CONDUCTION AND KADIATION. HI 



it ; but Fourier, who was the most distinguished of the cultivators of 

 this mathematical doctrine of conduction, follows a course of reasoning 

 in which the difficulty does not present itself. Indeed it is stated by 

 Laplace, in the Memoir above quoted, 3 that Fourier had already ob- 

 tained the true fundamental equations by views of his own. 



The remaining part of the history of the doctrine of conduction is 

 principally the history of Fourier's labors. Attention having been 

 drawn to the subject, as we have mentioned, the French Institute, in 

 January, 1810, proposed, as their prize question, "To give the mathe- 

 matical theory of the laws of the propagation of heat, and to compare 

 this theory with exact observations." Fourier's Memoir (the sequel 

 of one delivered in 1807,) was sent in September, 1811 ; and the 

 prize (3000 francs) adjudged to it in 1812. In consequence of the 

 political confusion which prevailed in France, or of other causes, these 

 important Memoirs were not published by the Academy till 1824 ; but 

 extracts had been printed in the Bulletin des Sciences in 1808, and iu 

 the Annales de Chimie in 1816 ; and Poisson and M. Cauchy had 

 consulted the manuscript itself. 



It is not my purpose to give, in this place, 4 an account of the ana- 

 lytical processes by which Fourier obtained his results. The skill 

 displayed in these Memoirs is such as to make them an object of just 

 admiration to mathematicians ; but they consist entirely of deductions 

 from the fundamental principle which I have noticed, that the quan- 

 tity of heat conducted from a hotter to a colder point is proportional 

 to the excess of heat, modified by the conductivity, or conducting 

 power of each substance. The equations which flow from this princi- 

 ple assume nearly the same forms as those which occur in the most 

 general problems of hydrodynamics. Besides Fourier's solution, La- 

 place, Poisson, and M. Cauchy have also exercised their great analyti- 

 cal skill in the management of these formulce. We shall briefly speak 

 of the comparison of the results of these reasonings with experiment, 

 and notice some other consequences to which they lead. But before 

 TVC can do this, we must pay some attention to the subject of radiation, 



3 Laplace, Nim. Inst. for 1809, p. 538. 



4 I have given an account of Fourier's mathematical results in the Report* 



of the British Association for 1835. 



