250 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



Other figures of Revolution besides the Sphere. Liquid Cylinder. 



37. Let us now endeavor to form some new liquid figures. Those best 

 adapted to tlieoretical considerations would be figures terminated by surfaces of 

 revolution otber than the sphere and lenticular figures, which we have already- 

 studied. Surfaces of revolution enjoy simple properties in regard to the radii 

 of the greatest and least curvature at every point ; we know that one of these 

 two radii is the radius of curvature of the meridional line, and that the other is 

 that portion of the normal to this line which is included between the point under 

 consideration and the axis of revolution. We shall now endeavor to obtain 

 figui-es of this nature. 



38. Let our solid system be composed of two rings of iron 

 wire, equal, parallel, and placed opposite to each other. One 

 of these rings rests upon the base of the vessel by three feet 

 composed of iron wire; the other is attached, by means of an 

 intermediate piece, to the axis traversing the central stopper, 

 so that it may be approximated to or removed from the former 

 by depressing or elevating this axis.* The system formed 

 by these two rings is represented in Plate VII, Fig. 20 bis; 

 the diameter of those which I employed was 7 centimeters. 

 After having raised the upper ring as much as possible, 

 let a sphere of oil, of a slightly larger diameter than that of 

 the rings, be formed, and conducted towards the lower ring 

 in such a manner as to make it adhere to the entire circum- 

 ference of the latter; then depress the upper ring until it 

 comes into contact with the liquid mass, and the latter is uniformly attached to 

 it. When the mass has thus become adherent to the system of the two rings, 

 let the upper ring be slowly raised; when the two rings are 

 at a proper distance ajiart, the liquid will then assume the 

 form the vertical projection of which is represented in Fig. 

 21, in which the lines a h and c d are the projections of the 

 rings. The two portions of the surface which are respect- 

 ively applied to each of the rings arc convex spherical seg- 

 ments; and the portion included. between the two rings con- 

 stitutes a figure of revolution, the meridional curve of which, 

 as is shown, is convex externally. We shall recur, in the following series, to 

 this part of the liquid figure. If we now continue gradually to raise the upper 

 ring, the curvature of the two extremities and the meridional curvature of the 

 intermediate portion Avill be diminished ; and if there is exact equilibrium be- 

 tween the density of the oil and the surrounding liquid, the 

 surface included between the two rings will be seen to assume 

 a perfectly cylindrical form, (Fig. 22.) The two bases of the 

 liquid figure are still convex spherical segments, but their cur- 

 vature is less than in the preceding figure. If the interval 

 between the rings be still further increased, it is evident that 



the surface included between them Avould lose the cylindrical 



form, and that a new figure would result. This is what 

 occurs; but the consideration of the figure thus produced must be deferred. 



Instead, then, of immediately increasing the distance between the rings, let 

 us commence by adding a certain quantity of oil to the mass, which will again 



J'l^.Zd. 



IY^.22. 



* In the experiments which we are now about to describe, the sliort axis represented in 

 Fig. 2 of the preceding memoir, and wliich has liitherto answered our purpose, must be 

 replaced by another of about 15 centimeters in length. 



