MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 1G5 



If, as before, we consider the state when the vibrations have subsided, we find that 

 the tangential condition is satisfied by assuming 



. 



rv- 



The total components of electric force at the surface are 



Z U + Z) = ^ -, s (.r, y, z) 

 (lK) p 



-<* *)*(<*> 



The surface density of the electricity a- is given by 



3Jca.fi/ r/n f \, ( 



~ <* + 



ea . r -i 



The terms in x'(^'0 an( ^ x''(^'0 contribute zero to the total charge of the sphere. 

 The mechanical reaction on the sphere in the direction of y is 



_ JL 



~ 2 



where the components of current are determined as before from the surface discontinuity 

 of magnetic force. 



Reducing the expression and neglecting squares and products of small quantities, 

 we get for the mechanical reaction 



! e% J (4F-1) - _ I+L>F1 



8 r^l/l/ /^tr' sm "'"' Fa ' 



Thus the equation of motion under a force F is 





Hence, to this order of approximation, a uniformly accelerated transverse motion is 

 possible when the vibrations have subsided. 



The initial electric inertia for a transverse acceleration is thus 



The expression, when converted in notation, is identical with that obtained by 

 J. J. THOMSON ('Recent Researches,' p. 21). 



The limiting value for A- = is found to be as before, |e 2 /aC 2 . 



