208 THE FORMS OF CELLS [ch. 



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 fotential 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 Me^ 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 Cq, 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 froprietate gaiidentes" 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. 



