MICROSCOPIC FOAMS 33 



they assume the shape of a spherical drop, if not acted upon 

 by any special influence, whether from within or from with- 

 out. Their surface will therefore be curved like that of a 

 sphere. Nevertheless, it is of course impossible for the 

 surface of such a froth to be a simple spherical surface ; 

 the tension of the lamellae, which attach themselves to 

 the surface, naturally tend to bring about a dipping in of 

 the surface at these points of attachment, so that each 

 alveolus or froth vesicle of the superficial layer projects 

 slightly over and above the general surface of the sphere, even 

 though with a very feeble curvature. As a matter of fact, 

 I could never observe this projection of the alveoli of this 

 layer with perfect distinctness in the finest froths, although 

 it often wore the appearance ; on the other hand, in the 

 coarser ones it was very prominent (see Photogr. III.) At 

 the point of insertion of a lamella reaching to the surface, 

 the tensions a and 6 of the two external curved lamellae 

 (see Fig. 3), touching one another, come into effect, and 

 maintain an equilib- 

 rium with the ten- 

 sion c of the lamella 

 first mentioned. If 

 this most external 

 layer of froth is formed 

 of alveoli of equal size, 



., . ,1 Fig. 3. 



it is easy to see that 



the lamellae of the external layer that reach to the surface 

 must all be placed vertically to it, so that equilibrium may be 

 established. Since, however, the three lamellae meeting one 

 another in one edge at the surface or rather their tangen- 

 tial planes must form angles of 120 each to each, at the 

 edge in which they meet, if both the external lamellae lie 

 nearly in the general surface of the sphere, then the lamella 

 reaching from the interior must be directed radially to the 

 surface, in order to form equal angles with both of them. 



One question still requires consideration before we 

 proceed to further investigations. It was noticed that the 

 drops of oil-lather behave as an ordinary fluid, inasmuch as 

 when other factors are excluded, they assume a spherical 



3 



