WITHDRAWN FROM THE ACTION OF GRAVITY. 227 



2. In order to guide us iu our experiments, and also to enable us to com- 

 prehend tlieir bearing, we shall first consider the question iu a purely theoretic 

 point of view. The action of gravity being eliminated and the liquid mass 

 being at rest, the only forces upon which the figure of equilibrium will depend 

 will be the molecular attraction of the liquid for itself, and that exerted between 

 the liquid and the solid system to which we cause it to adhere. The action 

 of the latter force ceases at an excessively minute distance from the solid ; 

 hence, in regard to any point of the surface of the liquid situated at a sensible 

 distance from the solid, we have only to consider the first of the two above 

 forces, i. e., the molecular attraction of the liquid for itself. 



The general effect of the adhesive force exerted between the liquid and the 

 solid is to oblige the surface of the former to pass certain lines ; for instance, 

 if a liquid mass of suitable volume be caused to adhere to an elliptic plate, the 

 surface of the mass will pass the elliptic outline of the plate. At every point 

 of this surface, situated 'at a sensible distance from this margin, the molecular 

 attraction of the liquid for itself alone is in action. 



Let us now examine into the fundamental condition which all points of the 

 •free surface of the mass must satisfy, in virtue of the latter force. 



The determination of this condition and its analytical expression are com- 

 prised in the beautiful theories upon which the explanation of the phenomena 

 of capillarity is based, although 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 sur- 

 face, each molecule is equally attracted in every direction ; but this is not the 

 case at or very near the surface. 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 molecule to be the 

 centre of a small sjihere having this same radius. It is evident that one por- 

 tion 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 rectilinear 

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

 at some point of the surface in a direction perpendicular to the latter, and ex- 

 tending to a depth equal to the above radius of activity, the molecules con- 

 tained 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 direction. 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 concave, 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 ex- 

 ternally to the plane, the pressure exerted by the line would be augmented. 

 Hence it folloM's 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 poiut at which the line of molecules commences, and let us imagine for 

 a moment that the space included between the convex surface and this plane is 

 filled with liquid. Let us then consider a molecule, m, of this space sufficiently 

 near, and from this point let fall a perpendicular upon the minute canal. The 



