292 Mr. E. P. Adams on the Electromagnetic 



perpendicular to the plane of the paper (fig. 3) . The needles 

 lie in one of the planes of revolution. The force at P due to 

 the sphere at A is required. 



Fig. 3. 

 P 



/ o = PA. 

 6=0B. 

 d=PJB. 



c = OC = OA = radius of revolution. 



€= angle between p and tangent at A. 



= angle between vertical radius and radius to A, 



p* = d 2 + b* + c 2 - 2c Vd* + b* cos #; 



n d 



p 8 = ^ + 6 2 + c«-2rfccos^; 

 dsind 



cose: 



sm e= 



/ (rfcosfl— c) 8 + 6 « 



V d 2 + 6 2 + c 2 -2dccos 



The force acts in a direction perpendicular to p and the 

 tangent at A. The component of this force in the direction 

 of the normal to the plane of revolution is required. Let yjr 

 be the angle between the direction of the force and the 

 normal to the plane of revolution. 



dcos0 — c 

 cos xr = — - -^- , 



Y \S{dcos0-c) 2 + b~ 



v = 2ttc~N, 

 where N is the number of revolutions per second. 



