WITH ELECTROMAGNETIC FORCE. 133 



Mr Hockin, who also made all the observations with the galvanometer and its 

 adjusting shunts. 



To determine v from these experiments, we have first, since the attraction 

 is equal to the repulsion, 



,214 



If x is the current of the great battery passing through the great resistance 

 R, and if x of this passes through the galvanometer whose resistance is G, 

 and x x' through the shunt S to earth, then 



E = Rx + Gx' .................................... (7), 



and Gx=S(x-x') ................................... (8). 



Also if g, is the magnetic effect of the principal coil of the galvanometer, 

 and g. 2 that of the secondary coil, then when the needle is in equilibrium 



9iaf=ff& ....................................... (9). 



In the comparison of the coils of the galvanometer, if x^ and y^ are the 

 currents through each, we have 



But y t is divided into two parts, of which x 1 passes through the galvan- 

 ometer G and the shunt 5", and the other, y l x', passes through the shunt 



of 31 Ohms. Hence 



x 1 (G + &)=(y 1 -x,)3l ........................... (11). 



From these equations we obtain as the value of v, 



1 a f~B IRQ n \ 31 



V= . .-TJ --+#+ G) -frq, -- ............ (12), 



-V 2^1 \ o - 



an equation containing only known quantities on the right-hand side. Of these, 

 n and ri are the numbers of windings on the two coils, a is the mean of 

 the radii of the suspended disk and the aperture, b is the distance between 



2A 

 the fixed disk and the suspended disk, -5- is found from a^ and a a , the mean 



radii of the coils, and b' their mean distance by equation (3). 



R is the great resistance, G that of the galvanometer, S that of the shunt 

 in the principal experiment, and & that of the additional resistance in the com- 

 parison of galvanometer-coils. 



