THE BALLISTIC GALVANOMETER 121 



These conditions will be fulfilled if 



kt /* / kt ~1 



so tf = -R e - 1 1 | e 2p eft I tet 2p dt (34) 



If the integral change in e is " instantaneous " 



t\U~*~ f (35) 



The first elongation occurs when 



de - o = i - w 



rf< 2P 



2P /P To 



' 1=: f = Vr "S 



Substituting this value of t\ gives 



F /*< 1 2 >/> /T 7 \ // \ 



loft ~ IB ,,e0'i = ( ) ( Dretf'i = K0i' (36) 

 LJ J ^o c Mr/ \e// 



where is the deflection due to a steady current, I G . 



It is seen that the elongation is proportional to the quantity 

 of electricity in the discharge, and that the galvanometer factor 

 is c times that of the undamped instrument. Consequently, 



the quantity sensitivity is -, or 37 per cent that of the undamped 



instrument. Also, the time necessary for arriving at the elonga- 



2 

 tion 0i is , or 64 per cent that of the undamped instrument. 



Equation (36) applies when the ballistic galvanometer is used 

 in a series circuit; the resistance, r, being such that the galvanom- 

 eter is critically damped. When the instrumental constants used 

 inequation (4) are introduced, (36) becomes 





