WITHDRAWN FROM THE ACTION OF GRAVITY. 421 



limit, it begins to approacli it: in this latter case, in effoct, the coufigurative 

 forces becoming of very little intensity, the slight weight of the film exerts a 

 sensible influence, and the figm-e shows itself more or less distended in its lower 

 half and constricted in its upper half.* The tallest cylinder that can be re- 

 alized in a regular manner with the rings indicated has a height of about 17 

 centimetres, and will be seen to be within the limit of stability, since this 

 corresponds to a height a little greater than the triple of the diameter, (2d series, 

 § 46.) 



Do we propose fo obtain a partial uuduloid consti'icted in its middle, (4th series, 

 § 13) ? We deposit on the lower ring a bubble having but about nine centi- 

 metres diameter, lay hold of it, as before, with the upper ring, and then raise 

 this latter, but we proceed beyond the jjoint where the figure becomes cylin- 

 drical ; this figure now becomes constricted at its middle, the more deeply in 

 proportion as the ring rises, and thus constitutes the desired unduloid. This, 

 like the cylinder, shows itself perfectly regular, and its bases are in like man- 

 ner convex spherical caps. By still raising the' upper ring, we reach a point 

 where equilibrium can no longer exist, and then the figure rapidly narrows at 

 its middle, where it disunites, becoming transformed into two spherical bubbles 

 respectively attached to the two rings. 



If it is a partial unduloid dilated in the middle, (4th series, § 10,) which we 

 propose to realize, we make use of the system of rings of three centimetres. 

 A bubble of about eight centimetres in diameter is to be formed and deposited 

 on the lower ring ; being then laid hold of with the upper ring, when this latter 

 is elevated the bubble passes by degrees to a figure composed of a dilatation 

 between two portions of constrictions, and again presenting convex spherical 

 caps as bases ; it is consequently the unduloid in question. In this experiment 

 it is necessary to stop at a degree of separation of the rings, for which the 

 tangents at the extreme points of the meridian line are still considerably in- 

 clined to the axis, and, with this condition, the figure appears regular like the 

 preceding. If we proceed so far as to approach the point where these tangents 

 would be vertical, the figure borders upon its limit of stability, (4th series, § 10,) 

 and, as with regard to the cylinder, the diminution of the coufigurative forces 

 leaves a sensible action to the weight of the film; the dilatation then shows 

 itself a little lower than the middle of the figure. 



The realization of the nodoid requires the employment of the system of 

 disks. We begin by inflating a bubble of a diameter of three or four centi- 

 metres ; we bring it into contact with the moistened face of the lower disk, to 

 which, spreading more or less, it immediately adheres, and we continue to in- 

 flate it until it forms part of a sphere about ten centimetres in diameter ; the 

 pipe is then removed, while the film springs from the "very edge of the disk. 

 The upper disk is now lowered until it touches the summit of the bubble, which 

 immediately opens at that point, and the film gaining likewise the edge of the 

 latter disk, forms, from one edge to the other, a portion of the dilatation of an 

 unduloid. While it is in this state we continue to lower the upper disk, and 

 when the point is overpassed where the figure would constitute a spherical 

 zoxie, we have the partial nodoid sought for, (4th series, §§ 31 and 32). If the 

 disk be still further lowered, we attain, just as with the full nodoid of oil, 

 (4, § 31,) a point beyond which the figure ceases to be one of revolution, and is 

 directed more laterally in proportion as the disk continues to be lowered. 



§ 16. These experiments are very curious ; there is a peculiar charm in con- 

 templating these slight figures almost reduced to mathematical surfaces, which 



* We shall see, in another series, a phenomenon of the same kind produced in regard to 

 full cylinders of oil, when they are near their limit of stability, and there remains a minute 

 difference between the densities ot the oil and of the alcoholic liquid. 



