WITHDRAWN FROM THE ACTION OF GRAVITY. 587 



geometricians have not specially studied the problem of the 

 figure of a liquid mass void of gravity adherent to a given solid 

 system. We shall therefore now resume the principles and the 

 results of the theories in question, at least those which relate 

 directly to our subject. 



3. Within the interior of a liquid mass, at any notable 

 distance from its surface, each molecule is equally attracted in 

 every direction ; but this is not the case at or very near the sur- 

 face. In fact, let us consider a molecule situated at a distance 

 from the surface less than the radius of the sphere of sensible 

 activity of the molecular attraction, and let us imagine this mole- 

 cule to be the centre of a small sphere having this same radius. 

 It is evident that one portion of this sphere being outside the 

 liquid, the central molecule is no longer equally attracted in 

 every direction, and that a preponderating attraction is directed 

 towards the interior of the mass. If we now imagine a recti- 

 linear canal, the diameter of which is very minute, to exist in 

 the liquid, commencing at some point of the surface in a direc^ 

 tion perpendicular to the latter, and extending to a depth etjual 

 to the above radius of activity, the molecules contained in 

 this minute canal, in accordance with what we have stated, will 

 be attracted towards the interior of the mass, and the sum of 

 all these actions will constitute a pressure in the same direc- 

 tion. Now the intensity of this pressure depends upon the 

 curves of the surface at that point at which the minute canal 

 commences. In fact, let us first suppose the surface to be con- 

 cave, and let us pass a tangent plane through the point in 

 question. All the molecules situated externally to this plane, 

 and which are sufficiently near the minute canal for the latter 

 to penetrate within their sphere of activity, will evidently attract 

 the line of molecules which it contains from the interior towards 

 the exterior of the mass. If therefore we suppressed that portion 

 of the liquid situated externally to the plane, the pressure exerted 

 by the line would be augmented. Hence it follows that the 

 pressure corresponding to a concave surface is less than that 

 which corresponds to a plane surface, and we may conceive that 

 it will be less in proportion as the concavity is more marked. 



If the surface is convex, the pressure is, on the contrary, 

 greater than when the surface is plane. To render this evident, 

 let us again draw a tangent plane at that point at which the 

 line of molecules commences, and let us imagine for a moment 



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