WITHDRAWN FROM THE ACTION OF GRAVITY. 237 



margin of the latter, tlie action of the solid system is completed ; and the move- 

 ments which subsequently ensue in the liquid mass, to attain the figure of 

 , equilibrium, can only then be due to an action emanating from the free part of 

 the superficial layer. It is, therefore, the latter which compels the liquid to pass 

 through the aperture in the plate ; and the phenomenon must necessarily result 

 either from a pressure exerted by that portion of the superficial layer which 

 belongs to the most convex segment, or by a traction produced by the portion 

 of this same layer belonging to the other segment. Our experiment not being 

 alone capable of determining our choice between these two methods of explaining 

 the effect in question, let us provisionally adopt the first, i. e., that which attributes 

 it to pressure. ■ In our experiment, this pressure emanates from the superficial 

 layer of the most curved segment ; but it is easy to see that the superficial layer 

 of the other segment also exerts a pressure which, alone, is less than the pre- 

 ceding. In fact, if for the most curved segment a segment less curved than the 

 other were substituted, the oil would then be driven in the opposite direction. 

 Hence it follows that the entire superficial layer of the mass exerts a pressure 

 upon the liquid which it encloses, and that the intensity of this pressure depends 

 upon the curvatures of the free surface. Moreover, as the liquid proceeds from 

 the most curved segment to that which is least so, it is evident that in the case 

 of a convex surface, the curvature of which is spherical, the pressure is greater 

 in proportion as the curvature is more marked, or as the radius of the sphere to 

 which the surface belongs is smaller. Lastly, since a plane siuface may be 

 considered as belonging to a sphere, the radius of which is infinitely great, it is 

 evident that the pressure corresponding to a convex surface, the curvature of 

 which is spherical, is superior to that which would correspond to a plane surface. 

 All these results were announced by theory. They perfectly verify, then, that 

 part of the latter to which they refer, and this concordance ought now to decide 

 in favor of the hypothesis of pressure. This same part of the theory was already 

 verified, in its application to liquids submitted to the action of gravity, by the 

 phenomenon of the depression presented by liquids in capillary tubes, the walls 

 of which they do not moisten ; but the series of our experiments, setting out 

 with the elements of the theory, and following it step by step, yields far more 

 direct and complete verification. Our last experiment leads us to still further 

 consequences. The liquid passing from one of its segments to the other, so 

 long as their curvatures have not become identical, and the pressures corre- 

 sponding to the two portions of the superficial layer becoming equal to each 

 other simultaneously with the two curvatures, it follows that the mass only 

 attains its figure of equilibrium when this equality of pressure is established. 

 We thus have a primary verification of the general theory of equilibrium which 

 governs our liquid figures, a condition in virtue of which the pressures exerted 

 by the superficial layer ought to be everywhere the same. Moreover, it is 

 evident that if a superficial layer, having a spherical curvature, exerts by itself 

 a pressure, this principle must be true, however small the ex-tent of this layer 

 may be supposed to be. It follows, therefore, that an extremely minute por- 

 tion of the superficial layer of our mass, taken from any part of either of the 

 two segments, ought itself to be the seat of a slight pressure; consequently, 

 that the total pressure exerted by the superficial layer is the result of individual 

 pressures emanating from all the elements of this layer. This was also shown 

 by theory. Further, following the same train of reasoning, we sec that the 

 intensity of each of the minute individual pressures ought to depend upon the 

 curvature of the corresponding element of the layer, which is also in conformity 

 with theory. Lastly, as in a state of equilibrium the two segments belong to 

 spheres of equal radii, the curvature is the same in all points of the surface 

 of the mass ; whence it follo\i^3 that all the minute elementary pressures are 

 equal to each other. The general condition of equilibrium (§ 5) is, therefore, 

 perfectly verified in the instance of our experiment. 



