192 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



we find that 



(f) = Ax {log coth ^rj 1/cosh *)} 

 where 



is tlie solution. 



With condition (1) the statement of the problem is: Determine a function, <f>, 

 which satisfies 



I _p 2 2 



a 



so that the tangential component of 



at / = a shall be equal to the tangential component of 



F (-1,0,0). 

 If 



g = (x + kaY 

 ^ 1-F 

 the solution is 



where 



Tli<- surface density of electricity is given by 

 - 



the appropriate values of'p, p 1} and p 2 at the surface r = a being substituted. 



We have seen in Section 3 that the production of a uniformly accelerated slow 

 motion is established by the aid of a rapidly damped harmonic train of waves and the 

 period equation has been found. 



Further, in Sections 5 and 6, where no limitation as to speed is made, we have 

 indicated that the production of a uniformly accelerated change of the motion is 

 established in a similar way. It was assumed that the initial vibrations set up were 

 rapidly damped, but the equations given are not sufficient to give the period equation. 



