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



When h is large the quantity in [ j 



-*-<Jf+ 1 ) ft + »-) 



vanishing when 7* = co . 



Thus, making use of ijlKv 2 —\ we have for the magnetic 

 energy 



m q 2 u 2 fa? + l 2 , a + l a -) 



Now by (17) we have at the surface of the ellipsoid 

 Mr _ 9 a C " dli q<% , a + l 



Hence the total electromagnetic energy of the ellipsoid is 



Here we must remember that l 2 = a 2 —ab 2 . 



(A) Energy of Hear iside Ellipsoid. If we put a/Z=S and 

 make S large we have 



= 2K-a( 1 + 1 3?) whenS = C ° < 24 > 



This corresponds to the Heaviside ellipsoid, for when S = oo 

 a 2 — ah 2 . The energy of the same ellipsoid at rest is 



q 2 \/a v . ,11 



. - sm" 



2Ka m ^ 



(B) Energy of a Sphere. Putting & = a we have I — an/v, and 

 thus 



w-ifca*^-!)- • • • w 



If m is small compared with t; we have 



It will be found that as far as u 2 /v 2 the magnetic energy is 

 q 2 u 2 _ /J,q 2 u 2 



3Kav 2 'da 



as has been found by Mr. Heaviside *. It follows from this 



* ' Electrical Papers,' vol. ii. p. 505. 



