68 Mr Pocklihgton, On the conditions of 



Hence in our case, 



O = it ( Pl /A, + P ,/A,) + M + 2 ^( + A^)/ i • ■ •■ (1) - 

 and therefore is not equal to the resistance of the thermopile ; 



B = 



\\HeA *Jn 



The expression under the radical sign is of the form 

 . (a + b/l)(cl + d), 



and hence for a minimum, we have I = \lbdjac, and its value then 

 is (*Jad + V&c) 2 . 



Hence in our case, 



2w(A 1 o- 1 + A 2 (r 2 ) /(_ , TffJ 



l=- 



JcA 

 8 = 



VI 1 + (A^ + A^X^/A, + p 2 /A 2 ){ - (2); 



^A^ + A 2 <x 2 ) ( Pl / A x + p 2 / A 2 ) + 2V/</ + V( A^ + A 2 cr 2 ) (pJA, + p 2 /A 2 ) 



We must make (AjO-j + A 2 o- 2 )(/c» 1 /A 1 + /o 2 /A 2 ) a minimum. As 

 before, 



A, 



:->/=* (*>■ 



0"l/?2 



8 = ^ _ _ /^_ __ ...(4). 



2 V2& Vp^ + Vp 2 o- 2 + n/cV/j^! + V^o-,) 2 + Te 2 /J 



4. It is clear from this that we must make A as large as con- 

 venient. It would be well to make k small, but, as we have 

 already assumed the face of the pile to be perfectly black, this 

 can only be done by diminishing the loss by convection. This 

 might be done by enclosing the pile in an evacuated vessel, bub 

 since a diminution of k is only a gain because it permits us to use 

 a larger pile with advantage, and, as will be seen, the pile is in 

 any case inconveniently long, this method of increasing the re- 

 sistance is impracticable. The number of bars is immaterial, 

 only affecting the winding of the galvanometer. 



