PHYSICAL PROPERTIES OF WATER 



curved surface at the top of the column (Fig. 2). Let V = the (email) 

 volume of liquid above this plane. 



The height of the column when in a state of equilibrium may be 

 deduced from the principle of virtual work, 1 i.e., by equating the work 

 done against gravity in any small vertical displacement of the column, to 

 that done by the surface tensions. 



If 5 x is this displacement we have, for equilibrium 



F[=0 



51 



4 V 



But T as - T ls = T al cos a 

 __ 4 T al cos a _ 4 F 

 w 6? T r/ 2 



(1) 



In general V is very small, so that with- 

 out sensible error (1) may be written 



w d 



Similarly it may be shown that the 

 vertical rise or fall between two parallel 



plates at a distance d apart = 



2 T COS a , 



w d 



(3) 



FIG. 2. 



It is with the former case of capillary 



action that we are chiefly concerned in hydraulics, as affecting the 

 accuracy of measurements of pressure in a liquid, when these depend 

 upon the height of a supported column of the liquid. Thus with a 

 piezometer, in which pressure is measured by means of a water column, 

 the artificial elevation of the pressure column by capillary action at about 

 68 F. is given by 



4 X '005548 cos 25 32' . 

 62-4 d 



1 More simply, it may be considered that the whole weight of the supported column is 

 carried by the surface films, and that this weight is equal to the vertical component of the 

 surface tension. This leads, as before, to the equation 



v d . T cos a = w TT d? 



--* 



4 r cos a 



w d 



2T 



With liquid in its spherical state we have 2 TT r T = ir r* p, or^ = , giving^;, the excess of 



internal over external pressure. Thus with small values of r a comparatively small value of 

 T may be accompanied by a large value of p. 



