OF AETS AND SCIENCES. 149 



Let Tf,, r^, r„ r.j, &c., be a series of points in such a line determined 

 by experiment, so tliut the galvanometer gives the same deflection 

 when one terminal is at /•„_! and the other at r« as it does when the 

 first terminal is at r^ and the second at r.^. If v is the temperature of 

 all points upon the circle whose radius is r^, the temperature of all 

 points at a distance from the heated point equal to r^ will be (v — V*'), 

 and all points at a distance of Vn will have a temperature equal to 

 (v — 7iVv). The temperatures may be determined as a function of 

 r, [y = qr(r)] by obtaining the equation of the curve drawn by 

 plotting the temperature as abscissas and the corresponding values of 

 r as ordinates ; and tlie form of the function y may be mathematically 

 obtained from the equation. 



/(gr(r)) = ^' + ^'logr, 



A' is the value of /(f/;(l)). 



Kelland unintentionally says that the assumption of 



dflv) 

 ^ dx 



as the law of flux will only necessitate the writing off(v) instead of 

 V in Fourier's formulas. This statement is evidently only true when 

 these formulas refer to a body which has attained its final state. 



Mr. E. B. Lefavour and myself are engaged upon the experimental 

 work laid out in this paper. 



Harvard University, April 4, 1877. 



