Tension of Liquid Films. 273 



two rings are first placed almost in contact, and the small inter- 

 val which separates them is filled with the glycerine liquid by 

 means of a pencil ; the upper ring is then raised, and the desired 

 surface is formed between them : the distance between the 

 two rings should be less than two-thirds of their diameter, as 

 otherwise the equilibrium would become unstable. Having thus 

 obtained the catenoid, I carefully applied to the film a closed 

 thread 14 centims. long ; in virtue of its weight, it sank to the base 

 of the figure, leaving generally a narrow lamina within its contour. 

 When I burst this, the tension of the liquid was exerted in all 

 directions ; the form of the residual film did not appear altered, 

 and the thread was arranged in the form of a perfectly stable 

 and symmetrical skew surface. Holding in the hand the upper 

 ring, and thus successively giving to the catenoid different heights, 

 I could procure variations in the shape of the curve described by 

 the thread. When the height was only 1 or 2 centims., I ob- 

 served two symmetrical arcs placed on each side of a vertical plane 

 passing through the axis of the catenoid ; the rest of the thread 

 adhered to the two metallic rings. In proportion as these were 

 more separated, the parts adhering were gradually detached; 

 and the two symmetrical arcs, coming closer, became longer, 

 while their curvature diminished. When I continued to raise 

 the upper ring, I observed the skew curve become continuous 

 and touch the lower ring. 



It is scarcely necessary to add that the experiment may also 

 be made by fixing two points of the flexible thread to the upper 

 ring and then bursting the portion of the film between this ring 

 and the thread. 



I then repeated the same operations on the surface having the 

 equation 



4 sin mz = {e mx — e~ mx ) (e m v — e~ m ^ , 



the mode of obtaining which, in the form of film, I have recently 

 described*. 



I have previously said that these experiments may be used 

 for certain accurate verifications of theory. In fact, let it be pro- 

 posed to obtain a mathematical solution of the following general 

 problem : — 



Given a laminar surface in equilibrium, to ascertain the curve 

 produced by a very flexible inextensible thread, without weight and 

 at its exterior contour solely acted on by the contractile force of 

 the liquid film ; this thread may, moreover, form a closed contour, 

 or it may have two points fixed on the solid skeleton, serving as sup- 

 port for the surface in question. 



* " Discussion et realisation experimentale d'une surface particuliere a 

 courbure raoyenne nulle," Bull, de VAcad. Roy. de Belgique, ser. 2. vol. xxi. 

 p. 552. 



Phil. Mag. S. 4. Vol. 33. No. 223. April 1867. T 



