1872.] Mr. J. Stuart on Galvanomagnetic Attraction. 67 



I a 1 2 a 3 3 ^ 2. 4 a 5 5 J ' 



and when r is greater than a, 



l« 2 p ,1.3 a* 1.3.5 a« p 1 

 U ~ 2 *M ~ 2 ^ Pl + 274 * ? P ~ 27476 ' P Ps + ' ' * j ' 



where h depends only on the intensity of the current, and where P„ P 3 , 

 P 5 are denned by the equation 



1 + P r r + P^ 2 + P 3 ^ + .... 



<yi—2x cosd + x 2 



If, therefore, X represents the resolved part perpendicular to the plane 

 of the circle and towards it of the force exerted by the current on a unit 

 of magnetism placed at Q, and if T represent the resolved part of that 

 force parallel to the plane of the circle and directed from its centre out- 

 wards, then 



Y dU . _ dJJ . 



A= sin — -— cos 0, 



r . dd dr 



v dU tiA _dJJ . . 



l = cos 6 + — - sm 0. 



r . dd dr 



To calculate these quantities, we know that 



P x =cos 0, 



P 2 =|(cos 3 6>- |cosd), 



T> 63/ 5o 10 3n . 15 A 

 P 3 =-(eos 0-_ C os 3 0+-eos0j. 



We shall only consider the case of those points for which r is greater 

 than a. Substituting these values in the expression which in such in- 

 stances holds for TJ, we have 



U=2^(-I. 4cos0+15. f 4fcos 3 0-?cos0) 

 { 2 r z lb r* \ 5 / 



■}• 



From which, after some reduction, we obtain 



* = - 1 ( - 1 + 3 cos 2 0) . * + i . (9 - 90 cos 2 + 105 cos 4 0) % 



- J_ ( - 75 + 1575 cos 2 0-4725 cos 4 + 3465 cos 6 0) % 

 128 v r 7 



(1) 



