502 WEBER OX THE MEASUREMENT 



of the two coils coincides with the axis of the bifilarly- 



suspended coil^ 

 when m designates the radius of the multiplying coil, n the 

 radius of the bifilarly-suspended coil, and a the distance of the 

 centres of the two coils, and for brevity we make 



mm 



=■ vv, 



aa + nn 

 nn 



aa + 9171 



4 aa + nn 

 \Q> {a a + n n) 



?, a^ + Auann + n'^ 



= WW, 



= f, 

 = 9, 



64 (a a + n n) 



the electro- dynamic momentum of rotation which the multiplying 

 coil exerts upon the bifilarly-suspended coil, when a current of 

 the intensity i piusses through both coils, is determined with suf- 

 ficient accuracy to be 



= — - 1^ nn ii . S, 



S designating the following series : — 



S = + [y — tf' w] 



— ^[§- — WW— {3 — 'Jw 'w)f'\ V V 



•+ \^ [j- — wiv — 2{5 — 9w iv)f -\- 3{b — \\ww)g]v* 



— mL — wto — i{1-\\ww)f+\\{T — \6 ww) g] if 

 + f ^f [tt — w^'} — A{9—\3w w)f + 26 (9 — 15 iv w) g'] w" 



— &c. 



If in this equation we substitute the values known from direct 

 measurement, in millimetres, 



ra = 44 '4, 



n = 55 "8, 

 and successively 



a = 300, 400, 500, 



we obtain as the rotating momentum sought, the following three 

 values to be multiphed by tt w i i : — 



- 1-4544 



- 0-654; 



- 0-3452. 



