346 FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
der, an iron wire 2 millimetres in thickness, the mass assumes almost exactly 
the spherical form, and, if we use a very fine wire, the variance from the spheri- 
cal form becomes wholly imperceptible. And inasmuch as the complete figure 
varies in this manner in all its parts, the dilatations and constrictions will be 
more and more decided, and, at the final limit, the figure will consist of a sue- 
cession of equal spheres, tangents to one another on the axis. 
The complete unduloid may, therefore, vary in form between two very wide 
limits, being, on the one hand, the cylinder, and, on the other, a succession of 
equal spheres which touch one another on the axis. In Fig. 10 are represented 
, Figo 
——————— ——— =< 
two unduloids, one ‘of which differs little from the cylinder, and the other ap- 
proximates to a series of spheres. In these different aspects the figure of equi- 
librium with which we are occupied has, as we see, an analogy with the succes- 
sive phases of the transformation of an indefinite liquid cylinder (Fig. 30 of 2d 
series.) 
§ 9. But the unduloid is susceptible of another kind of variation, which 
gives a third limit. Let us suppose a vase similar to that we have been using, 
but of dimensions much greater ; let us place therein horizontally, immersed in 
the alcoholic liquid, a solid cylinder 2 centimetres in diameter, for instance, and 
of considerable length, supported on feet sufficiently elevated. We cause to 
adhere to this cylinder a mass of oil which shall produce a portion of an undu- 
loid similar to that of Fig. 6, and then add a new quantity of oil; the figure 
will now increase in length and at the same time in thickness ; but let us push 
it slightly on one side, so that one of its extremities shall be brought back to 
the same place as at first, and tle other only remain extended. If we add 
successively new quantities of oil, still pressing back the first extremity of the 
figure to the same place, this figure will progressively acquire greater thickness, 
and its second extremity will retire more and more; and, as we may conceive 
the vessel as large and the cylinder as long as we please, there is nothing 
which prescribes a term to the theoretical possibility of the increase of the 
figure in thickness as well as length. If, then, we suppose this increase carried 
to infinity, the summit of the convex meridian are and the second extremity of 
the figure will exist no longer, so that the meridian line, beginning with the 
‘first extremity, will continue to retire indefinitely from the axis; and since the 
extremity last mentioned constitutes the neck (cercle de gorge) of a constricted 
portion, and since, on both sides of such a constriction, everything is perfectly 
symmetrical, (§ 6,) we perceive that the complete meridian line will be reduced 
to a simple curve with two infinite branches, like the parabola, having its axis 
of symmetry perpendicular to the axis of revolution; consequently the com- 
plete figure generated will itself be reduced to a single constriction, extending 
indefinitely from one part to the other of its cercle de gorge. We shall pre- 
sently learn, in a precise manner, the nature of this third limit of the unduloid. 
§ 10. Let us return, now, to the employment of two disks for the realization 
of the portion of unduloid comprised between the middle points of two neighbor- 
ing constrictions, (§ 5.) When we attempt this realization by attaching to the 
_two disks a greater mass of oil than should constitute the figure, and then 
