286 WITHDRAWN FROM THE ACTION OF GRAVITY. 



goual film at the middle. The projection on the plane of the base of one of 

 the assemblages of the system due to the first method is repre- ^.^ 



rented by Fig. 41 ; the projection referable to the second method 

 oould not be delineated, because the spontaneous modifications 

 iindergone by the system prevent it from being distinctly ob- 

 served.. The facts just described, joined to that stated at the 

 end of § 28, show that with certain frames the results differ 

 according to the manner in which these frames are withdrawn 

 from the glyceric liquid. 



Thinking that the instability of the second system of the heptagonal frame 

 might be occasioned by a want of sufiioient length in the frame, I caused 

 another to be constructed in which the length was double the diameter of 

 the inscribed circle ; but nothing was gained thereby, besides that the first two 

 systems were produced with more difficulty, and it was the third Avhich was 

 almost always obtained, the system, namely, which contains two oblique 

 heptagonal films proceeding respectively from one of the sides of the bases. 

 Indeed, with a frame still more elongated, it was only this last system which 

 resulted. As regards the octagonal prism, whatever the ratio between its 

 length and the diami ter of the inscribed circle, it yields no other than the im- 

 perfect systems with the octagonal film in the middle, or with two obliqu.e oc- 

 tagonal films, and again this last is the only one realized when the ratio is suf- 

 ficiently great. 



§ 37. I have said (§ 16) that with the pyramid with square base which had 

 served for the experiments of the second series, the laminar system always pre- 

 sented a little irregularity. This consists in the fact that one or more of the 

 four oblique liquid edges directed towards the summits of the base do not 

 exactly terminate at those summits. I am now able to indicate the cause : if 

 we inquire the height of a quadrangular pyramid in which two adjacent trian- 

 gular faces make between them an angle of 120°, it will be found that this 

 height is half the side of the base; when we employ, then, a frame having this 

 height or a less one, it is clear that the films will simply occupy the four trian- 

 gular faces, and this is verified by experiment, such a frame yields nothing else 

 in whatever manner it be withdrawn from the liquid. Now, in the frame of the 

 experiments of the second series, the length of the side of the base was 67™"^, 

 and the height of the pyramid 50"^"^; this height, therefore, was but about 

 three-fourths of the length of the side in question ; but, in such a pyramid, the 

 films which proceed from the sides of the base must have but a feeble tendency 

 to separate from the oblique solid edges, and it is to be inferred that they may 

 continue to adhere to them for a certain extent. 



§ 38. It has just been seen that with a quadrangular pyramid whose height 

 is at most equal to half the side of the base, none but plane films occupying 

 the triangular faces are ever obtained ; but an assemblage of this kind does not 

 constitute a laminar system, for all these films are rendered independent of one 

 another by the intermediate solid edges. 



From all that has been stated since § 32 may evidently be deduced the fol- 

 lowing conclusion: When, in a polyhedral frame, there is a continued and re- 

 curring succession of identical adjacent faces forming between them angles greater 

 than 120°, and all arranged after the same manner as the succession of lateral 

 faces of a prism, heptagonal, octagonal, &c., or as that of the lateral faces of a 

 pyramid, hexagonal, &c., that frame gives an imperfect laminar system — that is 

 to say, one containing films which, through a portion of their extent, adhere 

 at the same time to two solid edges ; or else it gives no system — that is to say, 

 all the faces but one are simply occupied by plane films; I say but one, for, in 

 this case, it is necessary that one face should remain open to allow the intro- 

 duction of air ; in the quadrangular pyramid mentioned above, for instance, the 

 face which remains open is the base. 



