360 FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
§ 27. The constrictions realized in the experiments of § 25 being gen-rated 
by a portion of the node of the complete meridian line, it is obvious that the 
figure generated by the entire node, from the summit of the latter to its point, 
would be concave in the interior of the oil; but it is indifferent, we know, (§ 15,) 
as regards equilibrium, whether the liquid be situated on one or the other sid 
of the surface; the figure generated by the node may, therefore, be equally w~ll 
supposed full or in relief, and it is in the latter state that our experiment will 
realize it. Only when the liquid is transported to that side of the curve, the 
quantities M and N at once change their sign, and consequently the quantity 
ca ; : : . ang 
mew ee being negative, as it was previously, becomes positive. 
We form, in a ring of iron wire, a bi-convex liquid lens, (2d series, § 18,) 
whose thickness shall be abont equal to the sixth of the diameter: for instance, 
with a ring 70 millimetres in diameter, the thickness of the lens should be about 
12mm. If we pierce perpendicularly this lens in its centre, by means which 
will be indicated below, we obtain a regular annular figure, limited externally 
by the solid ring, and continuing for two or three seconds; after which, the 
central opening is seen to stretch towards a point of the solid ring, the mass 
disunites at that point, and all the liquid flows towards the opposite part of the 
ring, there to form a large and perceptibly spherical mass. Now, the momentary 
annular figure, which is formed under these circumstances, is, though unstable, a 
figure of equilibrium, since it subsists for some moments, and its duration is 
long enough to enable us to observe that its meridian section has the form 
represented by Fig. 31, in which the dotted line is the section of the plane of 
the ring. This meridian section shows evidently that the surface of the figure 
produced is generated by a node having its summit turned towards the axis of 
revolution and its point to the solid ring, 
Let us dwell for an instant on the details of the experiment just described 
and on certain modifications of it. To pierce the lens, we should employ a 
small cylinder of wood pointed at one end and joined at the other to an irou 
wire, which is bent obliquely, so that, holding it with the hand, we can intro- 
duce the small cylinder into the vase and pierce the lens perpendicularly. If 
the diameter of the solid ring be 70 mm., as we supposed above, that of the 
small cylinder should be about 16 mm.; and the cylinder and its point should 
be covered with cotton cloth in order to prevent all adhesion of the oil. 
If we give the lens a thickness sensibly exceeding the sixth part of the 
diameter of the solid ring, the liquid returns upon itself as soon as the cylinder 
is withdrawn, and the mass resumes its lenticular form; but we may give a less 
thickness than the above limit, when the central opening will assume larger 
dimensions, and the node of the meridian line be consequently smaller. When 
the thickness of the lens is sufficiently inferior to the limit in question, the man- 
ner in which the spontaneous destruction of the unstable figure takes place is 
not the same; the central opening does not then extend towards a point of the 
solid ring, but the annular liquid mass contracts and disunites in several places 
at once, so as to be converted into a series of small isolated masses, which 
adhere to different parts of the metallic ring. The unstable liquid ring spoken 
of in § 19 of the second series pertains to the sort of figure which we are now 
studying, and it will be remembered that it proceeds from a lens whose thick- 
ness has been rendered as small as possible. 
§ 28. As the liquid ring may thus assume, in the same solid ring, very dif- 
ferent dimensions according to the thickness of the lens, or, in other words, ac- 
cording to the volume of the liquid of which it is formed, it results that, for the 
same distance from the point of the node of the meridian line to the axis of 
revolution, the length of the node may vary between wide limits: in the ex- 
periments above described, these variations are comprised between a very small 
