■476 Prof. A. Gray on Relations of 



The electric field intensity at P, resolved along the normal 

 to the con focal, is 



F.-J^jiooBtf.^, (7) 



where the integration is taken round the given elliptic strip. 

 By the previous equation this can he written 



i? 1 die ah C , n ds , ON 



where the integration is taken round the cont'ocal ellipse. 

 But by the geometrical theorem stated above, the value of 

 the component field intensity thus found becomes 



Ik abpn L* /ids' 



k. {{a 2 + u)(b 2 + u)\*J ~ 2 v ; 



•, if we write 



1 d/c qbpo 



F„=.w' 



k {{a 2 + u)(b 2 + u)^ 



(10) 



Fe=| 7 COS^ (11) 



This is evidently the magnetic field intensity F TO produced 

 at A by a current of strength y flowing round the confocal 

 ellipse. It is of course in the direction at right angles to F c , 

 that is perpendicular to the plane of the ellipse. 



This relation between the normal component of the electric 

 field intensity at P of the charged elliptic strip and the 

 magnetic field intensity at the corresponding point A due to 

 -a current in the confocal ellipse, is curious and appears to be 

 new. There is not, so far as I can see, any direct practical 

 application of the theorem which can be made with advantage. 



I may here recall that in the paper of April 1907, referred 

 to above, the expression 



* — 29 — 77-2 7772 \7~^2 vr^Po ] — o— dk (12) 



z k { {a" + u)(b 2 + u)(c 2 + w)}* J r 



[where p is the perpendicular let fall from the centre on 

 the tangent plane to the confocal at the point P, and 6' is 

 the angle between the perpendicular from the centre to the 

 tangent plane at the element dS', at E', of the confocal 

 surface, and the line KEt' (see fig. 3), and the integral is 

 taken over the confocal] was found, by the geometrical 

 theorem (1) quoted above, for the attraction of a homoeoid 

 at the external point P. It w:is remarked that this value of 

 F at P is, to a constant factor, equal to the potential 



