BALLISTIC GALVANOMETER. 265 



it follows that 



H T - arc tan - H T / A 2 - arc tan - 



(39) -," = a >* 



When the damping is very weak, we may take the approximate 

 value 



HT / ,0,, + aA 



The sensitiveness of the instrument is measured by the ratio 

 of the throw to the discharge, or by the expression 



'\ HK 



It is necessary that the time of vibration of the needle T be 

 sufficiently great not only to eliminate the influence of the time 

 of discharge, but also to enable the deflection to be read, and 

 accordingly the best experimental conditions are those in which 

 the intensity H of the field is diminished. In order further to 

 approach the theoretical conditions, the damping by the air is 

 reduced as much as possible, as its law is in that case somewhat 

 uncertain, and we only retain that arising from currents induced in 

 the coil. If, finally, we want to repeat a series of successive ob- 

 servations, the needle is stopped each time by an auxiliary damper, 

 magnet, or a current. 



As at the outset the needle is never absolutely rigid, its total 

 initial amplitude 2a is first observed. The angle of deflection 

 observed a l is then increased or diminished by a , according as 

 the throw is in the direction of the initial motion or is opposed 

 to it. 



The measurement of the quantity m in absolute value requires a 

 f* 



knowledge of the ratio , which is determined either directly or by 

 rl 



comparison with an absolute galvanometer (874). 



884. The use of shunts in a ballistic galvanometer may give rise 

 to serious errors, as the discharges only divide themselves between 

 the shunt and galvanometer according to the law of branch circuits 

 provided the needle is stationary throughout the discharge (547), a 

 condition which is difficult to realise. 



