121
§OUTHWlES1['
FORlE§T & RANGlE lEXlPlERU1IlEN1[' §TA1['llON
P.O Box 245
Berkeley ,
California
94701
" ',' ", ". .5'~:l, :; 1
Predicting Volumes
in Four Hawaii Hardwoods
ABSTRACT:
Multivariate regression
equations were developed for pre dicting board-foot(Int. 1/ 4-inch log
rule ) and cubic-foot vo lumes in each
S.IS-foot section of trees of four
Hawaii hardwood species . The species
are koa ( Acacia koa), ohis (Metro-
.. first multivariate
sideros polymorpha ).
robusta eucalyptus (EucaJyptus robusta),
and
equations d eveloped
saligna ( E. sa lj~na). The four independent variables us ed are d.b.h.,
merchantable l ength , form class, and
DAVID A.SHARPNACK
the diameter at th e top of the mer chantable length.
I n making volume predictions, foresters often need estimates for portions of trees as well as whole trees.
Such volume equations are available
for the first time for four Hawaii
hardwoods. The four species are; koa
(Acacia koa) , ohia (Metrosideros poLymorpha) , robusta eucalyptus (EucaLyptus robusta) , and saligna eucalyptus
(E. saLigna). The equations were developed for predicting the board-foot
(Int. 1/4 - inch rul e) and cubic foot
volume in each B.IS-foot section of a
tree.
To develop these equations, it was
necessary to find a predictor for a
set of interdependent variables (section volumes) based on another set of
variables (tree measurements) .
The
usual method of solving this problem
is to construct taper curves. This
approach is useful if one aim of the
equations is to determine the distribution of log volumes by small end
diameter class. But nothing is to be
gained by making two predictions when
one will be enough.
Instead of predicting log diameters
and using these data to predict volumes , we predict volumes directly. To
do so, we would find a separate univariate multiple regress ion for predicting volume in each section of a
tree. When section volumes are added
Forest
Service
-
U.
S.
up to give total tree volume, however,
no estimate of the variance of each
prediction could be made unless the
interdependence of section volumes in
a single tree is ignored. This interdependence can be handled in the multivariate regression framework used in
this study.
The form of the multivariate model
for each of the four species is as
follows;
•
•
•
•
+
8. ,X · k
1) )
+ .. . +
8. X k
1q q
+
e ,·
•
in which Y. ; dependent variable of
1
the ith equation.
Department
of
Agriculture
k
= volume
x.
J
=
of the ith 8.15foot section; board-foot
volume is used in models
with suffix a ; cubicfoot volume is used in
models with suffix b .
j th Independent variable.
from all the stands that had been visi ted for previous work . A point on a
road or trail in or next to a stand was
selected at random. A d,stance of 200
feet was paced Into the stand at right
angles to the road or trail. This
point was consIdered the plot center .
The 15 trees closest to the plot center which met the diameter class requirements were selected as sample
trees (table 1).
jth tree measurement;the
same X's are used in
each equation.
p'(q+l)
regression co=
efficients to be estimated .
= number of dependent variables .
total
number of sections
=
in tallest tree in the
species.
= number of independent variables.
random
term .
=
= the number of observation~
=
~
..
IJ
P
q
e
N
The trees In the first set of data
had diameters measured at stump,
breast height, and top of fIrst 16.3foot log by steel tape. The rest of
the logs were measured with a Relaskop
with the distance to the tree measured with a steel tape. The trees in
the second set were measured with a
Barr &Stroud optical dendrometer. 2
Data from both sets were processed
by Grosenbaugh's STX computer program. 3 A special subroutine of STX,
~~4S, interpolated between measurement pOInts to find the diameter at
the top of each 8.lS-foot log section . The subroutine also found the
top of the merchantable bole when this
was not determined in the field. The
board-foot and cubic-foot volume were
then calculated from these diameter
and length measurements .
k = 1,2, . .. ,N.
The Y. for top sections of trees
which ar~ shorter than the tallest
tree of the species are set equal to
zero.
Data Col lection and Process i ng
Two sets of data were collected.
The trees in each set were selected in
the same way, but were measured with
different instruments .
The tree selection procedure was
designed to give a good geographical
and size distribution without introducing personal bias In the selection
of individual trees to measure. Details of the selection procedure as
well as details of tree measurement
have been described by Nelson et
al . 1 Briefly, stands were selected
I Nelson , R. E .. Tagaw8 , T. K.
Previous univariate regressions
developed by the HawaIi Forest Survey
staff using the Relaskop data and
preliminary calculations wIth the
dendrometer data led to the following two models :
~lodel
1 (a & b) :
~il
DBH
• DBH +
2
• H
T
~i2
~i4
• TDrB
• TDrB
2
2Grosenbaugh L. R. OpL c Bl dend.rometers for
out-oF- r ea ch d i ameters : B c onspec tus and
s om e new th eory . 47 pp . Fa . SCl . Monog r . 4
1963 .
3Grosenbaugh L. R. STX--Fo Tt r an 4 p rogram-f or est I mat es of tree popuiat ! ons f r om 3P
sample - t r e e-me asu reme nts . 49 pp . U. S . Forest Serv o Pacl.ftc SW . For e st {I.; 'Range Exp .
Sta . .Berkeley....Qlhf -ReS . ~IP · ...~W .. l"S' '1964 .
Honda Nobuo
and Hornlbrook , E. M. Manual of instru ctions fo r i n J tiai su rvey c f the t i mber
resou rce ~ n the Stat e of Hawa .. .:. . 81 pp .
U. S . Forest Serv o Pac ifl c SW . Forest &
Range Exp . Sta . Berke ley , Callf ., and
DiV . Forestry , Hawsll Dep . Land & Natur .
Resources . 1958 . Rev . 1964 .
-2-
J
• H+ 8
. NS
is
[i
1,2,
=
H
total merchantable length
in feet .
FC = Form Class = Cd.i.b. at top
of first 16.3 ft. log) /DSB.
NS = number of B.ls-ft. sections
in merchantable length =
H/B .15 ft.
. . . , p1
~!odel
Y.
1
2 Ca & b):
=8iO
+
DSB
TDIS
+
. DBB +
2
DSH . H
8i l
8i3
TDIS2
H
FC
TDIS
8i2
FC
t
8i4
+
8is
.
=
Model 3 was formulated after coefficients "ere estimated for Models 1 and
2. Adding the variable H to Model 2
we get
FC
[i
1,2 , ... , pl
d.b.h. to nearest .1 inch.
diameter inside bark at the
top of the merchantable
length to nearest .1 inch.
=
=
=
Model 3 Ca & b) :
Y.
1
=
length is the
distance between the stump
and either 9-inch d.o.b. or
the point where the bole
breaks up such that none of
the branches contains a 12foot log wi th a small end
d.o.b. of at least 9 inches.
8
iO
TD IS
~lerchantable
[i
. DSH + 8i2
2 .
+ 8i3 . DSH
H
TDIS2 . H
8i4
8i l
+
FC
+
FC
+
FC
8i5
= 1 J 2,
••• J
+
8i6
H
pl·
Table 1 . --Distribution of sample , by species and d . b.h . cIa"
D. b . h . c lass
(inches)
Koa
I
Ollis
Species
Robusta
I
I
Saligna
Number of trees
11
17
23
29
35
41
47 •
53 +
16 .9
22.9
28.9
34 . 9
40 . 9
46.9
52 . 9
Total
18
19
13
16
13
10
8
3
21
20
17
14
12
7
5
2
35
28
27
25
2
17
17
15
15
14
8
6
3
100
98
117
95
Model Selection and
Final Results
Anderson's U statistic, used to
choose between the models, is defined
as:
The multivariate regression calculations were made by two computer
programs written for this study. The
programs calculated the estimates of
8 .. 's, predicted values, residuals,
sij~s of products of residuals matrix,
and Anderson's U statistic. 4
U=*N!
n
N ~
IN
tnl
w
in which
is the determinant of
the matrix of urn of products of residuals about the regression surface using the 8 .. as estimated from the data ;
4Anderson , T.W. An introduc tion to multivariate statistical analysis. 374 pp. New
York : John Wiley . 1958.
IN *w
A
-3-
I is 1Jthe
determinant of the matrix
of sum of products of residuals about
the regression surface using the 8 ..
of the null hypothesis.
1J
If we set 8. = 8. ~ . . . = 8. = 0
for each i as t~e nul! hypothesi~~ then
the estimate of 8'0 is the mean of the
Y. . The U stat i~ tic is then somewhat
k
analogous to the univariate ratio of
residual sum of squares to the total
sum of sq~ares. In fact, if p = 1,
U = 1 - R. The smaller the value of
U becomes, the larger the percentage
reduction of variance about the regression line as compared to the variance
about the mean. No hypotheses were
tested . The model with the smaller
value of U is considered the better
model.
Weighted regression was used because the generalized variance of the
residu2ls within subgroups increased
as DBH • H increased. The first set
of weights used was from Gedney and
Johnson. S Because these weights eliminated the trend of the variance in
all species, no further weights were
sought.
The dendrometer data were used to
calculate regression coefficients for
all species in models I and 2 (table
2). The number of observations and
the number of dependent variables (p)
used for each species are also shown
in the table. Form class appears to
be an important variable. The U values for model 2 are smaller by almost
a factor of 10 than those for model 1.
Since the computations took a large
amount of computer time, the pooled
data were first used for only four
model-species combinations (table 3).
The pattern of U values is similar to
that found in table 2. From the
above results model 3 was formulated .
Again only a few model-species regressions were calculated. Because
model 3 appeared better than either
models 1 or 2, only the remaining
model 3 regressions were run (table 4).
Tables 6 to 13 give the estimated
regression coefficients (~ . . ) for
predicting board foot and E6b1C foot
volumes for B. IS-foot sections of
trees of the four species . The
final row of each table gives the
coefficients for predicting total
tree volume. These coefficients
p
A
equal .f18 . . for each j. They are
also tfie e~timated coeff1cients of
model 3*. Model 3* has the same independent variables as model 3 but
only one dependent variable, Y =
P
.E IY . . These univariate regressions
1=
l.
were calculated for board foot and
cubic foot volume f2r each species.
Table S gives the R 's for these regressions and the weighted standard
error in percent. That is, percent
S.E. = lOOx (weighted standard deviation of residuals/weighted mean of
To further compare the models, the
residuals of the Relaskop data about
the surface estimated by the dendrometer data were found for three modelspecies combinations. Their U values
were .692, .749, and 3 . 024. The last
of these--ohia (model la)--indicates
that the mean of Y. of the Relaskop
1
SGedney , Donald R
data would make a better predictor for
section volume in these trees than the
regression surface estimated f r om the
dendrometer data. All three values
indicate that the two samples probably
differ. Both samples were from the
population for which predictions were
wanted. Either the samples are from
different subpopulations or this difference is due to sampling error. In
either case I think the best predictive ability can be obtained by pooling the data to estimate the coeffiC1ents for the whole population.
Y).
and Johnson Floyd A.
To predict section or tree volumes, measure DBH, TDIB, H, and Fe.
Then, the appropriate row of coefficients is Subst1tuted for the 8's in
We i ghting fa c tors fo r computing the rela-
between tree volume and DBH In the
Pad fie Northwest. 5 pp . U. S . For est Se rv o
Paciflc NW Forest & Range Exp . Sta Res
Not e 174 . 1959 .
tIon
-4-
Table 2 . --Values of Ander son· s U for models 1 and 2 ; q=5 , dendrometer data
Species
Koo
Ohia
Robusta
Saligna
Model number
I
10
I
20
'.,J . 215x10- 4
. 534x10 - 5
. 612x10- 3
. 341x10- 5
. 143x10- 3
. 499x10- 4
. 408x10 - 2
. 146x100
I
1b
. 899x10 - 4
. 138x10- 4
.322x10 - 2
.365x 10- 1
Observations
Number
p
2b
. 157x10 - 4
. 145x10 - 5
. 268x10- 3
. 513x10 - 5
30
28
55
40
9
11
15
18
Table 3 . -- Val ues of Ander son's U for mode l s 1 and 2 ; q:5 , pool e d data
Species
Koo
Chia
Robusta
Saligna
Model number
I
10
I
1b
---
. 174x10- 2
. 191x1 0- 2
--
--
--
--
. 239xl0- 2
---
I
2.
p
2b
--
--
10
11
15
18
---
. 179x10 - 3
Obs e rva tions
Number
100
98
117
95
Tabl e 4 . --Values of Ande r son' U for model 3 ; q:6 , pool ed data
Model
Species
p
I
3.
3b
Observations
Number
. 837x10- 3
. 398xl0- 3
. 10Ix10- 2
. 999x10 - 4
Koo
Ohia
Robust a
Saligna
Tabl e 5 .- -Va lues of
i2
. 285x 10- 3
.217x 10- 3
. 546x10 - 3
. 979x10 -t
R2
Ko.
Cl1ia
Robusta
Saligna
.986
.985
. 973
. 984
100
98
117
95
for univa ri ate model 3* . q:6 , pooled data
Model 3b*
Mod e l 3a*
Speci es
10
11
15
18
I Percen t S . E.
12 . 45
13 . 53
18 . 21
16 . 72
R2
. 989
. 988
. 979
. 988
- 5-
I
p
Percent S .E.
Obs e rvation s
Numbe r
9 . 51
10 . 50
14 . 02
12 . 69
1
1
1
1
100
98
117
95
then subtracted from the prediction of
total tree volume, except when the top
section is cull. Excluding portions
at the upper end of the stem should be
done by shortening H, changing TOIB,
and then predictlng total tree volume.
For example . if the top 8.15-foot section of the above koa were cull, the
net tree volume would be estimated by
calculating H as 57.0 - 8 . 15 = 48.85
feet. If the top section had a linch taper, the TDIB at 48 . 85 feet
would be 11 inches . The volume would
then be predicted by the equation:
model 3 along with the measurements of
the independent varlables . For example, to predict the board foot volume
in the first 1/2 log of a 24-inch
d.b.h. 57 foot koa with a form class
of .75 and a 10-inch TOIB, we use the
first row of coefficients ln table 6
to get the followlng equation:
VI
= 95.82708
T
T
10 . 18193 x 24
. 171 71 x 10.0 ; . 00285 x 242
2
x 57 . 0 x .75
T
.00270 x 10
x 57.0 x .75
+
31 . 1948 x .75
- 1 . 216054 x 57 . 0 = 186.1
VT'
98.0369
+
14.5390 x 24
- 10.9328 x 11 + .0175 x 242
bd. ft.
To predict the total volume of the
same tree, the last row of coefficients
in table 6 lS used as follows:
V = - 98.0469 + 14.5390 x 24
T
- 10 . 9328 x 10 + .0175 x 242
2
x 57.0 x .75 + .0285 x 10
x 57.0 x . 75
=-
+
- 2 . 4364 x 57.0
85.4659 x .75
= 619.54
bd. ft.
If the first half log is cull, the
net board foot volume of the tree is
VT - VI = 619.5 - 186.1 = 433.4
bd. ft .
This koa, without any cull, has 7
sections. Therefore an unblased estimate of total tree volume could be obtained by summing the predicted section volumes from the first seven
equations. The model glves zero volume to sections not present, however,
because the tree is shorter than the
tallest tree in the species. For this
reason the total volume equation for
all koa trees is the sum of the 10
section equations . The average error
will be smaller uSlng the total volume equation than by using the sum of
j equations for trees with j sections .
x 48.85 x .75
+
. 0285 x 112
x 48.85 x . 75
+
85.4659 x .75
- 2.4364 x 48.85
= 569.25
bd.
ft.
This procedure is opposite to the
usual one ln which full height to a
specified top is used to get the
proper amount of taper. H can be
changed in the present case because
TOIB is one of the variables in the
prediction equation. The change is
necessary because the error in predicting section volumes becomes larger as section number increases.
There is less error in predicting
the short tree volume than in predicting the difference in volume
between the tall tree and its top
sectlon.
To find the total volume of a
group of trees or sectlons WhlCh use
the same set of regression coefficients, the following form of the
equatlon slmplifies calculation:
n
k~lYk=
aO+ ai
n •
n
kh
Hk
In general, to predict volume for
a large portion of a tree, the excluded portion should be predicted and
• H
k
-6-
TOIB
+
k
a'3 •
+
a'4
. FC k +
as
FC
k
n
kh
n
kh
n
. kh
OBH
2
k
TDIB~
FC
k
T
a6 .
n
kh Hk
in which the subscript k indicates the
measurement in the kth tree in a group
of n trees. The a! are the 1i' . that
1
apply to the parti~ular group 6f trees.
this l eaves is TDIB. TDIB was used to
explain a source of variation which is
poorly correlated with DBH. The size
of TDIB, along with H, reflects the
breakup of the main bole into small
branches. In fact, the correlation
between DBH and TDIB is less than 0.5.
Therefore , using average TDIB per DBH
is not reasonable. It should also be
noted that the residual variance is
quite large. Although the regressions
explain a large proportion of the original variance, the original variance
is very large. The variables used
reduced the residual variance by a
significant amount.
To illustrate how the volumes vary
with changes in variables, a small portion of a volume table is given in
table 14. Because of the number and
range of the independent variables, the
construction of a complete volume table
is impractical; a complete table for
all four species would take nearly
5 , 000 pages. The possibility of making
a condensed table by using average values per DBH class of one variable was
considered, but was discarded because
none of the measured variables was
suitable for elimination in this way .
H is obviously too important a variable to use average H per DBH class.
Form class was shown earlier to reduce
residual variance by a factor of almost 10. The only measured variable
A procedure for estimating the
variances of the predlcted volumes of
parts of trees, trees, and groups of
trees is now being developed. This
procedure, along with the necessary
numbers, will be presented in a subsequent report.
Appendix
Table 6
Sect.ioh
number
1
2
3
4
5
6
7
8
9
10
. Re gr e ssion coeff, c ients For predictJng board-Foot volume of koa ( Int
Eo
95 . 82708
-98 . 9874
- 68 . 87314
7 . 695041
48 . 52265
45 65307
41 76758
15 86447
5. 825181
. 3226912
Totals -98 0369
B1
B2
B3
B4
10 18193
9 3395
5. 28700
480727
2. 85065
2. 84193
2 . 31423
1 28068
442723
0585186
0 17171
6 9892
7 . 41769
-2 175746
. 95769
1. 81631
1. 27148
1. 04170
334543
0563598
0 . 00285
0016
. 00200
002980
00296
. 00236
00160
00083
000280
0000520
0 00270
0102
01008
004667
00188
. 00044
00022
00057
000149
. 0000766
14 5390
10 9328
0175
-7-
-
0285
B5
I
1/ 4-in . rul e)
1
31 19480
110. 0857
99 . 45291
4 461617
48 85356
48 79502
39 . 71543
16 60251
5 615163
1474525
-
85 . 4659
%
1. 216054
1. 500098
741615
137687
331848
. 303930
117924
105860
025345
. 001241
2. 4364
Tabl e
7 . - -Regr es s~on
Sec tion
numbe r
1
2
3
4
5
6
7
8
9
10
Total s
c oeffi cients for predi c t i ng cubi c -foo t volume of koa
Bo
81
83
~
84
85
%
- 9 . 686990
1. 214020
0. 023089 0. 000394
0 . 000362
3. 576347
. 00120
- 86295
- 11.91520
1.13800
. 00022
14 . 77558
14 . 72008
- 11.10862
00015
00135
79387
-1. 04888
000334
000574
1.995580
1. 440857 - . 004906
288692
000170
6 . 460742
000387
5. 209516
377899
191257
000154
7 159193
000331
5. 789749
400744
312052
000237 - 000029 - 6. 129322
5 . 915681 - 352759
231965
000127 - . 000095 - 2. 670028
2 . 427013
200374
169549
000041 2 ~ 00002 15 ~ - 880641 3
. 8881901 . 0669086
051 261 2
. 049586 6£ ~1 00913714 . 00884829 . 00000812. · 0000I2CF ~ - 02262095'
-
-
- 13 . 8719
1. 7332
. 0022
- 1. 2125
11. 7450
. 0033
0 . 158056
. 175340
. 050964
063705
. 079629
066171
030363
019788
004412
000186
- . 1205
Tabl e 8 . - -Regression coef fi c i ent s for pr e d icti ng boa rd- foot vo lume of ohi a ( In t. 1/ 4 -i n . rul e)
Sec tion
numbe r
2
3
4
5
6
7
8
9
10
11
Tot a l s
Bo
- 170. 3914
- 120 . 5771
44 . 18240
52 . 81054
41. 31205
42 . 13990
19 . 19443
I!. 08655
12 47474
9. 690916
2. 818997
-143 6228
I
81
I
I
~
83
I
0. 0039
. 0030
. 00098
00109
. 00201
00227
. 00235
. 00187
. 00124
. 000458
. 000044
0192
8 . 6611
8 . 2664
2 . 1029
5. 6555
5. 46496 -' 3 78737
2 . 30632 - 10 04607
1 . 51536
69208
- 3 . 03324
1.94653
3. 15507
-2 . 68394
-1.92976
2. 11924
-1. 24408
. 86864
- . 466431
. 161346
042842 - . 179804
10 . 7775
- 1. 0132
-
I
84
- 0. 0049
. 0019
01464
. 01558
00396
00022
. 00444
. 00350
00140
. 000283
. 000298
0222
I
B5
62 . 3521
88 9183
88 . 82999
L 28497
-41.87429
48 . 86516
-30 . 33555
- 14 . 02272
8 . 82283
- 3. 608517
794831
93 . 0615
86
-0 . 843890
899460
- 1 009962
. 584072
. 282015
. 440775
. 380373
181155
. 012869
- . 062947
- . 026993
- 2. 1301
Tabl e 9 . - -Regr ession coe ffi c i ent s for pr e di c tin g cubi c - foot vo lume o f ohia
Sec tion
numbe r
1
2
3
4
5
6
7
8
9
10
11
Totals
Bo
- 19 . 41844
-14 . 47685
- 8 . 82702
5. 926268
5 . 301151
5. 977388
2 . 533931
1. 419499
1.649707
1 322752
. 4058990
- 18 . 1857
~
B2
B3
1. 01349
76226
. 84825
415849
198231
465099
- 422026
308002
207882
- 081551
- 0073059
1.3498
1 03132
. 19734
- 1.21373
1. 487051
083528
. 340442
. 542706
360319
177219
001187
- . 0247008
1585
0. 00050
. 00033
. 00002
. 000056
. 000231
. 000311
. 000358
. 000297
. 000206
. 000080
. 0000074
. 0240
-
-
- 8-
B4
- 0 . 00066
00024
. 00187
. OC220S
-
-
. 000582
. 000055
_000767
. 000604
. 000293
000001
. 0000407
0026
%
B5
8 . 00497
11 53981
14.47147
1 052171
6 . 326220
- 7. 753169
- 4 . 849127
- 2 . 098870
- 1 308878
- ,, <09818
- 1117655
12 . 1106
-
0. 104521
. 099139
- . 099642
048797
071528
. 088066
. 071285
033883
006680
. 007166
003833
. 0917
-.
-
Re~ r essjon c oeffi c i e nt s
Tabl e 10
Se c tlon
I
numbe r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Tot a ls
fo r pr e di c ting board- fo ot v olume of Robusta e uca lyptu s
( Int. 1/ 4 - in . rul e)
I
-
o
0 . 0023
0016
. 00113
00108
00140
. 001442
. 00163
00151
00141
00111
00081
. 00052
000311
. 000165
0000274
0164
1 3161
· 2 1968
1.86725
·3 . 92930
76797
313218
44369
. 27416
05596
26886
39112
37068
595504
400580
1016402
4 8679
6 9941
5 . 3265
4 . 38309
2 . 68275
. 32897
368779
- 1 45658
- 1.61878
1 59213
· 1 44648
1. 07266
. 73192
. 4416 27
246899
. 0378753
10 7017
147 4436
87 . 9867
71.08105
10 . 02939
25 . 13546
6 . 878988
29 20325
30 . 21361
30 4316 2
23 . 61735
13 70695
10 27594
1 846884
096042
. 4799474
· 196 0776
I
I
I
1350112
100 . 2585
62 . 60464
18 . 36333
13 65443
- 6 . 488287
17 . 50768
16 . 36067
17 . 37143
14 23213
7 27223
7 . 77690
3 182155
1.085088
0163414
238 . 6319
0023
0021
00204
00363
. 00057
. 001460
001 70
. 00160
00061
00040
00051
00026
000636
000475
0001236
0098
-0 590282
529313
. 215083
153004
082405
012552
081734
. 118055
124815
. 080985
019399
. 011313
019253
. 019980
004886
· 1.8100
-
Tabl e 11 - -Reg r ess ion coe ffi c i en ts for pr ed~ct i ng CClbi c- foo t vo lume o f Ro bu s t a e uca lyptu s
Sec tion
I
numbe r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Tota ls
17 . 82186
10 98505
10 . 93912
1. 851224
5 . 584770
0086459
3 . 753958
4 . 093590
4 . 430871
3 . 668604
2 . 441994
1. 749710
. 3331091
0366694
. 09175286
· 26 . 7566
I
o
90209
70596
68559
498383
. 091009
0178570
218191
. 254223
. 254877
. 240210
. 185444
131611
0818189
. 0473497
. 00728397
1. 4442
I
0 14525
27203
24740
. 723060
138066
. 0535476
. 032923
. 007515
019384
. 055913
. 050881
072097
. 1102678
0715013
. 01950573
6536
0 00026
. 00018
00008
000062
000139
0001619
. 000216
. 000214
. 000216
000177
000136
000092
0000568
. 0000312
00000526
. 0020
Io
I
00028
00024
. 00024
000610
000050
0002073
. 000229
000224
000066
000051
000075
000055
0001179
00008 47
00002374
. 0013
I
17 48416
13 34293
8 95076
3 . 034923
3 . 111704
6397084
2. 725338
2 . 473237
2 . 692627
2. 266640
1 . 207162
1. 362329
5863276
. 2227333
00257417
31.7509
0 . 0688 75
059877
005218
000017
. 041055
022332
008064
004053
. 012634
008779
002140
. 000462
003916
003627
. 000946
. 0821
Tabl e 12 .-Re~ r ess i on coe ff ic 1e nt s fo r pr e di c tin g boa rd- Fo o t vo l ume of Sa Li ~na e uca lyp t us
(I nt. 1/ 4 · in . r ul e)
Sec tlon
numbe r
1
2
3
4
5
Bo
139 . 4222
. 27 . 16889
·120 . 2769
·163 . 0663
- 101. 3343
Bl
13 . 4385
7. 92880
6 . 0060
2 6343
9542
B2
B3
34 . 3848
11.19857
. 5. 6035
6 . 9076
7. 6232
0 . 0009
. 00093
. 0015
. 0017
. 0016
-9-
B4
0 . 0150
. 00798
0012
. . 0042
- . 0035
B5
~
77 . 1701
80 . 57326
159 . 8142
98 . 9372
23 . 6212
- 1.656012
. . 799945
. . 600258
103804
. 317791
Table 12
~ - R eAression coeffi c lents
for predicting board ~ foot volume of Sallgna eucalyptus
( lot
Sectlon
number
6
7
8
9
10
11
12
13
14
15
16
17
18
Totals
Table 13
Sechon
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Totals
flo
53 70727
72 34748
74 . 52870
72 81351
85 20497
97 67553
62 83060
48 . 14582
87 . 60065
41 87644
23 01003
10 02657
3 543246
353 4721
I
Bl
49243
1 57365
2 42129
3 23532
2. 92933
2 76203
2 37526
1 89902
1.18257
79009
57185
18220
061057
10 4857
I
1/ 4 - .0
rule)
~
6 19461
3 . 36042
2 18962
• 53876
1. 87182
2 42418
1 09586
1 08436
4 . 77535
2. 09000
1.19807
63880
218041
- 47 5863
I
c ontinued
B3
00162
00163
00157
00150
00130
00120
00103
00078
00050
00033
00021
00007
000020
0184
I
B4
00212
00266
00247
00230
00293
00318
00160
00203
00395
00153
00025
00022
000119
0376
I
I
B5
%
49348
44 21681
47 86710
52 75278
56 59252
66 32821 ~
66 32523
51 . 76450 <6
42 41969
18 . 49814
7 . 53108
2 79567
1 096220
22 5655
2
•
I
291428
022817
065601
112728
044585
054258
000638
065606
242557
111464
020979
017864
009133
6187
Regression coeffic1ents for predicting cubic - foot vo lume of Saligna euca lyptu s
BO
Bl
~
B3
25 55281
10 75487
11 48821
33 17864
· 19 78817
10 82043
12. 42869
12 72470
12 46305
14 69305
16 81795
10 27860
7 441342
14 04546
6 530406
3. 960105
1.620516
5015038
74 5376
1 72446
1.09651
76538
44743
23582
01000
15716
30661
45758
41632
40787
. 35576
293802
18383
122940
093894
029141
0093961
1 4463
5 79898
3 63853
95195
1 77712
1 37509
97277
85970
65015
36738
59230
61724
10614
177972
78781
331550
216559
104540
0297491
11). 5373
0 00021
00020
00018
00018
00016
00018
00019
00019
00019
00017
00017
00015
000117
00008
000052
000035
000011
0000031
0025
-10-
B4
o 00236
.
00163
00033
00097
00065
00036
00055
00050
00045
00055
00056
00023
000275
00060
000221
000043
000034
0000159
0064
B5
20 35287
20 43980
18 59479
16 57859
5 31403
1.00509
5 96517
6 56025
7 27538
7 96605
10 15834
10 63589
8 282357
6 68389
2 834447
1 266801
443422
1562058
14 0570
%
0 314010
216379
071356
057898
071517
060427
006107
014429
023199
011469
. 004836
007449
" 003108
034834
- . 016085
003338
002728
001259
4154
Table 14. - -8oard- foot volume of koa (Int. 1/4-inch 1'Ule) ; f om clas.: 0. 85
9- I NCH TO I B
NUMBEK
SECTIUN
OBH
I
Hr. 1
1
2
3
,
4
6
7
8
14 . 0
2
3
4
5
6
65 . 7
6 1. 2
56 . 7
52 . 2
47 . 6
53 . 8
49 . 4
45 . 1
40 . 8
36 . 5
29 . 9
32 . 2
34 . 6
36 . 9
16 . 3
24 . 1
31 . 9
14. 6
22 . 4
13 . 4
3
4
5
6
7
85 . 1
8 1. 8
78 . 4
75 .1
71. 8
70 .1
66 . 5
62 . 8
,9 .1
55 . ,
43 . 0
46 . 1
49 . 3
52 . 4
55 . 6
20 . 3
29 . 3
38 . 4
47 . 4
15 . 1.
2 4 .1
3 3 .1
13 . 7
20 .1
9.9
3
4
5
6
7
109 . 5
107 . 5
105 . 5
103 . 5
10 1. 5
91 . 1
88 . 1
85 . 2
82 . 3
79 . 4
56 . 4
60 . 5
64 . 6
68 . 7
72 . 8
45 . 8
56 . 3
16 . 3
26 . 7
37 .1
14 . 7
22 . 2
10 . 5
3
4
5
6
7
134 . 4
1 33 . 9
133 . 4
132 . 9
132 . 4
13 1. 9
11 2 . 3
11 0 . 2
108 . 1
106 .1
104 . 0
10 1. 9
70 . 1
75 . 3
80 . 4
85 . 6
90 . 7
95 . 9
30 . 3
42 . 3
54 . 3
66 . 3
78 . 3
18 . 4
30 . 4
42 . 3
54 . 3
16 . 5
25 . 3
34 .1
11 . 8
17 . 3
8.3
8
159 . 7
160 . 9
162 . 0
163 . 2
164 . 4
165 . 5
133 . 7
132 . 6
13 1 . 5
130 . 3
129 . 2
1 28 . 1
8 4. 2
90 . 5
96 . 8
103 . 1
109 . 4
11 5 . 8
36 . 3
50 . 0
63 . 7
77 . 5
9 1. 2
21 . 3
35 . 0
48 . 7
62 .4
19 .1
29 . 2
39 . 4
13 . 7
20 . 1
9 .6
4
5
6
7
8
18 8 . 5
19 1. 5
194 . 5
197 . 4
200 . 4
155 . 4
155 . 2
1 55 . 1
1 55 . 0
15 4 . 9
106 . 2
11 3 . 8
12 1. 3
128 . 9
136 . 5
42 . 9
58 . 5
7 4. 2
89 . 8
10, . 4
56 . 2
71 . 8
22 . 4
34 .1
45 . 8
16 . 2
23 . 7
11 . 2
4
5
6
7
8
2 16 . 8
22 1. 7
226 . 7
23 1. 6
236 . 6
178 . ,
179 . 5
I BO . 5
18 1.4
18 2 .4
1 22 . 3
13 1 . 3
140 . 2
149 . 2
1 58 . 2
8'> . 6
103 . 3
121 . 0
29 . 6
47 . 2
64 . 8
02 . 5
26 . 6
39 . 9
53 . 3
19 . 3
i 7. 9
13 . 3
4
5
6
7
8
245 . 7
252 .7
25,9 . 8
266. 9
274 . 0
20 1 . 9
20 4 . 1
206 . 3
208 . 5
210 .7
138 . 8
149 . 3
1 59 . 8
17 0 . 3
180 .7
58 . 1
78 . 1
98 . 0
11 7 . 9
13 7. 9
35 . 0
54 . 8
74. 6
94 . 5
3 1. 6
46.7
6 1. e
23 .1
32 . 8
15 . "
4
5
6
7
8
275 . 2
28 4 . 6
293 . 9
303 . 3
3 12 .7
225 . 8
229 . 2
232 . 7
236 . 2
239 . 7
1 55 . 8
16 7. 9
180 . 0
192 . 1
20 4. 2
66 . 8
89 .1
Ill. 4
133 .7
156 . 0
41 . 2
63 . 4
85. 6
10 7 . 8
37 . 3
54 . 3
71. 3
27 . 4
38 . 5
18 .4
16 . 0
18 . 0
25 . 0
3~ .4
20 . 0
8
22 . 0
3
4
5
6
7
24 . 0
25 . 1
40 . 6
26 . 0
50 . 2
67 . 9
28 . 0
30 . 0
-11-
9
10
Table 14. --Board- f oot vo Lwne for koa (Int . 1/4-inch ruLe); f orm cLoss: 0. 85; continued
SECTIU"
DBH
1HT .1
1
2
3
4
4
5
6
7
8
305 . 3
317 . 2
329 . 0
340 . 8
352 . 6
249 . 9
173 . 3
254 . ~
1~7.1
259 . 6
264 . ,
269 . 3
200 . 9
2 14 . 7
228 . ,
76 . 0
100 . 9
12, . 8
150 . 7
17, . 0
4
5
6
7
8
336 . 1
350 . 6
365 . 0
37 9 .4
393 . 8
274 . 5
287 . 1
293 . 4
299 . 7
191 . 2
206 . 8
222 . 4
238 .1
253 .7
86 . 0
11 3 . 6
141. 2
4
5
6
7
A
36 7 . 5
384 . 7
40 I . 9
41 9 .1
436 . 3
299 . 4
307 . 2
315 . I
322 . 9
330 . 8
5
6
7
8
9
419 . 7
439 . 8
459 . 9
480 . 1
500 . 2
5
6
7
8
9
NUI"ISEK
5
6
7
~
9
lU
32 . 0
48 . 2
72 . ~
43 . ~
97.7
1 22 . 5
62 . 9
8 1. 9
32 .4
44 . 9
21.6
196 . 4
;0 . 0
83 . 5
ll O. 9
1 38 . 4
5 1. 2
72 : 4
93 . 6
38 . 1
52 . 0
25 . 1
209 . 5
227 . 1
244 . 6
262 . 2
279.8
96 . 6
127 . 1
157.6
188 . I
2 18 . 6
04 . 7
95 . 0
1 25 . 3
155 . 7
59 . 3
82 . 8
106 . 3
59 . 7
29 . 0
33 4 . 1
343 . 6
353 .1
362 . 6
372 . 1
247 . 9
267 . 5
28 7. 1
306 . 8
326 . 4
14 1. 4
174 . 9
208 . 5
242 . 0
275 . 6
74 .1
10 7. 5
140 . 9
174 . 2
2U7 . 6
68 . 2
9 4 .1
120 . 0
146 . 0
5 1. 1
68 . 2
85 . 3
33 . 2
42 . 1
13 . 6
455 . 5
47 8 . 7
50 1. 9
525 . 1
548 . 3
36 1 . 4
372 . 7
383 . 9
395 . I
406.4
269 . 3
29 1. I
312 . 8
334 . 6
3,6 .4
156 . 5
193 . 3
230 . 1
266 . 8
303 . 6
84 . 4
121. 0
1 57. 6
194 .1
230 .7
77 . 8
106 . 3
134 . 8
16 3 . 3
58 . 6
77 . 4
9 6.3
37 . 8
47 . 6
15 . 4
5
6
7
8
9
4 92 . 0
518 . 5
544 . 9
571 . 3
597.8
3~9 . 2
402 . 2
41 5 . 3
4 28 . 3
441.4
29 1. 2
3 15 . 3
339 . 3
363 . 4
387 . 4
172 . 5
212. 7
252 . 8
293 . 0
333 :1
9, . 5
135 . 5
17, . 4
215 . 3
2>5 .3
88 .3
ll 9 . 5
1, 0 .7
18 1. 9
66 .7
87 . 3
10 8 . 0
42 . 8
53 . 5
17 . 4
5
6
7
H
9
529 .4
559 . 2
589 . 0
618 . 9
648 . 7
417.4
432 . 4
447. 3
462 . 3
477. 2
313 . 7
340 . 1
366 . 6
393 . 0
419 . 4
189 . 3
233 . 0
270.7
320 . 4
364 . 1
107 . 5
1 ,0 . 9
194 . 4
237 . 9
28 1. 3
133 . 6
167.6
20 1. 6
120 •.5
48.2
59 . 8
19 . 5
6
7
8
9
10
600 . 9
634 . 3
667 . 7
701 . 0
734 . 4
463 . 0
480 . 0
496 . 9
513 . 9
530 . 8
365 . 7
394 . 6
42 3 . 5
452 . 5
481.4
254 . 3
30 1. 8
349.2
396 . 6
444 . 0
16 7 . 4
2 14 . 5
261 . 7
308 . 8
356 . 0
111.6
148.6
185 .6
222 . 5
259 . 5
84 . 8
109 .3
133 . 8
66.6
1 5~ . 4
79 , 3
6
7
8
9
10
643 . 5
680 . 6
717.7
754. 8
791 . 9
494 . 2
513 . 2
532 . 3
55 1.3
57 0 . 3
39 1. 9
423.4
455 . 0
486 . 5
5 18.• 0 .
276 .7
328 . 0
379 . 3
430. 6
481, 9
184 . 8
235 . 8
286 . 8
388 . 8
124 . 5
164.5
20 4.6
2 44.6
28 4 . 7
94 .7
1 2 1.3
148 . 0
174 . 6
60 . 0
73 . 8
87 . 6
6
7
8
9
10
687 . 1
7 28 . 1
769. 0
8 10. 0
851. 0
525 . 9
547.1
568 . 3
418 . 7
453 . 0
487 . 2
52 1.5
555.7
300 . 0
355 . 3
410 . 7
203 . 2
258 . 2
313 . 3
368 . 3
423 . 3
138 .1
181.4
224 . 6
26 7 . 9
3 ll. 2
105.3
134 .1
162.9
191.7
34 . 0
280 . ~
1 6~ . H
36 . 0
44 . 3
38 . 0
40 . 0
42. 0
44 . 0
~9 . 6
7~.4
9~ . 0
46 . 0
53 . 9
2 1.7
26 . 0
5. 1
48 . 0
337 . ~
2 4.1
28 .7
5.7
26.7
3 1. 6
6. 3
50 . 0
5~9 . 5
610 .7
466.0
521.4
-12-
66 . 4
8 1.4
96 . 3
Table 14 . --Board- foot volume for koa (Int. 1/4-inoh rule); form cLass: O . 85~ continued
SECT lUI,
OSH
NUMtsl:K
I HT.I
I
2
3
4
5
6
6
7
8
9
10
73 1. 6
776 . 6
82 1. 6
866 . 6
911 . 6
,,8 . 1
5K 1. 6
605 .1
628 . 6
6'2 . 0
446 . 3
483 . 4
'20 . 4
557 . ,
594 . 6
324 . 3
383 . 8
443 . 4
503 . 0
562 . 5
2<2 . b
1>2 . ,
199 . 1
245 . 7
2Y2 . 4
339 . 0
2{1~ . 7
73 . 3
89 . ;
10, . 4
6
7
8
9
777 . 1
826 . 3
875 . 5
924 . 6
973 . 8
,9{J . 9
616 . 7
642 . 6
668 . 4
694 . <
474 . 5
,14 . ,
5,4 . 5
594 . 5
634 . ,
349 . 6
413 . ,
477 . ,
541 . 4
605 . 3
167 . 7
Ll7 . i:'
267 . 9
31H . 0
368 . 1
120 . 3
Ih 1 . 7
19, . 1
22" . 5
97 . 8
11, • I
023 . 5
877 . I
930 . 6
984 . 1
1037 . 6
624 . 2
6,2 . ,
680 . "
709 . 0
737 , 3
503 . 3
54h . 4
,89 . 5
632 . ,
675 . 6
37, . 9
51< . "
58 1 . 3
649 . 8
103 . 7
237 . 4
29 1.1
344 . 8
398 . 6
140 . 8
176 . 6
212 . ,
240 . 3
870 . 9
928 . 9
987 . 0
1045 . 0
1103 . 0
6,8 . 1
608 . 9
719 . 6
7,0 . 4
701 . 2
532 . 9
579 . i
625 . 3
671 . >
717 . 8
403 . 1
476 . 3
549 . ,
h22 . 7
69, . 9
1,3 . 8
192 . 2
230 . 6
268 . 9
7
R
9
11)
52 . 0
2"I . A
34 1. 0
4UO . 2
4'~ . 4
116 . ,
147 . 6
17~ .
b
29 . 4
34 . 7
6."
;2 . 2
37 . 9
7. ,
106 . 6
125 . 2
35 . 1
41 . 3
8.2
9, . 9
115 . "
13, . 7
38 . 2
44 . "
H."
54 . 0
10
;:43 . 0
3Ub . b
370 . 1
433 . 7
497 . 2
t(O . 4
56 . 0
6
7
8
9
10
444 . 3
264 . 4
332 . 4
4uO . 5
460 . 6
036 . 6
HH . u
5H . O
6
7
8
9
10
286 . 7
3>9 . 5
432 . 2
'U4 . 9
,77 . 7
,WO . ,
2,7 . 9
31, . 4
3"l2 . K
430 . 3
1"- INCH TOI B
20 . 0
141. 5
145 . 5
149 . 6
153 . 6
157 . 7
161 . 7
2
3
4
5
6
I
2
3
4
5
6
tsl;> . b
100 . 9
116 . U
131 . 1
146. 2
54 . 3
76 . 4
9" . 5
1 20 . 6
42 . 1
62 . 0
81 . K
163 . 5
169 . 2
174 . 9
180 . 6
186 . 3
192 . 0
106 . 3
1 22 . 3
138 . 4
1,4 . 4
170.4
68 . 3
91 . 6
114 . 9
138 . 2
4" . 1
69 . 7
91 . 3
1
2
3
4
5
6
185 . 7
193 . 2
2UU . 7
200 . 2
215 . 8
223 . 3
127 . U
144 . 1
161. 1
178 . <
195 . 2
82 . 7'
10 7 . 3
13 1. 8
1 56 . 4
1
2
3
4
5
6
208 . 0
217 . 5
227 . 0
236 . 5
246 . 0
255 . 5
147 . 9
166 .1
104 . 3
202 . 4
220 . 6
97 . 4
123 . 4
14 9 . 3
17 5 . 3
42 . 9
>8 . 0
2H . 4
22 . 0
I
4?8
b~ . 6
3 1. 0
54 . 7
78 . 2
10 I . 7
49 . ,
60 . 2
34 . 3
62 . 0
87 . 6
1n . 1
'4 . 0
74 . 8
38 . 5
24 . 0
26 . 0
-1 3-
Table 14. --Board-foot
vo~ume
for koa (Int . 1/4- inoh
1
I
2
3
4
70 . 0
97 . 8
12' . 6
153 . 3
form class:
O . 85 ~
,
6
7
~
28 . 0
2
3
4
5
6
7
242 .1
253 . 8
265 . 4
277 . 0
288 . 6
300 . 3
169 . 0
188.4
207 . 7
227 . 1
246 . 4
265 . 8
112.5
140 .0
167 . 4
194 . 8
222 . 3
2
3
4
5
6
7
267 . 1
281 . 0
294 . 9
308 . 8
322 . 7
336 . 7
190 . 3
2 10. 9
23 1 . 5
252 . 2
272 . 8
293 . 5
127 . 9
157 . 0
186 . 0
215 . 1
244. I
2
3
4
5
6
7
292 . 3
308 . 7
325 . 1
341 . 4
357 . 8
374 . 2
2 11.7
233 . 7
255 . 7
277 . 7
3
4
5
6
7
59 . 4
105 . 4
43 . 5
57 . 8
37 . I
139 . 0
16 9 . I
65 . 6
91.0
/16 . 4
49.2
65 . 5
41 . 5
32 1. ~
143 . 6
174 . 4
205 . 2
235 . 9
266 . 7
87 . 9
120 . 6
153 . 4
/86 . 1
72 . 6
100 . 5
128 . ,
55 . 7
74 . 0
46 . 5
336 . 9
355 . 9
374 . 8
393 . 8
412 . 8
256 . 8
280 . 2
303 . 7
327 . 2
350 . 7
159 .7
192 . 3
224 . 9
257 . 5
290 .1
97 . 8
133 . 3
168. 7
204 . 2
80 . 5
111 . I
141. 7
63 . 1
83 . 5
52 . 1
3
4
5
6
7
365 . 5
387 . 3
409 . 0
430 . 7
452.5
280 . I
305 .1
330 . 2
355 . 2
3~0 . 2
176. I
210 . 6
245 . 2
279 . 7
314 . 2
108 . 4
146 . 8
185 . I
223 . 5
89 .1
1 22 . 6
1 56 . 1
7 1. 2
.93 . 9
58 . 3
4
5
6
7
8
4 19 . 3
444 . 0
468 . 6
493 . 3
518 . 0
330 . 4
357 . 0
383 . 7
410 . 4
4 37.1
229 . 4
266 . 0
302.6
339 . 2
375.7
119.7
161 . I
202 . 5
243 . 9
285 . 3
98 . 6
135 . I
171.6
2U8 . 2
105 .3
130 . 5
65 . 2
82 . 6
34 . 9
4
5
6
7
8
452.0
479.8
507 . 5
535 . 2
563 . 0
356.0
384 . 4
248 . 6
287 . 4
326 . 1
364 . 9
403.6
131. 6
176 . 2
220 . 9
26, . 5
3 10 . 1
108 . 9
148.6
18 8 . 3
228 .1
89 . 7
117.5
145.3
72 . 7
91 . 8
39 . 5
4
5
6
7
8
485.3
516 . 3
547.3
578 . 3
609 . 2
381.9
412.1
472 . 6
502 . 8
268 . 3
309 . 3
350 . 3
39 1. 3
432 . 4
144 .
192 .
240 .
288 .
336 .
2
2
2
2
2
1 20 . 0
16 3 .1
206 . 2
249 . 3
100 . 2
130 .7
80 .7
161.1 · 101 . 8
44 . 5
4
5
6
7
8
5 19 . 3
553 . 6
588 . 0
622 .4
656 . 8
408 . 2
440 . 4
472 . 5
504 . 6
536 . 7
288 . 4
33 1. 8
375 . 2
418.6
462 . 0
157 . 4
209 . 0
260 . 6
312 . I
363 .7
131 . 9
178 . 5
225 . 2
271 . 8
111.5
144. 8
178 . 0
49 . 9
tj2 . 4
30 . 0
7M.6
IO~ . ~
32 . 0
299 . ~
34 . 0
36 . 0
38 . 0
~O .I
40.0
412 . ~
441 . 2
469 . 6
42 . 0
442.4
continued
I~UMBl::k
SEC TIUN
OBH 1HT .1
l'U~e);
44 . 0
-14-
89 . 5
112.4
9
III
Tabl e 14.--Board- foot voLume of Twa (Int . 1/4-inch ru Le) ; form class : 0 . 85 1 continued
SECTIU"
I\fUMI)!:K
1
2
3
4
,
6
7
4
5
6
7
8
553 . g
591 . 8
629 . 7
667 . 6
7U5 . 6
434 . 9
469 . 0
'U3 . 1
,37 . 3
,71 . 4
308 . 9
3,4 . 8
400 . 7
446 . 6
492 . S
17 1. 3
226 . 6
281.9
337 . 2
392 . 4
144 . 7
19' . 0
24, . 3
2g' . 6
123 . 5
1,9 . 8
196.0
98 . 8
123 . 7
5, . 6
4
5
6
7
8
589 . 1
630 . 7
672 . 3
7 14 . 0
755 . 6
461 . 9
49B . 1
'34 . 3
570 . ,
6U6 . 7
329 . 9
378 . 4
426 . 9
475 . 4
523 . 9
18' . 9
24, . 1
304 . 2
363 . 4
422 . 5
1,8 . 2
212 . 4
206 . 6
320 . 8
136 . 4
17, . 7
215 . 0
108 . 8
13, . 8
6 1. 7
4
5
6
7
8
624 . 9
670 . 4
7 15 . 9
761 . 4
806 . 9
489 . 3
527 . 0
,66 . 0
604 . 4
642 . 8
351 . 4
402 . 6
453 . 8
505 . 0
,56 . 2
201 .
264 .
327 .
39u .
4,3 .
1
3
,
7
9
172 . 6
230 . 8
289 . 0
347 . 2
150 . 0
192 . S
235 . 1
119 . 3
148 . 5
68 .1
4
5
6
7
8
661 . 4
7 10 . 9
760 . 5
8 10 . 0
859 . 5
517 . 0
557 . 6
598 . 3
638 . 9
679 . '
373 . 2
427 . 3
48 1. 3
53' . 4
589 . 4
217 . 0
284 . 4
3,1 . 8
41g . 3
480 . 7
187 . 9
2,0 . 2
312. 6
375 . 0
164 . 4
210 . 3
256 . 2
130 . 5
102 . 0
75 . 0
4
5
6
7
8
698 . 5
752 . 2
805 . 9
859 . 7
9 13 . 4
545 .1
,88 . 1
63 1. 0
674 . U
7 17 . U
395 . 6
4'2 . 5
509 . 5
566 . 5
623 . 5
233 . ,
30, . 3
377 . 1
448 . 9
52U . 7
203 . 9
270 . 6
337 . 3
404 . 0
179 . 6
22g . 0
278 . 3
142 . 4
176 .1
82 . 1
4
5
6
7
8
736 . 2
794 . 3
852 . 4
910 . 4
968 . 5
573 . 5
618 . 9
664 .4
709 . 8
755 . 2
4 18 . 3
478 . 4
538 . 4
598 . 4
6,8 . 5
2'U . 8
327 . 1
403 . 4
479 . 8
556 .1
220 . 7
292 . U
363 . 2
434 . 4
195 . 6
248 . 6
30 1. 5
154 . 8
19 1. 0
89 . 7
4
5
6
7
8
774 . 6
837 . 2
899 . 7
962 . 3
1024 . 9
602 . 3
650 . 2
698 . 2
746 . 2
794 .1
44 1. 5
504 . 7
567 . 9
631 . 1
694 . 3
268 . 6
349 . 7
43U . 7
511 . 7
592 . 8
238 . 4
3 14 . 3
390 . 2
406 . 1
2 12 . 4
269 .1
325 . 8
167 . 9
206 . 6
97 . 6
OSH IHT.I
8
9
!U
46 . 0
48 . U
50 . 0
52 . 0
54 . 0
56 . 0
58 . 0
Th e Auth o r _________________________________________
DAVID A. SHARPNACK is s t udyin g probl ems in meas ur e me nt and a n a l ys i s t ec hniqu es for ma n age me nt
pl a nnin g, with h ea dqu a rt e r s in Be rk e l e y .
Na tiv e
of Chi cag o, h e ea rned a B.S . d eg r ee in for es try
a t th e Univ e r s ity of I da ho ( 1961 ).
He joined
th e For es t S e rvi ce and th e Station' s r ese ar c h
s t a ff ea rly in 196 2 .
- 15-
,
!