The question of pressure involves not only external pressures acting on the film, but also that which the film itself is capable of exerting. For we have seen that the film is always contracting to its smallest limits; and when the film is curved, this obviously leads to a pressure directed inwards,—perpendicular, that is to say, to the surface of the film. In the case of the soap-bubble, the uniform contraction of whose surface has led to its spherical form, this pressure is balanced by the pressure of the air within; and if an outlet be given for this air, then the bubble contracts with perceptible force until it stretches across the mouth of the tube, for instance the mouth of the pipe through which we have blown the bubble. A precisely similar pressure, directed inwards, is exercised by the surface layer of a drop of water or a globule of mercury, or by the surface pellicle on a portion or “drop” of protoplasm. Only we must always remember that in the soap-bubble, or the bubble which a glass-blower blows, there is a twofold pressure as compared with that which the surface-film exercises on the drop of liquid of which it is a part; for the bubble consists (unless it be so thin as to consist of a mere layer of molecules[283]) of a liquid layer, with a free surface within and another without, and each of these two surfaces exercises its own independent and coequal tension, and corresponding pressure[284]. If we stretch a tape upon a flat table, whatever be the tension of the tape it obviously exercises no pressure upon the table below. But if we stretch it over a _curved_ surface, a cylinder for instance, it does exercise a downward pressure; and the more curved the surface the greater is this pressure, that is to say the greater is this share of the entire force of tension which is resolved in the downward direction. In mathematical language, the pressure (_p_) varies directly as the tension (_T_), and inversely as the radius of curvature (_R_): that is to say, _p_ = _T_/_R_, per unit of surface. {217} If instead of a cylinder, which is curved only in one direction, we take a case where there are curvatures in two dimensions (as for instance a sphere), then the effects of these must be simply added to one another, and the resulting pressure _p_ is equal to _T_/_R_ + _T_/_R′_ or _p_ = _T_(1/_R_ + 1/_R′_)[285]. And if in addition to the pressure _p_, which is due to surface tension, we have to take into account other pressures, _p′_, _p″_, etc., which are due to gravity or other forces, then we may say that the _total pressure_, _P_ = _p′_ + _p″_ + _T_(1/_R_ + 1/_R′_). While in some cases, for instance in speaking of the shape of a bird’s egg, we shall have to take account of these extraneous pressures, in the present part of our subject we shall for the most part be able to neglect them.