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 
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