36G THE FORMS OF CELLS [ch. 



viously has its minimal area in the form of a plane. So long as our 

 wire ring lies in one plane (however irregular in outline), the film 

 stretched across it will still be in a plane; but if we bend the ring 

 so that it lies no longer in a plane, then our film will become curved 

 into a surface which may be extremely comphcated, but is still the 

 smallest possible 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 

 the utmost; and when the film is curved, this 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 across 

 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 Kquid layer, with a free surface 

 within and another without, and each of these two surfaces exercises 

 its own independent and coequal tension and its 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 cy finder 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 down- 



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

 of the molecular forces. 



t It follows that the tension of a bubble, depending only on the surface-conditions, 

 is independent of the thickness of the film. 



