UTAH ACADEMY OF SCIENCES 101 
movement is due to varying surface curvature. For 
spherical grains of uniform size the pressure (which is 
the product of the surface tension and the curvature) is 
a determinate function of the volume of the ringshaped 
water wedge and the pressure gradient is therefore a 
determinate function of the moisture gradient. Since 
the soil particles are not spherical, a rigorous solution of 
the problem would perhaps be only approximately cor- 
rect as applied to the soil. We have therefore attempted 
only an approximate (?) determination of the function, 
yielding the tentative relation :-— 
dp ee dp. 
dx d 
dx p v 
where p is the pressure, p the density of moisture at a 
point whose linear coordinate is x, and k is a constant 
involving the radius of the particle and the surface ten- 
sion of the liquid. 
Substituting this value in Stokes’ equation we obtain 
for the velocity, 
e dp 
hike ela 
where c involves the surface tension, coefficient of vis- 
cosity and the radius of the particle. 
A simple standard rigorous mathematical develop- 
ment yields the differential equation :— 
jd) 
dt Fi 
where v is the mean relative velocity between soil par- 
ticle and moisture at a point whose coordinate is x and 
(1) NOTE.—The curvature of the soil particle was neglected 
in the region of the water wedge, and the relation between the two 
radii of curvature of the surface was assumed to be of the form, 
By =" Gt 
