338 Mr. G. F. C. Searle on the Steady Motion 



The value of "W in terms of It thus becomes 



at, _ 9" f " ^ n 



~ Kjj A 2 -/ 2 ^ J 



17) 



Equation (11) now becomes 



,v 2 p 2 a 



so thatinsteadofthe cylindrical coordinates^ and p( = \A/ 2 + * 2 ) 

 we can take h and </> where 



x=hcos<f>, p = -=^-sin<£. . . . (19) 



\ a 



From (18) we have in terms of h and <p 



dji _ (A 2 -/ 2 ) cos <p dh^h s/lF^l 2 sin <j> \/a 



dx h 2 -t 2 cos 2 (p ' dp Ji 2 -I 2 cos 2 (p ' 



Hence 



-p, _ dW dh _ aq cos <p ,„ n . 



1 ~ ~ dk ' dx ~ K{h 2 -L 2 cos 2 <f>) ' ' ' ' * ( W > 



IdV dh _ qh sin <f> y« 



"~ adk'dp ~ K V^ 1 ^ 2 {h 2 -l 2 cos 2 <p) ' ' .^ ' ' 



gt/A sin </> >y/ a 

 VA^T 2 (A 2 -/ 2 cos 2 </>) 



H=KttE,= ,„/ „ /ia V..-,^ ( 22 ) 



I now pass on to calculate the total energy possessed by 

 the ellipsoid when in motion along its axis of figure. In 

 making the calculation I shall suppose that a 2 >ab 2 , i. e., 

 that I 2 is positive. The case in which a 2 < ah 2 can be deduced 

 by the appropriate mathematical transformation. 



I have shown {§ 22} that the total energy, viz. the volume 



integral of ^— — — , due to the motion of a charge on any 



surface, is W=ijM>„+2T, 



where ^o is the value of the convection-potential at the 

 surface of the body, and T is the magnetic part of the energy, 

 viz., the volume integral of /iH 2 /87r. 



