180 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



and 



, a_ 



k = ^J 



oV 



_ 



C 2 C 4 

 If squares and higher powers of ^ may be neglected, we get M = m + m' and 



3 , and this agrees exactly with the equation proposed by LORENTZ for the 

 motion of an electron. 



If we calculate the rate of radiation by means of the dissipation function it is found 

 that the mean rate of radiation is 



and this is also the result obtained by calculating the Poynting flux. We thus 

 obtain complete confirmation of LARMOR'S result for a vibrating electron. 



11. First Order Vibrations of an Insulating Charged Sphere. From Section 8 it 

 appears that the free vibrations of the first order are determined by the equations 



The assumption of a form x(^~ r ) = Ae~ A(C( ~ r+n)/a , with appropriate forms for ^ 

 and \//2, led to the equation for X, viz., 



m \ m \ m 



+ }-ll\-(K-I + K l/2 K 1/2 X 2 +K(K 1/a +l)\ 

 m/ \m/J\ in 



This equation may also be put in the form 



tanh K 1/2 X = K 1/2 X<! 1 + 



(K-i) i + -X -K 



m / m 



If the sphere has no resultant charge or is held fixed, the equation becomes 



