Mr. 0. Heaviside on the Differential Galvanometer. 471 



galvanometer and battery. Finally, if the best resistances for 

 the galvanometer and battery are also to be employed, we must 

 make every branch of the bridge of the same resistance, viz. that 

 of d, the resistance to be measured. 



Making e=co in (3) and (4), they become 



-v? 



(cd + df+fc), 



c (cd + df+fc), 



a= co, 



b = v / d(dTfj' ) 



C= 00, 



(5) 



(6) 



which may also be obtained by differentiation from (2). 



These formulae, (5) and (6), would not be of any particular use 

 if we had no means of varying at will the resistance of the coils 

 a and b. This cannot be accomplished directly without consi- 

 derable complication ; but by means of shunts the same end may 

 be reached. Thus, using (5), if the coils of our galvanometer have 

 resistances greater than those best suited for the particular resist- 

 ance to be measured, by means of shunts we may reduce their 

 resistances to the required extent. And here a remarkable pecu- 

 liarity presents itself. In general when a galvanometer is shunted, 

 its resistance and sensibility are reduced and in the same propor- 

 tion. Not so with the differential galvanometer; for its sensi- 

 tiveness will be increased or reduced by shunts according as the 

 normal resistances of its coils are greater or less thau their best 

 values in the particular case under consideration. The accuracy 

 of (5) may be easily verified experimentally. 



Proceeding to examine (6), we meet practical impossibilities, 

 and can only carry it out by making the resistance of the coil a 

 as great as possible by not shunting it. But as the values of b 

 and c in (6) correspond to #= co, it will be necessary to find 

 their values when a = a. Therefore, regarding both a and d as 

 constant, and b and c variable, subject to the condition ad—bc = 0, 

 we shall find by differentiating (3) that 





a+f 



(7) 



gives the most sensitive arrangement for measuring a resistance 

 d with a battery whose resistance is/. 



