DETERMINATION OP THE THERMAL CONDUCTIVITY OF MARBLE. 269 



whfro C, 11, find D ai'e constants, ;ni(l 

 n ncn 



The constants must lie determined so as to satisfy the surface 

 condition. In the present case, for tlie first half of the cycle or period, 

 the temperature of the surface is J,«., and during the last half of the 

 period, it is --,<(, Avhere a is the difference of temperature between the 

 two baths, and the mean temperature is adopted as zero. The surface- 

 condition is then satisfied by 



^ , 2a ( 1 . 27r 1 . ^ 27r 

 J (t)= — j ~pS(/i -7jr * + 7]"«'" 3 J, t + 



+ ^sini , t+ I 



T being the period, and i any odd number. 

 Xow if we take 



A, = Ve'-"'' + £+-"'■-'- 2 cos2Pi'x 



T, . -1 s'"'^'^ siH(Z»i—i^i-a;) — £"'■*■■' sin {Di+ v-^x) 

 til = tan 7 7 



Then 



M= ^Y.^,AiSm[-2nit + Bi) 



Putting x = X, ihe radius of the sphere, we have 



«.. 



■.r = X 



-fit). 



If we denote what becomes of Ai and Bi v\'hen x in them is 

 made equal to A', liy -^; and B,, then, comparing the two values 

 of /( t), we nuist have 



i being any infcger, jmd C; vanishing f »r even fcrnis. Hence 



• k is wliat ThouiRon calls (liffiisivity of heat. 



