* dept 
 
 LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA, 
 
 Class 
 
 UNIVERSITY OF CALIFORNIA 
 
 LIBRARY 
 
 OF THE 
 
 DEPARTMENT OF PHYSICS 
 
 Received N.QV...1.4..1.91.1 
 
 ^cessions No. & f Z Book m _/ 
 
SCIENTIFIC MEMOIRS 
 
 EDITED BY 
 
 J. S. AMES, PH.D. 
 
 PROFESSOR OF PHYSICS IN JOHNS HOPKINS UNIVERSITY 
 
 XV 
 THE LAWS OF RADIATION AND ABSORPTION 
 
THE LAWS 
 
 OF 
 
 RADIATION AND ABSORPTION 
 
 MEMOIRS BY PROVOST, STEWART, KIRCHHOFF, 
 AND KIRCHHOFF AND BUNSEN. 
 
 TRANSLATED AND EDITED BY 
 
 D. B. BRACE, PH.D. 
 
 PROFESSOR OF PHYSICS IN THE UNIVERSITY OF NEBRASKA. 
 
 NEW YORK : CINCINNATI -: CHICAGO 
 
 AMEEICAN BOOK COMPANY 
 
COPYEIGHT, 1901, BY 
 
 AMERICAN BOOK COMPANY. 
 
 Entered at Stationers'' Hall, London. 
 
 Radiation and Absorption. 
 W. P. i 
 
\ \ 
 
 PREFACE. 
 
 THE attempt of Prevost to explain the experiments of Pictet, 
 of the apparent concentration of cold at the focus of a mirror, 
 without attributing the quality of radiation to cold, as assumed 
 by Pictet, lead him to the enunciation of the very important 
 principle which he called the movable equilibrium of heat, now 
 designated as the theory of exchanges. Prevost, who was a dis- 
 ciple of le Sage, and who had issued, with many additions, his 
 memoirs, assumed, in addition to a corpuscular fluid caloric, a 
 free corpuscular radiant caloric, the equal interchange of which 
 between neighboring free spaces, constituted heat equilibrium. 
 Any interference with this equilibrium will be reestablished by 
 the inequalities of the exchanges. On this principle he was able 
 to explain the apparent concentration of cold and also to show 
 the inadmissibility of cold as an agent susceptible of radiation. 
 He was careful, however, to fortify his principle by showing that 
 the same results would follow on the then distrusted hypothesis 
 of undulatory exchanges, which has been adopted by his suc- 
 cessors. Later experimenters, particularly Leslie and De la 
 Provastaye and Desains, confirmed the theory and also showed 
 in many instances quantitative relations between radiation and 
 absorption. But the most important advance was made by Bal- 
 four Stewart in establishing, not only a quantitative relation, 
 but also a qualitative or selective one. By the introduction of 
 his ingenious idea of an impervious radiating inclosure he 
 demonstrated the equality between the emissive and the absorp- 
 tive power of any wave length. We owe to Kirchhoff, however, 
 the first rigorous proof of the celebrated law (usually designated 
 on the Continent as KirchhofFs law) of the emission and absorp- 
 tion of light and heat, and the application of the same by both 
 Kirchhoff and Bunsen to Spectrum Analysis. The radiation 
 of solids and liquids and gases follows the law exactly when the 
 conditions upon which he founded it are rigorously fulfilled, 
 namely, the complete transformation from one to the other of 
 
 222515 
 
PREFACE. 
 
 radiant energy and their intrinsic heat. "We now know that 
 most radiations from gases are not exclusively thermal, but that 
 the substances, cited by Kirchhoff and Bunsen, also give off so 
 called chemical and electrical and fluorescent radiations which 
 Kirchhoff excluded in the proof of his law. In fact none of the 
 gases giving line spectra at temperatures heretofore used do so 
 by simple thermal radiation, but essentially by luminescent 
 actions (chemical, electrical, and photogenic), so that we cannot, 
 in general, apply the law of Kirchhoff of the proportionality 
 between radiation and absorption to either terrestrial or celes- 
 tial substances. In these cases the principle of resonance usually 
 holds, since in luminescence the radiation of line spectra is 
 accompanied by selective absorption of the same spectral lines, 
 so that the law may be used qualitatively, which is in ftict the 
 way Kirchhoff and Bunsen actually attempted to confirm it. 
 The formulation of the complete law for radiations of a Hack 
 body is only given in part by Kirchhoff. The formula of Wien, 
 and more particularly the most recent one of Planck, deduced 
 on theoretical grounds, approximates closely the latest observa- 
 tions on a black body at different temperatures and over differ- 
 ent wave lengths. 
 
 D. B. BRACE. 
 University of Nebraska. 
 
 VI 
 
GENERAL CONTENTS. 
 
 PAGE. 
 
 Preface ' . v 
 
 On the Equilibrium of Heat. Pierre Prevost .... 1 
 Treatise on Radiant Heat (Selections). Pierre Prevost . . 15 
 
 Biographical Sketch of Prevost 20 
 
 An account of some Experiments on Radiant Heat, involv- 
 ing an extension of Prevost's Theory of Exchanges. 
 
 By Balfour Stewart 21 
 
 Researches on Radiant Heat. Second Series. By Balfour- 
 
 Stewart . . 51 
 
 Biographical Sketch of Stewart. ... . . 72 
 
 On the Relation between the Emissive and the Absorptive 
 Power of Bodies for Heat and Light. By G. R. Kirch- 
 
 hoff -73 
 
 Biographical Sketch of Kirchhoff ... . 97 
 
 Chemical Analysis by Spectral Observations by G. Kirch- 126 
 hoff and R. Bunsen ... .... 99 
 
 Biographical Sketch of Bunsen . . 126 
 
 Bibliography 127 
 
 Index , ..... 129 
 
 Yll 
 
MEMOIR ON THE EQUILIBRIUM OF HEAT. 
 
 BY 
 
 PIERRE PREVOST. 
 
 Journal de Physique, vol. 38, pp. 314-322. Paris, 1791. 
 
CONTENTS. 
 
 PAGE 
 
 Outline of the Proposed Discussion 3 
 
 Theory of the Equilibrium of Heat ..... 4 
 
 Rupture of the Equilibrium between two Portions of Space 6 
 
 Phenomenon of Reflection of Cold . . . . . 7 
 
 Exclusion of an Independent Explanation . . . . 9 
 Supplementary Remarks on Radiant Heat . . .11 
 
 Discussion of /Several Discrete Fluids . " . . . . 12 
 
MEMOIR ON THE EQUILIBRIUM OF HEAT. 
 
 BY PIERRE PREVOST. 
 
 I PROPOSE to analyse and fix with precision the sense of the 
 word equilibrium applied to such a fluid as heat. This idea is 
 not exactly defined in the theories which leave questions rela- 
 tive to the nature of this element undecided. If there is any 
 doubt that heat is material, if there is no explanation concern- 
 ing the contiguity or the noncontiguity of molecules of heat, 
 concerning their mobility or their immobility, the kind of 
 motion, vibratory or translatory, which is attributed to them, * 
 it is impossible to arrive at exact and complete ideas of their 
 equilibrium. It results from this that every phenomenon which 
 depends, not upon any equilibrium whatever but upon a spe- 
 cific kind of equilibrium, remains entirely unexplained. And 
 as the imagination determines to some extent, notwithstanding, 
 that which reason wishes to leave undetermined, the true 
 causes are lost sight of, and vain hypotheses are arbitrarily 
 preferred because they are suitable in certain respects and fav- 
 orable to first appearances. 
 
 I will not waste time in discussing the different natures 
 assigned to heat by various physicists. The true constitution" 
 of this fluid is connected with the theory of discrete fluids, now 
 known, although it has not been published by its author. For 
 its development and proof I refer to what M. DeLuc has said 
 of it both in his " Idees sur la meteorologie" and in his letters 
 published successively in this Journal: also what I have said of 
 it myself in my essay upon I'origine des forces magnetiques. 
 Assuming then the principles of this theory, I shall merely recall 
 them, and use them to establish true ideas on the equilibrium 
 of heat. 
 
 I shall afterwards make the application of this theory of the 
 equilibrium of heat to a very remarkable phenomenon which I 
 consider inexplicable without it. This is the phenomenon of 
 the reflection of cold. It has been observed by M. Pictet, who 
 
 3 
 
MEMOIES OK 
 
 has described it in detail in his essai sur le feu. This learned 
 scientist, with whom I have old and valued bonds of friendship, 
 does not at all disapprove of the discussion which I am under- 
 taking although it tends to indicate some inadequacy in the 
 explanation which he, himself, has given to this phenomenon. 
 It will be seen elsewhere by what I shall say of it, that a com- 
 plete explanation, such as the theory of M. le Sage furnished, 
 does not enter into the plan which M. Pictet has proposed. I 
 will discuss this phenomenon then, very freely. I shall show that 
 it explains itself without any effort, by the true theory of dis- 
 crete fluids. I shall also prove that it is not explained at all by 
 the imperfect theories to which physicists commonly limit 
 themselves. I shall close this memoir with two remarks which 
 have some connection with this subject, without being directly 
 related to it. 
 
 I. 
 
 THEORY OF THE EQUILIBRIUM OF HEAT. 
 
 Heat is a discrete fluid. Its elasticity consists in its expau- 
 ^ sive force. And this is the effect of the movement of its 
 particles. This movement is caused by the impulse of a much 
 more subtile fluid whose effect upon its particles is determined 
 to a certain extent by their form. It is so swift that when heat 
 NO is freed its translation from one place to another appears in- 
 stantaneous. It is also sensibly rectilinear, so that perfectly 
 free heat partakes, as far as the movement of its particles is 
 concerned, of all the properties of light, at least so far as our 
 senses can determine in the limited experiments which have 
 thus far been performed. 
 
 A discrete fluid whose particles radiate like those of light, 
 may be confined by barriers, but may not be confined by an- 
 other radiant fluid nor, in consequence, by itself. For it is 
 necessary to conceive of all these fluids as very rare, as having 
 many more void intervals than full ones in the space which 
 they occupy. Light does not stop the passage of light. If this 
 solar emanation is so dense that two luminous currents cannot 
 cross each other without being interrupted, the innumerable 
 crossings and reflections which they experience will destroy 
 entirely its rectilinear direction, and light will lose to our eyes 
 
 4 
 
RADIATION AND A B S R P T 1 N . 
 
 all its properties which depend upon this direction. What is 
 true of this fluid is true of all radiant fluids. Radiant heat 
 passes through heat, which upon the earth is present in all 
 places, and since it produces no sensible perturbation, it is nec- 
 essary that these particles should be separated by intervals great 
 relatively to their diameters. It is certain that free radiant 
 heat is a very rare fluid, the particles of which almost never 
 collide with one another and do not disturb sensibly their mu- 
 tual movements. 
 
 In conforming to physical hypotheses, one says ordinarily 
 that heat is coercible by itself : that two contiguous portions of 
 heat have a mutual relation when their temperatures are equal 
 (or as M. Volta has said, when their tensions are the same). 
 These expressions are exact, only in so far as they define an ap- 
 pearance. In reality the heat of any portion cannot arrest that 
 of another. These two heats give each other mutually free 
 passage. It would then be wrong for one to conclude from 
 these expressions that two portions of contiguous heat restrain 
 each other mutually, as two bent springs stayed against 
 one another, or as two masses of hair which repel each other 
 by their elasticity. 
 
 But in what does the equilibrium of these two portions of 
 contiguous heat consist ? In order to answer this question 
 clearly, I will suppose the two portions to be enclosed in an 
 empty space, terminated on all sides by impenetrable walls. 
 One may represent two cubes applied by one of their faces, 
 forming in consequence a rectangular parallelepiped perfectly 
 hollow, of which the six faces are of the same matter, absolutely 
 solid and without pores. The two portions which I consider 
 are, in this example, the two applied cubes. The heat occupy- 
 ing the interior of this space moves freely there, and as- 
 suredly one can see no reason why it should pass with less 
 facility across the boundary of the two portions than across 
 every other section of this space. There are then continual ex- 
 changes from one portion to another, and one can affirm (in 
 consideration of the number of particles and their continual 
 motion) that at each observable instant the state and quantity 
 of the heat in each portion are constant. There is then no 
 ceasing of the different particles, which are found at any one 
 
 5 
 
MEM OIKS ON 
 
 place, but their number and their meau distance in each 
 portion are constant. Concerning their speed, as it is in the 
 same free fluid (consider the constant nature of the cause 
 which produces and renews it continually), it is clear that it 
 does not change : and I shall leave it out of the question, since 
 at the present moment I consider only free radiant heat. 
 
 At all times that both portions of the space are found in the 
 circumstances which I have just described, the heat between 
 them is in a state of equilibrium. This signifies that the 
 phenomena which manifest their existence remain the same : 
 that if these phenomena change in the same manner and in the 
 same quantity in the two portions, the equilibrium in question 
 will not be disturbed. This would occur if one should remove 
 from the total space, which we are considering, a certain 
 aliquot part of all the heat found there, or indeed if this 
 aliquot part should be added. The identity of the phenomena 
 which implies the equilibrium of heat between these two por- 
 tions of space is a relative identity, which, as one can see, may 
 exist whatever may be the difference or the absolute in- 
 equality. 
 
 Let us now suppose that into one of the two portions of space 
 (which I will represent constantly by the two adjoining cubes) 
 one passes suddenly some new heat ; for example, one tenth of 
 all that which is contained in this portion. This heat, in- 
 stantly placed in motion, spreads immediately throughout all 
 the space where it can penetrate freely. Thus the exchanges 
 between the two portions would be unequal. One would send to 
 the other eleven particles, while the latter would return only 
 ten. This state causes a rupture of the equilibrium between 
 the two portions. 
 
 By reason of the unequal exchanges one may conceive that 
 the equality would be reestablished. Thus the rupture of the 
 equilibrium restores very quickly the equilibrium between two 
 portions of free heat. 1 
 
 1 Suppose that the densities of the heat in our two cubes are as the 
 numbers 1 and 2 (i. e., that one is twice as hot as the other) : suppose 
 further that in one second there passes from the one cube to the other a 
 number of igneous particles which on the whole are as 1 to 10 (so that 
 during this short time there is exchanged one tenth of all the heat). 
 
 6 
 
RADIATION AND ABSORPTION. 
 
 Absolute equilibrium of free heat is the state of this fluid in 
 a portion of space which receives as much as it allows to 
 escape it. 
 
 Relative equilibrium of free heat is the state of this fluid in 
 two portions oi' space which receive from each other equal 
 quantities of heat, and which are, moreover, in absolute equilib- 
 rium, or experience changes precisely equal. 
 
 The heat of several portions of space at the same temperature 
 and near each other is at once in the two kinds of equilibrium. 
 If one should change the temperature of all the space at the 
 same time, it would destroy the absolute equilibrium, but not 
 the relative equilibrium. Should the temperature of one or 
 of several portions be altered without affecting all, each kind 
 of equilibrium would be destroyed. 
 
 If the cause which throws out or which absorbs the heat of 
 any portion is an instantaneous cause, after the action of this 
 cause the relative equilibrium reestablishes itself incessantly 
 by means of unequal exchanges. And after this reestablish- 
 ment the absolute equilibrium remains destroyed, that is to 
 say, the temperature of the place is changed. 
 
 If, on the contrary, the cause is permanent, that is to say, if 
 there is opened in any one of the portions of this space a source 
 or a sink which gives out or which absorbs heat incessantly, rela- 
 tive equilibrium tends to establish itself, but does not reestablish 
 itself entirely during the action of the cause, and absolute 
 equilibrium is constantly destroyed. 
 
 II. 
 
 APPLICATION OF THE PRECEDING THEORY TO THE 
 PHENOMENON OF REFLECTION OF COLD. 
 
 Let us represent two spherical concave mirrors opposite to 
 each other on their axes, and let us suppose placed at their foci 
 
 After seven seconds the ratio of the densities of the heat in the two 
 cubes will be as 5 to 6. After fourteen seconds, these densities will be 
 as 28 to 29, i. e., very nearly equality : the equilibrium will appear 
 established. 
 
 I take this result from a calculation of M. le Sage thirty years since in 
 the case of discrete fluids different from heat. 
 
 7 
 
MEMOIRS ON 
 
 two bodies precisely equal and similar and of the same sub- 
 stance, which JL will call the two focal bodies. 
 
 To simplify this I will suppose, (1) that all the space where 
 the apparatus is immersed is absolutely cold and receives heat 
 only from part of the two focal bodies, (2) that these are hot 
 and give out radiant heat continuously, (3) that the mirrors re- 
 flect the heat but do not absorb it. 
 
 With these conditions, it is clear that the heat thrown out by 
 either one of the two focal bodies radiates on all sides. But I 
 shall consider only the part which strikes the mirror of which 
 it is the focus. 
 
 This heat is reflected parallel to the axis. Striking the op- 
 posite mirror in this direction, it is reflected to the focus of 
 this second mirror and enters as a consequence the body which 
 occupies this focus. Similarly inversely, the heat thrown out 
 by this latter against its mirror enters after two reflections the 
 body which occupies the focus of the first mirror. 
 
 Let us suppose, first, the two focal bodies are at the same 
 temperature, or each one sending out in equal intervals of time 
 an equal quantity of radiant heat to its own mirror. The 
 relative equilibrium of heat between the two focal bodies will 
 not be disturbed by this operation, ; for each of them will re- 
 ceive from the other exactly what it gives up to it. Radiation 
 will exactly compensate absorption. 
 
 Now let us change, to a greater or less degree, the tempera- 
 ture of one of the two focal bodies ; the exchanges made between 
 them by means of double reflection will cease to be equal : the 
 relative equilibrium will be destroyed. It will tend then to re- 
 establish itself, and the temperature of these two bodies will ap- 
 proach each other. If additional heat should be thrown upon 
 the first body, for example, a tenth of all that which it has, the 
 second body will make advantageous exchanges with it. For 
 ten particles transmitted by reflection, it will receive eleven by 
 the same means : in this way its heat will be augmented. 
 
 If one should withdraw heat from the first body, for example 
 a tenth, the- second body will make exchanges at a loss, receiving 
 nine against ten by means of the mirror. It will be cooled. 
 
 Such is the result of the theory conforming exactly to that 
 of the ingenious experiments of M. Pictet, in spite of all the 
 
 8 
 
RADIATION AND ABSORPTION. 
 
 conditions which 1 have made, since these conditions influence 
 only the quantity of cold or of heat produced by reflection, 
 and not the nature of these actions. It is known that this 
 physicist has observed heat and cold equally reflected in his ap- 
 paratus, which is such as I have just described. He has not 
 hesitated to explain the reflection of cold just as that of heat in 
 a reciprocal sense : but being limited (conformably to his 
 representation) to explanations drawn at once from experiment, 
 and it not being his purpose, in the important work which he 
 has published, to treat of the constitution of discrete fluids, he 
 has not been able to enter into the details which I have just 
 given. It has resulted from this that the view to which he has 
 come touching the cause of the reflection of cold, founded upon 
 these notions of equilibrium, inapplicable to discrete fluids, is 
 insufficient for the theory, however true as to appearances. 
 
 It is certain that when one produces cold at the focus of one 
 of the mirrors, the heat of the thermometer placed at the op- 
 posite focus follows the course which M. Pictet traces for it. 
 And this course is what I have just described. But what it is 
 that causes the excess heat of the thermometer to take this 
 course, this physicist has not shown me, because he has not 
 been called upon to consider heat according to its natural con- 
 stitution. Now if one holds to the ideas of tension, of stress, 
 in a word, of unvariable equilibrium, he finds that the progress 
 of the phenomenon of heat in the experiment of the reflection 
 of cold remains absolutely inexplicable. I shall now show, (1) 
 that in this hypothesis of unvarying equilibrium no heat ought 
 to pass from the thermometer to its mirror, (2) that if any does 
 pass, this heat should not converge to the focus of the other 
 mirror. 
 
 III. 
 
 EXCLUSION OF THE INDEPENDENT EXPLANATION 
 OF THIS THEORY. 
 
 (I) At the instant when one places a cold body, such as glass, 
 at the focus of one of the mirrors, the heat of all the neighbor- 
 ing bodies passes into it. This cause acts according to the law 
 B 9 
 
MEMOIRS ON 
 
 of the inverse square of the distance, when we suppose the 
 bodies to be of the same nature, as we do in this instance. 
 
 The mirrors employed in the experiment of the reflection of 
 cold were placed ten and one half feet apart. Their curvature 
 was that of a sphere with a radius of nine inches : so that their 
 foci were about four and one half inches from their surface, 
 measured on the axis. 
 
 If, then, we consider only the apparatus without taking into 
 account the supports, or the air or the surrounding and neigh- 
 boring bodies, it is clear that the mirror whose focus is occu- 
 pied by the glass, being twenty-eight times nearer this cold 
 body than the other mirror, ought to send out to it seven him-, 
 dred and eighty-four times as much heat in the same time. 
 
 Further, the thermometer placed at the focus of this other 
 mirror being nearer the glass than its mirror in the ratio of 26 
 to 27, ought to set free more heat than a portion of the mirror 
 equal to its bulb in the double inverse ratio (at least for the 
 part of the mirror which lies at the origin of the axis). This 
 ratio is that of 729 to 676, or of about 13 to 12 ; so that, 
 through the direct influence of the glass, the thermometer loses 
 about a thirteenth more of its heat than if it formed a part of 
 the mirror, at the focus of which it is placed. When the cool- 
 ing of the first mirror becomes sensibly equal to the second, the 
 thermometer being less distant than the former, is also more 
 affected by the latter in the double inverse ratio of 27 to 28 ; 
 that is to say, in the ratio of 784 to 729, or of about 14 to 13. 
 
 Thus the thermometer is cooled more than its mirror, either 
 directly by the glass, or indirectly by the mirror whose focus 
 this glass occupies. Heat here then is under less tension than 
 in the mirror. Consequently it cannot pass from the thermome- 
 ter to the mirror, nor in consequence, radiate from there to the 
 opposite mirror next the glass. This progress of the phenomena 
 in a system in unvarying equilibrium is contrary to the effect 
 which the cause should occasion. And it is still more inexpli- 
 cable when we consider the supports of the apparatus and all 
 the surrounding bodies which send heat into the glass, and 
 constantly draw out that of the thermometer, as well as of the 
 opposite mirror: effects independent of reflection and of the 
 particular position of the foci. 
 
 10 
 
RADIATION AND ABSORPTION. 
 
 (II). To which it is necessary to add, in reconciling the 
 same (which is demonstrated false in the hypothesis I have dis- 
 cussed), that the heat of the thermometer passes in part into 
 its mirror; as there is carried over only what replaces that which 
 escapes, this heat would not be reflected, but absorbed. Now, 
 all the heat which one of the mirrors sends out to the other, 
 aside from that by reflection to the focus, being an irregular 
 radiation, would not converge at the focus of the other mirror. 
 THUS the foci would not be more characteristic than two other 
 points, taken at random between the mirrors, for repeating the 
 experiment of reflection of cold, which is absolutely contrary 
 to the actual observation. 
 
 It is apparent, then, that if we refuse to consider heat 
 according to its true constitution as a discrete fluid, whose 
 particles are in motion, and if in consequence we do not arrive 
 at ideas which I have given of the equilibrium of radiant free 
 heat, it is impossible to give any satisfactory explanation (com- 
 patible moreover with the principles of sound physics), of this 
 beautiful and remarkable phenomenon of the reflection of cold. 
 The fact is established by an excellent observer, who has very 
 clearly recognized the progress of the phenomena of heat. The 
 discovery of the cause is due to the author of the true theory of 
 discrete fluids. 
 
 IV. 
 
 SUPPLEMENTARY REMARKS. 
 
 (1). Radiant heat is only a part of the heat that escapes from 
 a hot body. Let us suppose that in the preceding experiment 
 the two foci of the mirrors communicate by a metallic bar, termi- 
 nated at both ends by these foci: if we place at one end of the 
 extremities of this bar an exhaustless source of heat (a red-hot 
 iron, a blast-lamp flame, the focus of a powerful lens): immedi- 
 ately the radiant heat, following the course indicated above, 
 will warm the other extremity of the bar by the double reflec- 
 tion. At the same time the non-radiant heat, creeping gradu- 
 
MEMOIKJ3 ON 
 
 ally into the contiguous parts of the bar, will slowly heat it and 
 will finally come to the points most distant from the source. 
 
 The air being a discrete fluid much more dense 1 than heat, 
 arrests and intercepts the particles of the latter. But being 
 much more rare than the metal, it allows a portion of it to pass, 
 which produces the phenomena of radiant heat. Light, much 
 more rare and subtle than heat, is transmitted in much greater 
 proportion by this same air, the opacity of which is so incon- 
 siderable that it becomes sensible only in very great masses. 2 
 The transparency or the quantity of fluid transmitted through 
 another fluid, depends upon the rarity and the subtlety of the 
 particles of both fluids. I do not speak here of the affinities 
 and capacities of different bodies for heat. I speak only of the 
 mechanical interception of this fluid by its solid parts. This 
 interception is sufficient only to produce these two kinds of 
 heat or of cold, radiant heat, and nonradiant heat. 
 
 Entangled, further, in the small cavities or in the interstices 
 of solid particles, the heat may or may not recover all the veloc- 
 ity which properly belongs to it, according as these cavities or 
 interstices are or are not sufficiently spacious. When it recov- 
 ers only a portion of its velocity, it becomes in part insensible 
 or latent. When it can recover only a very little of it or none 
 at all, it yields to the affinities of the particles which surround 
 it and combines in a thousand ways. 
 
 (2). Heat is not the only fluid of its kind. Several discrete 
 fluids are known, radiant and nonradiant. 3 We often have 
 occasion to consider these fluids in the state of equilibrium. 
 The determination of the true sense of this word ought then to 
 be of much importance, independently of the theory of heat. 
 
 1 The density which I attribute to the air in this instance, consists 
 chiefly in the proximity of its molecules; for a discrete fluid maybe 
 composed of very dense particles, but with large spaces between them : 
 so that it could be more permeable than heat, although more dense. 
 
 2 Notice the remarks of M. de Saussure, upon the transparency of 
 the air, in his memoirs upon light. Academ. de Turin, 1790. 
 
 8 In the electrical phenomena, there are radiations of the correspond- 
 ing fluid. In magnetic phenomena neither of the two magnetic fluids is 
 radiant. 
 
 12 
 
RADIATION AND ABSORPTION. 
 
 If these remarks and the preceding discussion offer any 
 useful views, if they tend to throw light upon an important 
 class of phenomena, if they suggest any clear ideas upon the 
 method of motion of invisible and subtle fluids which manifest 
 their existence by such diverse appearances : finally, if these 
 conceptions naturally connect themselves with other theories, 
 either already proven, or rendered probable, concerning the 
 various effects of these subtle fluids (such, as the phenomena of 
 evaporation, of electricity and of magnetism), is it not the 
 requital of investigating the general theory upon which all 
 these special explanations depend ? This theory (I refer to 
 that of M. le Sage of Geneva, upon the nature of discrete 
 fluids) merits the further attention of physicists, since it depends, 
 itself, upon another principle, more general, which has also as 
 a proof of its reliability, the clear and satisfactory explanation 
 of very striking and very general phenomena, absolutely in- 
 explicable without it. 
 
 13 
 
ON RADIANT HEAT. 
 
 BY 
 
 PIERRE PREVOST. 
 
 Geneva, 1809. 
 (Selections.) 
 
 15 
 
CONTENTS. 
 
 PAGE 
 
 Questions Relative to the Nature of Caloric . _ . . 17 
 Resume of Principles and Conclusions. . . . . 19 
 
 16 
 
QUESTIONS RELATIVE TO THE NATURE 
 OF CALORIC. 
 
 CHAPTER IV. PP. 6 10. 
 
 THE word caloric (heat) has been originated to explain the 
 cause of heat, with the formally expressed intention of being 
 non-committal as to its nature. 
 
 It is desirable to leave it indefinite as to whether heat may be 
 produced by a specific fluid, or, merely, be a movement 
 impressed upon the molecules of a body, without the introduc- 
 tion of any fluid. 
 
 Many noted physicists believe there is no specific fluid to 
 which this word caloric is applicable. They believe that heat 
 is produced by internal movements of the molecules of a body. 
 More often, however, physicists have recourse to a vibrating 
 ether or to the air, or to some other medium propagating waves 
 to which they attribute the phenomena of heat. 
 
 Others believe that caloric is a specific fluid, which penetrates 
 the body and produces all the appearances of this kind. 
 
 Among the latter, many believe that caloric and light are 
 identical. Others are of a contrary opinion. 
 
 Some look upon caloric as simple ; a smaller number regard it 
 as a compound fluid. Mr. J. A. DeLuc believes that caloricis, a 
 kind of vapor composed of ponderable matter held in a state of 
 suspension by light. This conception throws some light upon 
 many phenomena and merits serious consideration. Meanwhile, 
 pressed to arrive at the chief object which I have in view, I 
 will refrain from all discussion as to the composition of caloric. 
 
 I have no desire to repeat here and weigh the general 
 arguments stated on the one side and on the other for sus- 
 taining the various views which I have just outlined. I will 
 limit myself to a very few remarks on this subject. 
 
 As stated below I propose to consider caloric as a specific 
 fluid. I will represent the radiations of this fluid as an emission 
 
 17 
 
RADIATION AND ABSOKPTION. 
 
 and never as an undulation. I believe this conception and this 
 representation to be more conformable than any other to the 
 nature of things and founded upon the soundest principles of 
 general physics. But if those who believe otherwise substitute 
 waves for an emission they may be able, perhaps, to adapt to 
 their opinion the explanations which I give for phenomena of 
 this crass. It is no desire of mine that they should attempt it, 
 because I am persuaded that this would be translating a 
 language clear and natural into a language obscure and artificial. 
 But I make this statement to make clear the kind of work 
 which I have undertaken. I do not contest any system. I do 
 not refute any explanation. It is my aim, in limiting myself in 
 my subject, to explain in my own way what seems to me to ad- 
 mit of clear explanation, and to indicate the phenomena of 
 which the explanation remains imperfect. If each one who 
 has an opinion upon the theory of caloric will give a concise ex- 
 position of his ideas on the subject, and will show how the facts 
 may be coordinated by means of these conceptions : physicists 
 can see at a glance which theory is most satisfactory, or if all 
 should be rejected. 
 
 RESUME OF THE PRINCIPLES EXPOUNDED AND OF THE PRINCI- 
 PAL CONCLUSIONS WHICH HAVE BEEN DEDUCED 
 FROM THEM. 
 
 SECTION IX. pp. 258261. 
 
 HEAT is a discrete fluid; each element of heat follows con- 
 stantly the same straight line, as long as no obstacle arrests it. 
 Every point of a hot space is constantly traversed throughout 
 by streams of heat. 
 
 If we admit this constitution of heat, the following conclu- 
 sions are inevitable. 
 
 The first three require nothing further. The others require 
 the assumption that heat is comparable with light in its move- 
 ments of reflection and refraction. 
 
 1st. conclusion: Free heat is a radiant fluid. Or, as the 
 surface of the body of heat becomes free, each point of the sur- 
 
 18 
 
MEM01KS ON 
 
 face of the body is a center to which tend, and from which are 
 carried, in every direction, streams of heat. 
 
 2nd. conclusion : The equilibrium of heat between two 
 neighboring free spaces consists in the equality of the 
 exchanges. 
 
 3rd. conclusion: When the equilibrium is disturbed, it is 
 reestablished by unequal exchanges, in a medium of constant 
 temperature, a body that is hotter or colder requires this tem- 
 perature according to the law that the periods of time being in 
 arithmetical progression, the differences of temperature are in 
 geometrical progression. 
 
 4th. conclusion: In a space of uniform temperatures, if a 
 reflecting or refracting surface is introduced it has no effect in 
 changing the temperature of any part of this space. 
 
 5th. conclusion: In a space of unequal temperature, if there 
 is placed a body which is either hotter or colder and if after- 
 wards a reflecting or refracting surface be introduced, the 
 points, upon which these surfaces direct the rays emanating 
 from this body, will be affected by it, being heated if the 
 body is hotter, or cooled if it is colder. 
 
 6th. conclusion: A reflecting body, having been heated or 
 cooled internally, recovers the surrounding temperature more 
 slowly than a nonreflector. 
 
 7th. conclusion: A reflecting body, having been heated or 
 cooled internally will have less effect on another body placed 
 at any distance (in heating or cooling it) than a nonreflector 
 would under the same conditions. 
 
 All these conclusions have been verified experimentally, ex- 
 cept that concerning the refraction of cold. This experiment 
 remains to be made, and I am confident of the result, at least 
 if the refraction of the heat is capable of being observed. This 
 result is indicated in the 4th. and 5th. conclusions, which could 
 in this way be submitted to a new test. It is hardly necessary 
 to indicate in this place the precautions by means of which one 
 would place himself beyond every kind of misobservation. 
 
 19 
 
RADIATION AND ABSORPTION. 
 
 BIOGRAPHICAL SKETCH. 
 
 PIERRE PREVOST was born in Geneva, March 3, 1751, and died 
 at the same place oil the 9th of April, 1839. He was the son of 
 a clergyman and was educated for a clerical career, but turned 
 his attention to law and later to educational work. He became 
 a professor of philosophy and a member of the Academy of 
 Sciences at Berlin in 1780. Here, through his acquaintance 
 with Lagrange, his attention was directed to science, which 
 later he followed up with his studies on Magnetism and Heat 
 at Geneva where he became professor of physics in 1810. He 
 published much on different subjects, including philology, 
 philosophy, political economy, fine arts, etc. He issued the 
 works of le Sage, supplemented by many additions of his 
 own. His Du Calorique Rayonnant appeared at Geneva in 
 1809 and was an exposition and extension of his theory of ex- 
 changes first advanced several years before. The original 
 memoir and later publications appeared in the Journal de 
 Physique and the Phil. Trans, from 1791 to 1802. His remark- 
 able versatility is indicated in the variety of his publications. 
 His most valuable contribution to science is undoubtedly his 
 Theory of Exchanges one of the most important principles in 
 the whole range of physical science. 
 
 20 
 
AN ACCOUNT OF SOME EXPERIMENTS 
 
 ON RADIANT HEAT, INVOLVING AN 
 
 EXTENSION OF PREVOST'S THEORY 
 
 OF EXCHANGES. 
 
 BY 
 
 BALFOUR STEWART. 
 
 Transactions of the Royal Society of Edinburgh. 
 Vol. XXII. Part I. pp. 120. March, 1858. 
 
CONTENTS. 
 
 PAGE 
 
 Division of Subject 23 
 
 Description of Instruments and Method . . . .24 
 
 On Radiations from plates of Different Substances . . 26 
 On Radiations from Polished Surf aces . . .32 
 
 On Radiations of Plates of Different thicknesses . . 33 
 
 Results Explained by Prevost's Ttieory of Exchanges . . 35 
 Peculiarities of the Radiation from Plates of Diatherm- 
 
 anous Substances 37 
 
 Equality of the Radiation and the Absorption . 40 
 Influence of the Reflective and Refractive Powers of Bod- 
 ies on their Radiation considered 42 
 
 Equal and Independent Radiation ..... 47 
 
 Internal Radiation and Conduction , 49 
 
 22 
 
l. AN ACCOUNT OF SOME EXPERIMENTS 
 ON RADIANT HEAT, INVOLVING 
 AN EXTENSION OP PEEVOST'S 
 THEORY OF EXCHANGES. 
 
 BY BALFOUR STEWART, ESQ. 
 
 COMMUNICATED BY PROFESSOR FORBES. 
 
 Read, 15th, March 1858. 
 
 Division of Subject. 
 
 1. This paper consists of two parts, the first of which is 
 confined to describing the experiments performed; while in 
 the second it is attempted to connect these with certain theo- 
 retical views regarding Radiant Heat. 
 
 2. The experiments were made with a fourfold object; at 
 least for the sake of clearness, it is well to class them into four 
 distinct groups: 
 
 Group L Contains those experiments in which the quanti- 
 ties of heat radiated from polished plates of different 
 substances, at a given temperature, are compared with 
 the quantity radiated from a similar surface of lamp- 
 black, at the same temperature. 
 
 Group II. Those in which the quantities of heat radiated 
 at the same temperature, from polished plates of the same 
 substance, but of different thicknesses, are compared 
 with one another. 
 
 Group III. Those in which the radiations, from polished 
 plates of different substances at any temperature, are 
 compared with that from lampblack at the same tem- 
 perature, with regard to the quality or nature of the 
 heat radiated. 
 
 23 
 
MEMOIRS ON 
 
 Group IV. Those in which the same comparison is made 
 between the radiations from polished plates of the same 
 substance, but of different thicknesses. 
 
 Instruments used, and Method of using them. 
 
 3. I am indebted to the kindness of Professor Forbes for 
 the use of a delicate thermo-multiplier, consisting of the sen- 
 tient pile, and its attached galvanometer and telescope; as 
 well as for much valuable information with regard to the 
 proper method of using the apparatus. 
 
 The following arrangement was adopted for the great mass 
 of the experiments: 
 
 A. Is the sentient pile, with a polished brass cone attache^ 
 to it, for collecting the rays of heat. 
 
 B. Is the galvanometer, the position of its needle being 
 read to ^th of a degree by the telescope C. 
 
 D. Is a screen placed before the mouth of the cone in 
 which there is a small hole or diaphragm .65 inch square. The 
 screen is covered with gilt paper, in order that, should it get 
 slightly heated, it might radiate as little as possible. 
 
 The heated body is placed behind the diaphragm, filling up 
 the field of view from the cone ; so that every ray reaching the 
 cone from behind the diaphragm comes from the heated body. 
 
 24 
 
RADIATION AND ABSORPTION. 
 
 In the following experiments, unless the contrary is men- 
 tioned, the distance of the diaphragm from the mouth of the 
 cone is 2 inches. 
 
 The dimensions of the cone itself are as follows : 
 
 Length of axis, or distance between centre of mouth and 
 
 pile, 5 inches. 
 
 Diameter of mouth or opening, 2.6 inches. 
 
 The temperature to which the heated body was raised was 
 generally 212, and the apparatus used for heating it was of the 
 following construction : 
 
 It consisted of a tin vessel, having its top, bottom, and sides 
 double (or a box within a box), and furnished on the top with 
 a lid, also double, by means of which the body to be heated was 
 introduced into the interior. 
 Water was poured into the 
 chamber between the outer and 
 inner boxes, and allowed to 
 boil ; and, when the lid was 
 shut, the temperature of the 
 interior was found to rise very 
 nearly to the boiling point ; a 
 thermometer placed in the 
 air of the chamber showing a 
 
 temperature of 200, and when lying on the bottom, 
 a temperature of 210. When an observation was to be made, 
 the hot body was taken out, and that surface which lay on the 
 bottom of the inner chamber placed behind the diaphragm, so 
 as to radiate into the cone. In the following experiments, un- 
 less the contrary is mentioned, the body has been heated in this 
 manner. 
 
 The first swing of the galvanometer needle was taken as rep- 
 resenting the intensity of the heating effect : and Professor 
 Forbes has shown, in a paper read before this Society, 2d May, 
 1836, that this will hold up to angles of about 20, which is the 
 maximum deviation used in these experiments. 
 
 Observations were always made with as little sunlight as pos- 
 sible ; and under these circumstances, it was ascertained that 
 the stray heat reaching the cone was inappreciable. The needle, 
 it was calculated, reached the limit of its swing about 12 
 
 25 
 
MEMOIRS ON 
 
 seconds after the heated body had been taken out of the 
 boiling-water apparatus. 
 
 Experiments were made to ascertain if the body cooled 
 sensibly during this short period of time, and it was found that 
 its cooling was so trifling as not to interfere in any degree with 
 the results of these observations. In the following experiments, 
 it is therefore assumed that the body remains at its original 
 temperature of 210 while the observation is being made. 
 
 Four observations were generally made, and three if they 
 agreed together exceedingly well, but never fewer. Very often 
 the agreement was exact. . 
 
 First Grout of Experiments described. 
 
 4. With these remarks, I proceed to describe the experiments 
 belonging to the first group, or those made with the view of 
 comparing the heat radiated from polished plates of different 
 substances with that radiated from a surface of lampblack at 
 the same temperature. 
 
 The reason why lampblack was chosen as the standard is ob- 
 vious ; for, it is known from Leslie's observations, that the 
 radiating power -of a surface is proportional to its absorbing 
 power. Lampblack, which absorbs all the rays that fall upon 
 it, and therefore possesses the greatest possible absorbing power, 
 will possess also the greatest possible radiating power. The first 
 substance compared with it was glass. 
 
 A. Glass. Apiece of plate glass, .3 inch thick, having paper 
 coated with lampblack pasted on its surface next the pile, gave 
 a deviation of 18.1. This may be taken as the radiation from 
 lampblack. 
 
 Three plates of crown glass, each .05 inch thick, placed 
 
 one behind the other, gave 17.7. 
 
 A single piece of crown glass of the same thickness, 
 gave 16.5. 
 
 This difference is probably owing to the single plate cooling 
 faster than the three plates. It may be argued that the 
 radiation from the glass is very nearly equal to that from lamp- 
 black ; and indeed this is already well known.* 
 
 * See Leslie's " Inquiry into Nature and Propagation of Heat." 
 
 26 
 
RADIATION AND ABSORPTION. 
 
 B. Alum. Here the boiling- water apparatus could not be 
 used, since alum becomes calcined at a temperature much 
 below 212 ; but a self-regulating apparatus, invented by the 
 late Mr. Kemp, was employed instead, giving a steady 
 temperature of 98. 
 
 A piece of plate glass .18 inch in thickness, gave 5.0 
 
 A piece of alum of the same thickness gave 5.0 
 
 The radiation from the alum may therefore be reckoned 
 equal to that from glass. 
 
 C. Selenite. At the temperature of 98 
 
 A piece of selenite .125 inch in thickness gave. . . .5.1 
 
 Under the same circumstances, glass .18 inch thick 
 
 gave 5.0 
 
 In the boiling-water apparatus, 
 
 The same piece of selenite gave 18.0 
 
 While blackened glass gave 18.5 
 
 The radiation from selenite may therefore be reckoned equal 
 to that of alum or glass. 
 
 D. Mica. A small box was constructed, having two windows 
 of mica, the thickness of the mica in the one being .0009 inch, 
 and of that in the other. 02 inch. This box was filled with 
 mercury (Professor Forbes having suggested the use of that 
 metal, to keep up the temperature, while interfering very little 
 with the radiation). The whole was then set on a glass dish in 
 the boil ing- water apparatus. 
 
 The radiation from the thin window was 11.2 
 
 While that from the thick window was 12.7 
 
 As it would have been manifestly erroneous to compare these 
 with the radiation from the blackened glass lying in contact 
 with the bottom of the apparatus, the thin window was 
 removed, and the blackened paper substituted in place of it. 
 
 While the thick mica window gave 12.7 
 
 The blackened paper gave 13.8 
 
 In comparing the radiations from the two windows, they 
 were observed alternately. We see, therefore, that the radia- 
 tion from mica, especially thin mica, is less than from lamp- 
 
 27 
 
MEMOiKS ON 
 
 black in the proportion of 11.2 to 13.8, or the heat from thin 
 mica is 80 per cent of that from lampblack. 
 
 E. Rock Salt. As in the experiments with rock salt, it was 
 desirable to obtain results of the greatest possible accuracy, the 
 radiation from rock salt was not compared with that from 
 blackened glass ; for it was found that glass cooled more 
 rapidly than rock salt. 
 
 The following plan was adopted : 
 
 A piece of rock salt .18 inch thick (the temperature as 
 in all the previous examples being about 210, gave 3.2 
 A canister with water kept boiling, coated with lamp- 
 black 22.0 
 
 In order to estimate how much the rock salt had cooled 
 during the observation, the following experiment was made, 
 without any diaphragm : 
 
 Rock salt .18 inch thick taken to the cone at once, 
 
 gave 5.1 
 
 After cooling for 15 seconds, it gave 4.9 
 
 It will be seen from this, that were the rock salt, instead of 
 cooling during the 12 seconds necessary for the observation, 
 kept at the temperature of 212 , it would not have given more 
 than 3.3, while the hot-water canister gave 22.0. 
 
 5. From these experiments, it appears that glass, alum, and 
 selenite, at low temperatures, have an intensity of radiation 
 very nearly equal to that from lampblack ; while mica radiates 
 somewhat less, and rock salt greatly less. This is shown by 
 the following table : 
 
 TABLE I. 
 
 RADIATING SUBSTANCE. 
 
 TEMPERATURE. 
 
 212 
 
 98 
 
 Lampblack, > 
 
 100 
 
 98 
 
 98 
 92 
 81 
 15 
 
 27 
 
 27 
 27 
 
 Glass 
 
 Alum 
 
 Selenite, 
 
 Thick mica, 
 
 Thin mica, 
 
 Rock salt 
 
 
 28 
 
RADIATION AND ABSORPTION. 
 
 Second Group of Experiments described. 
 
 6. I now proceed to the second group of experiments, or those 
 designed to compare together the quantities of heat radiated 
 at the same temperature from polished plates of the same sub- 
 stance, but of different thicknesses. 
 
 A. Glass. No direct experiment of this kind was made on 
 glass ; for although a thick plate gave a somewhat greater 
 radiation than a thin plate, it was imagined that this was due 
 to the unequal cooling of the two plates. Indirectly, however, 
 we may gather that thick glass radiates somewhat more than 
 thin glass, from the following experiment, which belongs more 
 properly to the fourth group: 
 
 A plate of crown glass .05 inch thick, being placed be- 
 fore the cone as a screen, and a similar plate .05 inch 
 thick, and 3.75 inches square, being used as the 
 source of heat at a distance of 6 inches, and no dia- 
 phragm used, the deviation was 0.95* 
 
 But when the source of heat was a similar plate .10 
 inch thick, the deviation became 1.45 
 
 Such a difference cannot be accounted for by the unequal 
 cooling of the plates ; and it would seem to indicate that a small 
 quantity of heat from the interior of the thick plate reached 
 the surface ; which heat, having already been sifted by. its pas- 
 sage through glass, was easily able to pierce the screen. 
 
 In another similar experiment, 
 
 One piece of crown glass .05 inch thick, gave a deviation 
 
 of 1.1 
 
 Two plates .05 inch thick, the one behind the other, 1.55 
 Three such plates, 1.9 
 
 B. and C. No experiments of this kind were attempted with 
 alum or selenite. 
 
 D. Mica. Experiments similar to those already described, 
 only at a distance of 2^ inches from the cone, gave 
 
 * Without any screen, it was calculated that the intensity of effect 
 would have been equal to about 150. 
 
MEMOIRS ON 
 
 For mica .0009 inch thick (average of two sets of experi- 
 men ts), 8.2 
 
 For mica, .02 inch thick (average of two sets of experi- 
 ments), .9.3 
 
 The experiments already quoted, which were made at a 
 shorter distance from the pile, gave 
 
 For mica, .0009 inch thick, 11.2 
 
 For mica, .02 inch thick, 12.7 
 
 E. Rock Salt. Three pieces of rock salt were used. Their 
 dimensions were: 
 
 1st Piece. 2nd Piece. 3rd Piece. 
 
 Length 1.15 inch 2.15 inches 2.5 inches 
 
 Breadth 1.15 " 1.4 inch 1.4 inch 
 
 Thickness... .0.18 " 0.36 " 0.77 " 
 
 For these pieces, as well as for the other substances, I am in- 
 debted to the kindness of Professor Forbes. When placed be- 
 hind the diaphragm, the farthest off surface was large enough 
 to fill up the field of view, that is to say, all rays from the 
 cone striking the nearest surface struck also the surface far- 
 thest off ; the distance between the two surfaces being the 
 thickness of the piece. 
 
 The following are the means of four sets of experiments : 
 
 Radiation from 1st or thinnest piece 3.4 
 
 " ' 2nd or middle piece 4.3 
 
 " (( 3rd or thickest piece 5.3 
 
 This proves that more heat is radiated by a thick than by a 
 thin piece of rock salt. 
 
 The following experiments were devised by Professor Forbes, 
 to confirm the above results. 
 
 (a.) The second piece of rock salt was placed obliquely behind 
 the diaphragm, making an angle of 20 with the prolongation 
 of the axis of the cone. A piece of fir wood of the same dimen- 
 sions was placed in the same way. The two substances being 
 compared in this position, and also in the usual position behind 
 
 30 
 
RADIATION AND ABSORPTION. 
 
 diaphragm (viz., perpendicular to the direction of the cone's 
 
 axis), the following was the result : 
 
 Oblique. Usual position. 
 
 Rock salt .36 inch thick, 4.0 4.0 
 
 Wood, same size as rock salt, 9.1 14.1 
 
 In order that this experiment may be understood, it may be 
 well to mention, that, when the plate was placed obliquely be- 
 hind the diaphragm it did not quite fill up the field of view. 
 Hence the wood gave out less heat to the cone in this than in 
 its ordinary position. 
 
 It appears, therefore, that the radiation from rock salt, in a 
 direction making a small angle with the surface, bears a 
 greater proportion to the corresponding radiation from wood 
 than when both radiations are taken perpendicular to the sur- 
 face. The reason undoubtedly is, that in the former case the 
 rays come from a greater thickness of the substance, so that 
 their intensity is increased. 
 
 P. The middle-sized piece of rock salt was bound tightly 
 to the thickest piece, with a slip of tin foil between, so that 
 the whole might cool as one piece, and thus obviate any ob- 
 jection that might be brought against the results, founded on 
 the unequal cooling of the plates, owing to their thicknesses 
 being different. 
 
 The surface of the middle-sized piece facing the pile, 
 
 gave 6.3 
 
 That of the thickest piece, gave 8.1 
 
 The plates, therefore, still retain their inequality of radia- 
 tion; but the amount from each was increased, owing, no doubt, 
 to the reflection and radiation from the tin foil. The radiation 
 from the tin foil may be estimated at 1.0, deducting which, 
 we have 5.3 and 7.1; the increase now being due to reflection 
 from the tin foil. 
 
 7, It thus appears, that while the difference between the 
 radiating power of thick and thin glass is so small as not to be 
 capable of being directly observed, there is a perceptible differ- 
 ence between the radiation from thick and thin mica, and a 
 
 31 
 
MEMOIRS ON 
 
 still more marked difference between the radiation from plates 
 of rock salt of unequal thickness. 
 
 But (at least with the thicknesses used) the greatest radia- 
 tions from mica and rock salt were still below that from lamp- 
 black, and the radiation from rock salt greatly so. 
 
 The following table exhibits the results of the second group 
 of experiments: 
 
 TABLE II. 
 
 SUBSTANCE. 
 
 RADIATION FROM 
 THICK PLATE. 
 
 RADIATION FROM 
 THIN PLATE. 
 
 Glass 
 
 100 
 
 100 
 
 
 100 
 
 89 
 
 Rock salt, 
 
 100 
 
 Middle 81 
 thin ) C4 
 
 
 
 
 Third Group of Experiments described. 
 
 8. I now proceed to consider the third group of experi- 
 ments, or those made with the view of comparing the radiations 
 from various polished surfaces with that from lampblack, as 
 regards the quality of the heat; its quality being tested by its 
 capability of transmission through a screen of the same mate- 
 rial as the radiating plate. 
 
 A. Glass. In an experiment already described, where a 
 plate of crown glass .05 inch thick was used as a screen, and 
 a similar plate of crown glass as a source of heat 
 
 We had , 0.95 
 
 A similar plate .1 inch thick as the source of heat, 
 gave 1.45 
 
 Blackened paper attached to a similar surface of plate 
 glass, .3 inch thick, the blackened side being next 
 the pile, , 1.95 
 
 Therefore heat from a thin plate of glass is less transmissible 
 through glass than heat from blackened paper. 
 
 B. and C. No experiment of this nature was made with 
 alum or selenite. 
 
 D. Mica. The apparatus already described gave 
 
 32 
 
K A D I A T 1 N AND ABSORPTION. 
 
 Without With mica screen 
 screen. .0025 inch thick. 
 
 For window (the window, it will 
 be borne in mind, is the radia- 
 ting surface), .0009 inch thick. .11.2 2.5 
 
 Window .02 inch thick 12.7 3.2 
 
 Blackened paper attached to 
 glass lying on the bottom of 
 the boiling-water appara- 
 tus, gave 21.0 6.3 
 
 We have therefore the proportion of heat passed by mica 
 screen 
 
 For heat from thin mica window, 223 
 
 " " thick " " 260 
 
 " " blackened paper, 300 
 
 E. Rock salt. The thickest piece of rock salt (thickness 
 .77 inch) being used as a screen, and the diaphragm withdrawn, 
 in order to give greater results; the middle sized piece of rock 
 salt gave 
 
 With screen. Without screen 
 6.1 19,6 
 
 The same screen stopped 3 rays out of 12 for ordinary lamp- 
 black heat. 
 
 This experiment is sufficient to show that rock salt is much 
 less diathermanous for heat from rock salt than for ordinary 
 heat. The common opinion, that rock salt is equally diather- 
 manous for all descriptions of heat, is therefore untenable. 
 
 9. From the third group of experiments it appears, therefore, 
 that heat emitted by glass, mica, or rock salt, is less trans- 
 missible through a screen of the same material as the heated 
 plate, than heat from lampblack ; this difference being very 
 marked in the case of rock salt. 
 
 Fourth Group of Experiments described. 
 
 10. 1 now proceed to the fourth group of experiments, or 
 those made with the view of comparing the radiations of plates 
 of the same substance, but of different thicknesses, with regard 
 to the quality of the heat radiated. 
 
 33 
 
MEMOIKS ON 
 
 A. Glass. It has been already shown (Art. 8), that heat 
 from crown glass .05 inch thick is less transmissible through 
 glass, than that from crown glass .10 inch thick. 
 
 B. and 0. No experiments of the kind were made on alum 
 or selenite. 
 
 D. Mica. It has been already shown (Art. 8), that heat from 
 thin mica is less transmissible through a mica screen than heat 
 from thick mica. 
 
 E. Rock salt. With a screen of rock salt .18 inch thick, the 
 following result was obtained : 
 
 Thickest piece of rock salt, heated to 210 
 
 (thickness .77 inch), gave 2.5 
 
 Middle-sized piece of rock salt, heated to 210 
 
 (thickness .36 inch), gave 1.7 
 
 Thinnest piece of rock salt, heated to 210 
 
 (thickness .18 inch), gave 1.1 
 
 Without any screen, the same pieces gave 
 
 Thickest, 4.9 
 
 Middle-sized, 4.1 
 
 Thinnest, 3.3 
 
 Proportion of heat from thickest piece passed 51 
 
 Proportion of heat from middle-sized piece passed .41 
 
 Proportion of heat from thinnest piece passed 33 
 
 A similar experiment, with a screen .29 inch thick gave 
 
 With screen. Without screen. Proportion passed. 
 
 Thickest piece. . .2.6 5.4 .48 
 
 Middle-sized, ....1.8 4.5 .40 
 
 Thinnest 1.2 3.5 .33 
 
 It follows from this, that a screen of rock salt passes heat 
 from thick, more easily than heat from thin rock salt, 
 
 11. From this fourth group of experiments, we learn that heat 
 from thick plates of glass, mica, or rock salt, is more easily 
 transmitted by screens of the same nature as the heated plate 
 than heat from thin plates of these materials. 
 
 The following table exhibits the results of the third and 
 fourth group of experiments : 
 
RADIATION A K D A B S E P T I K . 
 
 TABLE III. 
 
 
 No. of Rays out of every 
 100 that pass through 
 a screen of the same 
 
 No. of Rays of 
 Lampblack 
 Heat out of 
 
 SOUBCE OF HEAT. 
 
 material as the source 
 of Heat in 1st column, 
 
 every 100 
 
 
 the screen being of 
 only one thickness for 
 
 that pass 
 through the 
 
 
 each material. 
 
 same screen 
 
 Glass (crown ^th inch thick), 
 
 0.66) 
 
 1.33 
 
 Glass (crown ^th inch thick), 
 
 1.0 } 
 
 
 Mica (thickness .0009 inch), 
 
 22. 
 
 
 Mica (thickness .02 inch), 
 
 2GJ 
 
 30 
 
 Rock salt (thickness .18 inch), 
 
 33) 
 
 (Art. 12) 
 
 Rock salt (thickness .36 inch), 
 
 41 [ 
 
 82 
 
 Rock salt (thickness .77 inch), 
 
 50* 
 
 
 Lamp 
 
 Results deducible from the foregoing Experiments. 
 
 12. These experiments, as well as others yet to be described, 
 may be explained by Prevost's theory of exchanges, somewhat 
 modified. 
 
 In the first place, it would seem to be a consequence of this 
 theory, that radiation must take place from the interior as well 
 as from the surfaces of bodies. For, suppose that we have two 
 
 indefinitely extended surfaces of 
 lampblack, as in the figure, and 
 between them a plate of rock 
 salt of a certain thickness, also 
 indefinitely extended; and let 
 the whole be kept at the same 
 temperature. Then, since the 
 temperature of the. rock salt 
 remains the same, it must radiate 
 as much as it absorbs. But a thicker plate of rock salt, placed 
 under the same circumstances, would absorb more of the heat 
 radiated from the lampblack because each ray would have to 
 pass through a greater depth of the substance of salt; hence a 
 thick plate of rock salt must radiate more than a thin plate. 
 We see likewise, the reason for the small radiative capacity of 
 
 35 
 
MEM'OIRS ON 
 
 rock salt to be its small absorptive capacity. In order to prove 
 this deduction from Prevost's theory experimentally true, the 
 following experiment was devised: 
 
 A boiling-water canister, coated with lampblack, was put 
 behind the diaphragm, filling up the field of view, and the 
 three pieces of rock salt heretofore used as sources of heat, 
 were now separately used as screens, being put before the dia- 
 phragm, so that the heat from the canister had to pass 
 through their substance before reaching the cone. The follow- 
 ing was the result: 
 
 Without any Screen of Screen of Screen of 
 
 screen. Rock salt Rock salt Rock salt 
 
 .18 inch .36 inch .77 inch 
 
 thick. thick. thick. 
 
 Eadiation from canister, 21.3 17.6 16.8 15.8 
 
 The difference between heat absorbed by plate, 
 thickness = .18 inch, and that absorbed by 
 plate, thickness = .36 inch, 
 
 is 1.2) 
 
 Another similar experiment gives 0.9 J Mean *! 
 
 The difference between heat absorbed by plate, 
 thickness = .36 inch and that absorbed by 
 plate, thickness = .77 inch, 
 
 is 1.0 ) 
 
 Another similar experiment gives 1.3 f Mean 1.1 
 
 These should nearly correspond to the differences between the 
 radiation from the same place, under their ordinary circum- 
 stances of position (if the theory be true which asserts that the 
 absorption of such a plate equals its radiation); accordingly we 
 find that 
 
 The difference between heat radiated by 
 
 plate, thickness = .18 inch ) -.- 
 
 And that radiated by plate thickness = .36 inch, ) 
 While the difference between radiation of 
 
 plate thickness = .36 inch } 
 
 And that of plate thickness = .77 inch, f Is 1<0 
 
 (Art. 6, mean of four sets of experiments.) 
 We see, therefore, that there is an agreement between the 
 two sets of differences, as near as can be reasonably expected. 
 
 36 
 
 
RADIATION AND ABSORPTION. 
 
 13. If we now suppose a plate of glass, arid not a plate of 
 rock salt, placed between surfaces of lampblack, the plate, 
 whether thin or thick, will allow scarcely any heat to pass 
 through it; and, consequently, plates of different thicknesses 
 will all absorb very nearly the same amount, that is, nearly 
 all that enters them. In this case, therefore, the radiation 
 (which is equal to the absorption) will be very slightly increased 
 by an increase of thickness of the plate. Also the amount of 
 heat radiated, being equal to the heat absorbed, will be very 
 nearly as great as that from lampblack. 
 
 14. There are, therefore, two peculiarities of the radiation 
 from plates of diathermanous substances, and which are most 
 marked for those substances which are most diathermanons. 
 
 1st, That the amount of radiation from such plates is less 
 than that from lampblack. 
 
 2d, That the amount of radiation from such plates increases 
 with the thickness of the plate. 
 
 The correlation between these different properties of bodies 
 is seen from the following table: 
 
 TABLE IV. 
 
 Bodies ranked according 
 to their Radiating Ca 
 pacity (least radiating 
 
 Bodies ranked ac- 
 cording to their 
 Diathermancy 
 (most diatherman- 
 
 Bodies ranked according 
 to the proportion by 
 which their Radiation 
 is increased by increas- 
 
 first). 
 
 ous first). 
 
 ing the thickness. 
 
 A stratum of heated gas 
 
 
 
 (from Melloni's Exper- 
 
 
 
 iments), 
 
 A stratum of gas. 
 
 
 Rock salt. 
 
 Rock salt. 
 
 Rock salt. 
 
 Mica. 
 
 Mica. 
 
 Mica. 
 
 Glass. j 
 
 Glass. ^ 
 
 Glass. 
 
 Selenite. > 
 
 Selenite. ? 
 
 .... 
 
 Alum. ) 
 
 Alum. 
 
 
 15. The reason why radiation has hitherto been supposed to 
 be -confined to the surface, or to an exceedingly small distance 
 below the surface of a body now becomes obvious. The effect of 
 coating a surface of polished metal with gum, for instance, is 
 
 37 
 
MEMOIRS ON 
 
 to increase the radiation; but, after a very small thickness of 
 film, an additional coating is powerless to increase the radiation; 
 the reason being, not that radiation is incapable, in all cases, of 
 taking place except at the surface; but because such films be- 
 ing exceedingly impervious to heat of low temperatures, the 
 radiation from them is very little increased by increasing their 
 thickness. 
 
 Since, therefore, it appears that radiation takes place from 
 the interior as well as from the surface of bodies, the question 
 arises, are we to suppose each particle of each substance to 
 have, at a given temperature an independent radiation of its 
 own, equal, of course, in all directions ? A priori, this is the 
 most probable supposition, and it seems likewise to be conform- 
 able to experiment. 
 
 16. In an experiment already described, 
 
 A plate of crown glass .05 inch in thickness being used as 
 a screen, the quantity of heat radiated from crown 
 glass .05 inch thick that passed, was 0.95 
 
 While of that radiated from crown glass, .10 inch thick 
 there passed 1.45 
 
 Another experiment gave 
 
 Quantity of heat from crown glass .05 there passed . .1.1 
 
 Quantity radiated from two plates of crown glass, each 
 .05 inch thick the one placed loosely behind the 
 other, 1.55 
 
 From this we may infer, that the radiation from two plates 
 of glass placed loosely behind each other is the same as the ra- 
 diation from a plate of double the thickness, and, consequently, 
 that the radiation from a particle of a substance does not di- 
 minish owing to its being placed in the interior.* 
 
 17. Let us now refer to the radiation from rock salt: 
 
 The radiation from a piece .18 inch thick, was 3.4 
 
 That from a piece .36 inch thick, was 4.3 
 
 That from a piece .77 inch thick, was 5.3 
 
 * The idea of this experiment was derived from a remark of Professor 
 Forbes, who suggested that several plates of rock salt, the one behind 
 the other, might be advantageously substituted for a thick plate of the 
 same material as giving the very same result. 
 
 38 
 
RADIATION AND ABSORPTION. 
 
 Now if we suppose the radiation of a particle in the interior 
 to be as intense as that of a particle at the surface, why, it may 
 be asked (since rock salt is extremely diathermanous), does not 
 a piece of double thickness give nearly a double radiation and 
 so on, the radiation increasing very nearly as the thickness ? 
 
 If we still hold the doctrine of an equal and independent ra- 
 diation from every particle, we are shut up to the conclusion 
 that rock salt must be comparatively opaque to heat radiated 
 by itself, a result which is abundantly confirmed by experiment. 
 
 Thus while the radiation from rock salt .18 inch thick, with- 
 out any screen, is 3.4, with a screen of rock salt .18 inch thick 
 it becomes 1.1. 
 
 If, therefore, we have a piece of rock salt of double the 
 thickness, or .36 inch thick, we should expect that the radia- 
 tion from it would be = 3.4 + 1.1 = 4. 5. It is, in fact, 4.3. The 
 difference (0.2) being within the limit of error of observation. 
 
 In rock salt, therefore, we may suppose each particle to have 
 an independent radiation of its own, unaffected by its distance 
 from the surface. 
 
 18. We see, therefore, that the opacity of rock salt with re- 
 gard to heat radiated by itself, is a consequent of the admis- 
 sion, that the radiation from rock salt does not increase so 
 rapidly as the thickness increases ; ar.d this again results from 
 the fact, that the absorption of heat by a plate of rock salt 
 does not increase so rapidly as the thickness increases. This, 
 again, is due to the fact, that the first part of the plate of rock 
 salt sifts the heat so that it is more easily transmitted by the 
 second part; and this confirms the result arrived at by Professor 
 Forbes, who, finding that rock salt stopped heat of lower tem- 
 perature rather more readily than heat of high temperature, 
 concluded that there are a few rays for which rock salt is 
 opaque.* 
 
 * To take a numerical example, let us suppose the heat from a single 
 plate of rock salt to be = 1, then the heat from a plate four times the 
 thickness, or (which is the same thing) the heat from four single plates, 
 one behind another, should be nearly four times as much or = 4 (if we 
 suppose the heat from each of these four plates to be readily passed by 
 the plates between it and the pile), but the heat from the four-fold 
 plates, instead of being four times as much, is not double of the heat 
 
 39 
 
MEMOIRS ON 
 
 We conclude, therefore, that every body which sifts heat in 
 its passage through its substance is more opaque with regard 
 to heat radiated by a thin slice of its own substance, than it is 
 with regard to ordinary heat. 
 
 19. This conclusion may be also stated thus: We have before 
 proved (Art. 12) that the radiation of a thin slice of any sub- 
 stance equals its absorption; we now add that the heat radiated 
 is the same as that absorbed, with regard to quality as well 
 as quantity. 
 
 For this expresses the fact, that substances which sift heat 
 are likewise opaque with respect to heat radiated by themselves. 
 For, since the heat which they absorb is manifestly that kind 
 of heat for which they are opaque, if the description of heat 
 radiated is the same as that absorbed, then they also will be 
 opaque with respect to heat radiated by themselves. Consid- 
 ering, therefore, the heat of any temperature to consist of 
 heterogeneous rays, we may state the law thus : " The absorp- 
 tion of a plate equals its radiation, and that for every descrip- 
 tion of heat. " 
 
 20. A more rigid demonstration may be given thus: Let 
 AB, and EC be two contiguous, equal, and similar plates in the 
 interior of a substance of indefinite extent, kept nt a uniform 
 temperature. The accumulated radiation from D 
 
 the interior impinges on the upper surface of 
 
 the upper plate; let us take that portion of it - A! , 
 
 which falls on the particle A, in the direction B| 
 
 DA. This ray, in passing from A to B, will have | 
 
 been partly absorbed by the substance between 
 A and B, but the radiation of the upper plate being equal to its 
 absorption (since its temperature remains the same), the ray will 
 have been just as much recruited by the united radiation of the 
 
 from the single plate ; hence, the heat from any of the interior plates of 
 the compound plate is passed with great loss, by the plates between it 
 and the pile. Now, since the absorption of a plate equals its radiation, 
 the reason why the four-fold plate scarcely radiates twice so much as 
 the single one is, that it scarcely absorbs twice as much; and this again 
 is due to the fact, that the heat after it has passed the first plate of the 
 four-fold plate has become sifted, and passes with little diminution of 
 intensity through the other three plates. 
 
 40 
 
RADIATION AND ABSORPTION. 
 
 particles between A and B, as it was diminished in intensity by 
 their absorption. It will therefore reach B with the same 
 intensity it had at A. But the quality of the ray at B will also 
 be the same as its quality at A. For, if it were different, then 
 either a greater or less proportion would be absorbed in its pas- 
 sage from B to C, than was absorbed of the equally intense ray 
 at A, in its passage between A and B. The amount of heat ab- 
 sorbed by the particles between B and would therefore be 
 different from that absorbed by the particles between A and B. 
 But this can not be; for, on the hypothesis of an equal and in- 
 dependent radiation of each particle, the radiation of the parti- 
 cles between B and C is equal to that of the particles between A 
 and B, and their absorption equals their radiation. Hence the 
 radiation impinging on B, in the direction of DB, must be 
 equal in quality as well as in quantity to that impinging upon 
 A; and, consequently, the radiation of the particles between 
 A and B must be equal to their absorption, as regards quality 
 as well as quantity; that is, this equality between the radiation 
 and absorption must hold for every individual description of 
 heat. 
 
 21. The following experiment illustrates this law: 
 
 The quantity of heat radiated from crown glass screen, 
 .05 inch thick, which passes through a crown glass 
 screen .05 inch thick, . . . . , = 0.95 
 
 While that from plate glass .3 inch thick, covered with 
 blackened paper (the blackened paper being next the 
 pile), which passes through the same screen. .. = 1.95 
 
 But if the surface of crown glass .05 inch thick, farthest 
 from the pile, be coated with paper, the polished sur- 
 face being next the pile, then the amount which passes 
 the screen, = 1.85 
 
 And if three plates, the one behind the other, of crown 
 glass, each .05 inch thick, be used as the source of 
 heat, the surface farthest from the pile of the farthest 
 off plate only being covered with paper, the amount 
 of radiation which passes the screen, = 1.95 
 
 Such a plate of glass or series of plates, therefore, by having 
 the farthest off surface coated with paper, gives out heat 
 
 41 
 
MEMOIRS ON 
 
 similar to that from paper or lampblack; the reason being, 
 that the heat from the paper on the farthest off surface is as 
 much recruited as it is absorbed by its passage through the 
 glass, both as regards quantity and quality; so that the radia- 
 tion which falls upon the cone is virtually that from paper or 
 lampblack. 
 
 23. There is little difficulty in explaining why heat from a 
 thick plate of any substance should pass more readily through 
 a screen of the same substance than that from a thin plate. 
 The reason is, that the heat from the interior of the thick 
 substance, having been sifted in its passage, is, therefore, now 
 more easily able to pass through a screen of the same substance. 
 
 23. We see also why, generally speaking, bodies at the same 
 temperature radiate the same quality of heat; let us, for in- 
 stance, take a tolerably thick plate of glass, and a surface of 
 lampblack, and compare them together. Since the plate of 
 glass absorbs nearly all the rays that fall upon it, it will radiate 
 nearly as much as lampblack; and since the quality of the 
 radiated is the same as the quality of the absorbed heat, its 
 radiated heat will very nearly have the same quality as that 
 which is radiated by lampblack. 
 
 Tlie influence of the Reflective and Refractive Powers of Bod- 
 ies on their Radiation considered. 
 
 24. Hitherto in these investigations no account has been taken 
 of reflection at the surfaces of the plates, because 1st, those rays 
 only were considered which passed perpendicularly, or nearly so, 
 through such plates ; and, 2d, because the indexes of the re- 
 fraction for the substances experimented on were not very high. 
 
 But for rays passing obliquely through such media, or for 
 rays passing in any direction into substances such as metals, we 
 must take account of reflection from the surface which will in- 
 fluenoe materially our results. 
 
 Thus, no substance is so opaque for heat as metals, but yet 
 only a small portion of the heat falling on them is absorbed, 
 the rest being reflected back ; consequently for such bodies the 
 radiation (which must be equal to the absorption) is very small. 
 
 It is also desirable, for another reason, to investigate the 
 laws according to which the reflective nature of the surface of 
 
 42 
 
RADIATION AND ABSORPTION. 
 
 a body influences its radiation. For the question arises, is the 
 law of an equal and independent radiation of each particle of a 
 body theoretically consistent with equilibrium of temperature ? 
 That is, suppose we have an irregularly-shaped inclosure walled 
 round with a variety of substances, and each particle of each 
 substance radiating into the inclosure, from the sides of which 
 it is reflected many times backwards and forwards before it is 
 finally absorbed ; this being the case, will the law of equal and 
 independent radiation, and those of reflection and refraction, 
 so fit with one another, that every particle of the walls of the 
 inclosure shall absorb precisely as much heat as it radiates ? 
 It will be endeavored to show that these laws are so adapted to 
 each other ; and I shall select for the proof a definite form and 
 description of inclosure, the conclusions arrived at rendering it 
 highly probable (if not rigidly demonstrating) that the same 
 adaptation will hold good for every inclosure, however irregular 
 or varied. 
 
 For these reasons, I shall now endeavor to investigate what 
 connection the radiation of a substance has with the reflective 
 power of its surface ; and in doing so (in order to abstract 
 entirely from the effects produced by the variable thickness of 
 the radiating plate), I shall suppose it to be of indefinite thick- 
 ness ; so that all the heat which enters it is absorbed. Our 
 consideration is, therefore, limited to the effects of one surface. 
 
 25. Let AB be a portion 
 
 Lam p B!ack of the line of section of an 
 
 indefinitely extended sur- 
 face with the plane of the 
 paper supposed perpendicu- 
 lar to the surface, and let 
 this surface belong to a 
 body (M) of indefinite 
 thickness downwards ; also 
 let there be an indefinitely 
 extended surface of lamp- 
 black parallel to this lower surface, as in the figure. Lastly, 
 let the whole be kept at uniform temperature. In order that 
 the body (M) may be maintained at this temperature, it is 
 necessary that the heat which has left the surface AB, having 
 
 43 
 
MEMOIRS ON 
 
 come from the interior of (M), in the direction contaiued*in 
 any very small angle CAD, shall be replaced by an equal quantity 
 of heat entering the surface AB, to diverge into the interior 
 through the same small angle CAD. For, by this arrangement 
 it is clear the particles in CAD get back as much heat as they 
 give out. 
 
 Part of the heat, no doubt, which fell on A in any direction 
 DA, would be reflected back in the direction AD', making the 
 same angle with the surface as AD ; but this loss would be 
 made up for by part of the heat falling upon A, in the direction 
 D'A, being also reflected back in the direction AD. 
 
 The internal reflection at A being compensated for, if the 
 heat that really leaves the medium be also compensated for, 
 then as much heat will be passing at A in the direction AD as 
 will be passing in the direction DA. It will be the same, 
 therefore, as if the body, instead of having a surface at A, 
 were indefinitely extended upwards from A, as well as down- 
 ward ; in which case, as has been already shown (Art. 20), there 
 will be equilibrium of temperature, provided that the radiation 
 of a particle is equal to its absorption, and that for every des- 
 cription of heat. 
 
 Before proceeding further with this investigation, it will be 
 necessary to establish some preliminary propositions. 
 
 26. 1st Preliminary Proposition. 
 
 The heat which falls on the line AB in the directions con- 
 tained in the very small angle CAD, is 
 the same which falls on AE, perpendic- 
 ular, EB, through the same very small 
 angle. For every ray which fell on AB 
 passed through AE, with the exception 
 of a small quantity which passed through 
 B EF ; but the angle EBF being very 
 
 small, EF is very small compared with AE, and consequently 
 the heat falling on EF may be neglected in comparison with 
 that falling on AE. 
 
 It is clear, also, that the heat falling on AB is proportional to 
 AB, and to the size of the very small angle CAD. 
 
 The above will still hold if, instead of the substance of which 
 AB is the surface being supposed below AB, and the rays fall- 
 
 44 
 
RADIATION AND ABSORPTION. 
 
 ing on it through a vacuum, we suppose a substance to be 
 indefinitely extended upward and the rays to originate in the 
 substance itself, and fall on its surface AB. 
 
 For, although any ray GE, which falls on E, will be partly 
 absorbed between E and B, it will be as much recruited by the 
 united radiation of the particles between E and B as it was 
 absorbed ; so far, indeed, as regards quality and intensity (from 
 what has been already proved, Art. 20), we may consider such 
 a ray to be traversing a vacuum, it being recruited just in pro- 
 portion as it is absorbed. 
 
 It is evident, also, that in this case the quantity of heat fall- 
 ing on AB will be proportional to the size of the very small 
 angle CAD. 
 
 27. 2d Proposition. 
 
 First case. If AB represent a surface (the substance being 
 
 below AB), and OF a surface of lamp- c p G F 
 
 black indefinitely extended (as in Art. 
 25), from which rays fall on AB through 
 a small angle CAD ; then, if AE be 
 drawn perpendicular to GB, the heat 
 that falls on AB will = a const. X AE, 
 whatever be the value of the angle CAB. 
 
 For, since the angle CAD is exceedingly small, CD may be 
 considered very small in comparison with CF or CG ; therefore 
 the heat which impinges on AB through the angle CAD may 
 be taken to be that which radiates from CG in direction between 
 CA and DA; but since the radiative power of lampblack in 
 any direction varies as the sine of the angle which that direction 
 makes with the surface, this will = const. X AE. Hence, if 
 R X CAD be the quantity of heat which falls on AB, when AB 
 is perpendicular to GB, that which falls on it when GB makes 
 any angle GBA with AB. will be R X CAD sin GBA. 
 
 If i denote the angle which GB makes with the perpendicu- 
 lar to AB, then the heat impinging on AB will be R cos i 
 X CAD. 
 
 2d case. If the substance be above AB, and the rays falling 
 on AB originate in the substance, the same formula will hold, 
 for it has been shown, in Prop. 1st, that in this case, the heat 
 falling on AB through the small angle CAD = that which falls 
 
 45 
 
MEMOIRS ON 
 
 on AE through the same small angle; but, since the radiation 
 from the interior of the substance is the same in all directions 
 (each particle radiating independently and equally in all direc- 
 tions), the amount falling on AE will not be aifected by the 
 angle which AE makes with the surface; hence the heat falling 
 on AB = const. X AE = const. X sin GBA. 
 
 If R' X CAD = quantity which falls on AB when AB is per- 
 pendicular to GB, that which falls on it when GB makes any 
 angle GBA with AB, will be R' X CAD sin GBA ; also the 
 expression corresponding to R cos i' x CAD will be R' cos i' 
 XCAD. 
 
 28. 3d Proposition. Let a ray strike the surface of a me- 
 dium, at an angle of incidence = i; and another ray at an angle 
 of incidence i + 6 i, it is required to find the difference between 
 the two angles of refraction. 
 
 Let p be the index of refraction, then, 
 
 sin i== fj. sin i' 
 
 Hence, 6 (sin i) = p 6 (sin if) 
 
 cos i 6 i = ft cos i' 6 i' 
 
 TT ., cos i 
 
 Hence, 6 ^ - r,s i 
 
 29. I shall also make the following supposition with regard 
 to the laws of reflection and refraction. 
 
 1st. That if Q represent the quantity of heat falling on the 
 surface of a medium in any direction CA, and 
 0Q be the quantity reflected, then (1 a) Q is the 
 quantity of heat refracted into the medium in 
 the direction AC 7 . This follows from the law of 
 the conservation of vis viva. 
 
 2d. That if the same heat Q originate in the 
 Ic 1 medium, and strike A in the direction C'A, 
 the quantity reflected back into the medium will be #Q, and 
 the quantity refracted out in the direction AC will be (1 a) Q. 
 
 30. These preliminary propositions being established, and 
 suppositions made, let us suppose that heat from the surface of 
 lampblack strikes the surface AB of the indefinitely thick me- 
 dium (Fig. Art. 25) through a small angle 6i (i being the angle 
 of incidence), by Prop. 2d. the Quantity of this heat will 
 
 46 
 
RADIATION AND ABSORPTION. 
 
 be R cos idi; while the part of it which enters the substance 
 we shall call (1 a) R cos i 6 i. These rays will diverge in the 
 
 ff)Q -1 
 
 substance through an angle 6 i'= ^ r 6 i (Prop. 3). 
 
 p COS I 
 
 But the quantity of heat that falls on AB from the interior 
 through this angle will be 
 
 R' cos idi' = R' cos i' - u c * s \, *i = ~- cos iti, 
 
 and the portion of this which leaves the medium will be 
 (1-a) R' cos ;' di 
 
 * 
 
 Equating this with (I a) R cos 161, which enters the me- 
 
 R' 
 
 dium, we have = R or R '= /" R. With this supposition, 
 
 /* 
 
 therefore, the law of an equal and independent radiation of 
 each particle will give us equilibrium of temperature in the 
 particular case under consideration. Had R' been a function 
 of i', it would have shown that the law of an equal an inde- 
 pendent radiation was inconsistent with equilibrium of tem- 
 perature. 
 
 31. Only part, however, of the heat from the lampblack 
 falling on AB entered into the medium, a portion of it = a R 
 cos i 6 i being reflected back to the lampblack, hence the total 
 quantity of heat radiated and reflected which leaves the surface 
 AB through the small angle di will be = R cos i 6 i, the same as 
 if the substance had been lampblack, the only difference being, 
 that, in the case of lampblack, all this heat is radiated, 
 whereas in other substances only part is radiated, the remainder 
 being reflected heat. 
 
 32. Although we have considered only one particular case, 
 yet this is quite sufficient to make the general principle plain. 
 Let us suppose we have an enclosure whose walls are of any 
 shape, or any variety of substances (all at a uniform temper- 
 ature), the normal or statical condition will be, that the heat 
 radiated and reflected together, which leaves any portion of the 
 surface, shall be equal to the radiated heat which would have 
 left that same portion of the surface, if it had been composed 
 
 47 
 
MEMOIRS ON 
 
 of lampblack. And, indeed, we may see, from what has been 
 already proved, that should such a state of things only once 
 take place, it would always remain, there being no disposition 
 to alter it. 
 
 Let us suppose, for instance, that the walls of this enclosure 
 were of polished metal, then only a very small quantity of heat 
 would be radiated ; but this heat would be bandied backwards 
 and forwards between the surfaces, until the total amount of 
 radiated and reflected heat together became equal to the radia- 
 tion of lampblack.* 
 
 33. The equation R' = //R must necessarily hold for every in- 
 dividual description of heat. We have, therefore, two laws 
 necessary to the equilibrium of temperature 1st, That the 
 absorption of a particle is equal to its radiation, and that for 
 every description of heat ; 2d, That the flow of heat from the 
 interior upon the surface of a substance of indefinite thickness, 
 is proportional caeteris paribus to its index of refraction and 
 that for every description of heat. It will, however, be borne 
 in mind, that the former of these laws has been verified by ex- 
 
 * This will be clearly seen if we consider only those 
 
 rays that are radiated perpendicular to the surface 
 to the case of two parallel plates of polished metal 
 ~~ of the same description radiating to one another. 
 For let r be the common radiation of the point C in direction CD, and 
 of the point D in the direction DC, then since these radiations are 
 bandied backwards and forwards in the directions CD, DC. until they 
 are extinguished, we have the total quantity of heat falling on D in the 
 direction CD (if ar denote the proportion of r reflected after one single 
 reflection) expressed as follows: 
 
 Total heat radi- J ( r+aV+aV+etc, ) = r(l+a+^+a 8 ) 
 
 ated and reflected, P4 + ar +a 8 r+ B r+etc. f = (since a < 1) 
 falling on D, ) ( ) 1 a v 
 
 But 1 a denotes the absorptive power of the metallic surface (all the 
 heat not reflected being absorbed). Hence, since the radiative powers 
 of bodies are proportional to their absorptive powers (Leslie's Inquiry) 
 1 being the absorptive power of lampblack, the perpendicular radiation 
 
 of a lampblack point will be = which is the very same expres- 
 
 1 a 
 
 sion we have obtained for the total heat radiated and reflected together, 
 falling on D, in the same perpendicular direction from the metallic 
 point C. 
 
 48 
 
E AD I ATI ON AND ABSORPTION. 
 
 periment, while the latter is only deduced from a theoretical 
 investigation. It will also be seen, that by increasing the 
 thickness of the radiating plate indefinitely, the radiation be- 
 comes ultimately independent of the diathermancy of the plate 
 and is regulated only by its refractive index. 
 
 34. The connection which we have attempted to trace be- 
 tween the refractive and radiative power of a substance, pre- 
 sumes that those rays which we have been considering, have the 
 power of forming wave lengths with the medium under con- 
 sideration ; that is, of being capable of proper reflection and 
 refraction. 
 
 It may be, however, that glass and other similar substances 
 are so opaque, with respect to most of the rays of heat of low 
 temperature, as to stop them almost entirely at the surface. 
 
 As such rays may, therefore, be conceived to be absorbed 
 within the limit of physical surface of the medium, the cor- 
 responding radiation may be conceived to proceed from this 
 physical surface. To such a case we may perhaps suppose reason- 
 ing similar to that of Fourier (as given by Professor Forbes 
 in the Philosophical Magazine for Feb., 1833,) to be applicable ; 
 the intensity of radiation being therefore proportional to the 
 sine of the angle which the direction makes with the surface. 
 
 35. Let us now see, in conclusion, whether these investiga- 
 tions seern to point out any connection between internal radia- 
 tion and conduction. 
 
 Now, without in the least confirming that these are identical 
 there seern to be two points of similarity between them. 
 
 1st, Since the heat which enters metals is all absorbed at a 
 very small depth, it follows that the flux of radiant heat from 
 within upon the interior of metallic surface is derived from a 
 very small depth. 
 
 Also, if we allow (what it has been endeavored to prove, Art. 
 30) that the flux of heat upon the interior of the surface is pro- 
 portional to the index of refraction, this flux will be greatest in 
 the case of metals which may be supposed to have a very high 
 refractive power ; besides which, it will, as we have seen, be 
 derived from a very small depth. The radiation of a metallic 
 particle is therefore very great. 
 
 Now, if internal radiation be in nny way connected with con- 
 
 49 
 
MEMOIRS ON 
 
 duction, we might expect that good conducting substances 
 should also be good internal radiators of heat, and we see they 
 are so. 
 
 2d, The second bond of similarity is this. It seems to be a 
 law that substances are almost invariably more diathermanous 
 for heat of high temperature than for heat of low ; consequently, 
 at high temperatures, the radiation of a thin plate or particle 
 of a substance will bear a smaller proportion to the total lamp- 
 black radiation of that temperature than at low temperatures. 
 The internal radiations of particles of bodies would therefore 
 diminish at high temperatures (not absolutely, but with respect 
 to the proportion which they would bear to the total radiation 
 of these temperatures). If the same rule holds for metals, and 
 'conduction be connected with internal radiation, we should ex- 
 pect that at high temperatures the conducting power of metals 
 would be less than at low temperatures. Now this has been 
 proved to be the case by Professor Forbes. 
 
 50 
 
RESEARCHES ON RADIANT HEAT. 
 
 SECOND SERIES. 
 
 BY 
 
 BALFOUR STEWART. 
 
 Transactions of the Royal Society of Edinburgh. 
 Vol. XXII, PL I. pp. 5973. April, 1859. 
 
 51 
 
CONTENTS. 
 
 PAGE 
 
 Division of Subject . \ . . . . . , : 53 
 
 Instruments used and Method of Investigation . . .53 
 Effect of Roughening the Surface of a Body upon its Radi- 
 ation . . . . . . . . .53 
 
 Nature of the Heat Radiated by Rock Salt . . .56 
 Radiation of Glass and Mica at high Temperatures ... 59 
 On the Law which Connects the Radiation of a Body ivilh its 
 
 Temperature . . . . . . .s .. .64 
 
 On General Diathermancy . . . . . , .69 
 
 52 
 
VI. RESEARCHES ON RADIANT HEAT. 
 
 SECOND SERIES. 
 
 BY BALFOUR STEWART, M. A. 
 
 COMMUNICATED BY PROFESSOR FORBES. 
 
 (Read April 18th, 1859.) 
 
 Division of Subject. 
 
 1. The first part of this paper describes the following groups 
 of experiments : 
 
 Group I. On the effect which roughening the surface of a 
 
 body produces on its radiation. 
 II. On the nature of that heat which is radiated by 
 
 rock salt at 212 F. . 
 
 III. On the radiation of glass and mica, at high tem- 
 perature. 
 
 The second, or theoretical, portion of the paper, has refer- 
 ence to the law which connects the radiation of a particle with 
 its temperature and to Dulong and Petit's experiments on this 
 subject. 
 
 There is also an addition of a later date than the rest of the 
 paper on General Diathermancy. 
 
 Instruments used, and Method of Investigation. 
 
 2. The instruments used, and the method of using them, 
 were much the same as described in the first series of these re- 
 searches, Art. 3. Should any difference occur in the method of 
 conducting a particular experiment, it will be mentioned when 
 the experiment so performed comes to be described. 
 
 First group of Experiments Described. 
 
 3. This group of experiments has reference to the effect of 
 roughening the surface of a body upon its radiation. This was 
 
 53 
 
MEMOIRS ON 
 
 suggested to the writer by Professor Forbes. The first sub- 
 stance tried was rock salt. 
 
 A. Rock salt. It was found that roughening the surface by 
 means of emery paper, until it became quite dim, had little or 
 no effect in increasing the radiation, as will be seen from the 
 following statement embodying the mean result of three sets of 
 experiments.* 
 
 The pieces used were the middle piece (thickness =.36 inch) 
 and the thickest piece (thickness = -77 inch), described in first 
 series, Art. 6. These pieces were placed at a distance of about 
 four inches from the mouth of the polished brass cone, and in 
 order to increase the effect, no diaphragm was used. They 
 were heated in the boiling-water apparatus already described. 
 With this arrangement 
 
 The thick piece gave, when polished, a deviation of .21.! 
 
 when roughened, 21.8 
 
 The middle piece gave, when polished, a deviation of .13.6 
 when roughened, 13.5 
 
 4. The next point was to ascertain if roughening had any 
 effect upon the quality of heat radiated. 
 
 The following table will show that it does not alter the qual- 
 ity of the heat sensibly; its quality being tested by its capacity 
 of penetrating a screen of rock salt. 
 
 TABLE I. 
 
 SOURCE OF HEAT. 
 
 Percentage of whole 
 
 Heat 
 
 which penetrates a Rock 
 Salt Screen thickness .29 
 
 inch. 
 
 
 
 Rock salt, 
 
 .77 inch thick, 
 
 
 
 
 
 
 
 49 
 
 
 
 
 
 51 
 
 
 Rock salt, 
 
 .36 inch thick, 
 
 
 
 
 
 
 
 42 
 
 
 
 roughened, 
 
 
 43 
 
 
 *In the experiments with roughened surfaces, only one of the sur- 
 faces of the substance was roughened, the other being left polished. 
 In radiation experiments, therefore, the roughened surface was placed 
 next the pile; while in transmission experiments it was placed furthest 
 from the pile. 
 
 54 
 
RADIATION AND ABSORPTION. 
 
 The trifling difference between polished and roughened salt 
 in this table may fairly be attributed to error of experiment. 
 We may therefore conclude, that roughening by emery paper 
 neither alters the quantity nor the quality of the heat radiated 
 by rock salt. 
 
 5. Again, the transmissive power of rock salt for lampblack 
 heat of the temperature 212, is not sensibly altered by rough- 
 ening the surface. This will be seen from the following state- 
 ment : 
 
 The percentage of Lampblack 
 
 heat transmitted was 
 With Screen of Rock salt, thick- 
 ness .36 inch, polished, 77 
 
 With Screen of Rock salt, thick- * 
 
 ness .36 inch, roughened, 77 
 
 This result naturally follows from the previous one, for it 
 has been shown (First Series, Art. 19) that the absorption of a 
 plate equals its radiation and since roughening its surface does 
 not influence the radiation it ought not to influence the absorp- 
 tion. 
 
 6. B. Glass. It is already known that roughening the 
 surface of a plate of glass does not sensibly increase its radia- 
 tion. It is only necessary, therefore, to ascertain whether 
 roughening the surface of a radiating plate of glass alters the 
 capacity of its heat for penetrating a screen of glass. Accord- 
 ingly, a plate of crown glass .05 inch thick, 3.75 inches square 
 being placed before the cone as a screen, and a similar plate 
 roughened, heated in the boiling-water apparatus, being used 
 as the source of heat, and no diaphragm used, 
 
 The deviation was 1.0 
 
 When the source of heat was a similar plate, .10 inch 
 
 thick, the deviation became, 1.5 
 
 And lastly, when the source of heat was a plate 
 
 covered with lampblack, the deviation was, 1.9 
 
 With the same sources of heat, only the glass polished in- 
 stead of being roughened, these numbers were 0.95, 1.45, 
 1.95. From the correspondence between these two sets of re- 
 sults, we may infer that the quality of the heat radiated by 
 glass (at least in so far as transmission through a plate of glass 
 
 55 
 
MEMOIRS ON 
 
 can test it) is not altered by roughening the surface of the 
 glass. 
 
 7. And from all these experiments, we may infer (what has 
 indeed been already remarked by Professor Forbes), that 
 although roughening its surface with sand or emery paper ren- 
 ders a body dim for light yet it still remains specular for heat 
 rays, which, possessing a greater wave length than those of 
 light, are less liable than the latter to be influenced by scratches 
 or furrows. 
 
 Second Group of Experiments Described. 
 
 8. The second group of experiments has reference to 
 the nature of the heat which is radiated by rock salt at 212. 
 Its quality being tested by transmission through 
 
 a. A screen of mica. 
 
 /?. One of mica split by heat. 
 
 7. One of glass. 
 
 9. a. Mica Screen. By the mean of three sets of experi- 
 ments, a mica screen (thickness = .003 inch nearly) passed 
 about 31 per cent of ordinary lampblack heat, while it only 
 passed 18 percent of rock salt heat. Or if we call the proportion 
 of black heat passed by the mica 100, that .of rock salt heat will 
 be 58. 
 
 10. /5. Split Mica Screen. Two sets of experiments agreed 
 in giving twenty per cent as the proportions of lampblack heat 
 of 212, transmitted through a screen of mica split by heat, 
 while the proportion of rock salt heat transmitted by the same 
 screen was only 15^ per cent. These numbers are to one 
 another as 100 to 76. 
 
 11. y. Glass Screen. In order to avoid secondary radiation 
 from the screen, which, in this case, absorbs nearly all the 
 heat, two screens of microscopic glass were used, the one be- 
 hind the other, with an interval between. 
 
 Moreover, as in this case, the proportion of heat transmitted 
 is exceedingly small, the following arrangement was adopted to 
 make it measurable. 
 
 The experiment consisted of four parts, 
 
 1st. The effect of rock salt heat upon the pile without a 
 screen was observed by the ordinary galvanometer. 
 
 56 
 
RADIATION AND ABSORPTION. 
 
 2d. The effect of lampblack heat, also without a screen, 
 was observed by the same galvanometer. 
 
 3d. The wires of the pile were then transferred to a more 
 sensitive galvanometer, and the effect of lampblack heat 
 observed, the glass screen being interposed. 
 
 4th. The sensitive galvanometer and glass screen being re- 
 tained, the effect of rock salt heat was lastly observed. 
 
 By this method of experimenting, it was merely the relation 
 between the diathermancy of the screen for lampblack heat 
 and for rock salt heat that was measured; its absolute diather- 
 mancy for either of these heats not being determined. Two 
 sets of experiments, conducted in this manner, gave the fol- 
 lowing result: 
 
 By the first set, calling the proportion of the whole lamp- 
 black heat which passed the screen 100, that of the rock salt 
 heat which passed the same screen was 54. And by the second 
 set, these numbers were 100 to 60. 
 
 12. As in these experiments with a glass screen the propor- 
 tion of heat passed is very small, great numerical accuracy 
 cannot be looked for and the results obtained are valuable 
 rather as determining the direction and character of a fact, 
 than as measuring the extent to which it holds. 
 
 13. It is already well known that rays of great ref rangibility 
 or small wave length pass through glass and rnica more readily 
 than those of an opposite character. The difficulty with 
 which rock salt heat penetrates these substances as compared 
 with ordinary heat might therefore lead us to infer that the 
 wave length of this heat is greater than that of ordinary lamp- 
 black heat. 
 
 14. If, therefore, the heat radiated by rock salt is of great 
 wave length since (First Series, Art. 19) 'the quality of the 
 heat radiated is the same as that of the heat absorbed, it follows 
 that the heat most absorbed by rock salt must be heat of great 
 wave length; and this derives confirmation from a fact noticed 
 by Professor Forbes, viz., that rock salt passes a somewhat 
 greater proportion of heat of high temperature than of that of 
 low; heat of high temperature possessing a less average wave 
 length. 
 
 15. If we look now to the relative transmission of the two 
 
 57 
 
MEMOIES ON 
 
 descriptions of heat through mica split by heat, we see that 
 the facility of transmission is yet in favor of ordinary heat, but 
 not so strikingly as with a screen of common mica. This will 
 be seen from the following table : 
 
 TABLE II. 
 
 NATURE OF SOURCE. 
 
 Transmission of Or- 
 dinary Heat, at 
 212 F. 
 
 Transmission of 
 Rock salt Heat 
 at 212 F. 
 
 Mica 
 
 100 
 
 58 
 
 Mica split by heat 
 
 100 
 
 76 
 
 
 
 
 Compare this with the following table deduced from the 
 results given by Professor Forbes, in the Fourth Series of his 
 Researches, Art. 9. 
 
 TABLE III. 
 
 NATURE OF SCREEN. 
 
 Transmission of Heat 
 from Blackened Brass 
 at 700 F. 
 
 Transmission of 
 Black Heat 
 at 212 F. 
 
 iSlica 015 incli thick 
 
 100 
 
 52 
 
 
 100 
 
 64 
 
 
 
 
 From a comparison of these two tables, it will be seen that, 
 as tested by the two substances, mica and mica split by heat, 
 rock salt heat at 212 F bears to ordinary heat of that temper- 
 ature a relation similar to that which ordinary heat at 212 F 
 bears to heat at 700 F; that is to say, that just as heat of 212 
 F has a greater wave length than heat of 700 F, so rock salt 
 heat at 212 F has a greater wave length than ordinary heat at 
 that temperature. And the surface stoppage produced by 
 splitting the mica,* telling most powerfully upon heat of high 
 temperature, or small wave length, while the stoppage by sub- 
 stance is in the opposite direction, we see how the one effect 
 tends, to a certain extent, to neutralize the other, rendering the 
 proportions of different kinds of heat passed by split mica more 
 nearly alike than those passed by ordinary mica. 
 
 16. All these experiments concur in showing that heat from 
 rock salt possesses very great wave length, and probably heat 
 from a thin plate of this substance, at a low temperature, may 
 
 58 
 
HAD I ATI ON AND ABSORPTION. 
 
 C,E 
 
 be found to possess a greater average wave length than any 
 other description of heat which can be exhibited. 
 
 Third Group of Experiments Described. 
 
 17. I now proceed to describe the third group of experiments, 
 or those on the radiation of glass and mica at high tempera- 
 tures. 
 
 A. Glass. For the experiments on glass, the following 
 apparatus was used: The pile was placed within a box, and 
 surrounded with cotton wadding. The orifice through which 
 radiant heat was admitted into the box consisted of a brass 
 tube AB, blackened in the 
 inside. The diameter of this 
 tube was inch, its length 3 
 inches, and during the 
 greater part of its length it 
 passed through water, con- 
 tained in the chamber CEFD. The side of the box (CAD) next 
 the pile was lined with tin foil. Owing tothesmall divergence 
 of the rays of heat which hud to pass through the narrow tube, 
 the cone might be placed several inches to the left of A without 
 sensibly weakening the effect, and, on the other hand, the 
 source of heat might be placed some distance to the right of D 
 without ceasing to fill up the field of view. By this means, the 
 distance between the pile and the source of heat being consider- 
 able, no currents of heated air from the latter would be able to 
 reach the former; and as the tube AB was blackened in the in- 
 side, and passed through water, reflection and secondary radia- 
 tion would both be avoided. By means of a lid fitting on the 
 tube at A the aperture might be diminished at pleasure. The 
 pile was connected with a very sensitive galvanometer. 
 
 When glass at a high temperature was the source of heat, 
 a very small aperture was sufficient, and thus the advantage was 
 gained of having the whole field covered with glass, all at a 
 high temperature, which could not have been the case had the 
 aperture been large. 
 
 Slips of glass about inch broad were used, and were set ver- 
 tically, just touching a gas flame from a Bunsen's burner. 
 When two slips one behind the other were used, the one 
 
 59 
 
MEMOIRS ON 
 
 just touched that portion of the flame next the pile, and the 
 other that portion furthest from it. A cross section of the 
 arrangement is shown on page 59. 
 
 A single slip of glass about .1 inch thick thus heated gave a 
 deviation of 16. 5, while two slips, the one behind the other, 
 gave 18. 5. When the slips were .05 inch thick these numbers 
 were 29 M and36.3. 
 
 18. From these experiments we may conclude, that at a 
 high temperature, 700 or 800 F, the radiation from two 
 plates of glass, one behind the other, is sensibly greater than 
 that from one a result which does not hold for glass at 212. 
 Or the fact may be stated thus: 
 
 The radiation of a single plate of glass bears a smaller pro- 
 portion to the total radiation of 700 than at 212. 
 
 19. It was next tried whether the capacity of a glass screen 
 for passing heat from blackened copper at 700 was altered by 
 its being heated. 
 
 In order to ascertain this, blackened copper at 700 F was 
 placed behind a slip of glass, and the amount of heat from the 
 copper which passed the glass was observed. 
 
 Firstly, When the glass was cold. 
 
 Secondly, When it was heated to between 700 and 800 F. 
 
 20. As in these experiments the considerably fluctuating 
 temperature of the source of heat causes a somewhat large 
 difference between successive observation, and renders necessary 
 a great number in order to arrive at a correct result, it was 
 thought desirable, instead of using momentary deviations, to 
 employ permanent ones. This was done with complete success; 
 the application of the heated copper, or its removal, causing an 
 unmistakable alteration of the position of the needle. 
 
 21. The experiment was then varied in the following man- 
 ner: The needle was kept permanently deviated by the heated 
 glass, and the momentary swing due to the application or with- 
 drawal of the heated copper was noticed, and was compared 
 with that occasioned by the hot copper when the glass was cold 
 and the needle at zero. 
 
 22. These experiments, which are not, perhaps, individually 
 susceptible of very great exactness, agreed, however, in render- 
 ing it probable that glass, owing to its being heated up to 
 
 60 
 
RADIATION AND ABSORPTION. 
 
 about 700 F. does not change its diathermancy for heat of 
 700 F. 
 
 23. B. Mica. The experiments on mica were made with 
 the ordinary galvanometer. A piece of mica, thickness about 
 .008 of an inch, being used as a screen, and a diaphragm, .65 of 
 an inch square, at the distance of three inches from the mouth 
 of the pile, being employed, the mean of two sets of experiments 
 made the proportion of black heat of 200 F passed by the 
 mica to be 13 per cent. Placing an additional diaphragm of 
 the same size 3| inches beyond the first, and using as a source the 
 temperature of 400 F, the mean of two sets of experiments 
 made the proportion of heat passed by the mica screen to be 21 
 per cent. 
 
 In order to test whether the apparently greater diathermancy 
 of the screen for heat of 400 F was owing to the difference in 
 the nature of the heat, or to the heat at 400 F striking the 
 screen more nearly at a perpendicular incidence, and thus 
 experiencing less reflection as well as passing through a smaller 
 thickness of mica, an experiment was made on heat at 200 F, 
 with the arrangement and distance used for heat of 400 F, 
 which seemed to show that this difference of distance does not 
 affect sensibly the proportion transmitted. We may therefore 
 conclude that the difference in proportions transmitted is ow- 
 ing to a difference of quality in the two descriptions of heat. 
 
 24. A cast-iron box was next constructed having this same 
 plate of mica inserted as a window, so that, while one side of 
 the box consisted merely of a moderately thin plate of cast- 
 iron, the other, except round the edges, was composed of mica. 
 The cast-iron side was then blackened, and the box filled with 
 mercury. A thermometer inserted in the box measures the 
 temperature. At 200 F, with the usual diaphragm three inches 
 from the mouth of the pile, the proportion between the radia- 
 tion of the blackened side and the mica window was, by the 
 mean of three sets of experiments, as 100 to 87.8, while at 
 400 F, with the usual arrangement of two diaphragms, the 
 same proportion was 100 : 84.1. 
 
 25. Let us endeavor to discuss these results. The radiation 
 from the mica window consists of three portions : 
 
 a. The proper radiation of the mica plate. 
 
 61 
 
MEMOIRS ON 
 
 /?. That portion of the radiation of the mercury which has 
 been able to penetrate the mica plate. 
 
 y. That portion of the radiation of the mica which, strik- 
 ing upon the mercury, is reflected back by it and has pene- 
 trated the mica plate. 
 
 Now, supposing there was no mercury behind the mica, and 
 that rnica between 200 and 400 does not alter its diathermancy 
 as a screen in any respect, let us inquire what ought to have 
 been the result obtained. Then, since the radiation of a thin 
 plate equals its absorption (First Series, Art. 19), and since 
 the absorption of this mica plate was 8 per cent less at 400 
 than at 200 (Art. 23), its proportional radiation ought to be 
 8 per cent less at 400 than at 200. 
 
 26. But the effect of the mercury behind the mica mani- 
 festly tends to diminish this difference. For we know that 
 the mica (Art. 23) passes 8 per cent more of lampblack heat at 
 400 than at 200 ; it will therefore no doubt pass a greater pro- 
 portion of the heat from the mercury behind at 400 than at 
 200. But we have reason to think that the radiation of mer- 
 cury is nearly %' of that of lampblack.* Consequently we 
 may suppose that owing to this action of the mercury, the pro- 
 portional radiation of the mica window at 400 is increased 
 about y of 8, that is, 2 percent. This reduces therefore the 
 difference from 8 to 6 per cent. 
 
 27. But the mercury acts in another manner also in the 
 same direction. Had mercury been a perfect reflector, its 
 presence behind the mica would have been equivalent to doub- 
 ling the thickness of the plate ; for it would have sent the 
 whole radiation of the mica that fell upon it back through the 
 mica. But the difference between the proportional radiation at 
 200 and at 400 is less for a thick plate of mica than for a thin 
 one (indeed, when the plate is indefinitely thick, this difference 
 vanishes, and the proportional radiation is the same at all tem- 
 peratures); this action of the mercury, therefore, would tend 
 still further to diminish the already diminished difference of 
 
 * Provostaye and Desains estimated the proportion of heat reflected 
 by mercury to be 77 per cent. The radiation, being complementary to 
 this, may be reckoned to be 23 per cent nearly. 
 
 62 
 
RADIATION AND ABSORPTION. 
 
 6 per cent. The amount of this action cannot be far from 
 3 per cent, * in which case the 6 per cent would be reduced 
 to 4 per cent ; now 3.7, or, in round numbers, 4 per cent is the 
 observed difference between the proportional radiation of the 
 mica window at the temperatures 200 and 400. 
 
 28. We see thus that the behavior of the mica as a screen, 
 compared with its behavior as a radiator, agrees very well with 
 the supposition which we made in Art. 25; viz., the mica between 
 the temperatures of 200 and 400 does not alter its diather- 
 mancy in any respect; a result similar to that which we have 
 already deduced for glass (Art. 22) between somewhat wider 
 limits. 
 
 29. Experiments with the same object in view, but of a 
 more direct description, were made upon mica, similar to those 
 already described as having been made upon glass, that is, it 
 was endeavored to ascertain whether hot mica passed as much 
 heat from hot copper as cold mica; but in these experiments 
 the fluctuation was very considerable, probably owing to the 
 small body of the mica. Nevertheless, they confirmed the 
 results above obtained ; viz., that mica does not change its 
 diathermancy in any respect owing to its being heated. 
 
 30. We may therefore conclude that this property (at least 
 within moderate limits) is common both to glass and to mica, 
 and indeed, a priori, there appears no good reason why the mere 
 heating of a substance should change its diathermancy. It is 
 the theoretical importance of this property that has induced me 
 to take pains to verify experimentally and its importance will 
 be seen from some of the consequences which follow its estab- 
 lishment, which I shall now proceed to discuss. 
 
 * It would have been better to have tested, by means of a direct exper- 
 iment, to what extent the difference between the proportional absorp- 
 tion and radiation of mica at 200 F and at 400 F would have been 
 diminished by doubling the thickness of the plate; but unfortunately 
 the plate of mica was so much cut up by being used as a window, as to 
 be unfit for being formed into a double screen. 
 
 We see, however, from Art. 37, that while the difference between the 
 proportional radiation of a plate of glass (thickness imm) at 100 C and 
 and 390 C is 9 per cent, the same difference for a plate of double the 
 thickness is only 7 per cent, or 2 per cent less. We may, therefore, with- 
 out much risk of error, adopt this difference of 2 per cent for mica un- 
 der experiment. 
 
 63 
 
MEMOIRS ON 
 
 On the Law ivhich Connects the Radiation of a Body with its 
 Temperature. 
 
 31. The experiments of Dulong and Petit upon the cooling of 
 two thermometers, one naked, and the other covered with silver, 
 seemed to show that the proportion between the radiations of 
 these two substances was the same at the different temperatures 
 of experiment. 
 
 Now I have endeavored to prove in these researches 1st, 
 That the radiation of a thin plate at any temperature equals its 
 absorption of black heat of that temperature. 2nd, That the 
 diathermancy of glass and mica (and probably of other 
 substances) is not altered by heating the substances. Again, it 
 is well known that substances are generally more diathermanous 
 for heat of high, than for heat of low temperature; it follows 
 that the radiation of a thin plate of a substance at a high 
 temperature should bear a less proportion to the total radiation 
 of that temperature than at a low temperature. 
 
 32. While, therefore, it is likely that the radiation of a 
 silvered thermometer (silver leaf being quite opaque for all 
 heat) will bear a constant relation to that of a blackened 
 thermometer at all temperatures, we should expect that for a 
 naked thermometer, just as for the mica window, the radia- 
 tion should bear a somewhat less proportion to the total radia- 
 tion at a high temperature than at a low. We should therefore 
 expect the radiation of the naked thermometer to increase 
 somewhat less rapidly with the temperature than that of the 
 silvered thermometer. Dulong and Petit, nevertheless, 
 found the rate of increase to be the same for both. 
 
 33. Now, in the first place, since glass is exceedingly 
 opaque for heat even of 300 C (the highest temperature ex- 
 perimented on), the difference we are in search of (analogous 
 to the diiference of four per cent in the mica window) would 
 be exceedingly small. But, in the second place, Dulong and 
 Petit had two thermometers, one of which, containing about 
 three pounds of mercury, was used for high, and the other and 
 smaller one for low temperatures. This latter circumstance 
 will complicate or even vitiate their experiments so far as re- 
 gards this peculiar difference we are treating of. 
 
 64 
 
RADIATION AND ABSORPTION. 
 
 34. Although, for these reasons, attaching little importance 
 to Dulong's and Petit's observations, so far as varying diather- 
 mancy is concerned, yet it may be well to state that they show, on 
 the whole, a very small difference in the direction which would 
 indicate a superior diathermancy of the glass at a high tempera- 
 ture. 
 
 35. Assuming it proved that the proportional radiation of a 
 thin plate is less at a high than at a low temperature, I shall 
 now endeavor to show that this difference increases as we 
 diminish the thickness of the plate. To prove this, it is only 
 necessary to exhibit the following table, given by Melloni : 
 
 TABLE IV. 
 
 NUMBER OF RAYS OUT OF 100 PASSED. 
 
 Thickness of 
 Glass Screen. 
 
 Locatelli 
 Lamp. 
 
 Incandes- 
 cent 
 Platinum. 
 
 Black 
 Copper 
 at 390 C. 
 
 Blackened 
 Copper 
 at 100 C. 
 
 mm 
 
 
 
 
 
 0.07 
 
 77 
 
 57 
 
 34 
 
 12 
 
 .5 
 
 54 
 
 37 
 
 12 
 
 1 
 
 1.0 
 
 46 
 
 31 
 
 9 
 
 
 
 2 
 
 41 
 
 25 
 
 7 
 
 
 
 4 
 
 37 
 
 20 
 
 5 
 
 
 
 6 
 
 35 
 
 18 
 
 4 
 
 
 
 8 
 
 33.5 
 
 17 
 
 3.4 
 
 
 
 36. We have already seen that glass does not change its 
 properties with regard to heat, by being raised to the tempera- 
 ture of 390 C ; it is perhaps, however, too much to conclude, 
 that when heated to the temperature of a Locatelli lamp, its 
 properties would remain unchanged. At all events, in order to 
 make use of the whole of the above table, we may suppose the 
 properties of the glass to remain the same throughout, es- 
 pecially as the results we shall deduce from the supposition 
 will be of the same nature as if we had only extended it to glass 
 at 390 C. 
 
 37. Presuming, therefore, that the diathermancy of glass does 
 not alter through its being heated, and allowing 4 per cent as 
 the proportion of the heat striking it reflected from the first 
 surface of a glass screen, and supposing also the same propor- 
 tion of the heat which is able to reach the second surface to be 
 
 65 
 
MEMOIRS ON 
 
 reflected from it, we may, on the principle that the propor- 
 tional radiation of a plate equals its proportional absorption, con- 
 struct the following table : 
 
 TABLE V. 
 
 PROPORTIONAL RADIATION OF GLASS PLATES AT DIFFERENT 
 
 TEMPERATURES, (RADIATION OF LAMPBLACK = 100), 
 
 Thickness of 
 plate. 
 
 Temp, of Lo- 
 catelli Lamp. 
 
 Temp, of lu- 
 candescent 
 Platinum. 
 
 3900 C> 
 
 100 C. 
 
 mm 
 0.07 
 
 16 
 
 37 
 
 61 
 
 84 
 
 .5 
 
 40 
 
 58 
 
 84 
 
 95 
 
 1.0 
 
 48 
 
 64 
 
 87 
 
 96 
 
 2 
 
 53 
 
 70 
 
 89 
 
 96 
 
 4 
 
 58 
 
 75 
 
 91 
 
 .96 
 
 6 
 
 60 
 
 77 
 
 92 
 
 96 
 
 8 
 
 61.5 
 
 78 
 
 92.6 
 
 96 
 
 38. Let us call the proportional radiation of the glass plate 
 at 100 C unity, and we derive the following table. 
 
 TABLE VI. 
 
 PROPORTIONAL RADIATION OF GLASS PLATES AT DIFFERENT 
 TEMPERATURES, THEIR RESPECTIVE PROPORTIONAL RADI- 
 ATIONS AT 100 C. BEING RECKONED UNITY. 
 
 Thickness of 
 Plate. 
 
 100 C. 
 
 390 C. 
 
 Temp, of In- 
 candescent 
 Platinum. 
 
 Temp, of Lo- 
 catelli Lamp. 
 
 mm 
 0.07 
 .5 
 1.0 
 2 
 4 
 6 
 8 
 
 1 
 1 
 1 
 1 
 1 
 1 
 1 
 
 .72 
 .88 
 .91 
 .93 
 .95 
 .96 
 .965 
 
 .44 
 .61 
 .66 
 .73 
 
 .78 
 .80 
 .81 
 
 .19 
 .42 
 .50 
 .55 
 .60 
 .62 
 .64 
 
 39. We see thus that the radiation of thick plates of glass in- 
 creases most rapidly, and that of thin plates least rapidly, as the 
 temperature increases, and we may suppose, that if we could 
 procure a plate of glass of sufficient tenuity, we might (without 
 heating the plate at all), by finding its absorption for heat of 
 
 66 
 
RADIATION AND ABSORPTION. 
 
 different temperatures find its radiation at those temperatures, 
 which (if the plate were thin enough) would give us the law of 
 radiation of a glass particle. This law would not increase nearly 
 so fast with increasing temperatures asDulong and Petit's law ; 
 it may even be that the radiation of glass particles is propor- 
 tional to its absolute temperature. 
 
 40. But all substances (with the exception of black mica 
 and black glass, whose peculiarity may perhaps be otherwise ex- 
 plained) have the same properties as glass with regard to heat ; 
 that is, they are more diathermanous for heat of high than for 
 heat of low temperatures. The radiation of thin plates or 
 particles of all substances will therefore increase less rapidly 
 with temperature than that of black surfaces. It may there- 
 fore be, that the same law of radiation is common to very thin 
 plates or particles of all bodies ; this law (whatever it be) giving 
 in all cases, a less rapid increase of radiation with temperature 
 than is indicated by Dulong and Petit's law. Had, however, 
 the diathermancy of thin plates of different substances in some 
 cases diminished and in others increased for heat of high 
 temperature, the law of radiation of a particle could not have 
 been the same for all bodies. 
 
 The generality of this law of increased diathermancy of all 
 bodies for heat of high temperatures seems, therefore, to me, 
 to argue in favor of the universality of the unknown law of 
 particle radiation which depends upon the former. 
 
 41. What, then, does Dulong and Petit's law express ? 
 The answer is, it expresses the law of radiation of indefinitely 
 thick plates, and we have shown that it increases faster than 
 the law of radiation of a material particle. 
 
 To facilitate the comprehension of this subject as much as 
 possible, I have put it in the following shape. Suppose we 
 have two substances opposite one another, the one having the 
 temperature of 0, and the other of 100, the latter will of 
 course lose heat to the former let us call its velocity 100. 
 Suppose, now, that (the first surface still retaining its tempera- 
 ture of 0) the second has acquired the temperature of 400 ; 
 then we should naturally expect the velocity of cooling to be 
 denoted by 400 ; but by Dulong and Petit's law, it is much 
 greater. The reason of the increase may be thus explained. 
 
 67 
 
MEMOIRS ON 
 
 At the temperature of 100 we may suppose that only the ex- 
 terior row of particles of the body supplied the radiation, the 
 heat from the interior particles being all stopped by the ex- 
 terior ones as the substance is very opaque for heat of 100 ; 
 while at 400 we may imagine that part of the heat from the 
 exterior particles is allowed to pass, thereby swelling up the 
 total radiation to that which it is by Dtilong and Petit's law. 
 
 42. We have thus ascertained 1st, That Dulong and 
 Petit's law is not the law of radiation of a material particle ; 
 and, 2d, That this law increases less rapidly with the tempera- 
 ture than Dulong and Petit's law. But now the question arises, 
 can any method be indicated of ascertaining, experimentally 
 the law of radiation of a material particle ? Now, by con- 
 tinually diminishing the thickness of the plate whose radiation 
 at different temperatures we are ascertaining, we certainly ap- 
 proach nearer and nearer to the desired law, and, by using the 
 method indicated in Art. 37, we may avoid heating this plate 
 at all and thus overcome one source of experimental difficulty. 
 Yet the thinnest plate we can procure of a substance such as 
 glass or mica acts, to all intents, as an indefinitely thick sub- 
 stance for a great many of the rays of heat that is, it stops 
 them all. The change, therefore, of the unknown law of par- 
 ticle radiation into Dulong and Petit's law will to a great 
 extent, have taken place even within this very thin plate ; so 
 that, in order to reach the desired law or even approximate to 
 it, we should have to use much thinner plates than we could pos- 
 sibly procure ; and, even without the necessity of heating the 
 films, the experimental difficulty and labor of such an investi- 
 gation would be very great. 
 
 On the other hand, we may suppose that, since a thin film 
 stops so much heat, a portion may be stopped in the physical 
 surface of the body, and the absorption might thus influence 
 the law of reflection of heat from the surface. The amount 
 of this influence depending on the absorptive nature of 
 the particles, we might be able to measure the absorption, and, 
 consequently, the radiation of the physical surface, that is, of 
 a very thin plate. But, in the first place, the difficulties of 
 such an investigation would be even greater than in the previ- 
 
 08 
 
E A D I A T I N A N D A B S R P T I N . 
 
 ous case ; and, in the second place, the true law of reflection is 
 not yet finally settled. 
 
 I am therefore induced to think that it is nearly hopeless to 
 attempt to ascertain the true law of radiation of a material 
 particle, at least by any method of experimenting depending 
 upon the use of thin plates, or on the change which absorption 
 may be presumed to cause in the amount of heat reflected from 
 the surface of a body. 
 
 Edinburgh, March 22, 1859. 
 
 On General Diathermancy (added 15th June). 
 
 43. Circumstances having occurred which may interfere in 
 the meantime with my further experiments on heat, I annex 
 to this paper an account of some experiments made since the 
 day of reading. These were proposed with the view of ascer- 
 taining whether diathermancy is confined to rock salt or 
 whether bodies partake of this property. If the latter be the 
 case, the reason why we have not hitherto ascertained it to be 
 so is evidently the difficulty of obtaining crystals of many bodies 
 sufficiently large to operate upon ; and if we wish to prove these 
 diathermanous we must do so in a way that does not render nec- 
 essary the use of large crystals. 
 
 44. Now, a body that is transparent for light, forms, when 
 pounded, a white powder or one that reflects a great deal of 
 light. It will be granted that the reason of this is because we 
 have not only the reflection from the outer surfaces of the 
 crystals, but also from many interior surfaces. Now the same 
 remark is applicable to heat. A body that is diathermanous or 
 transparent for heat should, as a powder, be white for heat, or, 
 in other words, reflect it. But (First Series, Art. 31) the re- 
 flection plus the radiation of the body at any temperature 
 equals the lampblack radiation at that temperature. Hence a 
 powdered diathermanous substance ought to radiate less than 
 lampblack. Accordingly, different substances having been 
 pounded into a fine crystalline powder, made into a paste with 
 water, spread on the two sides of parallelopipedons of wood, 
 dried and one of the sides, when dry, rubbed over with lamp- 
 black, the following result was obtained : 
 
 69 
 
MEMOIRS ON 
 TABLE VII. 
 
 RADIATION 
 
 AT 212 
 
 
 NAME OF SUBSTANCE. 
 
 WHITE SIDE. 
 
 BLACK SIDE. 
 
 Table salt 
 
 S3 1 
 
 100 
 
 White su^ar 
 
 98.7 
 
 100 
 
 Alum 
 
 100.0 
 
 100 
 
 Sulphate of potash 
 
 881 
 
 100 
 
 Nitrate of potash . . 
 
 867 
 
 100 
 
 
 
 
 45. Tims we see that table salt being white for heat, the 
 radiation of the white side is less than that of the black side ; 
 and further, white sugar and alum being both nearly black for 
 heat, the radiation of the one side is nearly equal to that of 
 the other. We see, moreover, that sulphate of potash and 
 nitrate of potash, especially the latter, are white for heat, al- 
 though not quite so much so as table salt. May we not there- 
 fore presume that these substances are diathermanous ? There 
 is, moreover, the following method of confirming the testi- 
 mony in favor of the diathermancy of these substances as 
 derived from this experiment. 
 
 46. Table salt being white for heat, part of the reflected 
 heat will be composed of rays which have been reflected 
 from the internal surfaces of crystals. Such rays have there- 
 fore been sifted, having left behind that description of heat 
 which passes with difficulty through rock salt and also (Art. 
 9) through mica. The whole reflected heat from a surface of 
 table salt should therefore be of a nature which passes more 
 easily through mica than ordinary heat, and (First Series, 
 Arts. 31 and 33) since the sum of the reflected and the radi- 
 ated heat is equal both in quantity and quality to that from 
 lampblack, it follows that the radiated heat from table salt 
 (and probably from other substances white for heat) should, in 
 order to make up the average quality, have a somewhat greater 
 difficulty in passing through mica than ordinary lampblack 
 heat. Accordingly, it was found that the diathermancy of a 
 mica screen for heat from table salt was less than that for or- 
 dinary lampblack heat in the proportion of 92 to 100, while 
 it was less for heat from pounded sulphate of potash in the pro- 
 portion of 93 to 100, thus confirming the analogy between 
 
 70 
 
RADIATION AND ABSORPTION. 
 
 rock salt and sulphate of potash. No such difference was ob- 
 served for heat from sugar. 
 
 47. We see also from the above table that the radiation and 
 therefore the absorption of table salt is 83.1 per cent, leav- 
 ing 16.9 per cent for the reflected heat. Now Melloni found 
 that chalk absorbed 56.6 per cent, and consequently reflected 
 43.4 percent, of heat from a Locatelli lamp; and if we sup- 
 pose table salt to be at least as white as chalk for heat of that 
 temperature, we must conclude that table salt is less white for 
 heat of 212, than for heat from a Locatelli lamp, following in 
 this respect the same law as chalk, which, from being nearly 
 black for heat at 212, becomes comparatively white for heat 
 from a Locatelli lamp. There is also little doubt that table 
 salt reflects more than 16.9 per cent of the light that falls upon 
 it. Hence we may conclude generally that powders even of 
 diathermanous bodies are less white for heat of low tempera- 
 ture than for heat of high temperature and for light. 
 
 48. It would also seem, that, although comparing one 
 powder with another, there is no relation between apparent 
 whiteness and whiteness for heat, since it was found that very 
 white surfaces of pounded sugar and alum (the particles com- 
 pressed, not made into a paste with water) reflected little or no 
 heat ; yet, comparing powdered surfaces of the same diather- 
 manous body together, there seems to be some relation between 
 their apparent whiteness and their whiteness for heat, in- 
 sufficient pounding, or any circumstance which diminishes the 
 apparent whiteness, diminishing also its whiteness for heat. 
 
 71 
 
MEMOIRS ON RADIATION AND ABSORPTION. 
 
 BIOGRAPHICAL SKETCH. 
 
 BALFOUR STEWART was born Nov. 1, 1828 at Edinburgh. 
 He studied at the Universities of St. Andrews and Edinburgh, 
 and later entered upon commercial life. His particular taste 
 for physical science soon developed itself, however, and we have 
 in 1858 a couple of his earliest papers. He became associated 
 with Kelland and Forbes at this time and in 1858 contributed 
 his most important work on the extension of Prevost's Theory 
 of Exchanges in radiation. With the elaborate (at that time) 
 facilities at his command he was able to demonstrate the equal- 
 ity of the radiating and absorbing power of every substance. 
 For this and other work he was awarded the Rom ford Medal 
 some years later. In 1859 he was appointed director of the 
 Kew Observatory, where for eleven years he directed the im- 
 portant studies and investigations carried on there. During 
 this period he was seriously injured in an accident from which 
 he never recovered. In 1870 he was appointed to the chair 
 of Physics in Owens College, Manchester, which he occupied 
 until his death Dec. 19, 1887. During this time he issued 
 his well-known texts in Physics. His " Conservation of 
 Energy," " The Unseen Universe" (in conjunction with Tait), 
 his experiments on the viscosity of ether, etc., all illustrate the 
 comprehensiveness of his mind and the originality of his 
 genius. 
 
ON THE RELATION BETWEEN THE 
 
 EMISSIVE AND THE ABSORPTIVE 
 
 POWER OP BODIES FOR 
 
 HEAT AND LIGHT. 
 
 BY 
 
 G. R. KIRCHHOFF. 
 
 Reprinted from " Investigations on the Solar Spectrum and 
 the Spectra of the Chemical Elements," 2d. Edition, Berlin, 
 Ferd. Dummler's Publishing House, 1866, Gesammelte Abhand- 
 lungen, pp. 571-598, Leipzig, 1882. 
 
 73 
 
A 
 
 CONTENTS 
 
 PAGE 
 
 Nature of Heat Rays and Light Rays . . . . 75 
 
 #/#6'& Bodies defined . . . . . . . . 76 
 
 Definitions . . -. . . . .. . . . 77 
 
 Ratio between the Emissive and the Absorptive Poiver . 78 
 Proof of the Law of Emission and Absorption for Black 
 
 Bodies .: 78 
 
 Proof of the Law of Emission and bAsorption for Any 
 
 Body , . 89 
 
 Generalization of the Law of Emission and Absorption . 92 
 
 Some Results of the Law , . ' . ' . . . 94 
 
ON THE RELATION BETWEEN THE 
 
 EMISSIVE AND THE ABSORPTIVE 
 
 POWER OP BODIES FOR 
 
 HEAT AND LIGHT.' 
 
 1 
 
 HEAT rays have the same nature as light rays ; these con- 
 stitute a special class of the former. The invisible heat rays 
 are distinguished from light rays only by the period of vibra- 
 tion or the wave length. All heat rays follow the same laws 
 in their propagation, which are known for light rays. A 
 luminous body in space sends out light rays that are indepen- 
 dent of the bodies on which they fall ; similarly all heat rays 
 which a body sends out are independent of the bodies which 
 form its environment. 
 
 Of the heat rays that are sent out to a body by its surround- 
 ings a part are absorbed, the others are sent on in directions 
 which are varied by reflection and refraction. The rays re- 
 fracted and reflected by it pass off along with those sent out by 
 it, without any mutual disturbance taking place. 
 
 Through the radiations which a body sends out, the quantity 
 of heat which it contains will, according to the law, sustain a 
 loss which is equivalent to the vis viva of those rays and, 
 through the heat rays which it absorbs, a gain which is equiv- 
 alent to the vis viva of the absorbed rays. But in certain cases 
 an exception to this rule may occur, in that the absorption and 
 the radiation produce other changes in the body, as for ex- 
 ample in bodies which are chemically changed by light, and 
 light absorbing media which lose their power of shining 
 
 1 Investigations on the solar spectrum and the spectra of the chem- 
 ical elements, 2d. Edition, Berlin, Ferd. Dummler's publishing house 
 
 1862. 
 
 75 
 
MEMOIRS ON 
 
 through the radiation of the light which they have absorbed. 
 Such cases should be excluded on the assumption that neither by 
 means of the rays which it radiates or absorbs, nor by means of 
 other influences to which it is exposed, does the body possess the 
 power to undergo a change, if its temperature is kept constant by 
 the addition or the subtraction of heat. Under these conditions, 
 according to the law of equivalence of heat and work, the 
 amount of heat which must be transferred to a body in a given 
 time to prevent cooling, which would occur in consequence of 
 its radiation, is equivalent to the vis viva of the emitted rays ; 
 and the amount of heat which must be withdrawn in order to 
 counterbalance the heating from absorption of radiations, is 
 equivalent to the vis viva of the absorbed rays. 
 
 Let a body which satisfies these conditions be surrounded by 
 an enclosure, having the same temperature, through which no 
 heat rays can penetrate, whose temperature is kept constant 
 and which satisfies the same conditions. The body sends out 
 heat rays and is encountered by such heat rays, which, in part, 
 proceed from the enclosure, in part, are thrown back to the 
 same by reflection from it, absorbing a part of them. Its tem- 
 perature must thus remain the same, unless heat is withdrawn 
 from it or communicated to it as follows on the principle from 
 which Carnot's law results. For this reason, the vis viva of 
 the rays, which it sends out in a certain time, must equal the 
 vis viva of the rays which it absorbs in the same time. 
 
 The proof which rests upon this conclusion requires the ac- 
 curate investigation of the rays that travel back and forth be- 
 tween the body and the enclosure. This investigation will be 
 much simplified if we imagine the enclosure to be composed, 
 wholly or in great part, of bodies which, for infinitely small 
 thickness, completely absorb all rays which fall upon them. 
 
 I will call such bodies perfectly black, or more briefly black. 
 A black body, in this sense of the word, must have the same re- 
 fractive index as the medium in which the radiation takes 
 place ; then there will be no reflection at its surface, and all in- 
 cident rays will be wholly absorbed. Thick iodine vapour in 
 contact with air, or pitch in contact with glass, may be treated 
 as black bodies, approximately, but not iodine vapour in con- 
 tact with glass or pitch in contact with air. Next, the radia- 
 
 76 
 
RADIATION AND ABSORPTION. 
 
 tion in empty space will be investigated ; the Mack bodies re- 
 ferred to must therefore have a refracted index which differs 
 only infinitely little from 1. 
 
 The assumption that such black bodies are conceivable forms 
 an important aid in the proof which will be presented here. 
 Further, it will be assumed that perfectly diathermanous 
 bodies are conceivable, that is, such which will absorb none of 
 the incident heat rays of whatever nature these may be, and 
 finally, that a perfect mirror is conceivable, i.e., a body which 
 reflects completely all heat rays. A perfect mirror, like every 
 diathermanous body, can itself send out no rays ; for if it did 
 (confined in an enclosure of like temperature) it would warm 
 this enclosure more and more and cool itself more and more. 
 
 o n 
 
 DEFINITIONS. 
 
 Before a body C, Figure 1, imagine two screens, /Si and Sz placed 
 in which are two openings 1 and 2, whose dimensions are infi- 
 nitely small with respect to their distance 
 apart, and each of which has a center. s * 
 
 Through these openings passes a pencil 
 of rays sent out by the body C. Of this 
 pencil of rays, let us consider the part, 
 whose wave length lies between A and 
 /i-j-rJA, and let this be divided into two n 
 
 polarized components, whose planes of 
 polarization are the planes a and b per- 
 pendicular to each other, passing through 
 the axis of the ray pencil. 
 
 Let E&\ be the intensity of the com- 
 
 ponent polarized in a, or, what is the same thing, the increase, 
 which the vis viva of the ether beyond the screen S% experiences 
 through this component in the unit of time. The quantity 
 E is called the emissive power of the body C. 
 
 Conversely, upon the body C there falls through the open- 
 ings 2 and 1 a pencil of rays having the wave length A, polar- 
 ized in the plane a; of this, the body absorbs a part while it 
 reflects or transmits the remainder ; let the ratio of the inten- 
 
MEMOIRS ON 
 
 sity of the absorbed rays to the incident rays be A and let this 
 be called the absorptive power of the body C. The quantities 
 ^and A depend upon the nature of the condition of the body 
 6', besides also upon the form and position of the openings 1 
 and 2, the wave length A and the direction of the plane a. 
 
 3. 
 
 Under these conditions the following law holds : The ratio be- 
 tween the emissive and the absorptive power is the same for all 
 bodies at the same temperature. 
 
 This law will be proven, first, for the case where only black 
 bodies are compared with each other, that is, those whose 
 absorptic power = 1 ; i. e., it will be shown that the radiating 
 power of all black bodies is the same at the same temperature. 
 
 The proof of this special law is similar to that of the general 
 law, but simpler ; it will therefore facilitate the understanding 
 of the latter. Moreover, conclusions which are drawn from 
 the special law will be used in the proof of the common law. 
 
 4. 
 
 Proof of the Law 3 for Hack bodies. 
 
 Let (7 be a black body ; let its emissive power, which is com- 
 monly indicated by E, be called e ; it will be proven that e 
 remains unchanged, when C is replaced by any other black 
 body of the same temperature. 
 
 Imagine the body C' enclosed in a black covering, of which 
 the screen 82 forms a part, let the second screen 182, like the 
 first, be made of black substance and let both be united with 
 each other on all sides by black walls, as shown in Figure 2. 
 Suppose the opening 2 to be closed at first by a black surface, 
 which I will call surface 2. The whole system must have the 
 same temperature and the covering be maintained at a constant 
 temperature throughout. According to the statements made 
 in Figure 2, 1, the vis viva of the rays which the body C" sends 
 out in the given time, must then equal the vis viva of the rays, 
 which it absorbs in the same time ; in other words : the sum of 
 the intensities of the rays which it sends out must equal the sum 
 of the intensities of the rays which strike it, since according to 
 
 78 
 
KADI AT ION AND ABSORPTION. 
 
 supposition it completely absorbs the latter. Now suppose the 
 
 surface 2 removed, and the opening closed by a portion of a 
 
 perfectly reflecting spherical surface, placed directly back of it 
 
 and having its center at the middle point of the opening 1. 
 
 Equilibrium of temperature will then exist. There must also 
 
 be equality between the intensity of the rays which the body C 
 
 sends out, and of those incident upon it. Since the body C 
 
 now sends out the same rays as in the cases 
 
 previously considered, it follows that the 
 
 intensities of the rays incident upon C are 
 
 the same in both cases. By the removal of 
 
 surface 2 the rays are withdrawn from C 
 
 which pass through opening 1 ; therefore 
 
 the concave mirror placed at opening 2 
 
 throws just the same rays back to C which 
 
 this sends out itself through the openings 
 
 1 and 2, for the concave mirror forms from 
 
 opening 1 an image which coincides with 
 
 itself. 1 
 
 The law given would therefore be proved 
 
 if all rays of the two pencils compared have the wave length 
 \ and are polarized in the plane a. Both pencils of rays, 
 however, are made up of different components and form the 
 equality of the intensity of the whole pencil. "We may not 
 directly infer the equality of the intensity of corresponding 
 parts. 
 
 The necessary completion of the proof may easily be given 
 when a plate is supposed to exist, having the property of trans- 
 mitting undiminished rays whose wave length lies between a 
 and A + <tt. and whose plane of polarization is parallel to the 
 plane a; but which completely reflects rays of other wave 
 
 1 The diffraction of the rays at the edges of opening 2 may he neg- 
 lected, since the openings 1 and 2 may be assumed infinitely small with 
 respect to their distance and yet infinitely great with respect to the 
 wave length, that is, so great, that the defraction may be inappreciable. 
 
 From this it follows that the intensity of the pencil of rays, which the 
 body C sends ont through openings 1 and 2, equals the intensity of the 
 pencil of rays which the black surface 2 sends out through the opening 
 1. Since this intensity is independent of the form and further character 
 of the black body C, so, likewise, is the former. 
 
 79 
 
MEMOIRS ON 
 
 lengths or of an opposite polarization. If we should imagine 
 the arrangement shown in Figure 2 modified by bringing such 
 a plate before opening 1, then we may immediately arrive at 
 the law to be proved by the treatment employed in respect to 
 this figure. 
 
 The assumption that such a plate is possible is in no wise 
 justified. On the contrary, a plate is possible which, of the 
 rays striking it at the same angle, transmits and reflects them 
 in different degrees according to their wave length and plane 
 of polarization. A plate, which is so thin that the colors of 
 thin films are visible and which is placed obliquely in the path, 
 shows this. 
 
 Such a plate is required for the investigation under consid- 
 eration in order to compare them. Besides this, it is necessary 
 to make such an arrangement that both pencils of rays do not 
 pass through the plate, but are reflected from it at the polariz- 
 ing angle, the plane of reflection coinciding with the plane a. 
 This is advantageous in as much as the rays polarized perpen- 
 dicularly to a need not be considered. Further, the plate must 
 be made of a perfectly diathermanous medium, it will then 
 absorb no rays and send out none. 
 
 * 
 0. 
 
 In the arrangement described in Figure 2 imagine a plate of 
 s 2 the kind described and designated as P, 
 
 brought between the openings 1 and 2 (Fig. 
 3). Let it be so placed that the pencil of 
 rays passing through the openings 1 and 2 is 
 incident at the polarizing angle and the 
 plane of incidence is the plane a. Let the 
 wall which unites the screens Si and 83 be 
 so shaped that the image, which the plate 
 P casts from the opening 2 lies within it ; 
 in the place and of the form of this image 
 imagine an opening which I will call open- 
 ing 3. Let opening 2 be closed by a black 
 surface of the temperature of the whole 
 system, and let opening 3 be closed in the first place by a 
 similar surface, and in the second place by a perfect concave 
 
 80 
 
RADIATION AND ABSORPTION. 
 
 mirror having its center where the plate P forms the image of 
 the middle of opening 1. In both cases the equilibrium of 
 temperature is maintained ; through consideration given in 
 the preceding paragraph, it follows therefore that the sum of 
 the intensities of the rays, which the body C is deprived of 
 through the removal of surface 3 equals the sum of the inten- 
 sities of the rays which are brought to it through the agency 
 of the concave mirror. Let a black screen SB (of the temper- 
 ature of the whole system) be so placed that none of the 
 rays which surface 3 sends out are directly incident upon 
 opening 1. The first sum, then, is the intensity of the rays 
 which proceed from surface 3, and are reflected by plate P and 
 pass through opening 1; they will be designated by Q. The 
 second sum is made up of two parts ; one component comes 
 from C and is : 
 
 00 
 
 d/.er 2 
 
 o 
 
 where r represents a quantity dependent upon the nature of 
 the plate P and the wave length A; the second part consists of 
 rays which have come from a portion of the black wall which 
 unites the screen S l and $ 2 ,have passed through the plate P 
 and been reflected from the concave mirror, and then from the 
 plate P; this part will be designated as R. It is unnecessary 
 to examine further the value of R; it suffices to notice that R, 
 as well as Q, is independent of the nature of C. Between the 
 magnitudes introduced there exists the equation : 
 
 :/eV 2 -f- R = Q 
 
 If we now imagine the body C replaced by another black 
 body of the same temperature, letting e indicate for this what 
 e has represented for the other, there exists the equation 
 
 00 
 
 <T/e'r 2 -f E = Q 
 o 
 
 From this it follows that 
 
 dl. (ee') r' 2 = 
 
 Let us now assume that the index of refraction of the plate P 
 
 81 
 
MEMOIRS ON 
 
 differs but little from unity. From the theory of the colors of 
 thin plates it follows then that we can place 
 
 r = p sin 2 -?- 
 
 A 
 
 where p represents a quantity proportional to the thickness of 
 the plate P, independent of A, and a quantity independent of 
 this thickness. From this follows the deduced equation : 
 
 o 
 
 ' Since this equation must hold for every thickness of the 
 plate P> and hence for every value of p, it follows that for 
 every value A we may conclude that 
 
 To prove this, substitute in that equation for sin* ~- : 
 
 A 
 
 i(cos4 ~ 4 cos 2 ~ _i_Q) 
 
 A A ' ' 
 
 and differentiate twice with respect to p : we then have 
 
 4 -f- cos 2 f- ) = 
 
 In place of A let us introduce a new quantity into the equa- 
 tion ; where 
 
 -?-=a 
 
 A 
 
 and set 
 
 we thus obtain 
 
 00 
 
 daf (a) (cos 2 p a cos p a) =0 
 
 If we consider that when (a) represents any arbitrary func- 
 tion of a 
 
 J /* a 
 
 da? (a) cos 2 pa = I da<j> ( -~- ) cos pa 
 o *J o 
 
 from which we may conclude that if we substitute for c , we 
 may therefore write 
 
 00 a 
 
 d* \f( g- ) 2/ (a)] cos p a = 
 o 
 
 82 
 
RADIATION AND ABSORPTION. 
 
 Multiply this equation by dp cos xp, where x represents an arbi- 
 trary quantity, and integrate it from p = to p = oo. Accord- 
 ing to Fourier's formula which is expressed by the equation 
 
 /* C** TT 
 
 I dpcospx I da^ (a) cos pa = $ ( x ) 
 Jo Jo 2 
 
 we have 
 
 OP /(-I. ) = 2/(a) 
 
 From this it follows that /(a) either vanishes for all values 
 of a, or becomes infinitely great when a approaches zero. When 
 a approaches zero A becomes infinite. If we remember the 
 meaning of /(a) and consider that p is a proper fraction, and 
 that neither e nor e' can become infinite when A increases to 
 infinity, then it is evident that the second case cannot exist 
 and therefore, that for all values of A, e = e'. 
 
 In a similar way we may treat the case when C is not a black 
 body but is an arbitrary one. We shall not assume for the 
 same that it is homogeneous ; partly on its surface, partly in its 
 interior will the rays therefore, which are incident upon it from 
 the black envelope, experience the most manifold modifications. 
 On these grounds, there must be, as a preliminary to the pro- 
 posed proof, a study made of the radiation which takes place 
 between black surfaces of the same temperature, for arbitrary 
 bodies. To this investigation, which depends upon the formula 
 just proved, the following paragraphs are devoted. 
 
 6. 
 
 MUTUAL RADIATIONS OF BLACK SURFACES. 
 If the pencil of rays which the body C sends out through 
 openings 1 and 2 should be partly linearly polarized, the plane 
 of polarization of the polarized portion must rotate when C is 
 rotated around the axis of the pencil. Such a rotation must 
 therefore change the value of e. Since, according to the equa- 
 tion proved, such a change cannot take place, the pencil of 
 rays can have no linearly polarized portion. It can be proved 
 also, that it can have no circularly polarized part. But the 
 proof for this will not be given here. 
 
 We will also grant, without this, that black bodies are con- 
 
 83 
 
MEMOIKS ON 
 
 ceivable in whose structure there is no reason why they should 
 send out in any direction more right handed circularly polarized 
 rays than left handed circularly polarized rays. 
 
 Of this character will the black bodies, concerned in the fur- 
 ther treatment, be assumed ; they send out in all directions 
 unpolarized rays. 
 
 o ty 
 
 The quantity represented by e depends, aside from the tem- 
 perature and wave length, on the form and the relative position 
 of the openings 1 and 2. If w\, w? represent the projections of 
 the openings upon planes perpendicular to the axis of the pen- 
 cil, and if s is called the distance of the openings, then 
 
 where /is a function of the wave length of the temperature 
 only. 
 
 8. 
 
 Since the form of a body C is arbitrary, a surface may be 
 substituted, which exactly fills opening 1 and which I will call 
 surface 1 ; the screen Si may then be imagined removed. Fur- 
 ther the screen $2 may be considered removed if the pencils of 
 rays which e covers, is defined as that which falls from surface 
 1 upon surface 2, which the opening 2 exactly fills. 
 
 9. 
 
 A consequence of the last equation, which immediately fol- 
 lows and which will later be used, is that the value e remains 
 unchanged if we imagine the openings 1 and 2 interchanged. 
 
 We will now establish a law which may be treated as a gen- 
 eralization of the law presented in the last paragraph. 
 
 Between the two black surfaces of the same temperature 1 
 and 2, is placed a body which may refract, reflect, or absorb in 
 any way the rays which one sends to the other. Several pencils 
 of rays may pass from surface 1 to surface 2 ; choose one of 
 these, and consider the part of the one at 1 whose wave length 
 lies between A and A -f eZ/i, and divide this into two components 
 
 84 
 
RADIATION AND ABSORPTION, 
 
 whose planes of polarization are the planes of a\ and b\ which 
 are perpendicular to each other (otherwise arbitrary). Let the 
 part of the first component which enters 2 be divided into two 
 components whose planes of polarization are the planes a 2 and 
 b 2 perpendicular to each other (otherwise arbitrary). Let the 
 intensity of the component polarized in 2 be Kd'k. Of the 
 pencil of rays which passes over the same path as the preceding 
 one, from 2 to 1, let us consider the part at 2 whose wave 
 length lies between A and a + dA, and divide this into two com- 
 ponents polarized in # 2 and Z> 2 . Divide the portion, which 
 reaches 1 from the first component, into two parts whose planes 
 of polarization are a\ and b\. Let the intensity of the com- 
 ponents polarized in a\ be K'd'\. Then 
 
 The proof of this law will be made upon the assumption that 
 the rays under consideration undergo no weakening in their 
 path, and also upon the assumption that refraction and reflec- 
 tion occur without loss, that there is no absorption and that 
 the rays, coming from 1, polarized in a\, reach 2 polarized in 2 , 
 and vice versa. 
 
 Through the middle point of 1 pass a plane perpendicular to 
 the axis of the pencil of rays, either incident or emergent at 
 this point, and imagine in this a right-angled coordinate sys- 
 tem, whose origin is that middle point. Let 
 x\ y\ be coordinates of any point in the plane, 
 Figure 4. At the distance of unity from this 
 plane, imagine a second, parallel to it, and iu 
 this, a coordinate system whose axes are parallel 
 to each of those, and whose origin lies in the 
 axis of the pencil of rays. Let Xs y$ be coordi- 
 
 nates of any point in this plane. In a similar 
 FIG. 4. manner pass through the middle point of 2, a 
 
 plane perpendicular to the axis of the bundle of rays, incident 
 or emergent at this point, and introduce in this, a rectangular 
 system of coordinates whose origin is the middle point men- 
 tioned. Let x 2 y<2 be coordinates of a point in this plane. 
 Finally, at a distance of unity from this plane and parallel to 
 it imagine a fourth, and in it a system of coordinates whose 
 axes are parallel to the axis of x*, y? and whose origin lies in 
 
 85 
 
MEMOIRS ON 
 
 the axis of the pencil of rays. Let x, y be coordinates of any 
 point in this fourth plane. 
 
 From an arbitrary point let a ray pass to any other point 
 (#2, #2) ; let Tb& the time required to pass from one point to 
 the other ; we will suppose it to be a known function of x\, y\, 
 #2, y<2> If the points (x 3 , y 3 ) and (x, y*) He in the path of the 
 ray referred to, (and if for the sake of brevity the velocity of 
 the ray in vacua be taken as unity) the time which the ray re- 
 quires to pass from (x 3 , y 3 ) to (z 4 , y*) will be 
 
 -V 
 
 Assuming the points (#3, 2/3), (#4, y 4 ) given, and the points 
 (a?i, y\), (#2 #2) required, we could find these from the condition 
 that the above expression is a minimum. If we assume that 
 the eight coordinates x\, y\, x 2 , y 2 , x 3 , yz, x, y are infinitely 
 small, the following equations express the condition that the 
 four points (x\, #1), (z 2 , 2/2), (#3, #3), (x, ?/ 4 ) lie in one ray : 
 
 dx l ' dx 2 
 
 dT dT 
 
 Now let (xi,yi) be a point in the projection of surface 1 on the 
 plane Xi, y\ and let dx\ 9 dy\ be an element of this projection in 
 Ayjiich the point Xi, y\ lies and which is infinitely small with 
 respect to the surfaces 1 and 2. Let (x 3 , y 3 ) be a point in a 
 ray proceeding from (x\, y\) to surface 2, dx 3 , dijs, a surface 
 element in which the point (x 3 , y 3 ) lies, of the same order as 
 dx\, dy\. The intensity of the rays of the required wave 
 length and of the given plane of polarization, which, proceed- 
 ing from dx\, dy\, pass through dx 3 , dy 3 , is then according 
 to7; 
 
 d\ I dx\ dy\ dx 3 dy 3 . 
 
 According to the supposition, this amount of rays reaches 
 surface 2 undiminished and forms an element of u quantity des- 
 ignated by Kdh. JTis the definite integral 
 
 86 
 
RADIATION AND ABSOKPTiON. 
 
 / f f f f 
 
 \s \s \s */ 
 
 The integration here with respect to x%, ?/ 3 is to be taken 
 over those values which these quantities have according to the 
 above equations, while x\ and y\ remain constant and x 2 ,i/2 have 
 all the values which correspond to the projections of surface 2 
 upon the plane # 2 , y 2 . The integration with respect to x\, y\ 
 is then to be taken over the projection of surface 1. The 
 double integral 
 
 dx 3 dys so limited, 
 
 y y 
 
 is, however, 
 
 /* /* / 
 
 or from the equations for z 3 , f/ 3 
 
 C r / ^' 2y t) 2 r ^ 2 r _ __ 
 
 / / \^Xj fix 2 by i by 2 '^ '*'" ' x/> / * / " * ^^' 
 
 where the integration is taken over the projections of surface 2 
 Whence 
 
 C C C/ tfT fPT ^T tfT \ 
 
 )dxidyi dx 2 dy% 
 
 where the integration is taken over the projections of surfaces 
 1 and 2. 
 
 If the magnitude of a K' be treated in the same way, remem- 
 bering that a ray requires the same time to pass over a path be- 
 tween two points in either direction, the same expression 
 will be found for K' as for K. Thus, the enunciated law is 
 proved, subject to the limiting conditions under which it will 
 next be proved. This limitation may, however, be immediately 
 disposed of by an observation made by Helmholtz in his 
 "Physiological Optics," p. 169. Helmholtz says here (with 
 somewhat different notation) : " A light ray passes from point 
 1 to point 2 after any number of refractions, reflections, etc. 
 Through 1 suppose two arbitrary planes a\ and #1 passed in the 
 direction of the ray perpendicular to each other, in which its 
 vibrations are supposed to be resolved. Two similar planes, 2 
 and #2 are also passed through the ray at 2. Then the following 
 
 87 
 
MEMOIRS ON 
 
 may be proved : If a quantity i of light polarized in the 
 plane a\ proceeds from 1 in the direction of the ray mentioned 
 and of this, the quantity k of light polarized in the plane a\ 
 reaches 2, so will vice versa the quantity k of light polarized in 
 # 2 reach point 1 if the quantity i of light polarized in a 2 
 proceed from point 2." 1 
 
 Applying this law, and representing by 7 the value of the 
 
 ratio 4 for the two rays which pass in either direction between 
 
 the points (x\, y\) and (# 2 , 3/2), then an expression is obtained for 
 K &s well as for K which differs from that formed only in that 
 now y appears as a factor under the integral sign. 
 
 The equality of ./Tand 7T' exists accordingly when > has a 
 different value for the rays into which one of the pencils com- 
 pared may be divided ; for example, it is unaffected if a part of 
 the pencil is intercepted by a screen. 
 
 Of the same pencils which were compared in the preceding 
 paragraphs, the following law also holds : of the pencil passing 
 from 1 to 2, consider the part at 2 whose wave lengths lie be- 
 tween A and A + dl and resolve this into two components polar- 
 ized in 2 and #2 ; let the intensity of the first component be 
 Hd'k. Of the pencil which passes from 2 to 1, consider at 2 the 
 portion whose wave lengths lie between A and A + d% 9 and resolved 
 this into two components polarized in a 2 and Z 2 . Let the por- 
 tion of the first component reaching point 1 be H'd\. 
 
 Then H=ff'. The proof of this law is the following ; 
 ^and K are to have the same meaning as in the preceding 
 paragraph ; let L and L' be the quantities which arise form K 
 and K'. when plane a\ is interchanged with plane bi. 
 
 1 The law of Helraholtz, as he himself noted, does not hold good 
 when the plane of polarization of a ray undergoes any rotation, such as 
 magnetic force produces according to Faraday's discovery ; therefore, 
 in the following considerations magnetic force must not be considered 
 as present. Helmholtz limited his law also by supposition that light 
 undergoes no change of refrangibility such as occurs in fluorescence ; 
 this limitation is unnecessary in the application of the law, if rays of 
 only a given wave length are regarded. 
 
 88 
 
RADIATION AND ABSORPTION. 
 
 Then L = L' } similarly K = K', further H K+ L, because 
 rays polarized perpendicularly to each other do not interfere, 
 when they are brought back to a common plane of polarization 
 in case they are a part of an unpolarized ray ; and according to 
 6 the surface 1 sends out unpolarized rays. 
 
 Finally H' = K+ L', because two rays, whose planes of polar- 
 ization are perpendicular to each other, do not interfere. 
 From these equations it follows that H= H'. 
 
 Let Fig. 2 have the same meaning as in 4, only let the body 
 C be not a black body but an arbitrary one. Let opening 2 be 
 closed by surface 2. This surface sends out a pencil of rays 
 through opening 1 to the body C, which is partly absorbed by 
 this body, and partly scattered in different directions by reflec- 
 tion and refraction. Of this pencil consider the part between 
 1 and 2 whose wave lengths lie between A and A + d\ and resolve 
 this into two components polarized in plane a and the plane 
 perpendicular to this. Let that part of the first component 
 which escapes absorption by C, and hence strikes the black cov- 
 ering in which the body C is inclosed, be M'd"k. A certain por- 
 tion of the rays which a part of the covering sends out to the 
 body C, fall upon surface 2 through opening 1 ; thus by means 
 of the body C a pencil of rays is produced which passes through 
 opening 1 to the surface 2. Of this, consider the part whose 
 wave lengths lie between A and A + dh and divide it into two 
 components polarized in plane a and the plane perpendicular 
 to it. Let the intensity of the first components be Md\. 
 
 Then M= M '. The truth of this law follows from the propo- 
 sition from the preceding paragraph, if we apply this to all 
 pencils of rays, which surface 2 and all the elements of the 
 black cover surrounding the body C interchange with each 
 other by means of the body C, and then form the sum of the 
 equations so obtained. 
 
 13. 
 
 Proof of the proposition # for any body. 
 Let the arrangement shown in Fig. 3 and described in 5 be 
 
MEM OIKS ON 
 
 taken, only let the body C no longer be a black body, but ar- 
 bitrary. Ill both cases described there, the equilibrium of heat 
 subsists ; then the vis viva which is drawn out from the body 
 G by the removal of the black surface 3, must therefore be 
 equal to the vis viva which is supplied to this by the presence 
 of the concave mirror. The symbols used in 5 will be used 
 here with the same meaning. The letters E and A will have 
 the meaning given them in 2. 
 
 If surface 3 is removed, then the rays are withdrawn from 
 the body C which this surface sends to it ; the intensity of the 
 
 x 00 
 
 part of these rays which it absorbed is = f cUer A. 
 
 */ o 
 
 Now the rays must be examined which are transmitted to 
 the body by the presence of the concave mirror. All these rays 
 must be reflected from the concave mirror to plate P and from 
 this to opening 1, and these must pass in the same direction as 
 if they came from opening 2. Before they strike the concave 
 mirror, they have either experienced a reflection from it or not. 
 In the first case they can only be sent back again to the con- 
 cave mirror by means of the body (7 over the path which is the 
 reverse of that already described. It must next be premised that 
 the body (7 has such a position that, of the rays which pass to 
 it through 2 and 1, only an infinitely small part will be re- 
 flected back again through opening 1 to opening 2. Then, of the 
 rays in question, only an infinitely small fraction have suffered 
 multiple reflection at the concave mirror, audit is sufficient to 
 consider those which are reflected only once at the mirror. Of 
 these, a part proceed from the body (7, the rest from the black 
 covering. The first part has experienced a double reflection at 
 plate P ; the vis viva which the body absorbs from it is 
 
 A. 
 
 The second part which proceeds from the black enclosure 
 may again be considered as consisting of two parts ; one which 
 passes to the concave mirror without the mediation of the body 
 C., and a second, by means of it. Each arises from rays which 
 proceed from black partition opposite the concave mirror, 
 and have passed through the. plate P, have been reflected from 
 the concave mirror to the plate P and from this to opening 1. 
 
 90 
 
RADIATION AND ABSORPTION. 
 
 Without examining from which part of the black wall these 
 rays have proceeded, their intensity may be found by the law 
 established in 11. 
 
 By the application of this, the intensity of those rays which 
 were absorbed by the body C is shown to be 
 
 .00 
 
 (/ACT (1 r)A. 
 
 Finally in order to find the intensity of the rays which proceed 
 from the black covering by means of the body C to the concave 
 mirror, and pass back from this to the body C and are here 
 absorbed, let N designate the quantity which the quantity in- 
 dicated by M in 12 becomes in consequence of plate P being 
 brought into its place and the surface 3 removed ; the intensity 
 
 is then = f MNr* A. 
 
 J o 
 
 The difference between M and N arises only from .the varia- 
 tion which the rays, falling upon the body C from the black 
 covering through opening 1, undergo by the introduction of 
 plate P and the removal of surface 3. Suppose the plate P 
 brought into its position, without removing surface 3, then M 
 can undergo no change, since all the pencils of rays, which go 
 to the opening 1 remain unchanged ; the pencil proceeding 
 from surface 2, for example, suffers a loss through reflection at 
 plate P which will be exactly replaced by the reflection of the 
 rays going out from the surface 3. The difference MN is 
 therefore only produced by the removal of surface 3 and is also 
 equal to the part of M which arises from the rays sent out by 
 surface 3 to opening 1 by means of plate P. According to the 
 supposition made in these paragraphs concerning the position 
 of the body C, MNis infinitely small in comparison with the 
 intensity of the rays of equal wave length which surface 3 
 sends to opening 1 by means of plate P, as well as infinitely 
 small in comparison with the intensity of rays of equal wave 
 length and polarized in the plane a, which surface 2 sends to 
 opening 1 by the absence of the plate P, and therefore finite 
 and also infinitely small with respect to the quantity repre- 
 sented by M ' in 12 (assuming that 1 A is not infinitely 
 small). Since, however, as already pointed in the places cited, 
 M' = M , we may also place 
 
 91 
 
MEMOIRS ON 
 
 N*-M-~M', 
 
 But according to the definition given of M' 
 M' = e (1 A) and therefore 
 
 JOO x,GO 
 
 dA Nf 2 A = I eZ/e ( 1^ ) r 2 A. 
 o y o 
 
 The proposition presented at the beginning of this paragraph 
 would then be expressed by the equation : 
 
 JOO x00 sCO x00 
 
 o */ o */ o */ o 
 
 or by the equation f ^ (EAe) Af 2 = 0. 
 
 J o 
 
 By the same treatment employed in 5 with reference to a 
 similar equation, we may conclude that for every value of A* 
 
 - =e 
 or substituting for e its value in 7. 
 
 E_ _ j Wi W% 
 A = 82 * 
 
 Thus, the law 3 is proved under the assumption that, of the 
 pencil which falls from surface 2 through the opening 1 upon 
 the body (7, no finite part is reflected by this back to the 
 surface^ ; further, that the law holds without this limitation, 
 if we consider that when the condition is not fulfilled, it is 
 only necessary to turn the body C infinitely little in order to 
 satisfy it, and that by such a rotation the quantities ^and A 
 undergo only and infinitely small change. 
 
 A Generalization of tlie Laiv 3. 
 
 The discussions given assume that the space in which the 
 radiation occurs is a vacuum. But the same treatment also 
 obtains when this space is filled with any perfectly diather- 
 manous medium ; only the function / will then be different 
 than in the former case. The symbol /may then be retained 
 for a vacuum and /' may be called the corresponding function 
 of temperature and wave length for a certain diathermanous 
 medium ; if n is the index of refraction of the same for the 
 
 92 
 
RADIATION AND ABSORPTION. 
 
 temperature and wave length to which / and /' refer, then a 
 simple relation exists between I', I, and n ; the same follows 
 from the law already demonstrated as will be here shown. 
 
 Imagine a layer of a diathermanous medium bounded by two 
 parallel planes, and with one side in contact with the black sur- 
 face F. Let the thickness of the layer= 1. For this body, the 
 s , absorptive power of A , and the emis- 
 sive power E, in relation to a certain 
 pencil of rays will be investigated. 
 The opening 1 and 2 which determine 
 the form of the pencil will be in 
 screens S\ and $ 2 , of which the first 
 covers the surface of the layer hither- 
 tofore supposed to be free, and the sec- 
 ond is parallel to it; let the line 
 FIG. 5. joining the middle points of the open- 
 
 ings be perpendicular to the screens. Of any pencil of rays 
 of a definite wave length and direction of polarization, which 
 passes from the opening 2 to the opening 1, a fraction will be 
 reflected at the latter which may be designated by p ; the rest 
 passes to the surface J^and is here completely absorbed ; there- 
 fore 
 
 To find E, represent by x, y ; x\, y\ ; and # 2 , y<* the coordi- 
 nates of a point of the surface F, the opening 1, and the open- 
 ing 2, reckoned from those points which are found in the axis 
 of the pencil. If these points lie in a ray, then if s again rep- 
 resents the distance of the two openings, 
 
 must be a minimum with respect to x\ and y\ : i. e., 
 
 x = Xl - x ^- x i y = yi y*-yi 
 
 ns > ns 
 
 if w\ and w 2 are the surfaces of the two openings, we find by a 
 treatment, which is given in a more general form in 10, the 
 intensity of the rays (polarized in a and of wave lengths be- 
 tween A and 7i + d%) which, falling from J^upon opening 1, in 
 part, pass to opening 2, 
 
 93 
 
MEMOIRS ON 
 
 by dx 
 
 ,v , . 
 
 that is 
 
 Of these rays the fraction 1 p goes through the opening 1 
 and arrives at the opening 2. 
 
 Tims E- (1-,) T -2tf*- 
 
 If these values of E and A are substituted in the equation 
 
 E I 
 A = 
 then r = 
 
 Results of the Law 5. 
 When any given body a platinum wire for instance is 
 gradually heated, it emits, up to a certain temperature, only 
 rays whose wave lengths are greater than that of the visible 
 rays. At a certain temperature, rays of the wave length of the 
 extreme red begin to be visible ; as the temperature rises 
 higher and higher, rays of a shorter and shorter wave length 
 are added, so that for every temperature, rays of a corresponding 
 wave length come into existence, while the intensity of the 
 rays of greater wave lengths increase. If the law proven be 
 applied to this case, it will be seen that the function / for 
 any wave length vanishes for all temperature below that of a 
 certain temperature, depending on the wave length for higher 
 temperatures increases with the same. From this it follows, 
 when the same law is applied to other bodies, that all bodies, 
 whose temperature is gradually raised, begin to send out rays 
 of the same wave length at the same temperature, and begin to 
 glow with red rays at the same temperature, and at a higher 
 common temperature, yellow, and so on. The intensity of 
 rays of a certain wave length which different bodies send out at 
 the same temperatures may, however, be very different ; it is 
 proportional to the absorptive powers of bodies for rays of that 
 particular wave length. At the same temperature accordingly 
 metal glows more brightly than glass, and this more brightly 
 than a gas. A body that remains perfectly transparent at the 
 
 94 
 
RADIATION AND ABSORPTION. 
 
 highest temperature would never become incandescent. Into 
 a ring of platinum wire of about 5mm diameter, I introduced 
 some phosphate of soda and heated it in the nonluminous flame 
 of the Bunsen burner. The salt melted and formed a fluid 
 lens and remained perfectly clear; but it emitted no light, 
 while the platinum ring in contact with it radiated the most 
 brilliant light. 
 
 Draper 1 has drawn the conclusion from investigations that 
 all solid bodies begin to glow at the same temperature. From 
 his researches he lias, however, noted that certain bodies like 
 chalk, marble, fluor spar glow at a lower temperature than 
 they should according to this law; he called this luminosity 
 phosphorescence, and said it clearly differed from glowing, by 
 the color. But whatever name may be given to this luminos- 
 ity, it is in contradiction with law, 3, and a body which shows 
 it must therefore not satisfy the assumptions which were made 
 in the proof of the law, that, at a constant temperature, it must 
 remain unchanged ; phosphorescence is not purely an effect of 
 heat, and is not exclusively determined by the temperature, 
 but is produced by changes in the body ; if these changes 
 whether they are chemical or of another nature have ceased 
 then the phosphorescence must vanish. 
 
 16. 
 
 From the law, 3, it follows that a body, which absorbs more 
 rays from one plane of polarization than from another, sends 
 out in the same ratio more rays from the first plane of polar- 
 ization than from the second. Consequently, as is known to 
 happen, a glowing opaque body having a smooth surface sends 
 out light in directions oblique to this surface which is 
 partially polarized perpendicularly to the plane passing 
 through the ray and the normal to the surface ; of the incident 
 rays, which are polarized perpendicularly to the plane of in- 
 cidence, the body reflects less, but also absorbs more than it 
 does of rays whose plane of polarization is the plane of in- 
 cidence. According to this law the state of polarization of the 
 rays sent out may easily be given if the law ot the reflection of 
 the incident rays is known. 
 
 1 Phil. Mag. XXX. p. 345 ; Berl. Ber. 1847. 
 
 95 
 
MEMO in S ON 
 
 A tourmaline plate, cut parallel to the optic axis, absorbs, 
 at ordinary temperatures, moraof the rays which strike it nor- 
 mally, if the plane of polarization of these is parallel to the 
 axis than when it is perpendicular to it. Assuming that the 
 tourmaline plate retains this property when it is at a glowing 
 heat, it must give out rays in a direction normal to it, which 
 are partially polarized in the plane passing through the optic 
 axis and which is the plane perpendicular to that which is 
 called the plane of polarization of the tourmaline. 1 have 
 proved this striking deduction from theory by experiment and 
 it confirmed the same. The tourmaline plates employed with- 
 stood a considerable temperature, glowing for a long time in 
 the flame of the Bunsen burner without undergoing any per- 
 manent change; only after cooling did they appear dull at the 
 edges. The property of polarizing transmitted light was 
 retained even at an incandescence, although in a considerable 
 less degree than at a lower temperature. This appeared on 
 observing, through a double refracting prism, a platinum wire 
 made incandescent in the flame and placed behind a tourma- 
 line plate. The two images of the platinum wire were of un- 
 equal brightness, although the difference was much less than 
 when the tourmaline plate was outside of the flame. The 
 double refracting prism was then given the position in which 
 the difference of the intensities of the two images was a maxi- 
 mum ; suppose the upper image were the brighter ; then, after 
 removal of the platinum wire the two images of the tourmaline 
 plate were compared. The upper image was not strikingly, 
 but, unmistakably, darkerthan the other; both images appeared 
 exactly like to two similar incandescent bodies, of which the 
 upper had a less temperature than the lower one. 
 
 17. 
 
 Still another result of the law established may, in conclusion, 
 be admitted here. When a space is surrounded by bodies of 
 the same temperature, and no rays can penetrate through these 
 bodies, every pencil in the interior of the space is so consti- 
 tuted, with respect to its quality and intensity, as if it pro- 
 ceeded from a perfectly black body of the same temperature, 
 and is therefore independent of the nature and form of the 
 
 96 
 
RADIATION AND ABSORPTION. 
 
 bodies, and only determined by the temperature. The truth 
 of this statement is evident if we consider that a pencil of rays, 
 which has the same form, but the reverse direction to that 
 chosen, is completely absorbed by the infinite number of reflec- 
 tions which it successively experiences at the assumed bodies. 
 In the interior of an opaque glowing hollow body of given tem- 
 perature there is, consequently, always the same brightness 
 whatever its nature may be in other respects. 
 
 BIOGRAPHICAL SKETCH. 
 
 GUSTAV ROBERT KIRCHHOFE, the son of Counselor-at-law 
 Kirchhoff, was born March 12, 1824, at Kdnigsberg. He took 
 his degree of doctor of philosophy at the University in 1847. 
 The following year he became private-docent at the University 
 of Berlin. He early showed those rare mathematical faculties 
 which later distinguished him. As early as his eighteenth year 
 he decided upon physics as the branch to which he should 
 devote his life's work. By 1845 he had investigated electric 
 currents, and established the two so-called Kirchhoff's laws for 
 current conduction. Other important papers on electricity fol- 
 lowed in rapid order. In 1854 he was called to Breslau, where 
 he became associated with Bunsen. He went to Heidelberg in 
 1854 where Bunsen had preceded him. Here in his prime he 
 wrought and sought for twenty years, and in connection with 
 Bunsen achieved some of the most important discoveries in the 
 history of physical science. In 1875 he accepted, after twice 
 declining an invitation to the University, a call to the chair of 
 theoretical physics at Berlin where he became associated with 
 his former colleague von Helmholtz. Here he delivered for 
 eleven years (with serious interruption in the last two years) his 
 famous courses of lectures on theoretical physics. It is during 
 this period that we find the most brilliant aggregation at Berlin 
 of scholars in the faculty of mathematics and physics during 
 the century. His contributions extend over optics, heat, fluid, 
 motion, electricity, elasticity, etc., and all bear the imprint of 
 the great genius he was. He died unexpectedly Oct. 17, 1887, 
 after many months of disability. His papers and lectures 
 have been collected and edited and now form one of the endur 
 ing monuments in physical science. 
 
 97 
 
CHEMICAL ANALYSIS BY SPECTRAL 
 OBSERVATIONS. 
 
 BY 
 
 G. KIRCHHOFF AND R. BUNSEN". 
 
 Poggendorf ',? A nnalen, Band 1 10, 1 860 ; Gesammelte Abliand- 
 lungen von G. Kirclilioff. pp. 598-625, 1882. 
 
 99 
 
CONTENTS. 
 
 PAGE 
 
 Methods of Purifying Salts 101 
 
 Apparatus described . . . . . . .103 
 
 Sodium . . . . . . . , . . 107 
 
 Lithium . . . 109 
 
 Potassium . . . . . . . . . .113 
 
 Strontium, . . 113 
 
 Calcium . . . . . . . . . .115 
 
 Barium 119 
 
 Advantage of Spectrum Analysis over other Methods . . 122 
 Law of Reversed Spectra ... . 123 
 
 100 
 
CHEMICAL ANALYSIS BY SPECTRAL 
 OBSERVATIONS. 1 
 
 IT is well known that many substances have the property 
 when they are brought into a flame of producing in the spec- 
 trum certain bright lines. We can found on these lines a 
 method of qualitative analysis which greatly enlarges the field 
 of chemical reactions and leads to the solution of problems 
 unsolved heretofore. We shall confine ourselves here only to 
 the extension of the method to the detection of the metals of 
 the alkalis and the alkali earth and to the illustration of their 
 value iii a series of examples. 
 
 The lines referred to show themselves the more plainly, the 
 higher the temperature and the weaker the natural illuminating 
 power of the flame. The gas lamp 2 described by one of us 
 gives a flame of very high temperature and very small luminosity; 
 this is consequently especially adapted to investigations on 
 those substances characterized by bright lines. 
 
 In Figure 1 the spectra are represented which the flames 
 referred to give when the salts, as pure as possible, of potassium, 
 sodium, lithium, strontium, calcium, and barium are vaporized 
 in it. The solar spectrum is annexed in order to facilitate the 
 comparison. 
 
 The potassium compound used for the investigation was 
 obtained by heating chlorate of potassium which had been six to 
 eight times recrystallized beforehand. 
 
 The chloride of sodium was obtained by combining pure car- 
 bonate of sodium and hydrochloric acid and purifying the same 
 by repeated crystallization. 
 
 The lithium salt was purified by precipitating fourteen times 
 with carbonate of ammonium. 
 
 For the production of the calcium salt a specimen of marble 
 
 1 Kirchhoff and R. Bnnsen, Pogg. Ami. Vol. 110. 1860. 
 
 2 Bunsen, Fogg. Ann. Vol. 100 p. 85. 
 
 101 
 
I 1 & & S % M 
 
RADIATION AND ABSORPTION. 
 
 as pure as possible, and dissolved in hydrochloric acid, was 
 used. From this solution the carbonate of calcium was thrown 
 down by a fractional precipitation with carbonate of ammonium 
 in two portions, of which only the latter, precipitated in calcium 
 nitrate, was used. The calcium salt thus obtained we dissolved 
 several times in absolute alcohol and converted it finally into 
 the chloride by evaporating the alcohol and by precipitation 
 with carbonate of ammonium in hydrochloric acid. 
 
 In order to obtain the pure chloride of barium we extracted it 
 from the commercial salt by pulverizing and boiling repeatedly 
 in nearly absolute alcohol. The residue thus extracted and 
 freed from alcohol was dissolved in water and thrown down by 
 fractional precipitation in two portions, only the second being 
 dissolved in hydrochloric acid, and the barium chloride thus 
 obtained being further purified by repeated crystallizations. 
 
 In order to obtain chloride of strontium, as pure as possible, 
 the commercial salt was crystallized out from alcohol, and frac- 
 tionally precipitated in two portions with carbonate of ammon- 
 ium, the second part being dissolved in nitric acid and the ni- 
 trate freed from the last traces of calcium by pulverizing and 
 boiling with alcohol. From the product thus purified the chlo- 
 ride of strontium was obtained finally by precipitating with 
 carbonate of ammonium and dissolving the precipitate in 
 hydrochloric acid. All these purifications were made in plat- 
 inum vessels as far as it was possible. 
 
 Figure 2 represents the apparatus which we have used 
 
 mainly in the observation 
 of the spectra. A is a 
 box blackened on the in- 
 side the bottom of which 
 has the form of a trapez- 
 ium and rests on three 
 feet ; the two inclined 
 sides of the same form an 
 
 FIG 2 angle with one another of 
 
 about 58 and carry the 
 
 two small telescopes B and C. The ocular of the first is removed 
 and replaced by a plate in which is a slit formed of two brass 
 cheeks which are placed at the focus of the objective. The 
 
 103 
 
MEMOIRS ON 
 
 lamp D is so placed before the slit that the mantle of the frame 
 is intersected by the axis of the tube B. Somewhat beneath 
 the point where the axis meets the mantle the end of a very fine 
 platinum wire bent into a small hook and carried by the holder 
 E passes into the same; on this hook is melted a globule of the 
 chloride previously dried. Between the objective of the tele- 
 scopes B and C is placed a hollow prism F with a reflecting 
 angle of 60 and filled with carbon disulphide. The prism 
 rests on a brass plate which can be rotated on a vertical axis. 
 This axis carries on its lower end the mirror G and above it 
 the arm //which serves as the handle to rotate the prism and 
 the mirror. A small telescope is adjusted before the mirror 
 which gives an image of a horizontal scale placed at a short dis- 
 tance. By rotating the prism we can cause to pass before the 
 vertical thread of the telescope C the entire spectrum of the 
 flame and bring every portion of the spectrum into coincidence 
 with this thread. To every reading made on the scale there 
 corresponds a particular portion of the spectrum. If the spec- 
 trum is very weak the cross hair of the telescope C is illumi- 
 nated by means of a lens which throws some of the rays from a 
 lamp through a small opening which is placed laterally in the 
 ocular of the telescope C. 
 
 The spectra in Fig. 1. obtained by means of the pure chlo- 
 ride above mentioned we have compared with those which we 
 obtained if we introduce the bromides, iodides, hyd rated oxides, 
 sulphates, and carbonates of the several metals into the follow- 
 ing flames: 
 
 into the flame of sulphur, 
 
 " " " " carbon disulphide, 
 
 " " " " aqueous alcohol, 
 
 " " non-luminous flame of coal gas, 
 
 " " flame of carbonic oxide, 
 
 " " " " hydrogen and 
 
 " " oxyhydrogen flame. 
 
 From these comprehensive and lengthy investigations whose 
 details we may be permitted to omit, it appears that the dif- 
 ference in the combinations in which the metals were used, the 
 multiplicity of the chemical processes in the several flames, and 
 the enormous differences of temperatures of the latter exert no 
 influence on the position of the spectral lines corresponding to the 
 individual metals. 
 
 104 
 
RADIATION AND ABSORPTION. 
 
 How considerable the differences of temperature mentioned 
 are, is shown by the following treatment. 
 
 We may arrive at an approximation of temperature of a 
 
 flame by means of the equation t = -?~, in which t is the 
 
 temperature of the flame sought, g the weight of the substance 
 burning in oxygen, w the heat of combustion of the same, p the 
 weight and s the specific heat of one of the products of combus- 
 tion. 
 
 If we take as the heat of combustion 
 
 of sulphur as 2240 C 
 
 3400 
 34462 
 13063 
 11640 
 11529 
 
 2403 
 
 ' carbon disulphide 
 
 ' hydrogen 
 
 ' marsh gas 
 
 ' elayle 
 
 * ditetryle 
 
 ' carbonic oxide 
 
 and place according to Regnault the specific heat at constant 
 
 pressure 
 
 for sulphurous acid =0. 1553 
 
 " carbonic acid =0.2164 
 
 " nitrogen =0.2440 
 
 " aqueous vapor =0.4750 
 
 we find accordingly the temperature 
 
 of the sulphur flame 1820 C 
 
 ' bisulphide of carbon flame.... 2195 
 
 ' coal gas flame 1 2350 
 
 ' carbonic oxide flame 2 3042 
 
 ' hydrogen flame in air 3 3259 
 
 ' oxyhydrogen flame 4 8061. 
 
 It appears that the same metal compound gives in one of 
 these flames a spectrum as much more intense as the tempera- 
 ture is higher. Of the compounds of these metals, those give 
 the greatest intensity in a flame which have the greatest 
 volatility. 
 
 In order to obtain a further proof that each of the severally 
 mentioned metals always give the same bright lines in the 
 spectrum, we have compared the spectra referred to with those 
 
 1 Liebig's Ann. Vol. CXI. p. 258 
 
 8 Gasometric Methods by R. Bunsen. p. 254. 
 
 3 Ibid. 
 
 4 Ibid. 
 
 105 
 
MEMOIKS OK 
 
 which an electric spark produces which passes between 
 electrodes made from these metals. 
 
 Small pieces of potassium, sodium, lithium, strontium, and 
 calcium were fastened on a fine platinum wire and so melted in 
 pairs within glass tubes that they were separated by a distance 
 of 1 to 2mm from one another the wires piercing the sides of 
 the tubes. Each of these tubes was placed before the slit of 
 the spectroscope ; by means of a Bnhmkorff's induction 
 apparatus, we caused electric sparks to pass between the metal 
 pieces mentioned and compared the spectrum of the same with 
 the spectrum of a gas flame in which the chloride of the cor- 
 responding metal was brought. The flame was placed behind 
 the glass tube. When the Ruhmkorff apparatus was thrown 
 alternately in and out of action it was easy to be convinced, 
 without any accurate measurement, that, in the brilliant spec- 
 trum of the spark, the bright lines of thespectrnmof the flame 
 were present undisplaced. In addition to these there appeared 
 other bright lines in the spark spectrum a part of which must 
 be attributed to the presence of foreign metals in the electrodes, 
 others to nitrogen which filled the tubes after the oxygen had 
 partly oxidized the electrodes. 1 
 
 It appears, accordingly, beyond a question that the bright 
 lines of the spectra indicated maybe considered as certain proof 
 of the presence of the metal in consideration. They can serve 
 as reactions by means of which this material may be detected 
 more certainly, and quickly and in smaller quantities than by 
 any other analytical method. 
 
 The spectra, represented, refer to the case when the slit is 
 wide enough so that only the most prominent of the dark lines 
 of the solar spectrum are visible, the magnifying power of the 
 observing telescope being small (about four-fold) and the 
 intensity of the light moderate. These conditions seem to us 
 
 1 In one investigation with strontium electrodes we used a tube filled 
 with hydrogen instead of nitrogen, and the stream of sparks was trans- 
 formed very soon into an arc, while the sides of the tuhe were covered 
 with a gray precipitate. On opening the tube nnder rock-oil it appeared 
 that the hydrogen had vanished and a vacuum existed. The gns 
 appears, therefore, at the enormous temperature of the electric spark, to 
 have dissociated the strontium oxide which had not been completely 
 removed from the surface of the metal. 
 
 106 
 
RADIATION AND ABSORPTION. 
 
 most advantageous when it is necessary to carry out a chemical 
 analysis by spectral observations. The appearance of the 
 spectrum may under other conditions be quite different. If the 
 purity of the spectrum is increased, many of the lines appearing 
 as single, resolve themselves into several, the sodium line, for 
 example, into two ; if the intensity is increased new lines appear 
 in many of the spectra shown and the relation of the brightness 
 of the old ones becomes different. In general the brightness of 
 a darker line increases with greater luminosity more rapidly 
 than the brighter ones,but not so much that the former exceed 
 these. A clear example of this is given by the two lithium 
 lines. We have observed only one exception to this rule, 
 namely, with the line Ba ?, which, with low luminosity, is 
 barely visible while Zto^appears very distinct, and, with greater 
 luminosity, much brighter than the former. This fact appears 
 of importance, and we shall make a further study of the same. 
 We will now consider more closely the characteristics of the 
 several spectra, the knowledge of which is of importance from 
 a practical standpoint, and indicate the advantage which the 
 chemical analytical method founded upon it furnishes. 
 
 SODIUM. 
 
 Of all the spectral reactions that of sodium is the most sen- 
 sitive. The yellow line Na a, the only one which is shown in 
 the sodium spectrum coincides with Fraunhofer's line D and is 
 characterized by its peculiarly sharp boundary and its extraor- 
 dinary brilliancy. If the temperature of the flame is very high 
 and the quantity of the substance used very great, traces of a 
 continuous spectrum are seen in the immediate neighborhood 
 of the line. Lines of other substances, in themselves very 
 weak, lying near it appear still weak and will, therefore, often 
 first be visible after the sodium reaction has begun to disappear. 
 
 In the oxygen, chlorine, iodine and bromine compounds in 
 sulphuric acid and carbonic acid the reaction is most evident. 
 But it is present also in the silicates, borates, phosphates and 
 other non -volatile salts. 
 
 Swani has already called attention to the minuteness ef the 
 
 1 Pogg. Arm. Vol. C, p. 311. 
 
 107 
 
MEMOIRS ON 
 
 quantity of common salt which can produce the sodium line 
 clearly. 
 
 The following investigation shows that chemistry produces 
 no single reaction which in the remotest degree can compare in 
 sensitiveness with this analytical spectral determination of 
 sodium. We detonized in one corner of the experiment room 
 which contained about 60 cubic meters of air and as far as 
 possible from our apparatus three milligrams of chlorate of 
 sodium with milk sugar while the non-luminous flame was 
 observed before the slit. After some minutes, the flame, becom- 
 ing gradually colored pale yellow, gave a strong sodium line, 
 which, after ten minutes, again completely vanished. From the 
 weight of the detonized salt and the air contained in the room 
 it is easy to calculate that in a unit weight of the latter not a 
 ?oWr<rzrr>kh part of sodium smoke could have been suspended. 
 As the reaction can be readily observed in a second, and as, in 
 this time, according to the rate of flow and the composition 
 of the gases in the flame, onty about 50 ccm or 0.0647 grams of 
 air which contained less than ^otfoWoirth of sodium salt, reach 
 the state of incandescence in the flame, it follows that the eye 
 is capable of detecting less than ^ootrotfth f a milligram of 
 sodium salt with the greatest distinctness. With such a sen- 
 sibility of the reaction it is evident that only rarely is a sodium 
 reaction not visible in glowing atmospheric air. The earth is 
 covered over more than two-thirds of its surface with a solu- 
 tion of chloride of sodium, which, by the waves breaking into 
 foam, is transformed continually into spray; the particles of 
 sea-water, which reach the atmosphere in this way, evaporate 
 and leave behind them motes of salt which vary in magnitude, 
 but, as it appears, are rarely absent from the atmosphere, and, 
 perhaps, serve to supply the small organisms the salt which the 
 larger plants and animals secure from the ground. The 
 presence in the air of salt, easily shown by spectral analysis, is 
 yet of interest from another standpoint. If, as we yet can 
 scarcely doubt, there are catalytic influences which are the 
 cause of the miasmic spread of disease, it is possible that an 
 antiseptic substance, such as salt, even in vanishingly small 
 quantities, may indeed not be without definite influence upon 
 such processes in the air. From daily and long continued 
 
 108 
 
RADIATION AND ABSORPTION. 
 
 spectrum observation it would be easy to learn whether the 
 variation in the intensity of the spectral line Ncta, produced by 
 the sodium combination in the air, is related in any degree to 
 the appearance and the spread of endemic diseases. 
 
 In the exceedingly delicate sodium reaction may also be 
 sought the reason why all bodies exposed to the air show the 
 sodium line after a time when heated in the flame, and why it 
 is possible with only a few compounds to eliminate the last 
 trace of the sodium line No, a by crystallizing it out ten or more 
 times from water which has come in contact with platinum 
 vessels only. A hair wire of platinum, which has been freed, 
 by heating, from every trace of sodium, shows the reaction 
 most vividly again, if it is exposed some hours to the air. Dust 
 which settles in the room from the air shows it in the same 
 degree, so that, for example, the slapping of a dusty book is 
 quite sufficient to produce at a distance of several spaces the 
 most brilliant flashes of the No, a line. 
 
 LITHIUM. 
 
 The incandescent vapors of the lithium compound give two 
 sharply defined lines, one a very weak yellow Li (3 and a red 
 brilliant line Li a. In certainty and delicacy this reaction ex- 
 ceeds all those known heretofore in analytical chemistry. It 
 approximates in sensibility that of the sodium reaction perhaps 
 because the eye is more sensitive for yellow rays than for re'd. On 
 detonizing nine milligrams of carbonate of lithium with a large 
 excess of milk sugar and potassium chlorate in the room which 
 contained about 60 cubic meters of air, the line became quite 
 evident. The eye can therefore in this way, as a calculation 
 similar to the one made above will show, perceive less than 
 T _j TFTTTT th of a milligram of carbonate of lithium with the 
 greatest distinctness. 0.05 grams of the same salt, detonized in 
 the way already mentioned, made it possible to observe the Li a 
 line in the air of the same room during more than an hour. 
 
 The oxygen, chlorine, iodine and bromine compounds are 
 most suitable for observing lithium. But the carbonate, sul- 
 phate, and even phosphate are almost as well suited for this 
 purpose. Minerals containing lithium, as triphyllin, triphan, 
 petalit, lepidolith, need only to be held in the flame in order 
 
 109 
 
MEMOIRS ON 
 
 to give the line Li a with an intense lustre. In this way it is 
 possible to show the presence of lithium in many f eld -spars, 
 for example in orthoclase from Baveno. The line is seen only 
 momentarily immediately after the insertion of the specimen in 
 the flame. Thus mica from Altenberg and Penig indicates the 
 presence of lithium while on the contrary mica from Miask, 
 Ashaffenburg, Modum, Bengal, Pennsylvania, etc., is free from 
 lithium. When in naturally deposited silicates only a vanish- 
 ingly small quantity of lithium is present, it escapes immediate 
 observation. The test in such cases is then best made in the 
 following way: we digest and evaporate a small quantity of the 
 substance for examination with hydrofluoric acid or fluoride of 
 ammonium, moisten the remainder with sulphuric acid, and 
 dissolve the dry mass with absolute alcohol. The alcoholic 
 solution is then evaporated to dryness, again dissolved with 
 alcohol, and the fluid, thus obtained, evaporated in as shallow a 
 dish as possible. The product which remains can be easily 
 scraped together by means of an erasing knife and brought into 
 the flame on platinum wire, i^th of a milligram of the same is 
 usually quite sufficient for the experiment. Other compounds 
 than the silicates, in which we may wish to detect the least 
 traces of lithium, maybe transformed into sulphates by evapo- 
 ration with sulphuric acid or in any other way and then treated 
 as above. 
 
 By means of these experiments, the unanticipated conclusion 
 is readily drawn that lithium belongs to those substances which 
 are most widely distributed in nature. This is easily shown by 
 means of 40 cubic centimeters of sea-water which was collected 
 in the Atlantic ocean in latitude 41 41' and longitude 39 14'. 
 Ashes of Fucoids (kelp) which was driven on to the Scottish 
 coast from the Gulf Stream contained appreciable traces of it. 
 All orthoclase and quartz from the granite of the Oldenwald 
 which we have tested show a lithium content. A very pure 
 drinking water from a spring on the western granitic declivity 
 of the Neckar valley in Schlierbach near Heidelberg contained 
 lithium, while the spring rising in the red sandstone which 
 supplies the water pipes of this chemical laboratory was free 
 from it. Mineral water, in a litre of which lithium can 
 scarcely be detected by the ordinary analytical methods, shows 
 
 110 
 
RADIATION AND ABSORPTION. 
 
 the Li a line frequently if we put a drop of the same into the 
 flame on a platinum wire. 1 All the ashes of woods in the Olden- 
 wald which grow on granite soil, as well as Russian and 
 other commercial potashes examined by us, contain lithium. 
 Neither, even, in the ashes of tobacco, vine leaves, vine-wood 
 and grapes,' 2 as well as in the ashes of crops which were culti- 
 vated in the Rhine plain near Waghausel, Deidesheim and 
 Heidelberg on non-granitic earth, was lithium lacking, nor in 
 the milk of the animals which were fed upon these crops. 3 
 
 It will be scarcely necessary to remark that a mixture of 
 volatile sodium and lithium salts shows, along with the reaction 
 of sodium, that of lithium with a scarcely less preceptible sharp- 
 ness and distinctness. The red line of the last appears still 
 quite distinct when a small bead containing the y^^th part of 
 lithium salts is introduced into the flame, where the eye, 
 unaided, perceives in the same, nothing more than yellow 
 light of sodium without any indication of red coloration. On 
 account of the greater volatility of lithium salts, the sodium 
 reaction lasts somewhat longer. When, therefore, it is desired 
 to detect very small traces of lithium along with sodium, the 
 bead for testing must be introduced into the flame whilst we 
 are observing through the telescope. We then often observe 
 the lithium line only for a few moments during the first 
 products of volatilization. 
 
 In the production of lithium compounds on a commercial 
 scale spectrum analysis is a means of inestimable value in the 
 selection of the raw material used and the determination of an 
 efficient method of manufacture. Thus for example, it is only 
 necessary to evaporate a drop of the different mother-liquors in 
 
 1 When it is required to introduce a liquid into the flame we bend in 
 the end of a horse-hair platinum wire, a ring of suitable diameter and 
 hammer the same flat. If we let a drop of the fluid fall into the ring 
 thus formed a sufficient quantity for the investigation remains hanging 
 within. 
 
 2 Lithium is concentrated so much in the mother-liquors in the man- 
 ufacture of tartaric acid that we can obtain considerable quantities from 
 them. 
 
 3 Dr. Folwarcznyhas even been able to show with the lithium line Li a 
 the lithium compounds in the ash of human blood and of muscular 
 tissue. 
 
 Ill 
 
MEMOIKS ON 
 
 the flame and observe through the telescope, in order to show 
 at once, that, in many of these saline residues, a rich and 
 hitherto overlooked lithium source exists. Thus in the process 
 of preparation, we can follow any loss of lithium in the as- 
 sociated products and wastes by means of the spectral reaction, 
 and thus easily seek more efficient methods of production than 
 those heretofore used. 1 
 
 POTASSIUM. 
 
 The volatile potassium compounds produce in the flame a 
 very extended continuous spectrum which only show two 
 characteristic lines ; the first K a, in the outermost red border- 
 ing on the ultra red rays falls exactly on the dark line A of the 
 solar spectrum; the second K $ far in the violet toward the 
 other end of the spectrum, corresponds likewise to a Fraunhofer's 
 line. A very weak line, coinciding with the Fraunhofer's line 
 B, which, however, is only visible with an intense flame, is less 
 characteristic. The blue line is somewhat weak but is almost as 
 well suited for detecting potassium as the red line. The position 
 of both lines, in the neighborhood of the limits of the rays per- 
 ceptible by the eye, renders the reaction somewhat less sensitive. 
 
 In the air of our room it became first visible when we burned 
 about one gram of chlorate of potassium mixed with milk 
 sugar. We can, therefore, make clear to the eye in this way 
 about -nnr^h of a milligram of chlorate of potassium. 
 
 Potassium hydrate and all compounds of potassium with 
 volatile acids, show the reaction without exception. Potassium 
 silicate and similar non-volatile salts, on the contrary, produce 
 it only when the potassium is present in large quantities. 
 With small amounts, the test bead may be melted together 
 with some carbonate of sodium in order to make the char- 
 acteristic lines visible. The presence of the sodium does not 
 prevent the reaction and hardly affects the sensibility. Ortho- 
 
 1 We obtained by such an approved method from two jars of mineral 
 water (about four litres) a mother-water, which gave on evaporation 
 with sulphuric acid a residue of 1.2 K, half an ounce of carbonate of 
 lithium of the purity of the commercial, whose cost would be about 
 140 fl. per pound. A great number of other mother-waters which we 
 examined showed a like wealth iu lithium compounds. 
 
 112 
 
RADIATION AND ABSORPTION. 
 
 clase, sanidine, and adularia may easily be distinguished in 
 this way from albite, oligoclase, Labradorite, and anorthite. 
 In order to detect traces of potassium, vaiiishingly small, we 
 need to heat to a feeble incandescence the silicate, with a large 
 excess of fluoride of ammonium, in a platinum crucible and in- 
 troduce the residue into the flame on a platinum wire. In this 
 way we find that almost every silicate contains potassium. 
 The lithium salts disturb the reaction but little. Thus, for 
 example, it is only necessary to hold the ash end of a cigar in 
 the flame before the slit, in order to produce at once very dis- 
 tinctly the yellow line of the sodium and the two red ones of 
 potassium and lithium, the last metal being scarcely ever 
 absent in tobacco ash. 
 
 STRONTIUM. 
 
 The spectra of the alkali earths are not so simple as those of 
 the alkalis. That of strontium is characterized, particularly, by 
 the absence of green bands. Eight lines of the same are quite re- 
 markable namely six red, one orange and one blue. The orange 
 line Sr a which appears close to the sodium line toward the red, 
 the two red lines Srp, Sr y and finally the blue line Sr 6 are the 
 most important in their position and intensity. In order to 
 test the sensibility of the reaction we heated quickly in a plat- 
 inum dish, over a large flame, an aqueous solution of chloride 
 of strontium of known concentration until the water was 
 evaporated and the dish began to glow. The salt then began to 
 decrepitate into microscopic particles which were thrown into 
 the air in the form of white smoke. A weighing of the salt 
 residue in the dish showed that in this way 0.077 grams of 
 chloride of strontium had passed out into the 77,000 grams' 
 weight of air of the room in form of a fine dust. After the air 
 of the room had been thoroughly mixed, by means of an open 
 umbrella moved rapidly about, the characteristic lines of the 
 strontium spectrum were very beautifully outlined. We can ac- 
 cording to this experiment estimate the amount of chloride of 
 strontium preceptible at T WW fcn f a milligram. 
 
 The chlorine and the other haloid compounds of strontium 
 give the most distinct reaction. Strontium hydrate and carbon- 
 ate of strontium show them much more feebly; the sulphate 
 
 113 
 
MEM OIKS ON 
 
 still less distinctly; the compounds, with the non-volatile 
 acids, the weakest or not at all. We must therefore introduce 
 into the flame, first, the bead for testing by itself, and then 
 again, after previously moistening with hydrochloric acid. If 
 we assume sulphuric acid in the bead, we must hold it some 
 moments in the reducing part of the flame before moistening 
 with hydrochloric acid, in order to transform the sulphate into 
 the sulphide which is decomposed by hydrochloric acid. To 
 detect strontium in compounds of silicic, phosphoric, boracic 
 or other non-volatile acids we proceed best in the following 
 manner: for fusing with carbonate of sodium a conical spiral 
 of platinum wire is used instead of a platinum crucible. The 
 same is made white hot in the flame and dipped into dry fine 
 pulverized carbonate of sodium which, when possible, contains 
 enough water so that the necessary quantity of the salt remains 
 hanging to the same on the first immersion. Fusion can be 
 effected in this spiral much quicker than in the platinum 
 crucible, since the mass of the platinum heated is small and 
 the salt to be fused comes into immediate contact with the 
 flame. If we transform the fine pulverized substance to be 
 tested into the glowing fluid soda by means of a small plat- 
 inum spatula, and maintain it in a glowing state for a few 
 minutes, we need only to knock the spiral, inverted with its 
 vertex upward, on the edge of the lamp stand in order to 
 obtain the contents of the same in the form of a large solidified 
 bead. Wo then cover the bead with a sheet of writing paper 
 and press it by means of an elastic knife blade, which we also 
 use after removing the paper, in order to reduce the mass still 
 farther to the finest powder. This is collected on the edge of 
 a plate slightly tilted and carefully covered with hot water 
 which is allowed to flow backwards and forwards over the sub- 
 stance, heaped up by gentle tipping of the plate and finally, 
 the fluid, remaining over the sediment, is decanted. It is easy, 
 by repeated heating of the plate, to draw off the soluble salt 
 after several repetitions of this process without stirring up the 
 sediment and losing an appreciable amount of the same. If 
 instead of water we use a common salt solution, the operation 
 may be conducted more quickly and certainly. The residue 
 contains the strontium as carbonate, of which a few tenths of a 
 
 114 
 
RADIATION AND ABSOBPTION. 
 
 milligram, moistened with a little hydrochloric acid on a plat- 
 inum wire, give a brilliant reaction. In this way, without 
 platinum crucible, mortar, evaporating dish, and without 
 funnel and filter, it is possible to carry out, in a few minutes, 
 all the necessary operations of fusing, powdering, digesting 
 and washing. 
 
 The reaction of potassium and sodium is not affected by the 
 presence of strontium. The lithium reaction takes place along 
 with the three mentioned with perfect distinctness, if the 
 quantity of lithium is not too small with respect to that of the 
 strontium. The lithium line Li a then appears as a narrow in- 
 tensely red and sharply defined band upon the weaker red 
 background of the broad strontium band Sr p. 
 
 CALCIUM. 
 
 The spectrum of calcium can be immediately distinguished at 
 the first observation from the four spectra already considered 
 in that a very characteristic and intense line Ca ft is present in 
 the green. Also a second not less characteristic feature is the 
 very brilliant orange line Ca a which lies considerably farther 
 toward the red end of the spectrum than the sodium line Naa 
 and the orange line of strontium Sr a. By burning a mixture 
 of calcium chloride, chlorate of potassium and milk sugar we 
 obtain a smoke whose reaction is approximately of the same 
 sensibility as that of the fumes from the chloride of strontium 
 under the same conditions. It follows from an examination 
 made in this way that T <yo 6 (nnj- of a milligram of calcium chlo- 
 ride can be detected easily and with absolute certainty. Only 
 the calcium compounds, volatilized in the flame, show this re- 
 action, and the more volatile they are the more distinct it is. 
 Chloride of calcium, iodide of calcium, and bromide of calcium 
 are best in this respect. Sulphate of calcium gives a spectrum 
 only after it has become basic but then very brilliantly and 
 long continued. In the same way the reaction of the carbonate 
 becomes distinct after the acid has been driven off. 
 
 Compounds of calcium with non-volatile acids remain indif- 
 ferent in the flame, but if they are attacked by hydrochloric 
 acid, the reaction may be easily obtained in the following way: 
 
 115 
 
MEMOIKS ON 
 
 we introduce a few milligrams, or perhaps only a few tenths of 
 a milligram, of the finely pulverized substance on the flat plat- 
 inum ring, somewhat moistened, into the less heated portion of 
 the flame until the powder is frittered without being melted. 
 If we allow a drop of hydrochloric acid to fall on the ring the 
 greater part of it will remain hanging. If we pass this drop 
 before the slit of the spectroscope into the hottest part of the 
 flame it volatilizes without boiling on account of its spheroidal 
 condition. If during the volatilizing of the drop we look into 
 the telescope there appears at the instant when the last portion 
 of the fluid has been evaporated a brilliant calcium spectrum- 
 which flashes out but for a moment with a small amount, but 
 continues a longer or a shorter time with considerable quan- 
 tities of metal. 
 
 Only in silicates which are attacked by hydrochloric acid can 
 the calcium be found in this way; in silicates which are not 
 attacked by hydrochloric acid the test is best obtained in the 
 following way: a few milligrams of the substance to be tested 
 are pulverized as fine as possible and placed on a flat platinum 
 crucible cover with about a gram of half-dissolved fluoride of 
 ammonium and the cover held in the flame until it volatilizes 
 the fluoride of ammonium. We moisten the salt residue re- 
 maining on the cover with one to two drops of sulphuric acid, 
 and drive off the excess of the same by gently heating over the 
 flame. If the residue of the sulphates now remaining on the 
 cover be scraped together with the finger-nail or a spatula and 
 about a milligram of the same be introduced into the flame by 
 means of a wire, we obtain, if K 9 Na and Li are present, the 
 characteristic reaction of these three bodies simultaneous or 
 successively. If calcium and strontium be also present their 
 spectra usually first appear after K, Na and Li have been 
 vaporized. The reaction of these metals fails with weak con- 
 tents of calcium and strontium; we obtain it, however, imme- 
 diately if we introduce the wire for a few moments into the 
 reducing part of the flame, moisten it with hydrochloric acid, 
 and bring it again into the flame. 
 
 All these tests, as the heating of it alone, or with hydro- 
 chloric acid, the treatment with ammonium fluoride alone, or 
 with sulphuric and hydrochloric acid, provide the mineralogist 
 
 116 
 
KADI ATI ON AND ABSORPTION. 
 
 and still more the geologist with a series of highly simple tests 
 for determining many substances occurring in nature even in 
 the smallest particle, such, for example, as the minerals so 
 similar to one another, consisting of double silicates, contain- 
 ing lime, with a certainty which is scarcely attainable with an 
 abundant supply of material by means of an extended and pro- 
 tracted analysis. Some examples will illustrate this best. 
 
 1. A drop of sea-water evaporated on a platinum wire showed 
 a strong sodium reaction, and after volatilizing the chloride of 
 sodium a weak calcium reaction which, by moistening the wire 
 with hydrochloric acid, became for a moment very brilliant. 
 If we treat a few decigrams of the residue of sea-water, in the 
 way described for lithium, with sulphuric acid and alcohol we 
 easily obtain the reaction of potassium and lithium. The pres- 
 ence of strontium in sea- water can be observed best in the 
 boiler crusts of steamships. The filtered hydrochloric acid 
 solution of the same leaves, on evaporation and solution in the 
 smallest quantity of alcohol, a dull yellow coloring from the 
 basic iron salt which is deposited after some days and collected 
 on a filter and washed with alcohol. The filter burnt on a fine 
 platinum wire gives, along with the calcium line, a complete 
 and bright strontium spectrum. 
 
 2. Mineral waters often show at once the potassium, sodium, 
 lithium, calcium, and strontium reactions. For example, if 
 we introduce a drop of Durkheim or Krauznach mineral water 
 into the flame we obtained the lines Na a, Li a, Ca a, and Ca /?. If 
 we use instead of the mineral water a drop of the mother liquid 
 the same lines appear with great brilliancy. In proportion as 
 the chloride of sodium and lithium are volatilized and the 
 chloride of calcium has become more basic, the characteristic 
 lines of the strontium spectrum gradually develop themselves 
 and, becoming brighter, finally are seen in all their extent. We 
 obtain here also, by a mere glance at a single drop vaporized in 
 the flame, the complete analysis of the mixture of five sub- 
 stances in a few moments. 
 
 3. The ash of a cigar moistened with some HC1 and held in 
 the flame gives the lines Naa, Ka, Li a, Caa, Cap. 
 
 4. Potash glass of a combustion tube gave, both with and 
 without hydrochloric acid, Na a and K a, and treated with 
 
 11? 
 
MEMOIRS OK 
 
 fluoride of ammonium and sulphuric acid Caa, Cap and traces 
 of Li a. 
 
 5. Orthoclase from Baveno gives either alone or with hydro- 
 chloric acid only No, a. with traces of K a and Lia\ with fluoride 
 of ammonium and sulphuric acid the intense line Naa, K a and 
 somewhat less distant Li a. After volatilizing the constituents 
 thus observed the bead introduced, into the flame with HCl, 
 gives only a scarcely distinguishable flash of the lines Caa arid 
 Cap. The residue remaining on the platinum wire after this 
 test showed, when moistened with cobalt solution and heated, 
 the characteristic color of alumina. If we employ the well- 
 known reaction of silicic acid also it follows from this examina- 
 tion, made in a few minutes, that the orthoclase from Baveno 
 contains silicic, alumina, potash with traces of soda, lime and 
 lithia whilst every trace of baryta and strontia fail. 
 
 6. Adularia from the Gotthard conducted itself quite similar 
 to the orthoclase from Baveno only that the lithium reaction 
 fulled entirely and the calcium reaction nearly so. 
 
 7. Labradorite from St. Paul gives, by itself, only the sodium 
 line Na a and not the calcium spectrum. But the sample moist- 
 ened with hydrochloric acid gives the calcium lines CWand 
 Cap very brilliantly. With the test by means of fluoride of 
 ammonium we still obtain a weak potassium reaction and very 
 faint traces of lithium. 
 
 8. Labradorite from the Diorite of Corsica comported itself 
 similarly only that the traces of the lithium reaction were 
 wanting. 
 
 9. Mosanderite from Brevig and Tscheffkinite from thellmen 
 mountains gave by itself only the sodium reaction, but the cal- 
 cium line Caa and Cap when treated with hydrochloric acid. 
 
 10. Melinophane from Lamoe gave by itself only Naa but 
 with hydrochloric acid Caa, Cap and Li a. 
 
 11. Scheelite and Sphene gave, on treatment with hydro- 
 chloric acid, the very brilliant calcium reaction. 
 
 12. If small quantities of strontium are present with calcium 
 we employ the line Sr6 most advantageously to detect the for- 
 mer. By means of the same it is easy to detect a small content 
 of strontium in very many sedimentary limestones. Na a,Li a 
 R a particularly Li a are shown immediately on heating the 
 
 118 
 
KAUIATION AND ABSORPTION. 
 
 limestone in the flame. Those minerals, converted into cal- 
 cium chloride by hydrochloric acid and introduced into the 
 flame in this form, give the same lines and besides frequently 
 the line Sr 6 quite distinctly. But this appears only for a short 
 time and most distinctly whilst it is being developed in the 
 course of the volatilization in the flame and shortly before the 
 fading out of the calcium spectrum. 
 
 In this way the lines Naa, Li a, Ka,Caa,Cap, Sr 6 were found 
 in the following limestones : 
 
 Silurian limestone 1 from Kugelbad near Prague, 
 
 Shell limestone from Rohrbach near Heidelberg, 
 
 Lias limestone from Malsch in Baden, 
 
 Chalk from England. 
 
 The following limestones showed the lines Naa, Lia, Ka,Ca a , 
 Cap, without the blue strontium line: 
 
 Marble from the granite of Auerbach, 2 
 
 Devonian limestone from Gevolstein in the Eifel, 
 
 Carboniferous limestone from Planite in Saxony, 
 
 Dolimite from Nordhausen in the Hartz, 
 
 Jura limestones from the Streitberg in Franconia. 
 
 We now see from these few experiments that extended and 
 careful spectral analysis of the lithium, potassium, sodium, 
 and strontium content of various limestone formations are of 
 the greatest geological interest with respect to their order of 
 formation and their local disposition and may possibly lead to 
 unexpected conclusions on the nature of the earlier ocean and 
 sea basins in which the formation of these minerals took place. 
 
 BARIUM. 
 
 The spectrum of barium is the most complicated of the 
 spectra of the alkalis and alkaline earths. It is distin- 
 guished at the first glance from those heretofore examined by 
 
 1 The lithium line could not be detected with certainty in this class of 
 minerals, the line Sr <5 on the contrary was very strong. 
 
 2 By means of the experiment with alcohol above described enough 
 nitrate of strontium was obtained from twenty grams of marble to pro- 
 duce a bright and complete spectrum of strontium. Whether the re- 
 maining limestones treated in this way show a strontium content we 
 have not investigated. 
 
 119 
 
MEMOIRS ON 
 
 the green lines Ba a and Bap, which exceed all the others in 
 brilliancy, appearing first and disappearing last in weak reac- 
 tions. Ba y is less distinct but is still always to be treated as a 
 characteristic line. The relatively great extension of its spec- 
 trum is the reason why the spectral reaction of the barium com- 
 pounds is somewhat less delicate than those of the substances 
 heretofore examined. 0.3 grams of chlorate of barium 
 burned in onr room with milk sugar gave, after the air had 
 been thoroughly mixed by moving an open umbrella, the line 
 Ba a most distinctly, for a long time. We may therefore con- 
 clude from a calculation made similar to that for sodium, that 
 the reaction will show, with perfect distinctness, not less than 
 TTJ ^oth of a milligram. 
 
 Chloride, bromide, iodide, and fluoride of barium, the hy- 
 drated oxide, the sulphate, and the carbonate, give the reac- 
 tion most markedly and can therefore be determined by 
 immediate heating in the flame. 
 
 Silicates decomposable by hydrochloric acid containing ba- 
 rium give the reaction, if, as indicated in the case of lime, they 
 are introduced into the flame with, a drop of hydrochloric acid. 
 Thus, for example, barytharmotome treated in this way gives 
 the line Caa Cap along with the lines Baa.Bap. 
 
 Compounds of barium with non-volatile acids, which are 
 indifferent with or without hydrochloric acid in the flame, we 
 may fuse best, in the way given for strontium, with carbonate of 
 sodium and then test the carbonate of barium thus obtained. If 
 in such compounds Ca, Ba and Sr occur together in very unequal 
 amounts, we dissolve in a drop of sulphuric acid the carbonates 
 obtained by fusion and extract the salt with alcohol from the 
 evaporated residue. The residue then contains only barium and 
 strontium both of which may be easily detected if they do 
 not occur in too unequal quantities. When it is desired to test 
 for the smallest traces of Sr or Ba, we transform the residue, 
 by heating with sal ammoniac, into chlorides, from which the 
 chloride of strontium can be easily extracted in a sufficiently 
 concentrated state for detection by means of alcohol. If neither 
 of the substances to be tested is present in very small quantities 
 all such methods of separation are quite unnecessary, as the 
 following experiment shows: a mixture of sodium, potassium, 
 
 120 
 
RADIATION AND ABSORPTION. 
 
 lithium, calcium, strontium, and barium chlorides which con- 
 tained iUh of a milligram of each of these six substances at the 
 most, was introduced into the flame and observed. At first 
 the brilliant sodium line Naa appeared on the background of 
 a weak continuous spectrum. As soon as this began to fade 
 away, the sharply defined brilliant red line of lithium Li a ap- 
 peared and on the same side of the sodium line, still farther 
 away, the faint potassium line Ka whilst the barium lines Baa 
 and Ba p appeared very distinctly in their characteristic position 
 and peculiar shade. Whilst the compounds of potassium, 
 lithium, and barium were slowly volatilized their lines faded 
 away, or vanished again gradually in succession until, after a 
 few minutes, the lines Caa Cap and Sra /bV/s Sr% Sr 6 became 
 visible out of the less and less prominent lines of strontium, as 
 from a dissolving view, in all their characteristic form, shade 
 and position, and then faded away and entirely vanished after 
 a very long time. 
 
 The absence of any one or more of these components could 
 be instantly detected, in the observation, by the absence of the 
 corresponding lines. 
 
 For those who have become familiar with the individual 
 spectra by repeated observation, an accurate measurement of 
 the individual lines is unnecessary; their color, their relative 
 position, their characteristic definition and shade, the grada- 
 tion in their brilliancy, are criterions which are quite sufficient 
 for definite recognition even for the inexperienced. These 
 characteristics may be compared with the distinguishing fea- 
 tures which the various precipitates present in their outward 
 appearance, which we use as a reaction test. Just as the char- 
 acter of a precipitate determines whether it be gelatinous, pul- 
 verulent, flocculent, granular or crystalline, so also the spectral 
 lines indicate their characteristics in the sharpness of their 
 edges, in the shading off uniformly or irregularly on one or both 
 sides, or in their broader or narrower appearance, as the case 
 may be. And just as we use only those precipitates in analysis 
 which can be produced by the greatest possible dilution, so we 
 also use in spectrum analysis for this purpose only those lines 
 which require for their production the smallest amount of the 
 
 121 
 
MEMOIKS ON 
 
 substance and only a moderately high temperature. In such 
 characteristics therefore the two methods are quite similar. 
 On the contrary spectrum analysis furnishes, in the color phe- 
 nomena used in the reaction, a property which gives it unlimited 
 advantage over every other method of analysis. Most of the 
 precipitates which are used for the detection of substances are 
 white and only a few colored. Further the tint of the latter is 
 not very constant and considerably differentiated according to 
 the greater or less condensed state of the precipitate. Often 
 the smallest mixture of a foreign substance is sufficient to oblit- 
 erate completely a characteristic color. Small differences of 
 color of the precipitate can therefore be no longer used as a 
 chemical test. In spectrum analysis, on the contrary, the colored 
 bands remain undisturbed by such foreign influences and are 
 undisturbed by the presence of other bodies. The positions 
 which they have in the spectrum determine a chemical charac- 
 teristic which is of as unalterable and fundamental a nature as 
 the atomic weight of the substance, and therefore, permits us 
 to determine it with an almost astronomical exactness. What, 
 however, gives to the spectral analytical method a peculiar im- 
 portance, is the fact that it almost infinitely exceeds the limits 
 to which chemical analysis of matter has heretofore reached. 
 It predicts for us the most valuable conclusions on the distribu- 
 tion and arrangement of geological substances in their forma- 
 tion. Already the few investigations, which this memoir 
 contains, lead to the unexpected conclusion that not only 
 potassium and sodium but also lithium and strontium must be 
 counted among the substances of the earth most widely scat- 
 tered, though only in minute quantities. 
 
 Spectrum analysis will also play a not less important part in 
 the discoveries of elements not yet detected. For if there are 
 substances which are so sparsely scattered in nature that the 
 methods of analysis heretofore used in observing and separating 
 them fail, we may hope to detect and determine many of them, 
 by the simple examination of their spectra in flames, which 
 would escape the ordinary method of chemical analysis. That 
 there are actually such elements heretofore unknown we have 
 .already had an opportunity of showing. We believe that we 
 shall be able yet to declare with absolute certainty, supported 
 
 122 
 
RADIATION AND ABSORPTION. 
 
 by the unquestioned results of spectral analytical methods that 
 besides potassium, sodium and lithium, there is still a fourth 
 metal belonging to the alkali group which will give quite as 
 characteristic a spectrum as lithium a metal which shows, 
 with our spectral apparatus, only two lines, a weak blue line, 
 which almost coincides with the strontium line Srd and another 
 blue line, which lies only a little farther toward the violet end 
 of the spectrum, rivaling in intensity and distinctness the lith- 
 ium line. 
 
 On the one hand spectrum analysis offers, as we believe we 
 have already shown, a means of wonderful simplicity for de- 
 tecting the slightest traces of certain elements in terrestrial 
 substances, and on the other, it opens up to chemical investi- 
 gation a field heretofore completely closed, which extends far 
 beyond the limit of the earth even to our solar system itself. 
 Since, by the analytical method under discussion, it is sufficient 
 simply to see the gas in an incandescent state in order to make 
 an analysis, it at once follows that the same is also applicable to 
 the atmosphere of the sun and the brighter fixed stars. A modi- 
 fication with respect to the light which the nucleus of these 
 heavenly bodies radiate must be introduced here. In a memoir 
 "On the Relation between the Emission and the Absorption of 
 Bodies for Heat and Light " 1 one of us has proven, by theo- 
 retical considerations, that the spectrum of an incandescent gas 
 is reversed, that is, that the bright lines are transformed into 
 dark ones when a source of light of sufficient intensity, 
 which gives a continuous spectrum, is placed behind the same. 
 From this we may conclude that the sun's spectrum, with its 
 dark lines, is nothing else than the reversal of the spectrum 
 which the atmosphere of the sun itself would show. Hence the 
 chemical analysis of the sun's atmosphere requires only the 
 examination of those substances which, when brought into a 
 flame, produce bright lines which coincide with the dark lines 
 of the solar spectrum. 
 
 In the article mentioned, the following examples are given 
 as experimental proof of the theoretically deduced law referred 
 to: 
 
 1 Kirchhoff, Pog. Ann. Vol. CIX p. 275. See previous memoir. 
 
 123 
 
MEMOIRS ON 
 
 The bright red line in the spectr-um of a flame in which a 
 bead of chloride of lithium is introduced is changed into a 
 black line when we allow full sunlight to pass through the 
 flame. 
 
 If we substitute for the bead of lithium one of sodium chlo- 
 ride, the dark double line D (which coincides with the bright 
 sodium line) shows itself in the sun's spectrum with unusual 
 brilliancy. 
 
 The dark double line D appears in the spectrum of the Drum- 
 mond's light if we pass its rays through the flame of aqueous 
 alcohol, into which we have introduced chloride of sodium. 1 
 
 It will not be without interest to obtain still further confir- 
 mations of this remarkable theoretical law. We may arrive at 
 this by the investigation which will now be described. 
 
 We made a thick platinum wire incandescent in a flame and 
 by means of an electric current brought it nearly to its melting 
 point. The wire gave a brilliant spectrum without any trace 
 of bright or dark lines. If a flame of very aqueous alcohol in 
 which common salt was dissolved were introduced between the 
 wire and the slit of the apparatus, the dark line D showed it- 
 self with great distinctness. 
 
 We can produce the dark line D in the spectrum of a platinum 
 wire which has been made incandescent by a flame if we merely 
 hold before it a test tube into which some sodium amalgam has 
 been introduced, and then heat it to boiling. This investiga- 
 tion is important, on this account, in that it shows that far 
 
 1 In the March number of the Philosophical Magazine for 1860 
 Stokes calls attention to the fact that Foucault had made already an 
 observation in 1849 which is similar to that mentioned above. In the 
 examination of the electric arc between two carbon points he observed 
 (1, Institut 1849, p. 45) that in the spectrum the same bright lines were 
 present in the position of the double line D of the solar spectrum, and 
 that the dark line D of the arc is intensified, or produced, if we allow 
 the rays of the sun or one of the incandescent points to pass through it 
 and then resolve them in the spectrum. The observation mentioned 
 in the text gives the explanation of this interesting phenomena already 
 observed by Foucault eleven years before and shows that the same is not 
 influenced by the peculiarity of the electric light, which is still, from 
 many points of view, so enigmatical, but arises from a sodium compound 
 which is contained in the carbon and is transformed by the current into 
 incandescent gas. 
 
 124 
 
RADIATION AND ABSORPTION. 
 
 below the point of incandescence of sodium vapor, its absorbent 
 effect is exercised exactly in the same parts of the spectrum 
 as with the highest temperatures which we are able to produce 
 and at which that of the solar atmosphere exists. 
 
 We have been able to reverse the bright lines of the spectra 
 of K, Sr, Ca, Ba by the employment of sunlight and mixtures 
 of the chlorates of these metals with milk sugar. Before the 
 slit of the apparatus a small iron trough is placed; into this the 
 mixture was introduced, and the full sunlight passed along 
 the trough to the slit and the mixture ignited on one side by an 
 incandescent wire. The telescope was set with the intersection 
 of its cross hairs, which were mounted at an acute angle with 
 one another, on the bright line of the flame spectrum, the 
 reversal of which was to be tested; the observer concentrated 
 his attention on this point in order to judge whether at the 
 moment of ignition a dark line was visible, passing through 
 the intersection of the cross hairs. In this way it was quite 
 easy with the proper proportion of the mixture, to be burnt, to 
 establish the reversal of the lines Ba a and Ba ft and the line 
 K /3. The last of these coincided with one of the most distinct 
 lines of the solar system, although not indicated by Fraunhofer; 
 this line appeared much more distinctly at the moment of ig- 
 nition of the potash salt than otherwise. In order to observe 
 the reversal of the bright lines of the strontium spectrum in the 
 way described, the chlorate of strontium must be dried in the 
 most careful manner; a slight trace of moisture causes the sun's 
 rays to be weakened and produces the positive spectrum of 
 strontium on account of the flame becoming filled with salt 
 particles which have been spattered about by the ignition. 
 
 "We have limited ourselves in this memoir to the investiga- 
 tion of the spectra of the metals of the alkalis and alkaline 
 earths, and these only in so far as was necessary for the analysis 
 of terrestrial matter. We reserve for ourselves the further 
 extension of these investigations which are desirable in connec- 
 tion with the analysis of terrestrial substances and the analysis 
 of the atmospheres of the stars. 
 Heidelberg, April, 1860. 
 
 125 
 
MEMOIRS ON RADIATION AND ABSORPTION. 
 BIOGRAPHICAL SKETCH. 
 
 ROBERT WILHELM BUNSEN was born in Gottingen March 15, 
 1811. He received his doctor's degree in 1830 and became 
 private-decent in 1833 in that University. In 1836 he became 
 Professor of Chemistry in the Polytechnic School at Cassel and 
 in 1838 accepted a similar position in the University of Mar- 
 burg. In 1851 he went to Breslau and the following year to 
 Heidelberg, where he remained until his death. Both as a 
 teacher and as an investigator, he was one of the most eminent 
 of his generation, making many important contributions to 
 both Physics and Chemistry. His spectroscope, photometer, 
 calorimeter, gas burner, filter pump, battery, etc., on the one 
 hand, and his early contributions to organic chemistry, the 
 methods of gas analysis, photochemical action, etc., on the 
 other, illustrate the versatility of his genius. His work in con- 
 nection with his colleague, Kirchhoff, resulted in one of the 
 most brillant achievements of the century, the application of 
 the spectroscope to the analysis of terrestrial substances, 
 which revealed at once several new elements and showed the 
 common constitution of all bodies in the stellar system. His 
 final contribution was made in 1887 after an illustrious scientific 
 career of nearly sixty years. During his last years he was a 
 familiar figure on the streets of Heidelberg, in which city he 
 died Aug. 15, 1899. 
 
 136 
 
BIBLIOGRAPHY. 
 
 Brief list of publications of historical importance. 
 
 NEWTON. [Radiation.] Phil. Trans, p. 827. 1701 
 
 PICTET. Essai sur le Feu. 1791 
 
 PREVOST. Recherches sur la Chaleur, Jonr. de Phys. 1792 
 PREVOST. Du Calorique Rayonnant, 8 Geneva. 1809 
 
 PREVOST. Sur la Transmission du Calorique, etc., Jour. 
 
 de Phys. de Chim. 1811 
 
 HERSCHEL, W. [Radiations beyond spectrum.] Phil. 
 
 Trans. 1800 
 
 LESLIE, J. Inquiry into the Nature, etc., of Heat. 
 
 London. 1804 
 
 RUMFORD. Memoires snr la Chaleur. Paris. 1804 
 
 DELAROCHE. Obser. sur la Calorique Rayonnant, Journ. 
 
 de Phys. de Chim. 1812 
 
 FOURIER. Sur la Chaleur Rayonnant Journ. de Phys. 
 
 de Chim. 1817 
 
 DULONG ET PETIT. [Law of Cooling.] Ann. de Chim, 
 
 et de Phys. 1818 
 
 HERSCHEL, J. [Spectra of Colored flames.] Ed in. Phil. 
 
 Trans. 1822 
 
 FRAUNHOFER. [Spectra of flames] Gilbert's Ann. 
 
 1823, Harper's Series II. 1898 
 
 TALBOT. [Spectra of flames.] Brewster's Jour, of Sci. 
 
 1826 
 MELLONI. Sur la transmission de la chaleur Rayonnant, 
 
 etc., Ann. de Chim. et de Phys. 1833-37-39 
 
 MELLOXI. La Thermochrose ou la Coloration Calori- 
 que, Naples. 1850 
 DE LA PROVOSTAYE ET DESAINS. [Law of Cooling.] 
 
 Ann. de chim. et de Phys. 
 127' 
 
MEMOIRS ON RADIATION AND ABSORPTION. 
 
 DE LA PROVOSTAYE ET DESAINS. [Relation of Absorp- 
 tion and Emission.] Ann. de Chim. et de Phys. 1853 
 DRAPER, J. [Law of Draper.] Phil. Mag. 1847 
 
 DRAPER, J. [Max, Solar Energy.] Phil. Mag. 1857 
 
 FOUCAULT. [Reversal of D lines.] Soc. Philomatiqne 1849 
 STOKES. [Note on Foucault and KirchhofFs Obs.] 
 
 Phil. Mag. March. 1860 
 
 STEFAN. [Stefan's Law.] Wien. Akad. Ber. 1879 
 
 LANGLEY. Researches on Solar Heat. Washington. 1884 
 BOLTZMANN. [Deduction of Stefan's Law.] Wied. 
 
 Ann. XXII. 1884 
 
 WIEDEMANN, E. [Luminescence of Vapors.] Wied. 
 
 ;, ; ( 1879 
 
 Ann. < 1889 
 
 (1895 
 
 RAYLEIGH. [Radiation and Molecular Motions.] Phil. 
 
 Mag. 1889 
 
 WEBER, H. F. [Weber's Law A Jftf = const.] Berl. Akad. 
 
 Ber. 1888 
 
 WIEN. [Laws of Displacement, Emission, etc.] Wied. 
 
 Ann. j 1894 
 
 (1896 
 PLANCK. [Law of Emission.] Ber. Deut. Phys. GeselL 
 
 Oct. 1900 
 
 128 
 
INDEX. 
 
 A 
 
 Absorption and Radiation, Relation of .... 40 
 
 Assumption made in establishing Kirchhoff's law . . 76 
 
 Alum, Observation on . . 27 
 
 B 
 
 Barium, Observations on 119 
 
 Bath, Description of 25 
 
 Black bodies, Proof of law of radiation for . . 78 
 
 Bunsen, Biography of 126 
 
 C 
 
 Calcium, Observations on 115 
 
 Caloric, Nature of 17 
 
 " Clausins' " law ',. . . 94 
 
 Cold, Reflection of 7 
 
 Conduction and Radiation, Relation of .... 49 
 
 D 
 
 Diathermancy, Table of 37 
 
 " General 69 
 
 Distance, Law of 9 
 
 Draper's law 95 
 
 Dulong and Petit's law ........ 67 
 
 E 
 
 Emissive and Absorptive power 75 
 
 Equilibrium of heat, Meaning of the 4 
 
 F 
 
 Fluids, Radiant and non-radiant ..... 12 
 
 Foucault, Observations of . ' . . . . . . . 124 
 
 129 
 
INDEX. 
 
 G 
 Glass, Observations on . . . . . 26-29-12 
 
 H 
 
 Heat, Conduction of ...'.. . 12 
 
 Absolute and relative equilibrium of ... 7 
 
 " Nature of . . 4 
 
 Helmholtz, Law of . ; . ... . . . 88 
 
 High temperatures, Radiation at 59 
 
 K 
 
 Kirchhoff, Biography of 97 
 
 L 
 
 Lampblack, Use of 26 
 
 Le Luc, Ideas of / . . . 3 
 
 Le Sage, Theory of . . ..,.,. ;. ,. . 4-17 
 
 Leslie, Observations of . 26 
 
 Lithium, on ...... r . 109 
 
 M 
 
 Mercury, Eadiations from . ... . . . 61 
 
 Mica, Observations on . . , . . . . . . 27-29-32 
 
 Mutual Radiations of black bodies . | , . . 83 
 
 P 
 
 Pictet, Experiments of . .... .' . ', . . 8 
 
 Potassium, Observations on . . . . . . 42 
 
 Prevost, Biography of 20 
 
 Principles and Conclusions, Resume of .... 18 
 
 Q 
 
 Quality of heat radiated, Experiments on . . . . 33-34 
 
 R 
 
 Radiation and absorption, Relation of .... 40 
 
 " from polished surfaces and lampblack ... 26 
 
 " and refractive power, Connection between . . 42 
 
 *' and conduction, Relation of 49 
 
 " for different thicknesses, Law of . . . . 29-31 
 
 Radiant Heat, Second Series 53 
 
 Radiating Substances, Table of 28 
 
 Ratio between Emissive and absorptive power of ajl bodies 78 
 
 130 
 
INDEX. 
 
 Refractive power on radiation, Influence of ... 42 
 
 Reflective " ' 4< " "... 42 
 
 Reversal of Spectra . 123 
 
 Rock-salt, Observations on 28-30-33 
 
 " Quality of heat radiated from .... 54 
 
 Selenite, Observations on 27 
 
 Sodium, Observations on 107 
 
 Spectral Observations 101 
 
 Spectra produced by spark . 106 
 
 Stewart, Biography of .... .... 72 
 
 Strontium, Observations 011 113 
 
 Swan, Observations of 107 
 
 T 
 
 Temperature and Radiation, Law connecting ... 64 
 
 Temperature of different flames 105 
 
 Theory of exchanges, Extension of 23 
 
 Thermo-multiplier, Description of 24 
 
 Thick and thin Plates, Radiation from . 33-34 
 
 Tourmaline, Radiation and Absorption of .... 95 
 
 131 
 
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Gray's Series of Botanies 
 
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Biology and Zoology 
 
 DODGE'S INTRODUCTION TO ELEMENTARY PRACTICAL 
 BIOLOGY 
 
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 By CHARLES WRIGHT DODGE, M.S., Professor of Biology 
 in the University of Rochester . . . . . $1.80 
 
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 ORTON'S COMPARATIVE ZOOLOGY, STRUCTURAL AND 
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