of an Electrified Ellipsoid. 337 



line marked X = is the "image." The semi-length of the 

 line and the radius of the disk are each taken as unity. 



Fig. 3. 



1 have attempted to find the lines of the mechanical force F, 

 these being everywhere perpendicular to the equilibrium 

 surfaces. But the process involved an impracticable inte- 

 gration, and thus led to no result. 



1 will now w r rite down the values of E and H at any point 



near the ellipsoid of revolution with axes a, b, b. Instead of X 



it will be convenient to take as the parameter of any one of 



the equilibrium surfaces its x axis and to denote this by h. 



Thus 7 ,, _ 



h 2 = a 2 + aX ; 



and consequently if we put Z 2 for a? — ub' 2 , so that I is the semi- 

 length of the line which is the " image " of the ellipsoid, we 

 have 



h 2 — P 

 b 2 + \ = - -. 



