SURFACES OF DISCONTINUITY 667 



will fall according to the usual equilibrium rule [617]. As 

 they are supposed to be equal at the midway level it follows that 

 above that level the potential of the water in the film is greater 

 than that in the atmosphere and there the water will escape 

 into the atmosphere from the film, with the reverse process 

 occurring below. Following a similar line of argument the 

 reader will now find that the subsequent statements on page 

 310 are not difficult to verify. - 



The material in pages 312, 313 will be referred to in the brief 

 account of experimental work on soap films which follows. 



58. Foams. The Draining of a Film. The "Gibbs Ring" 



Apart from the blowing of soap bubbles the most common 

 illustration of the existence of liquid films is to be found in 

 foam, which is really a collection of bubbles of various sizes 

 which coalesce according to the following simple rule: when 

 three films meet they intersect in a line and their planes are 

 equally inclined, i.e., at an angle of 120°. Six such films can 

 meet at one point with the four common edges also passing 

 through this point in a manner which we have already discussed 

 at an earlier stage of the commentary. Thus in the interior of 

 the foam each bubble is bounded by hexagonal plane faces (in 

 general irregular hexagons). The pressure of the confined gas 

 is everywhere the same. Only the outer faces between the foam 

 and the atmosphere are curved to any extent, and only at these 

 faces is there any difference of pressure on the two sides. The 

 whole mass quickly drains to the "black stage" by the inter- 

 connected liquid channels. The existence of foam indicates 

 the presence in the liquid of capillary active substances such 

 as saponin. Such substances are to be found in many plants, 

 and the occurrence of stable foams is very marked on that 

 account in tropical rivers. 



Actually the line of intersection of three films is not a "line" 

 but a channel of finite cross-section which is in the form of a 

 curvilinear triangle as in Figure 10, where A, B, C, represent 

 three adjacent bubbles, D being the channel of liquid. On 

 account of the curvature the pressure of the gas in A, B or C 

 is greater than the internal pressure of the liquid in D, while 



