168 



MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



The results established are true without limitation as to the size of the sphere, but, 

 as will appear, it is only for velocities comparable with that of radiation that the 

 possibility of experimental discrimination can arise. We are thus at present limited 

 to experiments on negative electrons, arid among researches on the deflexion of such 

 particles KAUFMANN'S investigations on Becquerel rays rank first in historical order 

 ('Gcitt. Nachrichten,' 1903, Heft 3; 'Ann. d. Physik,' vol. It), p. 487, 1906). 



We propose to examine three expressions for the transverse electric inertia. 



With condition (l) we have 



4A- 2 -l 



f(J. J. THOMSON) 



or 



With condition (2) we have 



fl+P, 



,+k 2 -, 1 + k 



w l s k- 1 



-1 



[(Present No. 1). 

 . (M. ABRAHAM), 



(Present No. 2). 



In these expressions in' equals i^/'iC 2 , and k is the ratio of the velocity of the 

 sphere to that of radiation. They all agree in giving the value m' when / = 0. 



The expressions of THOMSON and ABRAHAM are derived from considerations of the 

 steady state. The ambiguity of interpretation from consideration of a steady state 

 has already been commented on in Section 1, and has been definitely admitted by 

 POINCARE. Thus it is not surprising that the expressions differ, although it so 

 happens that we have obtained expressions which agree with THOMSON'S result 

 for transverse motion and ABRAHAM'S result for longitudinal motion. 



The following table gives the numerical values of the co-efficient of m' at various 

 speeds according to the three expressions : 



