OBSERVATIONS ON THE DAUBREE EXPERIMENT 7 



2(7 



is less than that on the upper side by an amount equal to — ; 



P 



at the same time, however, this pressure difference is equal to the 

 hydrostatic head of a column of the liquid of height h. That is, 



— = hgd 

 P 



where g is the intensity of gravitation and d the density of the liquid. 

 Moreover, if a is the angle of contact between liquid and tube, 

 p = rcosa, where r is the radius of the tube; hence, 



, 2 0- cos a 



'^= T~ (3) 



which is the familiar formula for the rise of liquids in capillary tubes. 

 In the case of water in contact with many substances, a=o° 

 and the equation reduces to the form 



^=^. (4) 



For water at a temperature of 18°, provided that h and r are 

 expressed in centimeters,^ k has the value 0.00204 ^-nd a, the surface 

 tension in dynes per cm., is 74. The development of this formula 

 directly from the basis that there is a definite pressure discontinuity 

 at a surface of separation seems worthy of emphasis since it affords 

 us a clearer insight into the more complicated problems of capil- 

 larity.^ Starting from this basis, a number of conclusions are imme- 

 diately obvious; we state them here because they have not been 



' If h and ;■ are expressed in millimeters, the constant k must be increased, not 

 tenfold, but one hundred fold. 



^ Incidentally it may be remarked that by the same reasoning the pressure within 

 a small drop of water is greater than the external pressure; the water is thus under 

 greater pressure than the vapor derived from it. Now this type of pressure — "un- 

 equal" pressure — -raises the vapor pressure of the liquid; consequently the vapor 

 pressure of a drop is greater the smaller the radius of curvature of its surface — a 

 well-known conclusion which is exceedingly important in regard to a large number of 

 phenomena. In a perfectly analogous way the vapor pressure in equilibrium with the 

 curved surface of a liquid in a capillary surface is smaller than its vapor pressure as 

 ordinarily given; and this lowering of vapor pressure is greater the smaller the diameter 

 of the tube. Similarly (if it be permissible to speak of the surface tension of solids) 

 one may deduce the fact that the solubility of a substance increases as the size of grain 

 decreases. 



