It was Gauss who first shewed after this fashion how, from the mutual attractions between all the particles, we are led to an expression which is what we now call the _potential energy_ of the system; and we know, as a fundamental theorem of dynamics, that the potential energy of the system tends to a minimum, and in that minimum finds, as a matter of course, its stable equilibrium. ―――――――――― We see in our last equation that the term _M_ _e__{0} is irreducible, save by a reduction of the mass itself. But the other term may be diminished (1) by a reduction in the area of surface, _S_, or (2) by a tendency towards equality of _e_ and _e__{0}, that is to say by a diminution of the specific surface energy, _e_. These then are the two methods by which the energy of the system will manifest itself in work. The one, which is much the more important for our purposes, leads always to a diminution of surface, to the so-called “principle of minimal areas”; the other, which leads to the lowering (under certain circumstances) of surface tension, is the basis of the theory of Adsorption, to which we shall have some occasion to refer as the _modus operandi_ in the development of a cell-wall, and in a variety of other histological phenomena. In the technical phraseology of the day, the “capacity factor” is involved in the one case, and the “intensity factor” in the other. Inasmuch as we are concerned with the form of the cell it is the former which becomes our main postulate: telling us that the energy equations of the surface of a cell, or of the free surfaces of cells partly in contact, or of the partition-surfaces of cells in contact with one another or with an adjacent solid, all indicate a minimum of potential energy in the system, by which the system is brought, _ipso facto_, into equilibrium. And we shall not fail to observe, with something more than mere historical interest and curiosity, how deeply and intrinsically there enter into this whole class of problems the “principle of least action” of Maupertuis, the “_lineae curvae maximi minimive proprietate gaudentes_” of Euler, by which principles these old natural philosophers explained correctly a multitude of phenomena, and drew the lines whereon the foundations of great part of modern physics are well and truly laid. {209}