of an Electrified Ellipsoid. 333 



Thus, as Prof. Morton has also shown by the same method, 



qa d\ 



¥ 





2 K v/ (a 2 + «\) (6 2 + \) (c 2 + X) 



(12) 



Now I have shown {§21}- that if there is a surface A 

 carrying a charge q, and any surface B is found for which 

 X V is constant, then a charge q placed upon B and allowed to 

 acquire an equilibrium distribution will produce at all points 

 not inside B the same effect as the charged surface A. 



Fi<r. 1. 



1 

 B 



i 



' 















I 



k 



< 















< 



A 



r 



Hence the ellipsoid (11) when carrying a charge q produces 

 at all points not inside itself exactly the same disturbance as 

 the ellipsoid a, b, c with the same charge. 



If we make a = b = c = 0, the surfaces of equal " convection 

 potential " are the ellipsoids given by 



a 



They are therefore all similar to each other. Thus the 

 ellipsoid of this form produces exactly the same effect as a 

 point-charge at its centre, and thus an ellipsoid of this form 

 takes the place of the sphere in electrostatics. An ellipsoid 

 with its axes in the ratios V '« : 1 : 1 I have called a Heavi- 

 side Ellipsoid, since Mr. Heaviside* was the first to draw 

 attention to its importance in the theory of moving charges. 

 Whatever be the ratios a:b:c, the equipotential surfaces 



* ' Electrical Papers/ vol. ii. p. 514. 



