of a Liquid Mass without Weight. 131 



the drawing. The drawing, however, having been made upon 

 the supposition of the equality of the angles formed at the junc- 

 tion of the films, this superposition proves that the supposed 

 equality really exists. 



In the systems that we have been examining, one and the 

 same edge does not unite more than three films ; and in the 

 system formed by the junction of three hemispheres, four edges 

 come together in one point, namely that which unites the three 

 partitions, and those which unite the three hemispheres, two and 

 two. Now, as I have set forth in my Fifth Series of researches, 

 in the systems of films formed within skeletons of iron wire, we 

 never find more than three films coming together at a single 

 edge, nor more than four edges coming together at the same 

 point : these are, then, two general laws of the combinations of 

 films. 



I endeavour to find by experiment upon what these laws can 

 depend, and I arrive at the conclusion that the equilibrium of 

 every system of films in which more than three films come 

 together in one edge, or more than four edges unite at the same 

 point, is unstable. The following are two of my experiments on 

 this subject. 



1. If an iron- wire skeleton is constructed by the junction of 

 two squares so arranged that two opposite sides of each square 

 bisect two opposite sides of the other at right angles, and if each 

 square be supposed to be occupied by a plane film, the two films 

 will cut each other, forming a straight liquid edge joining the 

 points of intersection of the solid edges : the system so formed 

 will evidently, in consequence of its perfect symmetry, constitute 

 a system of equilibrium ; but the solid edge will be the line of 

 junction of four films. Accordingly, when such a skeleton is 

 taken out of the glycerine solution, it is never found to be occu- 

 pied by the system of films above described ; in that which is 

 actually formed there are two curvilinear edges starting from the 

 two points of intersection of the wires and bordering a plane film, 

 while two curved films starting from the solid wires attach them- 

 selves to each of these edges ; so that the law of three films 

 to a single edge is satisfied. Now the first system being, as I 

 have remarked, a system of equilibrium, and being more simple 

 than the one which is actually formed, we are forced to conclude, 

 from the fact of its never being produced, that it would be un- 

 stable. 



2. If we imagine twelve plane triangular films starting respect- 

 ively from the twelve solid edges of a cubic skeleton, and meet- 

 ing by their apices at the centre of the cube, we shall again have 

 a system which, by reason of its symmetry, is a system of equi- 

 librium. It is easy to see that in a figure so formed, never more 



