PROCEEDINGS 



OF 



THE ROYAL IRISH ACADEMY 



PAPERS READ BEFORE THE ACADEMY 



I. 



ON THE MOTION OF AN ELECTRIFIED SPHEIIE. 



By AETHUE W. CONWAY, M. A. (Oxon. and E. U. L), D. Sc, 

 Professor of Mathematical Physics, University College, Dublin. 



Bead December 13, 1909. Oidered for Publication January 12. Published February 24, 1910. 



CONTENTS. 



Page. 

 I. Introduction and Summary, . . 1 

 II. The Electromagnetic Equations and the 



Boundary Conditions, ... 2 

 III. The Harmonicoid Functions of the 



Fii'st and Second Kinds, . . 5 



Page. 

 IV. Method of General Solution and 



Examples, . . . . . 7 



v. On Oscillatory Distributions, . . 9 



VI. Quasi-stationary Motion, . . .11 



VII. Dynamical Results 13 



I.— INTKODUCTION and SUMiLLRY. 



In this Paper the following problem is dealt with : — A sphere perfectly 

 conducting and supposed not to be subject to a Lorentz-Fitzgerald shrinkage 

 is charged and moved in any field : required the distribution of electricity on 

 its surface. It was shown long ago by Searle that, if its velocity was uniform, 

 the surface-density remained uniform ; and an important paper by Walker,* 

 dealing with several cases of initial motions, was sufficient to show the 

 complexity of the problem. In any field of force, and for any state of 

 motion, there is an infinite number of solutions, namely, the simplest solution 

 and the solution due to the free oscillations of the sphere. In all cases the 

 current on the sphere can be divided (in a hydrodynamical sense) into an 

 irrotational and a rotational current. These give rise to two classes of 

 functions which we term harmonicoid functions of the first and second type 

 respectively. These functions are generalized forms of similar functions 

 employed by Lamb, Love, and others in the problem of the fixed sphere. 



*G. W. Walker, Proceedings of the Royal Society, vol. Ixxvii, p. 260. 



R. I. A. PROC, VOL. XXVIll., SHOT. A. [1] 



