Relying on the article of de Leeuw, Perram, and Smith [Proc. R. Soc. London, Ser. A 373, 27 (1980)] we justify the expression of the Hamiltonian actually used in the numerical simulations of electrolyte solutions in a periodic geometry. It involves the itinerant dipole moment M(i) of the charges rather than the electric moment M(B) of the simulation box. The vector M(i) is defined as the electric moment of the particles which were in the simulation box at t=0 and may have diffused away in the neighboring cells in the course of the simulation. Some comments on Stillinger-Lovett conditions are included.