WITHDRAWN FROM THE ACTION OF GRAVITY. 603 



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 extent of this layer may be supposed to be. It fol- 

 lows, therefore, that an extremely minute portion of the super- 

 ficial layer of our mass, taken from any part of either of the two 

 segments, ought itself to be the seat of a slight pi'essure ; con- 

 sequently, that the total pressure exerted by the superficial layer 

 is the result of individual pressures emanating from all the ele- 

 ments of this layer. This was also shown by theory. Further, 

 following the same train of reasoning, we see 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 equili- 

 brium the two segments belong to spheres of equal radii, the curva- 

 ture is the same in all points of the surface of the mass ; whence 

 it follows, that all the minute elementary pressures are equal to 

 each other. The general condition of equilibrium (§ 5) is there- 

 fore perfectly verified in the instance of our experiment. 



18. The principle of the superficial layer, applied to the pre- 

 ceding experiment, allows of the latter being modified in such a 

 manner as to obtain a very remarkable result. When the 

 figure of equilibrium is once attained, the perfoi-ated plate acts 

 upon the superficial layer by its external border only. The 

 whole of the remainder of this plate then exerts no influence 

 upon the figui*e in question. Hence it follows that this figure 

 would still be the same if the aperture were enlarged, only the 

 greater the diameter of the latter the less time is required 

 for the establishment of the equality between the two curva- 

 tures. Lastly, we ought to be able to enlarge the aperture 

 nearly to the margin of the plate without changing the figure of 

 equilibrium ; or, in other w ords, to reduce the solid system to a 

 simple ring of thin iron wire. Now this is confirmed by experi- 

 ment; but, to put it in execution, we cannot confine ourselves, 

 aa before, to making the solid system penetrate a sphere of oil 

 of less diameter than that of this same system, and subsequently 



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