Heat oy the Method of Mixtures. 275 



and S x the surfaces, of the calorimeter and the body respec- 

 tively, and T , the temperature of the cooling body. In general 

 <i is itself a function of T — 6 (see Kankine's Treatise on the 

 Steam Engine, p. 260). Thus for a plate of thickness y and 

 thermal resistance p immersed in a liquid the flow of heat 



1 T,— TJ 

 through the plate is — .— -.S^dx; T x and T x being the 



temperatures of the two sides of the plate. The flow of heat 

 from the liquid of temperature X into the plate on one side 



is — (T^— Oj^B^x, and from the plate into the liquid on the 



other is — (T x '—0 x )& x dx. If the temperature is uniform 



throughout the plate, i. e. if T x —1l x is zero, as will be prac- 

 tically true if the thermal resistance p is very small compared 

 to the external resistance a, we get for the total flow of heat 

 from the plate into the liquid at the time, x, 



dq x =z-S 1 (T s -O x )dx=—wsdT (11) 



But from Peclet's formula 



0" + ^ = . 



Kjl+B(T k -0,)} 



here 



hence 



i=2K{l+B(T,-0.)l 



(7 



Substituting in (11) we get 



dq x =z(T x -e s )2K{l+B(T x -0 x )}S 1 dx=-wsdT (12) 



and at maximum (9) =(10) =(12), or 



AS^-^)=2KS 1 (T -^ + 2KBS 1 (T -^) 2 (13) 



Hence if we determine T , all the quantities being known ex- 

 cept /3, this last may be readily calculated. 



The determination of T is attended with some difficulties, 

 which may be avoided by expressing T as a function of the 

 time x required for the contents of the calorimeter to acquire 

 the maximum temperature 0. 



The total heat imparted to the water of the calorimeter con- 

 sists of two parts : 



1st. Heat taken from body 



= (T-T )im, attimea; (14) 



