208 CALCULATION OF INERTIA [APP. B. 



The electrostatic energy resulting will be the integral of 

 AcE 2 /87r everywhere outside the moving magnetised sphere 

 of radius a, viz. 



Energy = 5 1 1 1 ( o ) sin 2 cos 2 $ dr.rdO.r sin dd> 



^ J STrJJJV r 3 / 



_AcM 2/ & 2 _ M 2 /'M'X 2 

 5<z 3 ~~ Spa? \v/ ' 



The displacement acts like an elastic strain set up in 

 the dielectric, storing the above energy statically; and so 

 long as the magnet continues moving steadily the electric 

 displacement exerts no force upon it. But acceleration 

 will be resisted; for if the magnet begins to go faster it 

 sets up more displacement, and the act of setting this up 

 constitutes a transient current, which opposes the motion 

 as long as the acceleration continues, but dies out the 

 instant the motion becomes steady again. 



Conversely if the motion of the magnet began to 

 slacken, the electric strain would begin to subside, and 

 its subsidence would constitute an inverse transient current 

 which would assist the motion, i.e., oppose the slackening. 

 In other words, the variations of the circular electric strain 

 in the surrounding medium confer upon a moving magnet 

 a spurious or apparent momentum, in addition to its real 

 mechanical momentum , and thus the elastic strain itself 

 may be said to represent a spurious or apparent inertia 

 due to magnetisation, in addition to any real mechanical 

 inertia which the body holding the magnetism may itself 

 possess. And the amount of this extra inertia is 



_2*M 2 = 2 M 2 8 

 = 5a 3 5 ,uaV 15 



= 5"^~' 



