CAPILLARY MOVEMENT OF SOIL MOISTURE. 47 
EVALUATION OF EMPIRICAL CURVES. 
In order to determine whether any mathematical relation could be 
found between the curves representing the movement of moisture in 
the different soils, mathematical equations to fit these empirical 
curves were found for typical flumes. The curves representing the 
movement of moisture in flumes at various slopes containing River- 
side heavy decomposed granite loam were evaluated to ascertain 
whether the movement of moisture was a function of the angle of the 
slope. 
The problem of finding a mathematical equation to fit a given 
curve is a tedious one. Since many soil physicists are perhaps un- 
familiar with methods of procedure other than by the method of 
least squares, which is so laborious as to limit its application, the 
method which w T as used to derive these formulae is explained in 
detail for two of these, one of which is a simple case and the other 
much more complicated. The method used is that explained in 
Engineering Mathematics, C. P. Steinmetz, New York, 1917, pages 
209-274, to which reference is also made for an explanation of the 
properties of different curves, 
In the following description, the number of days on which the 
moisture position was observed is denoted by x and the position of 
advancing moisture measured in inches above the water surface is 
denoted by y. The corresponding values of x and y were tabulated 
and plotted as a curve. It is apparent that the curve in every 
instance must pass through the origin, for when a?— 0, y=0, and 
the nature of the problem also suggests that the curve be in the form 
of a parabola. This was found to be true in the majority of cases, 
but, as will be seen in the formulae given on a subsequent page, the 
curve law in some instances changed within the range of the 
observations. 
Curves which are represented by y=za£o n are parabolic or hyper- 
bolic curves passing through the origin. When n is positive, the 
curve is parabolic. When n is negative, the curve is hyperbolic. 
The logarithm of the equation y=zax n is log y~log a-\-n log x, 
which is a straight-line formula. If the curve resulting from the 
plotting of the logarithm of y against the logarithm of a? is a straight 
line, the curve representing the data is a parabola or hyperbola. 
The equation for the exponential curve is y=«s ns , which usually 
occurs with negative exponent in the form */=a£~ nx , which gives log 
y=log a—nx log s. Log y is a linear function of x and plotting log 
y against a?, or log x against y : gives a straight line. Thus plotting 
log y and log x and x and y against each other permits the form 
of curve to be recognized. If constant terms exist, the logarithmic 
