WITHDRAWN FROM THE ACTION OF GRAVITY. 609 



more in diameter, and may thus be extended to within a tolerably 

 short distance of the solid surface. In my experiment, the dia- 

 meter of the metallic cylinder was 7 centimetres, and I have 

 been enabled to increase the* size of the layer until its circum- 

 ference was not more than about 5 millimetres from the solid 

 surface ; but at this instant it broke, and the liquid of which 

 it consisted rapidly receded towards that which still ad- 

 hered to the metallic band. The fact which we have just de- 

 scribed is very remarkable, both in itself and in the singular 

 theoretical consequences to which it leads. In fact, that part of 

 the mass to which the layer adheres by its margin presents concave 

 surfaces, whilst those of the layer are plane ; now the existence 

 of such a system of surfaces in a continuous liquid mass seems in 

 opposition to theory, since it appears evident that the pressures 

 cannot be equal in this case. But let us investigate the question 

 more minutely. 



24. According to theory, the pressure corresponding to any 

 point of the surface of a liquid mass, as we have seen (§ 3), is the 

 integral of the pressures exerted by each of the molecules com- 

 posing a rectihnear line perpendicular to the surface at that point, 

 and equal in length to the radius of the sphere of activity of the 

 molecular attraction. The analytical expression of this integral 

 contains no other variables than the radii of the greatest and of 

 the least curvature at the point under consideration (§ 4), con- 

 sequently the pressui'e in question varies only with the curva- 

 tures of the surface at the same point. This is rigorously true 

 when the liquid is of any notable thickness ; but we shall show, 

 that in the case of an extremely thin layer of liquid, there is. 

 another element which exerts an influence upon the pressure. 

 Let us conceive a liquid layer, the thickness of which is less than 

 twice the radius of the sphere of sensible activity of the mole- 

 cular attraction. Let each molecule be conceived to be the 

 centre of a small sphere with this same radius (§ 3), and let us 

 first consider a molecule situated in the middle of the thickness 

 of the layer. The little sphere, the centre of which is occupied 

 by this molecule, will be intersected by the two surfaces of the 

 layer, consequently it will not be entirely full of liquid ; but the 

 segments suppressed on the outside of the two surfaces being 

 equal, the molecule will not be more attracted perpendicularly 

 in one direction than in the other. Now let a small right line, 

 normal to and terminating at the two surfaces, pass through 



