OF ELECTRO-DYNAMIC FORCES. 503 



Moreover. 



2. In that case where the right line uniting the centres of 



both coils is at right angles to the axis of the bifilarly- 



suspended coil, 



m, n and a having the same signification, and 



m m 



vv, 



a a + nn 



aa 

 aa + n n 



nn 



= f, 



= Agvv, 



aa -^ nn 

 the rotatory momentum required is 



= + Tti^nn ii . S', 

 1^' expressing the following series : — 



S' = + i 



+ ¥ [7 + 1(1- IV) g + 42//5r^] 1,4 



+ fM [tV + 1(3 - 22f)g + V^ (1 - 22/+ \A^ff)gg 



— &c. 



If in this series we substitute for m and n the given values, 

 and successively a = 300, 400, 500 and 600, we obtain as the 

 rotating momentum required, the following values to be multi- 

 plied by., ii:- ^ 3.^^^^ 



+ 1-4661 



+ 07420 

 Lastly, + ^'4267 



.H. In that case where the centres of both coils coincide, — 

 when m designates the radius of the multiplier, and n' and n" 

 the least and greatest radius of the bifilarly-suspended coil, the 

 rotatory momentum sought is 



wv rn^ . n" 



= ^?rr^ ^ ' Li log nat -, 



, 9 /I \ 225/1 1\ . 



-^ T^ \n"n"-n'n') "'"^ " 14336 V^^ " Z^J "* 



6125 / 1 J_\ g 694575 /I 1 \ ,, 



^ 884736 W'« n"'} "' + 184549376 W'~^^) "* + -l- 



