THE BALLISTIC GALVANOMETER 109 



Hence 



There still remains the factor g- This may be evaluated as 



follows: If a current of constant intensity, I G , be sent through 

 the instrument, a deflection of constant magnitude will result 

 and 



Obviously, the ratio of the ballistic to the current sensitivity is 



27T 



T ' 



Formula for the Kelvin Galvanometer. With a Kelvin instru- 

 ment the work done in turning the suspended system through an 



angle 0'i,is M H(l cos 0'0 = 2MH sin 2 -x- 1 , where Mis the mag- 

 netic moment of the movable system and H the strength of the 

 controlling field. 



The moment of the force due to the current in the coils is at 

 any instant GiM cos 0, where G is the galvanometer constant or 

 strength of field at the needle, due to a unit current in the coils. 

 The time of vibration of the needle system considered as a mag- 

 netic pendulum is 



To = 2 



Therefore, in this case, the expression for Q is 



TM e\ 

 Q - ^G- Sin 2' 



Theory of the Damped Ballistic Galvanometer. In, the practi- 

 cal case a certain amount of damping is always present. It may 

 be due to: 



1. Induced currents set up in the metallic parts of the movable 

 system by their motion through the field of the instrument. 



