THE BALLISTIC GALVANOMETER 111 



f 



becomes CL The process of solution for I idt is the same as 



Jo 



Ji 

 edt. 



Assuming that L ~ is negligible, the solution of (4) is* 



= Ci ""' + 



m l* I ~ m l l dt 6 m 2* I C~ m - t (It (5) 



rP(wi w 2 )L J J 



The values of mi and ra 2 are given on page 26. 



When the e.m.f. is first applied to the circuit the movable system 



is supposed to be at rest in its zero position; that is, when 



dO 



t = 0, 0= 0. and (l( = 



Since t- is a function of / th- lit ions are imposed if 



<\= - I |^-i'r// I (6) 



/' mi - mt) IJ J<-o 



and 



r r r i 



(7) 



- / ) 



rr(tn\ - mt) \J J(-o 



With these values of Ci and C 2 substituted in (.' the deflection at 



any definite time, t, is 



1 I K-^'tlt - m -' I VfT n *tlt 



L Jo Jo J 



- (8) 



rP(mi-fiH) 



Equations (5) and (8) apply in all cases. A difficulty is en- 



countered in using them, >in<-r in comparatively few instances 

 is it possible to express e as an algebraic function of t. This 

 precludes the taking of the integrals by purely analyt ical methods. 

 In the preliminary study of a proposed investigation, if it is 

 found that the displacement of electricity through the ballistic 

 galvanometer will not be "instantaneous," it is necessary to 

 inquire how much the first elongation will be influenced by the 

 manner in which r varies. For, see pages 105 and 106, the galva- 



*COHKN "DifiVrrntial equations," p. 103. 



