522 HISTORY OF THERMOTICS. 



ties of curves, as the method of infinitesimals, or 

 the differential calculus ; and the truth or false- 

 hood of the law would be determined, according 

 to the usual rules of inductive science, by a com- 

 parison of results so deduced from the principle, 

 with the observed phenomena. 



It was easily perceived that this comparison 

 was the task which physical inquirers had to per- 

 form ; but the execution of it was delayed for some 

 time ; partly, perhaps, because the mathematical 

 process presented some difficulties. Even in a case 

 so simple as that above mentioned, of a linear bar 

 with a stationary temperature at one end, partial 

 differentials entered ; for there were three variable 

 quantities, the time, as well as the place of each 

 point and its temperature. And at first, another 

 scruple occurred to M. Biot when, about 1804, 

 he undertook this problem 1 . "A difficulty," says 

 Laplace 2 , in 1809, "presents itself, which has not 

 yet been solved. The quantities of heat received 

 and communicated in an instant (by any point of 

 the bar) must be infinitely small quantities of the 

 same order as the excess of the heat of a slice 

 of the body over that of the contiguous slice ; 

 therefore the excess of the heat received by any 

 slice over the heat communicated, is an infinitely 

 small quantity of the second order ; and the accu- 

 mulation in a finite time (which depends on this 



1 Biot, Traile de Phys. iv. p. 669. 



* Laplace, Mem. Inst. for 1809, p. 332. 



