Strength and Direction of a Varying Electric Current. 99 



dN 

 But -=- is the E.M.F. due to the inductive action ; hence, 

 at 



if R be the resistance of the circuit and a be small, the cur- 

 rent induced in the coil at any time t } is approximately 



_IA du 

 C ~R * dt' 



Now the couple or torque due to the action of the field on 

 the circuit is cIA ; and therefore the retardation of the 

 angular velocity of the coil at any time t is 



PA 2 du 

 jjlR ' dt' 



where /j, is the moment of inertia of the coil. Hence we have, 

 for equation of the motion of the coil, 



d?a PA? da 4a 2 



dt 2 + ^ ' dt+T 2 *-"' 



The motion represented by this equation will be oscillatory 

 or non- oscillatory according as 2-7r/T is greater or less than 

 PA 2 /2yL&R, so that in order to make the motion of the coil 

 non-oscillatory, all that is necessary is to have the magnetic 



field so strong that P > 4 £ . ^. 



J. A 



Now as regards the second condition. The method com- 

 monly used of recording the motion of the needle of a galva- 

 nometer is the photographic method, which is, undoubtedly, 

 very satisfactory. But this method, besides requiring an 

 elaborate arrangement of several pieces of apparatus, has a 

 serious disadvantage, namely that the observations must be 

 made in a darkened room. The method adopted in the new 

 instrument is one which, though, perhaps, not so accurate as 

 the photographic method, possesses the advantage of being very 

 simple and convenient. In this method, which may be called 

 the electrical method, there are several electrical circuits, 

 each of which is closed when, and only when, the coil or the 

 needle comes to a certain definite position corresponding to 

 it, and each circuit, when closed, makes a mark on a moving 

 paper ribbon chemically prepared, somewhat in the same way 

 as in the Bain's Telegraphs. If the coil turns round in one 

 direction, it successively closes those circuits which make 

 marks on one side of the centre of the ribbon, and if in the 

 opposite direction, those circuits which make marks on the 

 other side ; and further, the distance of the mark from the 

 centre of the ribbon is greater or less according as the turning 

 round of the coil is greater or less. 

 8 H2 



