Apr. 1, 1925 
The Construction of Taper Curves 
613 
The third system of curves is aimed 
to harmonize values in the same 
d. b. h. class, but in different height 
classes. There are never many height 
classes in a single d. b. h. class, for the 
variation in the height of trees of a 
given diameter never amounts to many 
ten-foot intervals (the usual classifica¬ 
tion) . The curves are, therefore, short 
&nd more open to error in direction than 
long curves. Their form is illustrated 
in Figure 2, C, and their function is 
similar to curves of the second series 
as shown in Figure 2, B, except that 
d. b. h. is constant instead of the 
lieight of the tree, and separate charts 
are drawn for each d. b. h. class. 
Their shape is different, however. In 
Figure 2, A, it is clear that the normal 
distribution of the lines is fairly evenly 
spaced across the sheet, at any given 
lieight, hence their relation is expressed 
By very nearly a straight line. In 
Figure 2, D, the spacing is even, but 
up and down rather than horizontally 
across the page. Curves as shown in 
Figure 2, C, however, if properly 
drawn, ought to have the effect of 
arranging the lines harmonically across 
the page, as is desired. 
If these curves are not properly 
drawn they lead to a variety of errors. 
If the curve is the wrong shape (pro¬ 
vided the end points are right) it means 
that in trees of medium height the 
diameters are incorrect. Curves which 
touch the basal line fortunately have 
one point fixed, for diameter at the top 
of a tree must always be zero. The 
curves representing points 10 and 20 
feet above the ground approximate 
straight lines and diverge but slightly, 
but higher curves are difficult to draw. 
In the first place, the values high in the 
tree are erratic, for reasons that will 
be shown later, and the curvings in 
series B do not remedy matters very 
much. Secondly, these points are in¬ 
capable of much correction by the 
curves, for the change of direction is 
rapid at that point, divergence is con¬ 
siderable, and the curves are widely 
spaced, all of which renders the proper 
placing and shaping of the curve very 
difficult. 
In practice it is found that the curves 
are most naturally drawn to pass 
through the point plotted to represent 
diameter 10 feet from the top, while 
actually such points often need severe 
correction. An error in diameter 10 
feet below the top may not exist in one 
diameter class alone, as such a pos¬ 
sibility has already been ironed out in 
the curves of Figure 2, B. Conse¬ 
quently, curves of Figure 2, C, pass it 
on, although theoretically they ought 
to remove it. For instance, in Figure 
2 , C, let us suppose the diameters of 
all the trees in the 50-foot class at the 
40-foot point are high because of the 
misplacement of the 40-foot line in 
the previous curving of the type 
shown in Figure 2, B (for the regular¬ 
ity of the spacing of these lines is 
difficult to judge on a large scale). 
Then in Figure 2, C, the point A will 
fall high at the 40-foot point. In 
40-foot and 60-foot tree classes (points 
B and C) the values we will suppose 
to be correct. Nevertheless, because 
of the rapid curvature, lack of paral¬ 
lelism and width of spacing in that 
part of the graphs, it is hard to make 
a choice between the solid line or the 
dotted line as shown in the figure, one 
confirming an erroneous value and 
changing a correct one, the other 
changing the wrong value to the right 
one. Curves of the form shown in 
Figure 2, C, serve to even up the 
erratic values, however, especially in 
tall trees and in the lower part of the 
bole, and to make changes run 
smoothly from height class to height 
class within the same inch class. 
As each inch class is adjusted 
separately, there is no assurance that 
the same relative adjustment will be 
made in the neighboring inch classes. 
Accordingly, values are read back 
again to make curves of the type 
shown in Figure 2, B, where the inch 
classes are again put in harmonious 
relations with each other, with some 
possible disarrangement of ideal re¬ 
lations existing between the different 
height classes. These curves are 
finally transformed back again to 
curves of the type shown in Figure 
2, A, the finished taper curve. 
Having briefly outlined the method 
and noted some of the difficulties 
encountered, its practical effectiveness 
must be considered. The first curving 
makes the form of the trees in each 
diameter and height class independ¬ 
ently smooth, although their forms 
may differ. This is good. Next, the 
lines are spaced evenly and are made 
to run through the right d. b. h. 
through the process shown in Figure 
2 , B. But although spaced evenly, 
what is the assurance that the spaces 
are the right distance apart? If 
wrong in a single height class, curves 
of series 3 (fig. 2, C) will tend to iron 
out the trouble when the erroneous 
value is placed in comparison with 
correct values in adjacent classes. 
But just here is where one error comes 
in. 
In practice, the first curves fail to 
converge as they are shown doing in 
