hp'^^h

STX

TIMBER ESTIMATING

WITH

3P

SAMPLING AND DENDROMETRY

U.S. DEPARTMENT OF AGRICULTURE

FOREST SERVICE

AGRICULTURE HANDBOOK NO. 415
STX

TIMBER ESTIMATING

WITH

3P

SAMPLING AND DENDROMETRY

Clement Mesavage, retired

Formerly Forester, Division of Timber Management

Washington Office, USDA Forest Service

USDA. National Agricultural Library

rN*AL B!dg

10301 !aa!tlmore B!vd

Beltsviüe. MD 20705-2351

December 1921

Agriculture Handbook No. 415

Forest Service U.S. Department of Agriculture
For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402 - Price $1

Stock number 0100-1579
CONTENTS

Page

INTRODUCTION 1

WHAT'S DIFFERENT ABOUT STX? 2

THE STX SYSTEM 3

Field tally 3

Sample blow-up 3

Accommodating differences in quality and defect - 4

Data processing 5

PREPARATION FOR STX ESTIMATES 6

Planning 6

Field work 6

Data processing (field level) 7

Data processing (processing center) 7

3P SAMPLING 7

Determining number of sample trees — 7

How 3P samples differ from conventional

samples 7

Basic for making predictions 9

Training estimators 9

Computing CV of predictions 9

Identifying sample trees in the field 10

Obtaining a list of random integers 11

Some 3P design considerations 12

Preparing random numbers for field use 14

FIELD WORK 17

Organization of field work 17

Equipment 17

Procedure for making predictions and

designating sample trees 19

General procedure for measuring sample trees 20

Recording tree measurements 21

Modes of tree measurement 26

Procedures when lines of sight are obscured 27

Other special recording procedures 28

111
Page

Defining merchantable sawtimber length 29

Classifying grade and defect of stem segments 31

Tally of cull trees 33

Some suggestions for dendrometry 33

DATA PROCESSING 36

Data preparation and general procedure 36

Program control cards 38

Job options 40

Card punching 42

Card listings 45

PROGRAM OUTPUTS 45

Diagnostics and errors 58

Function of value strata compared with

tree class 63

PROGRAM COMPUTATIONS 64

Field calculations 66

CONVERSION COEFFICIENTS 67

General procedure for obtaining and applying

conversion coefficients 67

APPENDIX A.—Computer output—preliminary

report, detailed log and tree report,

and summary reports 78

APPENDIX B.—Computer output—preliminary

report, detailed log and tree report,

and summary reports (same as Appendix A summaries, but using a different

set of conversion coefficients) 102

APPENDIX C—Examples of field tally sheets

(see text pages 21-26) 111

APPENDIX D.—Tables of trigonometric

functions 130

IV
INTRODUCTION

The STX system is a revolutionary method for estimating the volume and quality of standing timber. The system

is based on use of the STX computer program. STX

methods are more accurate, more efficient, more flexible,

and more consistent than earlier methods. The system

uses sampling and measuring techniques that have become feasible only since the advent of high-speed binary

computers.

The simplest use of STX is for estimating volumes

segregated into grade or quality classes. Options provide

for translating grade or quality class volumes into various

products and estimated values, based on mill studies.

The STX system has been tested and applied for sales

of a number of timber types throughout the United States.

Since its invention and introduction in 1963 by L. R.

Grosenbaugh,^ the system has been a subject of interest

among foresters. Thus, there has been a demand for a

guide for use of the system and for comparing its results

v^ith those obtained by other methods. This handbook is

intended to fill the need for such a guide.

STX (5-1-67) is programmed for use when it is feasible to enumerate each tree in the population being measured. A companion program—beyond the scope of this

handbook—^has been developed to adapt the procedures

for area-sampling of large tracts, or stands composed of

numerous small trees.

^L. R. Grosenbaugh. STX-Fortran-4 program for estimates of

tree populations from 3P sample-tree measurements. U.S. Forest

Service Research Paper PSW-13. Pacific Southwest Forest and

Range Experiment Station, 1967.
WHAT'S DIFFERENT ABOUT STX?

The STX system differs from conventional timber

estimating systems in several ways :

(1) STX uses 3P sampling, a method in which the

probability that a tree will be selected as a sample is

proportional to a prediction of volume or value made for

each tree in the population being sampled; it thereby

favors the selection of large or valuable trees. Rapid

ocular estimates of tree volume or value are used to reduce the number of sample trees needed to obtain estimates with a given degree of accuracy. The nature of

these estimates and why they are more efficient than

conventional sampling methods are discussed later under

"3P sampling.''

(2) STX provides for use of optical dendrometers to

measure out-of-reach stem dimensions on standing trees

(or direct measurements on felled or wind-thrown trees) ;

this eliminates the chance for bias that occurs with conventional systems.

(3) STX estimates are expressed by a trio of measurements (cubic-foot volume, square feet of log surface area,

and linear feet of log length) that are more descriptive

than single units of measurement, such as board feet,

cords, or pounds. This trio of measurements can be converted directly to estimates of potential for producing

primary products (such as lumber and plywood) or

secondary products (such as chips produced from slabs,

edgings, and peeler-bolt cores). Conversions to dollar

values of any products can similarly be made.

(4) This trio of measurements are additive without regard to log size. This permits aggregating contents of

similar stem sections in several quality-defect classes so

that estimates may be adjusted to reflect differences between stands. Conventional solutions to this problem

require a massive job of sorting (by log-sizes within

quality classes) to achieve the same objective because

single units of measure are nonlinear with respect to

product outturn.
THE STX SYSTEM

Field tally

The predicted volume is listed on a tally sheet for each

tree as it is marked for cutting or is otherwise encountered in the population being sampled. Each prediction

is then paired with a random number in a list generated

for that particular sampling job. When the random number equals or is less than the prediction with which it is

paired, the tree qualifies as a 3P sample to be marked for

conventional measurement or for measurement with a

dendrometer. The list of random numbers can be generated so that approximately any desired number of trees

will qualify as samples. The field tally consists of a list of

predictions for all trees and measurement data for those

that qualify as samples.

Sample blow-up

The procedure used to expand the sample information

to a total estimate consists of aggregating the predicted

volumes of the samples, comparing with the individual

predicted volume of each measured tree, and adjusting

accordingly the measured volume of each tree. Each sample tree is expanded individually, then totaled for the

population estimate. The blow-up factor for any given

sample tree, called frequency (i.e., the number of trees

in the population represented by that tree), is obtained

by dividing the sum of the predictions of all trees by the

product of the total mimber of samples and the prediction

for that particular sample tree. For example, if predictions for a 10,000-tree timber sale total 1,200,000 bd. ft.,

125 trees are drawn as 3P samples, and predicted volume

for one of the samples is 150 bd. ft., the frequency for that

particular tree is computed to be :

^ ^ 1,200,000 _ g4 ^

125 X 150 "" •

If the actual scaled volume of the sample tree was found

to be 175.2 bd. ft. (International 14, in. log rule), its

3
contribution to the total estimate is 175.2 x 64.0 =: 11,213

bd. ft.

When tree content is expressed in cubic volume, surface

area, and length—as it is by the STX program—^the expansion is made similarly, but volume, surface area, and

length are each multiplied by the frequency factor. Thus,

if the program showed that the sample tree with F = 64

contained 27.1 cu. ft., 103.6 sq. ft., and 32.0 linear ft., the

contribution of the sample tree to the total estimate would

be 64 X 27.1 = 1734.4 cu. ft., 64 x 103.6 = 6630.4 sq. ft.,

and 64 v 32.0 = 2048.0 linear ft. Other samples are expanded in similar manner and sumimed for totals of

cubic volume, surface area, and length. These totals are

then converted to estimated product units. For example,

assuming that Int. 14 bd. ft., gross volume = 9.1236 cu.

ft. — .70846 sq. ft. + .04222 linear ft., the expanded contribution of the sample tree is computed to be :

9.1236 X 1734.4

- .70846 X 6630.4

+ .04222 X 2048.0 = 11,213 bd. ft. Int. ¥4

Similar equations for converting cubic volume, surface

area, and length are available, or can be derived frommillscale studies, to show expanded volumes in other units of

measure, such as dry or green lumber tally, dollar value

of products, weight and value of chips produced, green

weight of logs, etc.

Accommodating differences in quality and defect

In STX procedure, the coefficients are not prepared for

the entire tree contents as shown in the example above,

because to do so would give the same volume to defective

material as to sound, and the same value to low-quality as

to high-quality material. Instead, the formulas include

a trio of coefficients for each of 11 quality-defect classes.

A conversion formula may therefore contain as many as

33 coefficients, rather than 3 as shown for the illustrative

Int. 14 equation.
The procedure used to account for differences in value

and yield resulting from differences in grade and defect

is as follows :

(1) Sample trees are divided ocularly into segments

according to the 11 quality-defect classes.

(2) Program computations of cubic volume, surface

area, and length are made for each segment and expanded

by the computed tree frequency.

(3) The expanded segment estimates are subtotaled

by species and grade-defect classes.

(4) The sums in each category are converted to estimates in other units of measure, as desired.

Data processing

The STX program is operational at a number of computer centers that serve processing sections of each of the

Forest Service regions. Only two data card forms—a tree

card and a dendrometer card—are needed; both are

punched from an STX tally sheet. The tally sheets are

sent to the regional center with data statements for five

control cards that must precede each set of data cards

to be separately processed.

The control cards offer a wide selection of outputs, both

in print and on cards, if the program is compiled with

appropriate constants. Controls discussed herein are

those required for appraisal data, but suggestions are

also made for alternative objectives.

Output reports include (1) preliminary report of tree

counts and predictions, (2) stem dimensions and computations for individual sample trees, (3) summary reports of expanded estimates and sampling error, (4)

tabulations of expanded estimates of volume, surface

area, and length by grade-defect classes, and (5) conversions of class subtotals to other units of measure. In

addition, processing statistics and error messages signal

input flaws and suspicious data.

Output reports contain far more information on dimensions, contents, and quality of sample trees than was
previously available; this feature should appeal to prospective timber purchasers. By simple substitution of

conversion constants, bidders can also use the program

to estimate product yields and returns for their particular

operations.

PREPARATION FOR STX ESTIMATES

These input items are required for the STX system to

estimate volume and value for tree-measurement timber

sales :

Planning

During sale area reconnaissance :

(1) Estimate:

(a) Total sale volume

(b) Total number of trees

(c) Volume of the largest tree.

(2) Decide on:

(a) Sampling accuracy objectives

(b) Species or species groups

(c) Products on which appraisal will be based

(d) Measurement units needed by purchasers

and for management planning and business

records

(e) Identification of size classes

(f) Subareas, such as payment units or any

other, for which separate volume or value

information will be needed.

(3) Calculate the number of sample trees needed for

the total estimate.

(4) Obtain a computer-generated list of random

integers for selecting 3P sample trees so as to approximate the desired number of samples.

Field work

(1) Prepare a short work plan to show organization of field work; necessary equipment, tools,

and aids; methods of making volume predictions ; and specifications for dendrometry.
(2) Provide cruiser training to develop estimating

skills.

(3) Arrange for check dendrometry.

Data processing (field level)

(1) Prepare data statements for STX control cards,

(2) Check card listings.

(3) Debug program output as required.

Data processing (processing center)

( 1 ) Punch and verify data cards.

(2) Arrange for machine processing, as required.

(3) Furnish coefficients for converting volume, surface, and length to estimates of product yield

and value.

3P SAMPLING

Determining number of sample trees

Equations used in conventional random sampling are

applicable to 3P sampling. For large populations

XT _ / CV in percent \ 2

\ sampling error in percent /

where N = estimated number of samples and CV = the

coefficient of variation of the ratio of measured-tree gross

volume to predicted-tree gross volume. Thus, 100 sample

trees are needed for a ±: 2% accuracy if CV is ± 20%.

How 3P samples differ from conventional samples

The difference in meaning of CV distinguishes 3P

sampling from conventional random sampling. In conventional sampling CV refers to the dispersion of individual tree volumes around the average volume per tree.

In 3P sampling CV refers to the dispersion of the ratios

of (measured volume/predicted volume) for individual

trees around the average of these ratios.

With conventional sampling, the estimator is, at the

mercy of volume dispersion as it happens to exist. The
range in tree volumes is usually wide and—even with

stratification by diameter classes—he cannot reduce CV

much below ± 35%. For an estimate with a sampling

error of ±: 2%, he therefore needs at least (35/2)^ =

307 sample trees. With 3P sampling, by contrast, CV

depends on the estimator's skill in holding as constant as

he can the ratio of measured gross volume to predicted

gross volume. Beginners may be expected to achieve a CV

of db 25% ; this drops the number of samples to 156.

Trained cruisers can readily attain a CV of ±: 15%, which

reduces the required number to 56 sample trees instead of

307 for a 2% sampling error.

Sampling efficiency with 3P also increases because

probability of sample selection increases with tree size,

while the cost of dendrometry increases very little as tree

size increase;?. In an east Texas pilot sale, for example,

trees ranged from 20 to 1600 bd. ft. per tree ; frequency

of samples in the smallest size group was 1 in about 90,

whereas for the largest group, the probability of sample

selection was 1 in about 6. Consequently, the average

volume of 3P samples is likely to be disproportionately

greater than that of the average tree.

Accuracy of the estimate is not affected by prediction

bias. A cruiser who is erratic in his predictions but who

averages out "on the button" will cause greater error

in the final estimate than will a cruiser who is severely

but more uniformly biased one way or the other.

It is important to keep the ratios as uniform as possible.

This is more difficult with small than with large trees.

In the east Texas pilot sale, for example, CV increased

from ±: 12.4% for the largest tree sizes to ± 20.9% for

the smallest. A factor in this disparity of CV among size

classes is complacency in making predictions for small

trees since so few are found to qualify. Although the odds

for sample selection are against the small trees, small

sample trees contribute as much to the total volume

estimate as large trees. Thus, for the east Texas sale,

a sample tree with a measured volume of 23 bd. ft. had

8
a frequency of 240.878, thereby contributing 23 x 240.878

~ 5540 bd. ft. to the estimate. For the same sale, a sample with measured volume of 1146 bd. ft. had a frequency

of only 4.866, thereby contributing 5576 bd. ft. In computation of CV the ratio (measured/predicted) for a

small tree similarly counts just as much as the ratio for

a large tree.

Basis for making predictions

Predictions are made directly in terms of gross volume

and may be weighted by relative value. Normally, it is

sufficient to use volume tables based on diameter and

height for the species being appraised, but form class

tables are preferable when they are available. Predictions

should not be reduced for breakage and cull.

Training estimators

A group of conveniently located trees should be measured with a dendrometer and used as a practice range.

At first, volume estimates should be made with table

lookup, based on estimates of diameter and other parameters, such as height and form class, required by the

volume table. As soon as the operation becomes familiar,

measurements should be preceded by a quick guess of

volume, however "wild," based on a visual impression

of tree size without recourse to measurements or tables.

In this manner, and with practice, only a modicum of skill

appears to be needed to make acceptable predictions (both

in speed and consistency) by cruisers having some aptitude for the work.

Estimators who base their impressions of tree volume

on practice with form class volume tables generally acquire a better knack for making consistent predictions

than those trained with diameter-height tables or tables

based solely on diameter.

Computing CV of predictions

As will be shown later, sampling error for an STX

cruise appears in the computer output and CV may be
derived by multiplying the sampling error in percent by

the square root of the number of 3P samples. Thus, CV

is ±: 20% if sampling error is ± 2.0% with 100 3P

sample trees. For practice sessions, however, CV must be

calculated with whatever facilities are available. A convenient formula for this is :

cy^ioo/v (^) (-^-^^ (xxy I

where CV == coefficient of variation in percent

iV =: the number of samples

X = (measured volume/prediction).

For example, if 3 sample trees have prediction ratios,

respectively, of 1.440,1.032, and 1.291

OF r= 100 .^/{ ^ \(^ ^^-^^Q' + ^-Q^^' + ^-^^'> \\

(1.440 -f 1.032 + 1.291)' /

identifying sample trees in the field

Since a list of the trees in a sale area or a map showing

their locations is rarely available in advance, the identification of qualifying sample trees and determination of

their locations present practical and statistical problems.

The object is to select, without bias, one sample tree jor

each accumulation of predictions that totals to

sum of all predictions

designed number of sample trees.

For example, for a sale of 1,000,000 bd. ft. where sample

design calls for 100 sample trees, one sample must be

drawn for any accumulation that totals to 1,000,000/100

=: 10,000 bd. ft. This problem of sample selection is solved

by use of either of two computer programs. One is called

THRP,2 the other is adapted to a wider variety of computers and is called RN3P, both prepared by Grosen-

^ L. R. Grosenbaugh. Three-pee sampling theory and program

THRP. U.S. Forest Service Research Paper PSW-21. Pacific Southwest Forest and Range Experiment Station, 1965.

10
baugh. These computer programs furnish lists of positive

random integers and nulls fitted to any particular sale or

sampling job. After predictions of volume are made, they

are compared with successive numbers in the lists. A

tree qualifies as a sample when the random number is

equal to or less than the prediction with which it is paired.

Trees paired with nulls are nonsamples.

The theory developed for this selection system is complex, but its application is very simple. The estimator

does not need to keep track of the accumulated predictions

and his tally may proceed in any order.

Obtaining a list of random integers

A list of random numbers and nulls must be obtained

for each sale and requires some advance information

about the sale area, based on data that is usually available

from field reconnaissance and diagnostic tallies made for

compartment prescriptions. Two control cards are needed

to obtain computer outputs of random integers :

For either THRP or RN3P, the first control card is left

blank in Columns 1-4, full identification of the sale area

is shown in Columns 5-64, and a brief coded identification

of the sale area is shown in Columns 73-76 (same as will

be used in program STX later).

For THRP, the second control card contains :

Column

1-4 Blank

5-16 L ~ any 12-digit identification number that

lacks eights or nines, different for each sale

18-22 LIM = total number of trees to be included

in the 3P estimate of volumes.* This number

should be a multiple of 500

24-27 K — volume of the largest tree that is to be

included by the 3P estimate ^

'All trees larger than K are sure-to-be-measured trees; their

volumes will be automatically added to the sample estimate based on

the 3P-measured trees.

11
29-3S KZ = total volume to be 3P-estimated divided

by the number of 3P sample trees that are

desired

For RN3P, the second control card contains the same

infoirmation arranged as follows :

Column

1 Blank

2^10 Any positive integer (0 through 999999999),

different for each sale

14-20 LIM (as for THRP above)

24-30 K (as for THRP above)

34-40 KZ (as for THRP above)

Figure 1 shows how data sheets are prepared for punching the control cards that are needed. Note that a job-end

card punched 9999 in Columns 1-4 must follow the last

card of each pair of control cards.

Some 3P design considerations

The value of LIM is not critical. Overestimates or

underestimates do not affect the 3P estimate. Always try

to overestimate the total number of trees. Excess random

numbers are cheap and are much cheaper than another

list. If an additional list is needed, change the number

shown as L in Columns 5-16 to provide a different set of

random numbers.

Overestimates or underestimates of KZ will affect the

number of samples that will be drawn, resulting in more

or less accuracy than planned. The volume estimate, however, will not be biased.

Setting the value of K may need consideration in some

situations because occurrence of trees larger than the

value of K will require the estimator to either (1) reduce

the prediction to K, a decision that will increase the CV

of his predictions, or (2) place the tree in a sure-to-bemeasured category, separate from the population being

3P-sampled, and thus increase expense of sample tree

measurement and subsequent computations.

In general, the value of K can be set high enough to

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rule out the occurrence of numerous trees with a prediction higher than K. For some estimates, however, it may

be advantageous to set K low enough so that a stratum

of the largest and most valuable trees is measured 100%.

When species vary considerably in value, weighting the

predictions by relative value will give high-value species

a better chance of being picked as samples. This is advisable if the high-value species form a minor component

of the stand.

Take, for example, a stand composed of 25,000 bd. ft.

of a high-value species (HIVA) and 90,000 bd. ft. of a

low-value species (LOVA). If HIVA is worth three times

the MBF value of LOVA, the volume estimate, weighted

by the relative value, is (3 x 25,000) + (1 x 90,000) =

165,000. Assume also that the largest HIVA tree has 400

bd. ft. (unweighted) and the largest LOVA tree has 1000

bd. ft. and that both species combined include fewer than

500 trees. To obtain an appropriate list of random numbers for drawing a sample of 25 trees assuming we wish

a sampling error of 5% and estimating the CV to be 25%

((25/5)2), parameters for the second data card needed

by THRP or RN3P will include :

LIM =500

K = 3 X 400 = 1200

KZ = 165,000/25 = 6600

Program statements needed for punching an RN3P

parameter card are shown by figure 1. Values of K and

KZ are in tens of bd. ft. Figure 2 shows the RN3P output of random numbers, also in tens of bd. ft. The figure

-99999 indicates a null, automatically a nonsample, unless

it is paired with a sure-to-be-measured tree.

With this design the number of LOVA samples that

can be expected is 90,000/6600 = 14, and the number of

HIVA is 75,000/6600 = 11.

Preparing random numbers for field use

For convenient field reference with a method that pre14
THREE-PEE SAMPLE-TREE MEASUREMENT AND APPRAISAL PAGE 1

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-99999 -99999 -99999 -99999 -99999 -99999 -99999 -99999 -99999 -99999

-99999 -99999 -99999 -99999 HO -99999 "99999 -99999 -99999 76

lie -99999 -99999 111 -99999 -99999 111 -99999 5 -99999

6 -99999 -99999 -99999 54 -99999 -99999 116 -99999 -99999

-99999 -99999 -99999 -99999 -99999 23 -99999 -99999 27 51

-99999 -99999 -99999 -99999 -99999 -99999 52 -99999 -99999 1

-99999 -99999 -99999 -99999 -99999 -99999 -99999 29 77 -99999

-99999 -99999 -99999 IB 113 -99999 -99999 -99999 -99999 -99999

-99999 "4 -99999 -99999 -99999 -99999 -99999 111 -99999 102

119 -99999 75 -99999 -99999 -99999 -99999 -99999 3 -99999

-99999 -99999 -99999 -99999 65 -99999 -99999 -99999 18 -99999

-99999 -99999 69 14 9 -99999 -99999 -99999 -99999 16

-99999 -99999 -99999 -99999 -99999 -99999 -99999 -99999 -99999 -99999

6107

TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST 106

THREE-PEE SAMPLE-TREE MEASUREMENT AND APPRAISAL PAGE 2

L= 192348613r LIM= 50U» K= 120» KZ= 660 TEST

TEST KSUM = 6107» NK = 106» NKZ= 500

EXPECTED NK*(K+l)/2= 6413» NKZ*K/KZ=: 90» LIM= 500

Figure 2.—RN3P output of random numbers.

/ents bias by premature disclosure of random integers,

:he lists of random numbers are slit, joined into strips,

md loaded into a special dispenser.^ Figure 3 shows the

letails of strip preparation, using an output from program THRP, which shows nulls as -0 instead of -99999.

* C. Mesavage. Random integer dispenser. U.S. Forest Service

Research Note SO-49. Southern Forest Experiment Station, 1967.

15
The random integer dispenser

ready for loading with tape. With tape on spools.

Cover closed, instrument ready

for use.

Figure 3.—Preparing random

numbers for field use.

t-HWV., '.«. lai '

5 - r* n 3 K ^î ? ii :;

» t »»

-«• «h - •« rj

U §• i

j

t* «• -• f« M

^ •* ir .'; -» t« t M

-• !• ^ •• i -»

*r

•' M .; î; ^ -« •! »i !

» • -* » •» -t

îî il »• W S?. 3 't a -•

» n

3 :ï ii * !! îj

»« " n

It 1» —, ;i ;; M M •<• :;

-, "X j; ;; •• ;) s « 'î _

• »• M

3 .Ï Ü w ;; 'J. J~ 2 S :: :; 3

H

i 1

^ *x " *

'il " Í 'î 5

»• •* »• K -*

i' u i! ^ « ii .: ;; -x ¿

'Í « --: *; 1' M Ü ^ 3 í S ^

"î

Mfct Hot

—3.6—

»«*t

HH^ m ».1

«MMMMItli. »NB HIM. *• * IML.

-• •* M •• -• Í ÎA w

,i il w

-« •4 s 3 • -•

u «t

«t M

•t --«I«-- 'M

!*

II -«-€- ni;;

M

Trimming specifications for preparation of a printout tape.

16
FIELD WORK

Organization of field work

Field work consists of listing predictions of volume for

each tree and measurement of trees that qualify as samples or as sure-to-be-measured trees. Experience indicates

that work should be organized to fit the conditions, changing in some cases on the same job, depending on density

of stocking, terrain, and size of the field crew.

When stocking is dense and maneuverability is restricted, a tallyman can eflficiently keep the records for a

crew of estimators and inform the estimators which trees

qualify as samples. If trees are large, sample trees occur

frequently and it may pay to have one or more dendrometerists keep up with sample tree measurements as the

crew progresses.

When stocking is not dense, it is usually better to have

each estimator keep his own tally and map the location

of sample trees for later dendrometry. String stripping

may facilitate such a two-stage procedure. The following

discussion assumes this type of work organization.

Equipment

Tools and supplies needed for STX estimating include :

(1) An aluminum letter-size sheet holder with a random integer dispenser attached to the front cover; the

dispenser is loaded with the tape of random numbers

generated for that sale

(2) A supply of STX tally sheets as shown in figure 4

(3) Volume tables needed to help make volume predictions

(4) Diameter and distance tapes

(5) Clinometer

(6) Map of the sale area

(7) Plastic nagging, bark shaver, and tree-marking

keel or tree labels.

17
TREE V.ARPS. COLS. 1- Il R < LL TREES. ]

*/hFN A SAMPLE TREE IS REACHED, SHOW » OR =

IN CÜL. li, AND START NEW PA 8E FOR NEXT TALLY

TOEE CARD FOR SAMPLE IS COMPLETED AT RI6HT.

STX TALLY SHEET

NONPUNCK

COUNT

TREE NO.

ONLY)" KPl

3

*

NON^P^Ü^N^C^H SALE NO... NAMF...

DAV IIMIT rOFU/

.UÍ3U Ul 7 sU 10 II DATE PAGE OF |

1 1

2 1 1 TREE CARD CONTINUATION FOR SAMPLE TREE

3 1 1 CLASS OBH OPT. BKA 8KB UML UDT

L- 4 1 M 1 : 1 ! : i 1 ! 1 i 1 i i ! ! 1 ! ! 1 .

5

6 1 1 ' ! 1 1 i ; 1 M 1 ! ! i : M 1 1 1 1 i 1 M 1 i

7 i 42 XTRA 57 XTR3 72

8 1 1

9

:o DENDROMETER CAROS FOR ABOVE SAMPLE TREE (9-CARD LIMIT )

—JJ^

1 TREE NO. J T GRADS F GRAOS SINELV GR

1 1 Ne.Cor.\ 1 ! 1 1^^^^'^i 1 1 1 1 1 1 1 1 1

13 1 1 1 1 s+

14

h '-. '

1 le*

15

S7| 1 1 1 1 1 1

16 N>^Card\ 1 1 1 IPIHBB^ 1 1

17 1 1 1

ta 1 1 i 1

19 1 1 1 1

20 1 1 1 N,.Corä\ 1 1 1 Ul^HI^ 1 1 1

21 1 ! 1 1 1 1

22 Mil

23 1 1 1 1 1

24 1 1 : L^HIHH 1 1 1

25 1 1 1 !

26 1 I 1

27 1 1 1 1 1

28 N^w Card\ \ ' l^tKÊÊÊÊÊÊÊ 1 1 1 1 1 1 1

29 1 I 1 II 1 1 j

30 1 1 II II 1 1

31 1 1 1 1 1 1 1

32 ...CarA 1 1 ¡ UlÊ^^m 1 1 1 1 1 I

33 -rr'^ Í I il 1 1 1 1

34 1 1 1 1 1 1 1

35 1 1 1 i

36 1 I^IH^HHH 1 1 1 1 1 1 1

37 1 ! 1 1 1 1 I 1 1 1

38 i 1 1 1 1 1 1

39 ! j 1 1 1 1 1 1 1 i 1

40 1 Ne.corA 1 1 1 u^im^am Mr 1 ' '

1 1 II

41 1 1 1 1 1

1 11_^

43 1 1 1 1 1

44 i New Card\ \ 1 I^HHHHII 1 1 1

1

45 1 -fff 1 1 r lili 1

46 ! 1 1 i 1 1 1 1 lili

47 1 ! 1 1 1 1 1 Jill :

48 RFMARKS

49 1 1 ! 1

SO ' 1 1 1

Figure 4.—STX tally sheet.

18
Procedure for making predictions and designating

sample trees

Estimators make predictions of volume as trees are encountered. (Stems of trees that fork below breast height

should be considered as separate trees.) The predictions

must correspond with the units on which the random

numbers are based. For example, since HIVA was

weighted 3X in the 3P design previously discussed, each

prediction for HIVA in that sale is multiplied by three

before it is recorded on the tally sheet, and since the

random numbers were generated in tens of bd. ft., predictions for both HIVA and LOVA must be in tens of

bd. ft. When relative value differs in this manner, each

stratum is coded numerically (1 through 9) and the

code for each tree is shown in Column 10 of the tally

sheet. When there is only one stratum, the 1 need not be

shown.

Each prediction is recorded as it is made in Columns

6-9 of the tally sheet (in the field headed KPI), and it is

then compared with the current random number to see if

the tree qualifies as a sample. To prevent selection bias,

the next number of a given column is rotated into view

after the prediction has been recorded. A tree paired with

a positive random number qualifies as a 3P sample when

the random number is equal to or less than the prediction.

It is a nonsample if paired with a null, unless it qualifies

as a sure-to-be-measured tree because the prediction is

greater than the value of K. For example, in the design

shown in figure 1, iC ~ 120, Any tree with a prediction of

121 or greater is a sure-to-be measured tree. When a

**sure" tree is encountered, the random number dispenser

is advanced as for any other tree.

A tree number is assigned only to sample trees. If more

than one estimator is employed, a temporary number incorporating the estimator's initials is recorded in the

remarks section at the bottom of the tally sheet. The

dendrometerist records a permanent number later.

19
Sample trees are flagged distinctively, and their locations are plotted on the sale-area map. Listing of additional predictions on the tally sheet ceases when a sample

tree is recorded. A new tally sheet is started for the next

tree.

Appendix C shows how tally sheets were prepared for

the first 18 of 33 sample trees measured for a hypothetical

population of 386 trees. Note that the tree predictions

were merely listed (under KPI and value stratum) until

a tree qualified as a sample. Each prediction was paired

successively with the list of random numbers shown in

figure 2. (The associated random numbers on the sample

tally sheets are listed in the non-punch column only as a

convenient reference for the reader. Do not record them

in the field.) The rest of the tally sheet is filled in by the

dendrometerist.

General procedure for measuring sample trees

Equipment. Tools and supplies required for dentrometry include :

(1) Optical dendrometer

(2) Slide rule for multiplication and division or, for

Barr and Stroud dendrometer,^ a Barr and Stroud calculator ^

(3) STX reference manual

(4) STX tally sheets (in aluminum sheet holder)

showing predictions made by the estimators

(5) Diameter tape

(6) Bark gauge, carpenter brace with 1-in. bit, and

Starrett No. 237 depth gauge with No. 61 IN rule; these

items are for bark measurement

* The use of trade, firm, or corporation names in this publication

is for the information and convenience of the reader. Such use does

not constitute an official endorsement or approval by the U.S. Department of Agriculture of any product or service to the exclusion

of others which may be suitable.

*C. Mesavage. Revised calculator for Barr and Stroud dendrometers. U.S. Forest Service Research Note SO-84. Southern Forest

Experiment Station, 1968.

20
(7) Telescoping pole, extendable to 13 ft.

(8) Hand level or clinometer (for level sightings)

(9) Small hand axe, bark scribe, tree identification

tags, marking keel, and plastic nagging tape

(10) Distance tape, range pole, and tree calipers;

these items, not carried in the field, are used for checks

of dendrometer.

The dendrometerist finds the sample trees and assigns

each a permanent sequential number, marking it on the

tree (for field identification) and in Columns 1-4 of the

tally sheet. He then obtains and records stem measurements, beginning with the stump, at breast height and at

points above that divide the tree into segments that are

uniform as to taper, quality, and defect. Quality and

defect of each segment, including stump to breast height,

are classified ocularly, based on surface indications. Tree

measurements are terminated at a designated top.

Although a dendrometerist can work alone, an assistant

is generally advisable. The assistant keeps notes, clears

lines of sight, obtains measurements as required at the

tree, and performs related work.

Recording tree measurements

The^ tally sheet is designed to facilitate field entries,

editing, and punching of data that relate to the tree as

a whole (on a tree card) and that relate to stem measurements made along the bole (on as many as nine

dendrometer cards per tree).

To assure successful processing of data, entries on the

tally sheet must follow explicitly the recording directions

discussed below :

Tally sheet (data for tree card) :

Column Entry on tally sheet

1-4 This field shows the tree number (for sample

trees only).

5 Blank.

6-9 This field shows the volume predictions (for

all trees).

21
Column Entry on tally sheet

10 This field shows the value stratum for each

tree by means of a one-character code (1

through 9). Strata are coded when trees differ in relative value, or when, for groups

having the same value, calculations of sampling error are desired for separate strata.

This is discussed further in the section on

program outputs.

11 This field is left blank until a tree qualifies

for measurement. An asterisk (*) is entered

for 3P samples ; an equal sign (:=) is entered

for "sure'* samples.

12-15 This field (labeled CLASS) shows how trees

are classified. For timber sales, this field is

normally used to identify species with a fourcharacter abbreviation, such as DFIR. Sometimes, it is desirable to defer the entry for

CLASS until the field work has been completed. If alternative classifications are being

considered, these may be entered in the nonpunch column.

16 This field is not normally used. However, it

may be used for blind labeling, i.e., the program will ignore the character, but it may be

useful in hand sorting.

17-21 This field (labeled DBH) shows the tape or

caliper measurement of the d.b.h.o.b. to 0.1

in. The decimal point need not be entered

since its position is implied as 0.1 by the program, but use of an explicit decimal point

makes the entry easier to read.

23 The fields 23-25 are labeled OPT. Field 23

codes the mode of measurement as follows:

0—Barr and Stroud FP-12 (or earlier

model) dendrometer

1—Barr and Stroud FP-15 dendrometer

(siNELV is coded)

22
Column Entry on tally sheet

23 (Cont.)

2—Direct measurements on felled or climbed

trees or those provided by direct-reading

dendrometers

3—Modified Zeiss Teletop dendrometer.

As explained further below, tape measurements of stump diameter and d.b.h. can be

combined with dendrometer measurements

of upper-stem diameters. In such cases, the

mode of measurement is coded to indicate

the type of dendrometer used on the upper

stem.

24 Column 24 codes machine procedure for reducing outside-bark measurements of stem

diameters to wood diameters, as follows :

0 or 1 d.i.b./d.o.b. at any point on the stem is

assumed equal to (d.b.h.i.b./

d.b.h.o.b.).

2 d.i.b./d.o.b. is projected hyperbolically.

d.i.b./d.o.b. is made to increase above

breast height and decrease below

breast height, i.e., relative bark thickness is programmed to decrease up

the stem.

3 d.i.b./d.o.b. is projected hyperbolically.

d.i.b./d.o.b. is made to decrease above

breast height and increase below

breast height, i.e., relative bark thickness is programmed to increase up

the stem.

25 Column 25 codes method for obtaining computer estimates when unseen but usable material occurs above the last measured section.

(The code is ignored unless -999 is recorded

as the last F GRADS, explained further below.)

1 This is a computer projection, based

on diameter at stump and at least

23
Column Entry on tally sheet

25 (Entry 1 Cont.)

three sets of measurements above the

stump (preferably above breast

height), that requires entries under

UDT (Columns 39-41) or under both

UDT and UML (Columns 36-38). UDT

is (desired minimum top d.o.b./

d.b.h.o.b.). UML is guessed or measured length of top section.

2 Computed from estimated taper rate

(recorded under UDT in inch per foot.)

and length (entered under UML). UDT

may be guessed or obtained from

taper tables. UML may be guessed or

measured with clinometer.

26 Blank.

27-34 These fields (labeled BKA and BKB) are used

for recording single bark thickness to 0.1 in.

If only one measurement (or average of

several measurements) is made, it is entered

under BKA (without decimal point). A second

measurement (or average) is entered under

BKB. When an entry is made only under BKA,

the program doubles it. If BKB is also shown,

the program adds the measurements.

If no entries of bark thickness are recorded,

the program assumes that d.b.h.i.b./d.b.h.o.b.

is .90 (a parameter that can easily be changed

in the program), and the mode of correction

is guided by the option coded in Column 24.

If a fictitious negative bark thickness (like

-009) is entered under BKA, no correction for

bark is made. In this manner, outside-bark

volumes may be computed from d.o.b. meaurements, or inside-bark volumes may be

computed from d.i.b. measurements.

35 Blank.

24
Column Entry on tally sheet

36-38 This field (labeled as UML) is for recording

length of unseen section above the last measured section. The current format implies

this is in whole feet. A value for UML must

be shown if Column 25 is coded 2, otherwise

it would imply that last section is of zero

length. UML is optional if Column 25 is

coded 1.

39-41 This field is labeled UDT.

If Column 25 is coded 1, and F GRADS of -999

is recorded after the last set of measurements, the program will compute top d.o.b.

as (UDT X d.b.h.o.b.). To obtain a projection

to 50% of d.b.h., for example, UDT is recorded as 500. The decimal point is implied

and need not be recorded. If a length is shown

under UML, the projection will terminate at

this length or at (UDT x d.b.h.), whichever

comes first. If UDT is omitted, the program

assumes a value of .45. This figure may

easily be changed to any other constant, if

desired.

If Column 25 is coded 2, and F GRADS of -999

is entered after the last set of measurements,

the unseen section will be computed as a conic

frustrum having the length entered under

UML, and a taper rate, in inches per foot, as

entered (without decimal point) under UDT.

42-71 These fields are reserved for future use

(when point sampling, etc., are employed).

72 This field is normally blank, but see comments below on tally of cull trees.

Tally sheet (data for dendrometer cards) :

Stem measurements are made, beginning with the

stump, and are recorded in the fields labeled T GRADS, F

25
GRADS, and SINELV. Four sets of measurements may be

recorded on each of up to nine dendrometer cards. An

asterisk is entered in Column 72 of the last set of dendrometer measurements to show that the next measurements

are for a new tree. Computer interpretation of these data

depends on the mode of measurement coded for Column

23 of the tree card.

The tally sheets in Appendix C illustrate most, if not

all, tree-measurement options available with the STX

program. Leading zeros should not be entered unless an

implied decimal point precedes the first zero, such as

01 for .01.

Modes of tree measurement

Any method of tree measurement can be accommodated

by the STX computer program, and the method may be

changed from tree to tree on the same job.

Barr and Stroud dendrometers. See tally sheets for

sample trees nos. 1 and 2, Appendix C. Drum calibrations

of T and F GRADS are read to 0.1 grad and entered without

a decimal point. Thus a reading of 45.2 is entered as 452.

Sine of the vertical angle, read from the clinometer of

model FP12, is similarly entered without the decimal

point, but the sign must be shown. Thus, angles with sines

of + .252 and — .135 are entered as +2520 and —1350,

respectively. Clinometer scales of model FP15 are graduated in terms (1 + sine). Angles having sines of +.252

and —,135 appear as 1.252 and .865 on the FP15 clinometer and are entered as 12520 and 8650, respectively.

The micrometer may be interpolated to show an additional decimal place, if desired. For example, an interpolated reading might show the sine coded as 1.2525, and

be entered as 12525. (Column 23 of the tree card is coded

0 for model FP12 or earlier models, and 1 for model

FP15.)

To measure total height, T GRADS and siNELV are

sighted to a terminal leaf, when possible, and P GRADS is

entered 0.1 grad greater than T GRADS. This is illustrated

26
by sample tree no. 16. When it is not possible to read

T GRADS, both T and F GRADS are recorded as -999, and

SINELV is the only actual measurement recorded.

Modified Zeiss Teletop. See tally sheet for sample tree

no. 5. The T GRADS field is used for recording slant distance to 0.1 ft. and F GRADS for recording stem diameters

to 0.1 in. The decimal point is not entered in either case.

Vertical angle, read to 0.1 degree in terms of (100 +

degrees), is entered with decimal point in the SINELV field.

(Column 23 of the tree card is coded 3.)

To include total height, T GRADS and SINELV to a terminal leaf are determined when possible, and F GRADS is

entered as 1.

Direct measurements on felled or climbed trees. See

sample tree no. 3. The T GRADS field is left blank. Diameters measured with tape or caliper are entered, to 0.1

in., in the F GRADS field. The decimal point is not entered.

Height in ft. (to 0.1 ft. above the last measured diameter)

is entered in the SINELV field with decimal point. (Column

23 of the tree card is coded 2.)

Other dendrometers. Readings from dendrometers not

specifically programmed for STX are first converted into

direct measurements, as illustrated by sample tree no. 3.

(Column 23 of the tree card is coded 2.)

Procedures when lines of sight are obscured

Several procedures are available to facilitate measurements or to estimate stem diameters when lines of sight

(LOS) are obscured:

LOS to stump and breast height are obscured. See sample tree no. 6. Actual measurements at stump and breast

height may be recorded as the first two F GRADS if the

initial T GRADS is shown as -999. The second T GRADS is left

blank. The first siNELV is recorded as the distance upwards from stump to breast height, and the second SINELV

is distance upwards from breast height to the point of first

dendrometer measurements. Diameters recorded as the

first two F GRADS are measured to 0.1 in. and may be recorded without decimal point, and distance upwards is

27
measured to 0.1 ft., recorded with decimal point. Mode of

measurement coded in Column 23 of the tree card identifies the dendrometer used for the upper-stem measurements.

LOS to merchantable top is obscured. When unseen but

usable material occurs above the last measured section,

contents of the section can be estimated by a convex-conicconcave projection based on lower measurements (if at

least three sets of measurements in addition to stump are

recorded) or by a conic projection based on estimated

length and taper of the unseen section. For either type

of projection, -999 is recorded as the final F GRADS to signal the presence of unseen material.

Sample tree no. 7 shows the field record for a tree in

which top diameter was extrapolated to a minimum d.o.b.

of UDT X d.b.h.o.b., in this case .425 x 22.8 = 9.7 in. Sample tree no. 8 shows the field record for a tree that was

extrapolated to a minimum d.o.b. of .500 x 27.1 = 13.6 in.

for a distance (recorded in UML) of 14 ft. Note that for

both trees Column 25 (tree card) was coded 1 to indicate

that top d.o.b. equals UDT x DBH.

For sample tree no. 9 the uppermost section was projected as a conic frustrum by coding Column 25 (tree

card) as 2 and furnishing estimates of .300 in. of taper

per ft. (recorded as UDT) for a length of 22 ft. (recorded

as UML).

LOS to terminal tip is obscured. When it is feasible to

measure SINELV to include total height but impossible to

measure T GRADS to a terminal leaf, a computer projection

is activated by recording -999 as the last T GRADS, -999

as the last F GRADS, and SINELV. This is illustrated by sample tree no. 17 for a Barr and Stroud dendrometer. The

same procedure is used for the modified Zeiss Teletop.

Other special recording procedures

Moving instrument location. The location ofthe dendrometer may be changed as needed for better visibility of

stem sections. When the move is on the same contour,

28
measurements and data recording are continued as

though a move had not been made. See sample tree no. 10.

If a move is to a higher or lower instrument location,

a -f sign is posted in Column 72 of the dendrometer card

to indicate that the next measurements will be from a new

location, but for the same tree. See sample tree no. 11. The

first set of measurements from the new location are for

the same stem section last measured at the previous location. A new dendrometer card is started for each move

made in this manner. An asterisk is entered in Column

72 of the last dendrometer card used.

The symbols ++ are entered under GR for the stump

(explained further below) to show that the instrument:

was moved on or off the contour.

If LOS to top is obscured from last instrument location,

at least three sets of measurements in addition to bottom

section and final F GRADS of -999 are needed to activate

computer projection when Column 25 of the tree card is

code 0 or 1.

Measuring forked trees. As shown by sample tree no,

15, measurements of the single stem below a fork are

made as usual, and a + sign is entered in Column 72 of

the dendrometer card to show that the next set of measurements will be from the base of a prong. The measurements (at base of the prong) are entered as the first set

on the next dendrometer card. This procedure is repeate^i

for every prong, each terminating with a + ir^- Column 78.

The tallest prong is left until last and terminated by B.n

asterisk in Column 72 of the last dendrometer card.

If LOS to top of any prong is obscured, at least three

sets of measurements in addition to base and fina! F GRADS

of -999 are needed for computer projection by method 0

or 1 in Column 25. This projection can be made for any

prong, but, if made for more than one, the same UDT and

UML will apply.

Defining merchantable sawtimber length

Sawtimber is utilized to some minimum diameter thaiproduces a log of marketable size, consistent with the cost

29
of log making and product recovery. Validity of coefficients for converting estimates of volume in standing trees

to estimates of net product yields and value depends in

part on unambiguous definition of the point of cutoff.

Recommendations for specifying merchantable length in

several common situations are as follows :

(1) When average tree is small and stems taper uniformly, a condition prevalent for many northern and some

western conifers, dendrometry may be terminated at a

fixed diameter of 6 or 8 in., depending on species and

product. In such cases the stem may be scanned with a

dendrometer that has been preset for the desired minimum diameter. If branches obscure the LOS, tree contents above the last measured section can be estimated by

computer extrapolation if at least three sets of measurements above the stump have been recorded. Column 25

of OPT is coded 1, UDT is shown as (min. d.o.b./d.b.h.o.b.),

and UML is estimated. Final F GRADS is shown as -999 to

activate the unseen option. (With Barr and Stroud dendrometers, F GRADS preset at 64.5 displaces 8-in. diameter

at any distance.)

(2) When average tree is relatively large and stem

taper is uniform despite occurrence of limbs, minimum

diameter frequently tends toward a fixed relationship

with d.b.h., a condition prevalent with most western conifers with tip terminals. In such cases the dendrometer

may be preset for scanning the stem to a diameter

equivalent to some fixed percentage of d.b.h. If LOS is

obscured, the desired ratio of minimum d.o.b. to d.b.h.o.b.

is shown as UDT. Maximum length may optionally be

shown as UML. (If desired UDT is .45, it need not be recorded since a blank UDT is implied to be .45.) Final

F GRADS must be shown as -999 to activate the unseen

option.

(3) When the uniformity of upper-stem taper is

broken up by relatively large branches (a condition prevalent for southern conifers, large hardwoods, and some

western conifers, such as ponderosa pine), merchant30
ability may be limited by excessive taper: taper is excessive when an increase in the length of the top log

results in reduced log scale. When the stem is visible, the

point beyond which taper is excessive is easily ascertained

ocularly by an experienced dendrometerist or by trial

and error based on dendrometer measurements at several

points.^

When LOS are obscured, computer projections are best

based on an estimate of top-log taper, recorded in in. per

ft. under UDT, and an estimate of length, recorded in

whole ft. under UML. Table 1 shows average upper-log

taper, in in. per ft., for southern conifers and eastern

hardwoods.

Classifying grade and defect of stem segments

Two columns, labeled GR on the tally sheet, are used

for two-character coding of segment quality and volume

losses caused by defect. The program is limited to 11

classes of segment for each of up to nine tree classes.

Nine quality-defect classes are used, as follows:

Quality classes

A Segment contains no indication of knots or limbs

B Segment has overgrown knots

C Segment has limbs, green or dead

Defect classes

A Segment is sound

B Segment has sound cull (crook or sweep)

C Segment has or is suspected to have rotten cull

For example, an AA segment is clear and sound.

Other definitions of class may be used if desired, but

they must be relatively unambiguous, and the criteria

must have promise of good correlation with grade and

yield. Segment lengths may be of any length if taper is

uniform.

Cull sections occurring anywhere below the designated

"^ C. Mesavage. Definition of merchantable sawtimber height.

Journal of Forestry 63:30-32, 1965.

31
^ Table 1.—Taper per foot in Iß-ft. logs, by d.b.h. and log position,

eastern hardwoods and southern pines

2 3 4 5 6

Logs Logs Logs Logs Logs

d.b.h. 2d 2d 3d 2d 3d 4th 2d 3d 4th 5th 2d 3d 4th 5th 6th

10 .09 .08 .09

12 .10 .08 .09 .07 .09 .12

14 .11 .09 .10 .08 .09 .12

16 .12 .09 .11 .08 .10 .13

18 .12 .10 .11 .08 .11 .14

20 .13 .11 .12 .09 .11 .15 .07 .10 .14 .18

22 .14 .11 .12 .09 .12 .16 .07 .11 .14 .18

24 .14 .11 .13 .09 .14 .16 .07 .11 .15 .19

26 .15 .12 .14 .09 .14 .17 .07 .12 .16 .20

28 .16 .12 .15 .10 .15 .18 .08 .12 .16 .21 .06 .09 .13 .20 .28

30 .16 .12 .16 .11 .16 .19 .08 .12 .17 .22 .06 .09 .13 .20 .28

32 .17 .12 .17 .11 .16 .19 .08 .13 .18 .23 .06 .09 .13 .20 .29

34 .18 .13 .17 .11 .16 .20 .08 .13 .19 .24 .06 .09 .14 .21 .29

36 .18 .13 .18 .11 .16 .21 .08 .14 .19 .24 .07 .09 .14 .21 .31

38 .18 .13 .18 .12 .16 .21 .08 .14 .19 .24 .07 .09 .14 .21 .32

40 .18 .14 .18 .12 .17 .21 .09 .14 .20 .25 .08 .09 .15 .22 .33
top, including jump butts, are classed as XX. Jump butts

should not be omitted.

The 11th category is a class identified in the program

as TJU that may be used to classify material such as pulpwood above the sawlog top, or in small trees. When it is

desirable to include the entire stem of sound timber from

stump to tip, material above the merchantable pulpwood

top may be classed XX. See sample tree no. 18.

Tally of cull trees

Cull trees are normally not tallied. They may be tallied

if they are assigned to a separate stratum. Each cull must

have prediction of at least 1 (fictitious or constant) and

the prediction may not be omitted from the tally unless

the tree has been classed as sure-to-be-measured. Culls

that qualify as 3P samples or sure-to-be-measured must

have a tree card containing stratum, sample category,

KPI, species, and DBH.

If individual cull tree detail is desired in the printout,

the tree card must be followed by a dendrometer card with

a 1 punched in Columns 5,19, 34, and an asterisk punched

in Column 72. A sample tree number is not assigned to

cull trees.

If no cull tree detail is desired on printout, the dendrometer card may be omitted. Instead, an asterisk is

punched in Column 72 of the tree card. Although no tree

detail will appear in the printout, its frequency, basal

area, and KPI are accumulated and are included in stratum

and grand totals.

Some suggestions for dendrometry

Checking dendrometers. Dendrometers should be

checked frequently and adjusted when necessary. With

Barr and Stroud dendrometers, T GRABS at 100 ft. should

be 50.77. F GRADS at this distance for diameters of 2 and

24 in. should be 54.45 and 87.86, respectively.

Sources of error. Some of the more frequent sources of

error in diameter measurement include (1) LOS not

square across a section, (2) lines of coincidence not in the

33
center of the viewing field, (3) imperfect alignment of

coincidence lines.

When stems are numerous, special care is needed to

avoid inadvertent sightings to background stems. T GRADS

should increase as elevation angle departs from a level

shot and decrease as a level shot is approached. P GRADS

normally, but do not necessarily, decrease up a stem.

Measurements should avoid bumps and swells.

Measuring procedures. Since actual measurements of

bark thickness and d.b.h. are normally required, it saves

time to measure d.o.b. at stumb as well as at breast height

and to record the two diameters as the first two F GRADS,

even when dendrometer LOS are clear. A light measuring

pole, extendable to 13 ft., is a useful accessory for measuring distance upwards from stump to breast height

and from breast height to the first point of dendrometer

measurement. Dendrometer measurements may begin at

breast height if this section is visible, thus showing two

measurements of d.b.h. (one recording tape measurement

as the second F GRADS, the second based on dendrometer

measurements recorded as the third T GRADS and F

GRADS). The second SINELV in this case will show distance

upwards to be 0.0.

If diameters are actually measured at stump and breast

height, the rest of the tree can often be measured from

one instrument vantage point. Experience dictates when a

new vantage point should be sought as an alternative to

clearing LOS from a single location.

Options for computer estimates of "unseen" upper

stem sections apply only to the topmost segment of a

tree. Whenever feasible, the instrument should be moved

to a new location to reduce length of unseen portion.

When a dendrometer location is changed to a different

elevation, it is necessary to begin new measurements by

repeating shots to the section that was last measured

from the previous location. It is usually difficult to see the

previous section from a new location, and hence it is

better to locate a new vantage point on the same elevation

34
so that measurements can be continued as though no

move had been made. Picking a new location on the same

contour is facilitated by using the dendrometer for level

sightings to new locations or by using a hand level to

check the contour by shooting back at the dendrometer

from new locations.

Bark options. To establish the proper option for any

species, measurements of bark and d.o.b. should be made

at stump, at breast height, and as high as can be reached

for at least 10 sample trees. D.i.b./d.o.b. should be computed and averaged at each level. Bark option is 0 or 1

if d.i.b./d.o.b. for the three levels is constant, 2 if it increases with height, and 3 if it decreases with height.

Studies have shown that code 2 should be entered in

Column 24 as the bark option for southern pines.^

Measuring bark. Sizable errors in bark thickness can

go undetected if bark is not measured properly.® Recommended procedures are as follows :

(1) Reducing ambiguity. Ambiguity in measurements

can be practically eliminated by measuring radially from

the wood surface to the contour of a diameter tape wrapped tautly around the section. In this procedure bark

thickness is regarded as the difference in diameters of two

concentric circles, one defined by the tape as the bark

surface, the other by the interior wood surface. The

radial distance from wood to tape may be measured even

where the tape crosses a bark fissure. However, measurements should be made well to either side of swells or bark

ridges that cause the tape to kink.

(2) Reducing sampling error. Bark thickness may vary

considerably around a stem on the same cross section. The

following guide is suggested for keeping sampling error

® C. Mesavage. Converting dendrometer estimates of outside-bark

stem diameters to wood diameters on major southern pines. U.S.

Forest Service Research Note SO-93. Southern Forest Experiment

Station, 1969.

•C. Mesavage. Measuring bark thickness. Journal of Forestry

67:753-754,1969.

35
in bounds with a minimum number of measurements:

Start with one pair. If one measurement of the pair is

30 percent or more greater than the other, measure a

second pair and average the four readings. Bark thickness should be measured "wood to tape" even when o.b.

diameters are taken with calipers.

(3) Increasing accuracy. Considerable experience is

needed to operate the bark punch so thatthe chisel reaches

the wood but goes no further. When bark is soft or thin

the position of the mark made by the chisel can be checked

by exposing the wood surface with a tree scribe. When

bark is thick or tough it is advisable to bore into it with a

light carpenter's brace and a 1-in. auger bit, instead of

using a chisel. The brace may be turned rapidly most of

the way, then slowed to the minimum torque needed to

drive the bit into the bark. When the wood is reached,

the brace will usually stall. Bark thickness is then measured from wood to tape. For bark thicker than 2.5 in.

(the limit for available bark-measuring gauges), a Starrett No. 237 depth gauge with No. 611N rule is a convenient substitute. Residual bark fibers left after boring

should be scraped from the surface of the wood before

measuring.

DATA PROCESSING

Data preparation and general procedure

The steps needed to prepare the data and to select, obtain, debug, and interpret the output include the following :

(1) Check the tally sheets for omissions and errors.

Careful editing of tally sheets is required because blanks

in some fields are not necessarily omissions that will cause

processing to cease, or produce incorrect results. For example, blanks in Columns 10, 24, and 25 on the tree card

are interpreted as code 1. If bark measurements are

omitted, the ratio d.i.b./d.o.b. will be assumed by the

program to be .90 (or as programmed). The program

ignores a blank UML if Column 25 is punched as code 1

or left blank but will abort if Column 25 is punched as

36
code 2. Processing will continue if final F GRADS are shown

as -999, even when UDT and Column 25 have inadvertently

been left blank, because Column 25 will be assumed to be

code 1 and UDT will be assumed to be .45 (or as programmed).

(One way to avoid omissions is to check with a zero

every column that is purposely left blank, except for

value stratum and sampling category. A dash should not

be used instead of a zero because it might be interpreted

asa minus sign.)

Common errors or omissions are as follows :

— Sampling category not shown for sample trees in

Column 11

— Sample tree number omitted on tree or dendrometer

card

— d.b.h. omitted in Columns 17-21

— Bark measurement omitted

— UDT omitted though final F GRADS is shown as -999,

and vice versa

— Grade-defect class not shown for unseen topmost

section

— Terminating asterisk omitted on last dendrometer

card

— Illogical progressions of T and F GRADS (not necessarily incorrect)

999 not shown as first T GRADS when tape measurements are made at stump and breast height

(2) If the population is not divided into two or more

strata, count and add the predictions for all trees, including measured trees (both sure and 3P) and predictedonly trees.

(3) Decide on tree class codings for Columns 12-15

if this decision was deferred. For timber sales, tree class

is normally used to code species or species-groups. Not

more than nine tree classes should be recorded if the data

are later to be converted to estimates of products or

product values.

(4) Prepare data statements for five STX control

37
cards (explained below) and send the statement sheet

with tally sheets to the data processing center.

(5) Check and correct (if necessary) data card listings

and program outputs sent back from the data processing

center.

Program control cards

Program statements for five control cards are illustrated by figure 5. The required control cards are as

follows :

Card no. Columns Entry

1 5-68 Name of sale, area, or job

73-76 Job identifier (same as used for

THRP or RN3P)

80 Card number

2 5-16 Initials of user and input date

17-43 Copy the instrument parameters

shown in Columns 17-43 of figure

5, if at least one tree was measured with any model of Barr and

Stroud dendrometer. Otherwise,

these columns may be left blank.

Card no. Columns Entry

45 Total number of value strata

coded in Column 10 of tally sheet

46-50 KZ (same as for THRP or RN3P)

51-55 K (same as for THRP or RN3P)

66-71 Job options (explained below)

73-76 Job identifier

80 Card number

3 Nine 8-column fields, beginning

with Columns 1-8, for total tree

count in each stratum. Card is left

blank if tree cards are punched

for nonsamples as well as

samples.

73-76 Job identifier

80 Card number

38
1

I

s

3

3

CD

3

sr

o

o

I

00

P/^r^ ¿IST/NG FO/? 80 Ci )LUMfi/PUNCHSD CARD

¿_ -2íító¿^¿£UsWAÍ¿d¿j2Íftí^ t ^Af4/WÀû 1 ! 1 1 ^àA 1 —^ a.^tfí;^ im] "iwm-mmmn n m m 4 m'^m mtú t

¥_ sû3ï ssaa ,, , X ::::::::::::::^|:::::::|::::|||m|:

_ --TT -4

4-J_ i_4_ _4_

1

'

1 J

--|_. _L _^ it +~^" "

'X 1

X

~i- -^—^-L|H j—LJ- If _ _.r — T

- - |+4_ijI[Tr^~''"^ -h—

Li , , 1 ,1 il r

4-- -Í -Eî " "'ii

1 ! 1 1 1

„^ .1 L„ _ _i_ , j 1 , 1 1 ^^ ^

~

1 2 1 4 S 1 7 1 « 10 II 12 13 14 15 1« n 11 tl 20^1 » n 24 2S X 27 21 21 30 31 32 33 34 3S 31 }7 11 31 «g
Card no. Columns Entry

4 Nine 8-column fields, beginning

with Columns 1-8, for aggregate

predictions in each value stratum.

Card is left blank if tree cards

are punched for nonsamples as

well as samples.

73-76 Job identifier

80 Card number

5 Nine 8-column fields, beginning

with Columns 1-8, for relative

value within each value stratum.

Card is left blank unless strata

differ in value per unit of volume.

73-76 Job identifier

80 Card number

Job options

Job options, coded in Columns 66-71 of the second

control card are as follows :

Column Entry on tally sheet

First 0 or 1 Input cards must be punched for

(Column 66) all trees (including nonmeasured

trees assigned predictions only),

but third and fourth control cards

are left blank.

2 Input cards must be punched only

for measured trees, but aggregate

number of trees and aggregate

predictions for each stratum (including sure-to-be-measured trees,

3P measured trees, and 3P predicted-only trees) must be

punched on the third and fourth

control cards.

40
Column

Second

(Column 67)

Third

(Column 68)

Fourth

(Column 69)

Entry on tally sheet

0 or 1 Processing will cease after the

program has calculated and

printed a preliminary report.

(See page 1 of Appendix A.)

2 Processing will continue beyond

the preliminary report if no fatal

errors occur.

0 or 1 No individual tree detail will be

printed.

2 Individual tree detail will be printed. (See page 2 of Appendix B.)

3 Individual tree and tree-segment

detail will be printed. (See pages

2-9 of Appendix A.)

0 or 1 No detail cards will be punched as

part of output.

2 Tree detail cards will be punched

as part of output. (See page 40,

PSW-13.^^)

3 Tree-segment detail cards will be

punched as part of output. (See

page 42, PSW-IS.^^)

0 or 1 No log and tree detail will be

written on tape for later gradeyield and realization processing.

2 Log and tree detail will be written

on tape and will be processed if

no fatal errors have occurred, but

subtotals only will be tabulated in

printout. (See page 13 of Appendix A.)

3 or 3+ Same as 2 above, but sorted individual log detail will also be

printed. (See page44,PSW--13.i^)

^®L. R. Grosenbaugh. STX-Fortran-4 program for estimates of

tree populations for 3P sample-tree measurements. U.S. Forest

Service Research Paper PSW-13. Pacific Southwest Forest and

Range Experiment Station, 1967.

Fifth

(Column 70)

41
Column Entry on tally sheet

vSixth 0 No further processing.

(Column 71)

1-9 Not more than this indicated number of sets of conversion coefficients will be searched to convert

subtotals to product outturn and

realization values. (See page 14

of Appendix A and page 7 of Appendix B.)

Card punching

Tree and dendrometer cards are punched directly from

the tally sheets. The four-character job identifier

(punched in Columns 73-76 on the control cards) should

be punched in Columns 77-80 of each tree and dendrometer card. A two-character (or one-character) label

may precede this to identify pay units, if desired, using

Columns 75-76 for two characters and Column 76 for one

character.

Column 66 of the second control card indicates whether

tree cards are to be punched for all trees or for sample

trees only.

Tree cards for nonsamples (if they are to be punched)

must contain the following items recorded on the tally

sheet :

Column Entry

6-9 KPI

10 Value stratum (implied as one stratum

if blank)

75-76 or 76 Pay unit number

77-80 Job identifier

Tree cards for measured trees (3P sample or sure-tobe-measured) must contain the following items recorded

on the tally sheet :

Column Entry

1-4 Sample tree number

42
Column Entry

6-9 KPi (if all trees are sure-to-be-measured,

KPI need not be estimated or shown)

10 Value stratum (blank is implied as one

stratum)

11 Sampling category (*, =, or blank)

12-15 CLASS

17-21 DBH

23-25 OPT (blank is not necessarily a field

omission ; it will = 1 except blank Column 23 = 0)

27-34 BKA or BKA and BKB (blank = .1 d.b.h.)

36-38 UML (blank is considered 0)

39-41 UDT (blank = .45)

75-76 or 76 Pay unit number

77-80 Job identifier

A tree card for a sample tree must be followed by one

or more dendrometer cards with entries as follows :

Column Entry

1-4 Sample tree number

5 Card number within-tree (first dendrometer card ~ 1, etc.)

6-11 Blank

12-2Q First set of stem measurements

27-41 Second set of stem measurements

42-56 Third set of stem measurements

57-71 Fourth set of stem measurements

72 Blank or + implies next card is a dendrometer card for the same tree. * implies next card is a tree card for the next

tree.

75-76 or 76 Pay unit number

77-80 Job identifier

43
In addition to the above data cards, cards 9 through 14

of subroutine BLD may have to be repunched to show

appropriate constants as follows :

Card no. of

subroutine BLD Entry

9 The positive or negative number following MRE should be the logical number

of the system input tape, the integer

following MPR should be the logical

number of the system output tape, and

the integer following MPU should be the

logical number of the system punch

tape. Integers following JW and JX

should be logical numbers for system

binary scratch tapes.

10 and 11 These columns label the manufactured

units or values into which volume, surface, and length are to be converted for

error computations.

12 The conversion coefficients corresponding to BORD, SLAB, and CLFT on BLD

card 12 convert cu. ft. of volume, sq. ft.

of surface, and ft. of length to arbitrary

units. The programa was initially supplied for conversion to Int. % (with

trim allowance) but these may be replaced by other units such as cu. ft. if

KPl's are made in cu. ft., etc.

13 Numbers and characters on BLD card

13 ensure that character code assumed

by program logic is identical with that

of the user.

14 The decimal fraction following RDE is

the ratio of d.i.b./d.o.b. at breast height

that will be assumed if no bark measurements are recorded for a particular

tree. RDE supplied with initial program

was .90.

44
Card no. of

subroutine BLD Entry

14 (Cont)

The decimal fraction following UDTRO

is the assumed ratio of d.o.b. of unseen

top to d.b.h. or the assumed taper in in.

per ft. UDT supplied with initial program was .45.

The decimal numbers following QUAN

and DENO are asymptotic bark parameters for hyperbolic extrapolation of

d.i.b./d.o.b. ratios above and below

breast height. QUAN and DENO supplied with initial program are 1 and 2,

respectively, for bark option code 2.

Initial program also contains a modification (FORTRAN function FFB3) to accommodate bark option code 3, in which

QUAN and DENO are 9 and 10, respectively.

Cards are also needed to insert conversion coefficients

into the program and to label certain special outputs

(explained later).

Finally, certain system cardó ^^ e needed to monitor the

programCard listings

Figure 6 shows a liciing of cards as they are arrayed

for processing. The control cards in this list should be

checked against the program scatements. Figures 7 and

8 show separate lists for tree and dendrometer cards,

respectively. These listings should be checked against the

tally sheets.

PROGRAM OUTPUTS

Processing by the STX program is organized in four

major sections (subroutines STll, ST22, ST33, and

ST44) that allow a wide choice of printed outputs. (Card

45
THRÈE-PEË SAiMPLk: TREE MEASUREMENT AND APPRAISAL

CM 03-16-70 Ü8Ü00 01964673-11905 15658 2 660

23^^ 152

903¿f 6933

1 3

HIVA

120

1

11

12

2

21

22

3

31

32

42

5

51

52

6

61

62

7

71

72

842

752

992

17.0 020 10 6

445 943+0140 443 831+0560AA

474 715+5250CA 484 707+5690CA

*HIVA 15.8 120 10 14

384 915U921Û 380 846 9940AA

415 74714630BA 436 72515800CA

HIVA 17.7 220 9 7

205 0,0 177 4.0AA

136 14.0BB 132 9.5CA

21.0 200 -009

216 0.0 196 4.0AA

169 6.7CA 153 15.9CA

15.6 320 6 10

190 96.6 675 156

110133.5BA 908

34.5 120 18

3Ö6 4.0

492 94213980BA 501

LOVA 22.8 121 18

-999 285 4.0

472 79415120CA

i382i:HIVA

25l*L0VA

676

810

i45l=L0VA

-999

571

444 805+114ÜAA

387 82811920AA

469 646Í6960CA

162 8.ÖAA

103 20.OCA

185 8.0AA

136 10.9CA

99.7AA 680 144106.8AA

84140.9CA

16

345 8.0AA

88414Ô50CA

6 425

228 8.0AA 443 87811090BA

-999 CA

4701058Í0920AA

508 835Í5510CB

TEST

223022 TEST

TEST

TEST

TEST

TEST

451 764+2890AA TEST

TEST

TEST

397 77613720BA TEST

TEST

TEST

148 14.6AA TEST

TEST

TEST

167 16.8AB TEST

TEST

TEST

727 136121.5AA TEST

TEST

TEST

478 98912520BB TEST

TEST

TEST

450 84613150CA TEST

TEST

1

2

3

4

5
ö 881*L0VA 27.1 121 11 15 14500 TEST

81 -999 301 4.0 271 8.0AA 413102711230AC 441 92214090CA TEST

82 ^70 8OÛ15840CA 475 80516730CA -999 CA *TEST

9 i09i*LOVA 32.4 122 15 19 22300 TEST

91 -999 404 4.0 324 6.0AA 426110711280AA 441 99414110BA TEST

92 ^79 8Ó715810CB -999 CA TEST

10 1211=L0VA 32.0 120 19 17 TEST

101 -999 3b2 4.0+ + 320 8.0AA 489 961Í0890AA 495 90812110AA TQST

102 514 87512720BA 504 85313950CA 515 809Í5020CB 526 73515970CA*TEST

11 1091*L0VA 31.3 120 15 15 TEST

111 -999 375 4.0+ + 313 6.0AA 44210291101ÜBA + TEST

112 465 99910950 482 91013400CA -»-TEST

113 4b4 93313770 480 85415350CA 493 77116110CA TEST

12 1031*LOVA 28.9 112 14 10170 TEST

121 -999 338 4.0 289 a.OAA 399111311350BA 418104713790BA TEST

122 448 91715900CA 459 857167Ö0CA -999 CA TEST

13 331*L0VA 18.8 130 8 10 TEST

131 -999 243 4.0 188 8.QAA 430 8631127ÜAA 447 81113340BA TEST

132 457 7bol4890CA 473 723157o0CA TILST

1^ 1322=HIVA 21.9 TEST

lí+1 41411Ü5-0510 413 919-0040AA 418 888+1990AA 432 831+3830CÄ TEST

lí+2 4b2 7bl->'5620CA 475 700+b34üCA TEST

lb 692*HIVA 16.8 120 8 12 TEST

Ibl -999 197 4.0 168 8.0AA 360 8521135ÜAA 374 80712970BA+TEST

152 374 80212980 413 7371b020CA + TEST

lb3 375 80512960 416 73815130CA 424 69616540CA TEST

Figure 6.—Listing of control, tree, and dendrometer cards in processing order.
»^

00

lb 212+HlVA il.l 12Ü 8 4

161 -999 lo2 3.5 111 8.5AA

162 4^25 6^6l54ifÜCA 468 46916300XX

17 331*L0VA 19.0 120

171 -999 218 3,b 190 8.5AA

172 i*25 72516110CA--999--99917500XX

18 1172*HIVA 20.1 120 11 11

Ibl -999 2^^ 3.5 201 8.5AA

182 4^6 75815270CA t+75 69716320CA

19 692*HIVA 19.5 120 lí| 16

191 -999 235 3.5 195 8.5AA

192 39b 67215780CA í+15 65516240UU

2Ü 3Ü2*HI\/A 13.if 120 10 8

2Ú1 -999 lob 3.5 134 8.5AA

202 39o büll5ó90CA

21 542*HIVA 17.0 120 10 10

211 -999 211 3.5 170 8.5AA

212 ^26 6721622ÜCA

22 612*HIVA ib.O 122 10 8 10190

221 -999 186 3.5 160 8.5AA

222 -•999 Cß

2Ó 452+HIVA 17.7 120 12 10

201 -999 226 3.5 177 8.5AA

232 i^bl 720l5750Cß 472 68916530CB

2tf 242*HIVA 15.2 120 14 10

2¿+l -999 lö^ 3.5 152 8.5AA

TEST

367 71110890CA 389 69413500CA TEST

TEST

TEST

350 91011570CA 385 84114240CA TEST

TEST

TEST

400 91111260AA 417 83913460CA TEST

484 66217030üU-999-99917460XX^TEST

TEST

314 909Í0680CA 347 80513850CA TEST

435 43617380XX TEST

TEST

323 77411b70AA 359 73114Ü20CA TEST

TEST

TEST

354 86111460CA 381 60314100CA TEST

TEST

TEST

340 85511660CA 383 77714390CA TEST

TEST

TEST

413 81611520AA 433 76214410CB TEST

TEST

TEST

192 81111340CA 226 61012990CB^TEST
2b 272*HIVA 11.8 120 8 6

2bl -999 Ibö 3.5 118 8.5AA

2Ó 692*HIVA 17.Í* 120 10 10

251 -999 201 3.5 174 8.5AA

262 í|í45 73714420CA 457 72115400CB

27 511+LOVA 23.1 120 12 8

271 -999 276 3.5 231 8.5AA

272 im3 Ö1116220CA

2ö 512+HIVA 15*8 122 12 10 10100

261 -999 207 3.5 158 8.5AA

2ö2 356 7Í4515810CA -999 CA

29 Ôif2*HlVA 18.3 120 14 10

291 -999 2^^ 3.5 18311230AA

30 1022+HlVA 19.0 122 12 10 14100

301 -999 24b 3.5 190 8.5AC

302 4üb 82015110CA -999 CA

31 1211=L0VA 31.0 122 18 14 10150

311 -999 3bb 3.5 310 8.5AA

312 ifb*f 89315160CA -999 CA

32 572*HIVA lb.8 122 8 12 10100

321 -999 202 3.5 158 8.5AA

322 3d3 727157bPCA -999 CA

33 6bl*L0VA 27.4 122 15 11 15130

331 -999 303 3.5 274 8.5AA

332 --999 CA

9999

9999

^

ço

Figure 6.—Con

281 76211590CA 305

419 81710830AA 427

383 98511510AA 419

279 83611690AA 327

417 77114080CA 451

356 91011740AA 374

419103811150AA 431

316 82511460AA 347

387106111350CA 406

TEST

69013430CA*TEST

TEST

78012580CA TEST

TEST

TEST

88015120CA TEST

TEST

TEST

77414600AA TEST

TEST

TEST

71616080CA^TEST

TEST

86613430AA TEST

TEST

TEST

97713360CA TEST

TEST

TEST

75014320CA TEST

TEST

TEST

97014150CA TEST

TEST
eno

1 Ô42*HIVA 17.0 020 10ó jEisx

'¿ 752*HIVA 15.8 120 10 14 -rpSj ó 992*HIVA 17.7 220 9 7 j^cj

** 13ö2=HIVA 21.0 200 -009 j^o^j b 251*L0VA 15.6 320 ó 10 rpsT 6 1451=L0VA 3í*.5 120 18 ló j^ST 7 571*L0VA 22.8 121 18 6 425 TEST Ô 861*L0VA 27.1 121 11 15 Í4500 TEST 9 i09l*LOVA 32.4 122 15 19 22300 TEST

10 1211=L0VA 32.0 120 19 17 TEST

11 1091*LOVA 31.3 120 15 15 TEST

12 1Ö31*L0VA 28.9 112 14 10170 TEST

13 331*L0VA 18.8 1308 10 TEST

14 Í322=HIVA 21.9

15 692*HIVA 16.8 1208 12

16 212*HIVA 11.1 12084

17 331*L0VA 19.0 120

18 1172*HIVA ¿0.1 12Û 11 11 j^^j

TEST

TEST

TEST

TEST
19 692*HIVA 19.5 120

m 16

2Ü 302*HIVA 13.

Í* 120 108

21 542*HIVA 17.0 120 10 10

22 512*HIVA Ib.O 122 10

8 10190

23 452*HIVA 17.7 120 12 10

2*+ 2i*2*HIVA 15.2 120 14 10

25 272*HIVA 11.8 1206

6

26 692*HIVA 17.4 120 10 10

27 511*L0VA 23.1 120 12

8

28 bl2*HIVA 15.8 122 12 10 lülOO

29 84f2*HIVA 18.3 120 14 10

3ü i022*HIVA 19.0 122 12 10 14100

31 1211=:L0VA 31.0 122 18 14 10150

32 572*HIVA 15.8 122

8 12 10100

33 651*L0VA 27.4 122 15 11 16130

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

TEST

Figure 7.—Listing of tree cards only.

en
Oí

11 í^^b 943+0140 443 831-I-0560AA 444 805+1140AA 451 764+2890AA TEST

12 í*74 715+5250CA 484 707+5890CA TEST

21 36^+ 915Ü9210 380 846 9940AA 387 82811920AA 397 77613720BA TEST

22 ífl5 74714630BA 436 72515800CA 469 64616960CA TEST 31 205 0.0 177 4.0AA 162 8.0AA 148 14.6AA TEST 32 136 14.0BB 132 9.5CA 103 20.OCA TEST

41 216 0.0 196 4.0AA 185 8.0AA lf)7 16.8AB TEST ^Z 169 6.7CA 153 15.9CA 136 10.9CA TEST

bl 676 190 96.6 675 156 99.7AA 680 144106.8AA 727 136121.5AA TEST 52 610 110133.5BA 908 84140.9CA TEST 61 -999 386 4.0 345 8.0AA 470105810920AA 478 98912520BB TEST 62 í+92 94213980BA 501 88414650CA 508 83515510CB TEST 71 -999 265 4.0 228 8.ÜAA 443 87811090BA 450 84613150CA TEST 72 ¡472 79415120CA -999 CA TEST

81 -999 301 4.0 271 8.0AA 413102711230AC 441 92214090CA TEST 62 470 8b015840CA 475 80516730CA -999 CA TEST

91 -999 404 4.0 324 8.0AA 4261107Í1280AA 441 99414110BA TEST 92 479 86715810CB --999 CA TEST

lül -999 362 4.0+ + 320 8.0AA 489 96Í10890AA 495 90812110AA TEST 102 514 87512720BA 504 85313950CA 515 80915020CB 526 73515970CA^TEST 111 -999 375 4.0+-Í- 313 8.0AA 442102911010BA +TEST 112 465 99910950 482 9101340ÜCA " •TEST 113 464 93313770 480 8541555ÜCA 493 77116110CA TF^T 121 -999 338 4.0 289 8.0AA 399111311350BA 41ñinU71.'^7Q0BA TEST
122 4i+ô 9Í7159Ü0CA

151 -999 243 4.0

132 4b7 75Ó14890CA

141 4141105-0510

142 4b2 761+5620CA

151 -999 197 4.0

152 374 80212960

153 375 80512960

loi -999 132 3.5

162 423 Ó4615440CA

171 -999 218 3.5

172 425 72516110CAloi -999 244 3.5

182 446 75815270CA

191 -999 235 3.5

192 396 67215780CA

2Ü1 -999 Ibb 3.5

202 396 66115690CA

211 -999 211 3.5

212 426 6721622ÜCA

221 -999 136 3.5

222 -999 CB

231 -999 22ü 3.5

232 457 72015750Cb

459 85716760CA

188 8.0AA

473 72315760CA

413 919-0040AA

475 700+6340CA

168 8.0AA

413 73715020CA

416 73815130CA

111 8.5AA

468 4691630ÛXX

190 6.5AA

'999-99917500XX

201 8.5AA

475 69716320CA

195 3.5AA

415 65516240ÜU

134 8.5AA

170 8.5AA

160 0.5AA

177 8.5AA

472 66916530CB

-999 CA

430 8631127ÜAA

418 888+1990AA

360 85211350AA

424 69816540CA

367 71110890CA

350 91011570CA

400 91111260AA

484 66217030UU314 909Í0680CA

435 4361738ÖXX

326 774ilb70AA

354 861Í1460CA

340 85511o6üCA

413 81611520AA

TEST

447 81113340BA TEST

TEST

432 831+3830CA TEST

TEST

374 80712970BA+TEST

+TEST

TEST

389 69413500CA TEST

TEST

385 84114240CA TEST

TEST

417 83913460CA TEST

-999-999l7460XX^TEST

347 80513850CA TEST

TEST

359 73114020CA TEST

TEST

381 80314100CA TEST

TEST

383 77714390CA TEST

TEST

433 76214410CB TEST

TEST

CO Figure 8.—Listing of dendrometer cards only.
oí

1^

2<^1 -999 loíf 3.5 152 S.5AA

251 -999 158 3.5 118 8.5AA

261 -999 201 3.5 174 8.5AA

262 ífifS 7371íf420CA 457 72115400CB

271 -999 276 3.5 231 8.5AA

272 *fí43 81116220CA

281 -999 2Ü7 3.5 158 8.5AA

282 356 7í*515810CA -999 CA

291 -999 244 3.5 18311230AA

301 -999 ¿45 3.5 190 8.5AC

302 « 05 Ö2Ü15110CA -999 CA

311 -999 365 3.5 310 8.5AA

312 « 54 89315160CA -999 CA

321 -999 202 3.5 158 8.5AA

322 363 72715750CA -999 CA

331 -999 303 3.5 274 8.5AA

332 -999 CA

192 81111340CA

281 76211590CA

419 81710830AA

383 98511510AA

279 83611690AA

417 77114080CA

356 91011740AA

419103811150AA

316 82511460AA

3871061Í1350CA

226 81012990CB*TEST

305 69013430CA*TEST

427 78012580CA TEST

TEST

419 88015120CA TEST

*TEST

327 77414600AA TEST

*TEST

451 71616080CA*TEST

374 86613430AA TEST

TEST

431 97713360CA TEST

TEST

347 75014320CA TEST

TEST

406 97014150CA TEST

TEST

Figure 8.—Continued
outputs for individual trees or tree-segments may also be

obtained.) The sections are activated by job options

(coded on control card no. 2) that enable the user to

terminate processing according to the availability of input

data, or to achieve partial STX objectives. Printed reports

include the following :

(1) Preliminary report of counts and aggregate predictions. This always appears as page 1 of the computer

output (p. 78-79 of Appendix A). The report is produced when subroutine STll has been able to complete

its processing of tree cards without encountering a fatal

error. The report can be obtained in advance of dendrometry if desired, once the sample trees have been

selected, if NE is changed to EQ on cards 108 and 111

of STll. The report shows, for each statum and total,

the observed number of trees and aggregate predictions, compares number and aggregate predictions of

observed sample trees with expected values, and shows

the standard errors of expected values. The table enables

the user to check input-totals of number of sample trees

and aggregate predictions and supplies machine-totals for

each stratum (when input includes tree cards for each

tree). The computer-comparison of observed and expected values alert the user to possible irregularities in

field procedures. STll also copies sample tree data onto

tape for later processing.

If STll is unable to complete processing, it flags input

errors by special printouts, as will be explained later, and

it will not print a preliminary report. STX processing

ceases after the preliminary report is produced, unless

the second job option is punched as code 2.

(2) Detailed **log" and tree report. This report, shown

on pages 80-94 of Appendix A, is printed when the second

job option is punched as code 2 and third job option is

punched as code 3, if no fatal flaws have been detected

by STll. The report shows volume, surface area, and

length between consecutively arrayed diameters. It also

55
shows the raw dendrometer readings and computed slant

distance to the top of each tree-segment. Raw SINELV

readings obtained with a FP15 dendrometer are reduced

by 1 before printing because the inclinometer is read as

sine + 1. Those obtained with a modified Zeiss Teletop

are similarly reduced by 100 degrees because the inclinometer is read as degrees + 100. Thus, an FP15 reading of

SINELV of 1.0920 is printed as .0920, and a Teletop reading of 99.7 is printed as —.3000.

A tree summary line is also printed below the detail

shown for tree-segments. If the third job option is

punched as code 2, the printed report will list only this

summary line information for each sample tree, as shown

on pages 104-105 of Appendix B. The summary lines,

read from left to right, include the following information :

— Tree identifying number

— Totals for volume, surface, and length

— Tree d.b.h. in inches

— Frequency represented by the tree

— Prediction (KPI)

— Double-bark thickness in inches (0. or —0 signals

that no bark measurement was recorded)

— Asterisk following bark thickness indicates that the

tree was forked, or that the instrument was moved

two or more times to a new contour

— Trio of figures indicating mode of tree measurement, bark option selected, and option governing

unseen length, the latter signaled by an asterisk if

unseen length actually occurred

— Tree classification

— Value stratum

(3) Summary report for the tree population. This is

shown on pages 95-98 of Appendix A. Summary printouts are furnished by ST33 when the second job option

is punched 2 and no fatal flaws have been detected by

either STll or ST22. Separate summaries are produced

for each stratum as well as for the whole. Sampling error

56
is computed for each stratum. For the combined strata,

sampling error is computed both for volume and for

volume weighted by relative value. The summary lists

expanded estimates of tree frequency, basal area, length,

surface area, and cubic volume, by sampling category. It

also shov^^s input aggregates of predictions, number of

sample trees, and the number of measured tree-segments.

Basal area includes only trees for which d.b.h. was recorded in Columns 17-21 of the tree card.

Sampling error is calculated in terms of the International 1/4 in. log rule, but this unit of measure may easily

be changed to another if desired by repunching BLD

cards 10,11, and 12.

(4) Surmnary report for data processing statistics.

The summary report for the tree population is followed

by a page, always numbered zero, that shows data processing statistics, checks, error counts, and a list of trees

with suspicious input data. These are discussed more fully

later. This summary report occurs on page 99 of

Appendix A.

When program outputs are made free of error, this

summary page can be removed without disturbing the

page sequence of the STX report.

The values shown in the last two lines of the page zero

summary should be checked. Unless the aggregate predictions agree exactly with the sample estimates, all

sample-based estimates must be rejected. Machine error,

failure to draw at least one sample from a nonempty

stratum, or the occurrence of some fatal flaw flagged by

a diagnostic message is usually responsible when this

check indicates a faulty estimate.

(5) Grade-yield and realization reports. If the second

and fifth job options are punched 2 or greater, subroutine

PREP and SORT rearray tree and tree-segment data, and

subroutine PROD will print class subtotals or complete

tree-segment data. Subtotals are printed, as shown on

page 100 of Appendix A, if code 2 is punched as the fifth

job option, and tree-segment data, as shown on pages

57
44-45 of PSW-13,11 ^YQ printed if code 3 is punched as

the fifth job option. Present versions of ST44 and supporting subroutines can subtotal up to 99 tree and treesegment classes.

If the sixth job option is punched (1 through 9), as will

be explained more fully later, ST44 also will convert the

class subtotals of volume, surface, and length into other

units of volume and value and print the results in a table

as shown on page 101 of Appendix A. Present versions of

ST44 can convert up to nine species with 11 tree-segment

classes into six end-products. The sixth job option must

be punched with the number of tree classes recognized

in the class subtotals, and the program must be modified

by data statements (explained later) that introduce appropriate conversion coeflScients.

The last line of the second grade-yield and realization

report (page 101 of Appendix A) shows "volume (cu. ft.

i.b.) paired with yield coefliicients." The volume shown

here must agree with that of the first grade-yield and

realization report (page 100 of Appendix A). Disagreement indicates that some volume was not matched with

conversion coefficients and has been omitted from product

yield and value.

(6) Card outputs. The program supplies card outputs

showing tree detail if code 2 is punched as the fourth job

option and supplies cards showing tree-segment detail if

code 3 is punched as the fourth job option. Facsimiles of

tree and log card outputs are shown on pages 40-45 of

PSW-13.11

Diagnostics and errors

The STX program prints out diagnostic or error messages at three stages of processing :

(1) A message is printed, as shown by figure 9, if an

" L. R. Grosenbaugh. STX-Fortran-4 program for estimates of

tree populations from 3P sample-tree measurements. U.S. Forest

Service Research Paper PSW-13. Pacific Southwest Forest and

Range Experiment Station, 1967.

58
F G H

0 TEST 13 64 9 = 12

A O unless special error recoveiy procedure E

is available F

B Brief job identifier G

C Tree number stored most recently H

D Card number within tree i

Prediction for tree

Value stratum

Sampling class (=, *, )

Terminal symbol (,+,*)

Previous tree number

Figure 9.—Information printout for error encountered by subroutine STll.

en
error is encountered by STll in processing data. No output reports will be produced if an error is detected by

STll. The message signals the following errors:

— A within-tree card sequence number that is negative

— A negative stratum number or one exceeding the

number of strata specified on the job control card

— A sample-tree prediction that is blank, zero, negative, or larger than the maximum (L) specified on

the job control card

The locations in the printed message (fig. 9) from left

to right include : — Ordinarily contain zero

— Four-character job identifier

— Current tree number

— Within-tree card sequence number

— Prediction for tree

— Sampling category

— Terminal symbol

(Sampling category symbols include —, *, or blank

to imply, respectively, sure samples, 3P samples,

and nonsamples. Terminal symbols include *, +, or

blank to imply, respectively, last card of a given

tree, last card prior to forking or establishment of

a new reference elevation, and a nonterminal card

continued normally on a following card.)

— Tree namber read previous to the one that is currently stored. If current and previous tree numbers

are the ^ame, it is likely that both represent the

previous number, and that the tree card for the

current tree contains an illegal character or reflects

some system irregularity.

(2) If STll encounters no errors and if a 2 or larger

number has been punched as the second job option on

the second control card, processing of individual trees

by ST22 is started. A different error message is printed

if certain errors are encountered by ST22, as shown by

figure 10. The first location in the message is a numerical

code for the particular error, the next is the tree num60
BCD

ERROR 4 TREE NUMBER l3 2 12

I.

A

B

Error code

Tree number

C Card number within tree

D Previous tree number

Figure 10.—Error message printed for errors encountered by

subroutine ST22.

ber, then within-tree dendrometer card sequence number,

and last the number of the tree previously processed.

Error codes in ST22 are as follows :

1. Implies negative diameter arising from faulty unseen length projection.

2. Implies machine error in failing to branch properly on +, *, or blank or failure to copy these correctly from input tape.

3. Implies negative length due to faulty dendrometry (progressing from top to stump, etc.),

faulty punching, or faulty unseen length projection. Dov^nward progression must be repunched

in upward progression.

4. Implies disarranged data deck or faulty punching.

Failure to punch terminal asterisk can cause this,

as can variation in tree number (caused by faulty

punching) during single within-tree card sequence.

The most common cause is failure of within-tree

card sequence to be in arithmetic progression with

unit interval starting with zero.

61
5. Implies earlier machine error (in STll) to detect

faulty data with stratum number larger than

maximum specified on second control card.

6. Implies machine error in failing to branch properly on sure-to-be-measured tree or in earlier failing

to detect faulty data with sample tree having

blank, zero, or negative prediction larger than

value specified as K.

7. Implies inadequate number of measured diameters

for computations (must be at least four when

Column 25 of the tree card is punched 0 or 1, at

least one if Column 25 is punched with code 2, and

at least two without any projection at all).

(3) After printing any of these seven error messages,

ST22 will continue to process and print individual tree

data. Further summarization or processing is suppressed

(after 25 error messages or misarrayed cards), but ST33

produces a summary printout for data processing statistics, page number of which is always zero. This printout,

page zero shown on page 99 of Appendix A, contains two

messages, one showing the number of input flaws that

blocked processing and a second identifying, by tree number, sample trees containing suspicious data. Input data

and outputs for these trees should be closely examined.

Reasons for suspicion are lack of recorded d.b.h. (the

program uses the second set of dendrometer measurements as a substitute but omits the tree from summaries

of basal area), a population frequency of one or less for

a 3P sample tree (no sample drawn without replacement

can represent less than itself; a tree with F—1 should

be a sure-to-be-measured tree), or an upper d.o.b. more

than one-half in. larger than its next lower d.o.b.

The amounts of input and processing done before encountering fatal flaws are helpful in verifying that the

same number of tree cards were read by STll and ST22

and that later processing was completed for all measured

trees.

A check may also be made on page zero of the summary

62
of the actual number of trees in the population (aggregate number of trees input) compared with the number

estimated from the sample. A difference of more than

three times the standard error of estimated number indicates that there may be errors in procedure, recording, or

transcription.

Function of value strata compared with tree class

To a limited extent, some of the same information can

be obtained for tree classes as for value strata, tending to

confuse the distinction between these two means of dividing a population. The important thing to remember is

that sample ''blow-up" and error calculations are kept

separate by value strata, whereas tree class is used to

allow separate tabulations of volume, surface area, and

length for conversion to estimates of product outturn or

realization values.

Value strata. If trees are not placed in value strata, i.e.,

Column 10 of the tree card is blank, the program infers

that only one stratum exists. Tree frequency (the ''blowup" factor) and sampling error are computed separately

by strata if strata are coded, otherwise these computations are based on a single stratum. Sampling error is set

as zero unless at least two sample trees are drawn from

a stratum.

Tree cla^s. Just as trees can be separated into value

strata without designating tree class, trees may be separated into tree classes without designating stratum. By

exercising the fifth job option, subtotals of volume, surface area, and length can be produced for each tree class,

as shown on page 100 of Appendix A. The totals for all

tree classes must agree with the totals shown for all

strata i.e., the totals shown on page 100 of Appendix A

must agree with those on pages 97-98. The subtotals

listed on page 100 may then be converted to other product

estimates as shown on page 101 of Appendix A.

Trees are normally not coded by strata unless they

differ in relative value because estimates of sampling

63
error are usually desired only for the totals. There are

other situations, however, in which sampling error by

strata may be of interest. For example, trees may be

coded by strata to indicate stocking within stands classified according to type, age class, pay unit, etc. Similarly,

if more than one estimator made predictions for the tree

tally, each man's work can be identified as a stratum to

facilitate checks of performance. In any case, the summary reports account for the stocking in each stratum

and show the sampling error.

When estimates of sampling error are not required,

tree class may be used to obtain the same summaries with

two added advantages: (1) subtotals for up to 99 tree

classes can be obtained if quality-defect class is left

blank, compared with a program capacity of only nine

strata, and (2) estimates for tree classes can be converted to products and values by exercising the sixth job

option if appropriate conversion coeflîcients are put into

the program.

PROGRAM COMPUTATIONS

When a Barr and Stroud dendrometer is used to obtain

sample tree measurements, the computer converts readings of T GRADS to distance in ft. and those of T GRADS

with F GRADS to diameter in inches. Theory and equations

used are discussed by Grosenbaugh in Forest Science

Monograph No. 4.^^

Heights above and below horizontal are calculated by

multiplying slant distance by the sine of the vertical

angle. Length of a tree segment is determined by subtracting height to the bottom of a segment from height to the

top of the segment.

Cubic volume and surface areas are calculated on the

assumption that each tree segment is a conic frustrum.

^ L. R. Grosenbaugh. Optical dendrometers for out-of-reach

diameters : a conspectus and some new theory. Forest Science Monograph 4, 1963.

64
Diameters are reduced for bark thickness by multiplying outside-bark diameter by a ratio of d.i.b./d.o.b. If

bark is measured at breast height, this ratio is d.b.h.i.b./

d.b.h.o.b., modified as directed by the option punched in

Column 24 of the tree card.

Assuming d.o.b. is 10.0 in., and d.b.h.i.b./d.b.h.o.b. is

20.0/22.0, d.i.b. is computed as follows:

Code 0 or 1

d.i.b./d.o.b. ^'^'^•^'^'

d.b.h.o.b.

= 10.0 X 20.0 =: 9.1 in.

22.0

Code 2

d.i.b. = d.o.b. X (1.0 - (l.O-d.b.h.i.b./d.b.h.o.b.)

(QUAN/(DEMO = d.o.b./d.b.h.o.b.) ) )

= 10.0 X (1.0 - (1.0 - .909) (1/(2.0-10.0

/22.0)))

= 10.0x (1.0— (.091) (1/1.545))

z= 10.0 x (1.0 - .0589) = 9.4 in.

Codes

d.i.b. zu d.o.b. X (d.b.h.i.b./d.b.h.o.b.) (QUAN/

(DENO - d.o.b./d.b.h.o.b.))

= 10.0 X (.9096) (9/(10.0 - 10.0/22.0))

= 10.0x (.9096) (.94285)

= 8.6 in.

If bark is not measured, d.i.b./d.o.b. at any point on the

stem is assumed to be .90, a value that is easily changed

in the program. If a negative bark thickness is recorded,

no reduction for bark will be made, allowing computations

of volume including bark or excluding bark, when diameters have been measured i.b. as on felled trees.

Tree frequency is computed separately for trees in each

stratum, or for all trees combined if they are not classified

by stratum, as follows :

F — ^^^ ^^^ ^^^ trees (less sure KPI)

~~ No. of samples multiplied by KPI

65
Thus, tree no. 1, shown on pages 80-81 of Appendix A

to have a prediction of 84 in stratum 2, has a frequency of

6663/(18 X 84) = 4.407. The sum of the predictions

(6663) and the number of 3P samples (18) are shown

by the stratum 2 summary report on page 96 of

Appendix A.

Field calculations

Rapid field checks of diameters, distances, and heights

measured with Barr and Stroud dendrometers can be obtained by use of scales designed for this purpose.^^ A

calculator is made by pasting the scales, available from

the Southern Forest Experiment Station, to the rails and

center bar of a double-face slide rule. The C and D scales

of the slide rule are not covered and remain available for

use in multiplication and division.

Appendix D shows the sine, cosine, and tangent equivalents of angles, by degrees and tenths, that may be used

in trigonometric solutions for unknowns, such as the

following :

(a) To determine height above or below horizontal:

Multiply slant distance by sine of vertical angle or

multiply horizontal distance by the tangent.

(b) To determine horizontal distance: Multiply slant

distance by the cosine.

(c) To set off height intercepts of equal length: Find

the diflference in tangents of vertical angles to

stump and top of desired segment-length. Add the

amount of this tangent difference successively for

each height increment. Preset the clinometer for

the corresponding angles. For Barr and Stroud

dendrometers, convert each tangent to the sine

equivalent before setting the clinometer.

^^ C. Mesavage. Revised calculator for Barr and Stroud dendrometers. U.S. Forest Service Research Note SO-84. Southern Forest

E icperiment Station, 1968.

66
CONVERSION COEFFICIENTS

General procedure for obtaining and applying conversion

coefficients

Coefficients used to convert volume, surface area, and

length to product outturn and value are derived from

vv^hole-tree data by fitting multivariate regressions. Once

the data are available, the coefficients are easily obtained

by a computer program called REX.^^ Data for the regressions are collected from mill-scale studies in a marketing zone for each species-group or tree class to be

converted. Separate studies are not required for each

STX sale. The general procedure is not unlike that nov^

used in mill-scale studies, but there are some differences,

as follows :

(1) Trees selected for the studies should contain the

entire range of quality-defect classes that normally occur

for the tree class. At least 34 sample trees must be input

if the range includes all 11 grade-defect classes. These

selected trees must be v^eighted for REX by the reciprocal

of the dendrometered utilizable volume for each tree. If

they are drawn by a 3P subsample the weights in REX

are the frequency represented by each tree.

(2) Each tree is dendrometered, or felled and measured, using the procedure previously explained for measuring sample trees. In filling out the STX tally sheet.

Columns 6-9 are left blank if no prediction is required and Column 10 is left blank because all trees are

in one stratum. Tree number must be shown, and Column

11 must show = as the sampling category. The remainder

of the tally sheet is recorded as required to show the tree

and stem measurements that are made and the gradedefect class of each tree segment. The entry for CLASS (in

Columns 12-15) depends on how STX processing is to be

" L. R. Grosenbaugh. REX-Fortran-4 system for combinatorial

screening or conventional analysis of multivariate regressions. U.S.

Forest Service Research Paper PSW-44. Pacific Southwest Forest

and Range Experiment Station, 1967.

67
organized : The object of STX processing is to ascertain

volume, surface area, and length, summarized for each

tree by grade-defect class, that will be used as input data

for the regression analysis. If CLASS is left blank, or

used merely to label the group of trees, job options 123000

(in Columns 66-71 of the second control card) will produce a report showing log and tree detail, as illustrated

on pages 80-94 of Appendix A. Volume surface area and

length may then be hand summarized to show totals by

grade-defect class for each tree.

An alternative way that will eliminate hand summarization is to group the trees into lots of nine, the first containing trees 1-9, the second, trees 10-18, etc. CLASS is

then coded so that the first column (Column 12) is numbered from 1 to 9 in each lot. The lots are stacked so that

separate STX reports will be produced for each lot by the

same machine run. If the job options are coded 123020,

the report for each lot will show, in addition to the log

and tree report, a tabulation (see page 100 of Appendix

A) of volume, surface area, and length summarized for

each tree by grade-defect class.

(3) The sample trees are milled into products. Every

log and bolt should be labeled so that total yield and value

of each product may be ascertained separately for each

tree. These whole-tree totals of yields and values are then

related to dendrometered quantities by grade defect class

of volume, surface area, and length to the actual utilized

top. Should "jump butting" be a common practice, then a

further adjustment can be made to reflect the beginning

point of basal utilization. Since there are 11 grade-defect

classes, the regression will be based on 33 independent

variables. Zeros are entered as quantities for volume, surface area, and length in grade-defect classes that are not

present in a given tree. The actual conversion coefficients

are processed by the REX program. (The mechanics of the

REX program are beyond the scope of this handbook.)

(4) The conversion coeflScients are assembled in matrices, one for each CLASS to be processed by the STX

68
program, by appropriate data statements that are put into

subroutine ST44 of the STX program and by alterations

of format cards in subroutine PROD. Figure 11 shows

the cards in PROD and ST44 that were altered to obtain

the STX output shown on page 101 of Appendix A. Up to

six end-products can be accommodated by each matrix

of coefficients.

When more than six end-products are required, the

data must be run again with a new set of coefficients.

Appendix B illustrates a rerun of the same data used for

Appendix A except that conversion coefficients were inserted for a new set of end-products. The job options

specified on the second control card were coded as 222022.

Since the third job option was made 2 instead of 3, the

log and tree report (pages 104-105 of Appendix B) shows

only the summary lines for each sample tree. The matrices inserted to obtain the conversions to a new set of

end-products are shown as figure 12.

Labels used for the ST44 matrices must correspond

with codes used for CLASS and GR on the tally sheet and be

entered in appropriate collating sequence. Thus, the

matrix for HIVA precedes that for LOVA. Note also (on

cards 26-27 and 68-69 of figures 11 and 12) that the

second element of the matrix name or matrix subscript

is changed to ascend numerically, thus, for HIVA it is 1,

for LOVA it is 2, etc.

Each card for the matrix contains data statements for

two sets of coefficients. Thus, card 28 corresponds with

the format to show that coefficients for converting GR AA

to rough log weight are 41.41222 cu. ft. volume + 5.542556

sq. ft. + 0 and for converting GR AA to chipweight are

16.75876 cu. ft. - 8.526190 sq. ft. + 19.34555 ft. Similarly, card 29 shows log volume as 1.0 cu. ft. + 0 sq. ft. +

0 ft. and log surface as 0 cu. ft. + 1.0 sq. ft. + 0 ft. Card

30 shows log length as 0 cu. ft. + 0 sq. ft. + 1.0 ft. and

Doyle scale (without bark) as 6.920394 cu. ft. - .6664733

sq. ft. + 0 ft. Subsequent cards show sets of coefficients

for GR AB, ascending alphabetically to XX.

69
o

®NW FOR#* p^QTf

70FORMAT ( IHl f 16A4r IXf A^^t 2Xf t+HPAGEf I^I/lXf 3A<+f

iFô.Of I5flXfI9rlXrIÓ /23X#3¿^HGRADE-YiELD AND

aiOXf 13HR0UGH LOG WT. #2Xa2HlNC . WT.CHlPSf i^X»

3 SURFACEf3X#lUHL0G LENGTH»2X»13HD0YLE(N0 BK

i+OHGREEN LBS.) r 5Xr 9HCU.FT. IB. r 5Xr 9HSQ.FT. IB.

5HNET BD.FT./lXr92(lH=))

@NW FORr* bT4i|

-26*109

DATA LC( If D/i+HHlVA/

ODATA LC( 2r 1)/2HAA/rPIAA/

1 i*1.4i222f+b.b42556» O.r l6.75876#-8.

2 l.ür3*0.r+l.üf 0.0»

3 2*0.fl.0f 6.920394t-.666^733» 0./

OüATA LC( 21f 1)/2HAB/#P1AB/

1 69.3í+íl0bf-2.22í+93í+r O.r 8.0629í*3»-í+.

2 l.ü»3*0. »-fl.üf O.Or

3 2*0,rl.0t 5.ü62638f-.5987217r 0./

ODATA LC( 40r 1)/2HAC/rPIAC/

1 69.3if'+u6t-2.22í*93ífr O.r 8. 0629'f3f-if.

2 1.0r3*0.»-l-l.ür O.Or

3 2*ü.rl.0r 5.062638»-.5987217r 0./

X)DATA LC( 59t 1 )/2HBA/f PIBA/

F7.3rF11.8»2F8.í+f I3r COí+6

REALIZATION REPORT/ C046

lOHLOG VOLUME»3XrllHL0GC0i+6

.)/lXf8HCLAS GR r2(t|XflC046

rifXf lOHLINEAL FT. » ifXr 10C0i|6

COi+6

526190» 19.34555»

176948» 19-34555»

176948» 19.34555»

ST44

ST44

ST44

ST44

ST44

5T44

5T44

5T44

5T44

ST44

ST44

5T44

5T44

ST44

30

31

32

33

34

34A

26

27

28

29

30

31

32

33

34

35

36

37

38

39
1 66.85595r-.1718965» 0.

2 l.üf3*0.f+l.Ü# O.Or

3 2*0.ri.Or 9.770582r-l.573353

ODATA LC( 78» 1)/2HBB/fPIBB/

1 10ü.8519r-2.838336» 0.

2 l.ü»3*Ü.f+1.0f 0.0»

3 2*0.»l.ü» 7.Ü20523»-.7513185

ODATA LC( 97» 1)/2HBC/»P1BC/

1 100.8519»-2.838336» 0.

2 1.0f3*0.»-»-1.0» 0.0»

3 2*0.»1.0» 7.Ü20523»-.7513185

OüATA LC(116» 1)/2HCA/»P1CA/

1 62.41123» .6513177» 0.

2 .8753891» 3*0.»+.8516752

3 2*0.» .8331825» 8.101181

ODATA LC(135» 1)/2HCB/»P1CB/

1 82.15363»-3.376700» 0.

2 .8755393» 3*0.»+.8599118

3 2*0.» .8118821» 7.676051

ODATA LC(151» 1)/2HCC/»P1CC/

1 82.15383»-3.376700» 0.

2 .8755393» 3*0.»+.8599118

3 2*0.» .8118821» 7.676051

16.75876»-8.526190» 19.31555» 5T11 10

5T11 11

0./ 5T11 12

ST11 13

8.062913»-1.176918» 19.31555» 5T11 11

ST11 15

0./ ST11 16

5T11 17

8.062913»-1.176918» 19.31555» 5T11 18

ST11 19

0./ ST11 50

ST11 51

11.67011»-7.287123» 16.11837» 5T11 52

0.» ST11 53

-1.111157» 0./ ST11 51

5T11 55

7.059123»-3.591807» 16.31171» ST11 56

0.» ST11 57

-.9321310» 0./ ST11 58

ST11 59

7.059123»-3.591807» 16.31171» 5T11 60

0.» ST11 61

-.9321310» 0./ ST11 62

Figure 11.—Data statements inserted in subroutines PROD and ST44 for conversion to end products

(first stack).
to

DATA LC(173r

DATA LC(192r

DATA LC( If

ODATA LC( 2r

1 m.i|1222#+5

2 l.OrS^O.r-fl

3 2*0.fl.Üf 6

ODATA LC( Zip

1 69.3^'4.06r-2

2 1.0r3*Ü.f+l

3 2*0.fl.0r 5

ODATA LC( tfOr

1 69.34i|06r-2

2 1.0r3*Ü.f+l

3 2*0.rl.Üf 5

ODATA LC( 59f

1 O6.ö5595f-.

2 l.üf3*0w+l

3 2*0.fl.ûr 9

ODATA LC( 7öf

1 100.8519^-2

1)/2HUU/1 P1UU/18*0./

l)/2HXX/fPlXX/18*0./

2)/i|HLÛVA/

2)/2HAA/fP2AA/

.bi*2556r 0.

•Or O.Or

.92039i+f-.666*1733

2)/2HAB/»P2AB/

.22493iff 0.

.Or O.Or

.Ü62636f-.5987217

2)/2HAC/rP2AC/

.22i+934f 0.

•Or O^Or

•062638r-.5987217

2)/2HBA/rP2BA/

I748965r 0.

.Or O.Or

.770582r-1^573353

2)/2HBB/rP2BB/

.838336r 0.

I6.75876r-8.526190r 19.3^555r

0./

8.0ó29í+3r-i|.1769i*8r 19.3it555r

0./

8.0629^3r-i+.l769if8r 19.3if555r

0./

I6.75876r-8.526190r 19.3^555»

0./

8.0629í|3r-if.l769¿l8r 19.3íf555r

STífil 63

5Tí|í| 67

5Tí|í^ 68

STí+M- 69

5T4ÍI 70

STifi* 71

STí+í* 72

5T¿fí| 73

STí+íl 7íf

ST4Í+ 75

STíf^V 76

5Tí+if 77

5Ti|if 78

5T4if 79

STí^¿f 80

STifíf 81

STí^í^ 82

ST4tf 83

5T¿í^ 8íf

5Ti|t^ 85

5TÍ+4 86
2 1.0r3*0.f+l

3 2*ü.rl.0f 7

ODATA LC( 97r

1 10ü.8519r-a

2 1.0r3*ü.f+i

3 2*0.ri.Of 7

OuATA LC(116r

1 b¿.mí*23# .1

2 .8753894f

3 2*0.f .

OüATA LC(135»

1 ô2.if53b3f-3

2 .8755393t

3 2*0.r .

ODATA LCdS^r

1 82.i*5383r-3

2 .8755393^

3 2*0.# .

CATA LC(173t

DATA LC(i92r

.Or 0*0f ST^t+ 87

.020523r-.7513185t 0./ STtfif 88

2)/2HBC/rP2BC/ STífíf 89

.838336» O.f 8.0629^+31-if. 1769íf8t 19. 3i+555t STí+if 90

.Or 0*0t STí|í+ 91

.020523t-.7513185t 0./ STí4^ 92

2)/2HCA/tP2CA/ STíftf 93

6513if77t O.t i4.670í+íft-7.287123t 16.11837t STí+íf 9^

3*0.t + .85tf6752t O.t STifíf 95

8331825t 8.10118í+t-l.lim57t 0./ STíftf 96

2)/2HCB/tP2CB/ STtfíf 97

..376700t O.t 7.059if23t-3<»591807t 16..3tfif71t STífí* 98

3*0.t+.8599118t O.t STílif 99

8^if8821t 7.676051t-.932if310t 0./ ST¿fí+ 100

2)/2HCC/tP2CC/ ST^íl 101

1.376700t O.t 7.059i+23t-3..591807t 16..3^if71t STifU 102

3*0.t+.8599118t O.t STifí+ 103

8'+^8821t 7.676051t-.932¿f310t 0./ STtfíf 104

2)/2HUÜ/tP2üU/la*0./ STí+if 105

2)/2HXX/tP2XX/18*0./ 5T4f4 109

Figure 11.—Continued

09
12

®NW FORp* PROD

70FORMAT ( lHl^l6A4r IXr A^+f 2Xf ¿fHPAGE» I^f/lXr 3Aif #F7.3f Fll .8t2F8.i+r 13»

lF8.0fI5flX»I9»lXrI6 /23Xr3^HGRADE-YIELD AND REALIZATION REPORT/

2mXr8HSCRIBNERf3X>i2HlNT, l/¿f IN. r2Xr 12HLUMBER TALLY»3X» IIHLBR.

30.B.#2Xfl2HADD.WT.CHIPS#2X»12HCHlPS F.O.B./lXf8HCLAS GR f3(i+Xrl

^ET BD.FT.)#2Xtl2HD0LLAR VALUEf2X> 12H0VENDRY LBS.#2Xf12HD0LLAR

5UE/iXr92(lH=))

@NW FORf* STW

-26»109

DATA LC( Ir D/ifHHiVA/

ODATA LC( 2t 1)/2HAA/fPIAA/

1 5.6825ô7f + .03951<+2f O.r

2 7.453517f-.3888483r O.r

3 8.íl25655f-íf.375114» 9.460729»

ODATA LC( 21» 1)/2HAB/»P1AB/

1 4.856914»-.2Ü71593» 0.» 5.377562»-.2922441»

2 15.12255»-3.185063» 0.»12.198771»-3.504285»

3 3.475934»-l.957713» 9.460729» .0234248»-.0131933»

ODATA LC( 40» 1)/2HAC/»P1AC/

1 4.856914»-.2071593» 0.» 5.377562»-.2922441»

2 15.12255»-3.185063» 0.»12.198771»-3.504285»

3 3.475934»-l.957713» 9.460729» .0234248»-.0131933»

ODATA LC( 59» 1)/2HBA/»P1BA/

5.561980»+.2654460»

3.149913»-.3917946»

.0567816»-.0294845»

0.»

0.»

.0637571/

0.»

0.»

.0637571/

0.»

0.»

.0637571/

C046 30

C046 31

F.C046 32

0HNCÖ46 33

VALC046 34

C046 34A

ST44 26

ST44 27

ST44 28

ST44 29

ST44 30

ST44 31

ST44 32

ST44 33

ST44 34

5T44 35

ST44 36

ST44 37

ST44 38

ST44 39
1 9.39'f626r-l,ü9003«ff 0.

2 7.107180r-.«17826> 0.

3 8.íf25655#-*4.375114r 9.tf60729

ODATA LC( 78f 1)/2HBB/»P1BB/

1 7.73i|8«+8#--5313729r 0.

2 9.313595t-1.356if07t 0.

3 3.f75934r-1.957713# 9.tf60729

ODATA LC( 97t l)/2HBC/tPlBC/

1 7.73i*848»-.5313729f 0.

2 9.313595f-1.356if07# 0.

3 3.f7593**f-l.957713» 9,^60729

ODATA LC(116r 1)/2HCA/*P1CA/

1 8.019529»-.7753361» 0,

2 5.690870»-.2*^10233» 0.

3 7.375729»-3.739302» 7.88251«*

ODATA LC(135» 1)/2HCB/»P1CB/

1 8.29Í+018»-.7891706» 0.

2 8.135322»-1.012106» 0.

3 3.043317»-!.683if61» 7.993200

ODATA LC(15if» 1)/2HCC/»P1CC/

1 8.294018»-.7891706» 0.

2 8.135322»-1.012106» 0.

3 3.043317»-1.683461» 7.993200

» 9.777942» -1.027430» 0.» 5T44 40

»1.5488091» -.0874188» 0.» ST44 41

» .0567816» -.0294845» .0637571/ ST44

ST44

42

43

» 7.061453» -.2500347» 0.» ST44 44

» .3011685» *".0817320» 0.» ST44 45

» .0234248» -.0131933» .0637571/ ST44

5T44

46

47

» 7.061453» -.2500347» 0.» ST44 48

» .3011685» +.0817320» 0.» 5T44 49

» .0234248» -.0131933» .0637571/ ST44

ST44

50

51

» 7.921466» -.5774056» 0.» ST44 52

»1.1640645» -.0103419» 0.» 5T44 53

» .0497060» -.0251996» .0531213/ ST44

ST44

54

55

» 8.186456» -.5942404» 0.» ST44 56

»2.21096101 -.2854149» 0.» ST44 57

» .02050931 -.0113451» .0538672/ 5T44

ST44

58

59

» 8.1864561-.5942404» 0.» ST44 60

»2.21096101-.2854149» 0.» ST44 61

» .0205093 r-.0113451» .0538672/ 5T44 62

Figure 12.—Data Statements inserted in subroutines PROD and ST44 for conversion to end products

(second stack)
Ci

DATA LC(173r

DATA LC(192#

DATA LC( Ir

ODATA LC( 2r

1 5.682587f»-.

2 7.453517r-.

3 8«425655r-^

OuATA LC( 21»

1 i*.85691<+r-.

2 15.12255f-3

3 3.if75934r-l

ODATA LC( if Or

1 4.856914»-.

2 15.12255»-3

3 3.475934f-l

ODATA LC( 59»

1 9.394628r-l

2 7.107180»-.

3 8.425655»-4

ODATA LC( 78»

1)/2HUU/»P1UU/18*

1)/2HXX/»P1XX/18*

2)/4HL0VA/

2)/2HAA/»P2AA/

0395142» 0.

3888483» 0.

.375114» 9.460729

2)/2HAB/»P2AB/

2071593» 0.

.165063» 0.

.957713» 9.460729

2)/2HAC/»P2AC/

2071593» 0.

.185063» 0.

.957713» 9.460729

2)/2HBA/»P2BA/

.090034» 0.

4317826» 0.

.375114» 9.460729

2)/2HBB/»P2BB/

0./

0./

5.561980»

1.049971»-

.0567816»-

5.377562»-

4.066257»-

.0234248»-

5.377562»-

4.066257»-

.0234248»-

9.777942»-

.5162697»-

.0567816»-

+.2654460»

-.1305982»

-.0294845»

-.2922441»

-1.168095»

-.0131933»

-.2922441»

-1.168095»

-.0131933»

-1.027430»

-.0291396»

-.0294845»

0.»

0.»

.0637571/

0.»

0.»

.0637571/

0.»

0.»

.0637571/

0.»

0.»

.0637571/

5T44 63

5T44 67

ST44 68

5T44 69

5T44 70

ST44 71

5T44 72

ST44 73

5T44 74

ST44 75

ST4U 76

ST44 77

ST44 78

5T44 79

ST44 80

ST44 81

ST44 82

ST44 83

ST44 84

ST44 85
1 7«73i^84Ôr-.5313729f O.r 7.061«f53r-.25003í*7» O.r

2 9.313595»-!.356if07t O.r . 1003895r + .0272<l40# O.t

3 3.^7593«*»-1.957713f 9.^60729# .023tf2^8»-.0131933f .0637571/

ODATA LC( 97f 2)/2HBC/rP2BC/

1 7.73i*8ifôt-.5313729» O.r 7.061í*53r-.25003íf7t 0.»

2 9.313595f-1.356íf07f O.r . 1003895r + .0272íf^0f O.r

3 3.*f7593t*r-1.957713r 9.if60729r .023íf2í*8r-.0131933r .0637571/

ODATA LC(116r 2)/2HCA/rP2CA/

1 8.019529r-.7753361r O.r 7.92m66r-.577<*056r O.r

2 5.690870r-.2<»10233r O.r .3880215r-.003i***73r O.r

3 7.375729r-3.739302r 7.88251ifr .Oi*97060r-.0251996r .0531213/

ODATA LC(135r 2)/2HCB/rP2CB/

1 8.29if018r-.7891706r O.r 8.186U56r-.5942í*0í*r O.r

2 8.135322r-l.ül2106r O.r .7369870r-.0951383r O.t

3 3.üi*3317r-1.683**61r 7.993200r .0205093r-.0113if51r .0538672/

ODATA LC(15i*r 2)/2HCC/r P2CC/

1 8.29<f018r-.7891706r O.r 8.186í*56r-.59W*0ífr O.r

2 8.135322r-1.012106r O.r .7369870r-.0951383r O.r

3 3.0ít3317r-1.683í^61r 7.993200r .0205093r-.0113451r .0538672/

DATA LC(173r 2)/2HUU/rP2UU/18*0./

DATA LCC192r 2)/2HXX/rP2XX/18*0./

STt^tf

STífí*

5Tif4

5Tt|tf

ST^if

STífíl

STifí*

STí*i*

5Tí|íf

STtfí+

ST^í*

STt*íf

STifí*

STí^í*

STt*4 100

STífí+ 101

5T4íf 102

ST^í* 103

ST^í* 10«+

ST4i* 105

STí*íf 109

86

87

88

89

90

91

92

93

9**

95

96

97

98

99

Figure 12.—Continued

-5
00 APPENDIX A.—Computer output—preliminary report, detailed

log and tree report, and summary reports

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 1

CM 03-16-70 8.000 .0196^673 -1.1905 1.5658 2 660. 120 0 223022

PRELIMINARY REPORT—COUNTS AND AGGREGATE PREDICTIONS

STRATUM 1 TREE COUNTS PREDICTIONS

SURE-TO-BE MEASURED TREES(=1)

THREE-PEE MEASURED TREES(*2)

THREE-PEE PREDICTED TREES( 3)

3

10

221

387

673

797tf

ALL TREES(lí2» 3) 23if 903«^

ALL MEASURED TREES(lf2)

ALL THREE-PEE TREES(2#3)

EXPECTED VALUES FOR (*2)

EXP. VAL. ST. ERRORS (*2)

STRATUM 2

13

231

13.102

3.íf8íf

TREE COUNTS

1060

86i*7

635.570

169.015

PREDICTIONS

SURE-TO-BE MEASURED TREES(=1) 270
THREE-PEE MEASURED TREES(*2)

THREE-PEE PREDICTED TREES( 3)

18

132

1128

5535

ALL TREES(l»2r3) 152 6933

ALL MEASURED TREES(lr2)

ALL THREE-PEE TREES(2f3)

EXPECTED VALUES FOR (*2)

EXP. VAL. ST. ERRORS (*2)

20 1398

150 6663

10.095 571.770

3.038 172.059

TOTALS FOR ALL 2 STRATA TREE COUNTS PREDICTIONS

SURE-TO-BE MEASURED TREES(=1)

THREE-PEE MEASURED TREES(*2)

THREE-PEE PREDICTED TREES( 3)

5

28

353

657

1801

13509

ALL TREES(lr2» 3) 386 15967

ALL MEASURED TREES(lt2)

ALL THREE-PEE TREES(2»3)

EXPECTED VALUES FOR (*2)

EXP. VAL. ST. ERRORS (*2)

33 2if58

381 15310

23.197 1207.3i*l

*f.623 2tfl.l85

CD
00

o

THREE-PEL SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 2

CM 03-16-70 6.000 .01964673 -1.1905 1.5658 2 660 . 120 0 223022

DETAILED LOG AND/OR[ TREE 1REPORT

=:=====-=====z==sz=z========r==:===:======ri:==

TREE/ VOLUME / SURFACE / LENGTH / D-I.B. / LOG/RANGE/

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS FGRADS SINELV

5.0 22.4 7.9 10.7 CA 86.8 48.4 70.7 .5890

16.6 67.6 21.9 10.9 CA 82.2 47.4 71.5 .5250

13.1 46.5 13.1 12.7 AA 73.7 45.1 76.4 .2890

5.0 16.2 4.2 14.3 AA 71.5 44.4 80.5 .1140

5.0 13.6 3.0 15.4 AA 71.2 44.3 83.1 .0560

.0 .0 19.6 71.8 44.5 94.3 .0140

1 44.7 166.2 50.1 17.0=D fF= 4.407f 84 r 1.6 021 HIVA 2

6.6 35.9 15.7 7.2 CA 80.2 46.9 64.6 .6960

6.3 28.9 10.6 10.2 CA 69.1 43.6 72.5 .5800

4.9 21.0 7.2 10.7 BA 63.8 41.5 74.7 .4630

9.1 35.7 11.2 11.5 BA 60.0 39.7 77.6 .3720

10.9 39.7 11.5 13.0 AA 58.1 38.7 82.8 .1920

4.7 15.8 4.2 13.4 AA 56.9 38.0 84.6 -.0060

.0 .0 .0 15.2 57.6 38.4 91.5 -.0790

2 42.5 177.0 60.4 15.8=D >F= 4.936f 75f 2.4 121 HIVA 2

13.1 57.3 20.0 9.6 CA .0 .0 10.3 20.0000

8.0 30.9 9.5 12.2 CA .0 .0 13.2 9.5000
00

13.2 48»1 14.0 12.6 BB .0 .0 13.6 14.0000

16.2 54.5 14.6 13.7 AA .0 .0 14.8 14.6000

10.5 32.if 8.0 14.9 AA .0 .0 16.2 8.0000

6.5 18.0 4.0 16.1 AA .0 .0 17.7 4.0000

.0 .0 .0 18.3 .0 .0 20.5

• 0000

3 67.«* 241.2 70.1 17.7=D fF= 3.739f 99» 1.6 221 HIVA

2

12.<* 41.2 10.9 13.6 CA .0

•0 13.6 10.9000

22.5 67.0 15.9 15.3 CA .0 .0 15.3 15.9000

10.3 29.5 6.7 16.9 CA .0 .0 16.9 6.7000

28.if 77.4 16.8 16.7 AB .0 .0 16.7 16.8000

15.8 39.9 8.0 18.5 AA .0 .0 18.5 8.0000

9.3 21.6 4.0 19.6 AA .0 .0 19.6 4.0000

.0 .0 .0 21.6 .0 .0 21.6 .0000

< 98.8 276.6 62.3 21.0=0 fF= l.OOOf 138# -1.8 211 HIVA

2

6.5 34.6 14.7 7.8 CA 90.8 90.8 8.4 40.9000

12.5 53.2 18.1 10.1 BA 81.0 81.0 11.0 33.5000

16.** 61.8 18.6 12.4 AA 72.7 72.7 13.6 21«5000

8.«f 29.7 8.4 13.0 AA 68.0 68.0 14.4 6.8000

4.6 14.6 3.7 14.0 AA 67.5 67.5 15.6 -.3000

.0 .0 .0 16.5 67.6 67.6 19.0 -3.4000

5 *f8.** 193.9 63.5 15.6=D rF= 34.588f 25r 1.6 321 LOVA

1
00

to

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 3

CM 03-16-70 8.0Ü0 .0196£^673 -1.1905 1.5658 2 660. 120 0 223022

DETAILED LOG AND/OR TREE REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.I.B. / LOG/RANGE/

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS FGRADS SINELV

20.5 ^7.5 6.8 19.4 CB 100.4 50.8 83.5 .5510

30.7 63.2 10.4 21.9 CA 95.9 50.1 88.4 .4850

52.1 99.0 15.0 24.6 BA 90.8 49.2 94.2 .3980

55.9 98.2 13.8 25.9 BB 84.0 47.8 98.9 .2520

39.0 62.6 8.0 28.7 AA 80.6 47.0 105.8 .0920

23.3 34.2 4.0 31.1 AA .0 .0 34.5 6.0000

.0 .0 .0 34.3 .0 -99.9 38.6 4.0000

6 221.5 104.9 59.9 34.5=:D#F= l.OOOf 145t 3.4 121 LOVA 1

• 0000

.5120

.3150

.1090

11.0 23.5 4.0 20.4 AA .0 .0 22.8 8.0000

36.7 141.5 44.5 9.0 CA .0 .0 -99.9

24.7 76.0 18.6 14.8 CA 81.4 47.2 79.4

24.2 68.4 15.3 16.4 CA 73.3 45.0 84.6

15.8 39.8 8.0 17.6 BA 71.2 44.3 87.8
• 0 .0 .0 24.5 .0 -99.9 28.5 4.0000

7 112.*f 349.1 90.4 22.8=D rF= 15.170» 57f 2.4 121*L0VA 1

3.9 14.9 3.5 12.7 CA • 0 .0 -99.9 .0000

13.5 38é2 8.6 15.7 CA 82.7 47.5 80.5 .6730

36.1 90.8 18.2 18.3 CA 80.6 47.0 86.0 • 5840

52.3 117.6 21.1 19.8 CA 70.6 44.1 92.2 .4090

24.4 49.6 8.0 22.8 AC 63.4 41.3 102.7 .1230

14.4 26.9 4.0 24.5 AA .0 .0 27.1 8.0000

.0 .0 .0 26.9 .0 -99.9 30.1 4.0000

8 144.7 338.0 63.3 27.1=D fF= 9.826» 88» 2.6 121*L0VA 1

31.9 93.4 22.0 13.2 CA .0 • 0 -99.9 • 0000

49.1 111.0 20.1 19.2 CB 84.4 47.9 86.7 • 5810

70.0 134.2 20.5 23.1 BA 70.6 44.1 99.4 .4110

34.1 58.6 8.0 26.9 AA 66.5 42.6 110.7 .1280

22.2 33.4 4.0 29-0 AA • 0 .0 32.4 8.0000

.0 .0 .0 34.8 .0 -99.9 40.4 4.0000

9 207.4 430.6 74.5 32.4=0 #F= 7.933r 109» 3.4 122*L0VA 1

00

09
00

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE ¡^

CM 03-16-70 Ô.000 •0196^1673 -1.1905 1.5658 2 660. 120 0 223022

DETAILED LOG AND/OR TREE REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.I.B. / LOG/RANGE/

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS FGRADS SINELV

21.1 63.6 15.3 13.6 CA 111.2 52.6 73.5 .5970

28.0 70.8 11.2 18.0 CB 105.3 51.5 80.9 .5020

21.7 56.2 10.2 20.0 CA 97.8 50.1 85.3 .3950

21.4 52.3 8.9 22.2 BA 101.6 51.1 87.5 .2720

35.5 71.8 11.6 22.5 AA 92.1 19.5 90.8 .2110

31.1 55.9 8.0 21.9 AA 89.2 18.9 96.1 .0890

19.6 31.1 1.0 28.1 AA .0 .0 32.0 8.0000

• 0 .0 .0 31.5 ++ .0 -99.9 36.2 1.0000

10 181.1 101.9 72.3 32.0=:D»F= 1.000 r 121» 3.6 121 LOVA 1

15.8 15.3 10.1 11.6 CA 91.3 19.3 77.1 .6110

35.6 81»3 15.9 18.7 CA 81.9 18.0 85.1 .5350

.0 .0 .0 21.8 78.2 16.1 93.3 .3770

65.7 133.7 21.7 21.9 CA 85.8 18.2 91.0 .3100

.0 • 0 • 0 25.2 78.6 16.5 99.9 .0950

30.9 55.7 8.0 21.9 BA 70.9 11.2 102.9 .1010
20.5 32.1 4.0 28.3 AA .0 .0 31.3 8.0000

• 0 .0 .0 33.0 ++ • 0 -99.9 37.5 4.0000

11 168.5 351.2 60.0 31.3=D fF= 7.933f 109» 3.0*121 LOVA 1

líf.7 «13.0 10.0 15.7 CA • 0 .0 -99.9 • 0000

16.2 42.1 8.8 17.2 CA 76.4 45.9 85.7 .6760

47.if 104.7 18.4 19.6 CA 72.7 44.8 91.7 .5900

53.7 104.8 16.3 23.8 BA 64.5 41.8 104.7 .3790

28.9 53.9 8.0 25.4 BA 60.4 39.9 111.3 .1350

17.5 29.6 4.0 26.1 AA .0 .0 28.9 8.0000

.0 .0 .0 30.5 .0 -99.9 33.8 4.0000

12 178.í+ 378.1 65.5 28.9=D tF= 8.395r 103t 2.8 112*L0VA 1

7.0 29.7 10.1 10.6 CA 81.8 47.3 72.3 .5760

12.0 44.0 12.8 11.9 CA 75.7 45.7 75.6 .4890

19.9 62.4 15.6 14.3 BA 72.4 44.7 81.1 .3340

12.1 34.8 8.0 16.2 AA 67.5 43.0 86.3 .1270

8.7 20.8 4.0 17.0 AA .0 .0 18.8 8.0000

.0 .0 .0 22.7 .0 -99.9 24.3 4.0000

13 59.6 191.7 50.6 18.8=D fF= 26.203f 33» 1.8 131 LOVA i

00
00

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 5

CM 03-16-70 Ö.OÜO .0196^1673 -1.1905 1.5658 2 660. 120 0 223022

DETAILED LOG AND/OR TREE REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.I.B. / LOG/RANGE/

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS FGRADS SINELV

----->-~- iXzizi—z¡r~»^ii' z^z:zz^z:'z:

6.1 26.0 8.9 9.8 CA 82.7 47.5 70.0 • 6340

18.0 62.6 17.5 12.5 CA 77.5 46.2 76.1 .5620

18.2 55.0 13.2 lif.9 CA 68.0 43.2 83.1 .3830

21.7 59.8 13.1 16.9 AA 64.5 41.8 88.8 .1990

7.9 17.2 3.0 18.0 AA 63.4 41.3 91.9 -.0040

.Ü .0 .0 25.9 63.6 41.4 110.5 -.0510

m 72.0 220.8 55.7 21.9=D rF= 1.000» 132» .0 Oil HIVA 2

5.7 27.2 10.3 9.Í+ CA 66.0 42.4 69.8 .6540

12.1 49.7 16.2 10.8 CA 64.0 41.6 73.8 .5130

.0 • 0 .0 12.6 56.1 37.5 80.5 .2960

11.1 46.0 15.1 10.7 CA 63.4 41.3 73.7 .5020

.0 .0 .0 12.5 55.9 37.4 80.2 .2980

8.9 32.if 9.3 12.6 BA 55.9 37.4 80.7 .2970

9.0 30.0 8.0 13.8 AA 53.8 36.0 85.2 .1350
5.5 16.6 4.0 14.6 AA .0 • 0 16.8 8.0000

• 0 .0 .0 16.9 .0 -99.9 19.7 4.0000

15 52.4 201.9 63.0 16.8=0 fF= 5.365^ 69 r 2.0*121 HIVA 2

l.<f lil.l 14.5 .0 XX 79.8 46.8 46.9 • 6300

5.5 32.5 15.3 7.4 CA 65.7 42.3 64.6 .5440

7.0 37.1 15.6 8.9 CA 58.5 38.9 69.4 .3500

í*.3 21.4 8.5 9.3 CA 54.8 36.7 71.1 • 0690

Z.Z 9.6 3.5 9.9 AA .0 .0 11.1 8*5000

.0 .0 .0 11.4 .0 -99.9 13.2 3*5000

16 20.<f 114.8 57.4 11.1=D fF= 17.627r 21 r 1.2 121 HIVA 2

3.9 26.6 19.0 .1 XX .0 -99.9 -99.9 • 7500

13.7 52.1 16.0 10.6 CA 66.2 42.5 72.5 • 6110

20.** 64.5 16.3 14.3 CA 57.8 38.5 84.1 • 4240

12.7 36.8 8.5 16.0 CA 52.4 35.0 91.0 • 1570

6.3 16.7 3.5 17.1 AA .0 • 0 19.0 8^5000

.0 .0 .0 19.2 .0 -99.9 21.6 3^5000

17 57.0

a*• » an «• « "»IM <M

196.7 63.2 19.0=D fF= 26.203f 33f

' • ■■••»« ••ai

.0 121 LOVA 1

00

<1
00

00

THREE-PEE SAMPLE IRLE .viEASüREMENT AND APPRAISAL TEST PAGE 6

CM 03•-16-70 b.{300 .01964673 «1. 1905 1.5658 2 660 • 120 0 223022

DETAILED LOGi AND/OR! TREE 1REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.I.B. / LOG/RANGE/

HO./ CU.FT. / SGl.FT. / FEET / INCHES /CODE/ FEET/ 'TGRADS FGRADS SINELV

1.0 8.9 8.1 .1 XX .0 -99.9 -99.9 .7460

^.0 20.9 8.7 8.3 uu 86.8 48.4 66.2 .7030

9.7 m.5 14.3 10.0 CA 82.7 47.5 69.7 .6320

15.9 56.1 15.7 12.3 CA 72.1 44.6 75.8 .5270

20.5 61.3 14.6 14.9 CA 64.3 41.7 83.9 .3460

m.a 39.0 8.5 17.1 AA 60.6 40.0 91.1 .1260

7.2 17.8 3.5 17.9 AA .0 • 0 20.1 8.5000

.0 .0 .0 21.0 .0 -99.9 24.4 3.5000

18 72.6 245.5 73.5 20.1=:DfF= 3.164 f 117r 2.2 121 HIVA 2

1.2 10.9 11.0 .0 XX 68.8 43.5 43.6 .7380

1.8 10.8 5.2 7.6 uu 63.8 41.5 65.5 .6240

8.1 38.3 14.5 8.1 CA 59.8 39.6 67.2 .5780

16.1 58.1 16.8 12.0 CA 52.0 34.7 80.5 .3850

11.2 34.5 8.5 14.5 CA 48.2 31.4 90.9 .0680

6.0 16.2 3.5 16.5 AA .0 • 0 19.5 8.5000

.0 • 0 .0 19.0 • 0 -99.9 23.5 3.5000
19 4íf.3 168.8 59.5 19.5=D tF= 5.365f 69t 3.0 121 HIVA 2

5.2 28.6 12.5 7.8 CA 59.8 39.6 66.1 .5690

7.6 35.6 13.3 9.8 CA 53.7 35.9 73.1 .4020

5.8 24.9 8.5 10.7 AA 49.7 32.8 77.4 .1670

3.1 11.6 3.5 11.6 AA .0 • 0 13.4 8.5000

.0 .0 .0 13.7 .0 -99.9 16.6 3.5000

20 21.7 100.6 37.7 13.4=0 fF= 12.339f 301 1.8 121 HIVA 2

11.ü 49.4 17.9 8.4 CA 66.5 42.6 67.2 • 6220

15.3 54.8 15.7 12.6 CA 57.1 38.1 80,3 .4100

9.8 32.3 8.5 14.1 CA 53.0 35.4 86.1 .1460

5.2 15.0 3.5 15.0 AA .0 .0 17.0 8.5000

.0 .0 .0 17.8 .0 -99.9 21.1 3.5000

21 ^1.2 151.5 45.6 17.0=D fF= 6.855» 54 f 2.0 121 HIVA 2

6.6 28.8 10.0 10.2 CB .0 .0 -99.9 .0000

1<^.8 55.7 16.7 11.8 CA 57.4 38.3 77.7 .4390

9.0 31.0 8.5 13.7 CA 51.1 34.0 85.5 .1660

4.** 13.9 3.5 14.2 AA • 0 .0 16.0 8.5000

.0 .0 .0 16.1 .0 -99.9 18.6 3.5000

22 34.8 129.4 38.7 16.0=D ^F= 7.258r 51 f 1.8 122*HIVA 2

00
o

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 7

CM 03-16-70 8.000 .01964673 -1.1905 1.5658 2 b60. 120 0 223022

DETAILED LOG AND/OR TREE REPORT

TREE/"VOLUMÍ" / SURFACE / LENGTH / D-I.B. / LOG/RANGE/ ^^r,*r.r. CTK.IT. w

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS^^FGRADS SINELV

-=-= --- - --- --^ ^^ ^^^^ ^^^^ ^^^g .6530

9.3 39.6 13.4 10.6 CB 75.7 45.7 72.0 .5750

18.3 68.6 20.5 12.0 CB 68.3 43.3 76.2 .4410

9.8 32.4 8.5 13.6 AA 63.4 41.3 81.6 .1520

5.6 15.7 3.5 15.5 AA .0 .0 17.7 8.5000

.0 .0 .0 18.7 .0 -99.9 22.6 3.5000

23 48.3 181.5 55.5 17.7=DrF= 8.226r 45» 2.2 121 HIVA 2

4.5

6.5

3.6

.0

20.1

26.2

12.6

.0

7.1

8.5

3.5

.0

10.9 CB

10.8 CA

12.8 AA

14.7

41.5

39.8

.0

.0

22.6

19.2

.0

-99.9

81.0

81.1

15.2

18.4

.2990

.1340

8.5000

3.5000

24 14.6 58.9

«M > «B4OT ^M> a» « ^

19.1 15.2=DfF= 15.424f 24» 2.4 121 HIVA 2
í*.3 22.0 9.0 8.4 CA 47.3 30.5 69.0 .3430

í*.9 22.9 8.5 10.2 CA 45.2 28.1 76.2 .1590

2.6 10.7 3.5 10.4 AA .0 .0 11.8 8.5000

.0 .0 .0 13.0 .0 -99.9 15.8 3.5000

25 ll.d 55.6 21.0 11.8=D fF= 13.710r 27r 1.4 121 HIVA 2

6.Ü 26.3 9.2 10.7 CB 75.7 45.7 72.1 .5400

11.3 45.3 14.5 11.2 CA 71.8 44.5 73.7 .4420

11.4 41.1 11.8 12.6 CA 66.7 42.7 78.0 .2580

10.0 32.6 8.5 13.9 AA 64.7 41.9 81.7 .0830

5.1 15.0 3.5 15.4 AA • 0 .0 17.4 8.5000

.0 .0 .0 17.4 .0 -99.9 20.1 3.5000

26 W.T 160.3 47.5 17.4=D fF= 5.365r 69 r 2.0 121 HIVA 2

15.5 46.5 11.1 14.9 CA 71.2 44.3 81.1 .6220

45.6 118.6 24.5 17.1 CA 64.7 41.9 88.0 .5120

19.5 45.6 8.5 19.9 AA 57.4 38.3 98.5 .1510

10.0 21.0 3.5 21.1 AA .0 • 0 23.1 8.5000

.0 .0 .0 24.6 .0 -99.9 27.6 3.5000

27 90.8 231.7 47.6 23.1=D rF= 16.955r 511 2.0 121 LOVA 1

CO
CO

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 8

CM 03-16-70 8.000 .01964673 -1.1905 1.5658 2 660. 120 0 223022

DETAILED LOG AND/OR TREE REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.I.B. / LOG/RANGE/

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS FGRADS SINELV

5.3 25.7 10.0 9.4 CA .0 .0 -99.9 .0000

^^•9 22.4 8.1 10.2 CA 53.2 35.6 74.5 .5810

10.9 45.7 15.2 10.9 AA 49.6 32.7 77.4 .4fe00

7.7 28.6 8.5 12.1 AA 45.1 27.9 83.6 .1690

4.3 13.8 3.5 13.6 AA .0 .0 15.8 8.5000

•0 .0 .0 16.5 .0 -99.9 20.7 3.5000

28 33.1 136.2 45.3 15.8=DrF= 7.258f 51f 2.2 122*HIVA 2

12.6

1.2

6.0

.0

54.2

4.1

16.3

.0

18.6

1.1

3.5

.0

10.3 CA

12.0 CA

15.9 AA

19.6

73.7

64.3

.0

.0

45.1

41.7

.0

-99.9

71.6

77.1

18.3

24.4

.6080

.4080

1.1230

3.5000

29 19.8 74.5 23.2 18.3=DfF= 4.407r 84 f 2.4 121 HIVA 2

13.3 48.4 14.0 12.6 CA .0 .0 -99.9 .0000

13.7 46.0 12.3 JL3.8 CA 61.6 40.5 82.0 .5110
12.7 39.7 9.9 14.8 AA 55.9 37.4 86.6 .3430

12.3 36.3 8.5 15.8 AA 53.2 35.6 91.0 .1740

6.7 17.1 3.5 16.8 AC .0 .0 19.0 8.5000

.0 .0 .0 20.5 .0 -99.9 24.5 3.5000

30 58.6 187.4 48.2 19.0=D rF= 3.629» 102# 2.2 122*HIVA 2

18.6 48.3 10.0 17.8 CA .0 .0 -99.9 .0000

36.0 84.3 15.8 19.1 CA 74.7 45.4 89.3 .5160

43.1 91.1 15.3 21.8 CA 67.8 43.1 97.7 .3360

30.8 57.3 8.5 23.7 AA 64.7 41.9 103.8 .1150

17.8 28.0 3.5 27.8 AA .0 .0 31.0 8.5000

.0 .0 .0 33.3 .0 -99.9 38.5 3.5000

31 1<I6.3 309.0 53.1 31.0=D #F= l.OOOf 121t 3.2 122*L0VA 1

5.0 25.0 10.0 9.1 CA .0 .0 -99.9 .0000

6.0 28.2 10.5 10.0 CA 57.4 38.3 72.7 .5750

10.9 45.9 15.4 10.4 CA 52.0 34.7 75.0 .4320

7.9 29.1 8.5 12.3 AA 48.4 31.6 82.5 .1460

^.^ 14.0 3.5 13.8 AA .0 .0 15.8 8.5000

.0 .0 .0 16.7 .0 -99.9 20.2 3.5000

32 34.2 142.1 48.0 15.8=D >F= 6.494# 57 f 2.0 122*HIVA 2

CO

CO
CO

4^

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 9

CM 03-16-70 Ö.000 .01964673 -1.1905 1.5658 2 660. 120 0 223022

DETAILED LOG AND/OR TREE REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.I.B. / LOG/RANGE/

NO./ CU.FT. / SQ.FT. / FEET / INCHES /CODE/ FEET/ TGRADS FGRADS SINELV

32.8 81.2 16.0 18.5 CA • 0 .0 -99.9 • 0000

45.4 100.7 17.8 20.3 CA 61.8 40.6 97.0 .4150

26.4 53.1 8.5 22.9 CA 58.1 38.7 106.1 .1350

12.9 23.8 3.5 24.8 AA • 0 • 0 27.4 8.5000

.0 • 0 .0 27.1 .0 -99.9 30.3 3.5000

33 117.5 258.8 45.8 27.4=DrF= 13.303» 65r 2.6 122*L0VA 1
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 10

CM 03-16-70 B.OOO .01964673 -1.1905 1.5658 2 660. 120 0 223022

SUMMARY REPORT~SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

STRATUM 1

/

1

SURE-TO-BE /

1

3P-EXPANDED / TOTAL SAMPLE /

/ MEASURED / SAMPLE / ESTIMATES /

SAMPLE VARIABLES/ AGGREGATIONS / ESTIMATES / PLUS SURE /

TREES(FREQUENCY) 3.000 166.510 169.510

PREDICTIONS(KPI) 387. 8647. 9034.

B.A.iSQ.FT.O.B.) 17.3 460.3 477.6

LENGTH(FT.) 185.2 10202.5 10387.7

SURFACE(SQ.FT.1B.) 1115.7 42251.1 43366.8

VOLUME(CU.FT.I.B.) 552.2 15437.1 15989.3

REL.VAL.PER MF.UNIT 1.00 1.00 1.00

GROSS MF.UNITS 4177.4 109296.1 113473.5

ST.ERRORCPCT.) 2.3 2.2

COMPONENT ITEMS

(1=)

NUMBER

(2*)

NUMBER

(1^2)

NUMBER

MEASURED TREES

MEASURED LOGS

3

18

10

50

13

68
CO THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 11

Oi CM 03-16-70 8.000 .01964673 -1.1905 1.5658 2 660. 120 0 223022

SUMMARY REPORT~SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

STRATUM 2

/

2

SURE-TO-BE /

2

3P-EXPANDED / TOTAL SAMPLE /

/ MEASURED / SAMPLE / ESTIMATES /

SAMPLE VARIABLES/ AGGREGATIONS / ESTIMATES / PLUS SURE /

TREES(FREQUENCY) 2.000 135.566 137.566

PREOICTIONS(KPI) 270. 6663. 6933.

B.A.iSQ.FT.O.B.) 5.0 178.0 183.0

LENGTH(FT.) 118.0 5953.2 6071.1

SURFACE(SQ.FT.IB.) if 97. 4 17if59.8 17957.2

VOLUME(CU.FT.I.B.) 170.8 4351.** 4522.2

REL.VAL.PER MF.UNIT 3.00 3.00 3.00

GROSS MF.UNITS 1188.3 27076.8 28265.1

ST.ERROR(PCT.) 6.3 6.1

COMPONENT ITEMS

(1=)

NUMBER

(2*)

NUMBER

(1»2)

NUMBER

MEASURED TREES

MEASURED LOGS

2

11

18

87

20

98
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 12

CM 03-16-70 Ö.000 .0196^673 -1,1905 1.5658 2 660. 120 0 223022

SUMMARY REPORT~SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

TOTALS ALL 2 STRATA***********************************************************

/ SURE-TO-BE / 3P-EXPANDED / TOTAL SAMPLE /

/ MEASURED / SAMPLE / ESTIMATES /

SAMPLE VARIABLES/ AGGREGATIONS / ESTIMATES / PLUS SURE /

CO

TREES(FREQUENCY) 5.00Ü 302.075 307.075

PREDICTIONS(KPl) 657. 15310. 15967.

B.A.(SQ»FT.O.B.) 22.3 638.2 660.6

LENGTH(FT.) 303.2 16155.6 16*158.8

SURFACE(SQ.FT.IB.) 1613.1 59710.9 6132ÍI.0

VOLUMEiCU.FT.I.B.) 723.0 19788.5 20511.5

REL.VAL.PER MF.UNIT l.ífíf l.t^O l.ifO

GROSS MF.UNITS 5365.7 136372.8 lifl738.6

ST.ERR0R(PCT.) I»««.». 2.2 2.2

GROSS WTD.MF.UNITS 77i*2.32 190526.36 198268.69

ST.ERROR(PCT.) 3.0 2.9
CO

00

(ir) (24^) (lr2)

COMPONENT ITEMS NUMBER NUMBER NUMBER

MEASURED TREES 5 28 33

MEASURED LOGS 29 137 166

MF.UNITS= BD. FT. UNT. 1/4-IN.) fAFTER ALLOWANCE FOR TRIM OF .3 FT. PER 16 FT

= ( .89560000+01 )*(CU»FT. )•»•( -.695*^0000+00) (SQ.FT. ) •( .íflíf50000-01)*(FT. )
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 0

CM 03-16-70 8.000 •0196^+673 -1.1905 1.5658 2 660. 120 0 223022

SUMMARY REPORT~SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

DATA PROCESSING BLOCKED BY

SAMPLE ESTIMATES INVOLVE

0

INPUT READ BEFORE FLAWrIF ANY

CARDS WITH TREE PREDICTIONS ONLY

CARDS WITH MEASURED TREE INFO

0 INPUT FLAWS.

0 SUSPICIOUS ITEMS NUMBERED

(FIRST)

(FIRST)

353

33

CARDS WITH MEASURED TREE INFO (SECOND)

CARDS WITH ADDITIONAL DENDROMETER INFO (SECOND)

33

65

PROCESSING DONE BEFORE FLAWrIF ANY

NUMBER OF MEASURED TREES PROCESSED

NUMBER OF MEASURED LOGS PROCESSED

TREE CARDS PUNCHED OR WRITTEN

LOG CARDS PUNCHED OR WRITTEN

LABEL ON CARD OUTPUT

33

166

0

0

TEST

CHECK OF INPUT AGGREGATES WITH EXPANDED 3P SAMPLE

AGGREGATE NUMBER OF TREES INPUT ( l+2-»'3)

SAMPLE ESTIMATE(EXPANDED 2)+NO.SURE(1)

STANDARD ERROR OF ESTIMATED NUMBER

386

307.075

34.7ifl

CD

CD

AGGREGATE PREDICTIONS(KPI) INPUT(l+2+3)

SAMPLE ESTIMATE (EXPANDED 2)+KPI SUREd)

15967

15967.
o

o

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 13

CM 03-16-•70 8.0Ü0 .0196^673 -1.1905 1..5658 2 660. 120 0 223022

GRADE:-YIELD AND REALIZATION REPORT

CLAS GR CU .FT.IB.VOL. SQ. FT.IB.SURF. LIN .FT.LENGTH FREQUENCY COUNT

HIVA AA 1Í413.16 4741.18 1297.49 219.89 36

HIVA AB 2ö.i*l 77.41 16.80 1.00 1

HIVA AC 2**.19 62.03 12.70 3.63 1

HIVA BA 117.02 453.95 140.87 15.24 3

HIVA BB <f9.22 179.69 52.35 3.74 1

HIVA CA 2m2.93 10227.29 3565.71 290.13 45

HIVA CB « 2Ü.43 1756.70 588.84 52.72 6

HIVA UU 22.08 123.98 55.81 8.53 2

HIVA XX 3«+. 76 334.74 340.57 26.16 3

LOVA AA 365Ô.ÎI5 9204.35 2024.48 293.78 22

LOVA AC 24U.17 486.98 78.61 9.83 1

LOVA BA 2762.70 7067.49 1608.91 110.62 9

LOVA BB 55.90 98.24 13.75 1.00 1

LOVA CA 8731.25 24812.55 5982.58 387.15 31

LOVA CB 437.78 999.20 182.10 9.93 3

LOVA XX 103.05 698.00 497.24 26.20 1

TOTALS 20511.50 61323.97~ 16458.79 1459.54 166
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 14

CM 03-16'-70 Ö.OOÜ .Oigbi+eTS -1.190b 1.5658 2 660. 120 0 223022

GRADE-YIELD AND REALIZATION REPORT

1ROUGH LOG WT. INC.WT.CHIPS LOG VOLUME LOG SURFACE LOG LENGTH DOYLE(NO BK.)

CLAS GR GREEN LBS. GREEN LBS. CU.FT.IB. SQ.FT.IB. LINEAL FT. NET BD.FT.

HIVA AA 6tfö00.22 8359.26 1413.16 4741.18 1297.49 6619.74

HIVA Ab 1797.70 230.72 28.41 77.41 16.80 97.47

HIVA AC 1539.09 181.63 24.19 62.03 12.70 85.30

HIVA BA 77^+4.36 815.85 117.02 453.95 140.87 429.16

HIVA BB « t*53.15 658.15 49.22 179.89 52.35 210.38

HIVA CA 157262.9Í* 183^i+.62 2112.26 8741.01 2970.88 8152.81

HIVA CB 28733.95 6282.63 368.10 1510.61 497.50 1589.22

HIVA UU .00 .00 .00 .00 .00 .00

HIVA XX • 00 .00 .00 .00 .00 .00

5UBT0T 286331.i*0 3H872.66 4112.35 15766.07 4988.59 17184.09

LOVA AA 202520.3^ 21997.72 3656.45 9204.35 2024.48 19183.49

LOVA AC 15570.71 14^23.12 240.17 486.98 78.61 924.32

LOVA BA 183^66.69 17165.90 2762.70 7067.49 1608.91 15873.50

LOVA BB 5359.22 306.m 55.90 98.24 13.75 318.67

LOVA CA 561115.75 » 3708.62 7643.24 21206.67 4984.58 43088.37

LOVA CB 32722.87 2*178.00 383.3Ü 859.22 153.86 2428.76

LOVA XX .00 .00 .00 • 00 .00 .00

SUBTOT 1000755.57 87079.77 14743.7o 38922.95 8864.19 81817.11

TOTALS 1287066.95 121952.62 18856.11 54689.03 13852.77 99001.20

VOLUME (CU.FT.IB.) PAIRED WITH YIELD (:0EFFICIENT5= 20511.51
o

APPENDIX B.—Computer output—preliminary report, detailed

log and tree report, and summary reports (same as Appendix A

summaries, but using a different set of conversion coefficients)

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST

CM 03-16-70 8.0Ü0 •0196i*673 -1.1905 1.5658 2 660. 120

PRELIMINARY REPORT—COUNTS AND AGGREGATE PREDICTIONS

PAGE 1

0 222022

STRATUM 1 TREE COUNTS PREDICTIONS

SURE-TO-BE MEASURED

THREE-PEE MEASURED

THREE-PEE PREDICTED

TREES(=1)

TREES(*2)

TREES( 3)

3

10

221

387

673

797Í*

ALL TREES{lr2# 3) 23if 9034

STRATUM 2

ALL MEASURED TREES(1»2)

ALL THREE-PEE TREES(2#3)

EXPECTED VALUES FOR ( 2)

EXP. VAL. ST. ERRORS ( 2)

13 1060

231 86if7

13.102 635.570

3.if8«* 169.015

TREE COUNTS PREDICTIONS

2 270

18 1128

SURE-TO-BE MEASURED TREES(=1)

THREE-PEE MEASURED TREES{*2)
THREE-PEE PREDICTED TREES( 3) 132

ALL TREES(l#2í3) 152

5535

6933

ALL MEASURED TREES(1^2)

ALL THREE-PEE TREES(2f3)

EXPECTED VALUES FOR ( 2)

EXP. VAL. ST. ERRORS (*2)

20 1398

150 6663

10.095 571.770

3.038 172.059

TOTALS FOR ALL 2 STRATA TREE COUNTS PREDICTIONS

SURE-TO-BE MEASURED TREES(=1)

THREE-PEE MEASURED TREES(*2)

THREE-PEE PREDICTED TREES( 3)

5

28

353

657

1801

13509

ALL TREES(lt2i 3) 386 15967

ALL MEASURED TREES(1»2)

ALL THREE-PEE TREES(2f3)

EXPECTED VALUES FOR (*2)

EXP. VAL. ST. ERRORS ( 2)

33 2if58

381 15310

23.197 1207.341

4.623 241.185

S
o

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 2

CM 03-16--70 8.000 .01964673 -1. 1905 1.5658 2 660. 120 0 222022

DETAILED LOG» AND/OR TREE REPORT

TREE/ VOLUME / SURFACE / LENGTH / D.B.H. /

NO./ CU^.FT. / SQ.FT. / FEET / INCHES /

1

===.

44.7 166.2 50.1 17.0=DrF= 4.407r 84» 1.6 021 HIVA 2

2 42.5 177.0 60.4 15.8=DfF= 4.936» 75» 2.4 121 HIVA 2

3 67.4 241.2 70.1 17.7=DrF= 3.739r 99» 1.6 221 HIVA 2

4 98.Ô 276.6 62.3 21.0=DfF= l.OOOf 138» -1.8 211 HIVA 2

5 48.4 193.9 63.5 15.6=D»F= 34.588» 25» 1.6 321 LOVA 1

6 221.5 404.9 59.9 34.5=DtF= 1.000» 145» 3.4 121 LOVA 1

7 112.4 349.1 90.4 22.8=DfF= 15.170» 57» 2.4 121*L0VA 1

ô 144.7 338.0 63.3 27.1=DfF= 9.826» 88» 2.6 121*L0VA 1

9 207.4 430.6 74.5 32.4=DtF= 7.933» 109» 3.4 122*L0VA 1

10 184.4 401.9 72.3 32.0=D>F= 1.000» 121» 3.6 121 LOVA 1

11 168.5 351.2 60.0 31.3=DrF= 7.933» 109» 3.0*121 LOVA 1

12 178.4 378.1 65.5 28.9=DfF= 8.395» 103» 2.8 112*L0VA 1

13 59.6 191.7 50.6 18.8=DfF= 26.203» :^3» 1.8 131 LOVA 1
14 72.0 220.8 55.7 21.9=DfF= l.^OOr 132» .0 Oil HIVA 2

15 52.H 201.9 63.0 16.8=DfF= 5.365f 69» 2.0*121 HIVA 2

16 20.4 114.8 57.4 ll.l=DrF= 17.627f 21i 1.2 121 HIVA 2

17 57.0 196.7 63.2 19.0=DrF= 26.203r 33i .0 121 LOVA 1

18 72.6 245.5 73.5 20.1=DfF=: 3.164r 117i 2.2 121 HIVA 2

19 44.3 168.8 59.5 19.5=DfF= 5.365» 691f 3.0 121 HIVA 2

20 21.7 100.6 37.7 13.4=D^F= 12.339f 301f 1.8 121 HIVA 2

21 41.2 151.5 45.6 17.0=D#F= 6.855f 541f 2.0 121 HIVA 2

22 34.8 129.4 38.7 16.0=DtF=: 7.258f 51if 1.8 122*HIVA 2

23 48.3 181.5 55.5 17.7=DfF=: 8.226f 45 f 2.2 121 HIVA 2

24 14.6 58.9 19.1 15.2=D#F= 15.424f 24 r 2.4 121 HIVA 2

25 11.8 55.6 21.0 11.8=DfF= 13.710# 27 f 1.4 121 HIVA 2

26 43.7 160.3 47.5 17.4-DfF= 5.365t 69 f 2.0 121 HIVA 2

27 90.8 231.7 47.6 23.1=D#F= 16.955f 51 f 2.0 121 LOVA 1

28 33.1 136.2 45.3 i5.8=DfF= 7.258f 51 f 2.2 122*HIVA 2

29 19.8 74.5 23.2 18.3=D#F= 4.407t 84 f 2.4 121 HIVA 2

30 58.6 187.4 48.2 19.0=DrF= 3.629» 102 f 2.2 122*HIVA 2

31 146.3 309.0 53.1 31.0=DrF= l.OOOf 121 r 3.2 122*L0VA 1

32 34.2 142.1 48.0 15.8=DrF= 6.494» 57 f 2.0 122*HIVA 2

33 117.5 258.8 45.8 27.4=DfF= 13.303» 65 » 2.6 122*L0VA 1

O

en
o

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 3

CM 03-16-70 8.000 .01964673 -1.1905 1.5658 2 660. 120 0 222022

SUMMARY REPORT—SURE-TO«'BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

STRATUM 1-

/

/

SAMPLE VARIAÖLES/

SURE-TO-BE /

MEASURED /

AGGREGATIONS /

3P-EXPANDED /

SAMPLE /

ESTIMATES /

TOTAL SAMPLE /

ESTIMATES /

PLUS SURE /

TREES(FREQUENCY) 3.000 166.510 169.510

PREDICTIONS(KPI) 387. 86<f7. 903«*.

B.A.(SQ.FT.O.S.) 17.3 460.3 477.6

LENGTH(FT.) 185.2 10202.5 10387.7

SURFACEiSQ.FT.lB.) 1115.7 42251.1 43366.8

VOLUME(CU.FT.I.B.) 552.2 15437.1 15989.3

REL.VAL.PER MF.UNIT 1.00 1.00 1.00

GROSS MF.UNITS 4177.4 109296.1 113473.5

ST.ERROR(PCT.) 2.3 2.2

(1=) (2*) (lf2)

COMPONENT ITEMS NUMBER NUMBER NUMBER

MEASURED TREES 3 10 13

MEASURED LOGS 18 50 68
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE <*

CM 03-lb-70 6.000 .0196t^673 -1.1905 1.5658 2 660. 120 0 222022

SUMMARY REPORT~SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

STRATUM 2 2— —•" —.i¿ "•" " ———c

/ SURE-TO-BE / 3P-EXPANDED / TOTAL SAMPLE /

/ MEASURED / SAMPLE / ESTIMATES /

SAMPLE VARIABLES/ AGGREGATIONS / ESTIMATES / PLUS SURE /

TREES(FREQUENCY) 2.000 135.566 137.566

PREDICTIONS(KPI) 270. 6663. 6933.

B.A.(SQ.FT.O.B.) 5.0 178.0 183.0

LENGTH(FT.) 118.0 5953.2 6071.1

SURFACE(SQ.FT.1B.) « 97. if 17if59.8 17957.2

VOLUME(CU.FT.I.B.) 170.8 íf351.** <f522.2

REL.VAL.PER MF.UNIT 3.00 3.00 3.00

GROSS MF.UNITS 1188.3 27076.8 28265.1

ST»ERROR(PCT.) —— 6.3 6.1

COMPONENT ITEMS

(1=)

NUMBER

(2*)

NUMBER

(lf2)

NUMBER

O

-:3

MEASURED TREES

MEASURED LOGS

2

11

18

87

20

98
o00

THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 5

CM 03-16-70 8.000 .0196*^673 -1.1905 1.5658 2 660. 120 0 222022

SUMMARY REPORT~SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

TOTALS ALL 2 STRATA***^********************************************************

/ SURE-TO-BE / 3P-EXPANDED / TOTAL SAMPLE /

/ MEASURED / SAMPLE / ESTIMATES /

SAMPLE VARIABLES/ AGGREGATIONS / ESTIMATES / PLUS SURE /

TREES(FREQUENCY) 5.000 302.075 307.075

PREDICTIONS(KPI) 657. 15310. 15967.

B.A.iSQ.FT.O.B.) 22.3 638.2 660.6

LENGTH(FT.) 303.2 16155.6 16^^58.8

SURFACE (SQ.FT. IB.) 1613.1 59710.9 6132if.O

VOLUME(CU.FT.I.B.) 723.0 19788.5 20511.5

REL.VAL.PER MF.UNIT l.ífí* l.*fO l.i|0

GROSS MF.UNITS 5365.7 136372.8 141738.6

ST. ERROR (PCT.) 2.2 2.2

GROSS WTD.MF.UNITS 7742.32 190526.36 198268.69

ST. ERROR (PCT.) 3.0 2.9

(1=) (2*) (lf2)

COMPONENT ITEMS NUMBER NUMBER NUMBER

MEASURED TREES 5 28 33

MEASURED LOGS 29 137 166

MF.UNITS= BD. FT. (INT. 1/4-IN.) »AFTER ALLOWANCE FOR TRIM OF .3 FT. PER 16 FT

= ( .89560000+01) *(CU.FT. ) + ( -.69540000+00) * (SQ.FT. )•»•( .41450000-01 )* (FT. )
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 0

CM 03-16-70 8.000 .0196^673 -1.1905 1.5658 2 660. 120 0 222022

SUMMARY REPORT—SURE-TO-BE MEASURED TREES PLUS EXPANDED 3P SAMPLES

DATA PROCESSING BLOCKED BY 0 INPUT FLAWS.

SAMPLE ESTIMATES INVOLVE 0 SUSPICIOUS ITEMS NUMBERED

0

INPUT READ BEFORE FLAWflF ANY

CARDS WITH TREE PREDICTIONS ONLY (FIRST) 353

CARDS WITH MEASURED TREE INFO (FIRST) 33

CARDS WITH MEASURED TREE INFO (SECOND) 33

CARDS WITH ADDITIONAL DENDROMETER INFO (SECOND) 65

PROCESSING DONE BEFORE FLAW t IF ANY—

NUMBER OF MEASURED TREES PROCESSED 33

NUMBER OF MEASURED LOGS PROCESSED 166

TREE CARDS PUNCHED OR WRITTEN 0

LOG CARDS PUNCHED OR WRITTEN 0

LABEL ON CARD OUTPUT TEST

CHECK OF INPUT AGGREGATES WITH EXPANDED 3P SAMPLE

AGGREGATE NUMBER OF TREES INPUT(l+2+3) 386

SAMPLE ESTIMATE(EXPANDED 2)+N0.SURE(l) 307.075

STANDARD ERROR OF ESTIMATED NUMBER 3*^.7«*!

AGGREGATE PREDICTIONS(KPI) INPUT(l+2'»-3) 15967

SAMPLE ESTIMATE (EXPANDED 2)+KPI SUREd) 15967.
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST PAGE 6

CM 03-16--70 Ö.OÜO .0196Í+673 -1.1905 1..5658 2 660. 120 0 222022

GRADE:-YIELD AND REALIZATION REPORT

CLA5 GR CU .FT.IB-VOL. SQ. FT.IB.SURF. LIN .FT.LENGTH FREQUENCY COUNT

:z==: :~rz :==r:zzz

HIVA AA 1413.16 4741.18 1297.49 219.89 36

HIVA AB 20.Í+1 77.41 16.80 1.00 1

HIVA AC 2**.19 62.03 12.70 3.63 1

HIVA BA 117.02 453.95 140.87 15.24 3

HIVA BB 49.22 179.89 52.35 3.74 i

HIVA CA 2412.93 10227.29 3565.71 290.13 45

HIVA CB 420.43 1756.70 588.84 52.72 6

HIVA UU 22.08 123.98 55.81 8.53 2

HIVA XX 34.76 334.74 340.57 26.16 3

LOVA AA 3650.45 9204.35 2024.48 293.78 22

LOVA AC 24Ü.17 486.98 78.61 9.83 1

LOVA BA 2762.70 7067.49 1608.91 110.62 9

LOVA BB 55.90 98.24 13.75 1.00 1

LOVA CA 8731.25 24812.55 5982.58 387.15 31

LOVA Cß 437.78 999.20 182.10 9.93 3

LOVA XX 103.05 698.00 497.24 26.20 1

I—zz; :-;:= r===r=z==r=: I—r::—zz

TOTALS 20511.50 61323.97 16458.79 1459.54 166
THREE-PEE SAMPLE TREE MEASUREMENT AND APPRAISAL TEST

CM 03-16-70 8,0Ü0

PAGE 7

0 222022

CLAS GR

bCRIBNER

NET Bu.FT

.01964673 -1.1905 1.5658 2 660. 120

GRADE-YIELD AND REAuIZATION REPORT

INT. 1/Í+ IN. LUMBER TALLY LBR. F.O.B. ADD.WT.CHIPS

NET BD.FT. NET BD.FT. DOLLAR VALUE OVENDRY LBS.

CHIPS F.O.B.

DOLLAR VALUE

HIVA AA

HIVA Aß

HIVA AC

HIVA BA

HIVA BB

HIVA CA

HIVA CB

HIVA UU

HIVA XX

SUBTOT

8217.73

121.9i^

lüif.62

Ó0Í+.57

285.11

im21.00

2100.69

.00

.00

9118.i^8

130.1^1

111.93

677.85

302.57

13208.66

2397.90

.00

.00

8689.Í+0

183.05

168.17

635.70

21i+.'+0

11266.68

16Í+2.3Í*

.00

.00

2593.76

75.28

77.66

141.56

29.53

2703.04

428.16

.00

.00

3438.79

106.14

62.80

332.62

314.15

7660.93

3028.86

.00

.00

94^474.57 101890.56 88999.14

TOTALS 117330.23 127838.12 111798.86

VOLUME (CU.FT.IB.) PAIRED WITH YIELD COEFFICIENTS=

7805.54

13854.53

20511.51

37924.25

52888.54

23.17

.72

.56

2.24

2.12

51.63

20.41

.00

.00

SUBTOT 22855.66 25947.55 22799.74 6048.99 14964.29 100.85

LOVA AA 21153.19 22791.51 23689.26 2639.20 9707.81 65.42

LOVA AC 1065.59 1149.20 2080.90 407.75 625.15 4.21

LOVA BA 18250.71 19752.14 16583.37 1220.35 7577.94 51.07

LOVA BB 360.21 370.20 387.42 8.29 132.08 .89

LOVA CA 50782.44 54837.38 43708.00 3302.38 18775.49 126.53

LOVA Cb 2842.44 2990.12 2550.21 227.58 1105.79 7.45

LOVA XX • 00 .00 .00 .00 .00 .00

255.58

356.42
APPENDIX C.—Examples of field tally sheets

(see text pages 22-26)

112
1 LF^EE ÇftRDS, COLS. 1 -II FOR ALL TREES.

IN COL. Il, AND «TA«T NEW PAOC rOR NEXT TALLY

TREE CARO FOR SAMPLE IS COMPLETEO AT RIOHT.

ÇTX TALLY SHfÇT

TREE NO.

(SAMPLES

ONLY) KPI

aili MON-PUNCH

^^ RANRf:*^ D'ST,

^* .N7OV2S?W oAv iikiiT ^to¿6. 1 indicatèft\ ■■

, .1,|. 5 6 rl.U olii^^^ DATE 1 FP-1S dpnr^^«^,A^»^ l PAfiF OP 1

/ 1 uir _ Vwas used.^-«— -^

2 1 1 M / _

3 1 i^f eg CLASS DBH yq^ BKA BKB UML UDT Ï- 4 1 1 1^ I rnnviAm \As\.\9m,\g\am \ \M I i/b« i i i i i

5

i3l/ 1 _

6 1 1 1 l¿ 1 , 1 M ¡ 1 ; 1 1 ; i 1 1 i 1 1 1 1 1 ! ¡ 1 ! M 1 1 1 1 1 1 1

7 1 1 1 Vif 1 ^ « XTRA S7 XTRV - n

a 1 1 1 If -2. ,

9

5^ / ^

10 ^n \ ~

II 1 ¿I4Í / /// TREE NO. J T GRADS F GRADS SINELV GH

12 1 1 i;i 1 1 iTinÍ íí' ¿. N,WCardV 1 1 LZP/^^^^H «l.^^bflfi iri/ir «ivJyl« 1 1"

13 1 '"131/1* 9\*AU fifii^c ^/9

14 1 «13(21-7 glUf y /ifi3-iA ^A r

15 "I3lfl7 7l7i¿ / 3I7I>.I« /3{^ "1 16 N,>,c<,rd\ 1 1 \p\^mÊ^mm lM/\s 7\¥i^ /M^IJIô

17 ¥\5\t 7l>!j" jU'^f\ú\£> r-i/9

13 1 ^C\<f l\¥iC /lL\9\C\e C\A

19 1 1 1 1 1 1 lili ^ 20 1 NewCcrd\ 1 1 1 |.,^^i^H 1 1 1 1 i lili

21 1 1 1 1 1 ! 1 1 1 1 1

22 1 1 1 1 i 1 1 1 1

23 1 1 1 i ! 1 lili 1 24 N»w Cord\ 1 1 LHIIIIH 1 1 1 1 1 1 Mil

25 1 1 1 1 1 i i 1 1

^g| 1 1 1 1 i 1 I 1

27 1 1 1 i 1 1 1 1 1

28 N,^Card\ 1 I 1 \jimÊ^mm 1 1 ! 1 1 1 lili

29 1 1 1 1 1 1 1 1 1 1

30 1 1 1 1 ! 1 1 1 1

31 1 1 i 1 1 lili

___j "1

32 New Cord\ 1 1 \s^^ÊÊÊÊÊM 1 1 1 1 1 1 1 1 1

33 1 1 1 i 1 1 1 1 1 1

34 1 - 1 1 lili

35 1 1 1 1 1 1 1 3

36 1 Vewcard] 1 1 IrHHHHH 1 1 1 1 1 1

37 1 1 1 i 1 lili

38 1 i 1 lili

39 1 1 ! lili 1

40 V..Cord\ 1 1 UHJ^IHH 1 1 1 lili

41 III 1 > > 1 1 1 1

42

' '

lili

43 1

' '

1 1 ! 1 1 1 1

44 1 1 11 VewCordl i ! 1 lo^HJjJI^^ 1 1 1 1 1 1 1 i 1

45 1 1 1 1 1 1 1 lili "T

46 1 1 1 1 1 i lili

47 1 1

R

ü

1 1 1 1 1 i lili "1

48 1 1

' ' EMARKs ST #2 FP-15 Barr and Stroud dendrooeter

49 1 1 1 1

50 _! 1 1 M 1 I

113
TREE CARDS. COLS. 7~ FOR ALL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COU. II, ANO START NEW PAGE FOR NEXT TALLY.

TREE CARD FOR SAMPLE IS COMPLETED AT RIOHT.

STX TALLY SHEET

PUNCH

TREE

COUNT

TREE NO.

(SAMPLES

ONLY) 51 iZSToN ::.".::r^ode l indicates direct \

iUUU, eUUU DATE Treading dendrometer or y PAGE OF

1 i \ÍM J

\taped measurementj,^-""^

2 1 1 lÄir / _ TREE CARD CONTINUATION FOR^MPLE TREE

3 1 ! IJ^7 } _ CLASS DBH .0SlPêf BKA BKB UML UDT .

4 ï~ 1 1 \¿\i f - ^^W\Am l/17Ni7H;d2^H 1 I i^i ! M7P 1 i 1 1 I 1

5 1 ! ^ í- / _ 12 17 \2^ 27 31 36 39 t=;

6 1 1 1 (- > J/f 1 1 1 1 1 ; M ; ; i 1 i 1 1 1 M 1 M 1 M 1 1 1 1 1 1

7 1 1 1 f 1

42 XTRA ST' XTRB 7Z

a 1 i I<t4 1

.

/Measured diameter to 0.1 inches>^

\Do not record the decimal point.j 9 A± 1

-

10 /\1 f

, PENPROMETER c ' 1 -^

n ,<i^ 1 _ TREE NO. J T GRAOS F (Sj^DS SINELV GR

12 /4f i _ »..»..LLUiñ^HHl ^ i 1 i2\á\S' 1 lol.io 1 '•

13 ¿If f _ '' 1/1717 1 m.io/fiA î^

14 -rií 7

- r 1 1 _L/_¿^ \ \3\.\c. ^A H

IS ¥^ % - *' 1 1 \/¥^e XA'MAC ^^ '1

le ^\^ )~ - Ne^Corä\ \ \ \3\pWÊK^^ 1 1 1/ 31 ¿ _U4Ö.|^ 8B

17 "TTT" ^1^ ^ - ] 1 l/ii:» 1 191.1:1^:1-4

18 i \3 ^i7 ? # r

1 1 \y\c\3 \^C\. Id c\^

19 1 1 I 1 1 1 1 1 ^ 1 ^

20 1 1 ^

21 1 ! Measured segment T.engcn,i

to 0.1 feet. Show J

\deciraal point^^^_^„..- 22 i

23 1 1

24 1 f^ewCardl 1 ! LHI^HIi 1 i 1 1 II

25 1 i 1 i

!" 26 \ i 1 i 1

1 27 i 1 1 1 1

28 ! IVew card | | i | | .^IHHHH 1 1

29 1

30 1

31 i 1

32 1 Ne^ Cardl | | i U ¡ ¡ ^H 1 1

33 1 1 1 1 í 1

34 ! 1 1

35 1 1 1

36 ¡ 1 /Vew Card\ 1 I^^HHHi 1 1

37 i

3B ¡

39 ! 1

40 1 ^ey,Card\ 1 1 U^HHHl

41 i

42 i

43 1

44 ¡ New Cord\ \ ! {.« ^ i

45 1

46 1 1 1

47 1 1

48 1 RFMARKs ST #3. Recordine tape m sasurements, or direct

49 1 ' reading dendrometers, The TGRADt3 column is left

50 1 blank. Col. 23 Is code 2.

114
1 TREE CARDS, COLS. i-ii FOR »LL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COL. II, ANO START NEW PA8E FOR NEXT TALLY

TREE CARD FOR SAMPLE IS COMPLETED AT RI8HT.

STX TALLY SHEÇT

LCOUNT

TREE NO.

(SAMPLES

ONLY) KPI

i' -§?Tro"ÍAi" SALE NO. /Tîegative bark thicknels>

PAY UNIT 1 No reduction for bark J

DATE V will be romr.,,hn,1 ^-—>^

' F

. zUU - AA^ u.^^^m "AGE OF

1 IV 1 /\3\f Jk 1 V«. ,.<< -'^

TREE 2 1 1 1 il:7^ TREE CARD CONTINUATION FOR SAMPAJT

3 1 /

III CLASS DBH . OPT. /^KA "^ BKB UML UDT

L- 4

indicates 'sure-to^ //irli^lAM \:i\/\. lómalo\am-\c\o\9l 1 M 1 1 i ! 1

5 be ' measured samplej » S" ^

fe. 36 39

6 1 1 1 1 1 ! 1 1 ; ; M i 1 i 1 1 1 1 i 1 1 ! ¡I 1 ! 1 1 1

7 ^iH-- -* *2 XTRA 57 XTRB «

a

9

10

II

_ TREE NO. J T GRADS F GRADS SINELV GR

12 1

IVeu< Cara[ \ | IA4°/HI^HBH 'M 1 i lAl/¡6 1 |¿»l. 10 ¡ ~

13 1 "1 1 1 !/Í9lé 1 l-V^.lá? 4i'4 t

14 1 ^111 1/ sir 1 l?l .10 A\/i

15 1 "1 1 1 l/él7 \/\C\.\2 A\fi «1

le 1 1 NewCord] i 1 UAJ>WI^KÊÊÊM 1 1 l/6lf 1 l¿!.|7 r\4

17 1 1 1 1 "TTÍTj 1 /IJl. \f ^^

IB 1 1 1 1 I/I3l¿ \/\aU \f CVi

19 1 1 1 1 1 1 1 ! I ! 1 f 1 «H 20 1 i i^e.cor.i 1 , 1 uimÊÊÊmÊ 1 1 1 1 1 ! 1

21 1 i 1 1 1 1 i i 1 M u 1

22 1 I 1 1 ! ! 1 Mil 1

23 1 i ! 1 i i 1 i 1 i 1 1 i

24 1 New Card 1 1 1 i 1 ^IHHHH ! 1 1 1 1 i i 1 i i 1

25 1 ! 1 i 1

26 1 1 1 1 1 I i i "T^

27 1 1 1 1 1 1 1 1 1 1

28 1 New Card\ | | \fS^tÊÊMÊlM 1 ! 1 1 1 1 1 ! 1 1 1

29 1 1 1 1 1 1 1 1 1 1 1 Mil i

30 1 1 1 M ! 1 1

31 1 1 ! " ¡" 1 1 1

1 1

32 New Cord\ \ \ le ■■ i i 1 i i 1 L.

1

33 1 1 !

! ¡ ¡ , 1

34 i 1 ! ! 1 1 1

1

35 1 1 1 1

i 1 { 1 1 1

36 ' I >Jew C0rd\ 1 1 1 I^HHI^HH 1 1 1 1 ! 1 1

37 1 1 1 1 1 '11 ! 1 T"

38 1 i 1 t 1 J - ! 1 i i ¡

39 1 1 i i 1 ¡ 1 1 1

40 i Mew Card Mil {^¡¡ H 1 ! 1 Mil 1

41 1 1 1 1 1 1 J 1 '

il M 1

42 1 1 1 ! M II 1

43 1 1 1 1 MM 1 1 44 New card] \ ] [« ■■■i

i 1 1 MM 1

45 1 1 1 1 MM !

46 1 ¡III 1

47 1 1 1 M ! 1 1 1

48 1 1 i FMARKs ST #4. A negative bark thickness (actual or

49 1 1 1 fictitious) is recorded in cols. 27-30 when no

50\ fill 1 reduction for bark is to be computed.

115
TREE CARDS, COLS. ,. II FOR ALL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW M OR s

IN COL. II, AND START NEW MOE FOR NEXT TALLY

TREE CARD FOR SAMRLE IS COMPLETED AT RIOHT.

ÇTX TALLY SHfÇT

mf^ ADMIN UNIT

»rc-H THEE

COUNT

TREE NO.

(SAMPLES

ONLY]

i'i ,;gg»i;^

^^ RAN^TFR DIST

PA^ONiT/code 3 indicates mod if

DATE ^Zeiss Tetetop Dendrome

ildX

, . ,'l. 'J '|.|. i2 ter/ PAGE OF _

Z IJS"

_

* ^?

3 CLASS OBH ^é^ BKA BKB UML UDT

f. 4

... ¿^4i\^\Am l/L5t.i6H3yioB ! 1 1¿| 1 l/I^H Mill

5

6 1 1 1 1 1 ; 1 1 ; 1 ¡ 1 i 1 1 1 1 1 i M 1 1 1 1 1 1

7 « XTRA ST XTRB «

8

9

10

II TREE NO. J T 6RADS F GRAOS SINELV GR

12 N,„Ccr</[ 1 1 kK>/^^^^ ^i^mi \/\9\e> \f\L\.\C 1 ~

13 1 1 ! "\¿\7ir l/bl¿ \f\9\' 17 ^4 a+

14 lC\t6 \A4\¥\/\ô\CU\8 313 u«

IS

'' t^7 l/3l¿ /i;íi/i.Lr4i^ "i

le »,.cor<,\ 1 1 \^,w^a^m / /¿> \/ AO /I3l3l. \SS\^

17 ^ ^ At \ \Ê\4^ yl44<»U If <^^

IB ^ 1 \ 11 III!

19 / 1 1 1 1 1 1 1 1 1 1 ^J

20 ^'-'^"'"X \y^nr>.^ ... ,f--. .,..., .. r. . '¿^^r^ "

21 1 FGKADS is diameter to 0.1 inches. / -

22

23 J

24 ' N,y,CarA 1 1 I^IIHBHH 1 1 1 1 1 1 1 1

25 1 1 1 1 i 1

26 1 1 1 1 1

27 1 1 lili 1

28 N,w Cord\ 1 1 .« ■■I 1 1 1 1 1 i I 1

29 1 1 1 ■■j

30 1 1 1

1

31 1 1 1 1 i

32 New cara] | | Iffl^HHHH 1 1 i

1

.33 1 1 1 1

34 \:\ I 1

35 1 1 1

1 ' i

3e »ewCarÀ 1 1 1 l/HHIHHI 1 i 1

1

37 1 1 1 1

38 1 1 1 1

39 1 1 1 lili 1 1

40 N..ccr,\ 1 I 1 UHBHI^ 1 1 1 1

41 1 1 1 1

42 t 1 1 1 1

43 1 1 1 1

1 1

44 1 1 Mew card \ j | [« ■■■I 1 1 1 1

45 1 1 1

46 i I 1 1 II 1

47 1 1 1 4 1 1 1 1 1

48 1 1 REMARKS ST #5. Recording Modified Zeiss Teietop mcasS ÍiiinH¿d fnr T a-nA TT CPAT»« 49 1 1 urements. Decimal point 1

but must be explicit for SO 1 1 |_ _u _ SINELV. Col. 2 3 is cod ä 3.

116
TRF.F. CARDS. COLS. l-ll POR ALL TREES.

WHEN .% SAMPLE Titee IS REACHED, SHOW > OR =

IN COL. II, ANO START NEW PAGE FOR NEXT TALLY.

TREE CARO FOR SAMPLE IS COMPLETED AT RI8HT.

ÇTX TALLY SHE|T

/U4S ADMIN UNIT

KP! % "gÍTf.i'ÍAi"

^^ RANGER DiST

icOUNT

TREE NO.

(SAMPLES

ONLY)

SALE NO. NAME

PAY UNIT , , r.RFW jH A^UU «uuu 10 H^HI^H DATE PA6Ê OF

1 i 1 U \3-M 5 _

1 i 1 l^lii* „

3 8 . "WL UOT , . ! ! 1 iS i Ulf / s-^ CLASS OeH OPT. BKA 9K

4 Il 1 la-M / \L\^\VVi^ \SWV'S^A%\cm i 1/1/! i \/'^m ! ! í M !í.

S TTT f? % - 12 17 23 27 31 ÏS ^* ^-í

g 1 1 1 !/ f ¿r II ! II ; Í 1 ; i M 1 1 1 M 1 1 1 M 1 i ¡ ! L1 !

T i 1 i 3f /

42 XTRA 57

^.

Trta

8 1 I 1 ^ O.L / - / tance upwards tir^

9 1 1 \G t/«^^ f - I next section, in feüdt

i 1 1

II ! 1 i ! 1 TREE NO. J X^IWUJ ("UHlMaS „öfffT?**^ OR

¡2 1 1 i 1 1 I

/

Ne,.car<fn | UP/liHBHHKI 91 ^1« \Sl^^j IS^J^ i

13 5r+* 1 i 1 1 1st TGRADS is -59y ""^Nrr L^l ! 1 \3\i^isi^i \^.\eâ/i^A

14 1 1 t i ' 2d TGRADS is blank 1 'M'^e \E^m^\m^A, (Ä|<4jg?

15 1 1 1 ^^ FGRADS are meas. dia. J '^\^i.8 Q?]/jf yi;iirr>i^Sii5i

16 ! i 1 N,^Cor<¡\ 1 1 l^l^'BUIllHI iMjîU \f^SL_^ ñ!>í!

i7 TT i .-rtv»l/ L !á1^Í4* <:\fi

18 1 1

1 ^4f ifliirlyLiljt/lö ¿ lí^

, 19 ! ¡ 1 1^ ! 1 i ! M i

í^

20 1 1 I 1 i ! N^*Carà\ 1 1 1 ijfeaiÉHiÉÉí 1 Al . i 1 i 1 , 1 1

21 1 1 1 i í /Dendroojeter measure•N

22 ! I 1 1 1 1| ments beein at third i_ju..

23 i i 1 Vsegment. _^^^.|J

24 1 I ! Htw card n M 1 «IAH^JUí^íü 1 IT"

25 ! 1 -\~ 1 1 , 1 i_, 1

l" 2€ 1 1 i i

!

! 1 1 I

27 1 ! \ '_L í

28 1 1 1 ! _,!_ NowCcrA 1 1 1 ].?BËHi^Éi

29 1 1 1 ! 'T 1 1 : ;"'

Nevi Car</\ t \ IsfKÍ^^BSEí

30 r ' ' _ L .LJ_.

31 ri ! i 1

32 lili

"M~i~ JL'ZL

i ; i

33 ¡Ti 1 1 1 1 !

34

"IT v\- 1 r¡ 1 ! í

1

i 1

T 1 i í !

St; ! 1 1 Ne>» cora\ \ \ \ Xr'WlSaÊBBaÊik .__._.__^ f"

37 i 1 1 1

38 i i 1 ! i 1 ' J i ¡ ' j„

I 39 1 1 ! -

i ! 1 "' 1 1 • ' il i

^'± 1 i T N»w Card\ 1 i 1 UHflfaSB

42 1 L__AJ 1 i _ _

43 ' 1 ! • ! i j

44 NtwCord\ ! ! 1 UmiHittfli

i 1 .

• 1 :

45 1 1 .J. L-__ L -i

46 I ! i 1 1 _i L ! j.i :

47 I I 1 t ! . • i : 1 i

48 SFMAPK«; ^"^ ^*^- Combining tape and dendrotnerer

1 49 ! 1 1 measurements when lines ot sight to iitu..r,p and riiP AVU

L££. ! ! ! obscured.

117
COLS. 1- II FOR ILL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

!N COL. II, AND START NEW PAOE FOR NEXT TALLT $TX TALLY SHÇÇT

NONHJNCh

TREE, m

TREE NO.

(SAMPLES im: KPI

1 1 :^^^^

^^ nAkf<SFP DIST,

SALE NO NAME ,

S T|.|S ^^^ DAT/If col. 25 is code 0 or 1, UDT must beA )F

1 1 \^H f

. í ítOD d.o.b./DBHOB^, Do not record 1

2 1 1 íXíAff 1 , TREE\declmal. UML may be blank. _ /

3 1 ! Mf 1 „ CLASS ' DBH OPT. BKA BKB UML"*Í^JDT\.

f

4 1 !

l^í f ^ i\^^\9m \:t\r,'^my\^um M//I i i \m \ \Msh

S c\f ( -

6 i\f 1 //a M 1 ! ! 1 M 1 ; i ! I i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 I

? t

« XTRA ST XTRB 72

8

! I f

-

9 1 17 s\^ / •íf- ^

¡O DENDROMETER CARDS FOR ABOVE SAMPLE TREE (9-CARD LIMIT5

II TREE NO. a y^GRADS F GRADS SINEL^T'^H. GR

12 1 New Card \^ | | [^^/^ ^^ ^l«?!«'!« l\J.\9\f\ i I-f^.lÄ» 1 "

IS /'Taoe meas, as 8'üown."'vHrs l\ \ i ^%.\í 1 \ru b. 4\A r

lA

... \ sr dendrometer meas. J «¡f^Wf "^1 yUu>l9\^U

15 " —' ri^^n* gW j\d\/\ira(ri/9 r.)

16 N,^carö\ 1 1 bb^HHHl (-/l7!A tt^ /\ST/i^a<:\A

IT 1 -^\9i£ i 1 ¡ 1 1 c\4

18 ^r lili !

I9\ 1 ^ i 1 ! i 1 ^ 20 N,y,Card\ I 1 1 |.Hi|^W^HI._.l . • l. 1

1 . . 1 •.

SI "

~ /Show tinal FUKAUS as -999. it "*\

22 I col. 25 is 0 or 1, at least three!

23 __L y[lè^gàu?llâV"°^^" «°°^^ ^^"%f

_2_4 1 -tew COM \ 1 1 1 ¡^HBHHHI TTT- Mir T

25 1 1 1

1

26 i 1 11 ¡ 1

27 i 1 1

1 1 28 New COM \ i ! ! I.^IWIMMII 1

2'J 1 i 1 '

SO 1 1

1 VTT 1 1

1 1 32 New Cordl ! 1 UHHH^B i 1

1

33

...

1 1 1

"751 ! ~

i r^ 1

35 1 ! i ! ^

se 1 »Jew Cord\ i 1 I j/HHpmP^ 1 1 1

37 ! ! 1

38 ! ! 1

39 i i 1 40 i / ^ewCarA 1 1 1 UIUHHHI 1

41 . 1

\_J¿_ ___

"

1

43 1 44 1 NewCard\ \ | | ioMHH^Hai 1

_4S_

46

1

lili

47 1 i 1 Mil 1

4a TTi i FMftpwc ST #7. When top section is obscured, top d,ö

40^ i 1 1 i nay be extrapolated from lower measurements. Procedui

I *£i í I 1 E_L_ ; Ls governed by code recorded in col. 25.

118
Tl^eE ÇARPSr COLS. I-Il FO« ALL TUCES,

WHEN A SAMPLE TREE IS REACHCO, SHOW » OR s

IN COL. II, ANO START NEW PA6E FOR NEXT TALLY.

TREE CARO TOR SAMPLE IS COMPLETED AT RISH

¡HE

1/1/1^

\9\9 i

TTT

_LL

I I I

XL

I I I

I ! I

J_IJ_

Í i

TTT

! !

TTT

JJ_L

i I

i i i

fl^ ADMIN. UNIT _

^^ RANGER OIST. _

SALE NO NAMEPAY ÜNITJÍAIE f\ML is estimated length o?^

unsee

<feet.

DBH

n top section in \

^Äp-^

CLASS OPT. BKA , "/JMLA UDT . ki^it^i^H i;ii7|.i/«/i^i/H 1 i/i/! \ vwM \AÀJ^O\à23 27 51 "TO^st " '^"

1 M I 1 1 ! 1 ! ; ¡ 1 1 i ¡M I t i i i i 1 1 1 i I 1 ! ! 1

« XTRA ST XTf?6 72

(9-ÇARD LIMIT)

REMARKS ST .^^^—If-jciiLuMiJilJLfiL CLudp 0 or_ I,_.j4n&ê.ejû. Jiup

d.o.b. is extrapolated to XUDT_x DÍJ'HJI or for length

shown as UML, ighlchever cotnesjfIr^t. _' ' ^

119
LHSS CARPS. SOl-í l-ll PO« ALU TÍEES,

HEN A SAídPUE TREE iî SKÄCHEb. SHOW * OR =

< COI.. Il, ANO START NEW t»*«* FOR NEXT TALLY.

-.-¡j pQ„ SAMPLE IS Ctt|.;.n.ETËO AT RISH

§TX TALLY SHggT

iU^ ADMIN. UNIT

^"^ RANGER DIST.

SALE NO NAME

PAY UNIT

DATE If col. 25 is code 2, UDT Is taper in

inches per foot, to .000", and IML is

ength of unseen section in whole feet

izi^lt^l^p iJJUT

BKA

hP I !^;rLlj¿.yÉi; L^u?iji<>¿^

DI i : I I I II 11 i 111 1111 m

DENDROMETER CARDS FOR ABOVE SAMPLE TREE (9-CARD LIMIT)

_ TREE NO J T GRADS F GRAOS SICiELV GR

^^,WCcrdV 1 1 kTP/HBflHAI ^L|9^i9 \McW- 1 \^. \a 1 "

"i 1 1 \3\z)4 1 1 fu le A^r

«14*1^16 f\/ \a\7 /|/|AJ£ig. ^M =^|4¿|^^ \^\7¥ /\¥ / 1/ IÄ »1

^'^^^^H1 i lî^WÊÊÊÊsm ^\'J\9 \3í\á\n /inf</-\ù <'\M

II ^-?l9i^ 1 1 I c\4

1 1 •H 1 ,-K^ 1 ! 1 1

1 i 1 1 1 ! M ^

Ne^Cor„\ | | | j,m||j||||Bi 1 1 lili

1 1 lili

1 1 1 i! i 1

' ' u i 1 i 1 i

Ne^C<.rä\ 1 1 ¡ UWSÊÊUM 1 ! 1 1 II

1 1 1 1 1

1 1 1 i 1

i 1 1 i 1 1 1

Neuí Card j | | | 15VHEBHHI I 1 i 1 i !

L1 J ! 1 II 1 ! I 1 _LI_Ij1 1 !

1 I 1 I 1

/Ve». Cartf! 1 I ! ifÉi^^^lB 1 1 ! ! 1

I i ""

1 1 1

1 1 1 1

<v«H' coTorl i \ |V0HmriE 1 i 1 1 i ! 1

1 1 i

1 1 1

¡ 1 1 1

«•""rrfi i ! 1 I^HHHkfl 1 1 1

1 1 1

1

1 1 1

1 i 1 1

A'rM'Cartfi | ! ! IdlÜiteÉÉyi L i 1 i

i 1 i 1 1 1 1

II 1 _^ 1 1 1 1 1 !

REMARKS ST #?. If col. 25 Í3 code 2, both I3ML and ÜDT

qre required. At least one measured section, preferab1y

120
TF^SE CAf^öS; CO -S. 1- M FOR kLL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COL. II, AND START NEW PAOE FOR NEXT TALLYJ

TREE CARD FOR SAMPLE IS COMPLETED AT RIOHT.

STX TALLY SHEÇT

cmgT

TREE NO.

O*N*LY") KP¡

3

-gUTfo^jAi"

INFORMATION

^^ BAMßFO niCT

«ÎAI F NO- NAMF

PAV HUIT r.DFUi -

M-V 6 7BU ^^^^^^H DATE PAGE OF 1

/ 1 1 1 /\9 1 _,

2 1 1 i 7IÍ 1 ^ TREE CARD CONTINUATION FOR SAMPLE TR^g

S 1 1 1 / z\t / = — CLASS OBH OPT. BKA BKB UML UDT

te. .

4 1 ) 1 L\ó\vvim \t\xw^cmf^\€m \ i/i/i i uvm \ \\\ \

5 1 Z 17 23 27 SI 36 39

6 i M 1 1 ; 1 1 : 1 1 1 i 1 1 1 M i M 1 M 1 1 1 1

7 « XTRA »r XTRB 72

a ! 1 .^TlwavQ roe-n-rA a4crna1 /'4-l-N \^a-^a t-/^

9 1 1 Ar\AAfa^t>' ( na^T llm0n^ uao n>/%i.a/1 /-.na /-.^ i

IP _ -_ 1 „_

12 -

1 -- N,wCard\> 1 \/\a¥lWBÊBÊÊBÊtm F6Rft2§_ S'N^LV

l-^.IO -

13 1 "! 1 1 libio jg'l.ld TTA ^

14 1 «l-V^/lf i?i¿i/ / a\i\?\€> 4\/i u<«

15 1 "w^r \W^ J í.\y\/\ó A^A «,

16 1 N»wCard\ 1 \A£A9^^^m^ irf/i4* !?!7Lr / a.\7\^\A SU)

17 1 !Jtö!^ \r,^3 Ab\9\S\o ^\/9

18 î lít/lr i^aif /irr<!^i4» <^fi

19 1 1^14 !7i^ir /\S\'9\7\o c\\i f^

SO ! N,wCOrä\ 1 1 i UHHHBI i 1 1 ! 1 III 1

21 1 i 1 1 1 1 1 1

1

22 1 1 1 1 Mil 1

23 1 1 1 1 1 1 1 1 1 ]

24 1 1 /V..C»rJ 1 1 1 UHHHHi 1 1 lili

25 i 1 1 1 1 1 1 1 "-p

2e 1 i 1 Il i 1

27 1 1 1 1 1 1 1 1 1

28 1 N,w Card\ 1 1 1 l^^imil^^^ 1 i 1 i 1 1 I 1

29 ! 1 1 1 1 1

1

30 1 1 1 ! 1 1 i

31 1 ! 1 1 1 1 1 1

32 ! NtwCarA 1 ! Ui^HHH 1 1 1 MI!

33 1 1 1 II 1 !

34 1 1 lili

35 I 1 1 1 ! ! 1 1

36 1 1 \rWÊÊIÊÊKÊIÊÊÊ 1 ! Mil

37 1 1 1 1 M 1

38 1 1 lili

39 1 i Mil 1

40 N9W Card 1 1 1 1 JAJBHHHHÍ 1 1 Mil

41 1 1 i 1 M 1

42 1 1 1 1 MM

43 1 1 1 1 Mil !

44 NemCard\ \ | | l.oHHKHÉ 1 i 1 1 ! Il M i

45 i 1 1 MM 1

46 1 ¡ 1 1 ! i M II

47 1

i

1 ! ! 1 1 i lit! 1 i

48 1 i »cyAo..f ST #10. Instrument avay se tojved for better

49 1 1 visibility. If move is on the same contour^ recording

SO ! ! ... _.. »roceeda as though instrument was not moved.

121
TREE CARDS- COLS. I - II rout ALL TWEES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COC. II, ANO START NEW PAOE FOR NEXT TALLY.

TREE CARO FOR SAMPLE IS COMPLETED AT R

^^ $TX TALLY SHEET

jJM ADMIN UNIT

^*^ RANaPB ni$T

SALE NO._ NAMF

PAY UNIT r.BFW

DATE -PAGE. ..OF

122
TREE CARDS. COLS. i-ii POR ALL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR s

IN COfL. II, AND START NEW PAOE fOR NEXT TALLY.

TREE CARD FOR SAMPLE IS COMPLETED AT RISHT.

§TX TALLY SHÇÇT

TREE NO.

(SAMPLES

ONLY) KPl

£ii

IH%«MAT1-OH

^^ RANÍTFR DIST.

PAY umr ASingle Bark Measurement "^ , A-V e . •l> 10 ,, ^ ^^^H DATE 1 is recorded a:! BKA. Two

.nts as BKA anc

\0F /_ i 1 il£ l_ _ /ol \bark measuremc 1 Bra/

3 1 ! ~JL

1 L ?L 2J_

CLASS DBH OPT. f BKA BKB X UML UDT

4 1 1 L\4\^\fi^m i^lf|.irB/!/biÉ i \A^ 1 1 i> \A<.\A7\o »~

5 lïï!

€ 1 1 1 1 ! ! 1 1 ; i 1 1 ¡ M 1 1 I'T 1 1 1 1 ! 1 M 1 i 1

7 .

« XTRA 57 XTRB ^2

B

9

10 DENDROMETER CARDS FOR ABOVE SAMPLE TBEE^ (9-CARD LIMIT)

II 1 TREE NO. j T GRAOS F GRADS SINELV GR

12 I N»wCorä\ 1 l/blH/^lH^^ '^-l^lflf IJiJi# 1 \^,\c 1 -

13 1 "1 1 1 1^1 ilf 1 !il. le 4A r

14 1

""W/S

k

7T

IS I

16 1 N,wCara\ 1 U\x\pWÊKÊÊÊÊÊk W\*A8 i\ /!? yl^ít^ÍAld ^^A

IT ! 44n? \i\S\'7 /\6.\'i\t\A r,\/i

IS 1 -It fl^ MM C\A

19 1 1 r i 1 M ^

20 i M..CarA 1 1 1 U^HHIH 1 M 1 i

21 i 1 i ! i 1

_J2_^ 1 1 Mil

\23 1 1 1 1 II M

24 i V..C...I 1 i 1 UHMHl 1 1 M

25 1 i 1 1 1 1

2e 1 1 1 1

27 1 1 1 1 1 1

28 i N,y, CorA 1 ! ! XfsWÊÊUKÊÊk ! ! M 1

29 i 1 1 M II ¡

30 i 1 1 !

31 ! 1 i 1 ^1 1 1

32 ! New coral 1 1 1 UHlHHi Il M

33 ! MM

34 1 MM

35 1 i M II

3e ! N,wCord\ 1 1 1 [TWÊÊKÊÊÊM 1 ¡Ml

37 1 1 1 M i

38 I ! 1 1 II

39 1 1 1 M 1

40 1 N,wCord\ 1 ! 1 !« 1 M II

41 ! 1 ¡ MM

42 1 ! Ml!

43 1 1 ! 1 M

44 1 NewCurA 1 i 1 {« H i i i M

4S 1 1 M i

46 1 MM

S

47 1 1 Mil

48 1 RFMARK«; ST #12. If only one single bark is measured.

49 1 . it Is recorded BKA. Proeram doubles it. If two bark

SO 1 ) 1 ^re recorded as BKA and B KB, pro Rras0 adds them.

123
La¿E CARPS, CO s. 1- n FOR »LL TREES. 1 WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

iN COL. II, AND START NEW PAOE fOH NEXT TALLY

TREE CARD FOR SAMRLE IS COMPLETED AT RIOHT.

STX TALLY SHEET

—1

¿ouw

TREE NO

KPI í INFORMATION

(Li^ ■■- ' ' '

<ÏAI F Wn NAMP

1 ^\l\. e M- 10 H^^^^^H *V PAGE OF

W\f. ( ^

¿ Aó\L / LF TRPP

3 ^o / CLASS DBH ^ oak. BKA SKS UML UDT

w¿

4 ^S / L\4^^AAm \A^.\BM/l3Lm i 1 !¿l 1 !/!<*' 1 1 ( 1 T"

5

.fl<? A. 2 ir ZsW^ 27 3. 36 Ss"

S ?!<. / ! ! 1 ! 1 M I ; i 1 1 1 1 1 i ! M 1 i 1 1 ! 1 1 1 i 1 1 1

7

/13 (

» XTRA 5T XTR6 ' ^ ^72 '

S 1 1 1 f*/? í

9 1/ l II? / ^

10 1 DENDROMETER CARDS FOR ABOVE SAMPLE TRFF fS-r.ARn MMITÍ

II i TREE NO. J T CRAOS F GRAOS SINELV GR

12 1 ¡ Ntw corA' \ l/kp/^^^^mmig '^m<f \X*á5 1 \^,\6 I "

13 -1 1 i \MM 1 ií!'l¿> 4\/9 ^

'4^ ^S^A !/l¿!J /U\¡^\-7\u AA

15 \ \ ^\JA^'J ! $r;/ /\3li\^aM ''I

î€ i ! ^e.CorA 1 lyl^pimiSHM ^^7\ ! -i ÍT4 /Wá'ifid <n^

17 1 1 Ji^tj^ Í7¡>i3 ^JT-Tfi^ia €:0^

!8 hi i ! 1 1 1 1 i !

19 1 ! i ! 1 Í~T^ 1 1 i 1 Ä!

20 i 1 I

/v.«.c»rrf| 1 1 1 UIHHHMÉ 1 1 1 L i ' i j lili i

21 1 1 1 I ! 1 1 ' 1 ! 1 ! 1

2k ! 1 1 1 ¡ ¡ 1 lili

23 1 1 1 1 1 1 1 1 I 1

1 !

24 1 New Card] I I I I^H^SHH 1 1 i 1 1 i MM

25 1 i ! 1 i ' ! 1 i 1 ._,_ 2e 1 1 !

1 i í

1 i ! ! M i

27 1 L ! I 1 i ! M

.... 1 28 1 i /Vi«-cor<^i ! ! ! UHB^^KHM

¡ 1 I '

i 1 1 ~11 1 '

MM 1

29 1 i 1 ~r'

30 1 1 i 1 i i I ^M M ,

i

31 1 1 i 1 1 ! 1 MM

-__ "1

32 1 /veM'cortfj 1 1 1 ïe^KMÈÊS^M ¡ í i i i I Mil 1

33 I 1 1 1 i ¡ 1 1 II 1

34 1 1 1 .l_Ll.. MM r~

3S 1 1 !

L|-|___

Il M

___^

3ilu_ 1 1 ! Hc^CorÁ 1 1 1 IrW il il ¡ i i ^ i i 1 MM

37 Î \ ! 1 1 i i T' 1 . 1 1

38

i 1

! 1 1 j III! 1

39 MI] MM

40 ...corA \ 1 1 UHHHi I 1 i MM ; */ 1 i 1 ! 1 1 Mil

42 1 J_

""l ! 1

1 ! ! MM i

43 i ! i 1 1 ! 1 1

44 /v«H. ctTrtf 1 i 1 1 isüHHHH 1 ! ¡ ! 1 i. II M 1

45 ! \ \ 1 i 1 M M"^ 1

46 1 i i MM

47

5

1 ! 1 1 ! 1 Mil !

48 VT\ FMARKs ST #13, Col. 24 under OPT codes the awthod to

49 ! 1 1 be used for reducing outslde-bark stem diactetçi:? to

sa ! 1 i L food diameters.

124
TREE CARDS. COLS. 71"IT FOR ALL TREES.

WHEN A SAHPLt TREE IS «ACHBO, SHOW » 0« =

IN COL. II, AND START NEW PAOC FOR NEXT TALLY.

TREE CARD FOR SAMPLE IS COMPLETED AT RISHT.

ÇTX TALLY SHÇÇT

>UNCH

tREE m

TREE NO.

(SAMPLES

ONLY) KPI i1 INFORMATION ::i^:° v^^ «»i- '" -" ""^i

lUUU. .ITI.U ^^^^^^H DATE 1 ^ ^'^ DianK y PAGE OF

1 1^14^ /

lUiB/lXJB » _yu^^

2 1 \X\S /

„

3 1 iflr J

, CLASS DBH a^ BKA BKB^^ UML UDT .

* 1 _ _ Ifl3 A - \Miiv\^m l;^l/Ui^(l 1 1 1 1 1 1 lip 1 1 1 M 1 1

6 - iW f _ 1 1 M 1 ; M : i M 11 i 111 II M II 1 1 1 1 1 i

7

*^f » . « XTRA S'' XTRB «

8 l\ f AJ9 3l¿ ( »ff

lO ^\f (

II *f ( _ T GRADS F GRAOS SINELV GR

12 IVI** / , cor^liAAitMimiKÊ ^WU\¥- /\/\c\S -IdLd/lo 1

13 /lA ;i 4/ nM/L3 l^l/ly -Ul^lVlO 4^

14 f^^ i «i4í/iy \2\sr\i »-I/I5I^I¿> ^^

15 / w- / ^\X ^ a « "\^5b. I/Ü1/ +i3l?ijrií C\A "

te N,^Car<,\ 1 ly|44^H^HHi \MQ7. 17! ti/ •*-liTci*iô c\^

17 \¥\7\r iTl^lfl -^^L\^\¥^ c\A

IB 1 1 1 1 I 1 1 1

19 1 1 1 I 1 1 1 ^

20 U,wCor.l\ 1 1 1 IJHHI^B 1 1 lili

21 1 1 1 1 1 1 1

22 1 1 1 lili

23 1 1 1 1 1 1 1 1

24 N»wCor</[ 1 ¡ UHHHIH 1 1 1 1 M 1 1

25 1

1 II 11

26 1 1 1

27 1 1

28 New Cttrd\ 1 1 1 I.^IHBHB 1 1 lili

29 1 1 lili

30 1 Il 1 1

31 1 1 1 1 1

32 /Vei» Cortff 1 1 UIHIHH 1 1 1 1 II

33 1 1 1 1 1 1 1

34 1 1 1 lili

35 1

36 1 1 1 IT'BHHBBI 1

37

38 1

39 1 1

40 1 1 ItfH^HlH

41 1 1

42 1

43

44 /VeirCffri/l | | | [« ¡ H

45 1 1

46

. 1 1 i 1 1 i 1

47 1 1 1 1 Mil 1

48 »PM.«.<: ST *14. If col. 24 under OPT is blank, and ti o

49 hark thickness Is recorded, oroeram assumes Dlb/Doh^s

50 _J ___ ^u

125
TREE CARDS, COLS, I-II FOR ALL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COL. II, AND START NEW PAGE FOR NEXT TALLY.

TREE CARD FOR SAMPLE IS COMPLETED AT RI8HT.

TREE NO.

(SAMPLES

ONLY ) m

mil 3¡n

\MC

-ZL4.

_ZU.

-MAJ

i/l> ,

.Jal.

-A±u

-3\3..

A^it

lAll

VéU

Mtl.

\'Af

_MZ:

JAL

m.£JL

h^.

É

_£^

M^ AOMIN. UNIT

^"^ RANGER DIST. _

SALE NO NAMEPAY UNIT CREW -

DATE

STX TALLY SHEET

TREE CARD CONTINUATION ^QR SAMPLE TREE

CLASS ^L UDT DBH OPT. BKA BKB U

Vfmvvtm \Ai\ ^ / x\^m 1 1 1/1 1 \/\M TTTTIf 31 36

1 1 1 i 1 1 : M ; i ¡ 1 i 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1

« XTRA 57 XTRB 72

DENDROMETER CARDS FOR ABOVÇ .SAMPLE TREE (9-CARD LIMIT)

ST #15. Trees forked above breast height are |_^

measured by terminating the single stem section_J__J

with (+) sign. Each prong except the last is

also terminated with a (+) sign. The tallest

prong is left till last and is terminated with_

an (*) to indicate that next card is for a new _

tree. Measurements for each prong begin at

base of prong.

i

126
TREE ÇARDSr COLS, I-II FOR ALU TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COL. II, ANO START NEW PAOE FOR NEXT TALLY.

TREE CARD FOR SAMPLE IS COMPLETED AT RIQHT.

TREE NO.

ONLY HE

J4i!ra,

1^14

¿il

31i

A

AL

/J£L

f\^

nzz wi

\o±

STX TALLY SHEET

_^^

n^ ADMIN. UNIT -

^^ RANGER DIST. _

SALE NO NAMEPAY UN IT CREW -

DATE

TRgg CAI^D CONTINUATION FQR ?AMPLE TREE

CLASS DBH . OPT, BKA BKB U ^L UDT

l/^rli^l»« \A/\.\/my\2\am 1 1 l/l 1 1 k4 1 1 1 1 1? ""ai '36 39

1 1 1 1 M ; 1 1 : 1 M 1 II 1 I ¡ 1 1 1 111 1 1 1 1 1 M 42 XTRA 57 XTRB «

PENPROMETER CARPS FOR ABOVE TREE (9-CARD LIMIT)

New Cord]

^endrometry is terminated

at total height when tip

^TGRADS + 0.1 = FGRADS 1*/

REMARKS ST #16. To terminate dendrometry at total

height, measure TGRADS to terminal leaf (if feasible),

and SINELV. Make FGRADS - (TGRADS + C.l) as shown above.

127
TREE CARDS, COLS, I-II ron ALL TREES.

WHEH A SAMPLE TREE IS REACHED, SHOW » OR _

. II, ANO START NEW PASE FOR NEXT TALLY.

JARD FOR SAMPLE IS COMPLETED AT RI6H

TTTTT s SITISI»

1±

JJL

-LL

Jzii mi

LíLí

IAL

ASL±

jh.

¿Í?

laiA

I If

M:

iali

Üö.

Mi

IgUó

44i JIMZ

-Jiii.

I I

TT

I I

I I

n

n

TT TT

^^ §TX TALLY SHEET

jÎJ^ ADMIN UNIT __

"""^ RANGER DIST

i SAI F NO NAMP

i PAY UNIT rOFW 1 LMTE PAGE OF 1

TREE CARD CONTINUATION FOR SA MPI F TREÇ

UML UDT CLASS OBH OPT. BKA BKB

\j.U\^Um \y\fu \omAs\ûm i 1 1 1 M "TTTTT3f

a 17 "36 3»

1 1 1 M 1 ! 1 1 ; i 1 1 i II 1 1 1 1 1 1 1 Mil

« XTRA ST

1 1 1 u XTRB n

PENPROMEiet? CARP? FOR ABOVE SAMPLE TREE (9-CARn MMIT^

TREE --. . T GRADS F GRADS

n N,wcara\ 1 1 l^i^HIHI 1 i 1 1 1 f II 1 1

1 ~T"

1 j

N,wcarä\ 1 1 i^^lHIHI 1 1 1 1

1 1 1 1

1 1 1

1 II

NewCorä\ \ 1 1 UWÊ^^KÊ

1 H 1 1 1

1 1 1 ~i""

1 1 1

1 1

1 1 j

M,w coral 1 1 |;'H^^H 1 1 "7~"

1 1 1

1 1

1 1 j

'^»u. carol 1 1 1 IsW^E^m 1 1 1 T"

1 1 1

1 1 I

1 1 1 J Mem coral \ | | [.« ^ H 1 1 1 1

1 1 1 -r

1 1 1

1 1 1

1 1

REMARKS ST #17. If TGRADS to t<jp are not feasible.

measure approx. SINELV at total leight. Record BôtîÏ

TGRADS and FGRADS as -999 to obtain a computer prolectlor

128
TREE CARDS, COLS, I - II FOR ALL TREES.

WHEN A SAMPLE TREE IS REACHED, SHOW » OR =

IN COL. II, ANO START NEW PAOE FOR NEXT TALLY.

TREE CARD FOR SAMPLE IS COMPLETED AT RISHT.

I I TT

' l/l<

TT

}¿UL.

^p. §TX TALLY SHgET

g^ AOMIN "MIT

*-^ RANfiPP ni«T

SALE NO. _ NAMF

PAY IIMIT rOFW

LBAIE PAGE OF

129
Natural Sines, Cosines and Tangents

0°-14.9*»

Degs. Function o.o° 0.1° 0.2° 0.3° 0.4° cs" 0.6° 0.7° 0.8° 0.9°

sin o.oooo 0.0017 0.0035 O.O0S2 0.0070 0.0087 o'.oios 0.0122 0.0140 0.0157

0 cos I.OOOO I.OOOO I.OOOO I.OOOO I.OOOO i.ooooj 0.9999 0.9999 0.9999 0.9999

tan o.oooo 0.0017 0.003s 0.0052 0.0070 0.0087' o.oios 0.0122 0.0140 0.0157

sin 0.0I7S 0.0192 0.0209 0.0227 0.0244 0.0262: 0.0279 0.0297 0.0314 0.0332

1 cos 0.9998 0.9998 0.9998 0.9997 0.9997 0.9997 o.9996^ 0.9996 0.9995 0.999S

tan 0.0I7S 0.0192 0.0209 0.0227 0.0244 0.0262 0.0279: 0.0297 0.0314 0.0332

sin 0.0349 0.0366, 0.0384 0.0401 0.0419 0.0436 0.0454 0.0471 0.0488 0.0506

2 cos 0.9994; 0.9993! 0.9993 0.9992 0.9991 0.9990 0.9990 0.9989 0.9988 0.9987

tan 0.0349 0.0367

0.0523 0.0S4I

0.0384 0.0402 0.0419 0.0437 0.0454 0.0472 0.0489 0.0507

sin 0.0558 0.0576 0.0593 0.0610 0.0628 0.0645 0.0663 0.0680

3 cos 0.9986' 0.9985 0.9984 0.9983 0.9982 0.9981 0,9980 0.9979 0.9978 0.9977

tan 0.0524 0.0542 O.OS59 0.0577 0.0594 0.0612 0.0629 0.0647 0.0664 0.0682

sin

1 1

0.06981 0.0715: 0.0732 0.0750 0.0767 0.0785 0.0802 0.0819 0.0837 0.0854

4 cos 0.9976 0.9974 0.9973 0.9972 0.9971 0.9969 0.9968 0.9966 0.9965 0.9963

tan 0.0699' 0.0717 0.0734 0.0752 0.0769 0.0787 0.0805 0.0822 0.0840 0.0857

sin 0.0872 0.0889 0.0906 0.0924 0.0941 0.0958 0.0976 0.0993 O.IOII 0.1028

5 cos 0.9962 0.9960 0.9959 0-9957 0.9956 0.9954 0.9952 0.9951 0.9949 0.9947

tan 0.08751 0.0892I 0.0910 0.0928 0.0945 0.0963 0.0981 0.0998 O.IOI6 0.1033

sin 0.l045j 0.1063 0.1080 0.1097 0.III5 0.II32 0.1149 0.1167 O.II84 0.120J

6 cos 0.9945 0.9943; 0.9942 0.9940 0.9938 0.99.36 0.9934 0.9932 0.9930 0.9928

tan 0.1051 0.1069 0.1086 0.1104 O.II22 0.1139 0.1157 0.ÏI7S O.II92 0.1210

sin 0.1219 0.1236 0.1253 0.1271 0.1288 0.1305 0.1323 0.1340 0.1357 0.1374

7 cos 0.9925 0.9923 0.9921 q.9919 0.9917 0.9914 0.9912 0.9910 0.9907 0.9905

tan 0.1228 0.1246 0.1263 0.1281 O.X299 O.I3I7 0.1334 0.1352 0.1370 0.1388

sin 0.1392 0.1409 0.1426 0.1444 0.146Ï 0.1478 0.1495 01513 0.1530 0.1547

8 cos 0.9903 0.9900 0.9898 0.9895 0.9893 0.9890 0.9888 0.9885 0.9882 0.9880

tan 0.1405 0.1423 0.I44I 0.1459 0.1477 0.1495 0.1512 0.1530 0.1548 0.1566

sin 0.1564 0.1582 0.1599 o.i6i6 0.1633 0.1650 0.1668 0.168s 0.1702 0.1719

9 cos 0.9877 0.9874 0.9871 0.9869 0.9866 0.9863 o;986o 0.9857 0.9854 0.9851

tan 0.1584 0.1602 0.1620 0.1638 0.1655 ,0.1673 0.1691 0.1709 0.1727 0.1745

sin 0.17.36 0.1754 O.I77I 0.1788 0.1805 0.1822 0.1840 0.1857 0.1874 0.1891

10 cos 0.9848 0.9845 0.9842 0.9839 0.9836 0.9833 0.9829 0.9826 0.9823 0.9820

tan 0.1763 O.I78I 0.1799 0.1817 0.1835 0.1853 0.1871 0.1890 0.1908 0.1926

sin 0.1908 0.1925 0.1942 0.1959 0.1977 0.1994 0.2011 0.2028 0.2045 0.2062

11 cos 0.9816 0.9813 0.9810 0.9806 0.9803 0.9799 0.9796 0.9792 0.9789 0.9785

tan 0.1944 0.1962 0.1980 0.1998 0.2016 0.2035 0.2053 0.2071 0.2089 0.2107

sin 0.2079 0.2096 0.2II3 0.2130 0.2147 0.2164 0.2181 0.2198 0.2215 ^.2232

12 cos 0.9781 0.9778 0.9774 0.9770 0.9767 0.9763 0.9759 0.9755 0.9751 0.9748

tan 0.2126 0.2144 0.2162 0.2180 0.2199 0.2217 0.2235 0.2254 0.2272 0.2290

sin 0.2250 0.2267 0.2284 0.2300 0.2318 0.2334 0.2351 0.2368 0.2385 0.2402

13 cos 0.9744 0.9740 0.9736 0.9732 0.9728 0.9-724 0.9720 0.971S 0.97II 0.9707

tan 0.2309 0.2327 0.2345 0.2364 0.2382 0.2401 0.2419 0.2438 0.2456 0.2475

sin 0.2419 0.2436 0.2453 0.2470 0.2487 0.2504 0.2521 0.2538 0.2554 0.2571

14 cos 0.9703 0.9699 0.9694 0.9690 0.9686 0.9681 0.9677 0.9673 0.9668 0.9664

tan 0.2493 0.2512 0.2530 0.2549 0.2568 0.2586 0.2605 0.2623 0.2642 0.2661

Degs. Function 0' 6' 12' 18' 24' 30' 36' 42' 48' 54'

130
Natural Sines, Cosines and Tangents

15 ^-29.9'»

Degs. Function o.o° 0.1° 0.2° 0.3° 0.4° 0.5° 0.6° 0.7° 0.8° 0.9°

sin 0.2S88 0.2605 0.2622 0.2639 0.2656 0.2672 0.2689 0.2706 0.2723 0.2740

15 cos 0.9659 0.9655 0.9650 0 9646 0.9641 0.9636 0.9632 0.9627 0.9622 0.9617

tan 0.2679 0.2698 0 2717 0.2736 0.2754 0.2773 0.2792 0.281I 0.2830 0.2849

sin 0.2756 0.2773 0.2790 0.2807 0.2823 0.2840 0.2857 0.2874 0.2890 0.2907

16 cos 0.9613 0 9608 0.9603 09598 0.9593 0.9588 0.9583 0.9578 0 9573 0.9568

tan 0.2867 0.2886 0.290s 0.2924 0.2943 0.2962 0.2981 0.3000 0.3019 0.3038

sin 0.2924 0.2940 0 2957 0.2974 0.2990 0 3007 0 3024 0.3040 c 3057 0.3074

17 cos 0.9563 0.9558 0.9553 0.9548 0.9542 0.9537 0.9532 0.9527 0.9521 0.9516

tan 0.3057 0.3076 0.3096 0.3115 0.3134 0.3153 0.3172 0.3191 0.32II 0.3230

sin 0.3090 0.3107 0 3123 0.3140 0.3156 0.3173 0.3190 0.3206 0.3223 0.3239

18 cos 0.9511 0.9505 0.9500 0.9494 0.9489 0.9483 0 9478 0.9472 0.9466 0.9461

tan 0.3249 0 3269 0 3288 0.3307 0.3327 0.3346 0 3365 0.338s 0..3404 0.3424

19

sin 0 3256 0.3272 0.3289 0.3305 0.3322 0.3338 0.3355 0.3371 0.3387 0.3404

cos 0.9455 0.9449 0.9444 0.9438 0.9432 0.9426 0.9421 0.9415 0.9409 0.9403

tan 0.3443 0.3463 0.3482 0.3502 0.3522 0.3541 0.3561 0.3581 0.3600 0.3620

sin 0.3420 0.3437 0.3453 0.3469 0.3486 0.3502 0.3518 0.3535 0.3551 0.3567

20 cos 0.9397 0.9391 0.9385 0.9379 0.9373 0.9367 0.9361 0.9354 0.9348 0.9342

tan 0.3640 0.3659 0.3679 0.3699 0.3719 0.3739 0.3759 0.3779 0.3799 0.3819

21

sin 0.3584 0 3600 0.3616 0.3633 0.3649 0.3665 0.3681 0.3697 0.3714 0.3730

cos 0.9336 0.9330 0.9323 0.9317 0.9311 0.9304 0.9298 0.9291 0.9285 0.9278

tan 0.3839 0.3859 0.3879 0.3899 0.3919 0.3939 0.3959 0.3979 0.4000 0.4020

sin 0.3746 0.3762 0.3778 0.3795 0.3811 0.3827 0.3843 0.3859 0.3875 0.3891

22 cos 0.9272 0.9265 0.9259 0.9252 0.9245 0,9239 0 9232 0.9225J 0.9219 0.9212

tan 0.4040 0.4061 0.4081 0.4101 0.4122 0.4142 0.4163 0.4183 0,4204 0.4224

sin 0.3907 0.3923 0.3939 0.3955 0.3971 0.3987 0,4003 0.4C19 0.4035 0.4051

23 cos 0.9205 0.9198 0.9191 0.9184 0.9178 0.9171 0,9164 0.9157 0.9150 0.9143

tan 0.4245 0.4265 0.4286 0.4307 0.4327 0..I348 0.4369 0.4390 0.44II 0.4431

sin 0.4067 0.4083 0.4099 0.411S 0.4131 0.4147 0.4163 0.4179 0.4195 0.4210

24 cos 0.9135 0.9128 0.9121 0.9114 0.9107 0.9100 0.9092 0.9085 0.9078 0.9070

tan 0.4452 0.4473 0.4494 0.4515 0.4536 0.4557 0.4578 0.4599 0.4621 0.4642

sin 0,4226 0.4242 0.4258 0.4274 0.4289 0.4305 0.4321 0.4337 0.4352 0.4368

25 cos 0.9063 0.9056 0.9048 0.9041 0.9033 0.9026 0.9018 0.901.T 0.9003 0.8996

tan 0.4663 0.4684 0.4706 0.4727 0.4748 0.4770^ 0.4791 0.4813 0.4834 0.4856

sin 0.4384 0.4399 0.4415 0.4431 0.4446 0.4462 0.4478 0.4493 0.4509 0.4524

26 cos 0.8988 0.8980 0.8973 0.8965 0.8957 0.8949 0.8942 0.8934 0.8926 0.8918

tan 0.4877 0.4899 0.4921 0.4942 0.4964 0.4986 0.5008 0.5029 0.5051 0.5073

sin 0.4540 0.4555 0.4571 0.4586 0.4602 0.4617 0.4633 0.4648 0.4664 0.4679

27 cos 0.8910 0.8902 0.8894 0.8886 0.8878 0.8870 0.8862 0.8854 0.8846 0.8838

tan O.SC95 0.5117 0.5139 0.5161 0.5184 0.5206 0.5228 0.5250 0.5272 0.5295

sin 0.4695 0.4710 0.4726 0.4741 0.4756 0.4772 0.4787 0.4802 0.4818 0.4833

28 cos 0.8829 0,8821 0.8813 0,8805 0.8796 0.8788 0.8780 0.8771 0.8763 0.8755

tan 0.5317 0.5340 0.5362 0.5384 0 5407 0.5430 0.5452 0.5475 0.5498 0.5520

sin 0.4848 0.4863 0.4879 0.4894 0.4909 0.4924 0.4939 0.4955 0.4970 0.4985

29 cos 0.8746 0.8738 0.8729 0.8721 0.8712 0.8704 0.8695 0.8686 0.8678 0.8669

tan 0.5543 0.5566 0.5589 0.5612 0.5635 ©.5658 0.5681 0.5704 0.5727 0.5750

Degs. Function 0' & 12' 18' 24' 30' 36' 42' 48' 54'

131
Natural Sines, Cosines and Tangents

30*»-44.9'»

Degs. Function o.o° 0.1"» o.a' 0.3" 0.4' 0.5' 0.6" 0.7' 0.8* 0.9^

sin 0.5000 0.5015 0 5030 0.5045 0.S060 0.507S 0.5090 0 5105 0.5120 0.5135

30 cos 0.8660 0.8652 08643 0.8634 0.8625 0.8616 0.8607 0.8599 0.8590 0.8581

tan 0.5774 0.5797 0 5820 C.5844 0.5867 0.5890 0..5914 05938 0.5961 0.5985

sin 0.5150 0.5165 0 5184 0.5195 0 52IO 0.5225 0.5240 0 5255 0.5270 0.5284

31 cos 0.8572 0.8563 0 8550 08545 0.8536 0.8526 0.8517 08508 0.8499 0.8490

tan 0.6009 0.6032 0 6056 0 6080 0 6104 0 6128 0.6152 0 6176 0.6200 0.6224

sin 0 5299 0.5314 0.5329 0.5344 0 5.358 0.5373 0 5.Î88 0 5402 0.5417 0.5432

32 cos 0 8480 0.8471 0.8462 0.8453 0.8143 0.8434 0.8425 0 8415 0.8406 0.8396

tan 0.6249 0.6273 0.6297 0 6322 0.6346 0.6371 0 6,395 0 6420 0.6445 0.6469

sin 0.5446 0.5461 0.5476 0.5490 0.5505 0.5519 0.55.34 0 5548 0.5563 0.5577

33 cos 0.8387 0.8377 0.8368 0.8358 0.8348 0.8339 0.8329 0.8320 0.8310 0.8300

tan 0.6494 0.6519 0.6544 0.6569 0.6594 0.6619 0.6644 0 6669 0.6694 0 6720

sin 0.5592 0.5606 0.5621 0.5635 0.5650 0.5664 0.5678 0 5693 0.5707 0.5721

34 cos 0 8290 0 8281 0.8271 0.8261 0.8251 0.8241 0 8231 0 8221 0.8211 0 8202

tan 0.674s 0.6771 0.6796 0.6822 0.6847 0.6873 0 6899 0.6924 0 6950 0.6976

sin 0.5736 0.57SO 0.5764 0.5779 0.5793 0.5807 0.5821 0.583s 0.5850 0.5864

35 cos 0.8192 0.8181 0.8171 0.8i6i 0.8I5I 0 8141 0.8131 0 8l2I 0.8111 0.8100

tan 0.7002 0.7028 0.7054 0.7080 0.7107 0.7133 0.7159 0 7186 0 7212 0.7239

sin 0.S878 0.5892 0.5906 0.5920 0.5934 0 5948 0.5962 0.5976 0 5990 0,6004

36 cos 0,8090 0.8080 0.8070 0.8059 0.8049 0 8039 0.8028 0.8018 0.8007 0.7997

tan 0.7265 0 7292 0.7319 0.7346 0 7373 0.7400 0.7427 0 7454 0.7481 0.7508

sin 0.6018 0.6032 0.6046 0.6060 0.6074 0 6088 0 6101 0 6115 0 6129 0.6143

37 cos 0.7986 0.7976 0.7965 0.7955 0.7944 0.7934 0.7923 0.7912 0.7902 0.7891

tan 0.7536 0.7563 0.7590 0.7618 0.7646 0.7673 0.7701 0.7729 0.7757 0 7785

sin 0.6157 0.6170 0.6184 0.6198 0.6211 0.6225 0.6239 0 6252 0.6266 0.6280

38 cos 0.-7880 0 7863 0.7859 0.7848 0.7837 0.7826 0.7815 0 7804 0.7793 0.7782

tan 0.7813 0.7841 0.7869 0.7898 0.7926 0.7954 0.7983 0.8012 0 8040 0.8069

sin 0.6293 0.6307 0.6320 0.6334 0.6347 0.6361 0.6374 0.6388 0.640Ï 0.6414

39 cos 0.7771 0.7760 0.7749 0.7738 0.7727 0.7716 0.7705 0 7694 0.7683 0.7672

tan 0.8098 0.8127 0.8156 0.8185 0.8214 0.8243 0.8273 0 8302 0 8332 0.8361

sin 0.6428 0.6441 0.6455 0.6468 0.6481 0.6494 0.6508 0 6521 0.6534 0,6547

40 cos 0.7660 0.7649 0.7633 0.7627 0.7615 0.7604 0.7593 0.7581 0.7570 0.7559

tan 0.8391 0.8421 0.8451 0.8481 O.8511 0.854t 0.8571 0,8601 0 8632 0.8662

sin 0.6561 0.6574 0.6587 0.6600 0.6613 0.6626 0.6639 0.6652 0.6665 0.6678

41 cos 0.7547 0.7536 0.7524 0.7513 0.7S0I 0.7490 0.7478 0.7466 0-7455 0.7443

tan 0.8693 0.8724 0.8754 0.8785 0.8816 0.8847 0.8878 0.8910 0.8941 0.8972

sin 0.6691 0.6704 0.6717 0.6730 0.6743 0.6756 0.6769 0.6782 0.6794 0 6807

42 cos 0.7431 0.7420 0.7408 0.7396 0.7385 0.7373 0.7361 0.7349 0.7337 0.7325

tan 0.9004 0.9036 0.9067 0.9099 0.9131 0.9163 0.919s 0.9228 0.9260 09293

sin 0.6820 0.6833 0.6845 0.6858 0.6871 0.6884 0.6896 0.6909 0.6921 06934

43 cos 0.7314 0.7302 0.7290 0.7278 0.7266 0.7254 0.7242 0.7230 0 7218 0 7206

tan 0.9325 0.9358 0.9391 0.9424 09457 0.9490 0.9523 0.9.556 09590 0.9623

sin 0.6947 0.6959 0.6972 0.6984 0.6997 0.7009 0.7022 0.7034 0,7046 0.7059

44 cos 0.7193 0.7181 0.7169 0.7157 0.7145 0.7133 0.7120 0 7108 0 7096 0 7083

tan 0.9657 09691 0.9725 0.9759 0.9793 0.9827 0.9861 0.9896 0 9930 0.9965

Degs. Function o' & xa' 18' 24' 30* 36^ 42' 48' 54'

132
Natural Sines, Cosines and Tangents

46''-69,9''

Degs. Function 0.0** 0.1«» 0.2° 0.3' 0.4" 0.5° 0.6' 0.7° 0.8" 0.9"

sin 0.7071 0.7083 0.7096 0.7108 0.7120 0.7133 0.714s 0.7157 0.7169 0.7x81

45 cos 0.7071 0.7059 0.7046 0.7034 0.7022 0.7009 0.6997 0.6984 0.6972 0.695ft

tan I.0000 1.0035 1.0070 I.0105 I.0141 I.0176 I.OÍ2I2 1.0247 1.0283 1.0319

sin 0.7193 0.7206 0.7218 0.7230 0.7242 0.7254 0.7266 0.7278 0.7290 0.7302

46 cos 0.6947 0.6934 0.6921 0.6909 0.6896 0.6884 0.6871 0.6858 0.684s 0.6833

tan I.0355 1.0392 1.0428 1.0464 I.0501 1.0538 1.0575 I.0612 1.0649 1.0686

sin 0.7314 C.7325 0.7337 0.7349 0.7361 0.7373 0.7385 0.7396 0.7408 0.7420

47 cos 0.6820 0.6807 0.6794 0.6782 0.6769 0.6756 0.6743 0.6730 0.6717 0.6704

tan 1.0724 I.0761 1.0799 1.0837 1.0875 I.0913 I.0951 1.0990 I.1028 I.1067

sin 0.7431 0.7443 0.7455 0.7466 0.7478 0.7490 0.7501 0.7.513 0.7524 0.7536

48 cos 0.6691 0.6678 0.6665 0.6652 0.6639 0.6626 0.6613 0.6600 0.6587 0.6574

tan 1.1106 I.II45 1.1184 1 1224 1.1263 I.1303 I.1343 I.1383 I.1423 I.1463

sin 0.7547 0.7559 0.7570 0.7581 0.7593 0.7604 0.7615 0.7627 0.7638 0.7649

49 cos 0.6561 0.6547 0.6534 0.6521 0.6508 0.6494 0.6481 0.6468 0.6455 0.6441

tan I.1504 I.1544 I.1585 I.1626 1.Ï667 I.1708 I.1750 I.1792 1.1833 I.1875

sin 0.7660 0.7672 0.7683 0.7694 0.7705 0.7716 0.7727 O.77;í8 0.7749 0.7760

50 cos 0.6428 0.6414 0.6401 0.6388 0.6374 0.6361 0.6347 0.6334 0.6320 0.6307

tan 1.1918 I.i960 1.2002 1.2045 1.2088 1.2131 I.2174 I.2218 I.2261 1.2305

sin 0.7771 0.7782 0.7793 0.7804 0.7815 0.7826 0.7837 0.7848 0.7859 0.7869

51 cos 0.6293 0.6280 0.6266 0.6252 0.6239 0 6225 O.62II 0.6198 0.6184 0.6170

tan 1.2349 1.2393 I 2437 I.2482 1.2527 1.2572 I.2617 1.2662 1.2708 1.2753

sin 0.7880 0.7891 0.7902 0.7912 0.7923 0.7934 0.7944 0.795S 0.7965 0.7976

52 cos 0.6157 0.6143 0.6129 0.6115 0.6101 0.6088 0.6074 0.6060 0.6046 0.6032

tan 1.2799 1.2846 I.2892 1.2938 1.2985 1.3032 1.3079 1.3127 1.3175 1.3222

sin 0.7986 0.7997 0.8007 0.8018 0.8028 0.8039 0.8049 0.8059 0.8070 0.8080

53 cos 0.6018 0.6004 0.5990 0.5976 0.5962 0,5948 O.S934 O.S920 0.5906 0.5892

tan r.3270 I 3319 1.3367 I.3416 1.3465 I..3514 1.3564 I.3613 1.3663 I.3713

sin 0.8090 0.8100 0.8111 0.8121 0.8131 0.8141 0.8151 0,8161 0.8171 0.8181

54 cos 0.5878 0.5864 0.5850 0.5835 0.5821 0.5807 0.5793 0.5779 0.5764 0,5750

tan 1.3764 I.3814 1.3865 I.3916 1.3968 I.4019 I.4071 I.4124 1.4176 1.4229

sin 0.8192 0.8202 0.8211 0.8221 0.8231 0.8241 0.8251 0.8261 0.8271 0.8281

55 cos 0.5736 0.5721 0.5707 0.5693 0.5678 0.5664 0.5650 0.5635 0.5621 0.5606

tan I.4281 1.4335 1.4388 1.4442 1.4496 1.4550 1.4605 1.4659 1.471S 1.4770

sin 0.8290 0-8300 0.8310 0.8320 0.8329 0-8339 0.8348 0.8358 0.8368 0.8377

56 cos 0.5592 0.5S77 0.5563 0.5.548 0.5534 0.5.519 0.5505 0 5490 0.5476 0.5461

tan I.4826 1.4882 1.4938 1.4994 I.5051 1.5108 I.5166 Ï.S224 1.5282 1.5340

sin 0.8387 0.8396 0 8406 0.S415 0.8425 0.8434 0.8443 0.8453 0.8462 0.8471

57 cos 0.5446 0.5432 0.5417 0.5402 0.5388 0.5.373 0.5358 O.S344 0.5329 0.5.3T4

tan 1.5399 1.5458 I.5517 1-5577 1.5637 1.5697 1.5757 I.5818 1.5880 I.5941

sin 0.8480 0.8490 0.8499 0.8508 0.8517 0.8526 0.8536 0.8545 0.8554 0.8563

58 cos 0.5299 0.5284 0.5270 0.5255 0.5240 0.5225 0.5210 0.5195 0.5180 0.S165

tan 1.6003 1.6066 1.6128 1.6191 1.6255 I.6319 1.6383 1.6447 1.6512 1.6577

sin 0.8572 0.8581 0.8590 0.8599 0.8607 o.86i6 0.8625 0.8634 0.8643 0.8652

59 cos 0.5150 0.5135 0..5120 0.S105 0.S090 0.5075 0.5060 0.5045 0.5030 0.5015

tan 1.6643 1.6709 1.6775 1.6842 1.6909 1.6977 1.7045 1.7113 I.7182 I.7251

Degs. Function 0' 6' 12' 18' 24' ^ 30' 36' 42' 48' 54'

133
Natural Sines, Cosines and Tangents

60°-74.9«

Degs. Function 0.0* 0.x' 0.3» 0.3° 0.4- 0.5* 0.6» 0.7' 0.8» 0.9'

sin 0.866o 0.8669 0.8678 0.8686 0.8695 0.8704 0.8712 0.8721 0.8729 0.8738

60 cos o.5000 0.498s 0.4970 0.4955 0.4939 0.4924 0.4909 0.4894 0.4879 0.4863

tan I.7321 I.7391 I.7461 1.7532 1.7603 1.767s 1.7747 1.7820 1.7893 1.7966

sin 0.8746 0.8755 0.8763 0.8771 0.8780 0.8788 0.8796 0.880s 0.8813 0.8821

61 cos 0.4848 0.4833 0.4818 0.4802 0.4787 0.4772 0.4756 0.4741 0.4726 0.4710

tan 1.8040 I.8II5 I.8190 1.8265 I.8341 I.8418 1.849s 1.8572 1.8650 1.8728

sin 0.8829 0.8838 0.8846 0.8854 0.8862 0.8870 0.8878 0.8886 0.8894 0.8902

62 cos 0.4695 0.4679 0.4664 0.4648 0.4633 0.4617 0.4602 0.4586 0.4S7I 0.4SSS

tan 1.8807 1.8887 1.8967 1.9047 I.9128 I.9210 1.9292 1.9375 I.9458 I.9S42

sin 0.8910 0.8918 0.8926 0.8934 0.8942 0.8949 0.8957 0.896s 0.8973 0.8980

63 cos 0.4S40 0.4524 0.4509 0.4493 0.4478 0.4462 0.4446 0.4431 0.441S 0.4399

tan 1.9626 I.97II 1.9797 1.9883 1.9970 2.00S7 2.0145 2.0233 2.0323 2.0413

sin 0.8988 0.8996 0.9003 0.9011 0.9018 0.9026 0.9033 0.9041 0.9048 0.9056

B4 cos 0.4384 0.4368 0.4352 0.4337 0.4321 0.4305 0.4289 0.4274 0.4258 0.4242

tan 2.0503 2.0594 2.0686 2.0778 2.0872 2.0965 2.1060 2.1155 2.I2SI 2.1348

sin 0.9063 0.907c 0.9078 0.9085 0.9092 0.9100 0.9107 0.9114 O.9I2I 0.9128

65 cos 0.4226 0.4210 0.4195 0.4179 0.4163 0.4147 0.4131 0.4115 0.4099 0.4083

tan 2.1445 2.1543 2.1642 2.1742 2.Ï842 2.1943 2.2045 2.2148 2.2251 2.2355

sin 0.9135 0.9143 0.9150 0.9157 0.9164 0.9171 0.9178 0.9184 O.919I 0.9198

66 cos 0.4067 0.4051 0.4035 0.4019 0.4003 0.3987 0.3971 0.3955 0 3939 0.3923

tan 2.2460 2.2566 2.2673 2.2781 2.2889 2.2998 2.3109 2.3220 2.3332 2.3445

sin 0.920s 0.9212 0.9219 0.9225 0.9232 0.9239 0.9245 0.9252 0.9259 0.9265

67 cos 0.3907 0.3891 0.3875 0.3859 0.3843 0.3827 0.3811 0.3795 0.3778 0.376^

tan 2.3559 2.3673 2.3789 2.3906 2.4023 2.4142 2.4262 2.4383 2.4504 2.4627

sin 0.9272 0.9278 0.9285 0.9291 0.9298 0.9304 0.9311 0.9317 0.9323 0.9330

68 cos 0.3746 0.3730 0.37x4 0.3697 0.3681 0.366s 0.3649 0.3633 0.3616 0.3600

tan 2.4751 2.4876 2.5002 2.5129 2.5257 2.5386 2.55Î7 2.5649 2.5782 2.5916

sin 0.9336 0.9342 0.9348 0.9354 0.9361 0.9367 0.93751 0,9379 0.9385 0.9391

69 cos 0.3584 0.3567 0.3551 0.3535 0.3518 0.3502 0.3486 0.3469 0.3453 0.3437

tan 2.6051 2.6187 2.6325 2.6464 2.660s 2.6746 2.6889 2.7034 2.7179 2.7326

sin 0.9397 0.9403 0.9409 0.9415 0.9421 0.9426 0.9432 0.9438 0.9444 0.9449 70 cos 0.3420 0.3404 0.3387 0.3371 0.3355 0.3338 0.3322 0.3305 0.3289 0.3272

tan 2.7475 2.7625 2.7776 2.7929 2.8083 2.8239 2.8397 2.8556 2.8716 2.8878

sin 0.9455 0.9461 0.9466 0.9472 0.9478 0.9483 0.9489 0.9494 0.9500 0.9505

71 cos 0.3256 0.3239 0.3223 0.3206 0.3190 0.3173 0.3156 0.3140 0.3123 0.3107

tan 2.9042 2.9208 2.9375 2.9544 2.9714 2.9887 3.0061 3.0237 3.0415 3.0595

sin 0.9511 0.9516 0.9521 0.9527 0.9532 0.9537 0.9542 0.9548 0.9553 0.9558

72 cos 0.3090 0.3074 0.3057 0.3040 0.3024 0.3007 0.2990 0.2974 0.2957 0.2940

tan 3.0777 3.0961 3.1146 3.1334 3.1524 3.1716 3.1910 3.2106 3.230s 3.2506

sin 0.9563 0.9568 0.9573 0.9578 0.9583 0.9588 0.9593 0..9S98 0.9603 0.9608

73 cos 0.2924 0.2907 0.2890 0.2874 0.2857 0.2840 0.2823 0.2807 0.2790 0.2773

tan 3.2709 3.2914 3.3122 3.3332 3-3544 3-3759 3.3977 3.4197 3.4420 3.4646

sin 0.9613 0.9617 0.9622 0.9627 0.9632 0.9636 0.964Ï 0.9646 0.9650 0 9655

74 cos 0.2756 0.2740 0.2723 0.2706 0.2689 0.2672 0.2656 0.2639 0.2622 0.260s

tan 3.4874 3.5105 3.5339 3.5576 3.5816 3.6059 3.6305 3..6554 3.6806 3.7062

Degs. Function 0' 6' 12' 18' 24' 30' 36' 42' . 48' 54'

134
Natural Sines, Cosmes and Tangents

76*'-«9.9*'

Dcgs. Function 0.0" 0.1' o.a° 0.3" 0.4° 0.5- o.6« 0.7' 0.8» 0.9"

sin 0.9659 0.9664 0.9668 0.9673 0.9677 0.9681 0.9686 0.9690 0.9694 0.9699

75 cos 0.2588 0.2571 0.2554 0.2538 0.2521 0.2504 0.2487 0.2470 0.245^ 0.2436

tkn 3-7321 3.7583 3.7848 3.8ÍI8 3.8391 3.8667 3.8947 3.9232 39520 3.9812

sin 0.9703 0.9707 0.9711 0.9715 0.9720 0.9724 0.9728 0.9732 0.9736 0.9740

76 cos 0.2419 0.2402 0.2385 0.2368 0.2351 0.2334 0.2317 0.2300 0.2284 0.2267

tan 4.0108 4.0408 4.0713 4.1022 4.1335 4.1653 4.1976 4.2303 4.2635 4.2972

sin 0.9744 0.9748 0.9751 0.9755 0.9759 0.9763 0.9767 0.9770 0.9774 0.9778

77 cos 0.2250 0.2232 0.2215 0.2198 0.2181 0.2164 0.2147 0.2130 0.2113 0.2096

tan 4.3315 4.3662 4.4015 4.4374 4.4737 4.5107 4.5483 4.5864 4.6252 4.6646

sin •0.9781 0.9785 0.9789 0.9792 0.9796 0.9799 0.9803 0.9806 0.9810 0.9813

78 cos 0.2079 0.2062 0.2045 0.2028 0.2011 0.1994 0.1977 0.1959 0.1942 0.1925

tan 4.7046 4-7453 4.7867 4.8288 4.8716 4.9152 4.9594 5.0045 5-0504 5.0970

sin 0.9816 0.9820 0.9823 0.9826 0.9829 0.9833 0.9836 0.9839 0.9842 0.9845

79 cos 0.1908 0.1891 0.1874 0.1857 0.1840 0.1822 0.1805 0.1788 0.1771 0.1754

tan 5.1446 5.1929 5.242« 5.2924 5.3435 5.3955 5.4486 5.5026 5.5578 5.6140

sin 0.9848 0.9851 0.9854 0.9857 0.9860 0.9863 0.9866 0.9869 0.9871 0.9874

80 cos 0.1736 0.1719 0.1702 0.1685 0.1668 0.1650 0.1633 0.1616 0.1599 0.1582

tan 5.6713 5.7297 5-7894 5.8502 5.9124 5.9758 6.040s 6.1066 6.1742 6.2432

sin 0.9877 0.9880 0.9882 0 9885 0.9888 0.9890 0.9893 0.9895 0.9898 0.9900

81 cos 0.1564 0.1547 0.1530 O.I5I3 0.1495 0.1478 0.1461 0.1444 0.1426 0.1409

tan 6.3138 6.3859 6.4596 6.5350 6.6122 6.6912 6.7720 6.8548 6-9395 7.0264

sin 0.9903 0.9905 0.9907 0.9910 0.9912 0.9914 0.9917 0.9919 0.9921 0.9923

82 cos 0.1392 O.I374 0.1357 0.1340 0.1323 0.1305 0.1288 0.1271 0 1253 0.1236

tan 7.II54 7.2066 7.3002 7.3962 7.4947 7-5958 7.6996 7.8062 7.9158 8.0285

sin 0.9925 0.9928 0.9930 0.9932 0.9934 0.9936 0.9938 0.9940 0.9942 0.9943

83 cos 0.1219 0.1201 0.1184 0 1167 0.1149 0.1132 0.1115 0.1097 0.1080 0.1063

tan 8.1443 8.2636 8.3863 8.5126 8.6427 8.7769 8.9152 9-0579 9.2052 9.3572

sin 0.9945 0.9947 0.9949 0.9951 0.9952 0.9954 0.9956 0.99S7 0.99S9 0.996c

84 cos 0.I04S 0.1028 O.IOII 0.0993 0.0976 0.0958 0.0941 0.0924 0.0906 0.0889

tan 9.5144 9.6768 9.8448 10.02 10.20 10.39 10.58 10.78 10.99 11.20

sin 0.9962 0.9963 0.9965 0.9966 0.9968 0.9969 0.9971 0.9972 0.9973 0.9974

85 cos 0.0872 0.0854 0.0837 0.0819 0.0802 0.0785 0.0767 0.0750 0.0732 0.0715

tan 11.43 11.66 II. 91 12.16 12.43 12.71 1300 13-30 13.62 13.95

sin 0.9976 0.9977 0.9978 0.9979 0.9980 0.9981 0.9982 0.9983 0.9984 0.9985

86 cos 0.0698 0.0680 0.0663 0.0645 0.0628 o.o6io 0.0593 0.0576 0.0558 0.0541

tan 14.30 14 67 15.06 IS. 46 15.89 16.35 16.83 17.34 17.89 18.46

sin 09986 0.9987 0.9988 0.9989 0.9990 0.9990 D.9991 0.9992 0.9993 0.9993

87 cos 0.0523 0.0506 0.0488 0.0471 0.0454 0.0436 0.0419 0.0401 0.0384 0.0366

tan 19.08 19-74 20.45 21.20 22.02 22.90 23.86 24.90 26.03 27.27

sin 0.9994 0.9995 0.9995 0.9996 0.9996 0.9997 0.9997 0.9997 0.9998 0.9998

88 cos 0.0349 0.0332 0.0314 0.0297 0.0279 0.0262 0.0244 0.0227 0.0209 0.0192

tan 28.64 30.14 31.82 33.69 35.80 38.19 40.92 44.07 47.74 52.08

sin 0.9998 0.9999 0.9999 0.9999 0.9999 1.000 1.000 1.000 1.000 1.000

89 cos 0.0175 0.0157 0.0140 0.0122 0.0105 0.0087 0.0070 0.0052 0.0035 0.0017

tan 57.29 63.66 71.62 81.85 95.49 114.6 143.2 191.0 286.5 573.0

Degs. Function 0' 6' \1' 18' 24' 30' 36' 42' 48' 54'

ir U. S. GOVERNMENT PRINTING OFFICE : 1972 O - 428-748 135