616 
Journal of Agricultural Research 
Vol. XXX, No. 7 
fact that the taper is the same for trees 
of all diameters within the same height 
and form class had already been proved 
by Maass, Schiffel, and others.) 
Whether Jonson’s dictum is strictly 
true or not is of little moment. It is 
sufficient to say that by application of 
this hypothesis he has developed a 
wonderfully accurate system of timber 
estimating in Sweden. If accurate 
enough for European conditions, it 
should be ample for our needs. 
Accepting Jonson’s statement, there¬ 
fore, that taper of trees of the same 
form quotient is the same from the top 
to bottom, we have only to gather all 
trees of the same form quotient together 
and determine the diameter at regular 
intervals up the stem in each class. 
base of the tree is considered to be at 
breast height, and the middle diameter 
is at a point halfway between breast 
height and the tip of the tree. 
Given the usual series of taper 
measurements, as collected in the field, 
the method of curve construction is 
not difficult. The different steps are 
illustrated by actual cases taken from 
the preparation of curves for Douglas 
fir in southwestern Idaho, which have 
been built by this method. 
These taper curves were built from 
a slender basis of trees as an experi¬ 
ment to see how the new method 
would handle a difficult case. The 
basis was 1,123 trees scattered from 
the 12 inch-60 foot class to the 48 
inch-150 foot class, a total of 136 
Fig. 4.—Crude taper curve for 16 inch-100 foot class Douglas fir. Numbers at points indicate number of 
measurements averaged 
Since trees of various heights are 
thrown together, the points of measure¬ 
ment must be at equal fractions of the 
tree height; and since various diameters 
are thrown together, the diameter at any 
point must be expressed in terms of 
diameter at the base of the tree (or 
some other fixed point). These figures, 
expressing diameter at various frac¬ 
tions of total tree height in terms of 
basal diameter, are very similar to the 
form quotient, which is this figure in 
the special case when the upper diame¬ 
ter is taken at half the height. Diame¬ 
ters at other points expressed in terms 
of basal diameter may with propriety 
be designated as subordinate form 
quotients. It must be remembered 
that here we are dealing all along with 
absolute form quotients in which the 
different individual diameter-height 
classes being involved, or an average 
of only about 8 trees to a class. The 
largest single-size group—the 16 inch- 
90 foot class—contained only 35 trees; 
and 35 classes were represented only 
by single trees. It is obvious that a 
difficult test was imposed. It must 
be borne in mind also that the exact 
figures and form relationships found 
are not to be considered as funda¬ 
mental and must not be used as the 
foundation of any generalized concepts 
of tree form—even of Douglas fir, for 
there are, as a matter of fact, a number 
of fundamental details that appear un¬ 
sound. This work is to be considered 
only for what it is—an attempt to use 
a new method in building up a practical 
set of taper curves. 
