122 



Article VI. 



On the Mathematical Theory of Heat ; by S. JD. PoissON, 



Member of the Institute, Sfc* 



From the Annales de C/iimie et de Physique, vol. lix. p. 71 et seq. 



J. HE work which I have just published under the title of The Mathe- 

 matical Tlieory of Heat ( Theorie Mathematique de la Chaleur^, fonns 

 the second part of a treatise on Mathematical Physics (^Physique Mathe- 

 matique), the first' of which is the New Theory of Capillary Action 

 (^Nouvelle Theorie de V Action Capillaire), which appeared four years 

 ago. It contains trvelve chaptei-s, preceded by some pages in which I 

 recapitulate in a few words the first applications of the calculus 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. I will 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 eai-th 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 (la 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 M'hich has 

 long since been observed at all depths to which man has penetrated. 



" According to this new explanation the phaenomenon depends on the 

 inequality of temperature of those regions of space which the earth suc- 

 cessively passes through in its translatoiy 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- 

 tiiis, Paris. 



