iO Proceedings of the Royal Irish Academy. 



moves without rotation. We find, on the surface »• = a, 



, /I k l~\ ^ ,./3 '6Jc lr\ 

 \a^ a- a) ^ \a' o} ay 



. pSapS.p (i + ?^' + ^^) + pSa. (i + ^)j C- 



+ ^|.(V5aV - aV') re-*-- + . . .; 

 and for the magnetic force we find 



- r,„ . ,.r' [v,r,.(i. . i). '•] -- |(i * „^ - !).-'■ .... 



To a first approximation we find that the non-normal terms vanish if 

 A-V + /a + 1 = 0. If /.,, denote this value of k, we may assume that the 

 complete value is of the form A,, + cH; + c'-k^ + . . . There is, how- 

 ever, no term containing a multiplied by a constant coefficient in the term 

 multiplying c-' in t + Finj, and no term will arise, as shall be seen, in 

 compensating there the non -normal force, so that A| = 0. The non- 

 normal term wiU be found to be 



kc-'VpVia^, 

 which can be annulled by a " harmonicoid " of second kind 



- .' = kc-^VpVoai^- + ^)c-*- + C-'-V.Voa{^- + ,^ - ^)':-*- + ■.. 



It will be found on inspection that the only term containing a in the 

 coefficient of e"' arises from 



On arrangement of terms we find 



til _ 7/3A 



c'\,4 12 y • ■ 



, l + v/3i 

 kfi = + 



where r is the velocity, and i = -/ - \. 



The general tendency is thus to diminish the damping factor and to 

 lengthen the period from which we may infer that the charge is less stable 

 than before. 



