256 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



iiicludc'il between the two rings constitutes one portion only of the complete 

 figure of equilibrium. Hence also, if tbe liquid muss were free, it could not 

 assume the cylindrical form as the figure of equilibrium; for the volume of this 

 mass being limited, it would be necessary that the cylinder should be termi- 

 nated on bolh sides by portions of the surface presenting other curvatures, which 

 would not admit of the law of continuity. But this heterogeneity of curvature, 

 which is impossible when the mass is free, becomes realizable, as our experi- 

 ments show, through the medium of solid rings. As each of these renders the 

 curvatures of the portions of the surface resting upon it (§ 20) independent of 

 each other, the surface comprised betAveen the two rings may then be of cylin- 

 drical curvature, whilst the two bases of the figure may present spherical 

 curvatures. We therefore arrive at the very remarkable result, that with a 

 liquid mass of a limited volume we may obtain isolated portions of figures of 

 equilibrium, which in their complete state would be extended indefinitely. 



44. With the vieAV of obtaining a cylinder iir which the proportion between 

 the height and the diameter was still greater than that in Fig. 23, I replaced 

 the rings previously employed by two others, the diameter of which was only 

 2 centimeters. I first tried to make a cylinder 6 centimeters in height, i. e., the 

 height of which was thrice the diameter; and in this operation I adopted a 

 slightly difierent process from that of paragraph 38. The uniformity in the 

 density of the two liquids being accurately established, I first gave the mass of 

 oil a somcAvhat larger volume than that which the cylinder would contain; 

 having then attached the mass to the two rings, I elevated the upper ring until 

 it was at a distance of G centimeters from the other; this distance was measured 

 by a scale introduced into the vessel and kept in a vertical position by the side 

 of the liquid figure. In consequence of the excess of oil, the meridional line of 

 the figure Avas convex externally ; and as there was still q, slight diflerence 

 between the densities, this convexity was not symmetrical in regard to the two 

 rings. I corrected this irregularity by successive additions of pure alcohol 

 and alcohol of 16°, an operation which requires great circumspection, and 

 towards the end of Avhich these liquids could only be added in single 

 _/jy. £S. drops. The figure being at last perfectly symmetrical, 1 carefully re- 

 moved the excess of oil by applying the point of the syringe to a point 

 at the equator of the mass, and in this manner I obtained a pei-fect 

 cylinder. Subsequently, after having added some oil to the mass, I 

 increased the distance between the rings until it Avas equal to 8 centi- 

 meters, i. e., to four times their diameter. The oil Avas in sufficient 

 quantity to alloAv of the meridional line of the figure being convex ex- 

 t(;rnally ; but the curvature Avas not perfectly symmetrical, and I en- 

 countered still greater difficulties in regulating it than in the preceding 

 case. The defect in the symmetry being ultimately corrected, the meri- 

 dional convexity presented a versed sine of about 3 millimeters, (Fig. 25.) 

 I then proceeded to the removal of the excess of oil; but before the versed sine 

 was reduced to 2 millimeters, the figure appeared to have a tendency to become 

 thin at its loAver part and to swell out at the upper part, as if the oil 

 /^. 2ff. had suddenly become slightly increased in density. At this moment I 

 \yithdrcw the syringe, so as to be enabled to observe the effect in ques- 

 tion better; the change in form then became more and more pronounced; 

 the loAver part of the figure soon presented a true strangulation, the 

 neck of Avhich AA-as situated nearly at a fourth part of the distance be- 

 tween the rings, (Fig. 2G;) the constricted portion continued to narroAv 

 gradually, Avhilst the upper part of the figure became saa'oIIcu ; finally, 

 the liquid separated into tAvo unequal masses, Avliich remained respcct- 

 iA-ely adherent to the tAvo rings; the upper mass formed a complete 

 sphere, and the loAver mass a doubly convex lens. The Avhole of these 

 phenomena lasted a very short time only. 



