142 
W. B. Crump. 
the method of least squares furnishes the two equations 
b = 
in 
'Sx'^xy- 
y r 2 .v„ 
n'lx- 
( 2 *) 2 
2 w 2 y — nlLxy 
(3) 
(4) 
( 2 *) 2 —» 2* 2 . 
where «=the number of observations. 
But if b=o simpler equations may be obtained, for then 
2 * 
and from equation (3) 
m 
2**2 xy == 2w 2 2y 
(5) 
yv 
zxy 
2 * 2 
'-xy 
in 
( 6 ) 
If then the curve passes through the origin there are two 
alternative methods of calculating the coefficient of humidity (in). 
Applying these methods to all the values of water-content and 
humus-content set out in the tables the following results are 
obtained :— 
By Equations 5 and 6 
Coefficient of Humidity (///). 
py_ 
2jt 
2 xy 
2 * 2 
Peats 14 ... 2-32 2-32 
Sub-peats 10 ... 3*03 2-91 
The two values of m are, in the case of the peats, identical in 
spite of considerable individual departures from this mean value. 
So the equation y=mx affords a complete solution and the water- 
content is found to be a function of the lnimus-content, and of that 
alone. This is expressed by the coefficient of humidity. 
In the case of the sub-peats the two values are not identical so 
that the simpler equation is again found to be insufficient. But 
turning to equations 3 and 4 the following values are obtained by 
their application to the analyses of the sub-peats:— 
Sub-peats. 
Residual water (b) ... ... 4-8% 
Coefficient of humidity (in) ... 2-33 
Hence for the sub-peats 
y=b 4 - nix 
and to deduce the value of the coefficient the water held by the soil 
particles, practically 5% of the air-dry soil, must first be deducted 
