220 



Royal Society :■ 



Let P be the attracted point, P M its perpendicular distance p 

 from A B. Let P AM=a, PBM=/3. 



Let C be the centre of any turn of the wire regarded as a 

 circle of radius a, CP=r, PCM=0, OC=x ; then it is readily seen 

 that for the whole cylindrical bobbin the forces X, T are given by 



--n 



rr 



Jjdccda. 



M.docda, 



Y 



where L and M stand for the expressions on the right-hand side 

 of (1) and (2) respectively, and where jj. depends on the strength of 

 the current. 



To perform the integrations for the length of the bobbin in 

 these expressions, we have the formulae 

 jp = r . sin0, 

 &» . sin d=—r . d6 ; 



and 



lv= 



V 

 r= -±— 



T 



sm 6 



Making these substitutions for d% and r, the integrals with respect 

 to oo become integrals with respect to d, which can be easily evalu- 

 ated by a continued application of the method of integration by 

 parts, the limits being from 6= a. to 0=/3. If we then integrate 

 the result thus obtained with respect to a, from the limit b to the 

 limit b-\-c, we finally obtain 



