WITHDRAWN FROM THE ACTION OF GRAVITY. 



251 



render the surface included between the rings convex. Let us then gradually 

 elevate the upper ring, and we shall produce a cylinder of greater height than 



Mg.23. 



li^. 24. 



the first. If we repeat the same manipulation a suitable number of times, we 

 shall ultimately obtain the cylinder of the greatest height which our apparatus 

 permits. I have in this manner obtained a perfectly cylindrical mass 7 cen- 

 timeters in diameter, and about 14 centimeters in height, (Fig. 23.) To allow 

 of the cylinder of this considerable height being perfect, it is requisite that per- 

 fect equality be established between the densities of the oil and the alcoholic 

 liquid. As a very slight diflFerence in either direction tends to make the mass 

 ascend or descend, the latter assumes, to a more or less marked extent, one of 

 the two forms represented in Fig. 24. Even when the cylindric form has been 

 obtained by the proper addition of alcohol of 16°, or absolute alcohol, as occa- 

 sion may require, (§ 24 of the preceding memoir,) slight changes in tempera- 

 ture are sufficient to alter and reproduce one of the above two forms. 



39. Let us now examine the results of these experiments in a theoretical 

 point of view. First, it is evident that a cylindrical surface satisfies the general 

 condition of equilibrium of liquid figures, because the curvatures in it are the 

 same at every point. Moreover, such a surface being convex in every direction 

 except in that of the meridional line, where there is no curvature, the pressure 

 corresponding to it ought to be greater than that corresponding to a plane sur- 

 face. The same conclusions are deducible from the general formulte (2) and 

 (3) of paragraphs 4 and 5. In fact, as we have already stated in paragraph 37, 

 one of the quantities R and R' is the radius of curvature of the meridional line, 

 and the other is the portion of the normal to this line included between the 

 point under consideration and the axis of revolution. Now, in the case of the 

 cylinder, the meridional line being a right line, its radius of curvature is every- 

 where infinitely great ; and, on the other hand, this same right line being 

 parallel to the axis of revolution, that portion of the normal which constitutes 

 the second radius of curvature is nothin"; more than the radius itself of the 



1 1 



dis- 



cylinder. Hence it follows that one of the terms of the quantity p , ^ 



appears, and that the other is constant ; this same quantity is, therefore, con- 

 stant, and consequently the condition of equilibrium is satisfied. Now, if we 

 denote by I the radius of the cylinder, the general value of the pressure for 

 this surface would become 



A 1 



P + 



1 "A" 



Now A being positive because it is directed towards the interior of the liquid, 

 (§ 4,) the above value is greater than P, i. e., than that which would correspond 



