206 Prof. Plateau on the Conditions of 



In these last expressions dx is to be treated as if it were an 

 ordinary symbol of quantity, and S is now denned by the equation 



M n y = md m -'y. 



Brisbane, Queensland, Australia, 

 May 30, 1864. 



XXIV. On the Conditions of Stability of thin Films of Liquids ; 

 a Report by Professor Plateau on a Memoir by Professor 

 Lamarle of Ghent*. 



IN the Sixth Series of my researches "On the Figures of 

 Equilibrium of a Liquid Mass without Weight "f> I nave 

 established, in part experimentally and in part theoretically, the 

 laws which relate to films terminating in a common liquid edge, 

 and to liquid edges which meet at the same liquid point. From 

 these laws I drew the conclusion, which I have tried to confirm 

 by experiment, that every equilibrated system of films in which 

 they are not fulfilled is an unstable system, and I ended this 

 series by saying : — 



" I will return once more to systems of films, in order to con- 

 sider the theory of them from a more general point of view. In 

 fact, as I have already observed, the liquid films of which they 

 are made up may be compared to stretched membranes, and 

 hence it will be seen that each system will arrange itself so that 

 the sum of the surfaces of all its films will be a minimum. But 

 I reserve this point for a future Series." 



In expressing myself thus, my intention simply was to take 

 as examples certain particular systems of films, which from their 

 simplicity are capable of being made the subjects of direct cal- 

 culation, and to show that the sum of the surfaces of the films is 

 a minimum relatively to some one mode of deformation ; but I 

 had no intention of treating the problem in all its generality, for 

 I did not consider it practicable to do so. I perceived that there 

 must exist a necessary connexion between the principle of the 

 minimum sum of the areas and my laws ; but I could not seize 

 the precise nature of this connexion, and it cr^emed to me next 

 to impossible to do so. All these difficulties, however, have been 



* Communicated by Professor Plateau, from the Bulletin de VAcademie 

 oyale de Belgique, 2 e scr. vol. xvii. No. 6. 

 t Phil. Mag. S. 4. vol. xxiv. p. 12S. 



