120 ELECTRICAL MEASUREMENTS 



From the figure it will be seen that t' is 20 sec. This means 

 that 6 is practically zero after this time; in reality, a very small 

 e.m.f. may persist for a considerably longer period but the quan- 

 tity of electricity displaced by it may be neglected. 



I edt is obtained from the area under the curve OABC. 

 Jo 

 Integrating the curves by a planimeter, and using (16) and (17). 



R = 0.920 



S = 0.320 

 therefore 



VR*~+~S 2 = 0.973 

 if X = 0.0611 



\ A . s 



-tan" 1 



By (21) 



= ^Sf = ?^7 = ' 966 - 



The error due to the prolongation of the discharge is 3.4 per 

 cent, for this particular form of e.m.f. curve. 



The Critically Damped Ballistic Galvanometer. Mathe- 

 matically, critical damping occurs when the roots of the equation 



k 

 Pm* + km -f r = are equal, or when mi = m * ~~ irp cor " 



responding to 



In this case, the solution of (4) becomes 



_kt_ r _ &_ / M _*./* *L 



= (Ci + C 2 *)e 2p + \U 2p j ee 2p dt - t 2p j te* 2p dt (31) 



The movable system is supposed to be at rest in its zero posi- 

 tion, when e is applied to the circuit, that is, when 



t = = 0. 



