EXPERIMENTAL AND THEORETICAL RESEARCHES 



ON 



THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



WITHDRAWN FROM THE ACTION OF GRAVITY, &C. 



BY J. PLATEAU, PROFESSOR IN THE UNIVERSITY, OF GHENT. 



Translated for the Smithsonian Institution from the Memoirs of the Royal Academy of Brussels. 



FIFTH SEISBES. 



CONTINUED FROM THE SMITHSONIAN REPORT FOR 1864, PAGE 369. 



Theory and description of a new process for the realization of figures of 



equilibrium. 



§ 1. In tlie second and fourth series of tliis treatise I tave applied my pro- 

 cess of the immersion of a liquid mass in another liquid of the same density, and 

 with which it cannot mingle, to the realization of a part of the figures of equi- 

 librium, infinite in number, which pertain to a liquid mass supposed to be with- 

 out weight and in a state of repose. In the present series 1 shall indicate a 

 wholly different process, much more simple and commodious, which enables us 

 to attain the same end, and I shall state a portion of the numerous consequences 

 which have been afforded by its employment and by the theoretical principles 

 on which it rests. 



§ 2. We will first notice some of the curious results which serve, so to speak, 

 as a transition between these two processes. It will be remembered that oil 

 immersed in the alcoholic liquid easily assumes a laminar form ; our liquid poly- 

 hedrons, for example, (2d series, §§ 31 to 35,) became transformed into sj^stems 

 of films by the gradual exhaustion of almost the whole of the oil. It will be re- 

 membered also that these films in general appeared plane, but that the octahe- 

 dron gave rise to a system of films evidently curved. Curved films were like- 

 wise developed in the experiment of § 22, 4th series. 



Let us recur to this last experiment and repeat in what it consists. After 

 having formed in the midst of the alcoholic liquid a cylinder of oil between two 

 equal rings of iron wire, parallel and placed opposite to one another at a distance 

 considerably less than two-thirds of their diameter, we gradually withdraw liquid 

 from the mass by means of the small syringe. The surface comprised between 

 the rings, it will be remembered, becomes then more and more concave, while at 

 the same time the bases of the figure sink, become plane, then concave, and all 

 these curvatures continue to increase with the progress of the absorption. Ulti- 

 mately we see three films produced, of which one has its , origin at the centre of 



