THOMSON'S DOUBLE BRIDGE. 375 



When equilibrium is established, the resistances a^ and b l are 

 respectively proportional to the resistances a and /3 of the portions 

 A 1 C 1 and B^ measured from the points A : and B x to the 

 equipotential surface which passes through the points C and C r 

 If 7 is the total resistance a + /3 of the conductor A^, we 

 have first 



(37) 



The same rule applied to the resistances measured from the 

 summits A and B to the point D, on the one hand, and to the 

 surface CQ on the other, gives thus 



i a, 



a + - 



a #i a 



~b' = ~T~ b l 



b+ * + ~ 



or, replacing the ratios and -^ by their values from equation (37), 





b + 



i + 



The current will evidently be null in the galvanometer if it is 

 connected to the points D and C r We may then consider 

 this arrangement as an indirect means of determining the ratio 

 of the resistances a and ft that is to say, the point of the 

 conductor A 1 B 1 which corresponds to the position of equilibrium, 

 by the ratio of resistances a^ and b lt relative to an auxiliary 

 conductor of larger dimensions. 



