Intelligence and Miscellaneous Articles, Id 



OX THE PRODUCTION OF PLATEAU'S FILM-SYSTEMS. 

 BY A. TERQUE3I. 



M. Plateau, by the use of a mixture of soap-water and glycerine, 

 has produced liquid films of a certain extent, and lias thus been 

 able to verify most of the laws respecting the form of the surfaces 

 which constitute the boundaries of liquids whose molecules are 

 subjected only to their reciprocal actions. 



I pointed out, some years since, that for the glyceric liquid a 

 mixture of soap-water and sugar might be substituted, the latter 

 substance having, especially, like glycerine, the effect of augmenting 

 the viscosity of the liquid, and preventing it from flowing away too 

 rapidly. The production of the film-systems of M. Plateau de- 

 mands the employment of a great quantity of liquid if polyhedra be 

 used the edges of which are of large dimensions. 



I have thought that large films of liquid might be easily obtained 

 by bounding them in part by flexible threads instead of using for 

 the purpose rigid wires only. 



Thus, if two horizontal rods be joined by two vertical and equi- 

 distant flexible threads, on dipping the system in the saponaceous 

 liquid and slowly lifting it out again, we get a vertical plane film 

 bounded above and below by the two rods, and laterally by the 

 flexible threads, which take the form of arcs of a circle. The radius 

 of the circle evidently depends on the stretching weight. It is 

 easily demonstrated that, if Ave designate by I the distance between 

 the two threads, by E the radius of the arc constituted by them, 

 by </> the angle made with the vertical by the tangent of the arc at 

 the point of attachment of the thread to the lower rod, by /the 

 superficial tension of each of the two surfaces of the liquid film, 

 and by p the stretching weight, we have the relation 



2) = 2f(l + 2~Rcos<p). 



Every thing happens, therefore, as if the distance between the 

 threads were equal to that between the centres of the two arcs, the 

 tension of the threads being omitted. 



I of course submitted this formula to a series of experimental 

 verifications, by measuring with the cathetometer the diminution of 

 the vertical distance between the two horizontal rods produced by 

 the existence of" a liquid-film between them. 



If H is the initial length of the threads, and H' the new vertical 

 distance of the horizontal rods, to find the radius of the circle and 

 the angle (p we have only to solve the two equations 



H' = 2Esm(7, and 2E(/> = H, 

 whence we derive 



11/9=11 sin#. 



As the angle 6 is generally very small, this transcendental equa- 

 tion can be solved with sufficient approximation by substituting 



<b—±- for the sine, 

 o 



