The experiment of M. Tyndall, of which I have attempted to give an idea, seemed to be of a nature to decide the question in favor of the English physicist. But it is in reality a very complex question, as is shown by the latest observations of M. Wild, of Berne, and those of M. Magnus. The state of the wall of the tube exerts a highly important influence on the effects obtained. It is true that humid air communicates less heat to the battery than dry, if a tube polished on the inner side be employed. But if the tube be blackened or lined with velvet an inverse effect is observed; humid air then conveys more heat to the battery than dry. The complication of the phenomenon is connected with the condensation of the vapor of water on the walls of the tube. It appears, therefore, extremely difficult to measure the absorbing power of aqueous vapor by the methods which have heretofore been practiced; all that can be concluded from numerous observations up to the present time is that this power is not so considerable as M. Tyndall thinks. If we consider, however, the terrestrial atmosphere in relation to the vesicular water it contains, absorption will appear due principally to that water, and the climatological conclusion of M. Tyndall be free from objection.

In what light should we regard the mechanism of absorption? If we admit in bodies the existence of ponderable particles and an ether, we can suppose that the movement of the ether is transformed into a different movement, effected by the particles of the body when absorption occurs. We are led to believe that this transformation is more facile in compound bodies that in simple, from seeing that the absorbent power of the former is in general greater, and we can imagine compound bodies to be aggregations of particles whose form is opposed to the vibrations of the ether. M. Tyndall says that simple gases are to compound gases what a smooth cylinder, revolving in water, is to a wheel with paddles. The verification of such a law is of very great importance, and we thus see how the research respecting the absorbent powers of gases and vapors may disclose remarkable correlations between the different properties of matter.

In the same way that we just represented to ourselves the absorption of heat by gases, we can also represent its emission; it will be the transmission of the movement of the particles of gas to the ether, and two gases will present the same relation between their absorbent and their emissive powers. The emission of heat by gases is well established by the experiments of MM. Tyndall and Magnus; there remains no uncertainty but with regard to the numbers which measure it. On this head new researches are indispensable.

There exist other phenomena calculated to reveal to us the relations of heat and light. It has been long known that the refractive properties of bodies vary with the temperature, and the study of this variation must greatly contribute to our knowledge of the constitution of bodies. M. Fizeau has been occupied with this study for many years, and he has been led to the origination of a new experimental method, the principle of which I proceed to explain.

The heat absorbed by a body is employed to produce many effects, among which is the change of its volume. When the question relates to a body sufficiently voluminous, the methods practiced leave nothing to desire. It is not so, however, in regard to bodies which can be obtained only in small fragments, such as crystals. The process of M. Fizeau is essentially as follows: The solid fragment, having the form of a lamina with two parallel faces, is placed on a horizontal metallic plane, supported by three long adjusting screws. The upper points of these screws support a plane of glass, beneath which is the solid lamina designed to be studied. By working these screws the lower face of the plane of glass is brought parallel to the upper face of the solid, at a distance of about two hundredths of a millimetre. By causing rays of simple light to fall perpendicularly on the lamina, rings, alternately brilliant and obscure, will be seen reflected on the latter. If the thickness of the small stratum of air interposed between the glass and the solid be gradually increased, the rings approach the

centre by a centripetal movement; the central dark ring becomes a black point and disappears; the second dark ring has taken its place, disappears in its turn, and so on in succession. Inversely, if the thickness of the stratum of air is diminished, the movement of the rings is centrifugal; a point appears at the centre, grows larger, becomes a ring; then a new ring is formed at the centre, and so in succession. When a ring proceeds thus to occupy the place of another ring, we know, according to the laws of light, that the thickness of the stratum of air has varied by a half length of the wave; for yellow light this variation is 294 millionths of a millimetre. Observation of the rings, therefore, will enable us to know the slightest variations in the thickness of the stratum of air.

The apparatus is placed in an air-bath, and is gradually heated. If the solid lamina dilates it tends to diminish the thickness of the stratum of air; the three screws, on the contrary, by dilating, tend to increase that thickness. The resulting effect will be a diminution or augmentation of the thickness, and consequently the centrifugal or centripetal movement of the rings will be observed, according as the dilatation of the lamina shall be greater or less than that of the screws. From the degree of displacement of the rings we deduce the dilatation of the lamina.

This method, the precision of which is extremely great if we take all the precautions indicated by M. Fizeau, enables us to resolve a great number of questions relating to the properties of crystals, and to establish new relations between heat and light. Thus there exist in a crystal three rectangular directions, which are called axes of elasticity, around which are grouped the most remarkable optical phenomena, and also the phenomena of conductibility and electricity discovered by De Sénarmont. These axes play the same part in the phenomena of dilatation by heat, and the ingenious researches of M. Fizeau have now completed our knowledge of the admirable structure of crystallized solids. Among the numerous unexpected results at which he has arrived, I may cite the contraction of the ioduret of crystallized or amorphous silver at every temperature which has been employed, and the existence of a maximum of density for the beryl, the protoxide of copper, and the diamond.

I pass now to the second part of my subject, the relations which exist between heat and movement. During the heating or the cooling of a body, there are in general three sorts of effects to be considered, the variation of temperature, the external mechanical labor which results from the change of the volume of bodies and from pressures exerted on their surface, and the internal mechanical labor which consists in the change of aggregation. There are definite relations between these effects and the quantities of heat lost or gained by the body, and the discovery of these relations is one of the most remarkable advances of modern physics. It serves as the basis for the mechanical theory of heat.

It is now well established by experiment that a given quantity of heat is equivalent to a definite mechanical labor, as if heat were convertible into labor, and vice versa. This experimental law leads us to regard the effects of heat as the result of the movement of the particles of bodies, and to frame hypotheses which enable us to conceive of this movement; but such is not the object of the mechanical theory of heat. Without forming any hypothesis respecting the nature of heat, it only sets forth a small number of principles, a sort of postulata suggested by experiments, and it links together all the known facts by means of general relations deduced mathematically from those principles. It is a physical theory in the rigorous acceptation of the word.

Till now two fundamental principles have served as a point of departure; but according to the recent researches of M. Hirn, the second principle would be a rational consequence of the first, so that thermodynamics would seem based in reality on the sole principle of the equivalency of heat and of labor. So important is such a proposition that I could not pass it by in silence.

The thermodynamic theory has opened a new horizon to all those who study

the physical and natural sciences. Admirable as has been its previous career, it has before it the most brilliant future. When our illustrious Ampère had divined the connection which exists between magnetism and electricity, electrodynamics was founded, and brilliant discoveries arose on every side. Our own generation nas no cause to envy its predecessor; to the former pertains the credit of the development and application of thermodynamics. The formulas deduced from this branch of science have undergone the test of experimental scrutiny, applied by M. Regnault and other physicists; those formulas have other tests to undergo, by suggesting new experiments which had probably never been attempted without them.

The scientific association of France will contribute to this progress by facilitating and stimulating research. In this spirit its committee of physics has charged me with the study of the properties presented by saturated vapors when they undergo expansion or compression, and the results obtained have been published. The creation of new apparatus has led to other researches. It is thus that M. Hirn and myself have recently solved an important problem, respecting which there had not, to our knowledge, been any previous experimental information. I may be permitted here to give a statement of that problem: “A vapor supersaturated with heat is suddenly expanded by producing an external labor, without addition or subtraction of heat; what is the relation of the pressure to the temperature during the expansion?" There is an agreement between the results we have reached and the principles of thermodynamics; they prove that the changes of volume in vapors are accompanied by a considerable internal labor.

The laws which govern the internal labor of bodies are of the highest importance towards a knowledge of the constitution of matter, and yet those laws have been scarcely so much as surmised. To this day, experiments have had for their principal object the relations of heat and of external labor; it is from these experiments that have been deduced the numerical data now in use. The experiments relative to internal labor are more difficult and more rare. We have had recently the researches of M. Edlung, in Germany, on the thermic effects of the traction of metals. The principal experiment, and which the author has submitted to careful study, is the following: Along a stout piece of vertical wood is arranged a bar of metal terminated below by a ring, and firmly fixed by its upper extremity. Through the ring a strong iron lever is passed, one extremity of which rests on an axis attached to the piece of wood at a short distance from the ring, and the other extremity bears a basin at nine times that distance from the ring. When we place on this basin a weight of 60 kilograms, we exert on the bar of metal a traction of about 600 kilograms, the lever being of the second order. A thermo-electric battery has one of its faces applied against the bar, and a galvanometer shows the depression of the temperature. Let us now gradually lift the weight in order to allow the bar to return to its primitive length; the galvanometer indicates a corresponding elevation of temperature. Finally, if we suddenly remove the weight, there is again an elevation of temperature; but this time greater than before.

How is this phenomenon to be explained? Let us consider the bar as elongated by the external traction; its particles have taken such positions that the internal forces form an equilibrium to the external forces. If we suppress the latter, the body resumes its original volume through the effect of the internal forces, and there is an internal labor expended; there is a manifestation, therefore, within the body itself of a quantity of heat proportional to that labor, and, consequently, a spontaneous elevation of temperature; it is here taken for granted that the calorific action of neighboring bodies may be overlooked.

In place of suddenly suppressing the traction, let us allow the molecular forces to restore the body, little by little, to its original volume, by gradually diminishing the force of traction. The external labor thus produced will correspond

to an equal part of the internal labor expended, and the other part will be equivalent to the heat made apparent, consequently, to the elevation of temperature. This elevation will be less, therefore, than that of the preceding operation, and the difference will be proportional to the external labor produced.

But this operation may be reversed, and when we proceed in such manner as to dilate the body mechanically, there is an internal labor produced which remains greater than the external labor expended; the difference of these two labors corresponds to the disappearance of a proportional quantity of heat, hence a spontaneous lowering of the temperature,

Thus experiments of this kind furnish us a relation between the external labor, the internal labor, and the heat created or destroyed. On the other hand the mechanical theory establishes a mathematical relation between these quantities. It is practicable, therefore, to submit a consequence of this theory to the test of experiment. Such is the object which M. Edlung proposed to himself, and it may be said that the verification has been as complete as possible. But it does not appear possible to draw from such experiments the exact value of the mechanical equivalent of heat, on account of the impossibility of preventing the calorific influence of neighboring bodies. As the traction is not instantaneous, neither can the thermometric effect be so; the effect which we observe is therefore too small, and the theoretic formula which serves to calculate the mechanical equivalent yields a value too great. If we establish a system of corrections in regard to the effect of the surrounding bodies, the uncertainty is not less great, because of the minuteness of the thermometric effect that is measured.

By the side of the speculative researches which have aggrandized our knowledge respecting heat within a few years past, of which I have been able to signalize but a small number, may be ranged certain interesting experiments which have been devised for the popularization of science, and with which most of us are already familiar. I have selected one of those which we owe to the celebrated English professor, M. Tyndall, because it is the reproduction of a striking natural phenomenon. I refer to the intermittent eruptions of water and vapor met with in Iceland. M. Bunsen has furnished a very simple explanation of volcanoes of this kind, which are called geysers, and M. Tyndall has very ingeniously imitated

them.

Imagine a pit of a depth of twenty metres, and a breadth of three; at the bottom there is water heated by the volcanic substances which proceed from the depth of the earth. The different strata of water occur under pressures increasing from above downwards, since each stratum must sustain the pressure of the atmosphere and that of the column of water which is above it. The temperature of ebullition of these strata will therefore increase, in like manner, from above downwards. Let us consider a stratum having a temperature a little below that of its ebullition, under the conditions in which it actually exists: if its prèssure be diminished, it is thrown into ebullition. This is precisely what takes place in the geyser. Aqueous vapor being formed at the bottom of the pit, where the heat is strongest, lifts up the strata of water above. If one of them be raised sufficiently high, it passes into a state of ebullition; the water which is below it. is less compressed; it boils in its turn, and a mass of vapor is instantly formed at the bottom of the pit. This vapor expels the upper strata of water, and itself issues with them, forming an immense sheaf-like jet. The expelled vapor io cooled, becomes liquid, and falls back with the projected mass of water; by its re-entry the temperature of the pit is reduced, and ebullition is suddenly arrested. We now hear a concussion proceeding from the formation of new bubbles fs water, because all the parts of the pit are not instantaneously chilled; until finally, repose is re-established. But the central heat gradually restores the column to its former state, and a new eruption takes place. In the experimental demonstration, the geyser is represented by a tube of metal, two metres in length, surmounted by a basin. It is filled with water, and two sources of heat are estab

lished-one at the bottom, the other 60 centimetres higher up. By regulating the heat, the water of the latter region is maintained at a temperature a little below 103 degrees, and therefore cannot boil; but if the strata of the bottom are raised to 105 degrees, they are thrown into ebullition, and the steam raises the middle stratum. This is immediately reduced to vapor, and the erruption takes place. The mixture of water and steam falls back into the basin, re-enters the tube, and a certain interval elapses before the fires can re-establish the temperatures requisite for a new erruption.

In thus presenting to my auditors a view of some of the recent researches of physicists, I have endeavored to indicate the philosophic tendency of those researches. They lead us to presage new advances which will draw closer the bonds which science has discovered between the various forces of nature. Is it enough for us to picture to ourselves the mechanism of phenomena by the help of ingenious hypotheses? Hypotheses are useful to the physicist for the discovery of the numerical laws, which reveal to us the harmony of the universe; they do not suffice for the philosopher who wishes to ascend higher in the search for causes. But to the data of experimental science it is necessary to join principles of a wholly other order, the germ of which has been implanted in our souls by the Creator. The origin and essence of natural forces are questions of philosophy whose solution, if it is possible, exacts all the powers of investigation of which the human mind is capable.

THE PRINCIPAL SOURCES OF HEAT.*

In selecting as the subject of this discourse the principal sources of heat, I have proposed to give a very simple example of the connection which exists between natural phenomena, even those to which we might, if we contented ourselves with a superficial examination, deny a community of origin. But when mental practice has habituated us to observe what surrounds us, and to draw general conclusions from our observations, when we have learned to read, in some sort, the great book of nature, we hesitate no longer to recognize the connections which escaped us at first, and we seek an expression for those connections; when we have found that expression, we have constructed a physical theory. The theory which will serve me to show the connection of the sources of heat is very recent; it is alluring from its very simplicity. But being a work purely human, it is but a rough portraiture, a pale reflection of the grand unity which reigns throughout nature. All the merit of this theory consists in its being better than those which preceded it, and in seeming to approach nearer to the truth. This must justify us in adopting it.

Let us understand, then, the limits to which we are restricted; as far as concerns us at present, to explain a phenomenon is to show the connection which exists between that phenomenon and a general principle which is the expression of a fact more simple than experiment has revealed to us. I shall commence by establishing the fundamental principle on which I propose to sustain myself.

When a ball of ivory falls on a horizontal plane of marble, it rebounds and returns almost to its point of departure. Repeat the experiment, by replacing the ivory with lead, and the ball will rise to a less height in rebounding; but now it will grow warm, which was not the case with the ball of ivory. Cause soft bodies or liquids to fall; these will no longer rebound, and if we measure their temperature we shall find the heat created by the impact to be greater than in the previous instance.

It is now known that every pound of every ponderous body, which loses its velocity by falling from a height of about 720 feet, and which does not rebound, disenages a quantity of heat capable of raising by one degree the temperature

Conférence de M. Cazin. "Soirée scientifique de Chartres." Revue des cours scientifiques de la France, &c., July, 1867.