Accelerated Motion of a Dielectric Sphere. 831 



resultant along the direction of motion the value 

 2 ec 



so that 



"»£'+ —*"(<*-«) =F (7) 



The initial conditions are as before, f =ff =0 at i=0, 



%(-«)=%'(-^)=o, W 



and the equations for determination of (x^i^) subject to 

 these conditions become 



fi { oyW+ (i + £) x _^} 



= ^{a(^i'-t 2 ')+ti + ^ 2 }; (9) 



and Walker's particular solution for % involving only non- 

 vibratory terms is 



1 eF j 2??2ae£ 2 / mm' 



X^-" a )-2 ( m + m ') c 3\ c * m + m'""" a VO + ™') 2 



+ (.-l)(l + m-) )}- (10) 



2 e 2 

 where m' = - — 5 and is the usual electrical inertia for slow- 

 speeds. 3ac 



The vibratory terms will be of the form 



x (ct-r) =Ae-^ ct - r+a ^ a 



^ l (c'-t-r) = Be- XK ^ ct - r ^ a y a ', . • (11) 



yfr^c't + r) = -Be- XKi( - ct + r + a V a 



or more strictly, summations of this form for the various 

 values of X satisfying the period equation 



tanh/A i -A, , m' \ / f , _ /„ m' \ m' ^ ,1 



- s _ SB l+A»(l + --x)^(«-l)(l + --.x)-*-X+A.J., 



• • • (12) 

 the real part of the summations being taken, \ being complex. 



