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 ãprinciple of minimal areasã; 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 ãcapacity factorã is involved in the one case, and the ãintensity factorã 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 equiôÙlibôÙrium. 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 ãprinciple of least actionã of Maupertuis, the ãlineae curvae maximi minimive proprietate gaudentesã 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}
In all cases where the principle of maxima and minima comes into play, as it conspicuously does in the systems of liquid films which are governed by the laws of surface-tension, the figures and conformations produced are characterised by obvious and remarkable symmetry. Such symmetry is in a high degree charôÙacôÙterôÙisôÙtic of organic forms, and is rarely absent in living things,ãsave in such cases as amoeba, where the equiôÙlibôÙrium on which symmetry depends is likewise lacking. And if we ask what physical equiôÙlibôÙrium has to do with formal symmetry and regularity, the reason is not far to seek; nor can it be put better than in the following words of Machãs10. ãIn every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. In each deformation positive and negative work is done. One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equiôÙlibôÙrium, is thus supplied by symmetry. Regularity is successive symmetry. There is no reason, therefore, to be astonished that the forms of equiôÙlibôÙrium are often symmetrical and regular.ã
As we proceed in our enquiry, and especially when we approach the subject of tissues, or agglomerations of cells, we shall have from time to time to call in the help of elementary mathematics. But already, with very little mathôÙeôÙmatôÙiôÙcal help, we