258 HENRY A. KOWLAND 



Needle constant. 



The disk-galvanometer windings have in the same way, for the lower 

 needle, the force due to current I in one turn 



For the four turns, 



X'=8-/<7. 



Upper needle. The force is got in the same way as for the disk, omit- 

 ting the integration, i. e. we must multiply the general term of B by 



_ an d replace 2* by /. This gives 



CL V 



yfil.3...(a-l)2Y\ M p 1. 



" 2.4 ... at 7 W ^ / ' 



a replacing c, and p, r. 

 For the total force, 



,_8^/r p /av_ 3p /Y n 



l - - r 1 \~ \ J- f ^4 I ~ I T. 



p L w \^/ J 



or 



Forces acting on the needle system: 



Let M = moment of lower needle, 

 Let M' = moment of upper needle, 

 then 



Couple on lower needle due to field = H M sin 6, 



Couple on upper needle due to field = H'M' sintf. 



Total couple = (EM H'M') sin 6. 



Due to disk-galvanometer: 



Couple on lower needle = MX' cos 6, 

 Couple on upper needle = M' X^' cos#. 



Total couple = { MX' + M'XJ }cos 6, 



= S7iI\MC + M'D \cos0. 

 .: for equilibrium, 



S-I\MO + M'D\ cos 6 = \HM- H'M'} sin fl, 

 or 



__ (HM- H'M'} tan e 



