of a Liquid Mass without Weight. 359 



approach to a cylinder, or rather to a very elongated cone ; only 

 one of the figures would exhibit as depressions what the other 

 exhibited in relief. Now, considered with regard to molecular 

 forces, the conditions of equilibrium and stability are exactly the 

 same for hollow figures as they are for figures in relief. Hence, 

 just as the liquid vein changes into isolated masses under the 

 action of the molecular forces, so the current of gas ought to 

 transform itself into separate bubbles — which, as every one knows, 

 is conformable to experiment. 



But I point out that there is this difference between them ; 

 that the liquid vein always presents a continuous portion of 

 greater or less length, while with the current of gas, unless it 

 has quite an enormous velocity of translation, the bubbles ought 

 to be formed very near the opening, and hence the current can- 

 not have a continuous part. I verified this deduction by means 

 of air escaping under a pressure of 130 centims. of water from 

 an opening 5 millims. in diameter, below a stratum of water 

 only 20 millims. in thickness : this current, notwithstanding its 

 great rapidity and its having to pass through a very shallow 

 layer of water, caused a bubbling at the surface, thus proving 

 that it had been already changed into bubbles. 



Tenth Series. — Results arrived at by Geometricians, and expe- 

 rimental verifications. 



Beer discussed analytically in a first memoir the rotation- 

 experiments of my First Series; in a second memoir he came 

 back to the same subject, treating it more precisely by the aid 

 of elliptic functions ; and he also gave by the same means the in- 

 tegral equation to the meridian lines of the equilibrium-figures 

 of revolution for the case of rest. M. Delaunay, considering 

 surfaces of revolution with a constant mean curvature from a 

 purely mathematical point of view, arrived at an elegant method 

 of generating their meridian lines. M. Lamarle has applied 

 his geometrical methods to the same subject. M. Mannheim 

 has pointed out a simple rectification of the meridian lines in 

 question. In relation to the surfaces generated by these same 

 lines, M. Lindelof has arrived at a series of remarkable results, 

 relating particularly to the measurement of areas and volumes. 

 Goldschmidt, and more recently MM. Lindelof and Moigno, 

 have discussed the catenoid analytically. In conclusion, as the 

 last result bearing specially upon equilibrium-figures of revolu- 

 tion, M. Lamarle has shown that, among ruled surfaces, the cy- 

 linder is the only one that has a finite and constant mean cur- 

 vature. 



Poisson was, I believe, the first to investigate the general dif- 

 ferential equation of the figures of equilibrium of a liquid mass 



