§ 1. The object of this communication is to partially realise the hope expressed at the end of my paper of July 1 and July 15, 1889, on the “Molecular Constitution of Matter”:—“The mathematical investigation must be deferred for a future communication, when I hope to give it with some further developments.” The italics are of present date.

Following the ideas and principles suggested in §§ 14–20 of that paper (referred to henceforth for brevity as M. C. M.), let us first find the work required to separate all the atoms of a homogeneous assemblage of a great number n of molecules to infinite distances from one another. Each molecule may be a single atom, or it may be a group of i atoms (similar to one another or dissimilar, as the case may be) which makes the whole assemblage a group of i assemblages, each of n single atoms.