70 Mr Pocklington, On the conditions of 



Maxwell for the current flowing in the galvanometer, but to 

 proceed from first principles. 



The maximum useful value of the electromotive force E of the 

 battery is determined by the condition that the rise of tem- 

 perature of the strip shall not be excessive. If the area of one 

 face of the strip is A, the current 0, and the maximum per- 

 missible rise 6 , we have, neglecting squares of small quantities, 



2kAd = bC* (1), 



since the strip radiates on both sides. 



Again, assuming the bridge to be balanced when = 0, the 

 current in the galvanometer is, neglecting squares of small quan- 

 tities, the same as that produced by an electromotive force Cbijd 

 in XZ when this arm has a resistance b. 



Since X W and YZ are conjugate, this is independent of B, 

 and therefore may be calculated on the hypothesis that B is 

 infinite. The current thus found is 



Cbvd c + B 



and the deflection, eliminating C by (1), and putting for d its 

 value H/2k, 



\ V H (c + /3) V& »JG *J2kA0 



3 = 



2k G(b + c + {3 + v) + (b + y)(c + (3) 



For a maximum G = (b + 7) (c + @)/{b + c + fi + 7), the ordinary 

 value, as might have been foreseen, and 



,Mff /Ad, I 6(c + /3) 



' 2 V 2k V (b + c + B + y) 



(b + c + B + y)(b+y)' 



Remembering that bB = cy, since the bridge is balanced when 

 6 = 0, 



\ V H /Ad 1 



8 = 



2k 



</{ 



-;'*? 



Hence b/c, y/b are to be made small. In this case the resist- 

 ance of the galvanometer is equal to b, and 



d__ 2 _ V 2k ' 



