of a Liquid Mass without Weight. 133 



equality of the angles formed by liquid edges which meet at a point. 

 To take a few examples. First, in the system formed by the cubic 

 skeleton, there is, as I have stated above, a small quadrangular 

 film ; but since the angles of this film must, in accordance with 

 what precedes, have the value 109° and a fraction, it is evident 

 that its sides must be slightly convex towards the outside ; and 

 this is just what happens in the figure which actually forms. 

 Again, the system of films formed by the hexagonal prismatic 

 skeleton contains at its centre a hexagonal film ; but the angles 

 of a regular hexagon with rectilinear sides being considerably 

 greater than 109°, namely 120°, it is plain that the sides of this 

 film must be concave, which is really the case. Lastly, the 

 pentagonal prismatic skeleton yields a system of films having 

 at its centre a pentagonal film ; and as the angles of a regular 

 pentagon with straight sides are 108°, or very nearly 109°, the 

 sides of the film in question ought not to show any curvature 

 perceptible by the eye; accordingly they appear to be recti- 

 linear. 



The foregoing laws being well established, I apply them to 

 another class of complex systems of films, namely, to the froth 

 which forms on certain liquids, such as champagne, beer, 

 &c. This froth, as every one knows, is made up of a multitude 

 of small films or partitions which confine between them small 

 quantities of gas; accordingly, notwithstanding that it all seems 

 to be governed by chance, it ought to obey the laws in question. 

 Consequently these innumerable partitions must necessarily be 

 everywhere joined three by three and at equal angles, and all the 

 edges must be so distributed that four always meet at the same 

 point and make equal angles with each other. I verify these con- 

 clusions experimentally, at least so far as regards the number of 

 films which meet in one edge, or the number of edges which 

 meet at one point, by blowing air under the surface of the gly- 

 cerine solution, thus producing above the liquid an edifice formed 

 of large chambers separated by partitions, just as children do 

 with soap-water. The structure of such an edifice is evidently 

 similar to that of froth, but the size of the partitions of which 

 it is made up makes it possible for the eye to examine the in- 

 terior. 



I next return to the systems of films formed by iron-wire 

 skeletons. Another law, which I enounced in my Fifth Series of 

 researches, is that in all these systems the mean curvature of 

 each film is equal to nothing. All these films are, in fact, in 

 contact with the free atmosphere on both sides, and therefore 

 evidently cannot exert any pressure upon the air either in one 

 direction or in the other — a condition which, according to what 

 is proved in the Fifth Series, further requires that the mean 



