Central Heat of the Terrestrial Globe
At any time the Théorie Mathématique 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 circumstance, 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 latitudes, 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 grass 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 analogous 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 circumference.
The lycopodes which, in the present day, whether in cold or temperate climates, are creeping-plants rising hardly to the height of a decimètre above the soil; which even at the equator, under the most favourable circumstances, do not attain a height of more than one mètre, had in Europe, in the primitive world, an altitude of twenty-five mètres.
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 shells three feet in diameter; lizards seventeen mètres long; pterodactyles, veritable flying dragons of such strange forms, that they might be classed 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 latitudes. 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 shores 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 space 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 space.
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.
Leibnitz conferred upon this hypothesis the honour of appropriating it to himself. He attempted to deduce from it the mode of formation of the different solid envelopes of which the earth consists. Buffon, also, imparted to it the weight of his eloquent authority. According to that great naturalist, the planets of our system are merely portions of the sun, which the shock of a comet had detached from it some tens of thousands of years ago.
In support of this igneous origin of the earth, Mairan and Buffon cited already the high temperature of deep mines, and, among others, those of the mines of Giromagny. It appears evident that if the earth was formerly incandescent, we should not fail to meet in the interior strata, that is to say, in those which ought to have cooled last, traces of their primitive temperature. The observer who, upon penetrating into the interior of the earth, did not find an increasing heat, might then consider himself amply authorized to reject the hypothetical conceptions of Descartes, of Mairan, of Leibnitz, and of Buffon. But has the converse proposition the same certainty? Would not the torrents of heat, which the sun has continued incessantly to launch for so many ages, have diffused themselves into the mass of the earth, so as to produce there a temperature increasing with the depth? This a question of high importance. Certain easily satisfied minds conscientiously supposed that they had solved it, when they stated that the idea of a constant temperature was by far the most natural; but woe to the sciences if they thus included vague considerations which escape all criticism, among the motives for admitting and rejecting facts and theories! Fontenelle, Gentlemen, would have traced their horoscope in these words, so well adapted for humbling our pride, and the truth of which the history of discoveries reveals in a thousand places: “When a thing may be in two different ways, it is almost always that which appears at first the least natural.”
Whatever importance these reflections may possess, I hasten to add that, instead of the arguments of his predecessors, which have no real value, Fourier has substituted proofs, demonstrations; and we know what meaning such terms convey to the Academy of Sciences.
In all places of the earth, as soon as we descend to a certain depth, the thermometer no longer experiences either diurnal or annual variation. It marks the same degree, and the same fraction of a degree, from day to day, and from year to year. Such is the fact: what says theory?
Let us suppose, for a moment, that the earth has constantly received all its heat from the sun. Descend into its mass to a sufficient depth, and you will find, with Fourier, by the aid of calculation, a constant temperature for each day of the year. You will recognize further, that this solar temperature of the inferior strata varies from one climate to another; that in each country, finally, it ought to be always the same, so long as we do not descend to depths which are too great relatively to the earth’s radius.
Well, the phenomena of nature stand in manifest contradiction to this result. The observations made in a multitude of mines, observations of the temperature of hot springs coming from different depths, have all given an increase of one degree of the centigrade for every twenty or thirty metres of depth. Thus, there was some inaccuracy in the hypothesis which we were discussing upon the footsteps of our colleague. It is not true that the temperature of the terrestrial strata may be attributed solely to the action of the solar rays.
This being established, the increase of heat which is observed in all climates when we penetrate into the interior of the globe, is the manifest indication of an intrinsic heat. The earth, as Descartes and Leibnitz maintained it to be, but without being able to support their assertions by any demonstrative reasoning,—thanks to a combination of the observations of physical inquirers with the analytical calculations of Fourier,—is an encrusted sun, the high temperature of which may be boldly invoked every time that the explanation of ancient geological phenomena will require it.
After having established that there is in our earth an inherent heat,—a heat the source of which is not the sun, and which, if we may judge of it by the rapid increase which observation indicates, ought to be already sufficiently intense at the depth of only seven or eight leagues to hold in fusion all known substances,—there arises the question, what is its precise value at the surface of the earth; what weight are we to attach to it in the determination of terrestrial temperatures; what part does it play in the phenomena of life?
According to Mairan, Buffon, and Bailly, this part is immense. For France, they estimate the heat which escapes from the interior of the earth, at twenty-nine times in summer, and four hundred times in winter, the heat which comes to us from the sun. Thus, contrary to general opinion, the heat of the body which illuminates us would form only a very small part of that whose propitious influence we feel.
This idea was developed with ability and great eloquence in the Memoirs of the Academy, in the Epoques sur la Nature of Buffon, in the letters from Bailly to Voltaire upon the Origin of the Sciences and upon the Atlantide. But the ingenious romance to which it has served as a base, has vanished like a shadow before the torch of mathematical science.
Fourier having discovered that the excess of the aggregate temperature of the earth’s surface above that which would result from the sole action of the solar rays, has a determinate relation to the increase of temperature at different depths, succeeded in deducing from the experimental value of this increase a numerical determination of the excess in question. This excess is the thermometric effect which the solar heat produces at the surface; now, instead of the large numbers adopted by Mairan, Bailly, and Buffon, what has our colleague found? A thirtieth of a degree, not more.
The surface of the earth, which originally was perhaps incandescent, has cooled then in the course of ages, so as hardly to preserve any sensible trace of its primitive heat. However, at great depths, the original heat is still enormous. Time will alter sensibly the internal temperature; but at the surface (and the phenomena of the surface can alone modify or compromise the existence of living beings), all the changes are almost accomplished. The frightful freezing of the earth, the epoch of which Buffon fixed at the instant when the central heat would be totally dissipated, is then a pure dream. At the surface, the earth is no longer impregnated except by the solar heat. So long as the sun shall continue to preserve the same brightness, mankind will find, from pole to pole, under each latitude, the climates which have permitted them to live and to establish their residence. These, Gentlemen, are great, magnificent results. While recording them in the annals of science, historians will not neglect to draw attention to this singular peculiarity: that the geometer to whom we owe the first certain demonstration of the existence of a heat independent of a solar influence in the interior of the earth, has annihilated the immense part which this primitive heat was made to play in the explanation of the phenomena of terrestrial temperature.
Besides divesting the theory of climates of an error which occupied a prominent place in science, supported as it was by the imposing authority of Mairan, of Bailly, and of Buffon, Fourier is entitled to the merit of a still more striking achievement: he has introduced into this theory a consideration which hitherto had been totally neglected; he has pointed out the influence exercised by the temperature of the celestial regions, amid which the hearth describes its immense orb around the sun.
When we perceive, even under the equator, certain mountains covered with eternal snow, upon observing the rapid diminution of temperature which the strata of the atmosphere undergo during ascents in balloons, meteorologists have supposed, that in the regions wherein the extreme rarity of the air will always exclude the presence of mankind, and that especially beyond the limits of the atmosphere, there ought to prevail a prodigious intensity of cold. It was not merely by hundreds, it was by thousands of degrees, that they had arbitrarily measured it. But, as usual, the imagination (cette folie de la maison) had exceeded all reasonable limits. The hundreds, the tens of thousands of degrees, have dwindled down, after the rigorous researches of Fourier, to fifty or sixty degrees only. Fifty or sixty degrees beneath zero, such is the temperature which the radiation of heat from the stars has established in the regions furrowed indefinitely by the planets of our system.
You recollect, Gentlemen, with what delight Fourier used to converse on this subject. You know well that he thought himself sure of having assigned the temperature of space within eight or ten degrees. By what fatality has it happened that the memoir, wherein no doubt our colleague had recorded all the elements of that important determination, is not to be found? May that irreparable loss prove at least to so many observers, that instead of pursuing obstinately an ideal perfection, which it is not allotted to man to attain, they will act wisely in placing the public, as soon as possible, in the confidence of their labours.
I should have yet a long course to pursue, if, after having pointed out some of those problems of which the condition of science enabled our learned colleague to give numerical solutions, I were to analyze all those which, still enveloped in general formulæ, await merely the data of experience to assume a place among the most curious acquisitions of modern physics. Time, which is not at my disposal, precludes me from dwelling upon such developments. I should be guilty, however, of an unpardonable omission, if I did not state that, among the formulas of Fourier, there is one which serves to assign the value of the secular cooling of the earth, and in which there is involved the number of centuries which have elapsed since the origin of this cooling. The question of the antiquity of the earth, including even the period of incandescence, which has been so keenly discussed, is thus reduced to a thermometric determination. Unfortunately this point of theory is subject to serious difficulties. Besides, the thermometric determination, in consequence of its excessive smallness, must be reserved for future ages.
RETURN OF NAPOLEON FROM ELBA.—FOURIER PREFECT OF THE RHONE.—HIS NOMINATION TO THE OFFICE OF DIRECTOR OF THE BOARD OF STATISTICS OF THE SEINE.
I have just exhibited to you the scientific fruits of the leisure hours of the Prefect of l’Isère. Fourier still occupied this situation when Napoleon arrived at Cannes. His conduct during this grave conjuncture has been the object of a hundred false rumours. I shall then discharge a duty by establishing the facts in all their truth, according to what I have heard from our colleague’s own mouth.
Upon the news of the Emperor having disembarked, the principal authorities of Grenoble assembled at the residence of the Prefect. There each individual explained ably, but especially, said Fourier, with much detail, the difficulties which he perceived. As regards the means of vanquishing them, the authorities seemed to be much less inventive. Confidence in administrative eloquence was not yet worn out at that epoch; it was resolved accordingly to have recourse to proclamations. The commanding officer and the Prefect presented each a project. The assembly was discussing minutely the terms of them, when an officer of the gendarmes, an old soldier of the Imperial armies, exclaimed rudely, “Gentlemen, be quick, otherwise all deliberation will become useless. Believe me, I speak from experience; Napoleon always follows very closely the couriers who announce his arrival.” Napoleon was in fact close at hand. After a short moment of hesitation, two companies of sappers which had been dispatched to cut down a bridge, joined their former commander. A battalion of infantry soon followed their example. Finally, upon the very glacis of the fortress, in presence of the numerous population which crowned the ramparts, the fifth regiment of the line to a man assumed the tricolour cockade, substituted for the white flag the eagle,—witness of twenty battles,—which it had preserved, and departed with shouts of Vive l’Empereur! After such a commencement, to attempt to hold the country would have been an act of folly. General Marchand caused accordingly the gates of the city to be shut. He still hoped, notwithstanding the evidently hostile disposition of the inhabitants, to sustain a siege with the sole assistance of the third regiment of engineers, the fourth regiment of artillery, and some weak detachments of infantry, which had not abandoned him.
From that moment, the civil authority had disappeared. Fourier thought then that he might quit Grenoble, and repair to Lyons, where the princes had assembled together. At the second restoration, this departure was imputed to him as a crime. He was very near being brought before a court of assizes, or even a provost’s court. Certain personages pretended that the presence of the Prefect of the chief place of l’Isère might have conjured the storm; that the resistance might have been more animated, better arranged. People forgot that nowhere, and at Grenoble even less than anywhere else, was it possible to organize even a pretext of resistance. Let us see then, finally, how this martial city,—the fall of which Fourier might have prevented by his mere presence,—let us see how it was taken. It is eight o’clock in the evening. The inhabitants and the soldiers garrison the ramparts. Napoleon precedes his little troop by some steps; he advances even to the gate; he knocks (be not alarmed, Gentlemen, it is not a battle which I am about to describe,) he knocks with his snuff-box! “Who is there?” cried the officer of the guard. “It is the Emperor! Open!”—“Sire, my duty forbids me.”—“Open—I tell you; I have no time to lose.”—“But, sire, even though I should open to you, I could not. The keys are in the possession of General Marchand.”—“Go, then, and fetch them.”—“I am certain that he will refuse them to me.”—“If the General refuse them, tell him that I will dismiss him.”
These words petrified the soldiers. During the previous two days, hundreds of proclamations designated Bonaparte as a wild beast which it was necessary to seize without scruple; they ordered everybody to run away from him, and yet this man threatened the general with deprivation of his command! The single word dismissal, effaced the faint line of demarcation which separated for an instant the old soldiers from the young recruits; one word established the whole garrison in the interest of the emperor.
The circumstances of the capture of Grenoble were not yet known when Fourier arrived at Lyons. He brought thither the news of the rapid advance of Napoleon; that of the revolt of two companies of sappers, of a regiment of infantry, and of the regiment commanded by Labédoyère. Moreover, he was a witness of the lively sympathy which the country people along the whole route displayed in favour of the proscribed exile of Elba.
The Count d’Artois gave a very cold reception to the Prefect and his communications. He declared that the arrival of Napoleon at Grenoble was impossible; that no alarm need be apprehended respecting the disposition of the country people. “As regards the facts,” said he to Fourier, “which would seem to have occurred in your presence at the very gates of the city, with respect to the tricoloured cockades substituted for the cockade of Henry IV., with respect to the eagles which you say have replaced the white flag, I do not suspect your good faith, but the uneasy state of your mind must have dazzled your eyes. Prefect, return then without delay to Grenoble; you will answer for the city with your head.”
You see, Gentlemen, after having so long proclaimed the necessity of telling the truth to princes, moralists will act wisely by inviting princes to be good enough to listen to its language.
Fourier obeyed the order which had just been given him. The wheels of his carriage had made only a few revolutions in the direction of Grenoble, when he was arrested by hussars, and conducted to the head-quarters at Bourgoin. The Emperor, who was engaged in examining a large chart with a pair of compasses, said, upon seeing him enter: “Well, Prefect, you also have declared war against me?”—“Sire, my oath of allegiance made it my duty to do so!”—“A duty you say? and do you not see that in Dauphiny nobody is of the same mind? Do not imagine, however, that your plan of the campaign will frighten me much. It only grieved me to see among my enemies an Egyptian, a man who had eaten along with me the bread of the bivouac, an old friend!”
It is painful to add that to those kind words succeeded these also: “How, moreover, could you have forgotten, Monsieur Fourier, that I have made you what you are?”
You will regret with me, Gentlemen, that a timidity, which circumstances would otherwise easily explain, should have prevented our colleague from at once emphatically protesting against this confusion, which the powerful of the earth are constantly endeavouring to establish between the perishable bounties of which they are the dispensers, and the noble fruits of thought. Fourier was Prefect and Baron by the favour of the Emperor; he was one of the glories of France by his own genius!
On the 9th of March, Napoleon, in a moment of anger, ordered Fourier, by a mandate, dated from Grenoble, to quit the territory of the seventh military division within five days, under pain of being arrested and treated as an enemy of the country! On the following day, our colleague departed from the Conference of Bourgoin, with the appointment of Prefect of the Rhone and the title of Count, for the Emperor after his return from Elba was again at his old practices.
These unexpected proofs of favour and confidence afforded little pleasure to our colleague, but he dared not refuse them, although he perceived very distinctly the immense gravity of the events in which he was led by the vicissitude of fortune to play a part.
“What do you think of my enterprise?” said the Emperor to him on the day of his departure from Lyons. “Sire,” replied Fourier, “I am of opinion that you will fail. Let but a fanatic meet you on your way, and all is at an end.”—“Bah!” exclaimed Napoleon, “the Bourbons have nobody on their side, not even a fanatic. In connection with this circumstance, you have read in the journals that they have excluded me from the protection of the law. I shall be more indulgent on my part; I shall content myself with excluding them from the Tuileries.”
Fourier held the appointment of Prefect of the Rhone only till the 1st of May. It has been alleged that he was recalled, because he refused to be accessory to the deeds of terrorism which the minister of the hundred days enjoined him to execute. The Academy will always be pleased when I collect together, and place on record, actions which, while honouring its members, throw new lustre around the entire body. I even feel that, in such a case, I may be disposed to be somewhat credulous. On the present occasion, it was imperatively necessary to institute a most rigorous examination. If Fourier honoured himself by refusing to obey certain orders, what are we to think of the minister of the interior from whom those orders emanated? Now this minister, it must not be forgotten, was also an academician, illustrious by his military services, distinguished by his mathematical works, esteemed and cherished by all his colleagues. Well! I declare, Gentlemen, with a satisfaction which you will all share, that a most scrupulous investigation of all the acts of the hundred days has not disclosed a trace of anything which might detract from the feelings of admiration with which the memory of Carnot is associated in your minds.
Upon quitting the Prefecture of the Rhone, Fourier repaired to Paris. The Emperor, who was then upon the eve of setting out to join the army, perceiving him amid the crowd at the Tuileries, accosted him in a friendly manner, informed him that Carnot would explain to him why his displacement at Lyons had become indispensable, and promised to attend to his interest as soon as military affairs would allow him some leisure time. The second restoration found Fourier in the capital without employment, and justly anxious with respect to the future. He, who, during a period of fifteen years, administered the affairs of a great department; who directed works of such an expensive nature; who, in the affair of the marshes of Bourgoin, had to contract engagements for so many millions, with private individuals, with the communes and with public companies, had not twenty thousand francs in his possession. This honourable poverty, as well as the recollection of glorious and important services, was little calculated to make an impression upon ministers influenced by political passion, and subject to the capricious interference of foreigners. A demand for a pension was accordingly repelled with rudeness. Be reassured, however, France will not have to blush for having left in poverty one of her principal ornaments. The Prefect of Paris,—I have committed a mistake, Gentlemen, a proper name will not be out of place here,—M. Chabrol, learns that his old professor at the Polytechnic School, that the Perpetual Secretary of the Institute of Egypt, that the author of the Théorie Analytique de la Chaleur, was reduced, in order to obtain the means of living, to give private lessons at the residences of his pupils. The idea of this revolts him. He accordingly shows himself deaf to the clamours of party, and Fourier receives from him the superior direction of the Bureau de la Statistique of the Seine, with a salary of 6,000 francs. It has appeared to me, Gentlemen, that I ought not to suppress these details. Science may show herself grateful towards all those who give her support and protection, when there is some danger in doing so, without fearing that the burden should ever become too heavy.
Fourier responded worthily to the confidence reposed in him by M. de Chabrol. The memoirs with which he enriched the interesting volumes published by the Prefecture of the Seine, will serve henceforth as a guide to all those who have the good sense to see in statistics, something else than an indigestible mass of figures and tables.