rrof. Ayrton and Mr. Mather on Galvanometers. 371 



This gives the difference of the two fields for any periodic 

 time of vibration, length of needle, and specific magnetism. 

 If 6 be the deflexion produced by a current 7, then 



Controlling couple = (H^ — H 2 ) M sin 6, 



and Deflecting couple = 2M7G cos 0, 



where G is the principal constant of the coil. 



Hence y = (H C, Ha) tan 0, 



4tt 2 / 2 



tan 6 ... . (12) 



~Sr 2 aGr 

 from (11). 



Now G = N «WH) • • • ^ 



(see Maxwell, vol. ii. p. 325, 1st ed.) ; 



where N=27r( V (sin 6)* old 



= 9*034. 



a the ratio of the radius of the wire to the maximum radius 



of the layer ; 

 ft the ratio of the distance between the centre of two 



adjacent wires to the radius of the wire ; 

 a the maximum radius of cavity in coil ; 

 x the outer radius of coil. 

 The resistance of the coil is given by 



R=N -^55 (---), • .(14) 

 7rorft J \a x) 



p being the specific resistance of metal used in the 

 winding ; 



P 



A little consideration will show that -= gives the value 



of G for a galvanometer whose resistance is one ohm. 



This is a maximum when ft =2 and x=x> . 



Since a = l + 0'1 . . {assumption (1)} 



we get A^PR 



y= * * P tan 6 from (12) and (15) 



-SSV^-' • • • • M 



