MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 157 



Thus, using condition (1), a uniformly accelerated motion under a constant force is 

 not possible, but since the deviation depends on the third power of F, it is clear that 

 a high degree of accuracy can be claimed for the results of the preceding section. 

 Using condition (2), a uniform acceleration is possible, including the third power of F. 



The constant part of the acceleration is modified in a way which depends on the 

 relative magnitudes of m and in'. In each case the effect may be to increase or 

 diminish the electric inertia by the existence of the field. The result differs from that 

 obtained by HEAVISIDE ('Nature,' April ID, 190G), and afterwards by SEARLE 

 ('Nature,' June 28, 1906), who find that the field always increases the electric inertia. 

 The argument is based on the energy of the steady state, and I have already shown 

 that no legitimate inference as to inertia can be drawn from this. 



It is noteworthy that if the field F was of the same strength as that produced by 

 the charged sphere at the surface, viz., e/ 2 , the term :! F 2 /C a would equal e 2 /aC~ 

 or f m'. 



If the approximation is valid for such a field, the effective modification of the 

 electric inertia would tlms be very considerable. 



This conclusion is of very great importance in experiments on Becquerel or Kathode 

 rays, where we must suppose that a large number of charged particles are moving 

 very close together. It seems impossible to estimate how much effect would be, 

 produced, but that some modification of the effective inertia would result from the 

 mutual field of the charged particles is beyond doubt. 



5. Initial Motion of a Charged Conducting Sphere morimj irilli any Speed after 

 Longitudinal Acceleration is imposed. The problem of the steady linear motion of a 

 charged sphere using condition (1) has been solved by THOMSON (' Recent Researches,' 

 p. 17). 



We now proceed to investigate the effect of an accelerating force in the direction ol 

 the existing motion. 



The general equations for the field in the tether referred to a fixed origin are those 

 in Section 2. 



If we refer the system to a moving origin, for which the displacement parallel to x 

 at any time is kCt+f(t), where k is a constant, the equations become 



fey 3/3 3a 3y v@ 8a\ 1 J3 lf . ,.,, 3 



3 ~ 3~> s 5> 5 a~" ) 7i 1 57 (**-'+./ V5~ 



\oy oz oz ox ax oy) C let ox 



BY az az ax ax av\ ira 



"~a-> a -5- 3 a~ = n1^ 



3// ox oz oi/ ox/ C [at 



f\ r\ f\ f\ 



^ + M+T- 

 ~ T ^ r ^~ ", 



ox oy oz 



ax ay az_ 



~~Z i "^ f\ v. 



ax oy oz 



