470 Mr. 0. Heaviside on the Differential Galvanometer. 



through e, and the resist- 

 ances as in the diagram) 

 when at a balance and 

 therefore ad— be a vanish- 

 ing quantity. 



To deduce from this the 

 expression for the force 

 acting on the needle in the 

 differential galvanometer, 

 let a and b be the two coils. 

 Then, in the first place, by 

 KirchhofFs rule, 



A«-B6=Ee, 



where A, B, E are the currents in a, b, and e respectively ; and 

 next, that as e is absent in the differential-galvanometer arrange- 

 ment, we must make e infinite. Therefore, multiplying (1) by 

 e and making e= oo, we obtain 



ad— be 



ha -M=^±±m± (2) 



(a + c){b + d) 



+f 



a-\-b-\-c + d 



for the differential galvanometer. This can, of course, be ob- 

 tained independently of any consideration of Wheatstone's 

 bridge, but makes it evident that the best arrangement of the 

 differential galvanometer with a given battery may be derived 

 from the WheatstoneVbridge formulas by making e infinite in 

 them. 



These formulae are as follows (Phil. Mag. February 1873). 

 When c, d, <?, and / are fixed, 



-w 



c cd-\- df+fc 

 d c-\-d+e 



h - /o TcJ+df+ft 

 V c * c + d+e ' 

 and if c be not arbitrarily fixed, 

 a = \/ef, 



(3) 



d+e 



x/ 



df. 



d+e 

 d+f 



(4) 



which is the most sensitive arrangement possible with a given 



