entire system, the _sum of the surface energies_ is a minimum; and, while this is attained by the _sum of the surfaces_ being a minimum in the case where the energy is uniformly distributed, it is not necessarily so under non-uniform conditions. In the diagram (Fig. 118) if the energy per unit area be greater along the contact surface _cc′_, where cell meets cell, than along _ca_ or _cb_, where cell-surface is in contact with the surrounding medium, these latter surfaces will tend to increase and the surface of cell-contact to diminish. In short there will be the usual balance of forces between the tension along the surface _cc′_, and the two opposing tensions along _ca_ and _cb_. If the former be greater than either of the other two, the outside angle will be less than 120°; and if the tension along the surface _cc′_ be as much or more than the sum of the other two, then the drops will stand in contact only, save for the possible effect of external pressure, at a point. This is the explanation, in general terms, of the peculiar conditions obtaining in Nostoc and its allies (p. 300), and it also leads us to a consideration of the general properties and characters of an “epidermal” layer. ―――――――――― While the inner cells of the honey-comb are symmetrically situated, sharing with their neighbours in equally distributed pressures or tensions, and therefore all tending with great accuracy {314} to identity of form, the case is obviously different with the cells at the borders of the system. So it is, in like manner, with our froth of soap-bubbles. The bubbles, or cells, in the interior of the mass are all alike in general character, and if they be equal in size are alike in every respect: their sides are uniformly flattened[361], and tend to meet at equal angles of 120°. But the bubbles which constitute the outer layer retain their spherical surfaces, which however still tend to meet the partition-walls connected with them at constant angles of 120°. This outer layer of bubbles, which forms the surface of our froth, constitutes after a fashion what we should call in botany an “epidermal” layer. But in our froth of soap-bubbles we have, as a rule, the same kind of contact (that is to say, contact with _air_) both within and without the bubbles; while in our living cell, the outer wall of the epidermal cell is exposed to air on the one side, but is in contact with the [Illustration: Fig. 119.]