Complex sentence: So the electrostatic energy behaves as having some sort of "apparent" electromagnetic mass, which can increase the ordinary mechanical mass of the bodies, or in more modern terms, the increase should arise from their electromagnetic self-energy.
Split into simpler sentences: So the electrostatic energy behaves as having some sort of "apparent" electromagnetic mass, which can increase the ordinary mechanical mass of the bodies. Or in more modern terms, the increase should arise from their electromagnetic self-energy.