of a Liquid Mass without Weight. 47 



bits the form just mentioned. In my memoir I have given the 

 theory of the phenomenon, and have indicated the conditions 

 requisite for its successful realization. * 



It may be seen from my preceding Series that, when an un- 

 stable liquid figure breaks up spontaneously into two or more 

 masses or partial figures, these remain united together two and 

 two, before their complete separation, by a liquid vein more or 

 less cylindrical in shape, which afterwards resolves itself into 

 separate spherules. I show that the phenomenon of the gene- 

 ration of these veins is analogous to the generation of films, 

 and that it also depends upon the cohesion and viscosity of the 

 liquid. 



I conclude with announcing a general principle concerning 

 the production, in the form of films, of surfaces whose mean 

 curvature is zero. This principle, to which I attach great im- 

 portance, is as follows : — 



A surface whose mean curvature is zero being given, imagine 

 that there is traced out upon it any closed outline whatever, subject 

 only to these conditions — (1) that it circumscribes a finite portion 

 of the surface, and (2) that this portion does not exceed the limits of 

 stability if the given surface has such limits ; bend an iron wire so 

 that it has exactly the shape of the closed outline in question, oxi- 

 dize it slightly with dilute nitric acid, plunge it completely into the 

 glycerine- solution and take it out again ; it will be found occupied 

 by a film representing the portion of a surface that has been sup- 

 posed. This outline must, of course, be provided with a projection 

 by which it can be held. 



For example, a plane is a surface whose mean curvature is zero, 

 and any closed figure traced upon a plane encloses a finite por- 

 tion of it ; now a slightly oxidized iron wire bent into the shape 

 of any arbitrary but closed plane figure, and immersed in the 

 glycerine-solution and then withdrawn, always brings with it a 

 plane film. Similarly, if on a catenoid contained between two 

 circular bases, we imagine an outline formed of two opposite meri- 

 dional arcs and of the halves of the circumferences of the two 

 bases, these two halves being taken on the same side of the plane 

 containing the meridional arcs, this outline, when constructed in 

 iron wire, gives with the glycerine- solution a film representing 

 the corresponding portion of the catenoid. 



Surfaces which for the most part are very curious, can be thus 

 realized, as if by enchantment. The only difficulty consists in 

 choosing the closed outline and exactly determining its form ; 

 but this can always be done when we know either the equation 

 or the geometrical generation of the surface. In a subsequent 

 Series I will make known some new examples of such realizations. 



