MATHEMATICAL THEORY OF HEAT.
The administrative duties of the prefect of l'Isère hardly interrupted the labours of the geometer and the man of letters. It is from Grenoble that the principal writings of Fourier are dated; it was at Grenoble that he composed the Théorie Mathématique de la Chaleur, which forms his principal title to the gratitude of the scientific world.
I am far from being unconscious of the difficulty of analyzing 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 passion, for the marvellous, which caused them to forget even the sacred duties of gratitude. 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 passing 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 constitute their prosperity. Even within this apartment has not an eloquent voice lately asserted, 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 analysis which I am about to submit to you.
Nobody 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 quantity 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 space, 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 space by passing 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 substituting balls 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 passage through the most transparent plate of glass!