PEIRCE. — TEMPERATURES WITHIN A HOMOGENEOUS LAMINA. 357 



The function 



V=l- W(x,y,c-z), 



(4) 



which satisfies (1), is equal to unity when z = 0, and also for all posi- 

 tive values of z not greater than c, when x = 0, or y = 0, or x = a, or 

 y = a. It vanishes when z = c, and the function 



or 



U= 7\ - W{T - To) - V(T t - T) (5) 



r - W(x, y, z)-{T - T ) +W(x,y,c-z)- (7\ - T) (6) 

 gives the temperatures in the slab if one face is kept at the temperature 



TABLE I. 



T , the other face at T lf and the edges at T'. In an infinite slab of 

 thickness c, the faces of which are kept at T and Ti, the temperatures 

 are given by the expression 



Z7-oo =(T 1 -T )-+To 



(7) 



so that the difference between the values of the temperature at any 

 point in the slab in the ideal case and the real case is 



(T.-^il-Wix^c-z^iT'-TonWi^y^ + Wix^c-z)-!]. 



(8) 



