WITHDRAWN FROM THE ACTION OF GRAVITY. 623 



the cylinder of this considerable height being perfect, it is requi- 

 site that perfect equality be established between the densities of 

 the oil and the alcoholic liquid. As a very slight difference 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 occasion may require (§ 24 of the preceding memoir), 

 slight changes in temperature are sufficient to alter and repro- 

 duce 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 cori'esponding to it ought to be greater than that cor- 

 responding to a plane surface. The same conclusions are de- 

 ducible from the general forraulce (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 meri- 

 dional 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 everywhere in- 

 finitely 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 nothing more 

 than the radius itself of the cylinder. Hence it follows, that one 



of the terms of the quantity tt + -m disappears, and that the 



other is constant ; this same quantity is therefore constant, and 

 consequently the condition of equilibrium is satisfied. Now if we 

 denote by X the radius of the cylinder, the general value of the 

 pressure for this surface would become 



P + ^.i. 



2 X 



Now \ 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 to a plane sui'face. It is therefore 

 evident that the bases of our liquid cylinder must necessarily be 



2 u 2 



