8 HYDRAULICS AND ITS APPLICATIONS 



lil in is increased by the molecular action between the plate and fluid, 

 with a consequent fall in the surface level in the immediate neighbour- 

 hood of the plate. That this variation of density actually occurs has 

 been indirectly proved in other ways, while results obtained by the 

 application of this theory are amply confirmed by experiment. 



The second theory attributes the phenomena to the action of a series of 

 surface tensions, which are assumed to exist at every surface of contact 

 of any liquid or gas with any solid, and also at the surface of contact of 

 any liquid with any other liquid, or with a gas. Thus at the common 

 line of intersection of a solid, liquid, and gas, i.e., at the line passing 

 through P (Fig. 1) and perpendicular to the plane of the paper, three 

 surface tensions, of intensity T^, T al , and T h per unit length of this line, are 

 in existence. For equilibrium then, their directions and magnitudes will be 



FIG. 



related according to the ordinary laws of statical equilibrium. Thus for 

 contact with a plane surface we have 



T M = T h + T al cos a, 



and the angle a will be acute or obtuse according as T as T ls is positive 

 or negative. 



If TO* = T ls -f- T alt a = and for this, and all greater relative values 

 of TW the fluid will immediately spread to cover the surface, the effect 

 being as though the liquid were pulled outwards in every direction by the 

 tension T M , the resultant of the tensions T ls and T al being insufficient to 

 this motion. On the other hand if T^ T ls is negative, cos a is 

 negative and the angle a is obtuse. If T ls !', = T al , a = 180, and 

 the liquid, if in sufficiently small masses, assumes the spherical state. 



On these assumptions, justified in so far as the results obtained by their 

 application go, the various phenomena of capillary action easily lend 

 themselves to mathematical treatment. 



Rise of Liquid in a Capillary Tube.-Let h be the height of the liquid 

 in the tube, of diameter d feet, and let w be the weight of unit volume of 

 the liquid, m-n- // is measured to a horizontal plane tangential to the 



