288 WITHDEAWN FROM THE ACTION OF GEAVITY. 



concerns eq^uilibrium, whether this parallelism exists in relation to one couple of 

 faces or to another; the lamina may, therefore, equally occupy three positions, 

 and it may readily be supposed that a slight cause suffices to decide its destina- 

 tion. Thus, when the frame is withdrawn from the glyceric liquid, the lamina 

 in question is found sometimes parallel to the anterior and posterior faces, some- 

 times parallel to the faces of the right and left, and it sometimes happens that 

 it is even placed horizontally. Further, it may be made to pass at will, and 

 several times in succession, from one of these three positions to another ; for this 

 purpose it is sufficient to blow very gently, on one of its edges by the face of 

 the frame on the side of which this edge presents itself; the lamina is then seen 

 to shrink in the direction of the blowing, to be reduced to a simple line, then to 

 be reproduced in its new position. These last phenomena were pointed out to 

 me by M. Van Eees, who was so obliging as to repeat my experiments in Hol- 

 land. 



In the second place a laminar system may be forced to deviate from our law 

 according to which it should not include any portion of air imprisoned on all 

 sides by films, and then, in several frames, we obtain by proper management 

 new and very pleasing results. The process, which was likewise indicated to 

 me by M. Van Eees, consists in producing at first the ordinary system, then 

 again immersing the inferior face of the frame to the extent of some millimetres, 

 and withdrawing it anew; there is thus formed, in this face, a plane film which 

 confines the air between it and the oblique films proceeding from the sides of 

 this same face, and which, immediately climbing up between these oblique films, 

 drives the portion of air before it, giving rise to a new system, which is symmet- 

 rical when circumstances will permit. For instance, with the cubic frame, the 

 new system, which is represented at Fig. 42, contains in its pjo-, 42 



middle a laminar cube attached by its edges to the films pro- 

 ceeding from the solid edges ; only the edges, and consequently 

 also the faces of this laminar cube are slightly convex, which is 

 easily explained by the law relating to the angles formed by 

 liquid edges with one another. So, too, with the frame of the 

 tetrahedron, the new system contains in its midst a laminar 

 tetrahedron with convex edges and faces. Analogous results 

 are obtained with the frame of the pentagonal as Avell as that of j ^\, 

 the hexagonal prism ; but that of the triangular prism gives a | 

 non-symmetrical figure. That of the octahedron, if one of its j ^ 

 faces be re-immersed parallel to the surface of the liquid and be \//^ 



withdrawn in the same way, furnishes a symmetrical result, 



in which, however, the central laminar octahedron has four faces triangular and 

 the four others hexagonal. These systems are evidently mixed ones, in which 

 a part of the films is of mean curvature null, while the other is of mean curva- 

 ture finite and constant. Again : if, after having realized one of these mixed 

 systems, we break one of the films which compose the central polyhedron, the 

 whole is seen to return instantly, or in a very short time, to the ordinary system. 

 For instance, when, in the mixed system of Fig. 42, we break off one of the 

 films of the laminar cube, the system immediately resumes the arrangement of 

 Fig. 28. This again is a curious transformation. For breaking these films it 

 is best to use a point of filtering paper. 



In the third place, if, after having formed the ordinary system of the cube, 

 (Fig. 28,) we break, by the means just indicated, the quadrangular lamina, the 

 system immediately assumes a wholly different and equally regular arrangement ; 

 the new system presents a void in the middle, but it may still be considered as 

 perfect in the sense that films proceed from all the solid edges. So when, in the 

 system of the quadrangular pyramid (Fig. 22) we break the superior lamina, a 

 *iew and beautiful system is obtained, which in like manner is perfect, though 

 also presenting a void in the middle. Finally, an analogous result is brought 



