630 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



mains of heterogeneity in the liquids ; it is probable that in the 

 first case neither of the two liquids was absolutely homogeneous, 

 and that the two contrary effects which thence resulted (§ 41) 

 partly neutralized each other, whilst in the second case, the 

 alcoholic liquid being rendered perfectly homogeneous, the effect 

 of the slight heterogeneity of the oil exerted its full influence. 

 However this may be, these differences in each case are so small, 

 that we may consider experiment as in accordance with theory, 

 of which it evidently presents a very remarkable contirmation. 



43. Mathematically considered, a cylindrical surface extends 

 indefinitely in the direction of the axis of revolution. Hence it 

 follows that the cylinder included between the two rings consti- 

 tutes one portion only of the complete figure of equilibrium. 

 Hence also if the liquid mass 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 terminated on both 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 

 experiments 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 between the two rings may then be of cylindrical 

 curvature, whilst the two bases of the figure may present sphe- 

 rical curvatures. We therefore arrive at the very remarkable 

 result, that with a liquid mass of a limited volume we may ob- 

 tain isolated portions of figui'es of equilibrium, which in their 

 complete state would be extended indefinitely. 



44. With the view of obtaining a cylinder in which the pro- 

 portion between the height and the diameter was still greater 

 than that in fig. 2.3, I replaced the rings previously employed by 

 two others, the diameter of which was only 2 centims. I first 

 tried to make a cylinder 6 centims. in height, i. e. the height of 

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

 a slightly different process from that of paragraph 38. The 

 uniformity in thu density of the two liquids being accurately 

 established, I first gave the mass of oil a somewhat larger volume 

 than that which the cylinder would contain ; having then at- 

 tached the mass to the two rings, I elevated the upper ring 

 until it was at a distance of 6 centims. from the other: this 



