Moving Charged Spheres. 163 



Force at lower needle due to calibrating coil : 

 — -3=2ttIC 



(A 2 +03 2 )"2 



h being the radius of the coil, and x its distance from the plane 

 of the needles. 



Force at upper needle due to calibrating coil : 



^ 1 [t(vJ F ^ 0S ^- 7 1(7)' p *( cos( » + ]= 2 ' ID 



r being the distance of the center of the coil to the upper 

 needle, and 6 the angle between the axis of the coil and r. 



Let M be the moment of the lower needle, and H the earth's 

 horizontal magnetic force at its center ; M' and H' the corre- 

 sponding values for the upper needle. Let 6 be the angular 

 deflection of the needle-system produced by the current in the 

 calibrating coil, and </> the angular deflection produced by the 

 moving charged spheres. 



Equating the couple acting on the needle-system due to the 

 earth's field to the couple acting on the needle-system due to 

 the current in the calibrating coil, and putting M/M r = l, we 

 have : 



HM-H'M' 2ttI(C-D) 

 M ~~ tan 6 



Similarly, equating the couple acting on the needle-system due 

 to the earth's field to the couple acting on the needle-system 

 due to the revolving charged spheres, we have : 



HM-H'M' __ 2?rNg(A-B) 

 M V tan 4> 



Hence _A — B Ng- tan 6 



~ C — D ~T tan <£ 



Let 8 be the scale deflection on reversing the current I in 

 the calibrating coil, and A the scale deflection on reversing the 

 charges of the spheres. Then : 



V ~C-D I A 



d and d\ the distances of the centers of the lower and upper 

 needles respectively from the axle, were determined by 

 means of a cathetometer, the distance of the mirror from the 

 center of the axle being directly measured, from which d and 

 d' were obtained. 



The current sent through the calibrating coil for determining 

 the needle-constant was measured by a Weston milliammeter. 



