616 Dr. J. W. Nicholson on the Accelerated 



Effect of a small Mechanical Force. 



The corresponding solution for a small applied force of 

 purely mechanical nature, which we may call G, has been 

 given in Walker's second paper. With the previous nota- 

 tion, the primary equations, of which the first expresses the 

 vanishing of the tangential electric or electromagnetic force 

 (these only differ to the second order) at the surface, 

 become 



a?x!'(ct-a) +ay;(ct-a) + x{ct-a)- e -!j = 



m^|fx''(c*-«) = G (16) I 



with the conditions 



(1) Y = ^ f = when the functions have argument —a, 



(2) f=£=0 at *=0 ; < . . .(17) 



and the solutions are 



X( ,_,) = A«— sin {( 3+ ^) ! £i^ + e} 



1 eF [ , . , ,„ 2am! . 2a 2 mm! \ 

 + 7i . -T7 Ki ( ct ~- r + a) 2 -(ct — r + a)—- --, > 



2 c^m + m')^ J m-\-m' K J (m-\-m') 2 J 



2 ek „ . fA,, 4m'\*c* . \ 



£= — - <?- c ^ 2a sin 1 3 + ) T~ + € r 



b 3wac (.V m J 2a ) 



1 F f, 2m' at 2m' 2 a 2 ") 



2m + m L m + m c (m + m y <r J v ' 



e¥a 2 mm / , 4m M a <?Fa 2 w (2m + 3/t/) 

 A sin e= ^77 ft*, I «H ) Acose = =- — — — ^ — . 



When the Newtonian mass becomes small, 



e¥a 2 m . 3 eFa*/m\i 



A sm €= , , , Acos e- ~ . -^— 7I — K 



and on reduction, 



satisfying all necessary conditions for values of m tending to 



where 



