WITHDRAWN FROM THE ACTION OF GRAVITY. 349 
little removed from its limit of stability, and that hence its meridian line con- 
tained very probably points of inflection. 
In describing the experiments of § 65 of the same series, experiments which 
commence with the momentary realization of a cylinder a little transcending 
the limit of stability, it was said that the spontaneous alteration of this cylin- 
der was sometimes manifested by the formation of two constricted portions 
comprising between them one dilated portion; that this state of the figure, 
after attaining no very decided development, appeared to remain stationary for 
some time; that then one of the constricted portions was slowly obliterated 
while the other deepened, and the transformation continued afterwards in the 
ordinary manner. Now, from the fact that this figure, with two contractions, 
persists for a considerable time, it must be inferred that it constitutes a figure 
of equilibrium, and consequently an unduloid little different from the cylinder 
and surpassing the limit of stability—that is, extending itself beyond the cen- 
tres of the two constricted portions. In effect, since such an unduloid, al- 
though unstable, is a figure of equilibrium equally with the unstable cylinder, 
it may likewise be formed, for some moments, between the disks, and it may 
be conceived that a slight accidental cause would suffice to transform the mass 
from one of these figures into the other. We see, finally, that, in the experi- 
ments of § 10 of the present series, the liquid mass thus always constitutes a 
portion of an unduloid which becomes modified, without ceasing to pertain to 
this kind of figure, in proportion as we absorb the excess of oil. ° 
§ 13. The transient unduloid, spoken of above, verifies the conclusions of § 6 
relative to the pursuit of the meridian line beyond points of the concave parts 
where the elements become parallel to the axis. Unfortunately this unduloid 
is not produced at will; its meridian curvatures are weak, and it is otherwise 
unstable; but another experiment, to which allusion has been made without 
describing its results, furnishes a precise verification of the same conclusions. 
If, after having formed between two rings a vertical cylinder whose height is 
much less than that which would correspond to the limit of stability, we 
slightly raise the upper ring, the cylinder is observed to become somewhat 
hollowed in the meridian direction, so that the figure presents a constriction ; 
if the ring be again raised, the constriction still deepens and the figure remains 
perfectly symmetrical on both sides of the cercle de gorge, which is, conse- 
quently, situated at the middle of, the interval between the rings. If, in‘the 
cylinder with which we started, the ratio between the height and diameter was 
suitable, we may, by proceeding thus, render the constriction very decided, and 
then the meridian line changes the direction of its curvature by tending towards 
the rings, so that it presents two points of inflection at an equal distance on 
both sides of the cercle de gorge; the bases of the figure, also, preserve their 
convex form, and even their curvature increases more or less. In this experi- 
ment there is always, we may conceive, a limit to the separation of the rings, 
beyond which equilibrium is no longer possible; if we overpass it, the con- 
stricted portion grows spontaneously more slender, till it breaks and the figure 
separates into two portions; but, for every degree of distance less than the 
limit in question, the equilibrium is stable, The cylinder which has appeared 
to give the above results most distinctly, is that whose height is to the diameter 
nearly in the ratio of 5 to 7. In employing, for instance, rings of 70 millime- 
tres in diameter, it is proper to form a cylinder of about 50 millimetres in 
height; the upper ring may then be raised until it is distant from the other 
nearly 110 millimetres, and we thus obtain a figure in which the cercle de gorge 
has but a diameter of some 30 millimetres. 
The experiment thus executed requires great precaution: the equality in the 
densities of the two liquids and the homogeneity of the oil should be perfect, 
and when the limit of separation of the rings is approached, it is necessary to 
proceed with much circumspection. But we succeed without difficulty by so 
