rilK MEASUREMENT OF CURRENT 31 



t X ' (21) 



From this it is seen that X must be large before it greatly affects 

 the time of vibration. 



Critical Damping. A galvanometer is critically damped when 

 the motion of the needle is just becoming non-oscillatory. 

 In this case, when the current I is constant and A: 2 = 4rP the 

 solution of (9) becomes 



e = e p +-/ [<\ + r,/; (22) 



To determine C\ and 



t = = 



- d,. 



- * 



2 



I'or this case t>/ , = JT 



nrid 



= ^ - v~^' ;i-f ^-i] (24) 



When the circuit is hrokcn the needle returns to zero, in accord- 

 ance with the equation 



^^-(iD'll+^f] (25) 



1 o J 



Fitf. 13 shows the character of the motion in this case when 

 r = 0.2 and P = 0.2. 



I "sing tin-above equations the time required for the deflect ion 

 to approach within a ;iven percentage of its ultimate value may 

 be calculated. The results for a particular case an shown in 



