— , VSS : . oe > sf Z Sn fh Gwe og wee oh 84 SEP Oe [ENTIFIC MEMOIRS, TN €2 - SELECTED FROM THE TRANSACTIONS OF FOREIGN ACADEMIES OF SCIENCE AND LEARNED SOCIETIES, AND FROM FOREIGN JOURNALS. EDITED BY RICHARD TAYLOR, F‘S.A., fELLOW OF THE LINNZAN, GEOLOGICAL, ASTRONOMICAL, ASIATIC, STATISTICAL, AND GEOGRAPHICAL SOCIETIES OF LONDON ; HONORARY MEMBER OF THE NATURAL HISTORY SOCIETY OF MOSCOW. UNDER SECRETARY. OF THE LINNZAN SOCIETY. VOL. I. LONDON: PRINTED BY RICHARD AND JOHN E. TAYLOR, RED LION COURT, FLEET STREET. SOLD BY LONGMAN, REES, ORME, BROWN, GREEN, AND LONGMAN; BALDWIN AND CRADOCK; CADELL; RIDGWAY AND SONS; SHERWOOD, GILBERT, AND PIPER; SIMPKIN AND MARSHALL ; B. FELLOWES; S. HIGHLEY ; WHITTAKER AND CO.; AND J. B. BAILLIERE, LONDON :—AND BY A. AND C. BLACK, AND THOMAS CLARK, EDIN- BURGH; SMITH AND SON, GLASGOW :—MILLIKEN AND SON, AND HODGES AND NW’ ARTHUR, DUBLIN :—DOBSON, PHILADELPHIA ‘AND GOODHUGH, NEW YORK. 1837. pie tes @. PREFACE. —— IN the publication of the four parts which complete the pre- sent volume of the Scientific Memoirs, I have ventured to make the experiment how far I might be able to succeed in supplying an auxiliary which, as was stated in the Advertisement prefixt to the First Part, appeared to be much needed for the progress and advancement of science in this country. My own conviction of the utility of such a work has been much strengthened since I have been engaged in it, both by the importance of the materials that present themselves, and by the expressed opinions of persons most competent to judge. How great ihdeed the disadvantage must be, under which those are placed who are engaged in any branch of scientific inquiry, from being uninformed as to what is doing, or has been done, by our active and laborious neighbours on the Continent, must be obvious to every one: and the cases are numerous to which the remark of Lenz, p. 312, speaking of Ohm’s theory of the gal- vanic battery, will apply,—that, although given to the world several years ago, yet, “being only published in the German language, it is unknown both in France and in England.” With regard to the execution of the work, I must submit it to the candid judgement of those who are aware of the difficulty of the task,—having availed myself of the valuable suggestions with which I have been favoured in the selection of memoirs, and of the best assistance within my reach for their translation. I shall be satisfied if what has been done should render the present volume useful to science, and if what there is still to do should induce the public to enable me to continue the work. Hitherto, as I can hardly yet boast of the sale of 250 copies, I am very far from having been repaid the cost of publication, to say nothing of the care and labour which have been required : nor could I be expected, having now finished a volume, which, from the nature of its materials, may be considered a complete work in itself, to proceed further unaided, until I have ascer- iv PREFACE. tained whether I may calculate upon adequate support. This, however, I cannot yet think it improbable that I shall obtain, when the plan and contents of the present volume shall have become better known ; and with this view, I shall gladly receive the names of those who may be disposed to uphold the work by purchasing what has been published, and forming the list of my future subscribers. I should hardly have been disposed to persevere further, had it not been for repeated expressions of strong interest in the success of the work, which have reached me from persons of the highest scientific eminence; among whom [ may perhaps without impropriety mention the names of Ivory, of Babbage, Powell, Forbes, Lloyd, Challis, Owen, Wheatstone, Phillips, Talbot, Hamilton, Faraday, and others in this country, and of Hare, Henry, and Bache in the United States. To several of them I have been indebted for very important suggestions ; and to Professor Wheatstone especially, for his valuable con- tributions. From the kind assistance of men of science, and from an increased acquaintance with the sources whence the best mate- rials are to be derived*, I think I may fairly hold out to the public the prospect of some considerable improvements in the work: and I shall be thankful for any suggestion for this purpose. I may perhaps give the titles or early notices of such foreign scientific papers as shall not be adopted for immediate translation: and as our first volume may be said to have cleared off some arrears, we may now come nearer to the present time, and endeavour to supply what is of the latest date and of in- trinsic value. However, this, as I have already stated, must depend upon my prospect of future support, and the success of the present volume ;—and, glad to have finished my humble but laborious task in completing it, I shall be able at my leisure to decide as to the future. RICHARD TAYLOR. Red Lion Court, June 29, 1837. * Arrangements have been made for obtaining such as may appear in the Swedish, Dutch, and Italian languages. CONTENTS OF VOL. I. \ PART I. Advertisement to the Reader. Art. I—Memoir on the Free Transmission of Radiant Heat through different Solid and Liquid Bodies ; presented to the Academy of Sciences of Paris, on the 4th of February, 1833. (AN OLLIE RE a cea Bo eee ts PAC ec i ae Art. IJ.—New Researches relative to the Immediate Transmis- sion of Radiant Heat through different Solid and Liquid Bodies ; presented to the Academy of Sciences on the 21st of April, 1834, and intended as a Supplement to the Memoir on the same subject presented to the Academy on the 4th of Memrmity S05... By IV. MELLONT n .. cecuhe me ooh. « eae op « Art. III.—Experiments on the Circular Polarization of Light. By Prof. H. W. Dove of Berlin ...... Arr. 1V.—Description of an Apparatus for ae i Paes nomena of the Rectilinear, Elliptic, and Circular Palos of Light. By Prof. H.W. Dove. : Art. V.—Memoirs on Colours in Sersiy aad erence ona new Chromatic Scale deduced from Metallochromy for Sci- entific and Practical Purposes. By M. Leoroitp Nositt of Reggio. . mee amet Arr. VI. >On “ates Mathematical aici cite Heat ae S. D. Potsson, Member of the Institute, &c.. 5 Art. VII.—Researches on the Elasticity oF MBodies seen ne stallize regularly. By Ferix Savarr.. Art. VIII.—Experiments on the Essential Oil of ig oes Ulmaria, or Meadow-Sweet. By Dr. Lowrie, Professor of Chemistry at Zurich ......... Art. IX.—Researches relative to tie’ Wicca, Se ‘to ‘the Ancients and Moderns, by which the Vine_is infested, and on the Means of prey hi their ae By M. Le Baron WALCKENAER. . = Nalanda aie: Page. ~I oO 86 94: 122 139 153 167 vi j €ONTENTS. PART II. Page. Art. IX. eb tnshiaenye: 5 1 See. CLE Art. X.—The Kingdoms of Nate this Life “ahd Aitinitys By Dr. C. G. Carus, he. - to His Majesty the King of Saxony ... 223 Art. XI. Researches: on the ‘Bastia of Bodies high ery fale lize regularly. By Fexrix Savart..... 225 Arr. XII.—Researches concerning the Nsture or the Bleatiing Compounds of Chlorine. By J. A. Batarp ..... . 269 Art. XIII.—On the Laws of the Conducting Powers of Wires = different Lengths and Diameters for Electricity. By E. Lenz 311 Art. XIV.—Memoir on the Polarization of Heat. By M. Met- LONE 5.4 82a serge Spee eee oe ae PART: IIt: Advertisement on the Publication of Part III. Art. XV.—Memoir on the Motive Power of Heat. By E. CLapeyron, Mining Engineer ..... oe OST, Arr. XVJ.—Remarks on the cause of the ‘Sound ‘produced by Insects in flying. By Dr. Hermann Burmeister, of the University of Berlin ome Art. XVII.—Note on the ficAuctiont of feighnant Heat. By M. WEMELON Ess y'o5 eke os ee ae anit 2 Oe 383 Art. XVIII.—Observations and Experiments on the Theory of the Identity of the Agents which produce Light and Radiant 377 Heat. . By M MELEONI 20m oo aes spe ca oe 388 Art. XIX.—On the Constitution of the Superior Regions of the Earth’s Atmosphere. By M. Brot ....... .* 393 Art. XX.—Remarks on the real Occurrence of F ‘att furan and their extensive Diffusion. By Prof. EHRENBERG...... 400 Further Notices of Fossil Infusoria. By the Same ........ 407 Art. XXI. On the Chemical Effects of Electric Currents of low tension, in producing the Crystallization of Metallic Oxides, Sulphurets, Sulphates, &c.; in forms frequently closely re- sembling the native combinations. By M. BecqurreL .... 414 Art. XXII. Ona New Combination of the Anhydrous Sulphuric _ and Sulphurous Acids. By Henry Ross, Professor of Che- mistry at the Royal University of Berlin ...... 443 Arr. XXIII.—On the Forces which regulate the Internal Consti- tution of Bodies. By O. F. Mossorrs. oH ommunicated nee M. Farapay, Esq., D.C.L., F.R.S., &¢.). . x, ... 448 CONTENTS. Vii Page. Art. XXITV.—On certain Combinations of a New Acid formed of Azote, Sulphur, and Oxygen. By J. Petouze ..... . 470 Art. XXV.—An Attempt to explain the Absorption of Take ac- cording to the Shenae wie By Baron FaBian von Warvr Ee ak oe. eI a ea ga nin UE, PART IV. Art. XXV.—(continued.) . . 483 Art. XXVI.—On the Repidation of Bader Ni orptileriy a ee Movement of Machines. By M.H. Jacos1, Doctorof Science, and Professor at the University of Dorpat .............. 503 Note on the Application of Electro-Magnetism as a Mechanical Power. By I. D. Borro, Professor of Natural Philosophy in the Royal University of Turin ...... 532 Part of a Lecture on Electro-Magnetism, Welivened, rm the Phi- losophical Society at Zurich, erie the 18th, 1833. By the late Dr. R. ScHULTHESS ...... . 534 On the Influence of a Spiral Conductor ir in fee ae sithe init sity of Electricity from a Galvanic Arrangement of a Single Pair, &c.- By Professor Henry, of New Jersey, U.S. .... 540 Art. XXVIJ.—A singular case of the Equilibrium of Incompres- sible Fluids. By M. Ostrocrapskvy. . 548 Art. XXVIII.—On the Origin of Organic Matter frot Be: Perceptible Matter, and on Organie Molecules and Atoms ; together with some Remarks on the Power of Vision of the Human Eye. By Prof. C. G. EHRENBERG ..... 555 Art. XXIX.—On the Application of Circular electra | to Or. ganic Chemistry. By M.M. Bror and CHEvreuL........ 584 On the Application of Circular Polarization to the Analysis of the Vegetation of the Graminez. By M. Biot .......... 584: Examination of an Optical Character, by which, according to M. Biot, Vegetable Juices capable of producing Sugar ana- logous to Cane Sugar, and those capable only of producing Sugar similar to Grape Sugar, may be immediately distin- guished. By M. Cuevreur ...... . 591 On the Application of the Laws of Ginemiae Beldeeation to Gite Researches of Chemistry. By M. Bior ..... 600 Arr. XXX.—On the Laws according to which the Mapnet acts upon a Spiral, when it is suddenly approached to or removed from it; and on the most advantageous Mode of constructing Spirals for Magneto-Electrical purposes. By E. Lenz .... 608 Vili ¥; VII. LIST OF PLATES. LIST OF PLATES. M. Mettonr’s Experiments on the Immediate Transmission of Radiant Heat, pp. 42 and 55. Dove’s Apparatus for the Polarization of Light, p. 79. . Savart’s Researches on the Elasticity of Bodies by means of Sonorous Vibrations, p. 143. Savart’s Researches on the Elasticity of Bodies which cry- stallize regularly, p. 262. BurMEIsTER’s Remarks on the Sound produced by Insects; and EnReENBERG’s Memoirs on Fossil Infusoria, pp. 378 and 413. VI. To illustrate Baron von WreEDE’s Memoir on the Absorption of Light, p. 480. Jacosi’s Electro-magnetic Machine, p. 507 ; and ScHULTHESsS’s Electro-magnetic Machine, p. 539. a] Fe TW Gs Yes Get 3) 5) En cas ERRATA. 156, line 4, for 8°35. read 5°35 158, line 37, insert a comma after Calcium 160, line 41, for 0:350 carbon read 0°350 carbonic acid —., line 43, for 0°450 carbon read 0°450 carbonic acid —, line 43, for 0°0759 read 0:075 water 162, line 3, for sesquichromate read sesquichloride 164, line 6, for them read bases — , line 22, for *754 read 0°754 —., line 34, after stated that insert from —., line 34, omit contained —., line 35, after chloride of spiroil insert more obtained —., line 37, for 11°56 read 111°56 165, line 18, for 0°510 water read 0'119 water 470, line 5, for vol. xvi. read vol. lxvi —., four lines from bottom, for (Reaum.) read (Centigr.) 471, last line, for precipitated read before-mentioned 472, line 11, for in the same manner, read of the same kind —, line 33, for discoloured read decoloured —., line 41, for — 15° read 15° 473, two lines from bottom, for give them read give it 474, three lines from bottom, for of read and 475, line 28, for Ka? read K a, 476, line 6, for sulphur read sulphite SCIENTIFIC MEMOIRS. VOL. I.—PART I. ARTICLE I. Memoir on the Free Transmission of Radiant Heat through different Solid and Liquid Bodies ; presented to the Royal Academy of Sciences of Paris, on the 4th of February, 1833, by M. Metuont1. From the Annales de Chimie et de Physique, t. i111. p. 1. Manrrorte was the first, so far as I am aware, who attempted to appretiate the action of diaphanous substances in transmitting or inter- cepting the calorific rays which emanate from terrestrial sources. After having observed that solar heat concentrated at the focus of a metallic mirror, suffered no sensible diminution of intensity by being made to pass through a glass plate, he took and placed his apparatus before the fire of a stove, and found, that at the distance of five or six feet the tempe- rature of the reflected image at the focus, when the rays were allowed to meet there without impediment, was such as the hand could not bear; but that when the plate of glass was interposed there was no longer any sensible heat, although the image had lost none of its brillianey. Whence he concluded that none *, or certainly but a very small portion, of the heat of terrestrial fire passes through glass. About a century after Mariotte’s time, the same experiment was re- peated by Scheele, who, instead of imitating the cautious reserve of his predecessor, asserted that from the moment when the glass was inter- posed there was no longer any heat whatever at the focus of the mirror +. * Mariotte, Z'raité de la Nature des Couleurs; Paris, 1686, part 2, at the end of the Introduction. + Scheele, Vraité del Air et du Feu ; Paris, 1781, § 56.—The original work of Scheele was published in 1777. Mariotte died in 1684. Vor. I—Parrt 1. B g M. MELLONI ON THE FREE TRANSMISSION Pictet, however, corrected the mistake by means of the apparatus known by the name of conjugate mirrors. A very transparent square of glass was placed between a thermometer and the heat of a lighted candle concentrated by the apparatus; the mercury in some moments rose se- veral degrees ; there was a perceptible elevation of temperature also when the candle was removed and a small jar filled with boiling water put in its place *. Some years later Herschel undertook a very extensive series of ex- periments on the same subject. They are described in the volume of the Philosophical Transactions for 1800. The author employs no artifice to increase the action of the rays of heat, and contents himself with the direct measurement of their effect by placing the thermometer at a very short distance from the diaphanous body. But doubts were started as to the conclusions drawn from these dif- ferent results. It was objected that part of the radiant heat was first stopped at the nearer surface of the glass, that it was gradually accu- mulated there and afterwards propagated from layer to layer, until it reached the further surface whence it began again to radiate on the ther- mometer. It was maintained even that nearly the whole of the effect was produced by this propagation. In short, some went so far as to deny altogether that the heat emitted by terrestrial bodies can be freely trans- mitted through any other diaphanous substance than atmospheric air. M. Prevost, by means of a very ingenious contrivance, demonstrated the erroneousness of this opinion. Having attached to the pipe of a fountain a spout consisting of two parallel plates, he obtained a strip of water about a quarter of a line in thickness. On one side of this he placed an air thermometer and on the other a lighted candle or a hot iron. The thermometer rose, almost always, some fraction of a de- gree+. Now it is quite evident that, in this case, a successive propa- gation through the several layers of the screen, which was in a state of perpetual change, could not take place. It was admitted, therefore, that other diaphanous media besides atmospheric air sometimes transmit the rays of heat as instantaneously as they always transmit those of light. M. Prevost’s process could not however be applied to solid bodies. It was therefore impossible to determine, by means of it, whether caloric was immediately transmitted through screens of glass. Delaroche completely solved this problem by employing a method invented by Maycock tf. * Pictet, Essai sur le Feu, § 52 et seq. + Journal de Physique, de Chimie, d'Histoire Naturelle et des Arts, par M. Delametherie, 1811.—P. Prevost, Mémoire sur la Transmission du Calorique a travers l Eau et d'autres Substances, § 42 et 43. t Nicholson, A Journal of Natural Philosophy, Chemistry and the Arts, vol. xxvi. May and June 1810.—J, D. Maycock, Remarks on Professor Leslie’s Doctrine of Radiant Heat. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 3 The method consists in observing the thermometer as in the preceding eases; that is, when the caloric rays fall upon it after having passed through the plate of glass. We thus obtain a complex measure of the ef- fects produced by immediate transmission and by that conducting power of the layers to which we have given the name of successive propagation. If we know the value of either of these, we have that of the other. Now it is easy to determine the influence of the conducting power by repeating the experiment after having blackened with Indian ink that surface of the plate which is turned towards the calorific source. In this case, theimme- diate radiation being intercepted, it is clear that the elevation of the tem- perature at the other side must be attributed only to the conducting power of the layers. Should the elevation be now found less than it was at first, it will be a decisive proof of immediate transmission. And such was the fact in almost all the experiments of Delaroche; I say almost all, be- cause it was found that the quantity of heat freely transmitted varied with the temperatures of the source. For temperatures lower than that of boiling water it was nothing, and when an Argand lamp* was employed, it was found to be more than half of the whole quantity. No doubt can be raised as to the truth of this beautiful discovery of Delaroche ; and yet the method which he has employed to measure the quantities of heat freely transmitted is by no means exact, especially in respect to high temperatures. In order to understand this seeming para- dox two things are to be observed; Ist, the difference produced by change of surface between the two quantities of heat which penetrate the glass by reason of its conducting power; 2nd, the difference produced be- tween those two quantities by the total or partial interception of the calorific rays. It is fully proved by the experiments of Leslie and others, that glass, when blackened with Indian ink, absorbs all the rays of heat, though, in its natural state, it reflects a certain number of them. The quantity of heat which penetrates the screen will therefore be greater in the former than in the latter case. However, as polished glass reflects but a very small portion of caloric rays, the error arising from a difference in the state of the surface will be reduced to a very inconsiderable quantity and may be safely disregarded. But the case is different when we examine the error produced by the total or partial interception of the caloric ra- diation. In some of the experiments of Delaroche one half, at least, of the incident rays immediately passed through the screen. Thus it was evident that it was the other only which was stopped at the first surface of the glass. The effect of conduction must therefore be limited to this latter half. Butas the screen, when blackened, stops the whole radiation, * Journal de Physique, §c., par Delametherie, 1812,—Delaroche, Observa- tions sur le Calorique rayonnant. BQ 4 M. MELLONI ON THE FREE TRANSMISSION itis then exposed to a heat twice as strong, and therefore exhibits a far greater effect of conduction. Hence it follows that when we deduct from the observation furnished by the transparent glass the observation fur- nished by the glass blackened, the result obtained will be lower than the true temperature of the rays transmitted freely. But the error will not be the same in all cases. Being of no account when boiling water is em- ployed, it will increase in proportion as the temperature of the source is raised. The measures of the free radiations which suffer the greatest diminution will be those furnished by the highest temperatures. Hence it is evident that this latter cause of error in the measure of the imme- diate irradiation, instead of invalidating the law of Delaroche, serves only to give it greater certainty. We are therefore justified in saying, as we have said, that the want of exactness in the method has no influence whatsoever on the truth of the law which it has served to establish. To Delaroche we are also indebted for a discovery, no less important than the foregoing, relative to the amount of loss sustained by the same rays of heat in passing successively through two squares of glass. But I abstain, for the present, from entering into any detail on this subject, as I shall have occasion to speak of it hereafter *. None of those whose labours we have been thus briefly noticing has thought of making an exact comparison between the transmissions of caloric rays through screens of different kinds; and, if we except the experiments of M. Prevost and those of Herschel, from which no con- sequence can be deduced, all the others were confined to the single pur- pose of.ascertaining the law of transmission through glass only. Neither has sufficient attention been given to the influence of the state of the * I must not omit to mention that, notwithstanding the results obtained by Delaroche, some most eminent philosophers (and of these it will be sufficient to name Laplace and Brewster) continued to deny the immediate transmission of heat through transparent solid bodies. ‘Their principal objection was founded on an experiment of that author, from which it was inferred that a thick glass intercepted a greater quantity of radiant heat than a thin glass, though the for- mer was much more transparent. It was insisted that this circumstance proved the presence and action of heat successively propagated from one surface to the other, and every elevation of temperature observed on the other side of the sereen was assigned to the conductible caloric. This opinion can no longer be maintained in defiance of the results furnished by the application of the ther- momultiplier to this species of phenomena. It will be seen, further, that the calorific action through a transparent layer is instantaneous, and that the time necessary for the instrument to mark its total effect is the same, whatever be the quality or thickness of the screens. Let the direct rays from an unvarying source of heat be received on the thermoelectric pile; let them be first made to pass through any diaphanous screen of one hundred millimetres in thickness: the index of the galvanometer sets itself in motion from the instant when the communications are established, and stops after having described an are of greater or less extent in an unvarying interval, which, with my apparatus, I find to be ninety seconds. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 5 surface, or that of the thickness of the layers and their internal structure on the quantities of heat which freely pass through them. I have en- deavoured to supply these different omissions, but the undertaking has proved too vast for me, and several parts of it are therefore incomplete. I hope however that I shall be able hereafter to return to these, and to treat them in a manner more satisfactory. In the mean time I present to the Academy the results of my first re- searches disposed in two memoirs. That which I offer at present con- tains an account of the method pursued in the measurement of calorific transmission and the application of the method in the case of an unva- rying source acting on bodies of different kinds. In the second I shall explain the facts connected with the succession of the screens and the variation of the sources. A General Considerations on the Free Transmission of Caloric through Bodies, and the Manner of Measuring it by means of the Thermo- multiplier. We have already observed that a diaphanous screen placed at a cer- tain distance from a calorific source stops a portion of the rays which strike its first surface, while the rest pass freely through. We have re- marked besides that after a certain time the heat stopped at the anterior surface, and accumulated there by successive radiations, passes on from layer to layer till it reaches the other surface, whence it begins to ra- diate anew ; and that this radiation mingling with the heat which passes through the screen by immediate transmission, prevents its being mea- sured exactly. - When the screens are liquid, the influence of the conducting power of the layers may always be destroyed if we incessantly renew the matter of the screen by means analogous to the strip of water employed by M. Prevost. But it would be always very difficult, and often impossible, to apply this artifice to solid bodies and even to such liquids as can be obtained only in small quantities. In order therefore to attain the same end in a general manner, and to render the experiments in some degree independent of conduction, other means must be employed. If we consider with due attention the manner in which the second surface of the interposed plate is heated, and the radiation which results from it, we shall see that the latter possesses properties very different from those that belong to the caloric which is freely transmitted. In order to be satisfied of this, we have only to observe that its action changes with the change of distance between the screen and the source ; a thing which does not happen, even in the slightest degree, to those rays that are transmitted freely. In fact, it is with the caloric trans- mitted immediately, as it is with light. 6 M. MELLONI ON THE FREE TRANSMISSION If between the flame of a candle and the eye we interpose a plate of glass or any other substance more or less transparent, we find the di- minution of the intensity of the light always the same, however the di- stance between the plate and the candle may vary. The effect produced by distance on the freely transmitted caloric is exactly similar; and if at a certain distance from the active source there be a thermoscopic apparatus sensible to this portion of heat, the apparatus will always give the same indication, whether the screen be laid close to the source or to the thermoscope. But it is clear that it must happen quite otherwise to the conductible caloric ; for this portion of the heat, when it has reached the further sur- face of the screen, leaves it in the form of diverging rays which become weaker in proportion to the distance. In other words, the further sur- face of the screen being heated becomes a new calorific source whose intensity of radiation must decrease as the distance increases. We possess, therefore, a very simple contrivance for destroying the influence of conduction, if we keep the action of the free radiation in- tact. This contrivance consists in removing the screen so far from the thermoscope that the radiation of its own heat may, on account of its extreme feebleness, be totally disregarded. There are, however, some precautions to be taken; for in proportion as the distance between the screen and the thermoscope is increased, the distance between the source and the screen is diminished. The latter is therefore more heated, and radiates with greater force upon the instrument. It is easy to show by calculation that we always gain; that is, that we always weaken the conductible caloric more and more by removing the screen from the thermoscope, until we have placed it midway between the thermoscope and the source*. Let us, therefore, put the screen in this position (which is the most favourable of all), and we shall see that its heat has then no appretiable influence on the re- * Let a be the distance from the source to the thermoscope, « the distance from the thermoscope to the screen, i the calorific intensity of the source, we i He : } : shall have (G@—aps the expression for the radiation which strikes the anterior ci surface of the screen. This quantity will become C=, at the further sur- face, c being a constant quantity depending on the conducting power of the matter of the screen. In fine, the radiation of the further surface on the ther- moscope will be expressed by 77 its minimum (y) is to be determined. : oar =a 2ci(2a—a : . . Now, by differentiating we obtain a = aa ; the equation which gives . . a the quantity will then be 2~—a=0, whence a= g. OF RADIANT HEAT THROUGH DIFFERENT BODIES. "{ sults obtained by means of the thermomultiplier*, and a source whose radiation is much weakened by distance. The apparatus is disposed in the following manner. A thermoelectric pile of thirty pairs is closed at one end and enveloped, at the other, in a small tube blackened inside to prevent reflection. Ata certain distance there is placed a large metallic diaphragm, with an aperture at the centre equal to the section of the pile. On the other side, in the same line, there is a lighted lamp, which is brought more or less close, until the needle which serves as the index of the galvanometer, marks an elevation of 30°. The radiation is afterwards intercepted by a screen of polished metal placed between the lamp and the diaphragm, and the needle returns to zero. Then there is placed on the other side of the diaphragm a stand, with a plate of glass fixed on it, and the whole ap- paratus is moved gently until it is brought midway between the pile and the calorific source. This being done, the opake screen is removed; the rays passing through the glass fall on the pile, and immediately cause the galvano- meter to move. In 58 or 6° it is driven through an are of nearly 215, but it afterwards returns nearly to zero, oscillates in an are of greater or less extent, and at last settles definitively at 21°. This last deviation decidedly marks the whole effect; for it is useless to continue the experiment for 15° or 20°. There is no longer any perceptible move- ment. The time which the needle takes to attain its position of steady equi- librium is a minute and a half+. When the experiment is repeated * For the description of this instrument see the number of the Annales de Chimie for October 1831. + Although the velocity with which radiant heat is propagated is unknown, we are nevertheless pretty certain, since the experiments of Saussure and Pictet, that this agent traverses spaces of from fifty to sixty feet in a time altogether inappretiable. It might be asked, therefore, why does not our apparatus in- stantaneously indicate the presence and the intensity of the rays emitted by the source? To this I answer, Ist, that the index of the galvanometer deviates at the very instant when the calorific communications are established, and we have just seen that in five or six seconds it describes almost the whole are of devia- tion. Ifa few seconds more are required to mark the entire action steadily, it is because the great conducting power of the bismuth and the antimony, and the great powers of absorption and emission belonging to their blackened sur- faces, render the lapse of a certain interval necessary, in order that a balance may take place between the rays which enter the pile and those which leave it or are extinguished within its interior. But the time required for the definitive equilibrium is much greater when common thermometers are used. If, for instance, one of Rumford’s most delicate thermoscopes, having the ball black- ened, and a metallic cover perforated on the side towards the source of heat, be submitted to the action of calorific radiation, it will be found that the time re- quisite to mark the whole effect is four or five times more than that required by the thermomultiplier. This delay is the consequence of the obstructions en- countered by the conductible heat in its passage through the glass, and in its 8 M. MELLONI ON THE FREE TRANSMISSION with other plates of glass, or of any transparent substance whatsoever, possessing different degrees of thickness, from the hundredth part of a line to five or six inches, the galvanometer exhibits deviations greater or less than 21°; but the time requisite to attain the equilibrium is in all cases the same. In short, if we mark the time which the needle takes to arrive at 30°, we shall find it to be one minute and a half. The invariability of this time, in such a variety of circumstances, affords the most decisive evidence that the deviations of the galvano- meter are exclusively due to that portion of heat which reaches the pile by immediate transmission. Whence it follows, that in the arrange- ment we have adopted, the heat of the transparent body has no appre- tiable influence on the instrument. But a direct proof of this proposition may be obtained by operating on opake screens. I take a plate of glass a millimetre in thickness. I blacken it on one uniform distribution over all the points of the mass of air within,—a distribution which will necessarily take place, because of the fluidity of the thermoscopic body. Another inconvenience produced by the interposition of the glass, and from which the thermomultiplier is free, is the lapse of a perceptible interval between the commencement of the action and its manifestation on the instrument; for there is always some time required, in order that the heat may pass from one surface to the other. I speak not here of the caloric which might pass to the air by free transmission through the diaphanous sides of the cover; for when we have to estimate the intensities of caloric rays by means of thermoscopes, we cannot dispense with the blackening of the glass. So necessary indeed is this, that in order to make sure of the opacity of the glass, it must be overlaid with several coats of colouring matter. Otherwise, a portion of the rays would freely pass through the mass of air contained in the ball without dilating it. Now, in the common thermoscopes, we always measure the radiation through an opake plate of glass. This plate, however thin, must offer a considerable resistance to the propagation of heat, because of the feebleness of its conducting power, and will therefore, as we have already observed, render the apparatus msensible during the first moments of action. Let it be observed, moreover, that the more we endeavour to increase the sensibility of the thermoscope by enlarging the dimensions of the balls, the more we diminish the promptitude of its indications ; for the increase of volume is proportionally greater than that of the part of the surface turned towards the source, and the mass of air within is increased in a proportionally greater degree than those points of the glass which can communicate to it the heat they have acquired. Hence arises a greater difficulty in attaining the moment of equal temperature in all the points of the fluid mass, and, of course, the necessity of a longer time to mark the en- tire effect. In fine, the thermoscopes are utterly useless when it is required to measure caloric rays that are very feeble, and distributed according to given lines, or forming sheaves of small dimension. In fact, it would be necessary in this case to preserve the whole sensibility of the instrument by considerably reducing the size of the balls. But this is impossible. Whoever takes the trouble to weigh these considerations duly, will not, I think, hesitate for a moment to prefer the thermomultiplier to every other ther- moscopic apparatus in studying the subject of caloric radiation. OF RADIANT HEAT THROUGH DIFFERENT BODIES, 9 side, and put it in the place of the transparent plate, taking care to turn its blackened surface to the lamp. The needle remains stationary, al- though the calorie rays continually fall on the anterior surface. It will be found immoveable also, if we employ a plate of copper coated on both sides with black colouring matter, or a thin flake of wood, or even a sheet of paper. Thus, though we should suppose the screen to be diaphanous, exceedingly thin, an excellent conductor of caloric, and possessing great powers of absorption and emission, the utmost eleva- tion of temperature that can be acquired during the experiment would not furnish rays sufficiently strong to move the index of the galvano- meter. ~ One is surprised at first to see caloric rays capable of giving a de- viation of 30° fail to produce any effect when they are absorbed by the screen, which must necessarily send its acquired heat upon the appa- ratus. But our surprise ceases when we reflect that this heat is sent equally in all directions by every point of the heated screen, and there- fore that the portion of total radiation which reaches the apparatus is but a very small fraction. We shall see hereafter, that the anterior surface of the pile does not measure six square centimetres. With these data, if we suppose even that the thirty degrees of heat are completely absorbed by the screen, and afterwards dispersed through space, we find that the quantity of the rays which reach the thermoscopic body dees not amount to the six-hundredth part of the whole. But the galvanometer that I use is capable, at the most, of marking only the 150th part of the force which moves the needle to 30°. Thus, even though the instrument were capable of discovering the presence of a heat four times as feeble, there would be no perceptible action. The experiments which I have been deseribing seem to me to leave no doubt whatsoever as to the truth of the proposition just now enun- ciated ; namely, that in my mode of operating the deviation of the gal- vanometer proceeds entirely from the heat instantaneously transmitted through the screen. These proofs, though so conclusive to my mind, seem however not to have been equally convincing to others ; for I have heard some persons say, “‘ We grant that the deviation of 21° obtained through the screen does not arise from the caloric propagated by con- duction from the anterior to the other surface, but it may be main- tained that it is caused by a heat instantaneously diffused, in the same manner as light, over all the points of the glass.” Before we admit such a mode of transmission, it seems to me that we ought to demonstrate its existence by some decisive experiment. But supposing it true, then we must also suppose one of these two things,—either that the molecules of the glass acquire from the action of the source such modifications that they themselves become so many calorific centres, and return to their 10 M. MELLONI ON THE FREE TRANSMISSION natural state when the radiation is stopped; or that the heat, which is supposed to be diffused through the material points of the screen, is but common caloric obeying the known laws of equilibrium. In the first case we should be only attempting to explain the very cause of the transmis- sion, and the hypothesis, true or false, does not at all invalidate the fact which we are desirous to establish. In the second case, this heat, when it has reached the interior of the body, must take some time to issue from it; besides, this time must vary with the thickness of the screen, and its powers of conduction and emission. But let us intercept the calorific communication in our apparatus ; let us remove the diaphanous screen from its stand, and expose it for some moments to the free radiation of the lamp on the other side of the diaphragm: if the supposition be true, the internal molecules of the glass will instantaneously acquire some heat. In order to see whether this heat really exists, let us replace the screen on its stand before the pile, still leaving the calorific communi- cation with the lamp intercepted. The further-surface of the plate of glass will, according to the hypothesis, immediately begin to emit to- wards the pile that caloric which reaches it successively from within, and the index of the galvanometer must lose its equilibrium. But what- ever be the nature or the thickness of the screen with which this expe- riment is performed, we never obtain the slightest indication of a move- ment in the magnetic needle. It is therefore completely demonstrated that the deviations of the galvanometer exhibited in the experiments made with the diaphanous sereens are not to be attributed, in the least degree, either to the external or the internal heat of the screen itself, but solely and exclusively to free transmission. Thus, whenever, in consequence of the radiant heat of the source being made to fall on a screen, a deviation of the galvanometer is perceptible, we may rest assured that the whole of the effect produced is to be ascribed to the rays of heat immediately transmitted through it, in the same manner as luminous rays. Before I conclude these preliminary considerations, it is necessary to remark, Ist, that galvanometers of very great sensibility, such as must be used for the thermomultiplier, do not directly indicate quantities less than half-degrees ; 2ndly, that the ratios of the degrees of the gal- vanometer and the forces of deviation are unknown. But it is often useful to have the fractions below the half-degree, and in certain cir- cumstances it is absolutely indispensable to know the ratios of the seve- ral degrees of calorific action which move the magnetic needles to dif- ferent distances from their primitive position. To find the fractions sought, we have only to take the means of a certain number of observations. As to the ratio of the deviations and the forces, it is difficult and, in the present state of the science, perhaps impossible to determine it generally. But electric piles, such as those OF RADIANT HEAT THROUGH DIFFERENT BODIES. ll employed in the construction of the thermomultiplier, furnish suffi- ciently simple means of solying the question in each particular case. Indeed there is nothing easier than to keep the index of the galvano- meter at any degree of deviation. All that is required for this purpose is to place a lighted lamp at proper distance from either side of the thermoelectrical pile. To prevent the possibility of mistake on this point, let us suppose the axis of the pile to be perpendicular to the magnetic meridian, and the communications so fully established that, when the left or the right side of the pile is heated, a corresponding de- viation will be exhibited by the galvanometer. Let there be now pro- duced a sufficiently marked deviation by placing a lamp near enough at the same side. Let this deviation be 44°. After having brought the needle back to 0° by interposing a metallic screen, let us make it move to the 42nd degree of deviation on the left, by means of a second lamp placed on the other side. To bring the needle back again to the zero point of the scale, we have only to stop the radiation by means of a metallic screen, as before. It is natural to ask what will be the effect now produced by the heat of both lamps being brought to bear simultaneously upon the opposite sides of the pile. The calorific effects will be partially destroyed, and the instrument will mark but their difference. If the same force were always required to make the needles describe arcs containing the same number of degrees, the index would stop at the second degree of devia- tion to the right; but we know that these effects continually increase to the right and to the left of zero. The difference of two degrees just now observed between the partial deviations of 44° and 42° was owing to the application of a force greater than what is required to make the index traverse the first two degrees of the scale. The position marked 2° will therefore be exceeded, and the more so in proportion as the first force is greater than the second, and the are described will, when com- pared with the difference of the two deviations, immediately give the measure of the corresponding force. If, for instance, the needle stops at 8°, it will be inferred that the force required to make the needle pass from 42° to 44° is four times greater than that required to make it pass from zero to 2°.. This effect would be five times greater if the needle stopped at 10°, and so of the rest. I shall not attempt to conceal the fact, that in this process the propor- tionality of the forces to the degrees in the are employed as a compara~ tive measure is tacitly assumed. But the assumption is fully justified by experience ; for we find that in galvanometers whose astatic system has been brought to a high degree of perfection, the magnetic needles, through the whole extent of the arc comprised between zero and the twentieth degree nearly, describe arcs proportional to the action of the electric current to which they are subjected. To be convinced of this, 12 M. MELLONI ON THE FREE TRANSMISSION it is by no means necessary to review in succession all the degrees that contribute to the formation of this are. The application of our method to the angles of 20° and 10° will be quite sufficient. This being done, we shall find an equal quantity between their difference and the effect produced by the simultaneous action of the moving forces. In other words, let us produce a deviation of 20° to the right and one of 10° to the left: let us then simultaneously expose the two opposite faces of the pile to the two radiations which produce these galvanometric indica- tions: the index will move to the right, and stop precisely at 10°. Hence we infer that the force necessary to make the needle describe the are comprised between 10° and 20° is equal to the force required to make it pass over the first ten degrees of the scale. Thus the pro- portion of the degrees to the forces is perceptible as far as the 20th de- gree on each side of zero. This fact seems opposed to the inference which might have been made in examining the nature of the galvanometric action ; for, in the successive rotation of the astatic system, the poles of the magnetic needles depart from the mean line of the electric currents. The inten- sity of the repulsive forces, therefore, decreases in proportion as the angle of deviation increases. Whence we should conclude that the effort necessary to make the needles exceed a given are should change as soon as the first degrees of the scale are passed. This would un- doubtedly take place if all the electric currents lay in a vertical plane passing through the line marked 0° ; but the cireumvolutions of the me- tallic wire which is wound on the frame placed under the graduated circle are distributed to a certain extent on each side of this plain. In the galvanometer which I have employed in my experiments, they cover the two opposite arcs of 76°, the chords of which are perpendicular to the line marked 0°. Thus so long as the oscillations take place within certain limits there will always be electric currents situated on each side of the needles. Now when the intensity of these currents is extremely feeble, their sensible effect on the needles must cease at a very short distance. Let us suppose this distance to be 18° of the division of the galvanometer intended to show the degrees of electric action which cause the deviations to the right and left for the first 20° of the scale. These degrees of action must be extremely feeble in a very delicate gal- vanometer. If, during these oscillations, the system of the needles is confined within the two initial ares of 20°, it is clear that it will always be subject to the same action, whatever may be the position in which it is placed; for there will always be near its plane a series of currents extending to 18° on each side, even when the system will occupy the extreme limits. The influence of the currents that are further distant will, according to our hypothesis, be nothing. As the moving force will therefore have a constant value, we shall have to consider only the OF RADIANT HEAT THROUGH DIFFERENT BODIES. 13 modifications which the active part of this force is made to undergo by the different inclination of the needles to the direction of the currents ; and these modifications are quite analogous to those which take place in the portion of gravity that acts on the pendulum in different ares of oscillation. Now the force necessary to make the pendulum vibrate from one in- clination to the other, is proportional to the difference of the cosines of the angles which the two directions form with the vertical. Whence it is clear that it remains sensibly constant in the ares that are not far re- moved from the line of rest. The same effect must therefore be pro- duced in the galvanometer also ; or, in other words, the force required in this apparatus to increase the deviation of the index by a degree will be constant near the line of zero, as is shown by experiment. From what we have just said it will be easy to see that the relation between the degrees of the galvanometer and the forces which cause the deviations of the needles, must depend on the sensibility of the astatic system and the distribution of the wire on the frame*. It will vary, therefore, according to the construction of the instrument, but may be always determined by the method we have mentioned. Experiment having shown that in my galvanometer the proportion of * In order to understand this clearly, it is sufficient to suppose a galvanome- ter in which the circumvolutions of the wire are more numerous towards the extremities than towards the central part. It is evident that under the action of such a system the forces which produce the deviations, instead of increasing or being merely proportional in the ares near zero, must decrease as we approach the extremities of the frame, in order to increase afterwards when the index has passed these positions. ! As to the influence of the sensibility of the astatic system, we shall be able to form a tolerably exact idea of it, if we imagine a galvanometer with the two needles possessing very different degrees of magnetism. Then the terrestrial globe will very powerfully affect both combined; and, in order to produce the least deviations, electric currents must be employed possessing much greater force than those required to produce small deviations in a more perfect astatic system. In the positions near zero, the electro-magnetic action produced by the most distant currents, that is, the action of the currents situated at the ex- tremities of the frame, will possess an energy sufficient at least to overcome the resistance arising from the twisting of the suspension thread and the inertia of the astatic system. It will therefore always contribute to move the oscillating mass. Hence it is evident that if the needles are displaced in the slightest de- gree, the consequence will be a loss in the moving force; for if the system ap- proaches a certain arc at a certain extremity, it recedes at the same time double the distance from the opposite extremity. Now we have already seen that, in delicate galvanometers, the moving force is constant when the angles are small ; and we have assigned the cause of this fact upon the incontestible principle that, in small deviations of the instrument, the action of the currents situated towards the extremities of the frame must be disregarded, not indeed because they have no value, but because it becomes, in consequence of its distance, extremely feeble, and incapable of surmounting the obstacles opposed to it by the torsion of the silk thread and the inertia of the needles. 14 M. MELLONI ON THE FREE TRANSMISSION the degrees to the forces was perceptible as far as the twentieth degree of the scale, I have attentively observed the passage of the index through every 4°, by commencing with this position and continuing my obser- vations as far as the forty-fourth degree. There I stopped; for my ex- periments on calorific transmission were to be confined to radiations considerably weakened by distance. The ares passed once in virtue of the forces acting on the system of the needles at different points of their course are in the following ratios to one another: The are comprised between 20° and 24° is equivalent to 5°12, commencing at zero. 24 — 28 6°44: 28 — 32 —— 8 -00 32 — 36 — 9°92 36 — 40 —-——. 12 44 40 — 44 19 *04 Each number in the third column represents the mean of eight obser- vations, which agreed with one another as exactly as could be expected from the nature of the instrument. Often equal, sometimes differing by 0%5, their greatest disagreement never exceeded 1°. A better proof cannot be given of the exactness of the method. The linear construction of these results, which gives a very regular curve convex towards the axis of the wes, has enabled me to obtain the values of the intermediate forces, degree by degree, from 20° to 45°. By connecting them with the fundamental observations, I have formed the following table of the intensities : Degrees. | Forces. | Degrees. | Forces. | Degrees. | Forces. 29° 33°4: 38° 30 airy, 39 31 374 32 39°6 33 41°8 34 440] 35 46°7 36 49°5 37 52-4 The use of a table requires no explanations. All the forces are re- ferred to that which makes the index describe the first degree of the scale. The values corresponding with the first twenty degrees are not exhibited in it; for through the whole extent of this are the number representing the force is equal to the number of degrees contained in the are passed over by the index. Thus, for instance, when we look OF RADIANT HEAT THROUGH DIFFERENT BODIES. 15 for the forces which produce the deviations 35° and 16°, the first (46°7) will be found in the table, but the second, being under 20°, will have the same value as the arc; that is to say, 16. When we want to find the forces which correspond to fractions of a degree, we have only to ascertain the proportional part of the degree in question ; for, in the interval between one degree and another, the curve visibly coincides with the tangent. If, for example, we wish to know the force that cor- responds to the deviation 31°7, it will be sufficient to take at first the difference between 37:4 and 39°6 (the intensities of the forces belong- ing to 31° and 32°); this difference being 22, we shall find the value (x) of the force corresponding to seven tenths of the degree contained between 30° and 32° by this proportion, Petes aie 2 ou lea Adding this to the number 37-4, which represents the force correspond- ing to 31°, we shall have 38-9 as the value sought. Of the Polish, the Thickness, and the Nature of the Screens. The suggestions which we have offered as to the manner of measuring the quantity of caloric instantaneously transmitted by diaphanous bodies, and as to the precautions to be taken during the experiments, leave us searcely anything more to say on this subject. Nevertheless it may not be amiss to mention some particulars relative to the construction of the apparatus before we proceed to the exposition of the results. The pile employed in these researches is of the form of a quadrangu- lar prism; its two ends are plane surfaces, each measuring 4°24 centi- metres; it consists of 27 pairs and a half, or 5 elements of bismuth and antimony, 32 millimetres long, 2°5 broad, and 1 in thickness. It was not without considerable difficulty that we succeeded in combining and soldering together these minute bars. The facility with which liquid antimony oxidizes, the difference between its fusibility and that of the bismuth, and the extreme fragility of the two metals, presented so many obstacles, that it cost many an effort to overcome them. But a pile of very small dimensions was indispensable in the investigation of the laws of immediate transmission through rare liquids and crystallized solids. This was, therefore, to be obtained, or the experiments to be aban- doned. By this conviction we have been induced to persevere in spite of repeated disappointments, and by redoubling our patience have at last succeeded. The electric pile is passed into a ring formed of a thin square flake of copper internally lined with pasteboard and having a screw which serves to fix it on the stand, so that the axis naturally takes that hori- zontal position which it is to keep during the greatest part of the ex- periments. To each side of the ring there is fitted a tube of six cen- 16 M. MELLONI ON THE FREE TRANSMISSION timetres in length, blackened on the inside; and at a certain distance from the mouths of these tubes are placed the stands destined to receive the screens. In strictness, a single tube and a single stand would be sufficient, and one of the sides of the pile might be closed by means of asmall metallic cover ; but, when we have to operate on bodies differing in quality and thickness, it often happens that they differ in tempera- ture not only from one another but from the pile also. Then if we place but one screen before the apparatus, the calorific actions at the two sides are unequal, the index of the galvanometer moves away from zero, and we must wait for some time until the equilibrium of the tem- perature is established and the index returns to its original position. Now this inconvenience cannot occur when the pile is furnished with two tubes and two stands; for, by placing before each side of it a plate of the same quality and thickness, it is clear that, if care be previously taken to place the two in the same circumstances, they will have the same temperature, and will consequently emit the same quantity of heat on the two sides of the pile. The index of the galvanometer will re- main stationary, whatever may be the difference of temperature between the plates and the thermoscopic body, and we may therefore immediately proceed with the experiments. Hence, if we would save time, we should always have a pair of screens of each sort; and, as we have just observed, put both sides of the pile in the same state. In order to ascertain the influence exercised on free transmission, by the different circumstances relating to the surface, the volume, and the composition of the sereens, we must procure a constant source of heat. For this purpose, there is nothing better than a good lamp with a double current of air and a constant level. When this apparatus is well pre- pared and filled with oil freed from mucilage, by means of sulphuric acid, we obtain a flame which maintains an invariable temperature for more than two hours. Of this I have been able to satisfy myself by means of the thermomultiplier. But in order to have things in this preparatory state, we must wait some moments until the pipe, the oil, and the glass funnel of the lamp shall have attained a maximum of temperature. This time, which varies a little with the construction of the lamp, is about ten or fifteen minutes. There may be some objections raised against the employment of an Argand lamp asa calorific source. It will be said, perhaps, that in this lamp the heat acts only through the glass funnel; that the funnel itself becomes heated, and mixes its rays of nonluminous heat with the lumi- nous caloric of the flame; and lastly, that such a source of heat is neither uniform nor separated from the agent which usually accom- panies it in high temperatures. But I wish it to be particularly observed, that the only thing about which we are interested at present is, to know whether the state of the. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 17 surface, the colour, and the internal structure of a body, as well as its chemical composition, have any influence whatever in the quantity of heat which it transmits immediately; and that, in this point of view, the origin and the qualities of the caloric rays become objects of perfect indifference; for it is enough for our purpose that the rays be invari- able and identical in all the circumstances in which they are employed. Now this actually is the case with the rays issuing from the well sup- ported flame of a Quinquet lamp placed at a fixed distance. When we shall have found the ratios of the quantities of heat trans- mitted by screens of different kinds under the influence of a constant source, then, agreeably to what we have stated in the introduction, we shall examine the changes which those ratios undergo in consequence of the variation of the sources. All our experiments of comparison have been made with the same calorific radiation. Previously to the commencement of each series the rays were allowed to fall directly on the pile, and the distance of the lamp was modified until the needle of the galvanometer fixed itself at 30° of the scale. ’ We have remarked in the preliminary considerations, that all the external parts of the thermoscope are sheltered from the caloric rays by means of a large screen of polished metal, having in its central part a hole to correspond with the opening of the pile turned towards the lamp. In order to establish or to intercept the communication between this aperture and the source of heat securely and commodiously, we make use of a moveable copper screen, consisting of two or three parallel plates fixed on the same support. The side of the pile opposite to the lamp may also be closed and opened by means of a screen altogether similar, and for the following purpose : When, after having observed the effect of any radiation whatsoever, we intercept the action of the source, we must wait until that face of the pile on which the rays of heat are darted has been restored to its natural state before we make a second observation. Now it appears that the heat emitted by the flame penetrates the apparatus with greater ease than it issues from it, because of its natural tendency to an equili- brium. At least the experiment shows that the time requisite to pro- duce the deviation is to that in which the needle recovers its original position nearly as one to five ; for the latter is from 7% to 88, and we have seen that the whole deviation is produced in a minute and a half: Whatever be the cause of this difference between the time required for heating and that required for cooling, we must always allow 8° to elapse after one experiment before we proceed to another, if we confine our- selves to the placing of the first moveable screen before the radiating source. But let the opposite side of the pile be opened and a lighted candle brought close to the corresponding face: it is evident that if the Vor. L—Parr I. c 18 M. MELLONI ON THE FREE TRANSMISSION candle be held for some minutes at a suitable distancé, and the com- munication then intercepted, the needle will be forced back to zero in an interval of time less than 8°. These operations would be impossible if the side of the pile opposite to the lamp were hermetically closed. The second moveable screen serves then to abridge the duration of the experiments. It is particularly useful when the calorific action has been very powerful or considerably prolonged, which sometimes happens in the first attempts at adjustment. During these, the portions of heat penetrate the pile toa great depth, and cannot return until a considerable time has elapsed. Before these simple means of correction had occurred to me, the difficulty of restoring the equilibrium of the two extremes of the pile, as well as that which I experienced in respect to ‘he different temperatures of the screens and the apparatus, often obliged me to stand still for fifteen or twenty minutes between two consecutive experiments. When any object of research requires numerous experiments, we should endeavour from the very outset to avail ourselves of all that contributes to make them more expeditious; for the least delay arising from imperfectness of method will, by gradually accumulating, ulti- mately render the labour of whole days utterly fruitless. Yet, the at- tention being absorbed by the main object, these little defects are at first unnoticed. At length, however, we become sensible of them, and endeavour to apply aremedy when it is almost too late. But the result of the experiment is not without its use, since it may be more or less serviceable in analogous circumstances. This consideration must be my apology for the minuteness of detail into which I have entered. The first problem that presents: itself, in the series of questions rela- tive to the passage of radiant heat through solid bodies, is to determine the influence which the degree of their, polish has, and the quantity of rays transmitted. In order to solve this, we have but to apply our thermometrical method to several screens perfectly similar in all re- spects, except as to the state of the surface. Out of the glass of a mirror which was very pure, and nine milli- metres in thickness, I cut eight pieces sufficiently large to cover the central aperture of the screen when they were placed on the stand; and, after having removed the quicksilver, I wore them down with sand, emery, and other such substances, so as to form by their succession a complete series of plane surfaces more or less finely wrought, from the first and coarsest to the highest and most perfect polish. These dif- ferent pieces reduced to one common thickness of 8™™-371* and ex- * All the measures of small degrees of thickness contained in this Memoir have been taken with a pair of calipers with pivots, a species of double com- passes, with a spring and with legs of unequal lengths, much used in the manu- facture of clockwork. This instrument measures directly, and with great nicety, even the fortieth part of a line. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 19 posed to a radiation of 30° of the thermomultiplier, have furnished the following results : Order of the screens. Deviations of the galvanometer. PoP. 4.60.2: .canteceuseders 538 QD. ——— hee eecseceeenees 6°50 Be ———$———. hs ss sncceccncceccscneces 8°66 Re Eien tS OE ENG 12°58 Oo Sar eR Re SCO COE CEC OC ERSCEL 14°79 C. Suehibe dal a5 ..ctge ssi excaeie 17°42 Met MEAN SDATOUG os nannnanchs ch =srned 18°79 8. 19°15 These transmissions present nothing extraordinary: the quantity of heat which passes through the medium is greater in proportion as the surface is more finely polished, as it happens in respect to light. The only thing to be remarked is, that in the high degrees of polish a slight difference produces a very slight effect. This is evident from the ob- servations made on Nos. 7 and 8. Similar processes enable us to determine the influence of thickness, which is one of the elements most necessary to be known in the theory of transmission. Four pieces cut out of a fine mirror were reduced with great nicety to different degrees of thickness in the ratio of 1, 2, 3, 4: particular care was taken to give to their principal surfaces a perfect parallelism, and the highest polish possible. The following are the deviations which they successively produced in the index of the galvanometer under the action of the same radiation, namely 30°: Thickness of the screens Deviations of the Corresponding in millimetres. galvanometer. forces. ° . 2:068 21°625 21°850 4°136 20°312 20°343 6°202 19°687 19°687 8272 19°375 19°375 Each number in the second column is deduced from fifteen observa- tions: the quantities registered under the denomination of forces, representing in this particular case the respective temperatures or quantities of rays transmitted, have been calculated according to the principles with the exposition of which we concluded our general ob- servations. The force or temperature answering to 30°, as given by the table of intensities, is 35°3; now, by dividing each number of the third column by 35°3, we shall obtain the ratios of the transmitted rays to the incident rays. The difference between each of these quotients and unity will give the corresponding loss; that is, the proportional part of ss Bits - 20 M. MELLONI ON THE FREE TRANSMISSION ; the rays that are stopped. By performing these operations, and repre- senting the whole radiation by 1000, we obtain TABLE A. Order of the Transmitted screens. rays. nore stopped. 1. 619 ok aa 2. 576 4.24. 3. 558 442 4. 549 451 Let us imagine the thickest of the screens split into four equal layers ; the quantities of heat falling upon each will be 1000, 619, 576, 558, and the quantities lost in successively traversing the four intervals 381, 424—381, 442-424, 451—442; that is to say, $81, 43, 18, 9. _ Weshall then have for the ratios of the respective losses to the incident quantities, 381 43 18 9 1000’ 619° 576° 553° or 0°381, 0-071, 0-031, 0-016. Thus the losses continue to decrease with great rapidity as the thickness increases by a constant quantity. We have seen that the action of the radiation on the thermomulti- plier commences at the instant when the communications are established, produces the greatest part of its effect in the first five or six seconds, and ceases entirely after a minute and a half. These facts, which are equally true of the direct rays and of those which reach the pile after having passed through screens of any thickness whatsoever, constitute the best proof that caloric is transmitted by radiation through the inte- rior of the diaphanous bodies. . If, nevertheless, a new confirmation of this truth were desired, it would be found in the successive diminution of the losses which the rays undergo in crossing the different layers of a transparent medium. Were the heat, which is the subject of our im- mediate inquiries, the effect of a species of conducting power, the losses would continually increase from layer to layer, or would remain con- stant, from the moment when the rays penetrated the medium, and could never follow the opposite law of decrease. The progressive diminution of the losses is, moreover, entirely pecu- liar to the calorific radiation, whose properties in this and in many other respects are altogether different from those of the luminous rays. In OF RADIANT HEAT THROUGH DIFFERENT BODIES. oT fact, everything leads us to believe that the equal layers which succeed one another in a diaphanous medium act in the same manner on the rays of light which come in succession to pass through them, and that they consequently absorb or reflect a quantity of light. proportional to the intensity of the incident rays; that is to say, that the loss sus- tained by the luminous radiation at every layer of equal thickness is constant. In the case under consideration, the invariable decrement of the light at each of the layers into which we suppose the screen divided is found to be none at all, or extremely feeble, because of the perfect transparency of the glass; and yet the caloric rays undergo in their successive passages an absorption, the sum of which is equal to about the half of their whole value ; and the losses at each layer, instead of being constant, as happens to those sustained by the luminous rays, are found to differ enormously from one another, being in the proportion of the numbers 381, 71, 31, and 16. The resistance of diaphanous media to the immediate transmission of the rays of heat is therefore of a nature altogether different from that which is presented by the same media to the propagation of light. Whatever be the cause of this singular difference, it is highly im- portant to determine with certainty whether it takes place at great di- stances from the surface at which the rays enter; and this may be done by repeating the experiments on layers of glass much thicker than those which we have been using. . With this view I took several pieces of the glass of Saint-Gobain, and caused them to be recast. This operation was not completely suecess- ful. The matter either formed itself into layers that were too thin, or was slightly striated. From among the thick pieces I selected that which was the purest. It was six inches in length. I divided it into three parts, of one, two, and three inches in thickness. The defects being uniformly distributed over all the points of the mass might probably enough alter the quantity of the caloric rays that would have passed through a per- fectly pure mass of the same matter and thickness; but it is clear that they could have no influence on the nature of the progression of the losses which these rays might undergo in passing from one layer to an- other. The following are the results obtained by exposing these screens to the ordinary radiation of 30° : Thickness of the screens See tae Galvanometric deviations. in millimetres. o 27 177105 54 13°458 81 - 10°702 By a calculation exactly similar to that already made we find that, 22 M. MELLONI ON THE FREE TRANSMISSION of every thousand rays emanating from the source, each screen transmits or stops the following quantities : Order. Rays transmitted. Rays stopped. 1. 484 516 2. ae 380 620 3. 303 697 By means of these data we obtain as the values of the calorific losses, considered with reference to the quantities of rays which present them- selves successively to pass through the three equal layers into which we may suppose the last screen divided, 0°516 0°215 0°203. These losses are still greater than those preceding, because of the badness of the material and the greater thickness of the layers, but they are still in a decreasing progression. Thus the diminution continues beyond 54 millimetres. To compare this diminution with that which took place in the last screen in the preceding experiments we must multiply 0012 (the differ- ence between 0°215 and 0°203) by 2:068, and divide the product by 27. In this way we obtain the mean diminution for a thickness of 2™-068 in passing from 54 to 81 millimetres, which is nearly 0-001; in the pre- ceding experiment it was fifteen times as much while the rays passed through the same layer of 2"™-068 placed at a distance of 6 millimetres. The difference would be still greater if we had used very transparent layers of glass, such as flakes of the glass of a mirror attenuated. Nevertheless I had some doubts as to the homogeneity of the glass: I was afraid that the striz might not be equally distributed over all the points of the mass. But not being able to procure large pieces of this material entirely free from defects, I thought that analogous experi- ments performed with liquids might answer quite as well. In employ- ing these instead of glass there was, in case of success, the additional advantage of extending the law of calorific transmission by making it independent of the physical constitution of the medium. I procured therefore several copper troughs, of the same breadth but of different lengths, bounded at each end by a glass plate. These I placed successively between the perforated screen and the pile in such a manner that the anterior glass plate was quite near the screen, the distance of which remained constantly the same. The common section of the troughs was much larger than the central aperture of the screen; the reflexions on the lateral faces could not take place, and the only rays that entered a little out of the perpendicular direction reached the anterior surface of the pile. The lamp was moved up so near that the needle of the gal- vanometer exhibited a deviation of 30° through the two glass plates of each trough. The radiation was then intercepted, the trough filled with. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 23 oil of colza*, and after having waited until the needle recovered its ori- ginal position we reestablished the calorific communication. The deviations obtained through the different thicknesses of the li- quid are exhibited in the following table. Degrees of thickness of Deviations of the galva- the liquid layer. nometer. mm o 6°767 15°642 13°535 12°831 27:069 10°389 54°139 9°540 81°209 8-988 108°279 8512 The free radiation being always represented by 1000, the respective quantities of the rays transmitted and those stopped are found to be : TaBLeE B. Degree of hckness of Guay transmitted, Rays slope mm 6°767- 443 557 13°535 363 637 27:069 294 706 54°139 270 730 71-209 255 745 108°279 44 756 If we suppose the last layer (of 108™"-274) subdivided into six paral- lel slices of the following degrees of thickness : 6™"*767, 6°767, 13°535, 27-069, 27-069, and 27-069, we shall be able to determine, by means of the numbers contained in the two last columns, the quantity of heat incident to the first surface of each of these slices and the quantity lost in the passage. Dividing the second by the first we shall ascertain the loss. It is unnecessary to exhibit the operations in detail, as they are in all respects similar to those which have been performed in reference to the screens of glass. Here are the final results: Degrees of thickness of the six Losses in the respective transmissions successive slices into which referred to the quantities of we suppose the layer of rays which arrive at the 108"™-274 to be divided. surface of each slice. mm 6°767 0°557 6°767 0°180 13°535 0°190 27-069 0°082 27:069 0°056 27°069 0:040 [* It may be proper to inform the English reader that “oil of colza”’ is an oil expressed from the seeds of the ChowColza of the French, Brassica arvensis, Linn. It must not be confounded with the rape oi! of England, obtained from the Rape, Brassica Napus—Evit.] 24: M. MELLONI ON THE FREE TRANSMISSION Whence it is concluded that the losses still decrease at a distance of about 100 millimetres. To comprehend at a single glance the law of the propagation of ca- loric radiating through diaphanous media we have only to reduce the results contained in the first two columns of the Tables A. and B, to a linear construction. The mere inspection of the curves thus constructed shows that the rays lose very considerably when they are entering the first layers of the me- dium. But in proportion to their distance from the surface we see that the loss decreases and that at a certain distance it is almost imperceptible, and the rays seem to continue their progress, retaining all their inten- sity ; so that in glass and in oil of colza, and probably in all other dia- phanous media, the portion of heat which has forced its passage through the first layers must penetrate to very great depths. Delaroche had found that the heat which has passed through one plate of glass becomes less subject to absorption when it is passing through a second. The identity of this fact with the law of resistance in continuous media shows that the solution of the continuity and the interposition of the atmosphere between the two screens do not alter the nature of the modifications which the rays undergo in the first plate of glass. It is therefore exceedingly probable that the proposition of Delaroche is true with respect to a very numerous series of thin screens; for we have just seen that in the same medium the losses still diminish to the depth of 80 or 100 millimetres. In reference to this point, the follow- ing is the result of the experiments I have made with four plates of the same glass that had been employed in the first attempts to investigate the law of propagation through continuous media ©The common thickness of these plates was 2™™-068. Numbers of Deviations of the galva- the screens. nometer. °o 8 21°62 2: 18°75 3. 17°10 4. 15°90 It is scarcely necessary to observe that the common radiation to which the screens had been exposed was always 30 degrees, answering to a force or temperature of 35:3. If we represent this radiation by 1000, as we have done in all the foregoing cases, we have: Numbers of the screens. Rays transmitted. Rays stopped. l. 619 381 2. 531 469 Se 484 515 4 4.50 540 Whence oe have 0381, 07134, 0'087, 0:058, OF RADIANT HEAT THROUGH DIFFERENT BODIES. 25 as the losses suffered by the rays in successively passing through the four plates of glass; it being carefully kept in mind that these values are not referred to the initial quantity, but to the number of rays which arrive at the surface of each screen. Thus the proposition of Delaroche is true as far as the third and the fourth screens; for in the transition from one loss to another a dimi- nution of each loss is observable. It will have been observed that the losses were not so great in re- spect to the four equal layers of the screen of a fourfold thickness ; and that this should happen will be easily conceived if we consider that in the latter case there is a solution of continuity which causes a greater dispersion of the heat by reflexion. But we see that in both cases the difference between two successive losses becomes less in proportion as the distance from the surface, at which the rays entered, is greater. Let us now proceed to consider the influence exercised on calorific transmission by the composition of the substance of the screen. M. Prevost had concluded from the experiments described in a me- moir already quoted, that water and glass ought to transmit rays of heat in different quantities ; for by causing the sheet of water to fall between the lighted candle and a very delicate air-thermometer, he obtained no indication of heat being transmitted unless when he had blackened the ball of the thermometer, and even then the increase of temperature was extremely small ; whilst a plate of glass substituted for the sheet of water produced effects sufficiently manifest*. But it was objected to him that the difference between the action of the water and that of the glass was owing to the conductible caloric which was perceptible in the latter case only. Delaroche subsequently observed that a square of greenish glass transmitted more heat than a plate of another species of glass perfectly pure. However, as the first flake was much thinner than the second, it was insisted that the difference in the effects was owing to the difference of thickness. At length, some time after the in- vention of the thermomultiplier, M. Nobili and myself made some ex- periments on olive oil, alcohol, water, and nitric acid; whence we in- ferred that water opposed a greater resistance than any of the three other liquids did to the passage of rays of heat emanating from a hot iron+. But these experiments are to be regarded only as mere trials, tending to show the facility with which the thermomultiplier may be employed in all sorts of inquiries relative to calorific radiation ; for we did not take sufficient precautions to prevent the heat from passing by _ * His own words are: “It appears, therefore, that water does not allow so much caloric to pass immediately as glass does. At least it affords a passage of that kind ouly to a quantity of caloric more minute than that which passes through the glass.” (Mem. already quoted, § 48.) + See the note in page 4, 26 M. MELLONI ON THE FREE TRANSMISSION means of conduction, and to be sure that the temperature was the same throughout. Thus it was still believed that the portion of heat trans- mitted through solid or liquid substances was governed by the same laws as the transmission of light, and that, ceteris paribus, the most diaphanous bodies transmitted the greatest quantity of caloric rays. The results which I am about to state seem to me to establish beyond the possibility of doubt a fundamental proposition in the theory of ra- diant heat, namely, that the power of transmitting caloric rays is by no means proportioned to the transparency of the media; it is subject to a different law, which, in bodies without regular crystallization, ap- pears to have many affinities to refrangibility. In crystals the pheeno- mena are still more interesting, since in them we find that bodies pos- sessing a high degree of transparency intercept nearly the whole of the caloric rays, while some others act in a manner directly contrary. These properties are invariably manifested whatever be the temperature of the source, and become yet more singular at low temperatures ; for in the latter case we find that the ordinary heat of the hand passes immediately through a solid body of. several inches in thickness. Let us not, how- ever, anticipate as to the facts, but first of all examine the methods pur- sued in this third series of experiments. In the first place it is unnecessary to dwell on the manner in which the solid screens have been exposed to the radiation and the indications of the thermomultiplier, for in this respect everything was the same as in the previous experiments. As to the liquids, these bodies are less permeable to radiant heat than solid bodies are. They must therefore be brought nearer to the thermoscope in order to obtain a well-marked transmission; but then the proper heat of the molecules themselves might be able to act on the instrument, and this the more certainly as the motions always developed in liquids unequally heated easily transfer the particles of the anterior to the further surface of the layers exposed to the source of heat. This effect of conductibility cannot be neutralized in a general manner by continually renewing the interposed layer, as in the experiments of M. Prevost ; for some of the liquids can be procured only in small quantities ; others, as soon as they are exposed to atmo- spherie air, undergo considerable alterations and evaporations which produce corresponding elevations or depressions of temperature that prove very annoying in experiments of this kind. The contrivance which I have employed for the purpose of avoiding these inconve- niences is very simple. It consists in putting the liquids into very flat glass recipients, whose two large lateral surfaces are perfectly parallel, and the height four or five times that of the surface of the thermo- electrical pile. The lower part of these vessels is applied to the mouth of the tube that envelops the face of the apparatus turned towards the source. The heat stopped by the anterior face of the vessel penetrates OF RADIANT HEAT THROUGH DIFFERENT BODIES. 27 the first infinitely thin layer of the liquid; but this layer, while it is becoming hot, undergoes a certain dilatation, becomes lighter than the rest of the fluid mass, and ascends immediately to the upper part of the vessel, whence it can have no longer any influence on the pile. It is replaced by a second layer, which undergoes a similar process, and this again by others; so that by these partial renovations of the liquid sereen, the hinder part of the glass applied to the aperture of the tube is not in contact with heated molecules, and retains the same tempera- ture for a long time. It was extremely difficult to make flat glass vessels with very regular surfaces of the same thickness throughout, and with the opposite sides exactly parallel. Metallic frames and glasses joined with gum could not be employed because of the corrosive action of the several liquids. After many a fruitless effort to surmount this difficulty, I thought at last that the process by which the index of refraction of liquids is measured in optics might be available in this case also. With this view I had quadrangular pieces of two centimetres in breadth and nine centi- metres in length cut out of several pieces of the same mirror unsil- vered and sufficiently thick. I laid close to the two faces of each of the pieces from which the excision had been made two flakes made out of another and a much thinner glass. It is known that the mere adhesion of two plates of polished glass is sufficient to prevent the passage of liquids. However, in order to be more secure, I introduced each reci- pient between two metallic frames, which held the thin glasses in their places by means of four screws placed at the angles. The liquid was poured into these vessels at a small aperture made at the top, and fur- nished with a glass stopper. In such a system there could be no doubt of the parallelism of the faces and the equal thickness of the layers. The results furnished by the several bodies, both solid and liquid, I have disposed in several tables, each of them exhibiting at the top the common thickness of the screens employed and, beside the substance, the indications of the thermomultiplier and the quantity of rays trans- mitted as compared with the whole radiation. This distribution, while it allows the use of plates of different thicknesses, has the additional ad- vantage of presenting distinct groups of each class of bodies. The free ra~ diation in each case was 30°. In order to link the results of these tables together, I have commenced the second and the third with the numbers given by a flake of glass placed in the same circumstances as the plates which constitute each group: thus the glass set down in the table of liquids was contained between the two thin plates of the recipients, and made of the thick looking-glass employed in their construction. It was therefore exactly of the same thickness as the liquid layers, and, like them, came into contact with the thin plates which formed the faces of the recipients. But as those faces themselves intercepted a portion of 28 M. MELLONI ON THE FREE TRANSMISSION the heat, the lamp was brought nearer and nearer until we obtained, through the combination of the three plates, the same indication of 19° that was furnished by the thick glass when exposed singly to the radia- tion of 30°. TaBLeE I.— Glass (uncoloured). Common thickness 188. Deviations of Rays the galvanometer. transmitted. No screen . noetgurceseae 30°00 100 Flint-glass - Guinand) .. Br 22°90 67 Flint-glass skank MOS 22°43 65 Flint-glass (French)... ag ligaivdnt re 22°36 64 Another kind. ..,:s000 cos sean if we wished to be rigorously exact, for by the table of intensities we see that, in the deviations below 20°, one degree is equivalent to a55 of the force which moves the needle to 30°. But let us admit only the limit z's, which will have the advantage of rendering the values inde- pendent of a knowledge of the ratios existing between the degrees of the galvanometer and the corresponding forces of deviation. Let us bring the source near, in order that we may obtain through the same plate of glass a deviation exceeding 2°; a deviation, for instance, of 8°. The quantity of incident heat is now increased fourfold, and the pro- OF RADIANT HEAT THROUGH DIFFERENT BODIES. 47 bability of error is diminished in the same degree*. Let us now sub: stitute for the plate of glass a flake of alum, sugar, or ice; we shall find that the needle of the galvanometer is perfectly at rest : if there is any heat transmitted, it is therefore not more than 4.35 = z4a of the whole radiation. Thus it is true that the transmission of these three substances reduced to plates of 2™™-6 in thickness and exposed to the radiation of a body heated to 390° is null or less than z}sdth part of the whole in- cident heat. It is by operations analogous to this that I have been able to ascertain the limits of the values of the zeros of transmission. Now that we know the degree of exactness to which the measures contained in our table have been carried, we may proceed to state the consequences to which theyead. Let us, for the moment, not notice the results obtained with the rock salt. The order of the transmissions has no relation to the degree of transparency, as we have already determined in our first series of expe- riments. It is not strictly the same when we change the calorific source ; but each substance exposed to the successive action of the four radia- tions presents a like order of decrease in respect to the quantities which it transmits from each of the sources; that is to say, that all the sub- stances transmit quantities of heat which are feeble in proportion as the temperature of the radiating source is low. There are several cases in which the transmissions are nothing; but these cases do not make * This mode of estimating the energy of the calorific radiations enables us to determine without difficulty the ratios existing between the arcs described by the magnetic needle of the galvanometer and the corresponding forces. Let us suppose the calorific source removed sufficiently far from the pile to produce but a feeble deviation of the galvanometer; one of 10°, for example. In the passage of the calorific rays let there be interposed a plate which transmits a certain fraction of the incident heat. We shall suppose this fraction to be 3; the needle will descend to 2°. __ By bringing the source near, the deviation produced through the plate will be increased. Let us stop, when the needle shall have reached 4°, 6°, 8°, &c. successively the calorific source will then emit upon the pile twice, thrice, or four times as much heat as before; for the transmission through the same plate exposed to a constant source of heat is always in a con- stant ratio, and the forces of deviation are proportional to the degrees in those ares that are very near zero. Let the force which causes the galvanometer to describe the first degree of the scale be represented as 1, we shall then have 10 for the first force or quantity of incident heat, 20 for the second, 30 for the third, 40 for the fourth, &c. Now we know that the first force answers to 10°. In order to determine the deviation produced by the force 20 we have only to re- nove the plate when the galvanometer points to 4°; the calorific rays will then fall immediately on the pile, the angle of deviation will increase, and if the pro- - portionality of the degrees to the forces continues through the whole extent of the are of the first 20 degrees we shall see the index stop at 20°: at all events we shall have the corresponding indication. By repeating the same operation when the galvanometer points to 6°, 8°, we shall obtain the quantities sought, that is to say, the degrees answering to the forces 20, 30, 40, &c. Thus we may verify the results contained in the tables of intensities already made, or de- termine the elements necessary for the construction of new tables. 48 M. MELLONI ON THE IMMEDIATE TRANSMISSION against the principle as the zero is never followed by appretiable trans: missions. The same principle holds in respect to all the liquids that I have been able to submit to experiment. It will be recollected that, in my mode of operating, the rays of heat, before they reach the liquid layer, must pass through a plate of glass. Now this substance becomes more and more interceptive in proportion as the sources employed are of a less elevated temperature, and consequently acts upon the calorific rays with an effect the same as that which a screen of variable transparency would produce in respect to light. The process therefore which I pursued in my first Memoir could not enable me to determine the exact ratios of the ca- lorific transmissions through the same liquids when the source is changed; but it was possible to make it available for the purpose of establishing, in the greatest number of cases, the general law of decrease which we have just determined in respect to solid bodies. Let us suppose that a thick plate of glass being submitted to the suc- cessive action of an equal quantity of heat, emanating from our four sources, gives these transmissions : 30," 18; 2; "0: Let us suppose a parallelopiped, with sides parallel to the faces of the plate, to be cut out of the glass, and the cavity thus made to be filled with a given liquid: let us then suppose that the transmissions of the system become all respectively inferior to the preceding, and are re- duced, for instance, to 20 a tSy salons it will be immediately concluded that the liquid acts on the calorific rays from different sources in the same manner in which its glass case does ; that is, that it exhibits an order of decrease similar to that exhibited by the glass and by solid bodies in general. Now this is precisely the result furnished by the liquids contained in my glass vessels *. * In many instances I was unable to obtain any transmission, even by em- ploying a very powerful radiation. It is thus that water, which transmits six or seven hundredths of the rays from a Locatelli lamp, completely intercepts the heat of the last three sources. Calculating the limit of error for the case least favourable to interception I found it ,4, : the source was then brought very close to the liquid and an equal layer of oil employed, which caused in the index of the galvanometer a deviation of several degrees. Now if the water allows a passage to the radiation from bodies heated even to incandescence or brought to lower temperatures, the part transmitted must be less than ,4, of the incident quantity. I here speak of a layer of 3"™ or 4™™ in thickness : for it is possible and even very probable that layers much thinner than these may be in some slight degree permeable to rays of this kind. Thus we have seen glass of 0-07 in thickness transmit 14%, of the rays emanating from boiling water, while a plate of 1™™ intercepted them totally. But as, in order to compare different transparencies, we must operate on a certain thickness of each medium (for the OF RADIANT HEAT THROUGH DIFFERENT BODIES. 49 In eight-and-twenty cases there have occurred but the three excep- tions presented by carburet of sulphur, chloride of sulphur, and proto- chloride of phosphorus, in which the transmissions did not change when the liquid was substituted for glass. I found it therefore impossible to decide at first whether these three substances acted in the same manner as the others; for if they had acted even in a contrary way, provided their least transmission were equal to 30°, the result obtained would be the same. But in all probability these three anomalies are merely apparent ; for the chloride of sulphur, the carburet of sulphur, and the protochlo- ride of phosphorus being in a high degree permeable to radiant heat, the same thing will happen in respect to these three liquids inclosed in glass vessels that happens when very pure fluate of lime is substituted for them; that is to say, the transmissions of the system retain their proper values, though the fluate of lime itself be subject to the general law. Thus the radiant heat from different sources is absorbed in greater or less proportions while it is passing through diaphanous bodies (solid or liquid); but while it is passing through the same body the absorption constantly increases as the temperature of the source decreases. It happens quite otherwise to the luminous rays. Let us look through a plate of glass at the most vivid flame or at any other phosphorescent substance. If the plate is very pure, its interposition will produce no sensible effect, and the images will retain all the relations of intensity which they had when viewed directly. The pale phosphoric gleam therefore suffers in the interior of the glass screen the same absorption as the strong light of the flame does. The bodies on which I have made my experiments have been taken indiscriminately from the three kingdoms of nature: some crystallized, others amorphous; some solid, others liquid; some natural, and others artificial : yet they all act in a similar order relatively to the rays of the different sources of caloric. Does not this constancy in their manner of acting, notwithstanding such great differences in their physical and chemical constitutions, indicate that this law of decrement belongs to the very nature of the heat? We should not however infer from this that there are not bodies which afford a passage equally free to calorific rays of every kind. For we see by the table that a flake of rock salt, most opake bodies become diaphanous when they are sufficiently attenuated), so, in order to judge of the ealorific transmissions through different bodies, we must take the greatest possible care not to employ excessively thin plates, or at least, if we are compelled by particular circumstances to use such, the substances compared should be perfectly equal in thickness; for in that state of tenuity the _ least difference of thickness might disturb the order of permeability and cause us to attribute a greater calorific transparency to substances possessing this pro- : perty in an inferior degree. This is probably the cause of the mistake into which _ those have fallen who have fancied that they could prove by their experiments that water is more diathermanous than glass. Vor. I.—Parr I. E 50 M. MELLONI ON THE IMMEDIATE TRANSMISSION whether exposed to the radiations of flame, of incandescent platina, of copper heated to 390°, or of boiling water, always transmits 92 of every hundred incident rays. The same constancy of transmission is observable when we operate on sources of a temperature yet lower than that of boiling water; such, for instance, as vessels containing this liquid heated to 40° or 50°. It is observable also when we employ pieces of rock salt 15™™ or 20™ thick. I have placed all the flakes of salt that I could dispose of side by side, so that the thickness of them all amounted to 86"". The quantity of heat transmitted by this series of flakes was considerably less than +34;, because of the great number of successive reflexions; but it was always invariable relatively to the four sources. Between these limits of thick- ness, therefore, rock salt really acts in respect to radiant heat just as co- lourless glass and colourless diaphanous bodies in general act in respect to light. This being premised, it is clear that if each substance contained in the table acted like the second specimen of rock salt, that is, if it trans- mitted the heat in a proportion less than 7% but always the same for each of the four sources, all these substances would be to radiant heat that which diaphanous bodies more or less dusky are to light. But they allow the rays from certain sources to pass through them and intercept the rays from others: they act therefore in respect to heat as coloured media act on light*. What do we find when we expose the same coloured glass successively * It appears that Sir David Brewster had lately arrived at the same conclusion by means only of the experiments of Delaroche and Seebeck on the transmis- sion through glass and on the distribution of heat in the solar spectra produced with different prisms. (See Report. of the First and Second Meetings of the British Association for the Advancement of Science. London, 1838, p. 294.) But these experiments did not prove that the rays in passing through the different bodies suffer a real internal absorption analogous to that which light suffers: above all, they were far from proving that this absorptive force, varying in each substance according to the temperature of the calorific source, could, in some particular cases, become constant, and in all respects similar to the action of co- lourless diaphanous media on luminous rays. On this ground it may be said that the inference of Brewster was yet premature; besides, the illustrious Scotch- man rested his conjectures on the erroneous supposition that water has the same absorbent force in respect to all sorts of calorific rays. Experiment indeed leads to the opposite conclusion, as we have already proved in respect to solar heat by the different action of a layer of water on the temperatures distributed in each band of the solar spectrum; an action so widely different relatively to two dif- ferent rays that all the heat of the violet light passes through the liquid without suffering any sensible diminution, while the nonluminous heat of the isothermal band is totally absorbed, (Annales de Chimie et de Physique, December 1831,) and we have just seen in the preceding note that analogous phenomena are obser- vable in the radiations from terrestrial sources also; for a mass of water some millimetres in thickness intercepts all but a very small portion of the radiant heat issuing from flame and the whole of those rays that issue from any other source. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 51 to differently coloured lights? Lights of the same tint as the glass pass abundantly, the rest are almost totally intercepted. These analogies lead us therefore to consider the radiations from dif- ferent sources of heat as not being of the same nature. This seems in- deed sufficiently established by the mere fact that the calorific trans- mission of glass, Iceland spar, or any other diathermanous body varies with the temperature of the radiating source. Thus boiling water, copper heated to 390°, incandescent platina, and the flame of oil will be to us the sources of a heat that is more or less coloured, that is to say, sources each of which gives out a greater quan- tity of calorific rays of a certain quality; but the flame will furnish ca- lorie rays of every kind as it furnishes light of all colours. We shall distinguish bodies into diathermanous and athermanous*. The diathermanous we shall subdivide into universal and partial. The first of these subdivisions, which is analogous to colourless media, will contain but one substance, namely, rock salt; the second, which cor- responds with the coloured media, will contain all the bodies comprised in our table, in addition to diaphanous liquids and diaphanous substances in general. As to the class of athermanous bodies I had supposed at first that every substance which completely intercepted light intercepted the whole of the radiant heat also. This is found to be the fact in the greatest number of cases. But subsequent experiments have shown me that flakes of black mica and black glass, though they completely intercept the most intense solar light, yet exhibit very strongly marked calorific transmis- sions. The following are the results: Transmissions out of 100 rays issuing from @ i) a incan- | copper | copper Locatelli] descent at lamp. | platina. | 390°. Black glass(1™™ in thickness)| 26 25 12 Ditto (2™™ ditto } 16 15°5 8 Black mica(O™™-6 ditto 29 28 13 Ditto (0™™9 ditto ) 20 20 9 * Athermanous, in contradistinction to diathermanous, evidently signifies the absence of the power of transmitting heat. I adopt this term merely for con- venience, without attaching to it a definite meaning; for, as there is no body which, if reduced to an extremely thin plate, may not become in some degree’ transparent, I think also that some rays of heat may pass through all substances in a state of great tenuity. Eg 52 M. MELLONI ON THE IMMEDIATE TRANSMISSION The black mica and black glass then, though perfectly opake, are dia- thermanous, but yet only partially diathermanous, because while they al- low some rays of heat to pass they intercept others. We may see, besides, that the heat of incandescent platina and that of the flame of oil are transmitted in nearly equal quantities by these two substances. As soon as I had made my first experiments on the trans- mission of opake bodies I found that the rays from incandescent pla- tina pass through a plate of black glass in a greater proportion than those from an Argand lamp. Now as it happens quite otherwise in respect to transparent glass and other diathermanous bodies, I thought at first that, in the particular case of the black glass, the variation in the quantity of heat transmitted was inversely as the temperature of the ra- diating source*. But it was not long before I discovered my mistake ; for, exposing two flakes of glass, the one colourless and the other opake, first to the direct rays of a Locatelli lamp and next to the rays that passed through a screen of common glass, I found that if the transmission through the first plate increases, as I have already stated in my first Me- moir, the transmission through the second decreases. These opposite variations exhibited by the transmissions of the black and the white glass relatively to the radiations from the Argand lamp. and the incan- descent platina, do not arise from any peculiar action of the calorific sources on the two bodies, but from a particular modification which the cylindrical screen or glass funnel attached to the Argand lamp pro- duces in the calorific rays passing through it,—a modification which changes their capability of ulterior transmission and enables them to pass through the other bodies in a greater or less quantity than if they were in their natural state. We shall presently see that almost all the screens produce analogous effects. The similarity of the action of glass and transparent bodies in general upon radiant heat to that of coloured media upon light, is established even in its most minute details by all the phenomena of transmission that we have been able to observe. For we have seen that the calorific rays from the flame of an Argand lamp lose much of their intensity while passing into the interior of a thick piece of colourless glass, and that their subsequent losses decrease in proportion as the distance from the surface at which they enter increases. Now the same thing takes place if we expose to white light any coloured transparent body, a red liquid, for instance; for in this case nearly all the rays, blue, green, yel- low, &c., which enter into the composition of this light are absorbed more or less rapidly by the first layers of the liquid, and the red rays alone penetrate to a certain depth. * Bulletin de la Société Philomatique, July 1838. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 53 It is also known from the experiments of Delaroche and others that the radiant heat which has traversed a plate of glass and suffered a cer- tain loss will in passing through a second plate sustain a second loss pro- portionally less than the first. In the same manner does the ineident white light in passing through the first layer of a coloured substance be- come considerably weaker, while the emergent colowred light passes al- most without suffering any diminution of intensity. By exposing a given plate of a diaphanous substance successively to equal quantities of calorific rays from different sources we have seen their transmissions vary with the temperature of the source, that is to say, with the nature of the rays emitted. We have seen moreover that the differences between one transmission and another decrease in pro- portion as the plates employed are thinner, until within a certain limit of tenuity they vanish or have a tendency to vanish altogether. All these effects are observable in the differently coloured lights transmitted through a coloured medium; for if the medium be red the quantities of light transmitted will be greater in proportion to the greater number of red rays contained in each radiation. The other rays will be absorbed in a greater or less degree. But the quantities of light transmitted ap- proach more nearly to an equality in proportion as the plate to be passed through is thinner. In short, the coloured media become more faint as their mass is reduced, and when sufficiently attenuated retain no sensible tint whatsoever, in other words, they become permeable to luminous rays of all colours. We have several times remarked the striking differences exhibited in the calorific transmissions of diaphanous substances. But this cu- rious fact, which constitutes, as it were, the basis of our inquiries, ceases to surprise us as soon as we feel convinced that bodies which are trans- parent and colourless act upon heat in a manner similar to that in which coloured media act upon light. For, as upon the intensity of the co- lour depends the degree of transparency, that is, the number of lumi- nous rays that.pass through the coloured substances, in like manner upon this species of invisible calorific tint which diaphanous bodies possess will depend whether a greater or a less quantity of heat be transmitted*. * Seeing that in respect to all the substances given in the table, the rock salt excepted, the order of decrement is similar though the sources of heat are dif- ferent, one might be inclined at first to infer that they belong to the same species of partially diathermanous bodies, that is, that they may be compared with co- loured media. But that such a conclusion is not legitimate will be shown by ~ one example: let a be the species of rays transmitted by the medium A, b that species which is transmitted by the medium B, and c the rays intercepted by the same media. Let us suppose a calorific source that will give 30 a, 30 b, and 40 c; it is clear that the two media A and B will intercept 70 parts of the hundred and transmit 30. However, the rays emerging from A will be different from those which emerge from B, If we suppose a second source of heat such: as will give 20 a, 20 b, and 60 c, we shall have 80 as the quantity intercepted and 54 M. MELLONI ON THE IMMEDIATE TRANSMISSION We shall presently see yet more striking analogies between the two classes of phenomena when we consider the modifications which the ca- lorific rays undergo in their passage from one screen to the other. But before we dismiss the present subject it may be advisable to bestow a few moments’ attention on the purposes to which the calorific proper- ties of rock salt may be applied. Glass is a substance but very slightly diathermanous, especially when the temperature of the source is low. The common prisms or convex © lenses could not therefore be employed for the purpose of ascertaining whether radiant heat be subject to changes of direction analogous to those of light in penetrating to the interior of refracting media. It was owing to the use of such instruments that some who applied themselves to the investigation of this point attained but very indecisive results, and often drew from them very false conclusions. Scheele asserted that “bright points not possessing the least heat may be formed before the fire with burning-glasses*.” Carefully conducted experiments have more recently shown that a thermometer rises some degrees when placed in the focus of a lens exposed to the radiation of flame or of incan- descent bodies+. But as the heat is then luminous, and as no very de- cided effect is observed if the operation is performed with nonluminous heat, it was inferred that the elevation of temperature was owing to the light absorbed by the thermometer and that isolated radiant heat is not susceptible of refraction. . This notion might derive additional support from the fact that lenses of rock crystal, Iceland spar, alum, and other diaphanous substances acted analogously to the glass lens: and yet it would have been wrong to attribute to the agent an effect which was due only to the particular structure of all those substances. To be satisfied of this we need only operate with a lens of rock salt; for the focal ther- mometer then always exhibits a marked elevation of temperature, even though the radiant heat be totally separated from the light. But it has been attempted to explain the effect of the lenses by an inequality in the heating of their different parts. It has been said that the heat is accu- mulated towards the centre, that the parts towards the margin, because of their thinness, quickly grow cold again, and that it is not surprising therefore to see the thermometer rise more rapidly when placed in the prolongation of the axis of the lens than in any other direction}. It would however still remain to be explained why the experiment is no 20 as the quantity transmitted by each of the screens. If the source gave 10a, 10 4, and 80 c, the transmission would be 10 and the interception 90. Thus two- substances exposed fo different radiations may furnish calorific transmissions not only varying according to thesame order of decrement, but equal inall their periods of variation, although the rays emerging from each may be of a different kind. * Scheele, Zraité de I’ Air et du Feu, Paris, 1778, § 56. + W. Herschel and Brande, Philosophical Transactions for 1800 and 1820. t Philosophical Transactions, vol. cvi. OF RADIANT HEAT THROUGH DIFFERENT BODIES. 55 longer equally successful when for the salt we substitute alum or any other diaphanous substance. But as recourse might be had to sup- posed differences between the conducting, the absorptive, or the emis- sive powers of these bodies, it seems advisable first to prove the refrac- tion of the nonluminous rays without using lenses. With this view I place, at a certain distance from the thermoelectric pile and out of the direction of its axis, a plate of copper heated to 390° by an alcoholic lamp, or, what is still better, a vessel filled with water in a state of ebullition. The pile being lodged at the bottom of a me- tallic tube blackened inside, the rays of nonluminous heat emitted from the vessel in a direction oblique to the axis cannot reach the thermosco- pie body, and the index of the galvanometer remains perfectly at rest. Matters being now in this state, I take a prism of rock salt and fix it at the mouth of the tube with its axis placed vertically and its refractive angle turned towards the angle formed by a line drawn from the source to the extremity of the tube. (See Plate I. fig. 2.) A considerable de- viation is immediately perceived inthe galvanometer. The rays of heat are therefore conveyed into the tube by the action of the prism. To show that the effect is really due to the refraction and not to the heat of the salt it will be sufficient to turn the angle of refraction in a contrary direction; for as soon as this is done the needle falls again to zero, notwithstanding the presence of the prism. The experiment is no less successful with the heat of the lamp, or that of the incandescent platina. Calorifie rays of every kind are therefore, like luminous rays, susceptible of refraction. But on the principle of analogy, as each species of light, so will each species of heat possess a different refrangibility. Hence it is evident that if the prism be left in its position and the radiant source changed it would become necessary at the same time to change the angle formed by the axis of the pile with the direction of the rays, in order to obtain the desired effect on the galvanometer. If however we attempt to ve- rify this conjecture we obtain no decisive result. This is easily con- ceived when we reflect that the aperture of the tube has a certain dia- meter and that it is placed quite close to the prism, so that the rays refracted at angles differing but very little from each other can always reach the pile though no change should be made in the inclination of the axis of the tube. But there is another process by means of which, if we cannot exactly measure the refrangibility of each, species of calorific rays, we prove at least that the angle of refraction varies with the measure of the radiating source. I took a graduated circle ABC (Plate I. fig. 3.) 22 inches in diameter carrying aruler CD as a moveable radius. At the extremity of this ruler I placed a thermoelectric pile M composed of fifteen pairs disposed in one line perpendicular to the plane of the circle. 56 M. MELLONI ON THE IMMEDIATE TRANSMISSION This apparatus being placed horizontally on a table, the centre C was brought within a little distance of the bottom of a vertical prism(N) of rock salt, so that when the ruler CD was properly placed the refracted parcel of hot rays fell on all the points of the linear pile. By establishing the electric communications with the galvanometer and moving the ruler over the graduated arc, the point at which the deviation of the magnetic index attained its greatest value was easily determined. The radiating source was then changed while everything else was allowed to remain in the same state. We had now a calorific action more or less intense than the preceding; but in order to obtain the maximum of effect it was necessary to slide the ruler in one direction or the other. Thus, for instance, when I commenced the experiment with the incandescent platina, that is, when I had found the correspond- ing position of the pile that gives the greatest galvanometric deviation, it was necessary to move the ruler about two lines towards B, on the side to which the most refrangible rays are directed, if I substituted the Locatelli lamp for the platina. But if I substituted for the platina a plate of copper heated to 390° I was obliged to slide the ruler three lines towards A, in the direction of the less refrangible rays. The action of the boiling water in this experiment was too feeble to be compared with that of any of the three other sources. The refraction and constant transmission of the calorific rays through the rock salt being placed beyond the possibility of doubt, we imme- diately see the use that may be made of this substance in investigating the nature of radiant heat. If, for instance, it is proposed to propagate to great distances the action of a heated body of small dimensions, we are now certain that we have only to place the body at the focus of a lens of rock salt, which will refract the calorific rays and make them form a real pharos of heat by issuing in a direction parallel to the axis. Is it desired that extremely feeble rays emanating from any source should be rendered perceptible? Let them be received on a lens of this sub- stance having a thermoscopic body placed in its focus. In this manner we may, with the aid of an ordinary differential thermometer with small balls, obtain very decided indications of the heat issuing from a vessel filled with tepid water and placed at a great distance. In short, rock salt formed into lenses and prisms acts upon calorific rays in a manner perfectly analogous to that in which optical instruments act upon lumi- nous rays. It constitutes then the ¢rwe glass of radiant heat, and there- fore the only glass that should be employed in appreciating the effects of its intensity. All other transparent bodies are but partial and in- complete transmitters of heat, totally intercepting calorific rays of a certain kind. It is easy to conceive, from these considerations, with what serious disadvantages those persons have had to contend who have undertaken to investigate the composition of solar heat with common OF RADIANT HEAT THROUGH DIFFERENT BODIES. 57 prisms of flint or crown glass, water, alcohol, or some other diaphanous body. It was exactly the same as if they pretended to be able to analyse solar light with a prism formed of coloured glass. Of the properties of the calorific rays immediately transmitted by different bodies. The radiant heat which has passed through a plate of glass is trans- mitted in a greater proportion by a second plate of the same substance and the same thickness ; the rays issuing from the second will be trans- mitted in a still greater proportion by a third, and so through any number of successive screens. The losses sustained by the calorific rays in their passage through a succession of screens, as compared with the quantity incident on each plate, will therefore form a decreasing series. But the difference between every two terms of this series becomes less and less as the number of terms increases, so that there must be somewhere a limit beyond which the difference has a tendency to vanish. We may conclude therefore that the rays after they have passed through a cer- tain number of screens, will in their further transmission be subject to a loss reducible to a constant quantity as compared with the quantity of heat incident to each of the screens through which this further transmis- sion is made. The same phenomena may be traced in a continuous mass of diather- manous matter; that is to say, that if we imagine a piece of glass di- vided into several equal layers and measure the loss sustained by the radiant heat in its passage through each layer, the greater the distance of the layer from the surface at which the heat enters, the less will be the diminution suffered by the rays passing through that layer, and the losses have a tendency to become constant within a limit depending on the thickness of the layers. Some of these results we have already verified in the preceding memoir, and it is easy to establish their truth, in reference to the sources of heat employed in our present inquiry, by means of the numbers which represent the transmissions of the plates contained in the first table*. * Let us imagine the screen of 8™™ divided into seven layers having for their degrees of thickness the differences between two consecutive plates. (See the first table in this Memoir.) The quantities of heat incident on the layers when the radiation is from a Locatelli lamp are 100, 77, 54, 46, 41, 37, 35, 33-5, and the Seeentien lost in the successive transmissions are 23, 23, 8, 5, 4, 2, 1d. Now the mean losses for the fuindxedth part ofa millimetre of each screen will be 23 23 8 5 4 2 1:5 7’ 43’ 50’ 100’ 100’ 100’ 100° or 3:286, 0-535, 0:160, 0-050, 0-020, 0-010, 0-007." Hence the losses sustained by the rays of the lamp in the first hundredth part 58 M. MELLONI ON THE IMMEDIATE TRANSMISSION The only difference observable between the transmission through a continuous medium and the transmission through a series of detached screens is in the amount of the losses, which, for a given thickness, are found to be greater in the latter, because of the reflexions produced by each separate surface. : These facts cannot surprise us after the idea we have formed to our- selves of the influence exercised by diaphanous substances on radiant heat. For the calorific sources always emit a certain portion of rays heterogeneous (if we may use the expression) to the calorific tint of the glass, which, through the absorbent action of the matter constituting the continuous medium or the detached screens, are successively extin- guished until no rays remain but those that are homogeneous to this tint. Now these homogeneous rays must suffer a loss greater or less in its amount, but constant in respect to layers of equal thickness, as is the case, in the transmission of light, with red rays passing through a medium of the same colour, and with white rays passing through a medium diapha- nous and colourless. What we have said of glass is equally true of every other partially diathermanous substance. The calorific transmission through aseries of homogeneous screens is then absolutely of the same nature as that which is effected through the of a millimetre of each layer, when referred to the quantities of incident heat, will have the values 3286 0°535 0:160 0:050 0:020 0:010 0-007 100 77 54 46 41 37 35 that is, 0°0328 0:0070 0:0030 0:0011 0:0005 0°0003 0-0002. By similar calculations the successive losses sustained by the radiations from the incandescent platina and the copper heated to 390° will be found to be 0:0614 0-0081 0°0032 0:0019 0:0010 0:0005 0-:0003 0:0943 0:0155 0°0050 0:0022 0-0014 0:0010 0-0008. Now the differences between every two terms of these series are for the Ist, 0°0258 0-0040 0-0019 0-0006 0:0002 0-0001; 2nd, 0:0523 0:0049 0:0013 0:0009 0:0005 0:0002; 3rd, 00780 0:0105 0:0028 0:0008 0-0004 0-0002. As to the fourth source it is useless to speak of it, as its rays are completely extinguished at the distance of one millimetre. Thus, notwithstanding the inequalities of the increase of the distance from the second and the third layer to the surface of entrance, we observe in the three series the two principles we have laid down, namely, Ist, the decrease of the losses; 2nd, the tendency of this decrease towards a limit at which the loss becomes constant: but for each particular case the points of the medium at which the rays begin to suffer this constant action are evidently placed at a fixed distance from the origin. Therefore, if the glass be divided into equal layers, the limit of the decrease of the losses will be attained more slowly in proportion as theayers are more numerous, that is to say, thinner. It is for this reason that in each series the limit at which the losses become constant depends, as we have already said, on the thickness of the elementary layers. a OF RADIANT HEAT THROUGH DIFFERENT BODIES. 59 interior of one continuous medium. This transmission we have ex- amined, and, as we have just seen, it presents nothing contrary to its ana- logy with the transmission of light through coloured media. There is however a particular case in which two homogeneous screens act in so singular a manner in respect to light that it must be interesting to know whether something analogous does not take place in respect to caloric. The optical phenomena presented by most of the slices of tour- maline cut parallel to the axis of crystallization are universally known. If these slices are placed one over the other and their axes laid in the same direction, they transmit light in considerable quantities. But if they be laid at right angles to one another, the light is totally intercepted. Do these phzenomena, arising, as is well known, from the polarization of the light in the interior of the slices, take place in respect to calorific rays also; or, in other words, is radiant heat capable of being polarized in its passage through tourmaline ? In order to ascertain this I have taken two square plates of the same dimensions. I have made an aperture in the centre of each. This aperture was likewise a square having its sides parallel to those of the plate and each equal to the least breadth of the two polarizing slices. I then took some soft wax and attached a tourmaline to each aperture, holding the axis of the former parallel to one of the sides of the latter. These two plates being laid one over the other, it evidently depended on one of the sides of the one plate being placed parallel or perpendicular to a side of the other whether the light was to be transmitted or inter- cepted. Yet this pair of plates being placed vertically on the stand of my thermoelectric apparatus and exposed to the radiation of a lamp or incandescent platina, uniformly produced the same calorific transmission, whatever might be the relative direction of the sides of each plate. That this fact might be put beyond the reach of doubt the galvano- metric index was carried to the 18th or 20th degree, and the calorific communication now established was suffered to remain while we placed one of the plates on each of its sides in succession. The flame or the incandescent platina was then observed to appear and disappear alter- nately while the magnetic needle continued invariably at the same point of deviation. . This experiment was repeated many times with several tourmalines, and the angle formed by the intersection of their axes varied. The re- sult was in all cases the same. The quantity of calorific rays trans- mitted through the two polarizing slices is then independent of the re- spective directions given to their axes of crystallization; that is to say, the heat radiating from terrestrial sources is not polarized in its passage through tourmalines*, * This result seems opposed to the experiments of M. Bérard on the polari- zation of reflected heat; but, ignorant as we are of the nature of the relations 60 M. MELLONI ON THE IMMEDIATE TRANSMISSION Let us now proceed to consider the transmission of heat through he- terogeneous screens. The calorific rays emerging from each plate ex- posed to the action of the same source produce a particular elevation of temperature when they fall on the thermoscopic body of our apparatus. Whence we have inferred that the quantity of heat which passes through a given screen varies according to the quality and thickness of the sub- stance. But, it may be asked, is this the only difference between the rays immediately transmitted through bodies of different kinds ? For the purpose of answering this question we have made the follow- ing experiments. If the rays from a Locatelli lamp be brought to act on a thermoelec- tric pile after having previously passed through a screen of diaphanous matter (such as citric acid) but in a slight degree permeable to radiant heat, the effect obtained in the ordinary case, in which the whole ac- tion is equivalent to 30° of the thermomultiplier, will be very inconsi- derable ; but it may be increased by bringing the source of heat nearer, or by concentrating its rays on the plate with the help of metallic mir- rors or lenses of rock salt. I suppose then that a deviation of 25° or 30° of the galvanometer has been produced through a plate of citric acid. I now interpose a plate of alum in such a manner that the rays emerging from the citric acid may be forced to pass through it before they can reach the thermoscopic body; the magnetic needle descends only about 3 or 4 degrees.” I now recommence the operation on any other diaphanous and colour- less substance different from the citric acid; that is to say, I vary the distance from the lamp to the pile until I obtain the same galvanome- tric deviation of 25° or 30° by the action of the radiant heat on this new substance also. I then interpose the plate of alum, and the magnetic index, as in the case of the citric acid, descends again not more than about 3 or 4 degrees, but it approaches nearer to zero, and the retro- that caloric and light bear to one another, we have no means of proving that, as no polarization of heat is produced by the transmission through the tourmalines, none can be produced by reflexion at the surface of the glass. Iam bound also to remark that some very able experimental philosophers having lately tried to polarize light by M. Bérard’s process, their efforts proved unavailing. Mr. Powell informs us that although he had taken the necessary precautions against the heating of the glass and other causes of error he has never been able to discover the least appearance of polarization when operating with nonluminous heat. But he thinks that when he employed luminous sources he was enabled to ob- ‘serve a small perceptible effect by making the rays previously pass through a screen of glass (Edinb. Journal of Science, N. S., vol. vi.) Mr. Lloyd communi- cated at the last meeting of the British Association for the Advancement of Science (Cambridge 1833) some new results tending to support the conclusions derived by Mr. Powell from his own experiments. [No communication upon this subject by Professor Lloyd appears in the Report of the British Association for 1833,—Epir. | OF RADIANT HEAT THROUGH DIFFERENT BODIES. 61 grade movement is sometimes so marked that the needle nearly resumes its natural position of equilibrium. If instead of alum other substances were employed as the invariable plate on which the rays issuing from each diaphanous body are succes- sively made to fall, we should still observe differences in the correspond- ing deviations of the galvanometer; but they would be in general of a less decided kind. It is on this account that we have preferred the alum. The following are the results, in hundredth parts, of the constant quantity of heat that falls on the plate of alum: Screens from which there issue 100 rays of heat which are made to fall succes- Number of rays transmitted sively on the same plate of alum. J es ORBISON WLS, chee. i otdin seus een 9 Fockisalt (limpid)ciec usc. de Seeds ove 9 Rock salt SS aN Ceon Th 9 EES OL SOAD. ono utansiennsier'piaes axes, itd AGULATIA TIDAL | oon... ccncenocaesene 14 MECIATU SPaly coetircscsidecsenncettoscse OE Bisehs crystal Ai: os. aeee cow cas cotess 25 Mirror elass ts) See 27 Carbonate of ammonia ............... 31 Sulphate of inten: 05... ssvwscetedcnvassihinn C2 Tartrate of potash and Jee Ehcrtde nce 80 WipmeraCldy. ster dee ase ch teeroechs + OD J: \IRELTEN Sy aia RRS BG Ra eS 90 We see that radiations of the same intensity emanating from the dia- phanous and colourless bodies contained in the tables pass through the same plate of alum in very different quantities. In the same manner sheaves of luminous rays issuing from different coloured media are transmitted some in greater and others in less proportions by a second transparent substance equally coloured, as the tint of each medium hap- pens to be more or less analogous to that of the invariable substance through which they are to pass. The calorific rays issuing from the diaphanous screens are therefore of different qualities and possess (if we may use the term) the diather- mancy * peculiar to each of the substances through which they have passed. The citric acid, the tartrate of potash and soda, and the sul- phate of lime transmit rays which pass abundantly through alum; the * IT employ the word diathermancy as the equivalent of calorific coloration or caloric tint, lest the latter should be confounded with tints or colours properly so called. The word has been suggested to me by M. Ampére, who has conti- nued to assist me with his valuable advice in the composition of this Memoir, for which I here take the opportwhity to tender him my grateful acknowledge- ments. 62 M. MELLONI ON THE IMMEDIATE TRANSMISSION diathermancy of these bodies therefore approximates nearly to that of the alum. The glass, the rock crystal, and the Iceland spar have evi- dently a different diathermancy, for the rays which pass through them are less transmissible by the invariable screen. ‘The same may be said of borax, adularia, and carbonate of ammonia. As to the heat emerging from rock salt (limpid or dull) it acts in a manner similar to that in which the unobstructed light of the lamp would. The reason is evident, since the salt, acting equally on the different species of calorific rays, must transmit them all without reflecting their relative properties in any man- ner whatsoever. These facts then completely confirm the conclusions which we had drawn from the preceding experiments: namely, that, 1st, flame sends forth rays of several kinds; 2nd, that diaphanous colourless bodies, with the exception of rock salt, act so as to extinguish certain caloric rays and allow others to pass, just as coloured media act in respect to light. Here a very interesting question is naturally suggested. If the dia- thermancy or quality which constitutes the tint of a medium relatively to the radiant caloric is invisible, what part then do colours act in the transmission of heat ? When the quantity of radiant heat that passes through coloured glass is measured, it is always found to be less than that which passes through white glass of the same thickness. The difference indeed is sometimes considerable, though having no apparent relation to the prismatic order or intensity of the colour. We have already remarked this in the first memoir, and the truth of the remark will be readily admitted by any one who casts an eye over the following little table. Screens of glass exposed to the radiation of a Locatelli lamp. (Common thickness 1"™-85.) Transmissions out of 100 rays of heat. CABS; TBS) Leh PS RBS, eee 40 ny ROH (deep) i. lassen Se are —- PRODUCED BY ELECTRO-CHEMICAL ACTION. 117 it impossible to obtain brightness of tint unless by sacrificing intensity, is sufficiently demonstrated. Beauty and Monotony. Beauty consists in a certain variety which some tints possess in a higher degree than others. The yellow, for example, and the red of the spectrum have a tone peculiar to themselves: the golden contains the essence of the red and the yellow, and is more agreeable to the eye than either. The most beautiful tints in the scale commence at the orange colours 22 and 23, and continue to the end. The first element of pleasing is variety; in this point of view the purity and homogeneity of a colour are defects, of which philosophical painters must have been sensible when they recommended the use of compound in preference to simple colours *. The purest tint of the scale is perhaps that of the yellow No.19. At the first glance it is extremely pleasing, but soon becomes monotonous and the eye turns away for relief to the higher tints, each of which pro- duces the sensation of several colours. A painting in which there is much yellow will therefore always fail to please on account of this mo- notony; for its effect is most disagreeable. Nothing can be more beautiful than the varying colours: when we call them varying it is unnecessary to say why they please. Painters, we know, in order to give a finish to their productions, overlay them with certain tints. The colours of the painting appear through the tint, are mingled but not confounded with it, and thus are produced a variety and vividness unattainable by any other means. Warmth and Coldness. Those tints which contain the element of red are by painters called warm, and those in which the element of azure abounds are termed cold. Red is the strongest and the most vivid colour : it is the colour of fire and of blood, and it warms and inflames all the tints into which it is in- troduced. If the idea of warmth is associated with red, azure gives rise to a very different feeling: it is indeed preeminently the cold colour. Yellow approaches more nearly to the nature of red than to that of azure, and is consequently rather warm than cold. Pure green cannot be said to be cold or warm: it inclines however to the former or to the latter accordingly as it is combined with blue or with yellow. Cheerfulness and G'loominess. Cheerfulness is not to be confounded with beauty, nor gloominess with monotony: they are more distinct sensations and seem to belong, the * Lecons Pratiques de Peinture, § v. 118 M. NOBILI ON COLOURS, AND ON A NEW CHROMATIC SCALE first to the lower colours of the spectrum, such as the red, orange, &c., and the second to the superior colours, such as the violet, indigo, &c. The most gloomy tints on the scale are, according to the generally received opinion, those of Nos. 10, 11 and 12, in which the higher co- lours of the spectrum abound. These colours, it cannot be denied, are also the least bright, and this quality may well be the cause of the gloominess which is felt in viewing them. It is possible however that there may be in this case an unknown ge- neral law, which it would be worth while to investigate with the aid of the analogies afforded by acoustic phenomena, of which the principles are better known. On the Pathetic and the Cheerful in Music and Painting. An exclamation or shout of joy consists of notes ascending from the grave to the acute; a cry proceeding from grief or pain consists, on the contrary, of notes descending from the acute to the grave. It is not more singular than true, although it has never before been remarked, that the same notes sung or executed on an instrument will produce in the ascending scale a very different effect from that which they produce in the descending scale. In the first case the feeling excited is decidedly cheerful; in the second it is as decidedly sad. This is a fact which in both a physical and a physiological point of view remains yet un- explained, but may serve nevertheless as a law for all analogous cases. Violet is a colour which certainly awakes a feeling of sadness. Can it be owing to a similar law that it produces such a sensation? I inspect the table of imaginary colours, and find that the green-yellow corresponds to the violet. We know that according to the theory of vibrations the violet is produced by shorter and the red by longer vibrations. The transition then from the violet, which is the real colour, to the green- yellow, which is the imaginary, is a transition from the acute to the grave, and analogous to that which takes place in the notes that produce sad- ness. The only difference between the two cases is, that in the one the sensation is the direct and immediate effect of the notes conveyed to the ear from without, whilst in the other the eye receives from without no- thing more than the impression of the violet colour, the rest of the ef- fect depending on the internal action of the optical nerves which are en- dowed with the power of passing of themselves from the real to the ima- ginary colour. A. difference of this kind however is not incompatible with the existence of the analogy : it only leads to the inference that the eye possesses the more exquisite sensibility, since in this organ a mere disposition or tendency is sufficient to produce an effect which in the ear is due to an external cause: for, the superior delicacy of the eye is evi- dently the cause of the existence of these imaginary colours, which have oe oo PRODUCED BY ELECTRO-CHEMICAL ACTION. 119 no counterpart in the other sense,—no succession of imaginary sounds resulting from those which had previously reached the tympanum. ~ In music there is awell-known and long-established distinction between harmony and melody: the former arises from a certain series of sounds produced all at the same time, the latter from the succession of certain sounds produeed according to a certain rule. Can the science of colours lay claim to a similar distinction ? I look at a fine painting, and amiat once struck with the harmonious disposition of its beautiful colours. This isthe first feeling excited, and it is excited ina moment. I afterwards examine and study the composition by looking attentively now at one point and then at another. The merit of the piece was at first confined to the beauty and harmony of the tints; now the same tints being observed with more attention awaken, or tend to awaken, the idea of the imaginary colours, and thus acquire an expression which was wanting to them when they were passed rapidly over. -It has already been observed that the green- yellow arose from the violet, and that the latter colour had a tendency to produce a sensation of sadness on account of its involving a necessary transition from an acute to a grave tone. The lower colours of the spectrum (the red and the golden) have as their imaginary colours azure-green and indigo. In both these cases the passage is from the grave to the acute, and the two colours should, according to the law under consideration, excite a feeling of cheerfulness. The theoretical inference is confirmed by every one’s experience. This analogy between sounds and colours may, after all, be rather ap- parent than real. I thought myself bound nevertheless to mention it, with a view to its development, and on account of the new ideas which it might suggest. Additional Note on the Law of Varying Colours. In speaking of this law, I have remarked an analogy which presents itself in the central tints of the second ring. After having concluded my labours it occurred to me to examine this interval once more, and I noticed a fact which had escaped me in my first inquiries. Beginning with the perpendicular incidence, in order to pursue the examination through the other incidences, I observed the rings attentively. As my point of view I took the central part of the second ring, and there, at an angle between 70° and 80°,I perceived a new ring formed. This ap- pearance was not accompanied by the disappearance of any of the other rings: it was really a new ring formed under this great inclina- tion at the centre of the second, which was at first almost entirely white. I shall distinguish this ring from the others by the epithet intruded *. * It may not be useless, perhaps, to mention that my rings are inverse to those of Newton; his begin at the centre, mine at the circumference, where, from the nature of the electro-chemical process, the thinnest layers are depo- sited: the thickest layers are evidently those of the centre. : 120 M. NOBILI ON COLOURS, AND ON A NEW CHROMATIC SCALE My rings can easily be so enlarged that the intruded ring may occupy a space two or three lines in breadth. The tints composing it will then be seen very distinctly, and will correspond exactly with those which are seen in detail on the plates 20, 19, 18, 17, 16 and 15; with this difference only, that, in place of these tints, a ring will be seen pererec of green, red and yellow. When the rings are smaller, as they usually are when oiitedned under the platina point, the intruded ring appears in the same place, and the observation, though made under circumstances less favourable, is equally decisive. Newton’s rings give no idea of this phenomenon: they vanish from the eye of the observer before the last degrees of obliquity are attained, and are consequently unavailable in an observation for which these great inclinations are an indispensable condition. ‘The smallness of the di- mensions of the rings cannot cause the observation to fail, whenever it can be made on my rings whether large or small. I cover a portion of my rings with a layer of alcohol, oil, or water, &c., and when the observation is made at the before-mentioned inclination of from 70° to 80°, the intruded ring appears only where the humid layer is wanting. Thus the phenomenon connects itself still more with the law of refraction. In my opinion there are but few facts that can puta theory so severely to the test as this, and the theory which can completely explain it will have every claim to credit. Ishall always add to my chromatic scales a plate exhibiting on its sur- face the coloured rings as much enlarged as is requisite for the conve- nient study of the properties of the intruded ring. This I feel the more inclined to do, as these large rings are likely to be useful in other re- spects ; they will serve, for instance, as a key to the chromatic scale, which is in reality no more than the development of the rings them- selves ; and this development is indispensable when we would judge of a colour. In the coloured rings, however large they may be, there is al- ways found between every two tints a third into which they melt: its tone and the feeling which it produces are always confounded with those of the contiguous tints. For this inconvenience there is no re- medy but to isolate the tints, so that the eye may be fixed on each of them without receiving at the same time any sensation from the others. The chromatic scale affords this advantage in its detached plates, not to mention the other advantages which in the course of this Memoir it has been proved to possess, and which it is therefore unnecessary to enu- merate here. Reggio, June 29, 1830. PRODUCED BY ELECTRO-CHEMICAL ACTION. 121 CHROMATIC SCALE. 44 | Lacca-rosea. Laque-rose. Rose-lake. (30 43 | Verde-giallo-rossic c. Vert-jaune rougeatre. Reddish yellow-green.(28 42 | Verde-giallo. Vert-jaunatre. Yellowish-green. er 41 | Verde. Vert. Green. (26 40 | Violaceo-verdognolo. Violet-verdatre. Greenish-violet. (25 39 | Lacca-violacea. Laque-violette. Violet-lake. (24 38 | Lacca-rosea. Laque-rose. Rose-lake. (22 37 | Rancio-roseo. Orange-rose. Rose-orange. 36 | Rancio-verde. Orange-verdatre. Greenish-orange. (21 35 | Verde-rancio. Vert-orangé. Orange-green. 34 | Verde-giallo. Vert-jaune. Yellow-green. (20 33 | Verde-giallognolo. Vert-jaunatre. Yellowish-green. 32 | Verde. Vert. Green. et 31 | Porpora-verdognola. Pourpre-verdatre. | Greenish-purple. (18 30 | Lacca-turchiniccia. Laque-bleuatre. Blueish-lake. (17 29 | Lacca-purpurea. Laque-pourprée. Purpled-lake. (16 28 | Lacca-accesa. Laque éclatante. Brilliant-lake. 15 27 | Lacca. Laque. Lake. 26 | Lacca-rancia. Laque-orangée. Orange-lake. (14 25 | Rosso-rancio. Rouge-orangé. Orange-red. 24. | Rancio-rosso. Orange-rouge. Red-orange. 23 | Rancio-rossiccio. | Orange-rougeatre. _ Reddish-orange. 22 | Rancio. Orange. Orange. (13 21 | Giallo-rancio. Jaune-orangé. Orange-yellow. 20 | Giallo-aeceso. Jaune éclatant. Brilliant-yellow. 19 | Giallo. Jaune. Yellow. 18 | Giallo-chiarissimo. Jaune trés-clair. Very bright yellow. (12 17 | Celeste-giallognolo. Azur-jaunatre. Yellowish-azure. 16 | Celeste. Azur. Azure. 15 | Bleu-chiaro. Bleu-clair. Clear-blue. 14 | Bleu. Bleu. Blue. 13 | Bleu-carico. Bleu-foncé. Deep-blue. 12 | Indaco. Indigo. Indigo. (10 |11 | Violetto. Violet. Violet. (8 10 | Rosso-violaceo. Rouge-violet. Violet-red. (7 9 | Ocria-violacea. Ocre-violette. Violet-ochre. | 8 | Ocria. Ocre. Ochre. | 7 | Rosso di rame. Rouge de cuivre. Copper-red. (6 6 | Fulvo-acceso. Fauve éclatant. Brilliant-tawny. | 5 | Fulvo. Fauve. Tawny. | 4 | Biondo-acceso. Blond éelatant. Brilliant-blond. (5 3 | Biondo d’ oro. Blond-doreé. Golden-blond. 2 | Biondo. Blond. Blond. _1 | Biondo-argentino. Blond-argentin. Silver-blond. (4 122 ArrTicLe VI. On the Mathematical Theory of Heat ; hy S8.D. Poisson, Member of the Institute, &c.* From the Annales de Chimie et de Physique, vol. u1x. p. 71 et seq. Tue work which I have just published under the title of The Mathe- matical Theory of Heat ( Théorie Mathématique de la Chaleur), forms the second part of a treatise on Mathematical Physics (Physique Mathé- matique), the first’ of which is the New Theory of Capillary Action (Nouvelle Théorie de U Action Capillaire), which appeared four years ago. It contains twelve chapters, preceded by some pages in which I recapitulate in a few words the first applications of the caleulus which have been made to the theory of heat, and the principal researches of geometers upon that subject, which have been- made of late years, namely, since the first Memoir presented by Fourier to the Institute in 1807. Iwill here transcribe the contents of the Preface; on the im- portant question of the heat of the earth. “In applying to the earth the general solution of the problem of a sphere at first heated in any manner whatever, Laplace was led to par- ticipate in the opinion of Fourier, which attributes to the primitive heat of the earth the increase in temperature which is observed in descend- ing from the surface, and the amount of which is not the same in all lo- calities. This hypothesis of a temperature proceeding from the original heat of the globe (da chaleur dorigine), and which must rise to millions of degrees in its central layers, has been generally adopted; but the dif- ficulties it presents appear to me to render it improbable. I have pro- posed a different explanation of the increasing temperature which has long since been observed at all depths to which man has penetrated. “ Aceording tothis new explanation the phenomenon depends on-the inequality of temperature of those regions of space which the earth sue- cessively passes through in its translatory motion, and which are com- mon to the sun and all the planets. It would be indeed opposed to all pro- bability that the temperature of space should everywhere be the same; the variations to which it is subject from one point to another, sepa- rated by very great distances, may be very considerable, and ought to produce corresponding variations in the temperature of the earth, ex- * The work of which this article is an analysis, is described as a quarto volume of more than 500 pages, with a plate ; published by Bachelier, Quai des Augus- tins, Paris. M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 125 tending to various depths according to their duration and amplitude. Suppose, for the sake of example, a block of stone transported from the equator to our latitudes ; its cooling will have commenced at the surface, and then become propagated into the interior; and if the cooling has ex- tended throughout the whole mass, because the time of its transporta- tion has been very short, that body thus transported to our climate will present the phenomenon of an increase of temperature with the distance from the surface. The earth is in the case of this block of stone; —it is a body coming from a region the temperature of which was higher than that of the place in which it now is; or we may regard itasa thermometer moveable in space, but which has not had time, on account of its magnitude and according to its degree of conducting power, to take throughout its mass the temperatures of the different regions through which it has passed. At present the degree of temperature of the globe is increasing below the surface ; the contrary has in former times been, and will hereafter be, the case: besides, at epochs separated by many series of ages this temperature must have been, and will in future be, much higher or lower than what it is at present; a circumstance, which renders it impossible that the earth should always be habitable by man, and has perhaps contributed to the successive revolutions the traces of which have been discovered in its exterior crust. It is necessary to observe that the alternations of temperature of space are positive causes which have an increasing influence upon the heat of the globe at least near its surface; while the original heat of the earth (chaleur dorigine de la terre), however slow it may be in dissipating, is but a transitory circum- stance, the existence of which it would not be possible at the present epoch to demonstrate, and to which we should not be forced to have recourse as a hypothesis except in the case of the permanent and neces- sary causes being insufficient to explain the different phenomena.” The following are the titles of the different chapters of the work, to- gether with a short abstract of the contents of each. Carter I. Preliminary Notions — After having given the definition of temperature and many other definitions, it is explained how we have been led to the principle of a continual radiation and absorption of heat by the molecules of all bodies. The interchange of heat between material particles of an insensible magnitude, but yet comprising im- mense numbers of molecules, cannot disturb the equality of their tem- peratures when it actually exists. From this condition we conclude, that for each particle the ratio of the emitting to the absorbing power is inde- pendent of the substance and of density, and that it ean only depend on _ temperature. In the case of the inequality of temperatures, we give the - general expression of their variations during every instant, equal and contrary for two material particles, radiating one toward the other. We 124 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. also give the law of absorption of radiant heat in the interior of homo- geneous bodies. ; Cuarpter II. Laws of Radiant Heat.—If a body be placed within a vacuous sphere on every side (enceinte vide fermée de toutes parts), the temperature of which is supposed to be invariable and everywhere the same, we demonstrate that the result of the interchange of heat between an element of its surface and an element of the surface of the inclosing sphere, is independent of the matter of which the sphere is formed, and proportional, ceteris paribus, to the cosines of the angle which the normal to the second element forms with the right line from one to the other element. Experiments, not as yet made, only can decide whether this law of the cosine is equally applicable to the elements of the surface of the body, of which the temperature is not invariable like that of the sphere; and until such experiments are made we may be allowed to doubt its existence while the body is heating or cooling. By consi- dering the number of successive reflexions which take place at the surface of the sphere we demonstrate also that in general the pas- sage (flux) of heat through every element in the surface of the body which it contains is independent of the form, of the dimensions, and of the material of the sphere; there is no exception, but when the heat, in the series of reflexions which it experiences, falls one or many times upon the surface of the body. It follows from this theorem that a thermometer placed in any point whatever of the space which the sphere terminates, will finally indicate the same temperature, which will be equal to that of the sphere; but in the case of the exception just mentioned, the time which it will employ in attaining that tem- perature will vary according to the place it occupies. The general ex- pression of the passage of heat through every element of the surface of a body of which the temperature varies, is composed of one factor re- lative both to the state of that surface and to the material of the body, multiplied by the difference of two similar functions, one of which depends on the variable temperature of the body, the other on the fixed temperature of the sphere, which are the same for all bodies; a result which agrees with the law of cooling im vacuo discovered by MM. Dulong and Petit. We next suppose in this second chapter, that many bodies differing in temperature are contained in the sphere of which the temperature is constant, and arrive then at a general for- mula, which will serve to solve the problems of the catoptrics of heat, the principal applications of which we indicate. When all these bodies form round one of them a closed sphere the temperature of which, variable with the time, is not the same throughout, the passage of heat to the surface of the interior body does not depend on its tempe- rature and that of the inclosure only, at least when these bodies are M. POISSON ON THE MATHEMATICAL THEORY OF HEAT, 125 formed of the same material. After having considered the influence of the air upon radiation which we had at first eliminated, we give at the end of this chapter a formula which expresses the instantaneous variations of temperature of two material particles of insensible magni- tude, by means of which the exchange of heat takes place after one or many reflexions upon the surfaces of other bodies through air or through any gas whatever. Cuarter III. The Laws of Cooling in Bodies having the same Tem- perature throughout.—While a homogeneous body of small dimensions is heating or cooling, its variable temperature is the same at every point; but if the body is composed of many parts formed of different substances in juxtaposition, they may preserve unequal temperatures during all the time that these temperatures vary, as we show in an- other chapter. Inthe present we determine, in functions of the time, the velocity and the temperature which we suppose to be common to all the points in a body placed alone in a sphere either vacuous or full of air, and the temperature of which is variable. If the sphere contains many bodies subject to their mutual influence upon each other, the determination of their temperatures would depend on the integra- tion,of a system of simultaneous equations, which are only linear in the case of ordinary temperatures, but in which we cannot separate the variables when we investigate high temperatures, and when the radia- tion is supposed not to be proportional to their differences. Experiment has shown that in a cooling body, covered by a thin layer or stratum of a substance different from that of which it is itself composed, the velocity of refrigeration only arrives at its maximum when the thickness of this additive stratum, though always very small, has notwithstanding attained a certain limit. We develop the consequences of this important fact in what regards extension of molecular radiation, and explain how those consequences agree with the expression of the passage of heat found in the preceding chapter. Cuapter IV. Motion of Heat in the Interior of Solid or Liquid Bodies.—We arrive by two different processes at the general equation of the motion of heat; these two methods are exempt from the difficulties which the Committee of the Institute, which awarded the prize of 1812* to Fourier, had raised against the exactitude of the principle upon which his method was sustained. The equation under consideration is appli- cable both to homogeneous and heterogeneous bodies, solid or fluid, at rest or in motion. It was unnecessary, as they appeared to have thought, to find for fluids an equation different from the one I ob- * This Committee consisted of MM. Lagrange, Laplace, Legendre, Haiiy and Malus. 126 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT: tained long since for heterogeneous bodies. The variations of tem- perature which take place at every instant, and arise from the mutual radiation of the neighbouring molecules, depend in fact only on their actual positions, and not at all on the positions in which they will be the instant after in consequence of the motions produced by their calorific action or by other causes : it is thus that in the problem of the flux and reflux of the tides, for example, we calculate the attraction of the sea upon each point of its mass, as if it were solid and at rest at the moment under consideration, and independently of the motions which this attraction may produce. Notwithstanding that the interior radiation takes place only between molecules the temperatures of which are extremely different, the equation of motion of the heat contains terms derived from the squares of their differences, and of the same order of magnitude as those which result from their first power; so that the exact equation differs, in the case of a homogeneous body, from that which we had already given; and it is not, like that, independent of the conductibility when the body has arrived at an invariable state. This equation of par- tial differences changes its form, when we cannot consider the extent of the interior radiation as insensible; it is then of a higher order, which introduces, in its integral, new constants or arbitrary functions. From this a difficulty of analysis arises, of which we give the solution, and explain how in every case the redundant quantities will be made to disappear, as will be seen from a particular example in another chapter. We form in this the general expression of the passage of heat through every element of a surface traced in the interior of a body which is heated or cooled, orhas arrived at an invariable state, and in which the extent of the interior radiation is considered as insensible. This pas- sage proceeds from the exchange of heat between the molecules of the two parts of that body near their surface of separation, and the tempe- ratures of which are very different; whilst the interior passage results from the exchanges between the molecules adjacent to the surface of the body and those of a surrounding medium, or of other bodies which may have much higher or much lower temperatures ; and notwithstand- ing that the respective magnitudes of these two passages (ces deux flux), due to causes also unequal, must be of the same order and com- parable with one another. We show how that condition is fulfilled, by means of a quantity resulting from the rapid decrease of temperature which takes place very near the surface of a body whilst heating or cooling. In this manner interior and exterior passages are found united with one another; and the law of interior conductibility expressed in functions of the temperature is deduced from that of exterior radiation which MM. Dulong and Petit have discovered. In a homogeneous prism which has arrived at an inyariable state, M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 127, and the lateral surface of which is supposed to be inrpermeable to heat and its two bases retained at constant temperatures, the passage of heat across every section perpendicular to its length is the same through- out its length. Its magnitude is proportional to the temperature of the two bases, and in the inverse ratio of the distance which separates them. This principle is easy to demonstrate, or rather it may be con- sidered as evident. Thus expressed, it is independent of the mode of communication of heat, and it takes place whatever be the length of the prism: but it was erroneous to have attributed it without restriction to the infinitely thin slices of one body, the temperature of which varies, either with the time, or from one point to another; and to have ex- cluded from it the circumstance, that the equation of the movement of heat, deduced from that of extension, is independent of any hypothesis and comparable in its generality to the theorems of statics. When we make no supposition respecting the mode of communication of heat, or the law of interior radiation, the passage of heat through each face of an infinitely thin slice is no longer simply proportional to the infinitely small difference of the temperatures of the two faces, or in the inverse ratio of the thickness of the slices; the exact expression of it will be found in the chapter in which we treat specially of the distribution of heat in a prismatic bar. CuaprTer V. On the Movement of Heat at the Surface of a Body of any Form.—We demonstrate that the passages of heat are equal, or become so after a very short time, in the two extremities of a prism which has for its base an element of the surface of a body, and is in height a little greater than the thickness of the superficial layer, in which the tempe- rature varies very rapidly. From this equality, and from the expression of the exterior radiation, given by observation, we determine the equa- tion of the motion of heat at the surface of a body of any form what- soever. The expression of the interior passage not being applicable to the surface itself, it follows that the demonstration of this general equa- tion, which consists in immediately equalizing that expression to the ex- pression of the exterior radiation, is altogether illusory. When a body is composed of two parts of different materials, two equations of the motion of heat exist at their surface of separation, which are demonstrated in the same manner as the equation relative to the sur- face; they contain one quantity depending on the material of those two parts respectively, and which can only be determined by experiment. Cuaprer VI. A Digression on the Integrals of Equations of partial Differences.—By the consideration of series, we demonstrate that the number of arbitrary constants contained in the complete integral of a differential equation ought always to be equal to that which indicates 128 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. the order of that equation: we prove by the same means, that in the integral of an equation of partial differences the number of arbitrary functions may be less, and change as the integral is developed in series, according to the powers of one or other variable; and when the equation of partial differences is linear, we show that by conve- niently choosing this variable all the arbitrary functions may dis- appear and be replaced by constants, infinite in number, without the integral ceasing to be complete. To elucidate these general considera- tions, we apply them to examples by means of which we show that the different integrals, in the series of the same equation of partial dif- ferences, are transformed into one another, and may be expressed under a finite form by definite integrals, which also contain one or several arbitrary functions. In the single case, in which the integral in series contains only arbitrary constants, every term of the series by itself satis- fies the given equation, so that the general integral is found expressed by the sum of an infinite number of particular integrals. Integrals of this form have appeared from the origin of the calculus of partial differences ; but in order that their use in different problems should not leave any doubt respecting the generality of the solutions, it would have been necessary to have demonstrated @ priori, as I did long since, that these expressions in series, although not containing any arbitrary function, as well as those containing a greater or smaller number of them, are not less on that account the most general solutions of equa- tions of partial differences ; or else it would have been necessary to verify in every example that, after having satisfied all the equations of one problem relative to contiguous points infinite in number, the series of this nature might still represent the initial and entirely arbitrary state of this system of material points; a verification which, until now, it has not been possible to give, except in very particular cases. The solu- tion which Fourier was the first to offer of the problem of the distribution of heat in a homogeneous sphere, of which all the points equidistant from the centre have equal temperatures, does not satisfy for example either of these two conditions; it was no doubt on this account that the members of the Committee, whose judgement we mentioned above, thought that his (Fourier’s) analysis was not satisfactory in regard to generality ; and, in fact, in this solution it is not at all demonstrated that the series which expresses the initial temperature can represent a function, entirely arbitrary, of the distance from the centre. For the use of these series of particular solutions, it will be neces- sary to proceed in a manner proper to determine their coefficients ac- cording to the initial state of the system. On the occasion of a pro- blem relative to the heat of a sphere composed of two different sub- stances, I have given for this purpose in the Journal del Ecole Polytech- nique, (cahier 19, p.377 et seg.,) a direct and general method, of M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 129 which I have since made a great number of applications, and which I shall also constantly follow in this work. The Sixth Chapter con- tains already the application to the general equations of the mo- tion of heat in the interior and on the surface of a body of any form either homogeneous or heterogeneous. It leads in every case to two remarkable equations, one of which serves to determine, inde- pendently of one another, the coefficients of the terms of each series, and the other to demonstrate the reality of the constant quantities by which the time is multiplied in all these terms. These constants are roots of transcendental equations, the nature of which it will be very difficult to discover, by reason of the very complicated form of these equations. From their reality this general consequence is drawn; viz. when a body, heated in any manner whatever, is placed in a me- dium the temperature of which is zero, it always attains, before its complete cooling, a regular state in which the temperatures of all its points decrease in the same geometrical progression for equal increments of time. We shall demonstrate in another chapter, that, if that body is a homogeneous sphere, these temperatures will be equal for all the points at an equal distance from the centre, and the same as if the initial heat of each of its concentric strata had been uniformly distributed throughout its extent. The equations of partial differences upon which depend the laws of cooling in bodies are of the first order in regard to time, whilst the equa- tions relative to the vibrations of elastic bodies and of fluids are of the second order; there result essential differences between the expressions of the temperatures and those of the velocities at a given instant, and for that reason it appears at least very difficult to conceive that the phzeno- mena which may result from a molecular radiation should be equally ex- ‘plicable by attributing them to the vibrations of an elastic fluid. When we have obtained the expressions of the unknown quantities in functions of the time, in either of these kinds of questions, if we make the time in them equal to zero, we deduce from that, series of different forms which represent, for all the points of the system which we consider, arbitrary functions, continuous or discontinuous, of their coordinates. These ex- pressions in series, although we might not be able to verify them, except in particular examples, ought always to be admitted as a necessary con- sequence of the solution of every problem, the generality of which has been demonstrated @ priori; it will however be desirable that we should also obtain them in a more direct manner; and we might perhaps so at- tain them, by means of the analysis of which I had made use in my first Memoir on the theory of heat, to determine the law of temperatures in a bar of a given length, according to the integral under a finite form of the equation of partial differences. Vou. I.—Parrt I. K 130 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. CuarrterVII. A Digression onthe Manner of expressing Arbitrary Func- tions by Series of Periodical Quantities —Lagrange was the first to give a series of quantities proper to represent the values of an arbitrary function, continuous or discontinuous, in a determined interval of the values of the variable. This formula supposes that the function vanishes at the two extremes of this interval ; it proceeds according to the sines of the multiples of the variable; many others exist of the same nature which proceed according to the sines or cosines of these multiples, even or uneven, and which differ from one another in conditions relative to each extreme. A complete theory of formule of this kind will be found in this chapter, which I have abstracted from my old memoirs, and in which I have considered the periodical series which they contain as limits of other converging series, the sums of which are integrals, themselves having for limits the arbitrary functions which it is our object to repre- sent. Supposing in one or other of these expressions in series, the interval of the values of the variable for which it takes place to be infinite, there results from it the formula with a double integral, which belongs to Fourier; it is extended without difficulty, as well as each of those which only subsists for a limited interval, to two or a greater number of va- riables. CuapTer VIII. Continuation of the Digression on the Manner of re- presenting Arbitrary Functions by Series of Periodical Quantities—An arbitrary function of two angles, one of which is comprised between zero and 180°, and the other between zero and 360°, may always be repre- sented between those limits by a series of certain periodical quantities, which have not received particular denominations, although they have special and very remarkable properties. It is to that expression in series that we have recourse in a great number of questions of celestial mecha- nics and of physics, relative to spheroids; it had however been disputed whether they agreed with any function whatever; but the demonstration of this important formula, which I had already given and now repro- duce in this chapter, will leave no doubt of its nature and generality. This demonstration is founded on a theorem, which is deduced from considerations similar to those of the preceding chapter. We examine what the series becomes at the limits of the values of the two angles; we then demonstrate the properties of the functions of which its terms are formed ; then it is shown that they always end by decreasing inde- finitely, which is a necessary consequence and sufficient to prevent the Series from becoming diverging, for which purpose its use is always al- lowable. Finally, it is proved, that for the same function there is never more than one development of that kind; which does not happen in the developments in series of sines and cosines of the multiples of the va- riables. This chapter terminates with the demonstration of another theo- M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 13i rem, by means of which we reduce a numerous class of double integrals to simple integrals. Cuarter IX. Distribution of Heat in.a Bar, the transverse Dimensions of which are very small—We form directly the equation of the motion of heat in a bar, either straight or curved, homogeneous or heterogeneous, the transverse sections of which are variable or invariable, and which radiates across its lateral surface. We then verify the coincidence of this equation with that which is deduced from the general equation of Chapter IV., when the lateral radiation is abstracted and the bar is cy- lindrical or prismatic. This equation is first applied to the invariable state of a bar the two extremities of which are kept at constant and given temperatures. It is then supposed, successively, that the extent of the interior radiation is not insensible, that the exterior radiation ceases to be proportional to the differences of temperature, that the ex- terior conductibility varies according to the degree of heat, and the influence of those different causes on the law of the permanent tempera- tures of the bar is determined. Formule are also given, which will serve to deduce from this law, by experiment, the respective conducti- bility of different substances, and the quantity relative to the passage from one substance into another, in the case of a bar formed of two heteroge- neous parts placed contiguous to and following one another. After having thus considered in detail the case of permanent temperatures, we resolve the equation of partial differences relative to the case of va- riable temperatures; which leads toan expression of the unknown quan- tity of the problem, in a series of exponentials, the coefficients of which are determined by the general process indicated in Chapter VIL., what- eyer may be the variations of substance and of the transverse sections of the bar. We then apply that solution to the principal particular _ cases. When the bar is indefinitely lengthened, or supposed to be heated only in one part of its length, the laws of the propagation of heat on each side of the heated place are determined; this propagation is in- stantaneous to any distance; a result of the theory presenting a real difficulty, but the explanation of which is given. CuarrTer X. On the Distribution of Heat in Spherical Bodies —The problem of the distribution of heat in a sphere, all the points of which equally distant from the centre have equal temperatures, is easily brought to a particular case of the same question with regard to a cylindrical bar. It is also solved directly; the solution is then applied to the two extreme cases, one of a very small radius, and another of a very great one. In the case of an infinite radius, the laws are inferred of the pro- pagation of caloric in a homogeneous body, round the part of its mass to which the heat has been communicated, similarly in all directions. We then determine the distribution of heat in a homogeneous sphere K 2 132 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. covered with a stratum, also homogeneous, formed of a substance differ- ent from that of the nucleus. During the whole time of cooling, the tem- perature of this stratum, however small its thickness may be, is differ- ent from that of the sphere in the centre, and the ratio of the tempera- tures of these two parts, at the same instant, depends on the quantity relative to the passage from one substance into the other, of which we have already spoken. From this circumstance an objection arises against the method employed by all natural philosophers to determine, by the comparison of the velocities of cooling, the ratio of the specific heat of different bodies, after having brought their surfaces to the same state by means of a very thin stratum of the same substance for all these bodies. The quantity relative to the passage of the heat of each body in the additive stratum, is contained in the ratio of the velocities of cooling ; it is therefore necessary that it should be known in order to be able to deduce from this ratio, that of their specific heats. A recent experiment by M. Melloni proves that a liquid contained in a thin envelope, the interior surface of which is successively placed in dif- ferent states by polishing or scratching it, always cools with the same velocity, whilst the ratios of the velocity change very considerably, as was known long before, when it is the exterior part of the vessel that is more or less polished or scratched. The quantity relative to the passage of caloric across the surface of separation of the vessel and the liquid, is therefore independent of the state of that surface, a cireum- ‘stance which assimilates the cooling power of liquids to that of the stratum of air in contact with bodies, which in the same manner does not depend on the state of their surface, according to the experiments ‘of MM. Dulong and Petit. When a homogeneous sphere, the cooling of which we are consider- ing, is changed into a body terminated by an indefinite plane, and is indefinitely prolonged on one side only of that plane, the analytical ex- pression for the temperature of any point whatever changes its form, in such a manner that that temperature, instead of tending to diminish in geometrical progression, converges continually towards a very different law, which depends on the initial state of the body; but however great a body may be, it has always finite and determined dimensions; and it is al- ways the law of final decrease enunciated in ChapterVI. which it is neces- sary to apply ; even in the case, for example, of the cooling of the earth. If the distribution of heat in a sphere, or in a body of another form, has been determined, by supposing this body to be placed in a medium the temperature of which is zero, this first solution of the problem may afterwards be extended to the case in which the exterior temperature va- ries according to any law whatever. In my first Memoir on the theory of heat, I have followed, in regard to this part of the question, a direct me- thod applicable to all cases. According to this method, one part of the value of the temperature in a function of the time is expressed in the M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 133 general case by a quadruple integral, which can always be reduced to a double integral like each of the other parts. By the method which I have used to effect this reduction we obtain the value of different de- finite integrals, which it would be difficult in general to determine in a different manner, and the accuracy of which is verified whenever they enter into known formule. Cuapter XI. On the Distribution of Heat in certain Bodies, and especially in a homogeneous Sphere primitively heated in any Manner.— It is explained how, in every case, the complete expression of exterior temperature, which may depend on the different sources of heat, and which must be employed in the equation of the motion of heat relative to the surface of bodies submitted to their influence, will be formed. After having enumerated the different forms of bodies for which we have hitherto arrived at the solution of the problem of the distribution of heat, the complete solution is given for the case of a homogeneous rectangular parallelopiped the six faces of which radiate unequally. In order to apply the general equations of the fourth and fifth chap- ters to the case of a homogeneous sphere primitively heated in any manner, the orthogonal coordinates in them are transformed into polar coordinates; the temperature at any instant and in any point is then expressed by means of the general series of Chapter VIII., and of the integrals found in Chapter VI.; the coefficients of that series are next determined according to the initial state of the sphere, by supposing at first the exterior temperature to be zero: by the process already em- ployed in the preceding Chapter, this solution is finally extended to the case of an exterior temperature, varying with the time and from one point to another. Among the consequences of this general solu- tion of the problem the most important is that for which we are in- debted to Laplace ; it consists in this: That in a sphere of very large di- mensions, and at distances from the surface very small in proportion to its radius, the part of the temperature independent of the time does not vary sensibly with these distances; and, that upon the normal at each point, whether at the surface or at an inconsiderable depth, it may be regarded as equal to the invariable part of the exterior temperature which corresponds to the same point. Hence it results, that the in- crease of heat in the direction of the depth which is observed near the surface of the earth cannot be attributed to the inequality of tempera- tures of different climates, and that it is necessary to look for the cause in circumstances which vary very slowly with the time. Whatever this cause may be, the difference of the mean temperatures of the surface and beyond, corresponding to the same point of the superficies, is pro- portional (according to a remark made by Fourier) to the increase of temperature upon the normal referred to the unity of length, so that 134 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. this difference may be determined from the observed increase, and from a quantity depending on the nature of the ground. This remark and that of Laplace are not applicable to the localities where the tempera- ture varies very rapidly round the vertical: it is shown that in these cases of exception the temperature varies even upon the vertical : and the law of this variation is determined from the variation which has taken place at the surface or in the exterior temperature. The mean temperature at a very small distance contains also a term which is not proportional to this depth, and which arises from the influence of the heat on the conductibility of the substance. CuArter XII. On the Motion of Heat in the Interior and upon the Surface of the Eurth.—It is shown that the formule of the preceding chapter, although relating to a homogeneous sphere the surface of which is everywhere in the same state, may notwithstanding serve to determine the temperatures of the points of the earth at a distance from the sur- face which is very small with regard to its radius, but which exceeds however all accessible depths. These formule contain two constants, depending on the nature of the soil, the numerical values of which may be determined in every point of the globe from the temperatures ob- served at different known depths. Observation in harmony with theory shows that the diurnal inequali- ties of the temperature of the earth disappear at very small depths, and the annual inequalities at greater depths, in such a manner that at a di- stance from the surface of about 20 metres and. beyond those two kinds of inequalities are entirely insensible. In this chapter are given tables of the temperatures, indicated by the thermometer, of the caves of the Observatory, at the depth of 28 metres. The mean of 352 observations, made from 1817 to the end of 1834, is 11%834. The increase of the mean temperature of the earth, in proportion as we descend below the surface, has long been established as a fact in all deep places, at different latitudes, and at different elevations of the soil above the level of the sea. The most adequate means to determine it is by sounding and boring. The results, still very few, which have hitherto been obtained are given. At Paris, this increase appears to be one de- gree for about 38 metres of increase in depth. As to the cause of this phenomenon, the difficulties are stated which the explanation of Fourier presents, founded upon the original heat of the globe, still sensible at the present time near the surface; the new explanation alluded to at the beginning of this article is then proposed. The following reflections extracted from the work tend to prove that the solidification of the earth must have commenced by central strata, and that before reaching the surface the cooling of the globe must have been incomparably more rapid. M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 135 “The nearly spherical form of the earth and planets, and their flattening at the poles of rotation, evidently show that these bodies were originally in a fluid or perhaps in an aériform state. Beginning from this initial state, the earth could not, wholly or partly, become solid, except by a loss of heat arising from its temperature exceeding that of the medium in which it was placed. But it is not demonstrated that the solidification of the earth could have commenced at the surface and been propagated towards the centre, as the state of the globe still fluid in the greatest part of the interior would lead us to suppose; the contrary appears to me more probable. For the extreme parts, or those nearer to the surface, being the first cooled, must have descended to the interior and been replaced by internal portions which had ascended to cool at the surface and to descend again in their turn. This double current must have maintained an equality of temperature in the mass, or at least must have prevented the inequality from becoming in any way so great as ina solid body, which cools from the surface; and we may add that this mixture of the parts of the fluid, and the equalization of their tempera- tures, must have been favoured by the oscillations of the whole mass, which must have taken place until the globe attained a permanent figure and rotation. On the other hand, the excessively great pressure sustain- ed by the central strata may have determined their solidification long before that of those nearer the surface; that is to say, the first may have become solid by the effect of this extreme pressure at a tempera- ture equal or even superior to that of the strata more distant from the centre, and consequently subjected to a much less degree of pressure. Experiment has shown, for example, that water at the ordinary tempe- rature being submitted to a pressure of 1000 atmospheres, experiences a condensation of about ~,th of its primitive volume. Now let us con- ceive a column of water whose height is equal to one radius of the globe, and let us reduce its weight to half of that which we observe at the surface of the earth, in order to render it equal to the mean gravity which would exist along each radius of the earth upon the hypothesis of its homogeneity; the inferior strata of this liquid column would experience a pressure of more than three millions of atmospheres, or equal to more than three thousand times the pressure which would reduce water to +4ths of its volume; but without knowing the law of the compression of this liquid, and although we do not know in what manner this law may depend on the temperature, we may believe, notwithstanding, that so enormous a pressure would reduce the inferior strata of the mass of water to the solid state, even when the temperature is very high. It seems therefore more natural to conceive that the solidification of the earth began at the centre and was successively propagated to- wards the surface; at a certain temperature, which might be extremely high, the strata nearer the centre became at first solid, by reason of the excessive pressure which they experienced ; the succeeding strata were 136 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. then solidified at a lower temperature and under a less degree of pres- sure, and thus in progressive succession to the surface.” If the increase observed in the temperature of the earth near its sur- face is due to its original heat, it follows that at the present epoch at Paris this heat raises the temperature of the surface itself only by the fortieth part of a degree. Not knowing the radiating power of the substance of the globe, we cannot estimate the quantity of this initial heat which traverses in a given time from within to without an extent, also given, of the surface ; but such would be its slowness in dissipating into space, that more than one thousand million of centuries must elapse to reduce the small increase of the fortieth of a degree to one half. With regard to periodical inequalities, the relation which exists be- tween each inequality at a given depth and the inequality corre- sponding to the exterior temperature is determined. Relations of this nature, for the knowledge of which we are indebted to M. Fourier, take place between the interior inequalities and those of the surface of the ground; these relations leave unknown the ratios of these latter in- equalities to those of the outside which are the immediate data of the question. ' The interior temperature to which the earth is subjected arises from three different sources, namely, from sidereal heat, from atmospherical heat, acting either by radiation or by contact, and from solar heat. These three sources of heat are successively examined. With regard to the first it is observed, that it is not at all probable that radiant heat emanating from the stars has the same intensity in all directions when it arrives at the earth. The experiments are indicated which it would be necessary to make in order to ascertain whether it really varies in the different regions of the sky. M. Melloni intends immediately to apply himself to these experiments, employing in them an extremely sensible instrument, of which he has made use in his researches on heat ; a cir- cumstance which cannot fail to lead to the solution of this important question of celestial physics. Before considering the influence of atmospherical heat, I have formeda complete expression for the temperature, marked every instant by ather- mometer suspended in the air, at any height above the surface of the earth exposed in the shade or in the direct rays of the sun. Although the greatest part of the quantities which this formula contains are unknown to us, many general consequences may however be deduced from it, which accord with experiment; it hence follows, that to determine the proper temperature of the air, it is necessary to employ the simultaneous observation of three thermometers, the surfaces of which are in a differ- ent state, and not two thermometers only, as is generally said. This for- mula also furnishes the means of comparing the temperatures indicated by different thermometers in relation to their radiating powers and to their property of absorbing the rays of the sun. M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 137 The mean of the annual temperatures, marked by a thermometer ex~ posed in the open air and in the shade, forms the elimateric temperature. It varies with the elevation of places above the level of the sea, and witlr the longitude and latitude, according to unknown laws. At Paris it is 10°822, as M. Bouvard has concluded after 29 years of observations. There will be found in this Chapter a table of the mean temperatures for the twelve months of each of those years, which that gentleman has been pleased to communicate to us, and which had not before been published. It appears that in every point of the earth this climateric temperature differs very little from the mean temperature of the surface of the soil, as is shown by several examples. Notwithstanding, the variable tem- perature of this surface, and that which is marked at the same instant by a thermometer as little elevated above the surface as may be, are often very different from each other ; it hence follows, that in a year the excess of the highest above the lowest temperature of the soil is at Paris nearly 24°, as will be seen in the course of this Chapter; and only about 17° for the thermometer suspended in the air and in the shade. We now determine the part of exterior temperature which results from the atmospherical heat combined with sidereal heat. The necessary data for calculating its numerical value, @ priori, being unknown to us, we show how this value, for every point of the globe, may be deduced from the mean temperature of its surface. At Paris this exterior temperature is 13°. Although we cannot determine separately the portion of this temperature of the earth which arises from the atmospherical heat, there is reason to think that it is also negative, so that the other portion arising _ from sidereal heat must be less than 13° below zero. If we suppose that radiant heat emanating from the stars falls in the same quantity on all points of the globe, this temperature, higher than 13°, will be that of space at the place where the earth is at this time. Without being able to assign the degree of heat of space, we may however admit, that its temperature differs little from zero, instead of being, as had been asserted, below the temperature of the coldest regions in the globe, and even of the freezing-point of mercury. As to the central temperature of the whole mass of the earth, even supposing its ori- ginal heat to be entirely dissipated, and that it is no longer equal to the present temperature of space, we have no means of obtaining a knowledge of it. According to a theorem of Lambert, the whole amount of solar heat which falls upon the earth is the same during different seasons, notwith- standing the inequality of their lengths, which is found to be com- pensated by that of the distances from the sun tothe earth. This quan- tity of heat varies in the inverse ratio of the parameter of the ellipse _ described by the earth ; it also varies with the obliquity of the ecliptic, 138 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. but it does not appear that these variations can ever produce any consi- derable effect on the heat of the globe. The quantities of solar heat which fall in equal times upon the two hemispheres are nearly equal ; but on account of the different states of their surfaces, those quantities are absorbed in different proportions; and the power of absorbing the rays of the sun inereasing in a greater ratio than the radiating power, which is greater for dry land than for the sea, we conclude that the mean temperature of our hemisphere, where dry land is ina greater pro- portion, must be greater than that of the southern hemisphere; which agrees with observation. The solar heat, which reaches each point of the globe, varies at dif- ferent hours of the day ; it is null when the sun is beneath the horizon ; during the year it varies also with its declination; and the expression changes its form as the latitude of the point under consideration is greater or less than the complement of the obliquity of the ecliptic. I have therefore considered the part of the exterior temperature which arises from this souree of heat as a discontinuous function of the horary angle, and of the longitude of thesun, to which I have applied the formule of the preceding Chapters, in order to convert it into series of sines and cosines of the multiples of these two angles. By this means I have ob- tained the complete expressions of the diurnal and annual inequalities of the temperature of the earth which arise from its double motion. These formule show, that at the equator the annual inequalities are much less than elsewhere; a circumstance which furnishes the explanation of a fact observed by M. Boussingault in his journey to the Cordilleras, and upon which he had relied in order to determine with great facility the climateric temperatures of the places which he visited. The same for-. mulz agree also, in a remarkable manner, with the temperatures which M. Arago has observed at Paris during many years, and at depths vary- ing from two to eight metres (from 6°56 to 26°24 English feet). —— 139 ArticueE VII. Researches on the Elasticity of Bodies which crystallize regu- larly ; by Fevix Savart. (Read to the Academy of Sciences of Paris, January 26th, 1829.) From the Annales de Chimie et de Physique, yol. xu. p. 5, et seq. Hirnerrto precise notions respecting the intimate structure of bo- dies could be acquired only by two means: first by cleavage, for opake or transparent substances regularly crystallized ; secondly, for transparent substances only, by the modifications ete they occasion in the propa- gation of light. The first of these means has taught us that crystallized bodies are col- lections of lamine parallel to certain faces of the crystal; but it has given us no information respecting the force with which these laminz adhere together nor their elastic state. The second, far more powerful than the first, because it renders evident actions depending on the very form of the particles, has given rise to the discovery of phenomena the exist- ence of which cleavage alone would never have allowed us to suspect. But although these two experimental processes have introduced many new ideas and notions into the science, yet it may be said that the part of physics which treats of the arrangement of the particles of bodies, and the properties resulting from it, as elasticity, hardness, fragility, malleability, &c. is still in its infancy. The investigations of Chladni respecting the modes of vibration of laminz of glass or metal, and the researches which I have published on the same subject, especially those which relate to the modes of division of dises of a fibrous substance, such as wood, allow us to suspect that we might acquire by this means new notions respecting the distribution of elasticity in solid bodies; but it was not clearly seen by what process this result might be attained, though the road which it was necessary to follow was one of great simplicity. But if this mode of experiment, which we are about to describe, is simple in itself, it is not the less surrounded by a multitude of difficul- _ ties of detail, which cannot be removed without numerous attempts; and I hope this will serve to excuse the incompleteness of these researches, _ which I only give as the first rudiments of a more extensive investi- gation. 140 FELIX SAVART’S RESEARCHES ON THE § 1. Statement of the Means of Examination employed in these Researches. Circular plates which produce normal vibrations are susceptible of several modes of division ; sometimes they are divided into a greater or fewer number of equal sectors, always even in number, which perform their vibrations in the same time; at other times they are divided into a greater or fewer number of concentric zones; and these two series of modes of division again may be combined together, so that the acoustic figures which result are circular lines divided into equal parts by dia- metrical nodal lines. If the plate which is caused to sound is perfectly homogeneous, cir- cular, and equal in thickness, it is obvious that in the case when the figure consists of diametrical lines only, the system which they form ought to be capable of placing itself in every direction, that is to say, that any point whatever of the circumference of the plate, being taken as the place of excitation, this single condition determines the position of the nodal figure, since the point directly put in motion is always the middle of a vibrating part. In the case of circular lines, under the con- ditions we have just supposed, these lines would be exactly concentric with the circumference of the plate. These results are a natural conse- quence of the symmetry which is supposed to exist either in the form or in the structure of the plate; but if this symmetry is deranged, it will easily be conceived that an acoustical figure composed of diametrical nodal lines ought no longer to place itself in a direction depending solely on the position of the point of excitation, and that, with regard to a figure consisting of circular lines, these lines ought to be modified, and will become, for example, elliptical or of some other more complicated form. It is thus that the system of two nodal lines which intersect each other rectangularly, can upon an elliptical plate only place itself in a single position, which is on the axes of the ellipse. There is how- ever a second position in which this mode of division can establish it- self; but then it is modified in its form, and it resembles the two branches of a hyperbola, the transverse axis of which corresponds with the greater axis of the ellipse: in this latter case, the number of vibra- tions is less than in the first, and more so as the axes of the ellipse differ more from each other. A similar phenomenon is observed when the same mode of division is attempted to be produced on a circular plate of brass, of very equal thickness, and in which several parallel saw-cuts have been made, penetrating only to a small distance from the surface : one of the crossed nodal lines always corresponds to a saw-cut which has been made in the direction of a diameter, and the system of the two hyperbolic lines arranges itself in such a manner that the same saw-cut becomes the conjugate axis of the hyperbola. Thus, in both cases, ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 14] the transverse axis of the hyperbola is always in the direction of the least resistance to flexure. ; Let us now suppose that, the plate remaining perfectly circular and of equal thickness, it possesses in its plane a degree of elasticity which is not the same in two directions perpendicular to each other; the sym- metrical disposition round the centre being then found to be destroyed, although in another manner than in the two examples we have just ad- duced, an analogous result ought still to be obtained. Thus, if we take a plate of this description, a plate of wood, for in- stance, cut parallel to the fibres, and fixing it lightly by its centre, en- deayour to make it produce the mode of division consisting of two lines crossed rectangularly, we shall find that when it thus divides itself, the lines of rest always place themselves according to the directions of the greatest and least resistance to flexure, and that putting it afterwards in motion at the extremity of the preceding lines, it may be made to produce a second mode of division, which presents itself under the aspect of a hy- perbola the branches of which are much straightened, and which would have for its conjugate axis that line of the cross which corresponds to the direction of the greatest resistance to flexure. In short, when the sym- metrical disposition round the centre is destroyed, no matter in what way, the mode of division formed by two nodal lines which intersect each other rectangularly can place itself only in two determinate posi- tions, for one of which it presents frequently the appearance of two hy- perbolic branches more or less straightened; and, as we shall soon see, it may even happen that, for certain distributions of elasticity, this mode of division presents itself undef the form of two hyperbolic curves in the two positions in’ which it becomes possible. Lastly, if a similar plate be caused to produce some of the high modes of division, but yet consisting of diametrical lines, experiment shows that they can likewise place themselves in two invariable positions, and pass through certain modifications analogous to those which the system of two lines crossed at right angles undergoes. Thus the immoveability of the nodal figures, and the double position which they can assume, are distinctive cha- racters of circular plates all the diameters of which do not possess a uni- form elasticity or cohesion. It follows therefore from the preceding, that by forming with different substances circular plates of very equal thickness, we may, by the fixed or indeterminate position of an acoustic figure consisting of diametrical nodal lines, ascertain whether the properties of the substance in ques- tion are the same in all directions. By applying this mode of examina- tion to a great number of plates formed of different substances regularly or confusedly crystallized, as the metals, glass, sulphur, rock-crystal, carbo- nate of lime, sulphate of lime, gypsum, &c., it is constantly found that the acoustic figure, formed of twolines crossed rectangularly, can only place 142 FELIX SAVART’S RESEARCHES ON THE itself on them in a single position; and that there is a second position in which two hyperbolic curved lines are obtained which are accompa- nied, according to the different cases, by a sound which differs more or less from that which is produced when the crossed lines occur. Plates are also met with which are incapable of assuming the mode of di- vision formed of two straight lines, and in which only two systems of hyperbolic curves are obtained, sometimes similar, yet giving different sounds. In short, I have yet found no body for which the same nodal figure can place itself in every direction; which seems to indicate that there are very few solid substances which possess the same pro- perties throughout. But what appears still more extraordinary is, that if in the same body, a mass of metal for instance, plates are cut accord- ing to different directions, some are susceptible of the mode of division consisting of two lines which cross each other rectangularly, whilst others present only two systems of hyperbolic curves. In both cases, the sounds of the two systems may differ greatly: there may, for example, be an interval between them of more than a fifth. To arrive at the discovery of the experimental laws of this kind of phenomena, it would be necessary therefore to be able to study them, at first in the most simple cases, for example, upon bodies the elastic state of which, previously known, would differ only according to two di- rections. This would obtain in a body which might be composed by placing flat plates formed of two heterogeneous substances upon each other in such a manner thatall the odd plates might be of one substance, and all the even plates of another, the elasticity in all directions of the plane of each of them being the same. * But it has appeared to me dif- ficult to attain this condition, since I have yet found no body the elasti- city of which was the same in all directions. - The most simple structure after the preceding would be that ofa body composed of cylindrical and concentric layers, the nature of which should — be alternately different for the layers next each other, as is nearly the © case in the branch of a tree free from knots. It is evident that the elasti- city ought to be sensibly the same in every direction of the plane of a plate cut perpendicularly to the axis of the cylinder, and it ought to differ greatly from that which is observed in the direction of the axis. Consequently we shall commence by examining this first case; after which we shall pass to that in which the elasticity would be different ac- ‘cording to three directions perpendicular to each other, as would take place in a body composed of flat plates alternately of two different sub- stances, and the elastic state of which would not be the same, according to two directions perpendicular to each other. Wood fulfills again these different conditions; for ina tree of very considerable diameter, the ligneous layers may be considered as sensibly plane for a small number of degrees of the circumference; and if we confine ourselves to plates of ELASTICITY OF REGULARLY CRYSTALLIZED BODIES, 143 a small diameter, cut at a little distance from the surface, we may sup- pose without any very notable error, at least for the whole of the phe- nomena, that the experiments have been made on a body the elasticity of which is not the same, according to three directions rectangular to each other, since, as is well known, this property does not exist in the same degree according to the direction of the fibres, according to that of the radius of the tree, and according to a direction perpendicular to the fibres and tangential to the ligneous layers. After these two cases—the most simple that we have been able to study—we shall pass to the much more complicated phenomena which regularly crystallized bodies, such as rock crystal and carbonate of lime, present. § II. Analysis of Wood by means of Sonorous Vibrations. Let us suppose that fig. 1 (Plate III.) represents a cylinder of wood the annual layers of which are concentric to the circumference ; let B C D E, fig. 2, be any plane passing through the axis A Y of the cylinder, and let nm n' be a line normal to this plane: it is obvious that the plates taken perpendicularly to BC DE, and according to the different directions 1, 2, 3, 4, 5, &c. round nx’, ought to present different phenomena, since they all will contain the axis of least elasticity 2m! in their plane, and the resistance to flexure, according to the lines 1, 2, 3, 4, 5, will go on increasing in proportion as the plates shall more nearly approach being parallel to the axis of greatest elasticity A Y. For the plate No. 1, fig. 3, perpendicular to this axis, all being sym- metrical around the centre, the mode of division consisting of two lines which intersect each other at right angles, ought to be able to place itself in all kinds of directions, according as the place of excitation shall occupy different points of the circumference: this is really the ‘ease; but it is no longer so, for the plate No. 2 inclined 22° 5! to the preceding. In the latter, the elasticity becoming a little greater in the direction 7 s contained in the plane B C D E, than in the direction x »/ normal to this plane, this circumstance ought to determine the nodal lines to place themselves according to these two directions. However, as this difference is very slight, the system of these two lines may still be displaced, when the place of excitation is made to vary ; but it will change its form a little, and it will assume the appearance of two hyper- bolic branches when it has arrived at 45° from its first position. In the plate No. 3, inclined 45° to the axis A Y, the difference of the two extreme elasticities being greater, the system of crossed lines becomes entirely fixed, or rather it can only move through a few degrees to the right or left of the position which it assumes in preference; but the hyperbolic system, the summits a and 6 of which recede more from each other than in fig. 2, will present the remarkable peculiarity of 144 FELIX SAVART’S RESEARCHES ON THE being capable of transforming itself into the rectangular system, when the position of the point put directly in motion is made to vary. Examining with care the nodal lines in fig. 2, it is found equally that its two nodal systems can thus change themselves one into the other; and the same phenomenon is reproduced in the plate No. 4, in which the values of the extreme elasticities differ still more, and in which the points a and 6 recede from each other at the same time as the curves become more straightened. In the plate No. 5, parallel to the axis A Y, these curves are no longer susceptible of assuming any other position than that indicated in the figure. Thus, in No. 1, the centres a and } coalesce into one, and there is only a single figure consisting of two crossed lines, the system of which can assume any position; these centres afterwards gradually receding, the modes of division can change them- selves from one into the other, and at last, when the branches of the curve are nearly straight lines, the two figures become perfectly fixed. The existence of these nodal points or centres is, without doubt, a very remarkable phenomenon, and which it will be important to study with great care. In order to give an accurate idea of it, I have in fig. 4 indicated by a dotted line the successive modifications which the two hyperbolic lines assume when the plate is fixed at one of the points a or b, and the place of excitation moves gradually from e to e! e!’, passing over a quarter of the circumference of the plate. When the motion is excited in the vicinity of e", the curves are by the union of their sum- mits transformed into two straight lines which intersect each other rectangularly ; and it is obvious that if it had been excited near e'”, the two branches of the curve would re-appear, but with this peculiarity, that their transverse axis would take the position assumed by the conju- gate, when the motion was produced on the other side of e’’. As to the numbers of the vibrations which correspond to each mode of division, for the different degrees of inclination of the plates, it will be seen by examining fig. 3, that, at first equal in No. 1, they go on continually increasing and receding from each other up to No. 5, which contains the axis of the cylinder; and it is indeed evident, that the elas- ticity in the direction perpendicular to the axis remaining the same for all the plates, whilst that which is perpendicular to this direction goes on continually increasing, this ought to be, in general, the progress of the phenomenon. These experiments were made with plates of oak 8-4 cent. (3°3071 inches) in diameter, and 3™7 (+1456 inch) in thickness: they were repeated with plates of beech-wood, and analogous results were ob- tained; only the ratio between the two elasticities not being the same, the interval between the two sounds of each plate was found to be greater. The most general consequence that can be deduced from the pre- ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 145 ceding experiments is, that in wood in which the annual layers are . hearly cylindrical and concentric, the elasticity is sensibly uniform in alt the diameters of any section perpendicular to the axis of the branch. We shall see further on, that plates of carbonate of lime or rock crystal, cut perpendicularly to the axis, very seldom present this uniformity of structure for all their diameters, although the modifications which such plates impress on polarized light appear symmetrical round this same axis. In the case which we have just examined, two of the three axes of elasticity being equal, the phenomena are, as we have just seen, exempt from any great complication. It is not so when the three axes possess each a different elasticity: it would then be indispensable to cut, first a series of plates round each of the axes, then a fourth series round a line equally inclined with respect to the three axes, and lastly, it would be ne- cessary again to take aseries round each of the lines which divide equally into two the angle contained between any two of the axes; and not- withstanding the great number of results which would be obtained by this process, the end would. be far from attained, since these different series would want connexion with each other, and consequently this process cannot give a clear idea of the whole of the transformations of the nodal lines. Nevertheless, I shall content myself to follow this route, which appears to me less complicated than any other, and is sufficient to render fully evident all the principal peculiarities of this kind of phenomena. In order that the relative positions of the lines round which I have cut the different series of plates of which I have spoken, and the rela- tions they have to the planes of the ligneous layers, as well as to the direction of their fibres, may be more easily represented, I shall refer them all to the edges of a cube A E fig. 5, the face of which AX BZ I shall suppose is parallel to the ligneous layers, and the edge A X to the direction of the fibres, which will allow the three edges A X, A Y, A Z to be considered as being themselves the axes of elasticity. After- wards I shall indicate the different degrees of inclination of the plates of each series, on a plane normal to the line round which they are to be cut; the position and outline of this plane being at the same time re- ferred to the natural faces of the cube. But before commencing to describe the phenomena which each of these series presents, it is indispensable to endeavour to determine the ratio of the resistance to flexion, in wood, in the direction of each of the three axes of elasticity: this may be easily done by means of vibrations, by cutting three small square prismatic rods, of the same dimensions, - according to the three directions just indicated ; for, the degree of their - elasticity can be ascertained by comparing the numbers of the vibrations which they perform, for the same mode of division, knowing besides Vor, I.—Part I. L 146 : FELIX SAVART’S RESEARCHES ON THE that, in reference to the transversal motion, the numbers of the vibra- tions are as the square roots of the resistance to flexion, or, which is the same thing, that the resistance to flexion is as the square of the number of oscillations. Fig. 6 shows the results of an experiment of this kind which was made upon the same piece of beech-wood from which I cut all the plates which I shall mention hereafter. In this figure I have, to impress the mind more strongly, given to these rods directions parallel to the edges A X, A Y, AZ of the cube fig. 5, and I have supposed that the faces of the rods are parallel to those of the cube. It is to be remarked that two sounds may be heard for the same mode of division of each rod, according as it vibrates in a 6 or ed; but when they are very thin the difference which exists between them is so slight that it may be neglected. The inspection of fig. 6 shows, therefore, that the ‘resistance to flexion is the least in the direction A Z, and is such, that being re- presented by unity, the resistance in the direction A Y becomes 2°25, and 16 in the direction of A X. It is evident that the elasticity in any other direction must be always intermediate to that of the directions we have just considered. This being well established, we shall proceed to the pepe in detail of the different series of plates we have mentioned above. First Sertes.— Plates taken round the axis AY and perpendicular to the face A X BZ of the cube. In the plates of this series, one of the modes of division remains con- stantly the same. (See figs. 5, 7 and 8.) It consists of two lines crossed rectangularly, one of which, a y, places itself constantly on the axis A Y of mean elasticity; but although this system always presents the same appearance, it is not accompanied, for the different inclinations of the plates, by the same number of vibrations; this ought to be the case, since the influence of the axis of greatest elasticity ought to be more sensible as the plates more nearly approach containing it in their plane: the sound of this system ought therefore to ascend in proportion as the plates become more nearly parallel to the plane CY A X. As to the ~ hyperbolic system, it undergoes remarkable transformations, which de- pend on this circumstance, that the line a y remaining the axis of mean elasticity in all the plates, the line ed, which is the axis of least elasti- city in No. 1, transforms itself gradually into that of the greatest elas- ticity, which is contained in the plane of the plate No.6. It hence follows that there ought to be a certain degree of inclination for which the elasticities, according to the two directions ay, e d, ought to be equal: now, this actually happens with respect to the plate No. 3; and this equality may be proved by cutting in this plate, in the direction of ay and its perpendicular, two small rods of the same dimensions: it ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 147 will be seen, on causing them to vibrate in the same mode of trans- versal motion, that they produce the same sound. It also follows, because the elasticity in the direction ay is sometimes smaller and sometimes greater than that which exists in the direction of ed, that the first axis of the nodal hyperbola ought to change its position to be able to remain always perpendicular to that of the lines ay, ed, which possess the greatest elasticity; thus, in Nos. 1 and 2, ed possessing the least elas- ticity, it becomes the transverse axis of the hyperbola, whilst in Nos. 4, 5 and 6, the elasticity being greater in the direction ed than in that of a y, the transverse axis of the hyperbola places itself on the latter line. As the ratio of the two elasticities varies: only gradually, it is obvious that the modifications impressed on the hyperbolic system ought in the same manner to be gradual: thus the summits of these curves, at first separated in No. 1 by a certain distance (which will depend on the nature of the wood), will approach nearer and nearer, for the fol- lowing plates, until they coalesce as in No. 3, at a certain degree of inclination, which was 45° in the experiment to which } now refer, but which might be a different number of degrees for another kind of wood. At the point where we have seen that the elasticities are equal in the direction of the axis, the two Gurves: transform themselves. into ‘two straight lines which intersect each other rectangularly, after which they again separate; but their separation is effected in a direction perpen- dicular to that of their coalescence. The sounds of the hyperbolic system follow nearly the same’ course as those of the system of crossed lines; that is to say, they become higher in proportion as the plates more nearly approach being parallel to the axis of greatest elasticity; but it deserves to be remarked, that the plate No. 3, for which'the elas+ ticity is the same in the two directions a y, ed, is that between the two sounds {of which there is the greatest interval: this’ evidently depends on the elasticity in the two directions: y, cd being very different from that which exists in the other directions of the plate. Lastly, it is to be remarked that, in the four first plates, the sound of the hyperbolic system is sharper than that of the system of crossed lines, and that it is the contrary for the plate No. 6, which renders it necessary that there should be between No. 4 and No. 6 a plate, the sounds of which are equal, which in the present case is exemplified in No. 5, although its two modes of division differ greatly from each other. There is another thing remarkable in this plate; its two modes of di- vision can transform themselves gradually into éach other by changing the position of the place of excitation, so that the two points e and ec’ | becoming two nodal centres, are in every respect. in the conditions indicated by fig. 4. _ The interval included between the grayest and the sharpest sounds of this series was an augmented sixth. L2 148 FELIX SAVART’S RESEARCHES ON THE It is almost useless to observe that the plates taken in the directions I, II, II, inclined on the other side of the axis A X the same number of degrees as the plates 1, 2, 3, would present exactly the same phzeno- mena as these latter. This observation being equally applicable to the following series, we shall not mention it again. Seconp Sertes—Plates taken round the axis A Z of least elasticity and perpendicular to the plane CY AX; figs. 9 and 10. As in the preceding case, one of the nodal systems of the plates of this series consists of two lines crossed rectangularly, one of which, a z, corresponds with the axis A Z; whence it follows that the second may be considered as the projection of the two other axes on the plane of the plate, which, whatever its inclination may be, ought consequently to possess a greater elasticity in the direction fg than in the direction az: thus the hyperbolic system of this series cannot present the trans- formations which we saw in the preceding series, where ed, fig. 8, possesses sometimes a less, at other times a greater elasticity than that of ay. In the present case, a@ z remaining constantly the axis of least elasticity, the resistance to flexion in the direction fg goes on gradually increasing from the plate No. 1 to the plate No. 6 parallel to the plane A X BZ, and the branches of the hyperbola straighten themselves in proportion as the plates more nearly approach this last position. As to the sounds which correspond to each of these nodal systems, it is observed that they ascend gradually from No. 1 to No. 6, and that the sound of the hyperbolic system is sharper in a part of the series than that of the system of crossed lines, whilst they become graver in the other part. There is therefore a certain inclination for which the sounds of the two systems ought to be equal; and this evidently would have taken place in the present expe- riment for a plate intermediate to No. 4.and No. 5. The interval between the gravest and the sharpest sound of each series was an augmented fifth. TuirD SertEes.—Plates taken round the axis A X of greatest elasticity, and perpendicular to the plane A Y DZ; figs. 11 and 12. The elastic state of these plates cannot present such remarkable dif- ferences as those we have observed in the preceding series; for, being all cut round the axis of greatest elasticity, they can only contain in their plane that of least or that of mean elasticity, or lastly, those in- termediate between these limits, which do not vary greatly from each other. Thus it is seen that their modes of division differ very little from each other, and that the sounds which correspond to them present rather slight differences, although they go on ascending in proportion as the plates more nearly approach containing the axis of mean elas- ticity in their plane. Here, as in the other series, one of the nodal ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 149 systems consists of two lines crossed rectangularly, one of which, a 2, places itself always on the axis of greatest elasticity, and this line serves as the second axis to the hyperbolic curves which compose the noda{ system. Doubtlessly these curves are not entirely similar in the different plates; but Ihave not beenable to perceive any very remarkable difference between them, unless that it appears that their summits gradually ap- proach bya very small quantity, in proportion as the plates more nearly approach containing the intermediate axis in their plane. Fourtu Series.—Plates cut round the diagonal AD, and perpendi- cular to the plane BC Y Z; figs. 13 and 14. These plates present much more complicated phenomena than those we have hitherto observed. Except for the first and the last, neither of the two nodal systems consists of lines crossed rectangularly, which shows that this kind of acoustic figure can only occur on plates which contain at least one of the axes of elasticity in their plane, since Nos. 2, 3, 4, 5, which are inclined to the three axes, present only hyperbolic lines, whilst No. 1, which contains two of the axes of elasticity, and No. 6, which contains only one, are susceptible of assuming this kind of division. - In this series, neither of the modes of division remains constantly the same for the different degrees of inclination of the plates: setting out from the plate No. 1, one of the systems gradually passes from two crossed lines to two hyperbolic branches, which are nearly transformed into parallel straight lines in No. 6; on the contrary, the other system appears in No. 1 under the form of two hyperbolic curves, the summits of which approach nearer and nearer until they coalesce in No. 6, where they assume the form of two straight lines which cut each other at right angles and this contrary course in the modifications of the two systems is such, that there is a certain inclination (No.3) for which the two modes of division are the same, although the sounds which cor- respond to them are very different. As in the preceding series, and for the same reasons, the sound of each nodal system goes on always ascending in proportion as the plate more nearly approaches containing the axis of greatest elasticity in its plane. Firru Series.—Plates cut round the diagonal A E, and perpendicular to the planer s t; figs. 5. 2 Bising all the plates which may be cut round the diagonal A E of Paice cube fig. 5, there are three each of which contains one of the axes vof elasticity, and which consequently we have already had occasion to observe; thus the plate No. 3, fig. 8, which passes through the diagonal “AB, and through the edge A Y, contains the diagonal A E in its 150 FELIX SAVART’S RESEARCHES ON THE | plane; also, the plate No. 4, fig. 10, which passes through one of the diagonals X Y or A C, and which is perpendicular to the plane C Y A X, contains also A E in its plane; and lastly, the plate No. 3 of fig. 12, parallel to the plane ADE X, is cireumstanced in the same manner. Thus, if rst, fig. 15, is a plane perpendicular to the diagonal A E, and if the lines 1, 3, 5 indicate the directions of the three plates we have just spoken of, in order to become acquainted with the progress of the transformations which connect the modes of division of these plates together, it will be sufficient to take round A E, the projection of which is in c, a few other plates such as 2, 4,6. The Nos. 1, 2, 3 of fig. 16 represent this series thus completed, and the dotted line ae indicates in all the direction of the diagonal of the cube. The nodal system represented by the unbroken lines consists, for No. 1, of two crossed nodal lines, one of which, ay, places itself upon the axis A Y, and the other in a perpendicular direction; it transforms itself in No. 2 into hyperbolic curves, which by the approximation: of their summits again become straight lines in No. 3, which contains the axis A Y of greatest elasticity: these curves afterwards recede again, No. 4, and in the same direction as No. 2; they then change a third time into straight lines in No. 5, which contains the axis A Z of least elasticity ; and lastly, they reassume the appearance of two mypesidfic branches in No. 6, The transformations of the dotted system are much less saeglicalials since it appears as two straight lines crossed rectangularly in No.1, and afterwards only changes into two hyperbolic branches, which con- tinue to become straighter until a certain limit, which appears to be at No. 3, and the summits of which afterwards approach each other, Nos. 5 and 6, in order to coalesce again in No, 1. As to the general course observed by the sounds of the two nodal sy- stems, it is very simple, and it was easy to determine it previously. Thus, the plate No. 5, containing in its plane the axis A Z of least elasticity, the two gravest sounds of the entire series is heard; these sounds afterwards gradually rise until No. 3, which contains the axis AX of greatest elasticity ; after which they redescend by degrees in Nos. 2 and 1, (the latter contains the axis A Y of intermediate elasticity in its plane,) and they return at last to their point of departure in the plates Nos. 6 and 5, The transformations of the nodal lines of this series, by establishing a link between the three series of plates cut round the axes, makes us conceive the possibility of arriving at the determination of nodal sur- faces, which we might suppose to exist within bodies having’three rect- angular axes of elasticity, and the knowledge of which might enable us to determine, @ priori, the modes of division of a circular plate in- clined in any manner with respect to these axes. But it is obvious, that to attempt such an investigation it would be necessary to base it on ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 151 experiments made with a substance the three axes of which shall be accurately perpendicular to each other, which is not entirely the case in wood. It would now remain for us to examine two other series of plates, one taken round the diagonal A B, and the other round the diagonal AC; but as it is evident that the arrangements of nodal lines which they would present would differ very little from those of the fourth series, we may dispense with their examination. Such are, in general, the phenomena which are observed in bodies which, like that we have just examined, possess three axes of elasticity: collected into a few propositions, the results we have obtained are re- ducible to the following general data. — Ist. When one of the axes of elasticity occurs in the plane of the plate, one of the nodal figures always consists of two straight lines, which intersect each other at right angles, and one of which invariably places itself in the exact direction of this axis; the other figure is then formed by two curves which resemble the branches of a hyperbola. 2nd. When the plate contains neither of the axes in its plane, the two nodal figures are constantly hyperbolic curves; straight lines never enter into their composition. 3rd. The numbers of vibrations which accompany each mode of di- vision are, in general, higher as the inclination of the plane to the axis of greatest elasticity becomes less. 4th. The plate which gives the sharpest sound, or which is suscep- tible of producing the greatest number of vibrations, is that which contains in its plane the axis of greatest elasticity and that of mean elasticity. 5th. The plate which is perpendicular to the axis of greatest elasti- city is that from which the gravest sound is obtained, or which is sus- ceptible of producing the least number of vibrations. 6th. When one of the axes is in the plane of the plate, and the elas- ticity in the direction perpendicular to this axis is equal to that which itself possesses, the two nodal systems are similar; they each consist of two straight lines which intersect each other rectangularly, and they oceupy positions 45° from each other. In a body which possesses three unequal axes of elasticity there are only two planes which possess this property. 7th. The transverse axis of the nodal curves always occurs in the di- rection of the least resistance to flexion; it hence follows, that when in a series of plates this axis places itself in the direction at first occupied by the conjugate axis, it is because the elasticity in this direction has become relatively less than in the other. _ 8th. In a body which possesses three unequal axes of elasticity, there “are four planes in which the elasticity is so distributed that the two a 152 SAVART ON THE ELASTICITY OF CRYSTALLIZED BODIES. sounds of the plates parallel to these planes become equal, and the two modes of division gradually transform themselves into each other, by turning round two fixed points, which, for this reason, I have called no- dal centres. 9th. The numbers of vibrations are only indirectly connected with the modes of division, since two similar nodal figures, as in No. 3, fig. 8, and in No. 3, fig. 14, are accompanied by very different sounds ; whilst, on the other side, the same sounds are produced on the occurrence of very different figures, as is the case for No. 5 of fig. 8. 10th. Lastly, a more general consequence which may be deduced from the different facts we have just examined is, that when a circular plate does not possess the same properties in every direction, or, in other words, when the parts of which it consists are not symmetrically arranged round its centre, the modes of division of which it is susceptible assume positions determined by the peculiar structure of the body; and that each mode of division, considered separately, may always, subject how- ever to alternations more or less considerable, establish themselves in two positions equally determined, so that it may be said that, in hetero- geneous circular plates, all the modes of division are double. By the aid of these data, which are no doubt still very few and im- perfect, a notion may be formed, to a certain point, of the elastic state of crystallized bodies, by submitting them to the same mode of investi- gation: this is what we have attempted for rock crystal, in a series of experiments which will be the subject of § 111. of this Memoir. ‘ 153 ArTicxeE VIII. Experiments on the Essential Oil of the Spirea Ulmaria, or Meadow-Sweet ; by Dr. Lowie, Professor of Chemistry at Lurich*. From J. C. Poggendorff’s Annalen der Physik und Chemie; Berlin, Second Series, vol. v. p. 596. Wuusr by the examination of plants and vegetable matters we have acquired the knowledge of a great number of oxyacids with compound radicals, with the exception of prussic acid no such hydracid has been shown to exist in organic nature; and of hydracids with ter- nary radicals, if we except the sulphocyanic acid, we have not the slightest knowledge. The constancy of the phenomena which oil of bitter almonds pre- sents, have not only led to the positive knowledge of the existence of ternary radicals, but also to the fact that oxyacids exist with ternary bases containing oxygen. By means of the experiments made with the essential oil of the blos- soms of the Spirea Ulmaria, described in the following treatise, the first hydracid with a ternary radical in organic nature has been discovered in a most extraordinary manner, and they give every reason to hope that the radical of the same may also be isolated. The reader must excuse the circumstances that the experiments are not carried further, and that some of the most important appearances when remarked have not been further pursued, as for all the experiments, there was only a very small quantity of material at the disposal of the experimenter. If also, on account of the small quantity of the oil which could be subjected to research, each experiment was conducted only on a small seale, especially as regards the analysis, and could only be seldom re- peated, the coincidence of each separate experiment may perhaps in part supply the want of repetition. Should however the analytical re- sults experience any small change by later repeated experiments, we may nevertheless be sure that the facts themselves of which this Memoir treats will lose nothing in importance. By means of this communication the attention of chemists may be drawn to the oil of the Spirea, so that not only a repetition of these experiments, but also a further extension of them may be expected with _ certainty from other chemists. ° [The Editor is indebted for the translation of this Paper to E.Solly, jun., Esq. ] 154 DR. LOWIG ON THE ESSENTIAL OIL M. Pagenstuher, an apothecary in Berne, had already drawn attention to the oil and distilled water of the blossoms of Spirea Ulmaria in a treatise which may be found in Buchner’s Repertorium, vol. xL1x. p. 337. He there describes exactly almost all the combinations which are the subject of this Memoir; and had he made analyses of the elements with only a few substances, the real nature, not only of the oil itself, but also several decompositions and recompositions which it experiences would not then have escaped him. M. Pagenstuher had the kindness to give me the oil for all the in- vestigations, and also to communicate to me his observations made up to that time. All his experiments which were of any importance on the present subject are incorporated into this Memoir, so that in many respects the present work may be considered as undertaken eon- jointly with M. Pagenstuher. To facilitate the general view of the fol- lowing experiments, a few of the leading results may be first stated. The oil of the blossoms of the SpireaUlmaria is a hydracid; it con- sists of one eq. of a radical = C12 HS O4, and one eq. of hydrogen, which uniting with the radical forms an acid. If the hydrogen, which by uniting with the radical forms the acid, be oxidized by nitric acid, 4 additional eqs. of oxygen are taken up by the radical, thus forming the oxyacid of the same radical. Instead of 1 eq. of hydrogen, the radical can unite with 1 eq. of chlorine, bromine, iodine, or even of a metal. These latter combinations are also formed when the hydracid is made to act on metallic oxides. With ammonia, on the contrary, the hydracid unites without undergoing any change. From these combinations the following compounds result: C12 H5 04+4 04 (C12 H5 O44 H) + NH3 or ammonia. The radical is designated by the name Spirzoyl, or for the conve- nience of shortness Spiroil. Another name would have been chosen for it had not a similar nomenclature been already applied to another sub- stance nearly allied to it. It is always doubtful policy to derive the name of a vegetable principle from the plant in whielf it is first disco- vered, for generally with great probability the same body may be found in other plants. Names which designate any principal peculiarity of the substance are therefore in such cases always preferable. One of the pe- culiarities of spiroil is its property of forming yellow compounds with oxygen, and withthe metals, alkalies, and earths; a name therefore which had reference to this quality would have been very suitable. A name OF THE MEADOW-SWEET. 155 however, is only a sign for a certain expression, and thus considered it is perfectly indifferent what name may be chosen for any substance. Hydrospiroilie Acid. The fluid oil of the blossoms of the Spirea Ulmaria is hydrospiroilic acid. This may be obtained by distilling the flowers with water ; about as much water is to be distilled off as was originally employed. ‘The product of the distillation is however subjected to a redistillation till about 3th is come over in the receiver. A concentrated aqueous so- lution of the oil is thus obtained, and the oil itself, though only in very minute quantities. The oil is heavier than water, is of a light yellow colour, and possesses the odour of the blossoms in a very great degree. It mixes in all proportions with alcohol and zther, and is slightly so- luble in water. It causes a burning sensation on the tongue. The fumes which come over during the distillation of the oil first render litmus- paper green, and then bleach it. The aqueous solution of the oil first of all slightly reddens tincture of litmus, and then deprives it of its colour excepting a greenish shade. It is inflammable, and burns with a shining smoky flame. If the oil be passed through a red-hot tube containing pieces of iron, neither ammonia nor prussic acid is obtained nor can the formation of any sulphuret of iron be detected. The oil does not ex- perience any change either in dry or moist oxygen gas ; it volatilizes unchanged. It solidifies at a temperature of —20°*. Its boiling-point is about + 85°*, when it evaporates entirely without leaving any residue. With the bases of salts, namely, with the alkalies and alkaline earths, it easily combines, forming insoluble or difficultly soluble compounds. Concentrated sulphuric acid converts the oil into a black carbona- ceous mass. Chlorine and bromine decompose it instantaneously, hy- drochloric or hydrobromic acid and chloride or bromide of spiroil being formed. Nitric acid, if not too concentrated, immediately forms spiroilic acid; if however the acid be very concentrated and fuming, it imme- diately changes it into a yellow, very volatile, bitter-tasting compound, having the appearance of butter. The experiments on the composition of the anhydrous oil, as well as the other compounds, were made in the usual manner with oxide of copper. 0°290 grms. of the oil gave 0°694 carb. acid 191-89 carbon OES water 16°10 hydrogen; _ according to which 290 parts of the oil contain SCOR ON ses tey 465 obtained by agitating the aqueous solution of hydrospiroilic acid with solution of bromine ; it is immediately precipitated in white flocks : the supernatant liquid is colourless, has no smell, and contains hydrobromic acid. In order to free the bromide of spiroil from excess of bromine and hydrospiroil, it must be kept melted in a water-bath so long as acid fumes are given off. Bromide of spiroil is exactly similar to the chloride of spiroil in all its properties; it is quite insoluble in water, and is easily soluble in ether and alcohol... By the spontaneous evapo- ration of the alcoholic solution it is obtained crystallized ; bromide of spiroil melts at a rather higher temperature than the chloride, and like the latter may also be entirely sublimed: when boiled with water it evaporates unaltered. Its behaviour, with regard to the saline bases, is exactly the same as chloride of spiroil, but the alkaline salts are more difficultly soluble: 0-480 grm. bromide of spiroil dissolved in potash and decomposed by nitric acid yielded only 0-02 bromide of silver. I. 0-510 grm, fused bromide of spiroil yielded 0°690 carbonic acid = 190°78 carbon. 0°510 water = 13:11 hydrogen. Further, by solution as above-mentioned in pure caustic potash, and combustion of the compound formed, 0-510 grm. bromide of spiroil became 0°485 bromide of silver = to about 0°2036 bromine. aEBON