224 CHARGE IN RAPID MOTION [APR K. 



The ordinary expression for deflecting force is euB. at 

 low speeds, for a charge e moving at speed u across a 

 magnetic field of intensity H; but whether this simple 

 expression is departed from at r high speeds must be a 

 question of etherial dynamics: the procedure of Larmor, 

 based on the principle of 'Least Action' (see ^Ether and 

 Matter, p. 97), would give an answer in the negative, 

 which agrees with the assumption of Lorentz. It has 

 been suggested by others that for speeds at which (u/v) 2 

 becomes sensible, we must use the more complex ex- 

 pression for deflecting force : 



rrV 2 U 2 /V, V + U , \ 



eH- (?r-l !) 



u \2u v u / 



This, however, at low speeds reduces not to the usual 



1 

 simple value, but to one-third of that value, viz. ^ Heu ; 



and Professor Schuster in the Philosophical Magazine 

 for January, 1897, calls attention to the variety of 

 numerical estimates of this quantity given by different 

 varieties of the main theory. But it appears to be now 

 considered that there is no real ambiguity and that 

 Larmor's view is correct. 



As has been said above, at high speeds, not only does 

 effective inertia vary with speed, but it has different 

 values for different directions of acceleration relative to 

 the line of motion; the value of what Abraham calls 

 "transverse inertia," which expresses reaction to a trans- 

 verse deflecting force, is quoted by Kaufmann in Comptes 

 Rendus, vol. cxxxv, p. 577, writing it with ra as the 

 equivalent inertia for slow motion, and with /3 as the 

 ratio u/v the ratio of the velocity of the particles to 

 the velocity of light thus 



