Motion of an Electrified Sphere. 611 



method employed is to obtain solutions of the primary electro- 

 magnetic relations which satisfy definite surface conditions, 

 and neither the relations nor the conditions are dispensed 

 with at any stage. After a calculation of the mechanical 

 reaction on the sphere has been made, the motion of the 

 sphere is worked out by the principles of Newtonian dynamics, 

 and Walker contends that this method, by its direct nature, 

 is the one most fitted to yield correct results. With this 

 view it seems necessary to agree, and as the method does 

 lead to a different formula for the electrical inertia, and, 

 moreover, indicates a redistribution of the charge in certain 

 cases of motion which is again contrary to the results of the 

 quasi-stationary principle, this principle has perhaps been 

 pushed too far. Its use is therefore not to be regarded as 

 definitely justified in cases of accelerated motion, until its 

 exact limits of validity have been examined in a more formal 

 manner, and the more direct method seems preferable in 

 every way for the solution of special problems. But on the 

 other hand, the conditions holding inside a conductor in a 

 state of accelerated motion are at present quite unknown, 

 and there is no certainty that the evanescence of either the 

 tangential electric force or electromagnetic force, conditions 

 hitherto used for a perfect conductor, at all represent the 

 facts. It is difficult to believe that there could be no elec- 

 trical effect inside a conductor with an acceleration, and all 

 that can be done at present apparently is to work out the 

 consequences of various possible assumptions. Thus Walker's 

 results do not necessarily disprove the quasi-stationary 

 principle for small accelerations, and the results of the 

 present paper will be found to cast some doubt upon the 

 theory that the usual treatment of the perfect conductor is 

 still valid when its motion is accelerated. 



The object of the paper is a brief discussion of the initial 

 motion under a small field of electric force, or a small force 

 of a purely mechanical nature, of a sphere whose charge is 

 initially uniform, and whose mass is purely of electric origin. 

 Walker states in his first paper that when the Newtonian 

 inertia is zero, the damped harmonic vibration present at the 

 beginning f the motion becomes evanescent, and it is 

 impossible to satisfy all the initial conditions, so that his 

 solution fails in this case. The formal deduction of this 

 solution as a limiting case from Walker's formulas is attempted 

 in the present paper. 



Prof. A. W. Conway, in a recent paper *, has concluded 

 that when a charged sphere without Newtonian mass is 

 * Proc. Royal Irish Academy, xxviii. p 1. 



2 S2 



