128 PEOCEEDINGS OF THE AMERICAN ACADEMY 



V. 



PRELIMINARY WORK ON THE DETERMINATION OF THE 

 LAW OF THE PROPAGATION OF HEAT IN THE INTE- 

 RIOR OF SOLID BODIES. 



By B. O. Peirce, Jr., and Edward B. Lefavour. 

 Presented Oct. 10, 1877. 



For a long time it has seemed probable, as stated in a paper * pub- 

 lished last spring in the Proceedings of the Academy, that the flux of 

 heat in any direction x, in a solid body, can be written, — 



dx 



where «' is the temperature, c a constant different for difTurent sub- 

 stances, and f{v) an undetermined function of v. The object of this 

 paper is to show that such a function y(t') can be found. 



This is not of necessity possible ; for denoting by X, Y, Z, the com- 

 ponents in three rectangular directions of the vector function which 

 represents the flux, we have 



_ ^ dF(T, y, z) ^ ^ 

 dx 



dF(x, y, z) 



C ; = I 



dy 



dF(x, y, z) 



= z 



dz 



whence 



— c dF{x, y,z) = Xdx^ Tdij-\- Zdz 



This equation is integrable, and F{x, y, z) can be found only when 



* Note on the Determination of the Law of Propagation of Heat in Solid 

 Bodies. 



