CONDUCTION AND RADIATION. 523 



excess) cannot be finite." I conceive that this diffi- 

 culty arises entirely from an arbitrary and unne- 

 cessary assumption concerning the relations of the 

 infinitesimal parts of the body. Laplace resolved 

 the difficulty by further reasoning, founded upon 

 the same assumption which occasioned it; but 

 Fourier, who was the most distinguished of the 

 cultivators of this mathematical doctrine of con- 

 duction, 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 obtained the true fun- 

 damental equations by views of his own. 



The remaining part of the history of the doc- 

 trine of conduction is principally the history of 

 Fourier's labours. 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 mathematical theory of the 

 laws of the propagation of heat, and to compare 

 this theory with exact observations." Fourier's Me- 

 moir (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 ex- 

 tracts had been printed in the Bulletin des Sciences 

 in 1808, and in the Annales de Chimie in 1816; 



3 Laplace, Mem. Inst. for !<)!), p. 538. 



