268 WITHDKAWN FROM THE ACTION OF GEAVITY. 



three caps being first united, the fourth unites itself with two of them ; in this 



arrangement, the four centres will be at the summits of a lozenge, and we 



shall have the system whose base is represented 



by Fig. 19, where there are five partitions. This 



system also is evidently, by reason of its symmetry, 



a system of equilibrium ; but here not more than 



three partitions terminate at the same liquid edge, 



forming between them angles of 120°. Now, if we/ 



attempt to realize on the glass' plate the first of \ 



these two systems, we shall either not succeed, or, if 



produced at all, its duration will be inappreciable, 



and it passes rapidly into the second. The second 



system is obtained directly without difficulty, and 



persists. Hence we may conclude that in the former system the equilibrium 



is unstable, and it thus becomes probable that four partitions terminating at 



the same edge cannot coexist. We may further remark that, in the laminar 



assemblage of Fig. 11, the semicircular liquid edge which unites the two 



spherical caps is only common to three films, namely, to these tAvo caps and to 



the partition; and these three films, we know, form between them equal angles. 



In the assemblage of fig. 17, likewise, each of the liquid edges which unite the 



caps two by two is like that which, unites the three partitions, only common 



to three films forming between them equal angles ; again, this is evidently the 



case in the assemblage of Fig. 19. 



Let us compare these facts with one of those shown by all the laminar systems 

 which occupy my polyhedral frames of iron wire, when these are withdrawn 

 from the saponaceous or the glyceric liquid. It has been seen (5th series, § 19) 

 that in each of these systems there are never more than three films terminating 

 at the same liquid edge. Here then is a general law of laminar assemblages. 

 Moreover, it follows from considerations before stated (§ 8) that the angles under 

 which the three films intersect one another must always be equal or differ only 

 by inappreciable quantities, and this equality is easily verified, as we shall 

 presently see, in all those systems which are composed of plane films. 



With regard to the instability of a system in which more than three films 

 should terminate at the same liquid edge, I will recall, as another proof, the 

 curious phenomenon presented in the production of the laminar system of the 

 regular octahedron, when I was experimenting with oil in the interior of the 

 alcoholic liquid. When, as I have said, (2d series, § 35,) after having 

 formed the full octahedron, we gradually withdraw oil from it by means of the 

 small syringe, the eight faces grow concave equally and at once, 

 and when the films begin to form, but are still joined by thick ^ig- 20 

 masses, they are all directed towards the centre of the figure, so 

 that the system tends towards the arrangement which I here 

 present anew, (Fig. 20,) an arrangement in which four films 

 terminate at one liquid edge ; but when the thickness of the 

 masses of junction is diminished to a certain limit, a sponta- 

 neous change .is effected, and the system takes definitively 

 another form. I will now add that, in this latter form, no 

 more than three films terminate at each liquid edge. In fine, 

 the laminar system of the quadrangular pyramid offers another analogous ex- 



