344 Prof. Plateau on the Conditions of . 



the prism is comprised between the typical value — -=. and a 



4/6 a 

 value which is either exactly or very nearly indeed equal to ^ it 



is possible to obtain at will, by proper manipulation, at the middle 

 of the figure resulting from a single immersion, a triangular film 

 parallel to the bases, or a liquid edge parallel to the lateral edges. 

 I had pointed out these two forms, but as belonging respectively 

 to limits of height differing more widely from each other. 



2. In order to be able to obtain a triangular laminar prism at 

 the middle of the figure, it is necessary that the ratio between 

 the height of the skeleton and the side of the base should not 

 exceed a certain limit. 



3. When this laminar prism is obtained, its faces never have 

 a spherical curvature : for them to assume such a curvature, it 

 would be needful for the lateral edges of this same laminar prism 

 to be diminished so far as to disappear. It is possible to ap- 

 proach as nearly as we choose to this condition ; and it may even 

 be attained, but not permanently, for in that case six liquid edges 

 meet at each of the summits of the laminar polyhedron ; and 

 this, as I tried to show by experiments, and as M. Lamarle has 

 demonstrated, in the first part of this investigation, involves the 

 instability of the system. 



III. System of the Cube. 



1. The faces of the laminar hexahedron formed at the middle 

 of the figure have a spherical curvature, and the radius of the 

 sphere to which they belong is half as long again as the straight 

 line joining two summits opposed to one of the faces. 



2. If the height of the skeleton be made greater than the side 

 of the base, so as to convert it into a right square prism, M. van 

 Rees's process still gives an internal laminar prism with curved 

 faces, provided the height of the prism is not too great; but the 

 faces of this prism never have a spherical curvature. 



3. If the height of the skeleton notably exceeds the side of 

 the base, the central film of the ordinary system always presents 

 itself parallel to two of the lateral faces ; but if the height exceeds 

 the side of the base by a sufficiently small quantity, this film 

 can be transformed by an appropriate method into one parallel 

 to the base — a transformation analogous to what we have seen 

 above in the case of the system of the triangular prism. 



IV. System of the Right Pentagonal Pi'ism with Regular Base. 



1. Denoting by r the radius of the circle inscribed in the 

 base, I had given, in my Sixth Series, for the typical height of 



