PEIRCE AND WILLSON. — THERMAL CONDUCTIVITIES. 



/( = 00 



+ B^ cosh { ^ 

 a 



where ^4^, jL, A3, B^, and ^3 are subject to the conditions 

 A, sinh f'^"J-\ = A, sinh ("^^ + i?2 cosh f"^) , 



21 



(26) 



(27) 

 (28) 



(29) 



k, A, cosh f^^ =: L Fj^ cosh ("^^ + i52 sinh (^')] , 

 J^siuh (^^ + ^2C0sh C'^'^^ =^3 sinh (^') + i^3C0sh (^) , 

 h r^ocosh (^) + ^2 sinh (^)l 



J^cosh r^^ + ^3 sinh ('^) 



^3 sinh ( — ) + i?3 cosh 



k 

 xj. 



2Vi 



and where Xp is the p\\\ root in order of magnitude of the Bessel's Equa- 

 tion /u {x) = 0. 



If, for brevity, we denote the quantities 



sinh f '' " j , cosli ' '' ' 



-'), .„u(^-^'), ...(^.•/), 



\ a ) \ « / x^.J^ {x^ 



by s, c, s', c', s", c", and O, respectively, these equations of condition 

 may be written 



