THE FIGURES OF EQUILIBKIUM OF A LIQUID MASS 285 



§ 35. If, in the different systems whicli we have been studying, we compare 

 the central polygonal films with one another, it will be seen that the curvature 

 of their sides goes on increasing from the hexagonal film to the decagonal film, 

 a circumstance which constitutes new facts to be added to those of § 20 in con- 

 firmation of the law relative to the angles under which the liquid edges termi- 

 nate at the same liquid point. The transverse curvature (§ 34) of the oblique 

 films which are directed towards the sides of the central polygonal film being 

 connected with the curvature of these sides, it must be less in the heptagonal 

 prism than in the octagonal, and still less in the hexagonal ; it is because of the 

 weakness of the curvature in question in the last prism, that this yields, when 

 ii has not too much height, a laminar system almost perfect, with its hexagonal 

 film. 



§ 36. In reflecting on the generation of laminar systems, the inquiry has 

 struck me whether there might not be realized, at least in the hexagonal prism 

 and with the frame of § 31, a system devoid of the central polygonal film by 

 withdrawing the frame from the glyceric liquid in such manner that the axis of 

 the prism should be horizontal instead of being vertical, as in the preceding ex- 

 periments. I have consequently so arranged the fork as to be able to operate 

 in that way, and with complete success : I have obtained, indeed, two different 

 systems, according as the frame was Avithdrawn in such a way that tAvo lateral 

 edges emerged at the same time from the liquid, or first one and then simultane- 

 ously the two neighboring ones. These tAvo systems are of the same kind with 

 that Avhich is realized in a pentagonal frame sufficiently high, (§ 30 ; ) that is to 

 say, they are composed of two assemblages of oblique curved films connected 

 with one another by other films directed in the length of the prism. The pro- 

 jection of one of these assemblages on the plane of the base is represented in the 

 Fig. 39 first mode by Fig, 39, in the second by Fig. 40. Fig. 40 

 Nor is this all : to produce the first of these tAvo 

 systems, it is necessary, when half of the frame 

 has been AA'ithdrawn from the liquid, to finish the 

 operation with very great sloAvness ; when we 

 operate without this precaution, there is formed 

 a third system of still another kind, a system of AA'hich, notAvithstanding its sim- 

 plicity, it is quite difficult to give a clear idea either by description or drawing : 

 it contains tAvo curA'^ed hexagonal films, resting, respectively, by one of their 

 sides, on one of those of the bases, and directing themselves obliquely towards 

 the inierior of the frame ; the other sides of these hexagons have, as usual, a 

 concave curvature; the curved sides of each of these same hexagons are con- 

 nected Avith the corresponding sides of the neighboring base and Avith the 

 homologoiis sides of the other hexagon by curA'ed films; lastly, at the liquid 

 edges Avhich unite these last films two by tAvo, terminate other films proceeding 

 from the lateral edges of the frame. The sides of the bases on Avhich rest the 

 tAvo hexagonal films pertain to the face of the prism which first emerged from 

 the liquid. 



The heptagonal prism yields analogous results, Avith a frame having its 

 dimensions in the same ratio ; only, at first, the three systems are imperfect, in 

 the sense that, in the two former, the films which proceed from the sides of the 

 bases remain, to a certain distance from the summits, adherent to the lateral 

 solid edges, and that, in the third, the films Avhlch pass from the curved sides 

 of one of the heptagonal films to the homologous sides of the other are attached, 

 for the greatest part of their length, to the lateral solid edges, presenting, 

 throughout this extent, a form decidedly plane ; moreover, by a new singularity 

 the system furnished by the second method is unstable ; when barely formed, 

 it undergoes a spontaneous modification : the two assemblages situated near the 

 bases become elongated, at first slowly, then more and more rapidly, reach one 

 another, and immediately there appears the imperfect system Avith the hepta- 



