TTIE riGUEES OF EQUILILKIUM OF A LIQUID MASS 273 



Let us take as a first example the laminar system of the cubic frame, a sys- 

 tem whose outline is reproduced in Fig. 28.* Each of the 

 , Jig. 28 angles of the central quadrangular lamina being 109 degrees 



and a half, and consequently superior to a right angle, it re- 

 sults that the sides of that lamina cannot be rectilinear and 

 must constitute arcs slightly convex towards the exterior; this, 

 in effect, is what the realized system exhibits. 



I have represented in Fig. 25 the laminar system of the 

 equilateral triangular prism, and have said that, designating 

 by a the lengtli of the edges of the bases, the height of 

 each of the laminar pyramids which rest on those bases is 



equal to — y- ; but it will be understood that if the height of 



the prism is less than double that quantity, or, in other terms, less than 0.4 of the 

 sides of the bases, the system in question could not be produced. In this case, 

 analogy, with other systems, of which I shall speak hereafter, had led me to 

 foresee that the system would be composed of an equilateral triangular film 

 parallel to the bases, placed at equal distances from these last, and attached by 

 other films to all the solid edges ; but as the angles of this laminar triangle 

 must be 109 degress and a half, and the angles of an equilateral triangle with 

 rectilinear sides are but 60°, it followed necessarily that the sides of our laminar 

 triangle were convex towards the exterior, like those of the lamina of the sys- 

 tem of the cube, but that their curvatures were much more decided ; now this 

 was fully verified by experiment, except that the curvatures showed themselves 

 very strong only in the vicinity of the summits. The height of my frame was 

 about a third of the lengtli of the sides of the bases. Fig. 29 repre- 

 sents this system as seen from above, which therefore constitute 

 a second example in support of the proposition in question. 



In the third place, if we take for a frame that of a regular pen- 

 tagonal prism whose height is not too great relatively to the 

 dimensions of the bases, the laminar system presents, at the mid- 

 dle of its height, a pentagonal film parallel to the bases, and to which attach 

 themselves, as to the triangular film of the preceding system, all the films 

 proceeding from the solid edges. Now, the angles of two contiguous side of 

 a regular pentagon being 108°, and thus very near our angle of 109^°, it fol- 

 lows that the sides of the pentagonal film must be obviously straight, and this 

 again experiment confirms. In the frame I employed, the length of the edges of 

 the bases is five centimetres, and the height of the prism six centimetres; the 

 sides of the pentagonal film are about two centimetres, and the eye can there 

 distinguish no curvature. In this system, the films which proceed from the solid 

 edges of the bases and attach themselves to the sides of the central pentagon 

 appear plane, as they should do, since they rest on one hand upcn the rectilinear 

 edges of the bases, and on the other upon the visibly straight sides of the central 

 film; it thence follows that the oblique liquid edges which pass from the sum- 

 mits of the bases to those of the central pentagon appear straight. As to the 



* In this system, the liquid edges which proceed from the summits of the frame are in 

 reality not altogether straight ; but, as was said in the fifth series with reference to this same 

 design, the cui-vatures of these edges are too feeble to be shown in the engraving. 



18 s66 



