WITHDRAWN FROM THE ACTION OF GRAVITY. 



423 



films vibiblj curved, is always seen by tlie new process to be composed of plane 

 films ; this singular difference I shall attempt hereafter to ex- 

 plain. I have here presented as an example (figure 7) the 

 laminar system of the cubic frame ; it is composed of twelve 

 films, proceeding respectively from the twelve edges, and all 

 terminating at a single quandraugular lamella or little film, situ- 

 ated at the middle of the assemblage of films. The sides of this 

 lamella are slightly curved, as well as all the other liquid edges, 

 and consequently all the films, with the exception of the lamella, 

 have feeble curvatures. The curvatures of the liquid edges 

 which proceed from the summits of the frame are too slight to 

 be indicated in the figure. By an error, for which I can scarcely 

 account, this system is badly executed in the plates of the 

 second series ; the central lamella, besides that it is seen obliquely and not in 

 front, is much too small. I will call to mind that my frame has a length of 

 seven centimetres to the side. In order to plunge it in the glyceric liquid it is 

 held by the extremity of the handle of the fork, which is soldered to it. 



§ 19. The laminar systems thus developed in the air by means of the glyceric 

 liquid have excited the admiration of all to whom I have shown them. They 

 are of a perfect regularity, their liquid edges have an extreme delicacy, and their 

 films display after some time the richest colors. The arrangement of these films 

 is governed by simple and uniform laws, of which the following is a statement: 

 1. From each of the edges of the solid frame proceeds a film. 2. If care be 

 taken that there be no bubbles of air on the surface of the liquid in the vessel 

 b'efore immersing the frame, the laminar system will present no space closed on 

 all sides by films ; in other words, each of the films of the system will be in 

 contact by its two faces with the ambient air, 3. At the same liquid edge not 

 more than three films ever terminate, and these make with one another equal 

 angles. 4. When several liquid edges terminate at the same point in the inte- 

 rior of the system, the edges are always four in number and form between them 

 equal angles. 5. When the conditions can be fulfilled by plane surfaces, the 

 films take that form; when this is impossible, all the films, or several of them, 

 are more or less curved, but always in such a manner as to constitute surfaces 

 of mean curvature null ; the first takes place, for example, in the systems of the 

 tetrahedron, of the triangular prism, and the octahedron; the second in those of 

 the cube, the hexagonal prism, &c. 



The system of the quadrangular pyramid, such ias it is represented in the 

 plates of the second series, would form an exception to the fourth of the above 

 laws; but, as I shall show in the next series, when I shall examine the laminar 

 systems under a theoretical point of view, this is attributable to the fact that in 

 realizing the system in question with oil within the alcoholic mixture, the ex- 

 haustion of the oil cannot be carried far enough, whence the liquid edges retain 

 too great thickness. When the present process is employed, the figure is modi- 

 fied, and fully satisfies all the laws. 



A frame being given as to its form, it might be proposed, as a geometric prob- 

 lem, to occupy the interior of it with an assemblage of surfaces subject to the 

 preceding laws; but the solution would be, in general, very difficult. Now, if 

 we have recourse to experiment, the liquid, in disposing itself in films, plays 

 the geometer, and it is an extremely curious thing to see it always resolve the 

 question in a simple and elegant manner, at least if the solution be possible. 

 For these experiments we may, in strictness, employ, in place of the glyceric 

 liquid, a simple solution of soap. In that case the figures will have little dura- 

 tion, but it is always in our poAver to renew the immersion of the frame, and 

 thus pursue our observation. 



§ 20. I have several times already, in the second and fourth series, insisted 

 on the principle that, for every figure of equilibrium in relief there is an identi- 



