216 THE FORMS OF CELLS [ch. 



surface which can be drawn continuously across the uneven 

 boundary. 



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*) 

 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 |. 



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 (/j) 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. 



* Or, more strictly speaking, unless its thickness be less than twice the range 

 of the molecular forces. 



I It follows that the tension, depending only on the surface-conditions, is 

 independent of the thickness of the film. 



