THE FIGURES OF EQUILIBFJUM OF A LIQUID MASS 275 



In describing (2d series, §§31 and 33) the operation by means of which the 

 himinar system of the cube is produced with oil in the alcoholic liquid, it was 

 said that we arrive, with certain precautious, but only during the action of the 

 small syringe, at the system of Fig. 34 ; and here again is curious proof in sup- 

 port of what precedes. In effect, the extremity of the beak of the syringe, 

 Avhich occupies the centre of the system, constitutes, at that centre, a solid 

 point, and we know that this condition suffices to maintain the stability : hence, 

 as Avas said in the paragraphs cited, a change takes place when the syringe is 

 n-moved. If it is withdrawn slowly, we observe the development of the quad- 

 rangular additional lamina of Fig. 28, and if quickly, the rapid formation of a 

 small central mass of a certain thickness, and the system is still maintained ; 

 but we know (§ IG) that a small thickish mass can give stability to a system 

 which would be unstable without its presence. 



We can liktwise obtain, and in a permanent manner, with the glyceric liquid, 

 the system of Fig. 34, but it is by introducing into this system also a solid 

 part ; it suffices, in effect, to stretch from one summit of the frame to the oppo- 

 site summit a very fine iron wire ; yet, when the fiame thus arranged is with- 

 drawn from the glyceric liquid, the system which occupies it is not immediately 

 that in question; it still contains a quadrangular lamina, but this is much smaller 

 than that of Fig 28, and is not placed symmetrically as regards the frame; it 

 rests by one of its summits on the middle of the solid diagonal, but it is soon 

 observed to diminish in extent, spontaneously, until it is completely annulled, 

 so that the system then becomes that of Fig. 34. Here things rest, and the 

 system rema'ns perfectly stable in that state, at least when the decrease of the 

 lamina is effected with sufficient slowness. But often this decrease is more rapid, 

 and then another singular phenomenon presents itself. At the instant wlien 

 the lamina is annulled, another much smaller is seen to be formed, situated on 

 the opposite side of the solid diagonal, having its plane perpendicular to that of 

 the first, and resting, no longer by a summit, but by the middle of one of its 

 sides on the middle of the solid diagonal;* then this second lamina decreases 

 and is annulled like the preceding. In this case, therefore, the system only at- 

 tains its definitive form by a species of oscillation. 



I shall indicate in another series the reason of the instability of systems in 

 which more than three films terminate at a single liquid edge, and more than 

 four edges at a single liquid point ; but it will be seen, in the mean time, that 

 stability must exist in the case of three films at the same liquid edge, and of 

 four edges at the same liquid point ; for three is evidently the smallest possible 

 number of films terminating at one single edge, and there can be no difficiilty 

 in admitting that four is the smallest possible number of edges terminating at 

 the same liquid point. 



§ 22. The two laws which we have been discussing must now, I think, be 

 regarded as well established for all laminar assemblages. Now, these laws con- 

 duct us to a very remarkable consequence. The froth which forms on certain 

 liquids, as, for instance, on champagne wine, beer, soap-water agitated, white of 

 eg'^ beaten, &c., are evidently laminar assemblages, composed of a multitude of 

 laminaj or partitions, which intersect one another and confine small portions of 

 gas. Consequently, though everything therein seems guided by accident, they 

 must be subject to these same laws, hence their innumerable partitions necessa- 

 rily unite throughout, three by three, under equal angles, and all their edges 

 are so distributed that there are always four terminating at the same point and 

 forming these equal angles. 



I have verified these facts by the following experiment : The bowl of a pipe 



* My frame having been accidentally put out of shape and then repaired, the second 

 lamina, when it was produced, no longer placed itself in the manner above indicated. The 

 difiorence proceeded, no doubt, from a slight irregularitj' existing in the frame, either before 

 or after its reparation. 



