420 THE FIGURES OF EQUILIBEIUM OF A LIQUID MASS 



the two rings, so as to fill the small space left between them. "We now raise 

 the upper ring and a laminar catenoid is seen extending from one to the other. 

 It will be remembered that between two equal rings whose distance apart is less 

 than the limitary separation, there are (4th series, § 10) two catenoids possible 

 unequally curved, and that when we realize with oil, within the alcoholic li- 

 quid, a full catenoid, it is always (4, § IS) the one least concave which is produced, 

 whence I drew the conclusion that the one most concave is unstable. Now, as 

 might be expected, the laminar catenoid of the experiment of § 3, and of the 

 present experiment, is always that which is least concave. 



By continuing to raise the ring gradually, we attain the point where equi- 

 librium ceases, and the catenoid is presently seen to contract in the middle and 

 become converted into two plane films occupying respectively the two rings, 

 like the laminar catenoid of oil, with this difference, that the phenomenon is ac- 

 complished in a much shorter time. As with the laminar catenoid of oil, like- 

 wise, there is a formation of a thread and of spherules; and although the thread 

 cannot be observed because of the rapidity of the transformation, a spherule of 

 some millimetres in diameter may be seen to fall, at the moment of disunion, 

 on the lower film, and then rebound for some instants ; this spherule then 

 changes into a bi-convex lens, laminar like itself, engaged by its herder in the 

 film. At this time the cathetometer gives, as the interval between the two rings, 

 about 46 millimetres, or very nearly two-thirds of the diameter of the rings, 

 being the same state of things which presented itself with the laminar cateuoid 

 of oil. 



A remark of importance should here be made in reference to this rupture of 

 equilibrium. A full limiUxry catenoid, formed with oil in the alcoholic liquid, 

 far from disuniting like our laminar catenoid, is, on the contrary, very stable, 

 (4th series, §§ 18 and 21,) although it be at its limit of stability. I have given in 

 the second of the paragraphs just cited the reason of this singular fact, and it 

 may be concluded irom the experiments of § 20 of the same series, that if the 

 distance of the rings be a little increased, the figure will simply pass to the un- 

 duloid by a slight modification. But it cannot be so with regard to a laminar 

 limitary cateuoid without bases: for, as has been seen, (§§ 11 and 12 of the 

 present series,) between two equal rings, parallel and placed opposite to one 

 another, the only figure of equilibrium possible in a laminar state and unclosed 

 is the catenoid.* Consequently, in these latter conditions, if the separation of 

 the two rings exceed by the least quantity that which corresponds to the limitary 

 catenoid, equilibrium can no longer exist, and the figure must necessarily sepa- 

 rate into two. 



To realize a laminar cylinder, the same system of rings is employed. After 

 having raised the u])per ring to a sufficient height, we inflate, by means of one 

 of the pipes, a bubble of about 10 centimetres in diameter ; we deposit it on 

 the lower ring, to which it immediately attaches itself, and withdraw the pipe ; 

 we then lower the upper ring until it touches the bubble, which attaches itself 

 thereto in like manner ; fiuiilly, we again gradually raise this ring, and the bub- 

 ble, which, thus vertically elongated, loses more and more its lateral mei-idian 

 curvature, is converted, at a certain stage of separation of the rings, into a per- 

 fectly regular cylinder, presenting convex bases like the full cylinders of oil. 

 We can give the bubble a diameter a little greater; but when it is too consider- 

 able, the cylindrical form is not attained, whether -because the cylinder which 

 we would realize exceeds ito limit of stabiHty, or because, if still within that 



*At least among' figures of revolution ; but as, between two rings thus arranged in the 

 akoliolic liquid, full masses never take other than forms of revolution, it must be ad- 

 mitted a p.riuri that the case is the same Avith tilms in that liquid or in the air, and experi- 

 ment A-crilics it. 



