WITHDRAWN FROM THE ACTION OF GRAVITY. 223 



round the lat^r, and with a velocity much less than that of this disc. This 

 inferior velocity, I may add, evidently also proceeds from the resistance of the 

 ambient liquid. 



If a greater velocity is given to the disc without, however, passing a certain 

 limit — if, for example, we give it one turn in three seconds, the phenomena are 

 still of the same kind ; only the mass is more elongated, the flexure due to the 

 resistance of the ambient liquid is more decided, and the j-j> 5 



form is more removed from an ellipsoid. Figure 5 repre- . 

 sents the mass viewed on the side, and showing to the eye 

 its greatest length. 



If the velocity of the disc is increased to a turn in two 

 seconds, the phenomena become less constant and less 

 regular. We should say that there is, for this velocity, a " 

 transition from one oi'dcr of phenomena to another, and that the mass hesitates 

 between the two. 



In fact, with a velocity still a little greater, namely, about one turn in a second 

 and a half, the pheaiomena begin again to be regular and constant, but they are 

 different from the first. They are exhibited in all their beauty Avhen the velocity 

 is increased to a turn in a second. The mass then is at first deeply hollowed 

 around the axis, as if the ring was on the point of being developed ; and it re- 

 mains under this form of a circular bourrelet during sixteen to eighteen turns of 

 the disc; we then see it elongate gradually according to a horizontal diameter, 

 but no longer eccentrically, so that, seen from above, it presents an elliptic 

 figure sometimes very perfect, of which the disc occupies the centre, (fig. 6.) 

 This ellipse then lengthens more and more, rather rapidly, and begins to bend 



Fis. 6. Fis. 7. 



by the resistance of the ambient liquid, (fig. 7.) Lastly, on a sudden the mass 

 becomes strongly inflected from both sides, and its form „. „ 



seen from above is then as represented in fig. 8. The ®* 



mass afterwards preserves this last form in a perfectly 

 fixed manner, as long as the movement of the disc con- 

 tinues. 



23. However capricious these phenomena may appear, 

 chance, or accidental causes, have still no part in them. 

 I have repeated a great number of times the experiments detailed above, and 

 the effects have aways been identically the same for the same velocities. 



After having seen the stable figures Avhich the mass takes in these circum- 

 stances, we cannot help making a comparison between these figures and the 

 ellipsoids of three axes of MM. Jacobi and Liouville, (§15,) — ellipsoids which 

 are also always, as the latter of these geometricians has shown, figures of stable 

 equilibrium. Would the identity of the phenomena in the case of universal 

 gravitation and in that of molecular attraction hold good so far 1 Doubtless 

 the singular figures which we have just described are not ellipsoids ; but their 

 aspect admits of our attributing the difference to the resistance of the ambient 

 liquid, Avhicli on one side determines the flexures of which we have spoken, 

 and on the other maintains a permanent inequality of angular velocity between 

 the poi-tions adjoining the disc and the more distant portions. Calculation alone 

 could inform us up to what point the above comparison is well founded ; the 

 complete solution of the problem, for the case of molecular attraction, would per- 

 haps not present difficulties so insurmountable as for that of universal attraction. 



