( 655 ) 



2. a,i A'B'C' t^ — t,^t,-\-hi^\cos(p, 



3. at infinite distance t, r=t^. 



The nornaal at ABC coinciding with the radius. 



The formiUae : 



t^ =:t„ -\- ByV COS tp in the wire, 



C 



«3 = i„ -f- B^ r cos<p -] ^ cos ip in the la ver of water, 



r 



C, . , ■■ • 



<3 = «„ -| COS (p 111 the surrounding ice 



r 



satisfy the equations r being the distance from tlie point M. For 

 the coefficients I find the relations 



B A — = — =b\ — ] . 



'^ {R-irdy {R^dy \dpJ,R^d 



Neglecting powers of dIR I find 



i?« 2(it:+ci)i^-,+rf//j(A-,-)t,)!' 



^' 2[R^d)%+dlj^(k^_k>,\ 

 For an element E' F' of A' B' C' the flow of heat into the ice 

 towards (he surfaces amounts to: 



— k, cos <p dw , 



' R-\-cP ^ 



if we write d(p for the angle E'MF' . Hence the total quantity of 

 heat conducted through the ice towards the surface A' B' per unit 

 of time : 







In the layer of water the flow of heat per unit of time is for jB'i^' 



