The administrative duties of the prefect of l'Isere hardly interrupted the labours of the geometer and the man of letters. It is from Gren.o.ble that the princ.i.p.al writings of Fourier are dated; it was at Gren.o.ble that he composed the _Theorie Mathematique de la Chaleur_, which forms his princ.i.p.al t.i.tle to the grat.i.tude of the scientific world.

I am far from being unconscious of the difficulty of a.n.a.lyzing that admirable work, and yet I shall attempt to point out the successive steps which he has achieved in the advancement of science. You will listen to me, Gentlemen, with indulgence, notwithstanding several minute details which I shall have to recount, since I thereby fulfil the mission with which you have honoured me.

The ancients had a taste, let us say rather a pa.s.sion, for the marvellous, which caused them to forget even the sacred duties of grat.i.tude. Observe them, for example, grouping together the lofty deeds of a great number of heroes, whose names they have not even deigned to preserve, and investing the single personage of Hercules with them. The lapse of ages has not rendered us wiser in this respect. In our own time the public delight in blending fable with history. In every career of life, in the pursuit of science especially, they enjoy a pleasure in creating Herculeses. According to vulgar opinion, there is no astronomical discovery which is not due to Herschel. The theory of the planetary movements is identified with the name of Laplace; hardly is a pa.s.sing allusion made to the eminent labours of D'Alembert, of Clairaut, of Euler, of Lagrange. Watt is the sole inventor of the steam-engine.

Chaptal has enriched the arts of Chemistry with the totality of the fertile and ingenious processes which const.i.tute their prosperity. Even within this apartment has not an eloquent voice lately a.s.serted, that before Fourier the phenomenon of heat was hardly studied; that the celebrated geometer had alone made more observations than all his predecessors put together; that he had with almost a single effort invented a new science.

Although he runs the risk of being less lively, the organ of the Academy of Sciences cannot permit himself such bursts of enthusiasm. He ought to bear in mind, that the object of these solemnities is not merely to celebrate the discoveries of academicians; that they are also designed to encourage modest merit; that an observer forgotten by his contemporaries, is frequently supported in his laborious researches by the thought that he will obtain a benevolent look from posterity. Let us act, so far as it depends upon us, in such a manner that a hope so just, so natural, may not be frustrated. Let us award a just, a brilliant homage to those rare men whom nature has endowed with the precious privilege of arranging a thousand isolated facts, of making seductive theories spring from them; but let us not forget to state, that the scythe of the reaper had cut the stalks before one had thought of uniting them into sheaves!

Heat presents itself in natural phenomena, and in those which are the products of art under two entirely distinct forms, which Fourier has separately considered. I shall adopt the same division, commencing however with radiant heat, the historical a.n.a.lysis which I am about to submit to you.

n.o.body doubts that there is a physical distinction which is eminently worthy of being studied between the ball of iron at the ordinary temperature which may be handled at pleasure, and the ball of iron of the same dimensions which the flame of a furnace has very much heated, and which we cannot touch without burning ourselves. This distinction, according to the majority of physical inquirers, arises from a certain quant.i.ty of an elastic imponderable fluid, or at least a fluid which has not been weighed, with which the second ball has combined during the process of heating. The fluid which, upon combining with cold bodies renders them hot, has been designated by the name of _heat_ or _caloric_.

Bodies unequally heated act upon each other _even at great distances, even through empty s.p.a.ce_, for the colder becomes more hot, and the hotter becomes more cold; for after a certain time they indicate the same degree of the thermometer, whatever may have been the difference of their original temperatures. According to the hypotheses above explained, there is but one way of conceiving this action at a distance; this is to suppose that it operates by the aid of certain effluvia which traverse s.p.a.ce by pa.s.sing from the hot body to the cold body; that is, to admit that a hot body emits in every direction rays of heat, as luminous bodies emit rays of light.

The effluvia, the radiating emanations by the aid of which two distant bodies form a calorific communication with each other, have been very appropriately designated by the name of _radiating caloric_.

Whatever may be said to the contrary, radiating heat had already been the object of important experiments before Fourier undertook his labours. The celebrated academicians of the _Cimento_ found, nearly two centuries ago, that this heat is reflected like light; that, as in the case of light, a concave mirror concentrates it at the focus. Upon subst.i.tuting b.a.l.l.s of snow for heated bodies, they even went so far as to prove that frigorific foci may be formed by way of reflection. Some years afterwards Mariotte, a member of this Academy, discovered that there exist different kinds of radiating heat; that the heat with which rays of light are accompanied traverses all transparent media as easily as light does; while, again, the caloric which emanates from a strongly heated, but opaque substance, while the rays of heat, which are found mingled with the luminous rays of a body moderately incandescent, are almost entirely arrested in their pa.s.sage through the most transparent plate of gla.s.s!

This striking discovery, let us remark in pa.s.sing, will show, notwithstanding the ridicule of pretended savans, how happily inspired were the workmen in founderies, who looked at the incandescent matter of their furnaces, only through a plate of ordinary gla.s.s, thinking by the aid of this artifice to arrest the heat which would have burned their eyes.

In the experimental sciences, the epochs of the most brilliant progress are almost always separated by long intervals of almost absolute repose.

Thus, after Mariotte, there elapsed more than a century without history having to record any new property of radiating heat. Then, in close succession, we find in the solar light obscure calorific rays, the existence of which could admit of being established only with the thermometer, and which may be completely separated from luminous rays by the aid of the prism; we discover, by the aid of terrestrial bodies, that the emission of caloric rays, and consequently the cooling of those bodies, is considerably r.e.t.a.r.ded by the polish of the surfaces; that the colour, the nature, and the thickness of the outer coating of these same surfaces, exercise also a manifest influence upon their emissive power. Experience, finally, rectifying the vague predictions to which the most enlightened minds abandon themselves with so little reserve, shows that the calorific rays which emanate from the plane surface of a heated body have not the same force, the same intensity in all directions; that the _maximum_ corresponds to the perpendicular emission, and the _minimum_ to the emissions parallel to the surface.

Between these two extreme positions, how does the diminution of the emissive power operate? Leslie first sought the solution of this important question. His observations seem to show that the intensities of the radiating rays are proportional (it is necessary, Gentlemen, that I employ the scientific expression) to the sines of the angles which these rays form with the heated surface. But the quant.i.ties upon which the experimenter had to operate were too feeble; the uncertainties of the thermometric estimations compared with the total effect were, on the contrary, too great not to inspire a strong degree of distrust: well, Gentlemen, a problem before which all the processes, all the instruments of modern physics have remained powerless, Fourier has completely solved without the necessity of having recourse to any new experiment. He has traced the law of the emission of caloric sought for, with a perspicuity which one cannot sufficiently admire, in the most ordinary phenomena of temperature, in the phenomena which at first sight appeared to be entirely independent of it.

Such is the privilege of genius; it perceives, it seizes relations where vulgar eyes see only isolated facts.

n.o.body doubts, and besides experiment has confirmed the fact, that in all the points of a s.p.a.ce terminated by any envelop maintained at a constant temperature, we ought also to experience a constant temperature, and precisely that of the envelop. Now Fourier has established, that if the calorific rays emitted were equally intense in all directions, if the intensity did not vary proportionally to the sine of the angle of emission, the temperature of a body situated in the enclosure would depend on the place which it would occupy there: _that the temperature of boiling water or of melting iron, for example, would exist in certain points of a hollow envelop of gla.s.s!_ In all the vast domain of the physical sciences, we should be unable to find a more striking application of the celebrated method of the _reductio ad absurdum_ of which the ancient mathematicians made use, in order to demonstrate the abstract truths of geometry.

I shall not quit this first part of the labours of Fourier without adding, that he has not contented himself with demonstrating with so much felicity the remarkable law which connects the comparative intensities of the calorific rays, emanating under all angles from heated bodies; he has sought, moreover, the physical cause of this law, and he has found it in a circ.u.mstance which his predecessors had entirely neglected. Let us suppose, says he, that bodies emit heat not only from the molecules of their surfaces, but also from the particles in the interior. Let us suppose, moreover, that the heat of these latter particles cannot arrive at the surface by traversing a certain thickness of matter without undergoing some degree of absorption. Fourier has reduced these two hypotheses to calculation, and he has hence deduced mathematically the experimental law of the sines. After having resisted so radical a test, the two hypotheses were found to be completely verified, they have become laws of nature; they point out latent properties of caloric which could only be discerned by the eye of the intellect.

In the second question treated by Fourier, heat presents itself under a new form. There is more difficulty in following its movements; but the conclusions deducible from the theory are also more general and more important.

Heat excited, concentrated into a certain point of a solid body, communicates itself by way of conduction, first to the particles nearest the heated point, then gradually to all the regions of the body. Whence the problem of which the following is the enunciation.

By what routes, and with what velocities, is the propagation of heat effected in bodies of different forms and different natures subjected to certain initial conditions?

Fundamentally, the Academy of Sciences had already proposed this problem as the subject of a prize as early as the year 1736. Then the terms heat and caloric were not in use; it demanded _the study of nature, and the propagation_ OF FIRE! The word _fire_, thrown thus into the programme without any other explanation, gave rise to a mistake of the most singular kind. The majority of philosophers imagined that the question was to explain in what way _burning_ communicates itself, and increases in a ma.s.s of combustible matter. Fifteen compet.i.tors presented themselves; _three_ were crowned.

This compet.i.tion was productive of very meagre results. However, a singular combination of circ.u.mstances and of proper names will render the recollection of it lasting.

Has not the public a right to be surprised upon reading this Academic declaration: "the question affords no handle to geometry!" In matter of inventions, to attempt to dive into the future, is to prepare for one's self striking mistakes. One of the compet.i.tors, the great Euler, took these words in their literal sense; the reveries with which his memoir abounds, are not compensated in this instance by any of those brilliant discoveries in a.n.a.lysis, I had almost said of those sublime inspirations, which were so familiar to him. Fortunately Euler appended to his memoir a supplement truly worthy of his genius. Father Lozeran de Fiesc and the Count of Crequi were rewarded with the high honour of seeing their names inscribed beside that of the ill.u.s.trious geometer, although it would be impossible in the present day to discern in their memoirs any kind of merit, not even that of politeness, for the courtier said rudely to the Academy: "the question, which you have raised, interests only the curiosity of mankind."

Among the compet.i.tors less favourably treated, we perceive one of the greatest writers whom France has produced; the author of the _Henriade_.

The memoir of Voltaire was, no doubt, far from solving the problem proposed; but it was at least distinguished by elegance, clearness, and precision of language; I shall add, by a severe style of argument; for if the author occasionally arrives at questionable results, it is only when he borrows false data from the chemistry and physics of the epoch,--sciences which had just sprung into existence. Moreover, the anti-Cartesian colour of some of the parts of the memoir of Voltaire was calculated to find little favour in a society, where Cartesianism, with its incomprehensible vortices, was everywhere held in high estimation.

We should have more difficulty in discovering the causes of the failure of a fourth compet.i.tor, Madame the Marchioness du Chatelet, for she also entered into the contest inst.i.tuted by the Academy. The work of Emilia was not only an elegant portrait of all the properties of heat, known then to physical inquirers, there were remarked moreover in it, different projects of experiments, among the rest one which Herschel has since developed, and from which he has derived one of the princ.i.p.al flowers of his brilliant scientific crown.

While such great names were occupied in discussing this question, physical inquirers of a less ambitious stamp laid experimentally the solid basis of a future mathematical theory of heat. Some established, that the same quant.i.ty of caloric does not elevate by the same number of degrees equal weights of different substances, and thereby introduced into the science the important notion of _capacity_. Others, by the aid of observations no less certain, proved that heat, applied at the extremity of a bar, is transmitted to the extreme parts with greater or less velocity or intensity, according to the nature of the substance of which the bar is composed; thus they suggested the original idea of _conductibility_. The same epoch, if I were not precluded from entering into too minute details, would present to us interesting experiments. We should find that it is not true that, at all degrees of the thermometer, the loss of heat of a body is proportional to the excess of its temperature above that of the medium in which it is plunged; but I have been desirous of showing you geometry penetrating, timidly at first, into questions of the propagation of heat, and depositing there the first germs of its fertile methods.

It is to Lambert of Mulhouse, that we owe this first step. This ingenious geometer had proposed a very simple problem which any person may comprehend. A slender metallic bar is exposed at one of its extremities to the constant action of a certain focus of heat. The parts nearest the focus are heated first. Gradually the heat communicates itself to the more distant parts, and, after a short time, each point acquires the maximum temperature which it can ever attain. Although the experiment were to last a hundred years, the thermometric state of the bar would not undergo any modification.

As might be reasonably expected, this maximum of heat is so much less considerable as we recede from the focus. Is there any relation between the final temperatures and the distances of the different particles of the bar from the extremity directly heated? Such a relation exists. It is very simple. Lambert investigated it by calculation, and experience confirmed the results of theory.

In addition to the somewhat elementary question of the _longitudinal_ propagation of heat, there offered itself the more general but much more difficult problem of the propagation of heat in a body of three dimensions terminated by any surface whatever. This problem demanded the aid of the higher a.n.a.lysis. It was Fourier who first a.s.signed the equations. It is to Fourier, also, that we owe certain theorems, by means of which we may ascend from the differential equations to the integrals, and push the solutions in the majority of cases to the final numerical applications.

The first memoir of Fourier on the theory of heat dates from the year 1807. The Academy, to which it was communicated, being desirous of inducing the author to extend and improve his researches, made the question of the propagation of heat the subject of the great mathematical prize which was to be awarded in the beginning of the year 1812. Fourier did, in effect, compete, and his memoir was crowned. But, alas! as Fontenelle said: "In the country even of demonstrations, there are to be found causes of dissension." Some restrictions mingled with the favourable judgment. The ill.u.s.trious commissioners of the prize, Laplace, Lagrange, and Legendre, while acknowledging the novelty and importance of the subject, while declaring that the real differential equations of the propagation of heat were finally found, a.s.serted that they perceived difficulties in the way in which the author arrived at them. They added, that his processes of integration left something to be desired, even on the score of rigour. They did not, however, support their opinion by any arguments.

Fourier never admitted the validity of this decision. Even at the close of his life he gave unmistakable evidence that he thought it unjust, by causing his memoir to be printed in our volumes without changing a single word. Still, the doubts expressed by the Commissioners of the Academy reverted incessantly to his recollection. From the very beginning they had poisoned the pleasure of his triumph. These first impressions, added to a high susceptibility, explain how Fourier ended by regarding with a certain degree of displeasure the efforts of those geometers who endeavoured to improve his theory. This, Gentlemen, was a very strange aberration of a mind of so elevated an order! Our colleague had almost forgotten that it is not allotted to any person to conduct a scientific question to a definitive termination, and that the important labours of D'Alembert, Clairaut, Euler, Lagrange, and Laplace, while immortalizing their authors, have continually added new l.u.s.tre to the imperishable glory of Newton. Let us act so that this example may not be lost. While the civil law imposes upon the tribunes the obligation to a.s.sign the motives of _their judgments_, the academies, which are the tribunes of science, cannot have even a pretext to escape from this obligation. Corporate bodies, as well as individuals, act wisely when they reckon in every instance only upon the authority of reason.

CENTRAL HEAT OF THE TERRESTRIAL GLOBE.

At any time the _Theorie Mathematique de la Chaleur_ would have excited a lively interest among men of reflection, since, upon the supposition of its being complete, it threw light upon the most minute processes of the arts. In our time the numerous points of affinity existing between it and the curious discoveries of the geologists, have made it, if I may use the expression, a work for the occasion. To point out the ultimate relation which exists between these two kinds of researches would be to present the most important part of the discoveries of Fourier, and to show how happily our colleague, by one of those inspirations reserved for genius, had chosen the subject of his researches.

The parts of the earth's crust, which the geologists call the sedimentary formations, were not formed all at once. The waters of the ocean, on several former occasions, covered regions which are situated in the present day in the centre of the continent. There they deposited, in thin horizontal strata, a series of rocks of different kinds. These rocks, although superposed like the layers of stones of a wall, must not be confounded together; their dissimilarities are palpable to the least practised eye. It is necessary also to note this capital fact, that each stratum has a well-defined limit; that no process of transition connects it with the stratum which it supports. The ocean, the original source of all these deposits, underwent then formerly enormous changes in its chemical composition to which it is no longer subject.

With some rare exceptions, resulting from local convulsions the effects of which are otherwise manifest, the order of antiquity of the successive strata of rocks which form the exterior crust of the globe ought to be that of their superposition. The deepest have been formed at the most remote epochs. The attentive study of these different envelops may aid us in ascending the stream of time, even beyond the most remote epochs, and enlightening us with respect to those stupendous revolutions which periodically overwhelmed continents beneath the waters of the ocean, or again restored them to their former condition. Crystalline rocks of granite upon which the sea has effected its original deposits have never exhibited any remains of life. Traces of such are to be found only in the sedimentary strata.

Life appears to have first exhibited itself on the earth in the form of vegetables. The remains of vegetables are all that we meet with in the most ancient strata deposited by the waters; still, they belong to plants of the simplest structure,--to ferns, to species of rushes, to lycopodes.

As we ascend into the upper strata, vegetation becomes more and more complex. Finally, near the surface, it resembles the vegetation actually existing on the earth, with this characteristic circ.u.mstance, however, which is well deserving attention, that certain vegetables which grow only in southern climates, that the large palm-trees, for example, are found in their fossil state in all lat.i.tudes, and even in the centre of the frozen regions of Siberia.

In the primitive world, these northern regions enjoyed then, in winter, a temperature at least equal to that which is experienced in the present day under the parallels where the great palms commence to appear: at Tobolsk, the inhabitants enjoyed the climate of Alicante or Algiers!

We shall deduce new proofs of this mysterious result from an attentive examination of the size of plants.

There exist, in the present day, willow gra.s.s or marshy rushes, ferns, and lycopodes, in Europe as well as in the tropical regions; but they are not met with in large dimensions, except in warm countries. Thus, to compare together the dimensions of the same plants is, in reality, to compare, in respect to temperature, the regions where they are produced.

Well, place beside the fossil plants of our coal mines, I will not say the a.n.a.logous plants of Europe, but those which grow in the countries of South America, and which are most celebrated for the richness of their vegetation, and you will find the former to be of incomparably greater dimensions than the latter.

The _fossil flora_ of France, England, Germany, and Scandinavia offer, for example, ferns ninety feet high, the stalks being six feet in diameter, or eighteen feet in circ.u.mference.

The _lycopodes_ which, in the present day, whether in cold or temperate climates, are creeping-plants rising hardly to the height of a decimetre above the soil; which even at the equator, under the most favourable circ.u.mstances, do not attain a height of more than _one_ metre, had in Europe, in the primitive world, an alt.i.tude of twenty-five metres.

One must be blind to all reason not to find, in these enormous dimensions, a new proof of the high temperature enjoyed by our country before the last irruptions of the ocean!

The study of _fossil animals_ is no less fertile in results. I should digress from my subject if I were to examine here how the organization of animals is developed upon the earth; what modifications, or more strictly speaking, what complications it has undergone after each cataclysm, or if I even stopped to describe one of those ancient epochs during which the earth, the sea, and the atmosphere had for inhabitants cold-blooded reptiles of enormous dimensions; tortoises with sh.e.l.ls three feet in diameter; lizards seventeen metres long; pterodactyles, veritable flying dragons of such strange forms, that they might be cla.s.sed on good grounds either among reptiles, among mammiferous animals, or among birds. The object, which I have proposed, does not require that I should enter into such details; a single remark will suffice.

Among the bones contained in the strata nearest the present surface of the earth, are those of the hippopotamus, the rhinoceros, and the elephant. These remains of animals of warm countries are to be found in all lat.i.tudes. Travellers have discovered specimens of them even at Melville Island, where the temperature descends, in the present day, 50 beneath zero. In Siberia they are found in such abundance as to have become an article of commerce. Finally, upon the rocky sh.o.r.es of the Arctic Ocean, there are to be found not merely fragments of skeletons, but whole elephants still covered with their flesh and skin.

I should deceive myself very much, Gentlemen, if I were to suppose that each of you had not deduced from these remarkable facts a conclusion no less remarkable, to which indeed the fossil flora had already habituated us; namely, that as they have grown older, the polar regions of the earth have cooled down to a prodigious extent.

In the explanation of so curious a phenomenon, cosmologists have not taken into account the existence of possible variations of the intensity of the solar heat; and yet the stars, those distant suns, have not the constant brightness which the common people attribute to them. Nay, some of them have been observed to diminish in a sufficiently short s.p.a.ce of time to the hundredth part of their original brightness; and several have even totally disappeared. They have preferred to attribute every thing to an internal or primitive heat with which the earth was at some former epoch impregnated, and which is gradually being dissipated in s.p.a.ce.

Upon this hypothesis the inhabitants of the polar regions, although deprived of the sight of the sun for whole months together, must have evidently enjoyed, at very ancient epochs, a temperature equal to that of the tropical regions, wherein exist elephants in the present day.

It is not, however, as an explanation of the existence of elephants in Siberia, that the idea of the intrinsic heat of the globe has entered for the first time into science. Some savans had adopted it before the discovery of those fossil animals. Thus, Descartes was of opinion that originally (I cite his own words,) _the earth did not differ from the sun in any other respect than in being smaller_. Upon this hypothesis, then, it ought to be considered as an extinct sun.