THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 281 



Jiff. 36 



JiS. 37 



would detain us too long to describe, and in consequence of which the system 

 tends towards the form represented at Fig. 36, where the two 

 faces abc and ah'c are each occupied by a phme fihn. This 

 form is completely attained at the moment when the inferior 

 summit of the frame emerges from the liquid, but a change 

 speedily occurs, and the system takes the form of Fig. 'Z'o. 

 Although this change is very rapid, we may yet, by proper 

 , attention and by repetition of the experiment, observe how it 

 ^ is produced : the two films which occupied (Fig. 36) the fjicea 

 ahc and a'h'c rise towards the interior of the frame by turning 

 around the solid edges ah and ah' , and at the same time there 

 is developed from the inferior summit a quadrilateral, at first 

 " very small, but which increases until its superior summit at- 



tains the centre of the frame, and which then constitutes the inferior quad- 

 rilateral of the definitive system; at the same time the summits y and g of 

 the curvilinear quadrilateral sfgc ascend by a certain quantity, this quadrilat- 

 eral shrinks, its edges become straight, and it finally forms the superior quad- 

 rilateral of the same definitive system. Fig. 37 represents the 

 phenomenon in course of formation, at the moment when the 

 quadrilateral, which is extending, has acquired half of its ulti- 

 mate height. It will be easily conceived from this drawing 

 how the four other quadrilaterals of Fig. 26 are generated. 



In order that all these phenomena should, with almost entire 

 certainty, be produced, it is necessary that the frame should be 

 withdrawn quite vertically ; it is further necessary that this 

 frame should be well constructed, that the iron wires which 

 compose it should be of the least possible thickness, and, above 

 all, that at the summits of the octahedron they should unite in 

 the neatest manner, at least on the side which faces the interior of the frame ; 

 when this is not the case, the laminar figures obtamed are often iri'egular. It 

 should be added that the frame in question sometimes gives, when it is a little 

 inclined in being withdrawn from the liquid, a system wholly different from 

 that of Fig. 26, regular like it, but formed of curved films. This second 

 system contains in the middle an hexagonal film, placed parallel to two faces 

 of the octahedron, and having its sides slightly re-entering (§ 20 ;) these sides 

 are attached to the summits of the above two faces by triangular films, and to 

 the edges of these same faces by trapezoidal films ; moreover, the summits of 

 the film in question are attached by triangular films to the other solid ed^s. 



The different examples which I have given in detail will suffice to make it 

 understood how laminar systems are generated, and to show that theory can 

 render an account of all the particulars which this generation presents. 



§ 29. In § 19, of the 5th series, I stated the laws which govern the laminar 

 systems of polyhedral frames, when these systems are formed. Of these laws, 

 which are five in number, three have already been discussed, (§§ 16 to 23:) 

 they relate to the number of films terminating at the same liquid edge, and 

 the equality of the angles between these films; the number of liquid edges 

 terminating at the same liquid point, and the equality of their angles; lastly, the 

 formation of a film proceeding from each solid edge. Let us now consider the 

 two other laws. 



One of these rests upon the fact that if care be taken that there .shall be no 

 bubble of air at the surface of the liquid of the vessel before the frame is 

 plunged therein, the laminar system will present no space closed on all sides by 

 fihns, and that hence all the fihns will be in contact by their two faces with the 

 ambient air. In effect, if, while the frame is being withdrawn, the system, 

 before it undergoes the rapid modification which gives to it its final arrangement, 

 contained a space closed uu all sides by films, this space must have originated 



