CAPILLARY ACTION. 569 



FORM OF THE CAPILLARY SURFACE. 



The form of the surface of a liquid acted on by gravity is easily deter- 

 mined if we assume that near the part considered the line of contact of the 

 surface of the liquid with that of the solid bounding it is straight and hori- 

 zontal, as it is when the solids which constrain the liquid are bounded by 

 surfaces formed by horizontal and parallel generating lines. This will be the 

 case, for instance, near a flat plate dipped into the liquid. If we suppose these 

 generating lines to be normal to the plane of the paper then all sections of 

 the solids parallel to this plane will be equal and similar to each other, and 

 the section of the surface of the liquid will be of the same form for all such 

 sections. 



Let us consider the portion of the liquid between two parallel sections 

 distant one unit of length. Let P lt P 2 (fig. 6) be 

 two points of the surface ; 6 it a , the inclination of 

 the surface to the horizon at P x and P 2 ; y lt ?/ 2 the 

 heights of P 1 and P 2 above the level of the liquid 

 at a distance from all solid bodies. The pressure at 

 any point of the liquid which is above this level is 

 negative unless another fluid as, for instance, the air, 

 presses on the upper surface, but it is only the differ- 

 ence of pressures with which we have to do, because Fi - 6 - 

 two equal pressures on opposite sides of the surface produce no effect. 



We may, therefore, write for the pressure at a height y 



where p is the density of the liquid, or if there are two fluids the excess of 

 the density of the lower fluid over that of the upper one. 



The forces acting on the portion of liquid PJP^A^ are first, the hori- 

 zontal pressures, -\pgy? and fogy? ; second, the surface-tension T acting at 

 P! and P, in directions inclined 1 and 2 to the horizon. Resolving horizontally 



we find 



T (cos 0, - cos 0,) + \g? (y? - y?) = 0, 



whence cos 2 = cos 6 l fajpy? + 3 -jr y*> 



VOL. II. ? 2 



