THE BALLISTIC GALVANOMETER 115 



Substituting ti in (18) gives 



<2 r p " ~' ' " ' '~ ' ^~^ 



If the same integral change in e had been made instantaneously, 

 then by (16) and (17) 



R = 1 5 = 



and the deflection would have been 



-* un "*rp^i (20) 



[JO JV7T 2 + X 2 



It follows in this case that 



This quantity is a measure of the error produced in the de- 

 flection by the prolongation of the discharge through the 

 galvanometer. 



The equations 19 and 20 are more conveniently expressed if C 

 and P are replcced by quantities which are more easily 

 determined. 



Since 



and 



rB = IoC, 



substituting in (19) and solving for 



LC-] 



gives 



T tan ~'r:H5 



r*i (22) 



^H 



edt \ ' 



Discussion. When the Displacement of Electricity is Instan- 

 taneous, The circuit in which e acts contains the inductance 



