FOURIER OBTAINS THE ACADEMY PRIZE. 417 



simple problem which any person may comprehend. A 

 slender metallic bar is exposed at one of its extremities 

 to the constant action of a certain focus of heat. The 

 parts nearest the focus are heated first. Gradually the 

 heat communicates itself to the more distant parts, and, 

 after a short time, each point acquires the maximum 

 temperature which it can ever attain. Although the 

 experiment were to last a hundred years, the thermo- 

 metric state of the bar would not undergo any modifica- 

 tion. 



As might be reasonably expected, this maximum of 

 heat is so much less considerable as we recede from the 

 focus. Is there any relation between the final tempera- 

 tures and the distances of the different particles of the 

 bar from the extremity directly heated ? Such a rela- 

 tion exists. It is very simple. Lambert investigated it 

 by calculation, and experience confirmed the results of 

 theory. 



In addition to the somewhat elementary question of 

 the longitudinal propagation of heat, there offered itself 

 the more general but much more difficult problem of the 

 propagation of heat in a body of three dimensions ter- 

 minated by any surface whatever. This problem de- 

 manded the aid of the higher analysis. It was Fourier 

 who first assigned the equations. It is to Fourier, also, 

 that we owe certain theorems, by means of which we 

 may ascend from the differential equations to the inte- 

 grals, and push the solutions in the majority of cases to 

 the final numerical applications. 



The first memoir of Fourier on the theory of heat 

 dates from the year 1807. The Academy, to which it 

 was communicated, being desirous of inducing the author 

 to extend and improve his researches, made the question 



18 * 



