272 M. G. Van der Mensbrugghe on the 



that of a minimum of the laminar surface which remains. We 

 shall see further on how statics lead to the same law. 



If the silk thread has a length equal to or greater than the 

 perimeter of the solid skeleton diminished by ??in, the whole of 

 the liquid film should be destroyed at the moment that the part 

 between m n and the flexible thread is burst. This is confirmed 

 by the following observation : when the contour is circular or 

 oval, the entire film disappears, and the thread lies along the 

 solid skeleton ; when this is polygonal, the adherence between 

 the flexible thread and the solid wire sometimes leaves little 

 films in the angles. 



The experiment described may be modified so as to be still 

 more striking. A fine silk thread of suitable length is chosen, 

 and its two ends tied, so as to form a closed contour ; it is 

 then moistened with the glycerine liquid ; the horizontal film is 

 then formed, and the moistened thread carefully placed in it ; 

 this remains on the surface, assuming an irregular figure; but 

 the moment the portion within its contour is burst, this assumes 

 suddenly the shape of a perfect circumference, which is retained 

 even if the film is placed in a vertical po- Fio-. 3. 



sition. Fig. 3 represents the liquid film 

 perforated by its circular aperture. 



I come now to the case where we work 

 with curved films. We are not concerned 

 here with surfaces of equilibrium whose mean 

 curvature is not zero — for example, the 

 sphere, the cylinder, the unduloid of M. 

 Plateau, &c. ; for when surfaces are obtained 

 in the laminar state, they always exert a pressure on the air they 

 contain; but if any portion of their figure were burst, this would 

 quickly disappear completely. Hence I have been obliged only 

 to operate on minima surfaces, or on those whose mean curva- 

 ture was zero; produced in the form of laminae, they exert no pres- 

 sure on the air in contact with them ; hence it is that I have 

 been able partly to burst these films without destroying them in 

 their entire extent. 



I first made some experiments on the catenoid, that is, the 

 surface produced by the revolution of a chain about the right 

 line perpendicular to its axis of symmetry. To obtain this figure I 

 employed M. Plateau's method*, which consists in using two 

 rings 70 millims. in diameter, for instance : one of these rests on a 

 tripod ; the other is provided with a fork by which it can be 

 held in the hand, or attached to a support if necessary. The 



* " Reeherehes experimentales et theoriques sur les figures d'equilibre 

 d'une masse liquide sans pesauteur," ser. 6. § 15, Bull, de VAcad. Roy. de 

 Belgiqne, vol. xxxiii. 



