274 



WITHDRAWN FROM THE ACTION OF GRAVITY. 



Fig. 31 



triangular films which proceed from the solid vertical edges, they are strictly- 

 plane by reason of the symmetry of their position. Tiie sys- 

 tem in question is represented by Fig. 30. 



In the fourth place, if the frame is that of a regular hexag- 

 onal prism, the laminar system is analogous to the preceding in 

 its general disposition, the central film, however, being hexag- 

 onal; but as the angle of two contiguous sides of a regular 

 hexagon is 120°, that is to say, considerably superior 1o our 

 angle of 109i°, the sides of the film in question must be sen- 

 sibly curved towards the interior, and this also is shown in the 

 realized system. The height of the frame which I have em- 

 ployed is to the distance of two opposite sides of the base, or, 

 in other terms, to the diameter of the circle which might be inscribed at that 

 base, as 7 to 6. 



§ 21. The facts I have stated (^§ 16) to show that a system in which more than 

 three films terminate under equal angles at the same liquid edge is in an un- 

 stable state of equilibrium, beat- also upon the systems which present more than 

 four edges terminating at the same time at the same liquid point. The instabil- 

 ity might, therefore, be attributed to this latter circumstance, and it is requisite 

 to determine whether it pertains exclusively to the one or the other, or only to 

 their combination. In order to do so, let us take as a solid frame 

 the assemblage of two rectangles which cut one another at a I'ight 

 angle in the middle of two of their opposite sides (Fig. 31.) The 

 most simple laminar system which we can imagine in this frame 

 would be composed of four plane films occupying, respectively, the 

 four halves of the rectangles, and terminating at a single rectilinear 

 edge a b, (Fig. 32,) which would join the two points -pj^ 

 of intersection of these rectangles. This system, by ° 

 reason of its symmetry, would evidently be a system of 

 equilibrium, and would present no liquid point com- 

 mon to several edges; but the edge a b would be common to four 

 films. Now, when we withdraw this frame from the glyceric liquid, 

 it is never found to be occupied by the system just indicated. In 

 that which is realized, instead of the edge a b, there 

 is (Fig. 33) a plane film terminated by two curved 

 edges, to which the films proceeding from the solid 

 edges attach themselves ; films which, then, are necessarily curved. 

 Here, it will be seen, each of the two liquid edges is common only 

 to three films; and it must be inferred from this, that instability 

 is really a property of laminar systems in which this condition is 

 not fulfilled. 



As to the second circumstance, I will first remark that if, in 

 the cubic frame, we imagine a system of twelve triangular plane 

 films proceeding, respectively, from twelve solid edges, and termi- 

 .nating at the centre of the frame, (Fig. 34.) this system, because 

 of its perfect symmetry, will necessarily be a system of equi- Fig. 34 

 librium, and it is readily seen that at each liquid edge only 

 tliree .films will termimdnate, which, moreover, will form among 

 them equal angles; but there will be eight liquid edges termi- 

 nating at the central point. Now, we know that with the gly- 

 ceric liquid this system is not produced, and that we always 

 obtain that of Fig. 28, in which only four liquid edges terminate 

 at each of the summits of the central quadrangular lamina. 

 From this fact we may conclude that instability pertains also to 

 every system in which one liquid point is common to more than 

 four edges. 



Fig. 33 



