614 
Journal o f Agricultural Research 
Vol. XXX, No. 7 
Figure 2, A, upon the exact height 
class. Seventy feet may be tall for 
9-inch trees and the average height of 
the 9 inch-70 foot class may be only 
67 feet. Likewise, 70 feet may be 
short for a 16-inch tree and the aver¬ 
age height may be 72 feet. So, ulti¬ 
mately, in a given diameter class, short 
trees are forcibly stretched out to the 
mean of their height class and tall 
trees are pulled down to the mean of 
the class, as already brought out and 
shown in Figure 1 and Figure 3 A, an 
idealized form of Figure 2 D, which 
leads to a distortion of form. 
In practice, in drawing the first 
curves of the form shown in Figure 
2 A, an irregular jumble and crisscross- 
certain degree all the way down to 
breast height and tends to make the 
diameters of small trees (short for 
their height class) run small, and large 
trees (tall for their height class) run 
high. All this tends to make trees in 
extreme size classes show a form they 
do not actually possess. 
In the next curving (fig. 2, C) values 
of trees in the same diameter class but 
in different height classes are combined. 
On every height line above the ground, 
values will run low in the short trees 
and high in tall, which merely shifts 
the tilt of the curves, a matter which 
is absolutely invisible when all are 
tilted equally or even harmonically. 
So this error passes on through to the 
ABCDEFGHI 
Diameter Breast High 
Fig. 3.—Failure of all taper curves in the same height class to converge upon the mean of the class 
ing of lines in the upper part of the 
graph always occurs. Theoretically 
the result should look something like 
Figure 3 B, but owing to miscellaneous 
errors and differences in form toward 
the tree tips, instead of a mere failure 
of the lines to converge on the mean 
height value of the class as shown, there 
is a tremendous tangle of crossing lines, 
for there may easily be 20 inch classes 
in a single height class. When this is 
straightened out graphically and each 
curve forced to end at the mean value 
of the height class, it results in a much 
wider spread of values toward the top 
than there should be. The second 
curving thus straightens out the criss¬ 
crossing, but leaves the total spread of 
the lines about the same; the spacing 
is made even, but abnormally wide, so 
that small trees are forced to take on 
abnormally slight taper toward the 
top and big trees are made to show a 
great taper. The effect extends to a 
end. Thus incorrect values caused by 
wrong spacing for any reason whatso¬ 
ever of lines in Figure 2 A, tend to 
persist, as actually occurred in one 
instance of lodgepole pine taper curves* 
The space between the lines is 
greater in the 70-foot class than in any 
other in the finished taper curve. 
This could be avoided to a certain 
degree by harmonizing the curves on a 
different basis to eliminate the in¬ 
efficient third curve. Several alter¬ 
native methods investigated by the 
writer, however, while more sound 
theoretically on account of the use of 
almost straight line curves throughout, 
proved practically as unsatisfactory in 
actual use and involved a great deal 
more labor than the system of harmon¬ 
ization outlined by Barrows. 
The only conclusion possible from 
this study of Barrows’s taper curve 
construction is that by it are readily 
obtained harmonized values that change 
