WITHDRAWN FROM THE ACTION OF GRAVITy. 257 



"With a view to determiue whether any particular cause had in reality pro- 

 duced the alteration of the densities, I approximated the rings; then, afrci 

 having reunited the two liquid masses, 1 again carefully raised the upper ring, 

 ceasing at the height of 7 J centimeters, so that the versed sine of the meridional 

 convexity was slightly greater than when this was 8 centimeters. The figure 

 was then found to be perfectly symmetrical, and it did not exhibit any tendency 

 to deformity; whence it follows that the uniformity in the densities had not 

 experienced any appreciable alteration. I recommenced, with still more care, 

 the experiment with that figure which was S centimeters in height ; and I waa 

 enabled to approach the cylindrical form still more nearly ; but before it was 

 attained, the same phenomena again presented themselves, except that the 

 alteration in form was effected in an inverted manner, i. e., the figure became 

 narrow at the upper part and dilated at the base ; so that after the separation 

 into two masses, the perfect sphere existed in the lower ring and the lens in the 

 upper ring. On subsequently uniting, as before, the two masses, and placing 

 the rings at a distance of 7 J centimeters apart, the figure was again obtained in 

 a regular and permanent form. Thus when we try to obtain between two solid 

 rings a liquid cylinder the height of which is four times the diameter, the figure 

 always breaks up spontaneously, without any apparent cause, even before it 

 has attained the exactly cylindrical form. Now as the .cylinder is necessarily a 

 figure of equilibrium, whatever may be the proportion of the height to the 

 diameter, we must conclude that the equilibrium of a cylinder the height of 

 Avhich is four times the diameter is unstable. As the shorter cylinders which I 

 had obtained did not present analogous effects, I was anxious to satisfy myself 

 whether the cylinders were really stable. I therefore again formed a cylinder 

 6 centimeters in height with the same rings ; but this, when left to itself for a 

 full half hour, presented a trace only of alteration in form, and this trace ap- 

 peared about a quarter of an hour after the formation of the cylinder, and did 

 not subsequently increase, which shows that it was due to some slight accidental 

 cause. 



The above fiicts lead us then to the following conclusions : 1st, that the cyl- 

 inder constitutes a figure the equilibrium of which is stable when the proportion 

 between its height and its diameter is equal to 3, and with still greater reason 

 when this proportion is less than 3 ; 2d, the cylinder constitutes a figure the 

 equilibrium of which is unstable when the proportion of its height to its diameter 

 is equal to 4, and with still greater reason when it exceeds 4; 3d, consequently 

 there exists an intermediate relation, which corresponds to the passage from 

 stability to instability. We shall denominate this latter proportion the limit of 

 the stability of the cylinder. 



45. These conclusions, however, are liable to a well-founded objection. Our 

 liquid figure is complex, because its entire surface' is composed of a cylindrical 

 portion and of two portions which present a spherical curvature. Now we can- 

 not affirm that these latter portions exert no influence upon the stability or the 

 instability of the intermediate portion, and consequently upon the value of the 

 proportion which constitutes the limit between these two states. To allow of 

 the preceding conclusions being rigorously applicable to the cylinder, it would 

 be requisite that the figure should present no other free surface than the cylin- 

 drical surface, which is easily managed by replacing the rings by entire disks. 

 I effected this substitution by employing disks of the same diameter as the pre- 

 ceding rings, but the results were not changed; the cylinder, G centimeters in 

 height, was well formed, and was found to be stable; whilst the figure 8 centi- 

 meters ill height began to change before becoming perfectly cylindrical, and was 

 rapidly destroyed. The final result of this destruction did not, however, consist, 

 as in the case of the rings, of a perfect sphere and a double convex lens, hut, 

 as evidently ought to have been the case, of two unequal portions of spheres, 

 17 s , 



