432 Mr. C. H. Lees on the Law of 'Cooling r , and its bearing 



bath and mercury-cups, the deflexion, and the resistance of 

 the circuit were determined. The resistance was ascertained 

 by shunting into circuit a known resistance, and observing the 

 diminution of deflexion. These observations give data for 

 reducing the observations of deflexion and resistance during 

 cooling to degrees Centigrade. During cooling observations 

 of deflexion were taken every two minutes ; of resistance, and 

 of temperatures of water-jacket and mercury-cups, every four 

 minutes. 



Writing e for the product of the deflexion and resistance, 

 v temperature of junction in bar, v 1 temperature of mercury- 

 cups, e, v values of e, v when bar is in hot bath, C some con- 

 stant, we have, according to Avenarius*, for an iron- German- 

 silver circuit, 



e= C(t7 - vj (l - -00034O + wO), 



e=G(v-v 1 )(l --00034(5 + «i)); 



■•^ 1=( *-^r i--00034U*i) 



= V ~~T 1 - K 1 -•00034(5-1?)) approx. 



Writing for v, in correcting factor, its approximate value i v, 

 we have e 



V — V-i 



(l --000345^), 



which determines (v— v^, in Centigrade degrees, from obser- 

 vation of deflexions and resistance. 



By applying this equation to the observations made, we get 

 a series of temperatures of the bar at two-minute intervals ; 

 and from this series the form which /(v) must have to best re- 

 present the variation of the outer conductivity is to be found. 

 We consider only simple forms of f(v), so as to complicate 

 equation (1) as little as possible, and commence with the 

 simplest. 



The simplest form isf{v)= v, the usual assumption. Substi- 

 tuting in (2), we deduce 



— +at = C, where a= — (C is an arbitrary constant), 



r 



or 



v =v e at , where v is value of v at time t =0. 

 If a in this equation be determined from the first eight 



* Pogg. Ann. cxxii. p. 199. 



