7 CAPILLARY ACTION. 



or if we suppoM P, fixed and P, variable, we may write 



ooa - i y\[- +constant. 



This equation gives a relation between the inclination of the curve to the 

 horuun and the height above the level of the liquid. 



Resolving vertically we find that the weight of the liquid raised above the 

 level most be equal to T (sin 0, sin 0,), and this is therefore equal to the area 

 /',/Vff^t multiplied by gp. The form of the capillary surface is identical with 

 that of the "elastic curve," or the curve formed by a uniform spring originally 

 straight, when its ends are acted on by equal and opposite forces applied either 

 to the ends themselves or to solid pieces attached to them. Drawings of 



the different forms of the curve may be found in 

 Thomson and Tait's Natural Philosophy, Vol. i. 

 p. 455. 



We shall next consider the rise of a liquid 

 between two plates of different materials for which 

 the angles of contact are a, and a,, the distance 

 between the plates being a, a small quantity. Since 



the plates are very near one another we may use the following equation of 



the surface as an approximation: 



whence 



y = h 1 +Ax+JBx t 

 h^h + Aa+Ea', 



cot 04 = A 

 cot a, = A + 2Ba 

 =pga (h, 



whence we obtain 



- (2 cot cu, cot a,). 



Let X be the force which must be applied in a horizontal direction to either 

 keep from approaching the other, then the forces acting on the first 



