﻿270 Prof. H. A. Wilson on the Theory of Moving Coil 

 the coil through an angle from its zero position is -»-, where 



a is the couple exerted by the wire when the coil is turned 

 through the unit angle. Let Gi denote the couple due to a 

 current i, then we have Gi = ucj). When a current i is passed 

 through the galvanometer for a short time dt, we have 



Gidt==GdQ = Kda>, 

 where K is the moment of inertia of the coil and co its angular 

 velocitv. Hence 



We have also 



Q o c 



hence 



Thus 



T = 27r\/ and — =iK 



v a '1 



/& _2tt0 



( -x _ Kft) otd 2 _ TocO 



() Ca> tirG 



Hut .- = - ; so that finally 



►Since the couple on the coil due to the current is inde- 

 pendent of y it is not necessary with this type of instrument 

 that the time during which the transient current passes should 

 be very small compared with T. 



Another type of moving-coii instrument in common use 

 has a narrow coil suspended between the poles of a magnet 

 and no iron core. In this case, the couple on the coil due to 

 a current i will be nearly Ci cos <£, so that Gi cos <j) = ad> or 



-z- = -—*-: hence the exact formulae for this type of instru- 

 ct <£ J1 



ment are 



n _Tafl _ Teflcos<ft 



In these formulae it is assumed that the plane of the coil at 

 its zero position is parallel to the magnetic field. 



It appears, therefore, that the first type of moving-coil 

 ballistic galvanometer considered is superior to the second in 

 respect of the simplicity of the exact formulae to be used with 

 it, and the absence of error when the transient current lasts an 

 appreciable time. 



