OF FIGURES OF EQUILIBRIUM 



377 



hardly changing outHne of a jet or waterfall is but in pseudo- 

 equiHbrium; it is in a steady state, dynamically speaking. Many 

 puzzling and apparent paradoxes of physiology, such (to take a 

 single instance) as the maintenance of a constant osmotic pressure 

 on either side of a cell-membrane, are accounted for by the fact 

 that energy is being spent and work done, and a steady state or 

 pseudo-equilibrium maintained thereby. 



Before we pass to biological illustrations of our surface-tension 

 figures we have still another matter to deal with. We have seen 

 from our description of two of Plateau's classical experiments, that 

 at some particular point one type of surface gives place to another ; 

 and again we know that, when we draw out our soap-bubble into 

 a cyhnder, and then beyond, there comes a certain point at which 

 the bubble breaks in two, and leaves us with two bubbles of w^hich 

 each is a sphere or a portion of a sphere. In short there are certain 

 limits to the dimensions of our figures, within which limits equi- 

 librium is stable, but at which it becomes unstable, and beyond which 

 it breaks down. Moreover, in our composite surfaces, when the 

 cyhnder for instance is capped by two spherical cups or lenticular 

 discs, there are well-defined ratios which regulate their respective 

 curvatures and their respective dimensions. These two matters we 

 may deal with together. 



Let us imagine a Hquid drop which in 

 appropriate conditions has been made to 

 assume the form of a cylinder; we have 

 already seen that its ends will be capped 

 by portions of spheres. Since one and 

 the same liquid film covers the sides and 

 ends of the drop (or since one and the 

 same delicate membrane encloses the 

 sides and ends of the cell), w^e assume 

 the surface-tension (T) to be everywhere 

 identical; and it follows, since the 

 internal fluid-pressure is also every- 

 where identical, that the expression (IjR + 1/i?') for the cylinder 

 is equal to the corresponding expression, which we may cafl 

 (1/r + 1/r'), in the case of the terminal spheres. But in the 



