134 On the Figures of Equilibrium of a Liquid Mass. 



curvature at each point of the films in question should be equal 

 to nothing. It would be difficult to verify this law very strictly 

 by observation ; but it can be seen at least that, whenever a 

 film exhibits a curvature in one direction, it exhibits an opposite 

 curvature in the direction at right angles. 



I have also enounced, finally, two other laws in my Fifth Series, 

 and I examine their causes in the memoir of which this is an 

 abstract ; but as they are of secondary importance, I will not 

 speak of them here. 



Lastly, I examine theoretically and experimentally the manner 

 in which film-systems are formed on wire skeletons. I will con- 

 fine myself here to a single example, namely, to the formation of 

 the system of films of the six-sided prism, when a skeleton of 

 that form is removed from the liquid, the axis of the prism 

 being kept vertical. At the moment that the lower base is 

 about to emerge from the liquid, the system consists only of 

 six plane films, which occupy respectively the six lateral faces 

 of the prism ; and it is obvious that these films cannot have any 

 tendency to enter towards the centre of the skeleton, because 

 they make with each other the angle of exactly 120°, which two 

 films belonging to the same system always make with each 

 other. When the lower base emerges, it remains at first united 

 to the surface of the liquid by a film, which soon contracts at 

 the bottom, closes up and separates from the liquid, and then, 

 as a plane film, comes to occupy the base in question. But this 

 plane film, making thus right angles with the films which oc- 

 cupy the lateral faces, cannot remain in such a position ; accord- 

 ingly it is seen to ascend between the others, bending them in 

 two by drawing them to itself, and thus diminishing them in size ; 

 at the same time six new films are formed, starting from the solid 

 wires and ending in the liquid edges which unite the first films 

 two and two. Equilibrium is at last established, when the 

 ascending film has arrived halfway up the prism. 



By this examination of the mode of formation of systems of 

 films, I am led to divide them into three classes — namely, per- 

 fect systems, imperfect systems, and abortive systems. 



In those of the first class, each solid wire serves as a base, 

 along its whole length, for only one film. I call them perfect, 

 because all the films depend from each other throughout their 

 whole extent, and because such of the liquid edges as have one 

 end upon the skeleton start from its extreme points. With a 

 very few exceptions, such systems are formed in the skeletons 

 of all the polyhedra whose dihedral angles are all of them less 

 than 120°, — such, for instance, as those of the tetrahedron, octa- 

 hedron, cube, &c. 



In some systems, parts of the solid wires of the skeleton serve 



