H. Poincaré, Sur une théorème de M. Liapounoff relatif a l’équilibre d’une masse fluide, Comptes Rendus de L’Academie des Sciences 104, 622–625 (1887).
As discussed by G.C. Evans, Poincaré assumes tacitly that there do exist one or more bodies of a given volume, with smooth boundaries, which provide relative minima for the Coulomb energy with respect to neighboring forms; and his treatment amounts to a proof that among these the sphere provides the absolute minimum.