622 
Journal o f Agricultural Research 
Vol. XXX, No. 7 
same fact applied to all classes, and 
that any failures to agree were due to 
insufficient numbers of trees as a basis 
of computation. Curves were con¬ 
structed upon the hypothesis. It may 
be noted in passing that these curves 
conform very closely to lodgepole pine 
taper curves already published (11). 
In order to take advantage of this 
short-cut method it is only necessary 
to discover whether the taper curves 
in the size classes having the best basis 
in trees conform to the theoretical 
paraboloid curve. If they do so con¬ 
form, the short method will suffice. 
If they do not conform, the method 
described before can be used. The 
methods of compilation start the same 
in either case. The original sheets are 
thrown into diameter and height classes 
as usual, the measurements inside 
bark are averaged, and separate rough 
taper curves are constructed for each 
diameter and height class. The form 
quotients are then computed, and the 
values smoothed by curves, as in 
Figure 6. Then, choosing several size 
classes where the basis in trees is heavy, 
the general correspondence between the 
theoretical curve and the actual curve 
should be noted. If it is close, the 
general similarity of all size classes to 
the paraboloid can be assumed. Then 
if FQ = form quotient, r =— 
r being the exponent in the parabolic 
formula Y 2 = px T . 
The value of r always falls near 1. 
Then if x equals the distance from 
breast height to the top of the tree and 
Y = diameter breast high inside bark, 
Y 2 = px r , from which p can be ascer¬ 
tained. Then by use of this same 
equation, by introducing different 
values for x, the diameter at various 
heights can be readily ascertained. 
The process sounds complicated, but 
can be done rapidly when once mastered, 
especially with the aid of an alignment 
chart. Such a chart is illustrated in 
Figure 10 (6). It may be mounted on 
a drawing board and arranged with a 
strip of celluloid bearing a straight line 
pivoted with a thumb tack moving on 
the FQ-R line, and a thread fastened 
to a pin moving on the P line (fig. 10). 
To solve the equation by this chart, 
take any diameter and height class— 
say the 60-foot height class—look up 
the form quotient for that class and 
pivot a line on the celluloid strip at 
the appropriate value. Make this line 
pass through the height of the tree 
minus 4J^ feet (the distance from the 
tip of the tree to the “base” at breast 
height) on the H line. Then take the 
pin and thread and stick the pin in the 
value of diameter breast high inside 
bark for the particular class you are 
dealing with. Make the thread inter¬ 
sect the line on the celluloid strip on 
the unlettered and ungraduated line 
and stretch on to intersect a certain 
value of p, which should be marked. 
Then reverse the process. Stick the 
pin at the marked value of p. To find 
the diameter of the given tree 10 feet 
from the tip, pivot the celluloid line 
till it cuts 10 on the line H. Then 
stretch the thread from p across the 
intersection of the celluloid line and 
the plain line, until it intersects a value 
on line D , which is the diameter 10 
feet from the tip of the tree. The 
method is rapid. 
The advantage of this method, as well 
as the one first outlined, over the older 
method lies in their ability to iron out 
errors (especially those due to failure 
of the data in any diameter and height 
class), and to average up to the middle 
of the class, while the results are ex¬ 
pressed in the same useful taper curves. 
Their advantage over the system of 
frustum form factors lies in the fact 
that they have the same ability to get 
accuracy from scant data and are only 
slightly more laborious, while the re¬ 
sults are expressed in taper curves in¬ 
stead of board feet. The wide useful¬ 
ness of taper curves in all kinds of 
volume computation, yield, etc., is too 
well known to need enlarging upon. 
The last method is also useful, for if 
trees are proven paraboloids, a very 
simple relation exists between form 
quotients and the regular conventional 
form factors, by the use of which total 
cubic contents can be very easily 
computed. 
CONCLUSION 
The whole subject of tree form needs 
deeper study so that the fundamental 
laws may be learned, which will lead 
to further simplification of methods in 
volume table construction. This study 
represents only the development of a 
simple but nevertheless empirical 
method based upon what is known at 
present of tree form, i.e., that trees of 
a given species having the same form 
quotients have the same form from top 
to bottom (excluding basal flare), and 
the very safe hypothesis that form (as 
expressed by the form quotient) varies 
regularly with changes in diameter and 
height. 
