led to propound the exponential formula Aat + B to represent the radia-tion from a black surface at temperature t. As this is an exponential formula, we may take t as representing absolute temperature, for the only result will be a definite change of value of the constant A. Hence if ta be the temper-ature of the enclosure, the rate of loss of heat should be vl(a( - a'0), or ^aio(a("'° - 1). The quantity A was found by them to depend on the nature of the radiating surface, but a was found to have the constant value P0077. As the approximate accuracy of this expression was verified by the experiments of De la Provostaye and Desains for temperature differences up to 200° C, it may be well to point out two of its consequences. (1) For a given differ-ence of temperatures the radiation is an exponential func-tion of the lower (or of the higher) temperature. (2) For a given temperature of the enclosure the radiation is as (1-0077)*-1, or 0(1 + 0-003861+ . . . ), where 6 is the temperature excess of the cooling body. Thus the New-tonian law gives 4 per cent, too little at 10° C. of difference.

22. Dulong and Petit have also given an empirical formula for the rate of loss by simultaneous radiation and convection. This is of a highly artificial character, the part due to radiation being as in the last section, while that due to convection is independent of it, and also of the nature of the surface of the cooling body. It is found to be proportional to a power of the pressure of the surrounding gas (the power depending on the nature of the gas), and also to a definite power of the temperature excess. The reader must be referred to French treatises, especially that of Desains, for further information.

23. Our knowledge of the numerical rate of surface-emission is as yet scanty, but the following data, due to Nicol, may be useful in approximate calculations. Loss
in heat units (1 lb water raised 1° C. in temperature) per square foot per minute, from

Bright copper 1-09 0'51 0'42
Blackened copper 2-03 1-46 1-35.

The temperatures of body and enclosure were 58° C. and 8° C, and the pressure of contained air in the three columns was about 30, 4, and 0'4 inches of mercury respectively. The enclosure was blackened.

25. Scanty as is our knowledge of radiation," it is not at all surprising that that of convection should be almost nil, except as regards some of its practical applications. Here we have to deal with a problem of hydrokinetics of a character, even in common cases, of far higher difficulty than many hydrokinetic problems of which not even ap-proximate solutions have been obtained.

26. What is called Doppler's Principle (LIGHT, vol. xiv. p. 614) has more recently led Stewart to some curious speculations, which a simple example will easily explain. Suppose two parallel plates of the same substance, per-fectly transparent except to one definite wave-length, to be moving towards or from one another. Each, we pre-sume, will radiate as before, and on that account cool; but the radiation which reaches either is no longer of the kind which alone it can absorb, whether it come directly from the other, or is part of its own or of the other's radiation reflected from the enclosure. Hence it would appear that relative motion is incompatible with temper-ature equilibrium in an enclosure, and thus that there must be some effect analogous to resistance to the motion. We may get over this difficulty if we adopt the former speculation of Stewart, referred to in brackets in § 13 above. equation, MECHANICS, vol. xv. p. 719) that the measure of the pressure per square unit on the surface of an impervi-ous enclosure, in which there is thermal equilibrium, must be one-third of the whole energy of radiation per cubic unit of the enclosed space. We may now consider a re-versible engine conveying heat from one black body to another at a different temperature, by operations alternately of the isothermal and the adiabatic character (THERMODYNAMICS), which consist in altering the volume of the enclosure, with or without one of the bodies present in it. For one of the fundamental equations gives

dv~ dt p'

where t is the absolute temperature. If / be the pressure on unit surface, 3/ is the energy per unit of volume, and this equation becomes

t% -f=Sf. dt J J

Hence it follows at once that, if the fundamental assump-tions be granted, the energy of radiation of a black body per unit volume of the enclosure is proportional to the fourth power of the absolute temperature. It is not a little remarkable that Stefan had some years previously shown that this very expression agrees more closely with the experimental determinations of Dulong and Petit than does their own empirical formula.

27. It would appear from this expression that, if an impervious enclosure containing only one black body in thermal equilibrium is separated into two parts by an impervious partition, any alteration of volume of the part not containing the black body will produce a corresponding alteration of the radiation in its interior. It will now correspond to that of a second black body, whose tempera-ture is to that of the first in the inverse ratio of the fourth roots of the volumes of the detached part of the enclosure.

Lecher has endeavoured to show that the distribution of energy among the constituents of the radiation from a black body does not alter with, temperature. Such a result, though apparently inconsistent with many well-known facts, appears to be consistent with and to harmonize many others. It accords perfectly with the notion of the absolute uniformity (statistical) of the energy in an enclosure, and its being exactly that of a black body, even if the contents (as in § 25) consist of a body which can radiate one particular quality of light alone. And if this be the case it will also follow that the intensity of radiation of any one wave-length by any one body in a given state depends on the temperature in exactly the same way as does the whole radiation from a black body. Unfor-tunately this last deduction does not accord with Melloni's results ; at least the discrepance from them would appear to be somewhat beyond what could fairly be set down to error of experiment. But it is in thorough accordance with the common assumption (§ 14) that the percentage absorption of any particular radiation does not depend on the temperature of the source. The facts of fluorescence and phosphorescence, involving the radiation of visible rays at temperatures where even a black body is invisible, have not yet been dealt with under any general theory of radiation; though Stokes has pointed out a dynamical explanation of a thoroughly satisfactory character, they re-main outside the domain of Carnot's principle, (P. G. T.)


1 Trans. R. S. R., 1858 ; see also Phil. Mag., Ï86S, i. p. 354.

2 Brit. Assoc., President's address, 1871.

The above article was written by: Prof. P. G. Tait.

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