WITHDRAWN FROil THE ACTION OF GRAVITY. 417 



bat its action, on tlie contrary, be directed towards the exterior, tbe imprisoned 

 mass of air will be dilated until tbe assemblage of forces which result from its 

 elasticity thus diminished and from the action of the films be neutralized by the 

 external atmospheric pressure, and then, it is clear, the figure will be still in 

 equihbrium if all these actions are equal, or if the above equation, in which C 

 will be negative, is satisfied. Lastly, if the system is not closed, the thing is 

 evident of itself, and it will be remembered that, in this case, equilibrium requires 

 that should be null. 



Now, the gravitating liquid films which we can develop in the air, soap- 

 bubbles for instance, being extremely thin, their mass is very small, and conse- 

 quently the action of gravitation may in general be here regarded as insensible 

 in relation to that of the molecular forces ; whence it follows that the figures 

 which we would realize with these films should not difier in an appreciable 

 manner from those which would be constituted by films without weight. We 

 ought, therefore, to be able to obtain, in the air, with films of soap and water, or 

 an analogous liquid, the same figures of equilibrium as with filrat^ of oil in the 

 alcoholic mixture, and consequently the figures which would correspond to a 

 liquid mass, full and withdrawn from the action of gravitation. It is in this that 

 the new pi'ocess which I announced at the commencement of the present series 

 consists. 



Thus we arrive at this curious consequence, that with a liquid exposed to the 

 action of gravitation and in repose we can realize on a great scale all the forms • 

 of equilibi'ium which correspond to a liquid mass withdrawn from the action of 

 gravitation and equally in repose. Soap-bubbles afford a first example of the ■ 

 employment of the process in question : isolated in air, they are spherical as 

 would be a full liquid mass withdrawn from the action of gravitation and free 

 from all adhesion. We shall now show that, in adopting as a more general 

 example the figures of revolution, it is easy to procure by this same process a 

 realization of all the figures of equilibrium. 



§ 13, Let us first consider the liquid. Films obtained with a simple solution 

 of soap have but a brief existence unless they are enclosed in a vessel : a soap- 

 bubble one decimetre in diameter, and formed in the free air of an apartment, 

 rarely subsists for two minutes; more frequently it bursts in one or even half a 

 minute ; it was, therefore, important to seek some better liquid, and, after several 

 fruitless attempts, I was so fortunate as to discover one which furnished, in open 

 air, films of remarkable persistence. This liquid is formed by mixing, in suit- 

 able proportions, glycerine, water, and soap. The glycerines which occur in 

 commerce differ considerably in purity and concentration, and the preparation of 

 the mixture consequently varies ; but by procuring it from London, where it is 

 manufactured by a particular process, we obtain, without great expense, a gly- 

 cerine which appears to be very pure and concentrated; it is almost colorless, 

 and of a wciik odor. I shall confine myself at present to a description of the 

 mixture prepared from this glycerine ; in a note, at the end of the memoir, will 

 be found an account of the means proper for obtaining satisfactory results with 

 other qualities of glycerine. 



As far as possible we should operate in summer, and when the exterior tem- 

 perature is at least 66° Fah. Let a portion, by weight, of Marseilles soap, 

 previously reduced to small parings, be dissolved, at a gentle heat, in forty parts 

 of distilled water, and, when the solution has cooled, let it be filtered. This 

 having been done, we may choose between the two following modes of proce- 

 dure: 1st process. — Carefully mix in a flask, by a brisk and protracted agita- 

 tion, two volumes of glycerine with three volumes of the solution of soap, and 

 then leave the mixture at rest; this, though limpid at first, after some hours 

 begins to grow turbid: a light white precipitate is produced, which remains at 

 first suspended throughout the mass, but which afterwards ascends with extreme 

 slowness, and, in some days, forms a layer distinctly, separated at the top of the 

 27 s 



