THE BALLISTIC GALVANOMETER 107 



Concerning the use of standard condensers, see page 357. 



Theory of the Undamped Ballistic Galvanometer. A D'Arson- 

 val galvanometer with a uniform radial field will be assumed. 

 With such an instrument when it is traversed by a steady current 

 of strength 7 G , 



I G C = r6 



C is the coil constant or factor which when multiplied by the 

 galvanometer current gives the turning moment acting on the 

 movable system. Its value depends on the strength of field, the 

 length of active wire and the breadth of the coil, r is the torsion 

 constant of the suspension, or the restoring moment per unit 

 angular deflection; r6 is then the restoring moment due to twisting 

 the strip through an angle 0. 



It will be necessary to recall that when a body having a moment 

 of inertia, P, is rotating about a fixed axis with an angular veloc- 



ity, -IT, its kinetic energy is given by E = J^P-jr ; that when 

 a body so rotating has its angular velocity changed, the moment 

 of the forces producing the change is M = P-jfi, where -^ is 



the angular acceleration. 



Suppose the coil to be at rest in its zero position and a tran- 

 sient current whose intensity at any instant is i to be sent 

 through the instrument. Its electromagnetic action gives risa 

 to a force which lasts for the very short time during which the 

 current flows. This imparts a certain amount of energy to the 

 movable system, which swings to its extreme deflection in oppo- 

 sition to the restoring force due to the suspension. At any 

 instant the total energy of the system is in part kinetic and in 

 part the potential energy stored in the twisted suspension. When 

 the coil swings through its zero position all the energy is kinetic, 

 while at the end of the swing it is all potential. These two 

 amounts of energy must be equal, for by supposition there is no 

 damping and therefore no dissipation of energy as the coil swings. 



The turning moment acting on the coil at any instant is 



i C - rB 



