118 ELECTRICAL MEASUREMENTS 



sin(^)*, (30) 



This ratio gives a measure of the effect produced on the first 

 elongation by the prolongation of the discharge. 



As another example, take one which may be realized by the 

 manipulation of the apparatus used for calibrating a ballistic 

 galvanometer by means of a mutual inductance. 



Suppose the primary circuit to be traversed by a current. At 

 a time t = the circuit is broken by the reversing switch. 



This instantaneously removes ~ magnetic linkages from the 

 secondary. After an interval of 10 sec., the circuit is made in 

 the reverse direction and a second instantaneous change of ~ 



linkages is made. 



It is desired to know how the deflection so obtained will com- 

 pare with that which would have been obtained had the change 

 of n linkages been made instantaneously. 



In this case using (16) and (17) 



r^ 10 

 ee^ cos btdt 5+5 ioo cos 10 & 



ng 10 =g ~ 



I n 



J edt 



10 

 ee at sin btdt + ^ e 10 sin 106 



,510 



edt 

 Suppose the following data apply to the galvanometer in question 



Time of a complete vibration = T = 149 sec. 



c\ 

 Ratio of two successive swings = -- = 1.063. 



02 



Logarithmic decrement = X = log 1.063 = 0.0611 



6 = = 0.0422 

 a = = , 0.00082 



