Electromagnetic Effect of Convection-Currents. 453 



Forces acting on the needle system : — 



Let M = moment of lower needle, 

 M'= „ upper „ 



then 



Couple on lower needle due to field = HM sin 6, 

 „ upper „ „ =— H'M'sin^. 



Total couple = (HM-H'MO sin (9. 



Due to disk-galvanometer : 



Couple on lower needle = MX' cos d, 

 „ upper „ = M'Xi' cos 0. 



Total couple = { MX' + M'X/ } cos 0, 

 = 87rI{MC + M'D}cos6>. 



.*. for equilibrium, 



87rI{MC + M'D} cos^={HM-H'M'}sin6', 

 or 



(HM-H'MOtan^ 



1 = 



8,r(C + D)M|l + ^(f-l)j 



D M' . . 



But -p- = 0*03 nearly, and -^ is approximately unity. 



•• 87rM(C + D) 



or 



(HM-H'MO 87r(C + D)^ ^. . 

 M = tan^ -I = ^(say). 



Similarly, for the revolving disks, 



Q 2^0-, . . -p, (HM-H'MO, . 



= /3tanA. 



.. Y-OTT ^ ^^^. 



For the sine-galvanometer : 



T H . . 

 1 = Yt sin 9. 



r = 1831. 



