V. The initial accelerated motion of electrified systems of finite extent, and the reaction produced by the resulting radiation

As far as I am a ware, the problem of the electrodynamics of accelerated motion of finite bodies has not been seriously attacked. Attention has been mainly directed to the question of very small charged bodies, and even in this case the results are not as exact as one could desire, in view of the important bearing they have on the theory of the constitution of matter. Among results which have been generally accepted two call for special attention. The first of these is the equation of linear motion of a small charged sphere determined by L orentz (‘ Theorie Electromagnetique,’ p. 124). In the usual notation this equation is (m +m ')ẍ —kẍ = X, wherem' = 2/3e2 /aC2 andk = 2/3e'2 /C'3 ,e being the charge anda the radius of the sphere.