588 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



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 sufficient-ly near, and from this point let fall a per- 

 pendicular upon the minute canal. The action of the molecule 

 m upon the portion of the line comprised between the base of 

 the perpendicular and the surface, will attract this portion towards 

 the interior of the mass. If afterwards we take a portion of the 

 line equal to the former from the other side of the perpen- 

 dicular, and commencing at the base of the latter, the action of 

 the molecule m upon this second portion will be equal and op- 

 posite to that which it exerted upon the first ; so that these two 

 portions conjointly would neither be attracted, towards the in- 

 terior nor the exterior of the mass ; if beyond these two same 

 portions another part of the line is comprised within the 

 sphere of activity of m, this part will evidently be attracted 

 towards the exterior. The definitive action of m upon the 

 line will then be in the latter direction. Hence it follows 

 that all the molecules of the space comprised between the sur- 

 face and the tangent plane which are sufficiently near the line 

 to exert an effective action upon it, will attract it towards the 

 extei'ior of the mass. If then we suppress this portion of the 

 liquid so as to reproduce the convex surface, the result will 

 be an augmentation of the pressure on the part of the line. 

 Thus the pressure corresponding to a convex surface is greater 

 than that corresponding to a plane surface, and its amount 

 will evidently be greater in proportion as the convexity is more 

 marked. 



4. If the surface has a spherical curvature, it may be demon- 

 strated that, representing the pressure corresponding to a plane 

 sur'ace by P, the radius of the sphere to which the surface belongs 

 by r, and by A a constant, the pressure exerted by a line of mole- 

 cules, and reduced to unity of the surface, will have the following 

 ^■al"^' p + ^ ^j_^ 



•*• being positive in the case of a convex, and negative in that of 

 a concave surface 



Whatever be the form of the surface, let us imagine two 

 spheres, the radii of which are those of greatest and least curva- 

 ture at the point under consideration. It is evident that the 

 pressure exerted by the line will be intermediate between 

 those corresponding to these two spheres, and calculation shows 



