216 THE FIGURES OF EQUILIBRIUM OF A LIQUID MAS3 



nomcna arc manifested. The liquid sphere first takes rapidly its maximum 

 of tlattcniug, then becomes hollow above and below 

 •^'o* "*■ around the axis of rotation, stretching out continually 



in a horizontal direction, and, finally abandoning the 

 disc, is transformed into a j^crfccthj rarular ring. 



This ring is rounded transversely, and appears to have 

 a circle for its generatrix. At the moment of its form- 

 ation its diameter increases rapidly up to a certain limit; 

 when this is reached the movement of the disc must be 

 stopped. The ring now remains for some seconds in 

 the same state. Then, the resistance of the ambient 



liquid weakening its movement of rotation, it returns upon itself and changes 



back into a sphere around the disc and its axis. 



The velocity of the handle most suitable for producing a beautiful ring, is 



about three turns per second. The ring thus obtained has a mean diameter of 



9 to 10 centimetres. 



12. "Wlu'rt, at the instant of the formation of the ring, the mass of oil which 

 constitutes it separates from the disc, a singular circumstance is ob.^ervablc ; the 

 ring rem;iins iniited to the disc by an extremely thin pellicle or film of oil, 

 which fills all the space between them. But at the instant that, the ring having 

 reached its greatest extent, wc stop the motion of the disc, this pellicle breaks 

 and disappears of itself, and the ring then remains jterfectly isolated. 



It may be conceived that this pellicle is not a circumstance essential to the 

 phenomenon of the formation of the ring ; and we shall see, in another part of 

 these experiments, that it is probably connected with an order of facts wliolly 

 diflFerent. 



13. The heavens exhibit to us also a body of a form analogous to our liquid 

 ring. I allude to Snturn's ring. That, indeed, is flattened, whilst the trans- 

 verse contour of ours appears altogether round ; but I do not think that this dif- 

 ference is so great as it appears at first. 



In fact, the centrifugal force, which goes on increasing from the inner cir- 

 cumference of the ring of oil xap to its outer circumference, necessarily tends 

 to stretch this ring in the direction of its breadth, or, in other words, to flatten it. 

 But the flattening must be of very small amount ; for, on account of the in- 

 considerable dimensions of the ring, and the slowness of its angular movement, 

 the kind of traction which results from the variation of centrifugal force must 

 be very trifling in comparison with the forces developed by molecular attrac- 

 tion. 



14. It appears to me, then, that we may reasonably admit that our ring of 

 oil is in reality slightly flattened, and that in consequence it only dilfers from 

 that of Saturn, with regard to general form, in the less quantity of flattening.* 

 But further, in the system of Saturn, the flattening of the ring is in part deter- 

 mined by the attraction of the central planet. Now, at the first moment of 

 the formation of the ring of oil, the latter is submitted to a particular force, 

 which plays a ])art analogous to that of the above attraction. In fact, this 

 attraction acts with the greatest intensity .4t the inner circumference of Saturn's 

 ring, and thence decreases rapidly in the rest of this body. Now, at the first 

 moment of the formation of the ring of oil, avc have seen (§ 12) that the latter 

 remains united to the disc by a thin film of the same liquid, and we may con- 

 vince oui-selves that this film exerts, on the inner circumference of the ring. 

 a considerable force of traction. In fact, if we stop the movement of the disc 

 a little too soon, that is to say a little before the ring has reached its maximum 



* I leave out of tbe question here the subdivision of the ring of Satum. This subdivision, 

 as is known, is not essentially connected with the conditions of equilibrium of the ring. 



