MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 173 



LORENTZ' formula is derived from the " quasi-stationary " principle, which may or 

 may not give correct results. But, as was stated in Section 2, I have not yet seen 

 how to apply the method of this paper to a body which alters its dimensions as the 

 velocity alters. 



Discussion of BlJCHEBBE's results by the present method cannot therefore be 

 adequately done. We may note that THOMSON'S formula would not agree with 

 BUCHERER'S numbers as well as does LORENTZ' formula, but would give much better 

 agreement than ABRAHAM'S formula, or the corrected value using condition (2) for an 

 accelerated motion. 



8. Initial Motion of an Insulating Charged Spit ere. We shall suppose that the 

 sphere, initially at rest, has a uniform surface charge c, that the material lias a 

 dielectric ratio K, and that the velocity of radiation in the material is C', thus 



K = (?/(.?*. 



The equations for the aether outside the sphere remain the same as before, but 

 while the field inside the sphere is initially zero, the motion must give rise to a 

 disturbance inside the sphere. 



While the fundamental equations for the rether are unaltered by the motion of 

 electrified bodies, this is not the case with the equations for the moving matter 

 itself. 



As will be shown in Section !), there is still considerable uncertainty as to what 

 the true equations are. This difficulty does not, however, enter in the first order 

 approximation. 



If we refer to the equations for the tether in Section 5 and put k equal to zero, we 

 see that the problem of a first order approximation there turns on a solution <f> of the 

 equations for a state of rest along with a solution depending on the initial field, the 

 latter depending on the form .-of the equations. 



Now in a similar way the disturbance in an insulating body will depend on a 

 solution of the equations for the insulator at rest along with a solution depending on 

 the form of the equations for a moving insulator and the initial field. Since, however, 

 the initial field inside the sphere is zero the difficulty is removed, and we require only 

 a solution of the equations for the insulator at rest, and these we know to be of the 

 form given on p. 148 supra, with C replaced by C', at all points where there is no 

 charge. The units must be suitably chosen. 



Hence at points outside the sphere the electric force is given by 



