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XL VI I. On the Conditions of Stability of thin Films of Liquids ; 

 a Report by Professor Plateau on a Memoir by Professor 

 Lamarle of Ghent. — Second Part*. 



IN the first part of this investigation f, M. Lamarle considered 

 more particularly the theoretical questions connected with 

 the stability of systems of films ; in the present part he examines 

 the matter experimentally, by means of skeleton figures of iron 

 wire and the glycerizecl liquid, or a simple solution of soap. He 

 studies first of all the systems of the seven typical polyhedra, 

 which he had discussed in the First Part, — those, namely, which, 

 disregarding for the moment the question of stability, would be 

 composed of plane films, all meeting in a single point at the 

 centre of the figure, and conforming to the laws I have esta- 

 blished. With regard to these systems, he arrives at the same 

 results as those which I have described in my Sixth Series, and 

 shows their connexion with the formulae deduced in his First 

 Part ; but he has obtained in addition, partly by direct experi- 

 ment, and partly by the help of reasoning and calculation, a series 

 of new results of which I am about to give an outline. 



But, to avoid repetitions, it may be pointed out previously 

 that, according to an observation communicated to me by M. van 

 Rees, and mentioned in my Sixth Series, when, after obtaining 

 upon a skeleton its ordinary system of films, the base of the 

 skeleton is again plunged into the liquid and then withdrawn, 

 there is formed in the base a film which afterwards ascends be- 

 tween the films of the system, shutting in a certain quantity of 

 air, and thus causing a closed laminar polyhedron with curved 

 faces to be generated in the middle of the figure. We now pro- 

 ceed to the results obtained by M, Lamarle. 



I. System of the Regular Tetrahedron. 



In the laminar tetrahedron with convex faces, produced in the 

 middle of the figure by the above process : (1) The curvature of 

 the faces is spherical, and consequently the curvature of the edges 

 is circular. (2) The centre of the sphere to which any one of 

 these faces belongs is situated at the opposite summit. (3) The 

 centre of the circumference to which any one of the edges belongs 

 is situated at the middle of the chord of the opposite edge. 



II. System of the Right Triangular Prism with Equilateral Base. 

 1 . If the side of the base is denoted by a, and the height of 



* From the Bulletin de VAcademie Royale de Belgique, S. 2. vol. xx. 

 No. 7. 



t See Professor Plateau's Report thereon, Bull, de F Acad. Roy. Belgique, 

 S. 2. vol. xvii. p. 591 ; and Phil. Mag. Ser. 4. vol. xxviii. p. 206. 



