280 WITHDEAWN FEOM THE ACTION OF GRAVITY. 



solid edges. No essential cliange takes place when the elevation of the frame 

 is continued ; the plane film just mentioned increases in height and becomes 

 broader at its lower part, until the inferior base of the prism begins to appear 

 at the surface of the liquid: at this time the two descending liqmd edges rest by 

 their extremities on the middle of two opposite sides of that base; after the com- 

 plete emergence of which the film which occupies it is rapidly transformed into 

 four oblique films, two trapeziums, and two triangles, which complete the system. 

 In the particular case of the cube we have thus the system of Fig. 28. If the 

 height of the frame be greater than the length of the sides of the bases, the oblique 

 films which rest on these last are identically the same as for the cube, and the 

 films proceeding from the lateral edges as well as the central plane film have 

 simply more height. 



Lastly, with the frame of the triangular prism, the curvilinear triangle at the 

 surface of the liquid decreases more rapidly, and disappears when the frame 

 has emerged by a very small quantity, so that the triangular pyramid which is 

 to rest on the superior base in the definitive system is already completed ; if 

 the frame be still raised, we see a vertical and straight liquid edge extend itself 

 from the summit of this pyramid to the surface of the liquid, an edge which is 

 common to the three films proceeding from the lateral solid edges. This state 

 of things continues while the elevation of the frame proceeds, the three films 

 and the vertical liquid edge merely go on increasing in height until the emergence 

 of the inferior base ; then the film which presents itself in this base is instan- 

 taneously converted into the second triangular pyramid, which thus completes 

 the system of Fig. 25 ; it should be understood, hoAvever, that the frame is 

 supposed to have sufficient height not to give the system of Fig. 29. 



§ 28. Let us take now a frame which is symmetrical around an axis passing 

 by a summit, such as that of a regular pyramid, a regular octahedron, &c., 

 and withdraw it by this summit. It is evident that in this case there could not 

 be formed films occupying the faces which terminate at the summit in question, 

 for the space which they would leave between themselves and the liquid would 

 be void of air. It is absolutely necessary, therefore, that the films proceeding 

 respectively from each of the solid edges should be directed towards the interior 

 of the frame. 



If there are only three solid edges meeting at the summit in question, and 

 symmetrically disposed, as in the tetrahedron, or the cube when withdrawn 

 by a summit, it is clear that the films proceeding from these three solid edges 

 will be united by a single liquid edge descending vertically from the solid sum- 

 mit to the surface of the liquid of the vase, and this, in fact, is what takes 

 place. With the regular tetrahedron this state of things continues until after 

 tho withdrawal of the solid base, when the system completes itself in the same 

 manner with that of the triangular prism, and yields the result shown in Fig. 

 24. If there are more than three solid edges terminating at the summit which 

 we withdraw, it follows necessarily, from the fact of the instability spoken of in 

 §§16 and 21, that additional films should be formed. Let us take as an example 

 the regular octahedron. It will readily be conceived that the films proceeding 

 from the four solid edges will unite, not by a single liquid edge, but by two 

 liquid edges proceeding from the summit and bounding a vertical auxiliary film, 

 so that at each of these last edges terminate three films, forming between them 

 equal angles. The auxiliary film is destined to form, in the complete laminar 

 system, the superior quadrilateral, (Fig. 26.) Until the square, a common 

 base of the two pyramids which constitute the octahedron, emerges from the 

 liquid, the assemblage of films preserves the same arrangement ; then, while 

 the withdrawal of the frame proceeds, modifications are produced, which it 



