100 TRANSACTIONS OF THE i 
A THEORY OF CAPILLARY FLOW. 
BY DR. WILLARD GARDNER. 
Slichter, in the Nineteenth Annual Report of the U. 
S. Geological Survey, has given us a theoretical solution 
for the flow of water through homogeneous sand under 
pressure, and various investigators have measured the 
distribution of capillary water at “equilibrium.” Buck- 
ingham, in Bureau of Soils Bulletin No. 38, has proposed 
an equation for the flow assuming a capillary potential 
gradient and a resistance function, both of which depend 
upon the amount of moisture present. His solution is, 
however, incomplete and involves an empirical evaluation 
of the potential as a function of the moisture content. 
Slichter’s solution for free water is a rather success- 
ful application of Poiseuille’s law for capillary tubes to 
the irregular pore tubes in the sand. The case of the 
movement of moisture in unsaturated soil is only formally 
analogous to free water movement, the cause of motion 
being a moisture gradient. Stokes’ law is developed for 
the case of an isolated particle moving in a fluid at a 
distance remote from the boundary surface, and these 
conditions are of course not rigorously fulfilled in the 
case of adjacent particles moving relatively through 
thin irregular columns of water. With the hope, how- 
ever, of approximating a correct solution we have made 
the assumption that Stokes’ law is applicable to hori- 
zontal one-dimensional capillary flow, substituting in 
place of the gravitational constant a variable kinemati- 
cal factor which depends upon the moisture content and 
the moisture gradient. 
While the physical state and properties of 
the so-called hygroscopic moisture is an _ unsettled 
question, it is believed that the capillary moisture is 
located primarily at points of contact of adjacent par- 
ticles and the pressure gradient giving rise to capillary 
