V] OF LIQUID FILMS 215 



wliich, under the influence of surface tension, a surface can possibly 

 assume. In doing so, we are obviously limited to conditions 

 under which other forces are relatively unimportant, that is to 

 say where the "surface energy" is a considerable fraction of 

 the whole energy of the system ; and this in general will be 

 the case when we are dealing with portions of liquid so small 

 that their dimensions come within what we have called the 

 molecular range, or, more generally, in which the "specific 

 surface" is large*: in other words it will be small or minute 

 organisms, or the small cellular elements of larger organisms, 

 whose forms will be governed by surface-tension ; while the 

 general forms of the larger organisms will be due to other and 

 non-molecular forces. For instance, a large surface of water sets 

 itself level because here gravity is predominant; but the surface 

 of water in a narrow tube is manifestly curved, for the reason 

 that we are here dealing with particles which are mutually within 

 the range of each other's molecular forces. The same is the case 

 with the cell-surfaces and cell-partitions which we are presently 

 to study, and the effect of gravity will be especially counteracted 

 and concealed when, as in the case of protoplasm in a watery 

 fluid, the object is immersed in a liquid of nearly its own specific 

 gravity. 



We have already learned, as a fundamental law of surface- 

 tension phenomena, that a liquid film in equilibrium assumes a 

 form which gives it a minimal area under the conditions to which 

 it is subject. And these conditions include (1) the form of the 

 boundary, if such exist, and (2) the pressure, if any, to which the 

 film is subject; which pressure is closely related to the volume, 

 of air or of liquid, which the film (if it be a closed one) may have 

 to contain. In the simplest of cases, when we take up a soap- 

 film on a plane wire ring, the film is exposed to equal atmospheric 

 pressure on both sides, and it obviously 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 complicated, but is still the smallest possible 



* Cf. p. 32. 



