THE BALLISTIC GALVANOMETER 113 



1 Nmz 



../i=- - loge 77 



mi mz Mmi 



Substituting this value of ti in (11) gives for the first elongation 



or 



/m t \ 

 * WOT,/ 



rP(mi m 2 ) [Jo ~ J [ \m^ 



mt 



- (^) m t \N mi - mt M~*-~"i (12) 



The quantity in the brackets ( } depends only on mi and m 2 and 

 is therefore independent of the manner in which e varies. If the 

 displacement of electricity through the galvanometer is "in- 

 stantaneous," that is, if e goes through its cycle of values "in- 

 stantaneously, " then by (9) and (10) 



M = 1 N = 1 



Therefore when the motion of the movable system is non-peri- 

 odic, the ratio of the actual elongation to that which would 

 have occurred had the same integral change in e been made 

 instantaneously is 



0i **' *" 



= N m t - m,JV/. - ', (13) 



It is seen that (13) gives a measure of the error produced in the 

 deflection by the prolongation of the discharge through the gaj- 

 vanometer. 



To obtain the numerical values of M and N, the ordinates of 



the graph connecting e and i are multiplied by ~ mi< and ~ mi * 



and the two curves thus obtained are plotted to the original scale. 



All three curves are then integrated by a planimeter giving the 



sary data for calculating both M and N. 



\\ hon the motion of the movable system is periodic, that is, 



when ^p 2 <p, mi and m 2 are complex. 



8 



