eas

ee
aes

Ze

=

ty
a
a

ae

oye

oe
a

a
Semen
ee

ie

te

Heat

ie

eae

=

aes

ie

tee

ee
at

my

Aras
sie

 

aa

iS ri
Bere

sagt

Bini

 
Production Note

Cornell University Library produced this volume to
replace the irreparably deteriorated original. It was
scanned at 600 dots per inch resolution and
compressed prior to storage using CCITT/ITU
Group 4 compression. The digital data were used to
create Cornell's replacement volume on paper that
meets the ANSI Standard Z39.48-1992. The
production of this volume was supported by the
United States Department of Education, Higher
Education Act, Title H-C.

Scanned as part of the A. R. Mann Library project to
preserve and enhance access to the Core Historical
Literature of the Agricultural Sciences. Titles
included in this collection are listed in the volumes
published by the Cornell University Press in the
series The Literature of the Agricultural Sciences,
1991-1996, Wallace C. Olsen, series editor.
(Aaumoy, “Ay sawef ropar jo Asajmmog) “sunurjd pue
Sunno-reap Aq paonposda st ysai0j SIU, ‘*syUaUJAVdWOD puP saltag BUIIIND 230N “Ku0xvg ur anag gy KDn40

INAWAOVNVI YAGNG) LsAIOT VY

 

 

 

 

*a0a1g Suns y — "J ALVIG
FOREST MANAGEMENT

BY
A. B. RECKNAGEL, B.A., M.F.

Professor of Forest Management and Utilization, Cornell University

AND

JOHN BENTLEY, Jr., B.S., M.F

Professor of Forest Engineering, Cornell University

DEPT. OF FORESTRY
CORNELL UNIV,
ITHACA, N.Y.

FIRST EDITION

NEW YORK
JOHN WILEY & SONS, Inc.
Lonpon: CHAPMAN & HALL, Limi1TED
1919

By
io
Coryricur, T9T9,
BY
A. B. RECKNAGEL anp JOHN BENTLEY, Jr.

Stanbope press
¥. H.GILSON COMPANY
BOSTON, U.S.A.
To
THE CORNELL FORESTERS

WHO
AS STUDENTS, CO-WORKERS, AND FRIENDS
HAVE BEEN AN UNFAILING SOURCE
OF INSPIRATION
PREFACE

TEXTBOOKS on forestry have multiplied so rapidly in the past
decade that an explanation is due the profession for adding
another to an already long list.

The textbooks extant are either highly technical or else very
elementary in their presentation. It seemed to the authors
that there was room between these two extremes, for a condensed
and simple treatment of the subjects included. Without
impinging on the realm of such standard works as Graves:
“Forest Mensuration,” Chapman: ‘Forest Valuation,’ and
others of the same class, there appears to be a real need for a
treatment of these subjects, which, while comprehensive, is
sufficiently condensed so as to be readily understood and used by
the layman timber owner and manager. At the same time, the
book should be of use to non-professional students of forestry in
colleges and universities and in professional courses which are
not of post-graduate grade.

Special acknowledgment is due Mr. C. H. Guise for his assist-
ance in the chapters on Forest Organization and Forest Finance,
particularly the latter. This chapter is modeled on Chapman’s
treatment of the subject in his ‘“‘Forest Valuation,” a relation-
ship which is gladly acknowledged.

It is the earnest hope of the authors that this humble contribu-
tion to an ever-growing English literature on forestry may
stimulate the practice of forest management by owners of timber-
land — large and small, public and private — to the end that
this important natural resource may be systematically main-

tained and developed.
A. B. RECKNAGEL,

JOHN BENTLEY, Jr.
Irgaca, NEw York,
November, 1918.
iii
CONTENTS

CHAPTER I
SURVEY OF AREA
ARTICLE

Ts, NECESSITY Of a: SUPVEY edi isiceidcrns cE Cad ae aes Sha ce Rana ee iS
2. Instruments used in making a survey..............cec ee eceeeecceees
Bay Method ses ica Ged ae sores elaeo ee aan np svausious: | OGiara a Mavermialnaewte e acaate
4o: MAPPING. siciencasdrady ategiens tiorsaaneaae entero eeee eS
5. Plotting the map by courses and distances. .............0-eeeeeueeee
63; APC ai ces eoeeree cus coers Ayaee dy kee E44 pEENe Rees Eade eG MOREY EE
76 COstS iis 2s4 sntkinwaind os tea duwiemes vies See cakide ss viataeaehedie ek

CHAPTER II

FOREST MENSURATION

8. Definition of forest mensuration............ 0. sce ete e eee ten eee eens
g. Units of measure................... sds monet ace aS Lecce ad;
to. The need for standards of measurement.............0eeceeeeereeeree

CHAPTER II

LOG RULES
Eis, Definition ii shi cdicena cee ce bane 3 sealant eke Moen id Gaisiaw ekoed be aac
12. Methods of constructing log rules............ 0... c cee eeeeeeene cence
13. Application of log rules............ 0... c cece ence nce eee e cere eereees
14. Comment on existing log rules. .............. 0.0 ccc eeeecceeeceeeecs

CHAPTER IV

INSTRUMENTS FOR FOREST MEASUREMENTS

15. Forest instruments. Calipers................2 eee e cece eee eeeeeees
16:. THY PSOMeters’ sc .s.ccvagwawe aimed dee Seek awe RAMI E e ee4
172. SCale StiCkS's:3o5: siasrete iy x y's vias sareaarawielse’o aiste'aisiamwoeiewere etree
18. Increment: borers... sscedessecccs piveee deve s cess vice ewe eaeeceras
19: -Dendrometers ice. ss4.cisisciniiaysie's ¢a4ive ais shestunie sedate BM acrecsw aR RE EAS
20.: Biltmoreistick:.. 5.3.4 scijseews ce ede autavninisndis Sanaa 6 seapstbcararn ernigide gc0: 018
vi CONTENTS
CHAPTER V
THE MEASUREMENT OF FELLED TREES
ARTICLE
2x. Antroduction\s si. yi saau a Sawie ad Gas odad bdaa kn da ed SURREY
22. Selection of trees for measurement..............0. 000 cece cece eens
23. Measurements made on a felled tree............00000 cece eee ee eee
24. Application of log rules, or mathematical formule................--++
25. The forms of trees in general............0. 000 cece eee e eee eee
26. Xylometric methods...........000. 00 cece cece e cece eee eer eeenee
CHAPTER VI
THE MEASUREMENT OF STANDING TREES
27. Measurement of diameters. ............. 0.0 eee eee
28. Measurement of height... w..0.5 6.6 c ce be epee nen dene ee budiswele ees
29. Measurement of volume.............. 0200 eee cece teen ee eens
BOs OL LA CCOLS joo cd go k g.craseeatrs tan sae wide PsenBSA EMS Bids Aird Blau eavsnaneaind bd
i. Usesoi forint faCtOrs: ccsicceccsice oven eo caecnnene nage GA alae we aA ee
CHAPTER VII
VOLUME TABLES
32. Definition and uses of volume tables... ..........0. 00 c cc eeeeeeaees
33. Classification of volume tables.............. 0.0... eee eee eee eee ees
34. Kinds of trees from which volume tables are constructed..............
35. Methods of constructing volume tables.................00-. eee ee eee
36. The method by taper curves........... 0... cece eee eee eee eens
37. Checking volume tables by mill scale studies...................2.046-
38. Application of volume tables............ 0... cece eect eee
CHAPTER VIII
TIMBER ESTIMATING
39. Definition and general remarks. ........... 0... 0c cece eee eee eee
40. Dependence of methods on objects of the work..................005.
Ai: Ocular methods’: occ 6 sasages baseace sad hid ea ack A RD bas, DRAINS
42. Approximate methods......... 00... cece cece cece e ence nent eeees
43. Approximate methods as applied to surveyed land...................
44. The method of small plots.........0.. 0... c cee eee eee eee eee
45. Method of stripsiin sates svt 494 feheneeteey <n ee ae eee BSR ees
46. Approximate methods as applied to unsurveyed land.................
47% Strip: SUPVEYVS) a5 oisadenariea vou qareinaems es Vie bad bP avencie Nes drese aceoeneeenceas
48. Narrow Strips ici cisauiawns geese ein Si: Gye edad See aes
403 Broad: stripseucecs.cee eng ter sas os Sobewh Mesias see haus

50. Accurately measured plots... 10... cece cece eee ener eee neta eens
CONTENTS

ARTICLE
51. The method of the mean sample tree
52. The volume curve method.............. 2.00.0 e eevee ee eee eee eeee
53. Factors affecting the accuracy of timber estimates..................
54. The cost of timber estimating............ 00.0 cee cee eee eeee
55. Computing the volume of stands from the tally sheets...............

CHAPTER IX
AGE OF TREES AND STANDS

56. Practical value of a knowledge of age
67.. Age OL SCCMN GS: ss cdeiwuas vedas ea ORE Vang ead aoe ede eeg acleelbios
58... Age of felled! treesic..c.... cso n eds tenia cadet seemed y eoes ee deen’ ve
§6;. Stiiip-taper: CUPVES .. s.cisc2 ccs epaidiie daa cao nee 2 Reed Raye Pe Oe
606. Age of Standing treés:. c.cj.cc neenen in doar eaaiesas yeeees Hhaiwad tem
61. Correlation of age with diameter, height and volume
62. Age of stands

CHAPTER X
GROWTH OF INDIVIDUAL TREES

63. Importance of a knowledge of growth
64. The several kinds of increment...............002 00 ce cece eee eeee
65. Methods of studying increment............000. 000 ccc ccseeeeeeeees
66. Stem analysis as applied to a large number of trees............... =
67. Increment per cent
68, Pressler’s formulasineic.¢2s c2e52 neewa lees sada seaecdavee sea ea weeks
69. Schneider’s formula

CHAPTER XI
INCREMENT OF STANDS

70. Increment in stands
His. Niele tables sistecssces cig xanga Gparanase ss. 9 wae nee Spee neha 5 Saad See HAS REE
72. Construction of yield tables for pure, even-aged stands
73. Construction of yield tables for uneven-aged stands
74. The study of increment in mixed stands
75. Permanent sample plots

CHAPTER XII

FOREST ORGANIZATION
96. Definitions vee cs ssc sonia ngs soa Weta pv ho. Mea A ROSES ETE SE oSS

79s: Sustained Wield). ccs secesees 4.0.8 a aver wiw sacl gs b-a sere end | Slgnessedse siese a aeateie
78. The normal forest.............. ccc cece eee e cece nsec eeeeeeeeeeees
79. Determination of the normal growing stock

PAGE
86
87
89
89
go

92
g2
93
95
97
97
98
vill CONTENTS

ARTICLE PAGE
80. Comparison of actual with normal distribution of age-classes......... 130
8r. ‘Division of thé area js cce ce go at awe ee PRLS AGS CRAY I 132
82. Designation of divisions. ........... 2.0. c cece cece cee ete tenes 133
83. Boundaries of divisions...........0.-.ee eee eee cece eee e eee e een aee 133
84. Working plan conference.............- 00sec eee eee e ene e eee eee 134
85. Objects of management.............. cece cece cere ete nent teens 135
86. Silvicultural methods......... 2.0.0: cee eee eee eee e ener nen eeeneee 135
87. The clear-cutting methods.......... 0. e cece cece teeter eee erene 138
88. The seed tree method. ........... cece ee eee cece eee teenies 1390
89. The selection method.............. cece cece eee eee eee e en eeeeee 139
go. The shelterwood method.............: cece eee eect eee eene nen eeeee 139
Olz, ROtAtHON esc xa) eset anne ae bogie we SET nee dloeN ieiet 140
92. Technical rotations........... 0.0. ccec eect een e ee te eee earner nc eenee 140
93. Economic rotations... 2.0.2.0... ccc e ec eee eee eee en ene eeeee I41
o4. Financial rotations: «once cco eaea khaki ss 2584 Sageeea leeds 142
6§.. ‘Choice Of TOtAHON wane 2.c00 Gis 2a cneaaa canes bls ooh bE SIS BASE 144

CHAPTER XIII

REGULATION OF THE CUT

06:. Definition: ves acn wae aweii’s depos ca eek Dadee tired testes eee AIA Ss 146

97: Determination of Cute: cccessseescccaaad sewieas cobs tg Oe KtRaw ees 146

98. Determination of cut in even-aged forests. By area................ 146

99. Determination of cut in selection forests. By area.................. 148
too. Determination of cut in both even-aged and selection forests. By

VO an Ga set ele cre weg ee chen ong ag AIR en Tenintave TY ae gegen 148

I. Von Mantel’s method...........0ccc cece cca e sees ee eeeneteeees 148

Il. Heyer’s method:..:s.4sceesdascrcscsad pi eende cease eee sees 150

tor. Determination of cut in selection forests. By volume............... 152

TE Swiss method. ..o.02424nscda lend ee eae saupiogimarecch amd .oes 152

IL. “Hufnagl’s:method cists cacy sia se paknamianunaaaeraw ses 155

102. Determination of cut in even-aged forests. By area and volume..... 157

103. Summary of results by different methods...................000eeee 158

104. Selection of stands to be cut... ......... 0... e eee eee eee eee aes 159

105. CUtting SEMES) «a nies sie sed nian d aie da canlombeaue en eavea eaarenale aes 159

106. Plan of cutting........... ccc eee e eee ce cee ccuceeeeeeeeens ree 160

1075. Planvof planting’. 9.3.53..2 3 ssa caeie ee oes ds MeereeeK ees Me anewn eae 161

CHAPTER XIV

THE WORKING PLAN DOCUMENT

ro8. Contents and form............ cece cece cece eect eenneeeeeenees 163
tog. Outline for working plan... 1.0.0... . cece eee eee ence eee e eee 164
t1o. Control and revision... ...... 0. ccc c cece eee ene nee e teense Hoaees 175
CONTENTS ix
CHAPTER XV
FOREST FINANCE
ARTICLE PAGE
Ti. Dehmitioncsoeiass. paaneia awl decent eases 4 sae ceuaio aus te awees 179
112% “Valuers 2 rrcawieen'vd a ninsetoeg bers 2s Ves me eeu meee eee wee OAS 179
113. Capital, «c¢scee ses 45 peeeeta ce cet ai eeewee ees oes MOOR eWR RY eaa aS 180
HLA COSC aa eo opdpe ics ind ns 8 Ez Sk epee Sw SH as a ee es ince Whe ae da ebaadhIOS Red Rk oO 180
TUG INCOMES 45 cacdawan ecuwanainn Oe dads Gwelaw 6-4-0 Wie Newlands ars ene ee 183
116. Compound interest formula...................005 peg et yumi eve ae 183
1z7., Rate-of interests osx <4 essay aeanen tees ey atuieee ens tenss weeRe eeays 186
T18 Calculation of Costsicc. cc <5 sacked vec c0 sedan eieste a dadeeeet acl’ 188
119. Determination of profits.......... 0.0 cece cece cence nee e ee nees Ig
120. Financial advantages of sustained annual yield.................2005 194
T2i. Stumpage values... «2 2+. 42svevecsa cy aneexsnadesee ress eaenemes vee 195
122. Appraisal of damages. ...........ccsececseesccscccseeecanesseees 200
CHAPTER XVI
FOREST ADMINISTRATION
123: Introduction iss. spade s)25 doa da aisiiene reco ne ae aceadieln oe hererneacendenes 209
124. Organization of Forest Staff... 0.0.0... eee cece eee cece e eee eee 209
125). Functions and grades: 6 aoe Madeaaegins Gees ea haeawehee ve se sands 209
126; DirechOns peace sa eeeue Nye dee aso obueda wens sk Peswawe as cexe Canes 209
127. Inspection................. ee ee er ee ee 2m
E28. EXECUHON s4 55:5 scecdijquceela’s. 3 Seas diaystceseeave. ¥ Spo-dave a Soabnete nls 4.4848 eaVeNreve 212
136.. ProvectlOn a. 2 avs-cmacectaee ata dwantad Candas ea Reet tad meas | 213
130.: Spéciall:détail svc au eak ev ou eee dimin ae Sees Gea ane Me tess add 214
131. Distribution according to area............ eee eee eee eee reece nee 215
¥32:.. Personnel relations: wesc os csss sdideamany ods sessment ineee cians 218
133; APPOmMement ss. occi.4 aS naiad weieoe a ndanuern C2 ded OA Romenen ae Sa NOD 218
134. PromMOllOd oi4iccdcwnoraaes Gtea 4 Sinden eae iarwmdesaar eetacaees 220
D395. PAY, cdrssucietenectat.o-ac wiacnunietis sous MOS EGE RE Oaeloe 4 ME AE vewee ae 222
APPENDIX
Tables, outlines for forest description and planting plan, and form for

tree‘measurementSss cyecd se ec sae i eunses NA idee e STEKO Cae eae 226
INTRODUCTION

Forestry has been defined * as the science and art of manag-
ing forests in continuity for forest purposes. The five main
branches. of forestry are: Forest policy, Silviculture, Forest
protection, Forest utilization, and Forest management. The
last named, the subject of this book, is the practice or application
of forestry in the conduct of the forest business. Forest manage-
ment consists of four main parts, each of which will be taken up
separately in the order named: (1) Forest mensuration, (2)
Forest organization, (3) Forest finance, and (4) Forest adminis-
tration.

(x) Forest mensuration deals with the determination of the
volume of stands, trees, logs and other timber products, and with
the study of growth and yield of trees and stands.

/(2) Forest organization concerns itself with the organization
of a forest property for maintenance, ordering in time and place
the most advantageous use of the property, with the ultimate
aim of securing a sustained yield.

(3) Forest finance relates to the forest as an investment.

(4) Forest administration deals with the principles of business
conduct and methods employed in the administration of forest
properties.

The Committee of the Conference of Forest Schools in 1912,
recognized that ‘‘Forest management in its broadest sense in-Y
cludes a group of subjects which deal ‘with the quantitative and
financial aspects of forestry, and with business considerations.
Forestry as a business must conform to the principles which make
for success in any other business. This means securing the high-

* Definitions throughout from terminology of the Society of American Foresters

Journal of Forestry, Vol. XV, No. 1, pp. 71-101; reprinted 1917.
t “Standardization of Instruction in Forestry,” Forestry Quarterly, Vol. X,

No. 3, Pp. 341-394.
xi
xii INTRODUCTION

est returns on the investment, the most efficient organization
and conduct of operations and the regulation of the forest output
so as to secure a permanent and steady income.

“While the attainment of these results is dependent on knowl-
edge of practically all conditions which affect forests, from the
academic point of view it is desirable to segregate two groups of
subjects which deal, to be sure, with methods and conditions on
which management must be based, but may be treated separately,
namely, the technical group, including silviculture, lumbering,
protection — crop production and harvest; and the economic
group, including studies of forest influences, statistics, forest
laws, which determine guiding principles or objects to be at-
tained by the management. Forest management is to harmonize
these abstract principles and technical methods with the financial
condition of the owner, map out the exact nature and extent of
the operations which can be most effectively carried out, or-
ganize the work, and secure the quantitative and financial
results desired for the tract as a whole.”

The term forest economy has been suggested as a collective
name for the subjects which deal with business problems as
separated from forest crop production, i.e., forest economy would
be a comprehensive term including all matter dealing with the
business aspects of forest management. This can be shown
diagrammatically as follows:

Forest Management

 

[ \
Technological Branch Business Branch
(Forest Crop Production) (Forest Economy)
; Forest Forest
Silviculture Utilization mensuration organization
Forest Forest
Protection finance. administration.

 

The logic of this classification is incontrovertible; nevertheless,
the term “forest economy”’ has the serious drawback of tonal
similarity to “forest economics.” The latter is akin to politics
or political economy; development of state policies with regard
INTRODUCTION xiii

to natural resources. ‘“‘Economy”’ suggests the more confined
sense; household arrangement of an establishment, rules and
regulation and orderly system by which an establishment is run
or managed.*

The term “forest management” is simple, inclusive, and
readily understood. It is the term in common usage to-day for
the subjects included in this book.

* From letter by Dr. B. E. Fernow to one of the authors under date of De-
cember 4, 1916. See also Forestry Quarterly, Vol. III, p. 260.
FOREST MANAGEMENT

CHAPTER I
SURVEY OF AREA

1. Necessity of a Survey. — Except in the case of woodlots of
very small area in which every tree can be counted and estimated,
or in those rare cases where trees of unusual value are being
appraised, an estimate of standing timber will be based on a
general inspection of the entire tract, followed by a more or less
detailed count and estimate of the trees on a fractional part of
the area, which represents, as nearly as may be judged, the
average of the entire stand, or type. The area of this fractional
part, which may be in the form of one or more plots or strips,
‘must be known; and the area of the entire tract or type of which
the samples are a part must also be known, in order that the ratio
between the two can be established; only in this way can the
estimate-figures obtained be translated into terms of the entire
area. The area of a piece of timber-land can sometimes be gotten
quite accurately from the description in the deed referring to it,
but more often it will be necessary to make a fresh survey in
order to be sure of accuracy. The forest may have spread by
natural reproduction beyond the limits described in an old deed;
or cuttings, fires, and the like may have been the cause of open
spots within the exterior boundary lines; so that unless a careful
survey has been made within the past few years, the accuracy of
which is beyond question, it is necessary to ascertain by measure-
ment with instruments the area occupied by the timber to be
estimated. Under average conditions, this work can be done at
a very moderate cost, and is the first step to be taken.

2. Instruments Used in Making a Survey. — The chief factor

in determining the choice of instruments with which to make
I
2 SURVEY OF AREA

the survey is cost, which should always be reasonably proportional
to the value of the property, and should be as low as possible,
consistent with the degree of accuracy required by the nature
and objects of the work. A survey made with instruments of
precision, such as the transit, level, and plane table, would be
far too costly in the case of the average farm woodlot or small
piece of timber-land; these instruments can be used economically
only on tracts of large size, e.g., one thousand acres or more;
much depending, even in such cases, on the value of the land and
the timber. Such instruments as the small hand compass,
however, are usually too inaccurate for survey work, except in
the case of very small areas, or in the hands of an experienced
surveyor who knows how to make allowances for the limitations
of the small compass. Intermediate between these extremes,
both in cost and in degree of accuracy, is the staff compass,
usually equipped with a needle at least 2} inches long, and en-
abling one to read bearings to the nearest half-degree. This is
close encugh for ordinary work and moreover, since the compass
error in most forest survey work is not cumulative, it is possible
to secure very satisfactory results with the staff compass. A
description of this instrument is unnecessary here; for those.
who wish to consult articles on the surveyor’s compass and its
adjustments, a few selected references are given at the end of
this chapter.

A compass serves merely to give direction. For the measure-_
ment of distance a surveyor’s chain or a steel tape is needed.
The former is 66 feet long, and composed of roo links, each.
0.66 foot (= 7.92 inches) in length. (See Table 1, page 226.)
This unit of measure for distance is very useful in forest survey
work because of the readiness with which square chains may be
reduced to terms of acres. (See Table 2.) The steel tape may
be graduated either in feet or in links, and has the advantage
of being lighter in weight, and more easily handled, although it
is at the same time more susceptible to damage. Both chains
and steel tapes, the latter graduated to chains and links, are
used extensively in forest surveys. For marking the chain-
or tape-lengths in the measurement of lines, steel pins may be
METHODS 3

used; or stakes made of material picked up in the woods, to be
discarded at the end of the work, are often just as satisfactory,
and are much lighter to carry around.

To assist in the work of sighting the compass along a line, a
rod or a staff is often a great convenience. Especially in the
woods, where branches and foliage may obscure the view, a staff
or rod painted with alternate bands of white and bright red will
help in obtaining the sight quickly and easily. A cheap, handy
substitute for the painted rod is a sapling which may be cut near
by, and the bark peeled from it in alternate bands, in order to
make it conspicuous. Or a white rag may be tied to the top of
a straight sapling, and used successfully as a sighting rod.

Such accessories as note-books, pencils, crayons for marking
stakes, hatchets or hand-axes, and other tools with which to
accomplish the work of the survey, need no special comment;
each one will adopt his own standards, and use such material
as will suit individual tastes and the needs of the particular case.

(For further details of equipment and methods of measure-
ment, the reader is again referred to standard textbooks on sur-
veying, such as those mentioned at the end of this chapter.)

3. Methods. — The boundary survey of a woodlot or other
piece of timber-land should begin, if possible, at some established
point in the property the location of which is definitely described
in the deed. If no such point exists on the border of the wood-
lot, the nearest point on the property so established should be
chosen, and a line run from this point to the nearest corner of
the woodlot. The bearing and the length of this line should be
measured, thus establishing definitely the location of the woodlot
with reference to a known point. It is now possible to make a
traverse of the boundaries of the area to be measured and have
it tied in to an established point.

A survey which ascertains the direction and distance of a line,
or of a series of lines, or of a route, is called a traverse; and sucha
survey is generally made by commencing at some definite point
and continuing by measured bearings and distances to the other
points, one after the other; it may, or may not, return to the
starting point. In the case of a woodlot the boundaries and area
4 SURVEY OF AREA

of which are to be determined, the traverse should begin at a
known point and after going completely around the tract, return
to the starting point, thus making a closed survey. For example,
let us assume that the boundaries and area of the woodlot in
Fig. 1 (page 5) are to be determined. The nearest established
point, or corner, is the point A, which is on the property line,
and is the northernmost corner of the woodlot. This corner is
therefore selected, the staff-compass set up there, and the
bearing and distance of the corner B (which is visible from A)
determined with the aid of the compass and chain (or tape).
This done, the compass is set up at B, and from this point it is
now possible to obtain the bearing and the length of the line
B-C; from C, it is possible to obtain the bearing and length of
the line C-D; and so on, taking the corners D, E, F,G, and H in
turn; finally the bearing and distance of H—A are obtained,
which completes the traverse by returning to the point of begin-
ning. The field notes for such a survey might well take the
following form:

SuRVEY OF WOODLOT ON THE SMITH Far. September 2, 1915.

Description. — A is an iron pipe, 2 inches in diameter, set in the ground
and marking a point on the property line. South corner of the house bears
N. 70° W., 1.70 chains distant. South corner of barn bears S. 86° W.,
3.68 chains distant.

TRAVERSE OF WOODLOT.

 

 

Station.* Line. Bearing. Distance. Remarks.

A A-B S. 66° 30’ W. 3.81 chains

B B-C S. 23° 00’ E. 5.98

Cc C-D N. 66° 30’ E. 1.28

D D-E N. 39° 30’ E. 1.95 ‘*

E E-F N. 19° oo’ W. 0.790‘

F F-G N. 23° 00’ E. Igr

G G-H N. 14° 00’ W. 1.03‘!

H H-A N. 45° 00’ W. 2.14 ‘

 

 

 

 

 

* Any point that is occupied by the surveyor for the purpose of measurement of angles is called
astation.’’ Stations are generally lettered alphabetically, or if there are very many of them,
numbered consecutively.

If desired, a few descriptive notes may be added at the time
the survey is made. They may be entered in the column
“Remarks,” or written more at length on the page of the book
METHODS 5

 

MAP OF SMITH WOODLOT

Fic. 1. Map of Smith Woodlot.
6 SURVEY OF AREA

opposite the recorded measurements. It is customary to enter
the figures for the angles and lines on the left-hand side of the
note-book, reserving the right-hand side for descriptive notes
and computations. The descriptive notes, if carefully written,
frequently help to interpret properly the figures on the opposite
page, or they may help to identify points used in conducting the
work, should it become necessary to refer to the survey notes or
marks at any time in the future. For example, the point A,
which happens to be described with reference to the house and
the barn, might also have been described with reference to two
or more trees, which on account of their proximity and distinctive
character would serve to identify the point should it become
necessary to do so. In the same way, the point B might be
described by referring to the south and the west corners of the
barn, giving the bearings, but not necessarily the distances to
these points. (Two or more bearings serve to locate a point, if
they are not in the same straight line.) Reference marks should
be chosen from among permanent objects if such objects are
conveniently close.

Care should be taken to avoid setting up the compass too close
to a wire fence, or any other metallic object which might deflect
the compass needle, and give erroneous bearings.

A word should be added here regarding the measurement of
land surfaces which are not level. All measurements of distance
are to be made horizontal. If the surface of the ground is not
level, the chain or the tape must be held level, and the measuring
should be done in units short enough to make this possible.
Thus, half a chain-length, or even ten links or less, may be taken
as the unit in very steep country. For this work a plumb-bob
will be found very useful. In going up hill, the plumb-bob is
held by the rear chain-man; in going down hill, it is held by the
head chain-man. If land surfaces are not measured horizontally,
very unreliable results will be obtained, besides making it prac-
tically impossible to map the area correctly. (For detailed
discussion of the measurement of lines and angles, measurement
of slopes, etc., see text books referred to at the end of this
chapter.)
MAPPING 7

Large obstacles, such as cliffs, rocks, bodies of water, etc., may
be avoided simply by making the traverse run around them.
The area may be corrected later on the map. Small obstacles,
such as trees in the line of sight, may be gotten around most
readily by off-setting. This may be done by moving the compass
a known distance to the right or to the left of the line of sight,
and at right angles to it, the off-set, as it is called, being made
just large enough to clear the obstacle. The obstacle is passed
by running past it on a line parallel to the original traverse line,
returning to this line as soon as it is possible to do so conveniently.

4. Mapping. — It is always a great advantage to have an
accurate map of any piece of property, no matter how large or
how small. Forest land is no exception to this rule. A map
conveys to the mind in a graphic way much information that is
obscure when stated in terms of figures, dimensions, or directions,
and often serves to correct misconceptions regarding relative
locations and areas.

The scale to be selected should generally be the smallest that
will serve the purposes of the map and permit the entry of all
necessary data upon it without overcrowding. The following
table shows approximately the scale suitable to tracts of differ-
ent sizes, although it should be remembered that no strict rules
can be given, for the purposes of maps vary so greatly

 

 

 

Area of tract Scale of map.
(Acres). (Feet per inch). (Chains per inch).
t to 10 100 1.0
10 to 100 200 2.0
100 to 1000 500 5.0
1ooo and upwards 1000 20.0

 

 

 

 

 

Much will depend upon the outline of the area and the amount
of detail that must be shown on the map. It is rarely possible
to show the details of topography, forest-cover, and cultural
features on a scale smaller than 4 inches to the mile (1 inch =
1320 feet) unless there is great uniformity of conditions. Except
8 SURVEY OF AREA

under unusual circumstances, this scale should be regarded as
the minimum for forest maps.

After an appropriate scale has been decided upon the next
step is to draw the map from the field notes, according to this
scale. For this purpose, the following articles are necessary:

1 Engineer’s scale-rule.

1 Protractor, at least 23 inches radius.

1 Straight-edge.

2 Triangles: one 45-degree, one 30—-6o-degree.

1 pair dividers.

1 or more hard pencils, at least 4 H.

A good grade of drawing paper, erasers, etc.

(A drawing-board, upon which the paper can be secured
with thumb-tacks, together with a “T-square,” makes
the work of drafting considerably easier. These articles
are not absolutely indispensable.)

There are two common methods of mapping, namely:

(x) The method of courses and distances.
(2) The method of latitudes and departures.

The first of these two methods consists in plotting the angles
directly on paper, and scaling off the appropriate distances on
the lines drawn. The second method requires computations
before any plotting on the paper can be done. For each course,
the distance east or west of a north-south line (meridian) must be
computed, and likewise the distance north or south of the east-
west line (base). Latitude is reckoned as the distance north or
south o the base line, north latitudes being reckoned + and
south latitudes —; departure is reckoned as the distance east or
west of the meridian, east departures being considered + and
west departures being considered —. As a matter of fact, it is
quite common to compute the latitudes and departures for the
several courses of a closed survey, even though this method is
not followed in mapping, for, as will be shown in Article 5, a
method is thereby furnished for eliminating the error of closure.
For small areas, or where the field methods have been rather
PLOTTING THE. MAP BY COURSES AND DISTANCES 9

rough, because of the necessity for keeping the cost of the work
low, it will rarely pay to employ the method of latitudes and
departures. In these cases the method of mapping by courses
and distances, correcting any errors which develop by simple
methods, is clearly the most economical and. satisfactory.

5. Plotting the Map by Courses and Distances. — Select a
point on the paper for the initial point of the survey and through
it draw a straight line which is to be the north-south line, 7.e.,
the meridian. The initial point should be chosen after an
inspection of the notes to determine approximately how the
map will appear on the paper, and so located that all the courses
and distances may be plotted without danger of running off the
paper. It is well to have a sheet of paper large enough to extend
the meridian, and the lines parallel to it, to any distance re-
quired for easy handling of the protractor, triangles, and straight-
edge. Next, with the protractor placed carefully along the
meridian and centered over the initial point, mark the bearing
of the first course, and draw a line from the initial point through
this mark, extending it a sufficient length to scale off the distance.
Since direction and distance fix a point, we now have established
on paper the position of the second station occupied in the survey.
Through this point now draw a second meridian, parallel to the
first one, and repeat the process just described, to locate the
position of the third station. The process is repeated again and
again, until the last station has been located. If the field-work,
note-recording, and plotting have all been perfectly accurate the
last course should strike the point of beginning and its scaled
distance should be equal to the distance called for in the field
notes. If there is an error in either the field-work, the note-
recording, or the plotting, the survey will fail to ‘‘close,” as it
is called, —i.e., there will be a discrepancy between the point of
beginning and the point of ending, as shown on the map. The
work must, therefore, be examined critically to see if any errors
can be detected. The map should first be inspected; if there
has been no mistake in laying off the angles and scaling the
distances on the map, and if the error of closure is large, it is
probable that there is an error in the field-work, which can be
10 SURVEY OF AREA

corrected only by a re-survey. Bearings may have been read
wrong, or distances may have been measured incorrectly, and
such mistakes would of course make it impossible for the survey
to close. If the error of closure is small, however, it may be
assumed that the angles were read as closely as possible on the
compass, and the distances measured accurately; the field-work
is, therefore, acceptable. Making allowances for the facts that
angles cannot be read closer than one-half degree on the average
staff compass, or plotted any closer than one-half degree with
the average protractor of 23-inch radius, we may consider a
slight error in closure as permissible. This error, which may be
reckoned in terms of percentage, by scaling the error of closure
and comparing it with the total length of all the courses, may be,
for work in the woods with compass and chain, as much as one-
half of one per cent, or 1 in 200, without seriously affecting the
results in determining area. If a degree of accuracy greater
than this is required, then instruments of greater precision should
be used. It is impossible to perform absolutely perfect work,
and the instruments chosen should be consistent with the degree
of accuracy and refinement required by the work.

The error, as determined, should be distributed in some way,
and eliminated. We may assume, for example, that if all the
courses presented about the same conditions, no one of them
being more difficult of measurement than any of the others, the
error is likely to be quite evenly divided among all the courses.
We can, therefore, distribute the error in proportion to the length
of the several courses. One way of doing this is extremely
simple and easy of application; and will be described here because
it can be used to advantage in most surveys of small area, with
comparatively few courses. It may be called the graphic
method.

Since the error is undoubtedly composed of two parts, namely,
errors in angular measurement and errors in linear measurement,
the correction must take into consideration both angles and lines.
If-it is assumed as above, that the error is proportionate to the
length of the courses, then it may be distributed by drawing the
line which represents the closing error (the line E-A in Fig. 2)
PLOTTING THE MAP BY COURSES AND DISTANCES II

and scaling it; next, draw lines parallel to this closing error line
from each station (see Fig. 2) and scale off, on these lines, the
proportional part of the
error, found by comparing
the length of each course
with the total length of all
courses. For example, in
Fig. 2, where, for the sake
of clearness, the error has B
been greatly exaggerated, Fic. 2. Graphic Method of Distributing
suppose there are four thE EET AB NEY
courses, A-B, B-C, C—D, and D-A, and in plotting the map
the error Z-A is found.

A-B 2.40 chains

B-C 1.25 chains

C-D 2.25 chains

D-A 1.10 chains

7.90 chains, total length of all courses.
Error = E-A = 0;50 chain.

 

 

 

Error to be distributed as follows:

A-B = 34 per cent of 0.50 chain = 0.17 chain.
B-C =18percent “ ‘= 0.09 chain.

C-D =32percent “ “= 0.16 chain.
D-E =16percent “ “= 0.08 chain.
100 per cent = 0.50 chain.

Lines are then drawn parallel to H-A from B, C, and D, and
the distances,

0.17 = 0.17 chain,
0.17 + 0.09 = 0.26 chain,
0.17 + 0.09 + 0.16 = 0.42 chain,

0.17 + 0.09 + 0.16 + 0.08 = 0.50 chain,

scaled on them, respectively, so as to bring the corrected corners
at the points B’, C’, and D’ as shown. If these points are now
connected, the survey closes, and it may be accepted as repre-
senting, approximately, the angles and distances as they actually
12 SURVEY OF AREA

appear on the ground. It must be remembered that in case
the error exceeds the ratio 1: 200 the field-work had better
be done over again in order to eliminate errors of measurement.

Those who have a knowledge of mathematics sufficient to
apply the method of latitudes and departures will find that
method a very good one to use, for it not only gives an oppor-
tunity to correct and balance errors in the most satisfactory
way, but it makes the task of plotting the map easier. A
further advantage of the method of latitudes and departures is
that with these quantities known area may be determined easily
by the method of Double Meridian Distances. This method is
described in standard works on surveying, to which reference
has already been made.

Having adjusted the lines and corners so that the survey
closes, it may be taken for granted that the outline map resulting
represents with sufficient accuracy for the purposes in mind the
size and shape of the woodlot, drawn to scale. The addition of
details, such as streams, roads, and ponds, and all cultural
features, also topography and forest types, will be possible after
other surveys incident to the timber estimate have been made;
and it is needless to add that the same scale should be used in
entering these details upon the map.

6. Area.— If the traverse is composed of relatively few
straight lines an easy way of obtaining the area of the land
mapped is to divide it into a number of triangles (the number
always being two less than the number of sides to the figure) and
then find the area of each triangle separately by scaling the
bases and the altitudes, and applying the well-known formula;
then add together the areas of the several triangles, thus finally
obtaining the area of the entire tract. (See Appendix, Table 3,
Area of Triangles.)

If the traverse is composed of a great many lines, or if any of
the boundary lines are crooked (e.g., the banks of a stream, or
lake), by far the easiest way of obtaining the area is to use a
planimeter, an instrument which will be found described in
standard books on surveying. Another, but extremely rough,
method of determining area is to place over the drawing a thin
COSTS 13

piece of tracing paper, on which squares are drawn, representing
a unit of area, say square rods, or square chains. The number
of squares lying within the boundary of the area can then be
counted, — first the full squares, then approximating the frac-
tional parts of squares, as nearly as may be, — thus enabling one
to get the area at least approximately. This method is at best
only rough and rather inaccurate, and should be employed only
as a last resort.

7. Costs. — As stated in Article 2, the cost of mapping and
estimating timber should be kept as low as possible, consistent
with the degree of accuracy demanded by the nature and the
objects of the work. It would be folly to spend $100 in mapping
and estimating a piece of timber worth only $500, and while no
inflexible rule can be laid down, it might be said that on large
areas (10,000 acres or more) it will generally be considered un-
wise to spend more than two cents per acre for this part of the
work, 7.e., boundaries and area. On smaller tracts, the follow-
ing figures may be taken as a guide:

 

Size of tract. Limit of cost of boundary survey.

 

Io to roo acres $0.05 to $0.10 per acre
1000 tO 10,000 acres $0.03 to $0.04 per acre

 

 

 

 

Everything depends on the value of the land and the timber.
On the basis of values, it will rarely be wise to spend more than
from two-tenths of one per cent to five-tenths of one per cent
(0.2 to 0.5 per cent) of the combined value of the land and timber
in making an outline map from which the area can be determined
and on which the timber-estimating strips may later be entered.
(See Chapter VIII.)

REFERENCES

BREED AND Hosmer: “The Principles and Practice ot Surveying,” New York
John Wiley & Sons, Inc., 1916.

Tracy, Joun C.: “Plane Surveying,’ New York, John Wiley & Sons, Inc., 1917.

Cary, A.: “A Manual for Northern Woodsmen,” Cambridge, Harvard University
Press, 1918.
CHAPTER II
FOREST MENSURATION

8. Definition of Forest Mensuration. — Forest Mensuration
is that branch of forestry which deals with the determination of
the volume of stands, trees, logs, and other timber products, and
with the study of growth and yield of trees and stands.*

The measurement of any article implies the use of one or more
units that are accepted throughout a given region or country as
standards. This is necessary to facilitate buying and selling the
commodity. Many of our weights and measures are standard-
ized by state or federal laws and in like manner some of the
standards for the measurement of logs and lumber have been
approved by legislative bodies, and declared legal, or standard,
for a given state. It is unfortunate, however, that owing to the
great variety of uses for wood, and the lack of uniformity in the
specifications for certain pieces in different localities, there has
grown up not only a long list of units of measurement for wood,
but the commonly accepted meaning of these units is not always
the same in all parts of the country. Moreover, the stems of
trees, from which lumber is produced, display a great difference
in straightness, degree of taper, and quality; so that in the
process of manufacturing lumber from logs, the proportion of
sound, merchantable lumber which can be produced varies
greatly. Thus, from two trees of the same height and the same
diameter, but of different form, the amount of lumber produced
from the straight, cylindrical tree will exceed that produced
from the crooked or misshapen tree with quickly tapering trunk.
The amount of lumber obtainable from these two trees will also
depend on a number of other factors, as noted in Articles 12 and

* Throughout this book, terms are defined in accordance with the nomenclature
and definitions adopted by the Society of American Foresters. See “Journal of
Forestry,” vol. XV., No. 1, January, 1917. This is the official organ of the Society
of American Foresters.

14
UNITS OF MEASURE 15

13, and it should be understood at the outset that for no other
class of material, perhaps, is there such a wide range in the
number of different units of measurement, and in their applica-
tion. In this respect, lumber and wood products are almost
unique. The more important of these units will now be dis-
cussed.

9. Units of Measure‘— (a) The Board Foot. — This is the
commonest unit of measure for lumber in general use. It is
used both to measure sawed lumber, and to express the estimated
merchantable contents of logs, trees or stands. It is defined as
a board one foot long, one foot wide, and one inch thick, or its
equivalent. It is customary to speak of board feet in terms of
thousands, because lumber is generally handled in large quanti-
ties in the market; when so spoken of, the Roman numeral M
is used as an abbreviation. For example, hemlock may sell in a
certain market for $18 per M, and this means that one thousand
board feet of hemlock lumber, whether in inch boards or two-
inch planks, or “‘two-by-fours,”’ or other dimension timbers,
cost $18.00. The rule for determining the board-foot contents
of any regular piece of sawed lumber may be stated as follows:

Multiply together the width in inches, the thickness in inches,
and the length in feet; divide this product by 12.

Example: (1) A board 1 inch thick, 8 inches wide, 12 feet
long:

8X 1X 12
12

= 8 board feet.

(2) A plank, 10 inches wide, 2 inches thick, and 16 feet long:

10 X 2 X 16
12

= 262 board feet.

(3) A piece of dimension stuff, 10 inches wide, 6 inches thick,

14 feet long:

1O ROTA 70 board feet, etc.
12

It will sometimes be found upon close measurement that
planks and dimension timbers do not fully measure up to the
%
16 FOREST MENSURATION

thickness called for. They may lack y of an inch, more or less,
of being the full size. The reason for this is that green lumber
shrinks, and not all mills adjust their saws to allow for this
shrinkage. To make proper allowance for shrinkage, boards to
be one inch thick when seasoned, should be sawed slightly
thicker, ¢.g., tp, inches. (See Chapter III.) Again, if inch
boards are planed on one or both sides, or if flooring is tongued
and grooved, so as to match properly, the pieces will be slightly
less than the full inch in thickness, and less than the specified
width; nevertheless they are reckoned as full size because, in
the beginning, a piece of lumber of full size was used to produce
the finished, planed board. These slight differences are under-
stood and accepted in the trade.

As an aid to the ready determination of the board-foot contents
of a piece of manufactured lumber of any size, lumber dealers
and inspectors use a special stick called a ‘‘board rule,” which
‘shows at a glance the board-foot contents of a piece of lumber
when the width, thickness, and length are known. Board rules
simplify the labor of calculating board-foot contents of lumber,
and are especially useful in measuring large quantities of boards
which run in a great variety of widths and lengths.

(b) The Cord. — Perhaps the next commonest measure for
wood is the cord. Fuel, pulp-wood, and the like are generally
measured by this unit, which is a convenient one for sticks that
are too short, or too small in diameter, or too irregular to be
scaled by the board foot. A cord is defined as a pile of stacked
wood 8 feet long, 4 feet wide, and 4 feet high. It is customary
to saw the individual pieces into 4-foot lengths, and to pile them
transversely to the 8-foot dimension as compactly as possible.
A cord of standard size contains 128 cubic feet of stacked wood,
although the actual solid cubic contents rarely exceeds go cubic
feet. This number varies considerably, as is shown in Appendix,
page 227. Sometimes wood in lengths much shorter than 4 feet
is stacked into a pile 4 feet high and 8 feet long, and sold as a
cord. Thus, wood for small stoves is often cut into 18-inch,
16-inch, or even 12-inch lengths, and a stack of such wood, 8 feet
long and 4 feet high will be called a cord. Such practices, how-
UNITS OF MEASURE 17

ever, are understood, and the price of these so-called ‘‘short
cords” is adjusted accordingly.

(c) The Cubic Foot. — The use of the cubic foot as a unit of
measure is not common in commercial practice in this country,
except in the measurement of rare and costly woods. As wood
becomes less plentiful and rises in value, it is quite possible that
the cubic foot will be used more and more as a commercial unit;
but for the present it is confined largely to calculations of growth
and yield, by foresters and lumbermen who are planning on a
definite system of forest management. Long-continued usage
has made the board foot and the cord the two commonest units
of measurement, and they will doubtless continue so for a long
time to come, for the reason that everybody is thoroughly
familiar with these units.

(d) Standards. — A peculiar unit of measurement which is a
relic of the early days of lumbering in the Adirondack Mountains
of New York is the ‘‘standard,” or “market,” which, in the
particular locality mentioned is a log 13 feet long and 19 inches
in diameter at the small end. Other standards are the 22-inch
standard, sometimes called the Saranac River Standard Rule;
the 24-inch standard; and some others of less general usage.
With the exception of the Adirondack standard, they are com-
monly based on a log of 12 feet. They may all be expressed
mathematically by the general formula:

2
V= xt x= Es;
in which d and / are the diameter and the length, respectively,
of the log to be measured; and D and L the diameter and the
length respectively of the standard log. V expresses the contents
in standards.

Example: A log 16 feet long, 21 inches in diameter, by the
Adirondack standard, would contain 1.5 standards, or
markets, derived as follows:

(21) ge = 44 y 16 _ 7056

= 1.5 (nearl
(a9?) * 361 13 4093 5 (nearly).
18 FOREST MENSURATION

To convert this into terms of board feet it is necessary to know
how much the standard, or market, itself scales by some accepted
log rule. In the case of the Adirondack 19-inch standard, the
scale is about 200 board feet, depending on what log rule is used:
(Doyle gives 183; Scribner gives 195; and Clark’s “‘Interna-
tional’? Rule, reduced to a kerf of one-fourth inch, gives 208
board feet.) These range close to 200 and it is, therefore, com-
mon practice to consider five (5) standards or markets of this
particular size equivalent to one thousand board feet. and the
relation is expressed: ‘‘5 standards to the M.”

In New Hampshire a rule known as the Blodgett Rule, which
is really a standard rule, and which has been adopted as the
statute rule of that state, is based on a unit log one foot long and
16 inches in diameter. Theoretically this unit is considered
equivalent to one cubic foot (it is actually equal to 1.396 cubic
feet) and it is also considered as producing 10 board feet. Logs
of all other dimensions are referred to this as a unit. In practice,
it has been found that the amount of lumber which a Blodgett
foot will yield depends on the diameter of the log, and whether
it is measured in the middle, or at the small end. Locally, the
lumbermen and woodsmen who are familiar with the rule recog-
nize 115 ‘‘Blodgett feet” as equivalent to 1000 board feet, if the
logs are measured at the middle, and 106 “‘ Blodgett feet’ equiv-
alent to tooo board feet, if the logs are measured at the small
end.* This subject is discussed more in detail in Chapter III,
which treats of Log Rules.

(e) Poles, Posts, Railroad Ties, anid Other Pieces. — Pieces ot
timber which satisfy certain standards as to size, length, girth,
etc., are generally sold by the piece. Thus, in the East, the
commonest of such units are the following: poles, posts, ties, and
in mining districts, props, stulls, lagging, etc. In some parts of
the West there are still other units, such as converter poles,
shakes, etc. A table showing the equivalents of these units in
board feet will be found in the Appendix, page 226. While in
some localities these units are used more or less loosely, neverthe-
less the markets, especially for ties and poles, are usually quite

* See Graves, H. S.: “Forest Mensuration,” page 55.
THE NEED FOR STANDARDS OF MEASUREMENT 19

definite in their specifications. Moreover, the pieces are subject
to rigid grading and inspection rules, so that the quality of the
piece influences to a very large degree the market price. The
usual specifications for some of the commoner pieces are as
follows:

R. R. ties, standard gauge, 8 feet x 8 inches x 6 inches.

R. R. ties (recent specifications by some railroads), 84 feet
x g inches x 7 inches.

Poles, top diameter, 7 inches; lengths, 20, 25, 30, 35, 40,
etc., feet.

Posts, 7 feet long, and a specified diameter, or girth, at the
top.

(f) Linear Foot. — Pieces of very small girth, too small’ to be
measured by the board foot, yet straight enough to find a use in
some industries, may be sold by the linear foot, or running foot
as it is often called.

There are still other units used for certain articles of manu-
facture, but they are generally of sizes determined by local
conditions. Thus in some parts of the country blocks of maple
or beech find a ready market for manufacture into shoe-lasts.
These blocks are furnished in sizes specified by the manufacturers.
Material for making wheels (spokes, hubs, and felloes) and the
parts of agricultural and sporting implements are often required
to meet certain specifications, and these must be made to con-
form to the local demands. No hard and fast dimensions can
be given.

10. The Need for Standards of Measurement. — From the
foregoing articles it is plain that there is a great multitude of
units for the measurement of wood products in this country, and
that some of these units, going by the same name in different
localities, may nevertheless have different dimensions and con-
tain more or less wood. The confusion which follows as a result
is greatly to be deplored, for it often makes it impossible for
buyer and seller properly to appraise stumpage. Some definite
standards, to be acknowledged as such in all parts of the country,
are urgently needed, and the adoption of such standards would
20 FOREST MENSURATION

do much to eliminate the sense of uncertainty which pretty
generally surrounds any deal in standing timber nowadays,
whether the amount be large or small. While the use of many of
the commoner units, such as the board foot and the cord, will
doubtless persist for many years, it is to be hoped that some
day the use of the cubic foot (or, if the metric system should be
adopted in this country, the cubic meter) will become general.
This will bring about a standardization very desirable both from
the standpoint of the buyer and the seller of timber and lumber,
and especially from the standpoint of the forester, who must
deal not only with wood products that are manufactured, but
with growing trees and forests, whose volumes and values are
constantly changing.

There are so many units of measure, and so much variation
in the method of applying the several units, that it is extremely
difficult to formulate any table of comparisons. Nevertheless,
comparisons, although not exact, are often useful when compiling
statistics, and a table of converting factors has therefore been

included in the appendix. (See page 226.)
CHAPTER III

LOG RULES

11. Definition. —In buying or selling standing timber or
logs, it is necessary to have some means of determining about
how much lumber can be obtained from them after sawing.
Most standing timber is bought or sold on the basis of an esti-
mate, and this estimate is usually made in terms of thousands of
board feet, board measure — expressed “‘M. feet, B. M.” Or,
if logs are bought or sold, the price is quoted at so much per
thousand feet, board measure (M. feet, B. M.), and the logs are
measured, or scaled, to determine approximately the number of
board feet of lumber they will yield when sawed. In the case
of standing trees, the only things that can be measured are the
diameter (usually at breast-height, — that is, 43 feet from the
ground) and the height — either the total height, or the mer-
chantable height; and since the taper, crooks, thickness of bark,
and soundness of a standing tree cannot be measured directly,
but can be judged only by the eye, it follows that the estimate
of the merchantable contents thus made is decidedly approxi-
mate, and often exceeds or falls short of the actual sawed product
by as much as to per cent or 20 per cent. Experience and
familiarity with the trees of a region soon lead to considerable
accuracy on the part of careful estimators, but the results are
always approximate.

In the case of felled trees and logs there is the advantage that
certain additional measurements can be made, and the estimate
of the contents of the tree or log can, therefore, be made much
more closely — usually within 5 per cent. The length, diam-
eter, thickness of bark, any eccentricities or crooks, and any
visible unsoundness can be measured or observed, and then by
reference to a standard table of values, the board-foot contents

can be estimated. It is still an estimate, however, because no
2iI
22 LOG RULES

one can tell positively what the saw will disclose in the interior
of the log; and the degree of unsoundness or other defect will,
of course, influence the final product. The table of values
referred to above is called a log rule, and may be defined as

7 follows: A Log Rule is a tabular statement indicating the estimated
or calculated amount of lumber which can be sawed from logs of
given lengths and diameters. The tabular statement is generally
arranged in columns, the board-foot values being printed in
horizontal lines opposite the left-hand column of numbers rep-
resenting diameters in inches, and under the numbers 8, 10, 12,
14, 16, 18, 20, etc., representing the standard lengths of logs
in feet. (See Appendix, Tables 6 and 7.)

There are a great many log rules in use, and for convenience
in scaling logs the values of any particular rule are usually
printed on a stick, graduated to inches, showing for logs of any
given diameter and length the corresponding contents in board
feet. Such a stick is called a scale stick, and is made in a variety
of forms, some of which are shown (Fig. 3, page 23).

That the board-foot as a unit of measure for sawed lumber has
been in use for over a century is shown in a very interesting
discussion on the early history of log rules, by H. S. Graves,
Forester, U. S. Dept. of Agriculture.* The early rules were
based either on a rough mathematical formula, — often the
result of repeated trials, and hence, really empirical, — or on
diagrams, drawn to scale, representing the cross-sectional view
of a log sawed into inch boards. The contents of logs of differ-
ent sizes were then computed from these diagrams, applying
the rule for finding the contents of sawed lumber, given on
page 15.

12. Methods of Constructing Log Rules. — Log Rules may
be constructed in any one of three ways, namely: -

(x) By diagrams drawn to scale. ce a
(2) By mathematical formule. aly,
(3) By mill scale studies. myer?

* Graves, H.S., “Forest Mensuration,” pages 22-26, New York, John Wiley
and Sons, Inc., 1906.
METHODS OF CONSTRUCTING LOG RULES 23

    
 

a, 13_28PAULDING_ e

   

 

 

 

 

 

 

    
   

   
 

i = —=6=scripnen== | 16=23| 36
= ul?
= 79-= BCALE 12] 19, =27

      
    

 

Si ie = 36 ——
EY eS =poy.Le=— =
GC = 4 22 arsed
12_SCRIBWER 14] 19 “eh a
ee == PAS DECIMAL SL 3 al = 1
=a =8CALE “i Se
G

 

 

 

 

 

 

 

Fic. 3. Various Forms of Scale Sticks.
24 LOG RULES

Of course it is possible to modify the results obtained by either
of the first two methods, by applying a correction factor, as found
under method number 3, where logs of known size are followed
through the mill, and the sawed product measured as lumber.
As a matter of fact, nearly all mathematical formule for con-
structing log rules contain a factor of correction which is based
on observation at the mill and is purely empirical. In other
words there are certain losses, due to normal crook and taper,
the allowances for which can be determined only by following an
average lot of logs through the mill. All of the mathematical
formulz which are based on sound principles contain such a factor.

(1) Log Rules Based on Diagrams. — The earliest log rules,
as mentioned in Article 11 were diagrammatical. Circles were
drawn for every inch-size, from 12 to 44, or more, and then
beginning at one side of the circle a segment (slab) with a 6-inch
side was first cut off; next, an allowance for saw-kerf was made
(in the old rules, this was at least one-quarter of an inch) and
then an inch board was cut off. This process was continued
until all the available part of the circle was used, which would
make a board 6 inches wide. Then the round edges (wany
edges) were trimmed off in the diagram, and the board foot
contents of the standard size logs — 8, 10, 12, 14, 16, etc.,
feet — calculated by the rule already given. (See page rs.)
Later, as logs smaller than 12 inches in diameter became mer-
chantable, the log rule values for sizes 6 to 11 inches, inclusive,
were calculated, and incorporated in the table.

It is possible, of course, to draw diagrams for all sizes, allowing
for a kerf other than one-fourth inch, and for boards with smaller
merchantable widths. Thus, if it were desired to construct a
rule to be used where a band-saw taking out a kerf of one-eighth
inch is employed and where boards as narrow as 3 inches are
merchantable, the diagrams could be drawn accordingly, and a
rule constructed that would give accurate results when used
under those particular conditions. Before attempting to use any
log rule, it is wise to discover upon what basis it is constructed,
and how it is applied, so as to be able to judge of its applicability
to particular conditions.
METHODS OF CONSTRUCTING LOG RULES 25

(2) Log Rules Based on Mathematical Formule. — Logs from
normal, sound trees approach pretty closely in form certain
geometric solids (see Chapters V and VI), and since the contents
of these solids can be found by applying appropriate formule it
follows that the board-foot contents of these solids can be found
by applying formule in which correction factors are introduced
for taper, saw-kerf, slabs, edgings, normal crook, and (as some
authors claim) for shrinkage.

If they pretend to any accuracy, mathematical formule for
determining the board-foot contents of logs begin with the funda-
mental formula for the contents of a cylinder, as given in solid
geometry. This formula, it will be remembered, is simply the
area of the base, B, multiplied by the height H; or, in terms of
the diameter of the base, D, and the height, H, the formula
becomes:

2
~ i = 0.7854 DH.

In the case of logs, D is expressed in terms of inches and H in
terms of feet. In order to obtain a formula which will give us
the number of board feet in such a cylinder, we must first reduce
H to terms of inches, which is done by multiplying by 12. Then,
since the ratio between board feet and cubic inches is 1 : 144, it
will be necessary to divide the product, D? x H, which is in
terms of cubic inches, by 144. We then have, as the formula
which expresses the board-foot contents of a cylindrical log
when no allowance is made for slabs, saw-kerf, and other losses,

(0.7854 D? x H X 12) + 144 = board feet.

It will be observed that when H = 12, the formula reduces, by
cancelation, to a very simple expression, namely:

Theoretical board feet of a 12-foot log = 0.7854 D*.
(no allowance for slabs, kerf, etc.)

Another way of expressing this is as follows: Since a board foot
is equivalent to 144 cubic inches, then in a 12-foot log, every
square inch on the base represents a board foot, z.e., the square
26 LOG RULES

inch at the base multiplied by 12 feet (= 144 inches) will give
144 cubic inches. On account of this relation, nearly all mathe-
maticians have used the 12-foot log as the standard on which to
base their computations, and after making certain allowances
for saw-kerf, slabs, etc., they have simply multiplied the results

for any given inch-class by a to find the values for logs of the

same diameter, but of lengths other than 12 feet.

Since there are certain losses, such as slabs, saw-kerf, and some
others to be noted presently, by which the board-foot contents
of logs are affected, there must be certain corrections applied to
the fundamental formula for a 12-foot log, 0.7854 D? x H,
which, as we have seen above, is the starting point.

In the first place the width of the smallest board which can be
considered merchantable will determine the width of the slabs
which must be taken off. The increased demand for lumber
together with the rise in price and the general effort now being
made to reduce waste so far as possible, has made it practical to
use boards as narrow as 3 inches, and this width has been used
as a minimum by many recent writers in their work of calculat-
ing the contents of logs. The edgings also constitute a loss of
material which can be classed with the slabs, and since the more
boards a log produces the more edgings will it be necessary to
account for, it will be noted that slabs and edgings are two
sources of loss which depend on the size of the log; they are, as
a matter of fact, proportional to the “barked area”’ of the log,
as has been shown by Mr. H. E. McKenzie.*

Secondly, since no logs are perfectly straight and symmetrical,
there is a loss due to normal crook which must be allowed for.
Thirdly, there is a loss in saw-dust. The saw in passing through
a log leaves a path that is spoken of as the saw-kerf; the material
lost in this manner is saw-dust. This loss is proportional to the
cross-sectional area of the log, i.e., D?.

Again, the taper of the log is a fourth factor which must be
taken into account, especially in the longer standard lengths.

* McKenzie, H. E., “A Discussion of Log Rules,” California State Board of
Forestry, Bulletin 5, 1915, page 17.
METHODS OF CONSTRUCTING LOG RULES 27

Logs are scaled at the small end, therefore taper, if it be pro-
nounced, or if the log be long, will make it possible, under certain
circumstances, to obtain more lumber from a tapering log than
from a cylindrical log. Dr. J. F. Clark * was, perhaps, the first
to recognize this factor and allow for it in his “International”
Rule.

A fifth factor is the average dimensions of the lumber sawed.
It is very obvious that a log sawed into two-inch planks, or larger
dimension stuff will yield more than the same-sized log sawed
into inch boards, for the simple reason that the loss in saw-kerf
is less. Most log rules are constructed on the theory that 1-inch
boards are to be sawed; scalers and mill men have learned to
allow for an overrun if much dimension stuff is produced.

Dr. Clark in his discussion * argued that shrinkage should be
a legitimate factor. To quote him:

“A point that has been overlooked by some rule makers
is that the scale given should refer to the amount of seasoned '
inch lumber which can be sawn from the logs scaled. In-
asmuch as logs are ordinarily scaled green, it becomes
necessary to allow for the shrinkage of the boards in thick-
ness and in width which accompanies the seasoning. The
margins of safety adopted by different mills vary consider-
ably, but usually run from 4-inch to 3-inch in the width of
the boards, and from a scant 5'5-inch to 3;-inch in thick-
ness.”

Summing up, the factors which should be taken into account

in constructing a mathematical formula which give the board-
foot contents of a log of given dimensions are six in number:

(1) Slabs and edgings.
(2) Normal crook. ae
(3) Saw-kerf.

(4) Taper.
(s) Average dimensions of lumber sawed.

(6) Shrinkage.

* Clark, J. F.: “The Measurement of Saw Logs.” Forestry Quarterly, IV,
No. 2, 1906, page 79.
28 “LOG RULES

(3) Empirical Rules. — If logs are followed through the mill
and a tally kept of the exact amount of lumber produced from
each one, it is possible by this means to secure a set of values for
a log rule which are based entirely on the average production, and
hence, empirical. Such a table of values would be useful locally;
and they could also be used for the determination of a correction
factor, to be applied to any recognized rule so as to obtain more
accurate results in scaling. Thus in Arkansas, where the Doyle
Rule is the statute rule of the state, there are many mills that
apply a correction factor to the scale, varying with the size of
the log, because their experience tells them that the Doyle Rule
underestimates the contents of small logs, and overestimates the
contents of the larger logs. While they use the Doyle Rule,
and thus conform to the law of the state, they are, in effect, using
an empirical rule, because, based on their experience, they make
allowances, correcting the Doyle Rule where they know it fails.

In Article 14 the rules commonly known are classified and
commented upon briefly.

13. Application of Log Rules. — It must be remembered that
log rules show the estimated contents in board feet of sound
logs, which are reasonably straight and free from excessive taper,
and which are sawed by skilled men. No allowance is made
for defect or wasteful sawing, and this is the only safe method
to adopt, otherwise it would be impossible to credit a sound log
with its full scale. In all cases, defect is allowed for in the
process of scaling, by considering the logs as though sound, and
then making a proper deduction for the visible defect, plus a
further deduction for invisible defect, if this appears necessary
after observing the product of average logs at the mill.

14. Comment on Existing Log Rules. — The following list of
log rules includes those described in Graves’ ‘‘ Forest Mensura-
tion” (1906) together with a few others more recently de-
scribed.* They have been grouped, so far as possible, into the
three classes recognized, the mathematical, the diagrammatic,
and the empirical. Where the origin is unknown, a separate
class has been made. Those rules that have enjoyed a use wide

* See Forestry Quarterly, Vol. VII, page 144.
COMMENT ON EXISTING LOG RULES 29

enough to prove their merit are followed by the sign (1); those
that are mainly theoretical, and, although based on sound
principles, have not been tested under conditions sufficiently
diverse to prove their practicability, are followed by the interro-
gation-point (?); those about which little is known, or which
have not been used extensively, are left unmarked. Where
there is any further comment, it will be found under ‘“Com-
ments” following the number corresponding to the list-number.

CLassIFicaTIon oF Loc RULES

 

 

 

 

 

 

Mathematical. Diagrammatic. Empirical. Unknown.
(1) Champlain (?) (22) Scribner f (29) Chapin (32) Drew
(2) Universal (23) Maine t (30) Boynton (33) Quebec +
(3) International ft (24) Hanna f (31) Massachusetts] (34) New Brunswickt
(4) Doyle + ; (25) Spaulding + (35) Dusenberry
(5) British Columbia t | (26) Baughman (36) Northwestern
(6) Constantine (theoretical)! (27) Favorite (37) Derby
(7) Vermont + (28) Herring (38) Partridge
(8) Baxter (= Beaumont) (39) Parsons
(9) Two-thirds Rule (= Ten- (40) Stillwell

nessee River Rule) (41) Saco River
(10) Square of Rule (= Port- (42) Wilson

land = Noble and Cooley (43) Ballon

= Cook = Crooked River (44) Wilcox

= The Lumberman’s (45) Warner

Rule) (46) Carey
(11) Cumberland River = (47) Younglove

Evansville = Third and (48) White

Fifth Rule (49) Finch and Apgar
(12) Orange River = Ochil-

tree Rule = Sabine River;

Rule Combination, mathe-
(13) Preston matical and diagram-
(14) Ropp matic
(15) Forty-five Rule (50) Doyle-Scribner +
(16) Ake
(17) McKenzie (?)

(18) Tiemann (?)
(19) Clement’s Rule
(20) Click’s Rule
(21) Calcasieu Standard
CoMMENTS

(1) Values run high, except where used with a band saw.

(2) Gives good results for average logs, where a circular saw cutting }-inch kerf is
used.

(3) Gives good results where logs are utilized closely. Can be adapted to saws
taking out }-inch kerf, by reducing the table values by 9.5 per cent.

(4) Values run too small on small logs, and too high on very large logs.

(7) Unsatisfactory; too large for small logs.

(x17) A new rule, described in the California State Board of Forestry Bulletin 5.
Very carefully worked out, and adaptable to any conditions by changing the
formula slightly. Not in common use.

(18) Theoretical. Not in actual use.
30 LOG RULES

(22) One of the commonest and most widely used of all rules. . In a modified
form, where the units are rounded off to the nearest 10, and the final cipher
dropped, it has been adopted by the U. S. Forest Service, as the official rule.
In the form thus described it is known as the Scribner Decimal “C” Rule.
While its values are very conservative, it gives satisfaction, in most cases, for
by careful sawing, average logs will produce slightly more than the rule gives.

(23) Satisfactory for logs of short length.

(24) Much like the Scribner Rule.

(47) For an account of this rule, see Forestry Quarterly, XII, page 395.
CHAPTER IV
INSTRUMENTS FOR FOREST MEASUREMENTS

THE measurement of area has been discussed in Chapter I,
and the instruments used in that work have already been re-
ferred to specifically. It remains now to discuss some of the
instruments which are peculiar to forest work. While the
principles involved in some of these instruments have been used
in many other arts and sciences, nevertheless, the requirements
of forest work have created a demand for some instruments of
a specialized character, peculiarly adapted to the needs of
foresters and lumbermen.

 

 

 

 

Fic. 4. Tree Calipers.

15. Forest Instruments. — Foremost among these instru-
ments is the éree caliper. The most commonly used dimension
of a tree or a log is the diameter, and this is obtained most readily
with the aid of calipers, a common style of which is illustrated in
Fig. 4. A hardwood beam, measuring approximately 37 inches
long, 13 inches wide, and 3 inch thick, is graduated on both sides

3r
32 INSTRUMENTS FOR FOREST MEASUREMENTS

to inches and ¢enths of inches, from 0 to 36.* At the o-end of the
beam is attached a fixed jaw, set at right angles to the graduated
beam. A second jaw, which is movable and slides along the
graduated beam by means of a metal-lined slot, is so constructed
and adjusted that it has play enough to move easily, but when
applied to the tree in making a measurement, it assumes a posi-
tion perpendicular to the graduated beam, on which the diam-
eter of the tree may then be read, directly from the scale. The
metal plates lining the slot in this movable jaw are adjustable by
means of screws, so that in case the jaw, by continued use, or
changes in the wood due to moisture, should fail to assume a
perpendicular position, the error can be eliminated by loosening
the screws just mentioned, and re-adjusting the plates. The
movable jaw can be slid off the beam, and the fixed jaw is de-
mountable by means of two screws; so that the instrument can
be taken down and arranged compactly for shipment or trans-
portation. The standard size tree caliper (36-inch) weighs but
30 ounces, and is extremely portable and convenient. During
_the last few years, the so-called ‘Biltmore Stick” (see Article
20) has to some degree displaced the caliper in work of timber
cruising where diameters to the nearest inch-class only are
required; but the Biltmore stick, even when used with great
care, is less accurate than calipers, and in any work requiring a
degree of refinement closer than whole inches, the caliper, gradu-
ated to tenths of inches, is indispensable.

For measuring the diameter of very large trees, or for meas-
uring and re-measuring diameters of trees on permanent sample
plots, a circumference tape isrecommended. This is a steel tape
so graduated that when placed in a position encircling the tree
trunk, the diameter at that point may be read directly.

16. Hypsometers. The next commonest instrument for
measuring trees is the hypsometer, an instrument for measuring
heights; and since it is employed almost exclusively for meas-
uring the heights of standing trees, the term has been defined

* These dimensions apply to the so-called 36-inch calipers. These are the
most generally useful in the north-eastern United States. Calipers are also made
with beams 20 inches long and with beams 54 inches long, to suit the needs of
special cases or localities.
HYPSOMETERS 33

* “Can instrument for meas-

by the committee on terminology
uring heights — especially of trees.”

Hypsometers are of many styles and kinds, but they all depend
upon the geometric principle of similar triangles, or upon the
trigonometric principle of tangents. To illustrate these princi-
ples, only two or three of the many kinds of hypsometers will be

described here.

 

 

Fic. 5. The Faustmann Hypsometer.

(a) Hypsometers Based on the Principle of Similar Triangles

Faustmann. — This instrument, made originally in Germany,
but also made in this country under patent rights, con-
sists of a metal frame (or, in the cheaper models, a rectangular
board), about 7 inches long and 33 inches wide. (See Fig. 5.)
The following description of the instrument is reprinted from
Bulletin 36, U. S. Dept. of Agriculture, Forest Service, the
‘“Woodsman’s Handbook,” page 99:

“This instrument consists of a skeleton rectangular metal

* See “Journal of Forestry,” vol. XV, No. 1, 1917.
34 INSTRUMENTS FOR FOREST MEASUREMENTS

frame having two crossbars at one side of its longitudinal center,
the frame and bars being in one piece. A slide, reversible end
for end and having beveled edges, works in undercut grooves
formed in the inner edges of the crossbars. This slide is provided
at its ends with thumb notches and with transversely arranged
index marks, designated I and II. A plumb line carrying a
plummet is attached to the slide in the center of the index mark
II. A retaining spring secured to the back of the frame and
bearing against the inner face of the slide holds it in any position
in which it may be set. The left-hand end bar of the frame is
furnished with an eyepiece, and the right-hand end bar with an
objective, these being made of metal and hinged so as to be
folded down out, of the way when the device is not in use. A
long, narrow mirror, hinged to the frame at a point below the
objective, is furnished to reflect a right-hand horizontal scale
and a left-hand horizontal scale engraved upon the lower bar of
the frame, and meeting at a zero point which is intersected by a
line passing through the longitudinal center of the slide. The
right-hand scale runs to 75 and the left-hand scale to 225, the
latter scale extending upward on the left-hand end bar of the
frame. The right-hand crossbar is provided with a vertical
scale running upward from zero to 100, and continued on the

"left-hand crossbar with a scale running upward to 175. These
scales are divided in fifths and numbered. The lines forming
the scales are equally separated from each other and represent
units of distance under any system of measurement that may be
adopted. The handle of the device is attached to the left-hand
crossbar.

“To use the instrument, the observer measures the horizontal
distance in feet, yards, or in any other desirable unit, from where
he is to stand to the base of the tree. He then sets the slide by
one or the other of its two index marks, which is brought into
line with the graduation on the vertical scale corresponding to
the measurement just secured. If the distance is less than 75,
‘the slide should be set so that the upper end of the plumb line
will take a position opposite the required number on the portion
of the vertical scale on the right-hand crossbar. If the distance
HYPSOMETERS 35

is more than 75, the slide should be pulled out and reversed end
for end and adjusted until the index mark at its then lower end is
brought opposite the required number on that portion of the
vertical scale on the left-hand crossbar. The observer then
looks through the eyepiece and objective and brings the hair of
the latter into line with the top of the tree. The plumb line is
allowed full play and crosses the left-hand horizontal scale. As
soon as the plumb line is at rest the number which it crosses is
read off in the mirror. This number indicates the height of the
tree from the level of the observer’s eye to its top. He then
sights through the instrument to the base of the tree and reads
the number crossed by the plumb line on the right-hand hori-
zontal scale. This number indicates the distance from the level
of the observer’s eye to the base of the tree, and is added to the

 

Fic. 6. Christen Hypsometer.

number before secured, which gives the total height of the tree.
If the observer should be standing so that the level. of his eye is
below the base of the tree, he should first determine the height
from the level of his eye to the top of the tree, then the height
from the level of his eye to the base of the tree, and subtract the
last result from the first, which gives the true height of the tree.”

A very simple instrument which gives approximate results is
the Christen Hypsometer, an instrument used in Switzerland
and other European countries to some extent. It consists of a
flat piece of metal with a notched edge of known length. The
instrument is held lightly between the thumb and forefinger and
allowed to assume a vertical position at such a distance from the
36 INSTRUMENTS FOR FOREST MEASUREMENTS

eye of the observer that the image of the tree to be measured fits
precisely into these notches. (See Fig. 6.) The point on the
graduated scale, ¢, where the line of sight from the eye to the top
of a pole of known length, standing against the tree, cuts it,
gives the height of the tree, provided the relation between the
length of the pole and the distance between the notches of the
graduated scale is known, and the graduations placed accord-

ingly. The principle is one of similar triangles. If = is the

ratio of the tree to the pole, and s = the length of the scale (z.e.,
the distance between the notches on the instrument), and ¢ =
the part of the scale subtended by the image of the pole, then,

and if, with known values for p and s a value of H is assumed,
the corresponding value of ¢ may be computed and marked on
the scale. Similarly, other values of H are assumed (usually at
intervals of 5 feet, e.g., 30, 35, 40, 45, 50, 55, etc.), and by apply-
ing the formula, the corresponding values for ¢ are computed and
marked on the scale.

(b) Hypsometers based on the Principle of Tangents

An example of the type of hypsometer operating on the prin-
ciple of tangents is the Forest Service Grademeter, or Hypsom-
eter. This instrument serves equally well to determine grades
and heights. Combining as it does the ability to perform these
two classes of work, so common in forest work, with a small
compact form of light but strong construction, this instrument is
decidedly useful to the forester. It consists of a circular metal
box about 3% inches in diameter and 3 inch thick. (See Fig. 7.)

A weighted dial on the inside, which is released by pressing a
control-spring, shows by a printed scale the tangent of the angle
at which the instrument is held, x 100. Or, in other words, the
scale shows directly, in terms of percentage of the measured
base-line, the elevation above the level of the eye, or the depres-
SCALE STICKS 37

sion below the level of the eye. From these two readings the
height of the tree is readily obtained.

The Goulier clinometer operates on exactly the same principle
as the Forest Service Grademeter, and while extremely useful,
is not of such compact, durable construction.

A hypsometer to give the greatest satisfaction in the field
must combine lightness, strength, durability, ease of manipula-
tion, and accuracy. Some
of them sacrifice one or
more of these qualities to
obtain others. For ex-
ample, the Christen hyp-
someter is light, strong,
durable, and simple; there
is nothing to get out of
order; but the necessity
for carrying about a pole of Ses
known length, together Fic. 7. — Forest Service Standard
with the fact that it is a TIN pHOMetes:
physical impossibility to read the scale very accurately makes
this instrument of doubtful practicability. The Faustmann is
capable of very accurate readings when the wind does not blow
the weighted thread, but this fact, together with the frail con-
struction, the liability of the mirror to breakage, and the fraying
of the thread, makes it an instrument of limited usefulness.
The Forest Service Grademeter, while not capable of such
great accuracy as the Faustmann under favorable condi-
tions, combines so many of the desirable features that it
is perhaps the most generally useful of any of the instruments
mentioned.

17. Scale Sticks. — Scale sticks are usually made of some
tough, flexible wood, like hickory, and present no such variety
of forms as hypsometers. While there is a choice offered in the
style of ferrule which fits on the end of the stick, the common
forms are flat rules, about 14 inches wide, } inch thick, and from
40 to soinches long. One edge is graduated to inches; the other
edge to some little-used log length, as, for example, 20 feet. The

 
38 INSTRUMENTS FOR FOREST MEASUREMENTS

two flat sides are graduated to show the contents in board feet
for logs of standard length, the 12’s, 14’s, and 16’s on one side,
and the 8’s, 10’s, and 18’s on the other side. Thus the scaler
has conveniently arranged, all on the same side, the board foot
values of the commoner log lengths, 12, 14, and 16. Some of
the styles are shown in Fig. 3, page 23.

18. Increment Borers. — The increment borer is an instru-
ment for determining the rate of growth in diameter of standing
trees. It consists of a hollow augur, which when bored into the
tree at right angles, extracts, by means of a removable plug
called the “extractor,” a core of wood, about a quarter-inch in
diameter, on which the annual rings of growth show. Increment
borers are made in several types, the commonest of which is the
so-called Swedish increment borer; they come in various sizes,
classified as to the length of the wood core which they are capable
of extracting. They are extremely useful in obtaining reliable
data as to diameter growth, and while not adapted for use in
trees with a very hard wood, are nevertheless indispensable to
the practical forester.

19. Dendrometers. — A dendrometer is an instrument com-
bining height and diameter measurement, adapted to measuring
diameters indirectly. Some of the simpler forms require no
lenses, but most of them, if they pretend to any degree of accu-
racy, or applicability to a wide range of uses, employ telescope-
tubes, with lenses of moderate magnifying power. A very
elaborate, yet thoroughly practical form of dendrometer, is
described in Forestry Quarterly, vol. XI (1913), page 467. The
inventer of this instrument, Dr. J. F. Clark, claims that its use
is justified in cruising very tall timber, or very valuable timber.
Such instruments have no place in the rough cruising methods
generally employed in extensive work, nor would they be econom-
ical in estimating the timber in a farm woodlot.

20. Biltmore Stick.— An instrument for measuring the
diameters of trees which has come into quite general use among
foresters in this country, especially in reconnaissance work and
rapid cruising, is the Biltmore stick. So far as the authors
know, this stick was first described in the Forestry Quarterly, in
BILTMORE STICK 39

1911.* It is defined as a graduated rule, usually of wood, the
graduations of which indicate the diameter of the tree at the
point measured, when the rule is held tangentially to the tree.
It is so much lighter than a pair of calipers, and when used
with care gives results so little less accurate, that for cruising,
or measuring trees where diameters to the nearest inch-class are
sufficient, this instrument can be recommended heartily. It
must be remembered, however, that in the hands of careless men,
very inaccurate results may be obtained. The Biltmore stick
has been tested in field-work, and for a discussion of the results
of this test, the reader is referred to the Forestry Quarterly,
1911.* It is possible to combine on one stick, of suitable size
for a Biltmore rule, not only the graduations spoken of above,
but also the values for a log rule, so that the stick serves not
only to measure the diameter of standing trees, but also to scale
logs. Or a hypsometer, based on the principle of the Christen
Hypsometer, may be incorporated with the other uses of the
stick. For a discussion of the mathematical principles on which
this rule is constructed, and the errors to which it is liable, the
reader is referred to the citation in the Forestry Quarterly, already
mentioned, and to an article in the Proceedings, Society of Ameri-
can Foresters. +

The authors believe that the range of use for the Biltmore
stick might well be extended and, in the hope that many cruisers
will adopt it as a rapid and easy means of measuring tree-
diameters, there is included in the Appendix a table of values for
the Biltmore stick, suited to various arm-lengths.

* Jackson, A. G.: “Biltmore Stick,” Forestry Quarterly, IX, page 406.
¢ Bruce, D.: “Notes on the Biltmore Stick,” Proc. Soc. Am. For., IX, page 46.
CHAPTER V

THE MEASUREMENT OF FELLED TREES

21. Introduction. — One of the chief objects of forest men-
suration is the measurement of whole stands of trees, z.e., timber
cruising, or timber estimating. The only way to secure accuracy
in this kind of work is to study, first, the form of the individual
trees. Standing trees are hard to measure, but felled trees can
be measured in detail — scaled to determine their contents in
board feet, or measured in a sufficient number of places to cal-
culate their cubic contents. As the basis for determining the
contents of whole stands, therefore, the volumes of individual
trees of different species, sizes, classes, and so forth, must first
be known. These volumes, usually appearing in the form of
volume tables (see Chapter VII), are determined from measure-
ments made on hundreds— perhaps thousands — of felled
trees, and since they are to be multiplied by large factors in
arriving at the estimates for whole stands, it is of the utmost
importance that the volume table values shall be as nearly fault-
less as possible for average trees. This can be accomplished only
by making careful measurements on many felled trees, classified
as to diameter and height, or merchantable length, or some other
function which has a determining influence on the merchantable
contents of a tree. (See Article 33.)

22. Selection of Trees for Measurement. — While the ideal
method of procedure would be to inspect the stand for normal
trees (i.e., trees that are symmetrical, regular in form and de-
velopment, sound, and free from excessive taper, crook, etc.),
and to measure these normal trees in detail after felling them and
dividing them into sections of even, standard length, such a
course would obviously be very costly, both in time and money.
A much cheaper way, and one which gives results nearly as satis-
factory, is to follow the tree-felling crews in the woods, where a

40
MEASUREMENTS MADE ON A FELLED TREE 41

lumbering operation is in progress, and as they fell the trees,
make the necessary measurements. For example, before the
tree is felled, it can be inspected and judged for normality, and
its breast-high diameter measured. As soon as it has been felled
and cut into logs (and before these have been moved from their
relative positions), all the measurements necessary can be made.
(See Article 23.) To do this requires some little speed and
agility in escaping the falling trees, but with practice, the work
can be carried on without risk. No time is lost, no money need
be spent for labor, and the slight inconvenience of having the
sections made at different heights above the ground is more than
offset by the large number of trees that can be measured.

23. Measurements made on a Felled Tree. — After felling a
tree, it is usual y trimmed of all branches and stubs to a height
which represents the limit of merchantability, and cut into logs
of standard lengths at the discretion of the boss of the crew.
The following measurements are then recorded on forms pre-
pared in advance, to save time:

(1) Diameter breast-high, in inches (taken before felling).
(2) Average height of stump, in feet and tenths.
(3) Length and diameter of each section (log).
(4) Length of top in feet and tenths.
(5) Clear length (stump to first stub or branch).
(6) Used length (= sum of values in (3)).
(7) Merchantable length.
(8) Length of crown (from first green limb to top).*
(9) Width of crown.*
(10) Total height (sum of 2 3 and 4).

In addition to the above data, space is provided on the blank
forms for the entry of the species, the locality, the date, the
names of the men composing the crew, and any other information
that would be useful. If mill scale studies are to be made on the
same trees, each tree receives a number, and each log the same
number and a letter, so that the logs can be identified when they

* The 8th and oth measurements are not always taken. They are useful if
growth studies are also to be made on the same trees.
42 THE MEASUREMENT OF FELLED TREES

reach the mill. For example, a certain tree, as it is felled, re-
ceives a consecutive number; this number is written on the
stump with a crayon. The first log is then marked with the
same number, followed with a dash and the letter “a” (e.g.,
117-a). The second log receives the tree-number followed by
a-dash and the letter ‘“‘b” (e.g., 117-b). In this way, each log
can be identified, and it can be referred to the prope tree. Later,
when the logs are sawed at the mill, the exact product of each
log in sawed. lumber can be measured and recorded, and in this
way figures obtained which serve as a check not only on the
scaling as done in the woods, but also on the volume tables
which have been constructed from trees in the same locality, if
such volume tables exist. A sample form, suitable for recording
all the above data, is shown in the Appendix, page 261.

A word of explanation is needed with reference to measure-
ment number 7 — merchantable length. It not infrequently
happens that the lumbermen, because of certain restrictions in
the trade, cannot use all of the merchantable portion of a tree.
In other words, there may remain in the tops certain material
which, under conditions permitting closer utilization, would be
considered merchantable. It is customary to include this extra
length, if there be any, under measurement number 7.

24. Application of Log Rules, or Mathematical Formule. —
If only sound, normal trees have been measured, scaling need
not be done in the woods, but it can be done ‘n the office later.
It has been pointed out in Article 13 that log rules show the
estimated contents of sound logs which are reasonably straight and
free from excessive taper. Therefore the computations for
board-foot contents can be made directly from the data in the
field note-books. Similarly, the cubic contents of the several
sections of a felled tree can be computed by the application of
certain formule which will now be discussed.

25. The Forms of Trees in General. — Under normal con-
ditions a tree grows in height and diameter simultaneously; to
be sure, the height-growth takes place much more rapidly than
the diameter-growth, but the rate of each kind of growth follows
certain rather well-defined laws, modified more or less by the
THE FORMS OF TREES IN GENERAL 43

differences in the seasons and the circumstances under which the
tree grows. The product of growth in diameter and height is a
solid which resembles certain geometric solids for which there
are mathematical formule which enable one to calculate the
cubic contents when certain dimensions are known. These
solids are all cone-like, —i.e., they taper as they ascend from
the base, and finally come to a point (the growing tip of the tree).
If the bole of the tree has a tendency to fill out in the middle and
upper portions becoming more nearly cylindrical, it may ap-
proach very closely the geometric solid known as the paraboloid,
because it can be conceived of as generated by the revolution of
a parabola about its central axis. If, on the other hand, the tree

ie

 

PARABOLOID CONE NEILOID

Fic. 8. Fic. 9. Fic. to.

has a spreading root-system, and there is considerable of a flare
at the butt, so that it tapers very rapidly at the start, but be-
comes more and more like a cone as the top is approached, then
the form will resemble that of a Neilian paraboloid, or Neiloid,
which can be conceived of as generated by a curve of the third
degree about i s central axis.* Midway between these two forms
is the true cone, which has a perfectly regular taper, and can be
conceived of a generated by the revolution of a straight line

* Expressed in terms of analytic geometry, the equations for the curves which
generate these solids are as follows:

Parabola: y = 2mx.
Neilian Parabola: y= 2mx,
Cone: ye = 2mx*.

In each case, m = an independent variable, called the parameter. See standard
texts on mathematics, such as Woods and Bailey: “ Analytic Geometry and
Calculus,” Boston, Ginn and Co., 1917.
44 THE MEASUREMENT OF FELLED TREES

about a central axis.* It is, therefore, possible to recognize
three type forms which the stems of trees resemble, and these
are shown in Figs. 8, 9, and 10 on page 43.

The formule for expressing the cubic contents of these solids
are derived by methods of geometry or by integral calculus, and
are presented here without proof.

Formule for Contents of Geometric Solids

In each case:
H = height,
B = base (lower); 6 = base (upper).f
Bx = base taken at half the height.
Bx = base taken at one-third the distance up from lower

base.
V = volume.
H
1. Cone V=Bx-: (1)
3
2. Paraboloid V=BxX 4. (2)
x Nelbta V=Bx . (3)
4. Frustum of cone V = (B+b + VBb) =“ (4)
3
H
and V= ie (5)

5. Frustum of paraboloid

v=(B+0)4 y 6)

and V=Bixd. (7)

* Perhaps an easier way to conceive of this is to say that a right-angled tri-
angle revolves on its axis, the axis in this case being the longer side opposite the
hypotenuse.

+ Geometric proofs for these formule are shown in Baur’s “Holzmesskunde”
(Berlin, 1891), pages 46-65.. Proofs by integral calculus are shown in Miiller’s
“Lehrbuch der Holzmesskunde” (Leipzig, 1899), pages 9-15, and in other standard
text-books on the subject.

} The area of the base is expressed in terms of square feet. To facilitate the
calculations tables of basal areas have been constructed, showing for any diameter
in inches, the corresponding area in square feet. See Appendix, page 231.
ys yt
THE FORMS OF TREES IN GENERAL a) 45

6. Frustum of Neiloid
V = (8 FRe +H) 2. (8)

By taking advantage of the formule for frustums of the solids
mentioned, it will be seen that the tree, instead of being con-
sidered as a whole, may be considered as composed of several
parts, or sections (stump, logs, and top), and in this manner the
contents can be computed very accurately. For example, the
first or butt log may include some of the root swelling at the
base of the tree, and, therefore, resemble closely the frustum of
a neiloid; the second log may have a very even taper, and the
form of it would, therefore, be the frustum of a cone; the third
log of a three-log tree will very frequently resemble the frustum
of a paraboloid; while the top may resemble either a cone or a
paraboloid in form, depending on the rate of taper. Thus, if we
have the formule for the frustums of these solids, we are enabled
to apply the appropriate formula for each separate section of the
tree and by adding all together obtain the total volume quite
accurately — much more so, in fact, than could be done by
applying a single formula. The formule included in the fore-
going paragraph are merely a few of the more useful of the
complete list, which numbers a great many more. Experience
has shown that for most trees, the formula for the frustum of a
paraboloid applied to the logs, and the formula for a cone applied
to the top, will give very satisfactory results. If any one of the
logs is very obviously of a different form, its volume may be
found by applying the most appropriate formula. It should
also be stated that the stump, being short, is usually considered
as a cylinder. Although this introduces a slight error, it is
negligible, especially when it is remembered that the stump is
almost always but a small part of the total volume of the tree,
and is not merchantable. The principal reason for including it
in the computations is to obtain, as nearly as may be, the volume
of the entire stem — a very important consideration in dealing
with the subject of growth, or increment (See Chaper X.)

A formula which will give the volume of the entire stem of a
46 THE MEASUREMENT OF FELLED TREES

tree is often a great convenience, especially if approximate results
will fulfil the purpose, or if time is lacking to make a detailed
computation of the contents by sections. Two formule are
herewith presented, which, with a measurement made in one
additional place besides the height and base, will give very fair
results. They are, in fact, much more reliable than formule
number 1, 2 or 3 (page 44), because most trees are not quite
true to form, either of a cone, or a paraboloid, or a neiloid, but
are intermediate; and the measurement of the diameter in an-
other critical point, together with a measurement of the base and
the tota height, enables us to compute the volume with con-
siderable accuracy. These two formule are as follows:

Schiffel’s formula: V = (4B+42b:) x H. (9)*

Pressler’s formula: V =2B x Hid (10)*

It will be noticed that Schiffel’s formula is merely Formula
No. 8, in which the upper base, 6, has become a point (the tip of
the tree), and hence, equal to o. It therefore disappears from
the formula. This formula requires that a diameter measure-
ment be taken at a point midway between the base of the tree
and its extreme tip. This can be done with any degree of ac-

.curacy desired, and either outside bark, or inside bark, on a
felled tree; on a standing tree, the approximate diameter, out-
side bark, can be gotten by the aid of a dendrometer (see Article
19). Pressler’s formula requires that a measurement of the
height be made at tha point on the stem where its diameter is
just one-half that of the base. This can be done very accurately
on a felled tree, but in the case of a standing tree, it must, of
course, be obtained by the aid of a dendrometer. Pressler’s
formula is a very ingenious one, and it can be proved to be abso-
lutely correct in the case of a tree whose form is that of a cone or
a paraboloid. It is not quite correct in the case of a tree whose
form is that of a neiloid, but the error, even in this case is less
than one per cent, so that the formula is an extremely useful one,

* B = lower base; by = base taken at one-half the height; H = height; Hya =
height at which the diameter is one-half that at the base.
XYLOMETRIC METHODS 47

since the vast majority of trees will fall, in form, between a
paraboloid and a, neiloid.

26. Xylometric Methods. — In the case of parts of a tree
which are very irregular, as is the case with branches, crotches,
and deformed parts the only way to obtain the volume with any
degree of accuracy is to plunge the part to be measured in a tank
of water, and measure the volume of water displaced. This
method is resorted to on\y under exceptional conditions, or
where very accurate figures are required. It is not a method of
common practice. One instance of its application, however,
may serve to show how it can be made very useful. It is a well-
known fact that the amount of solid wood in a cord of stacked
wood varies considerably according to several factors (see
Appendix, page 227). About the only way in which irregular
pieces of wood of this kind can be measured accurately is by
measuring the amount of water they displace. Several exhaus-
tive studies of cordwood have been made, with the result that it -
has been found that the amount of solid wood in a stacked cord
varies all the way from 73 cubic feet to 92 cubic feet. The signi-
ficance of these figures to manufacturers and buyers of pulp-
wood is immediately apparent.*

* See Zon, R.: “ Factors Influencing the Volume of Solid Wood in the Cord,”
Forest Quarterly, vol. I, pages 126-133.
CHAPTER VI
THE MEASUREMENT OF STANDING TREES

STANDING trees can be measured to obtain diameter, height,
and volume. Only the first of these three can be obtained by
direct measurement; the other two quantities can be gotten by
indirect methods, the degree of error depending on the refine-
ment and accuracy of the instruments employed, and the care
with which they are operated by the users.

27. Measurement of Diameter. — Diameter can be measured
by the tree calipers, by the Biltmore stick, or by the circum-
ference-tape. (See Chapter IV.) For trees of small and
medium diameters, —e.g., up to 36 inches, — the calipers or
the Biltmore stick are to be preferred; for trees of large diameter,
such as. those growing in the forests of the Pacific slope, the
circumference-tape is the only practicable means of measure-
ment. This is because calipers of a size sufficient to measure
these very large trees would be too cumbersome, and the Bilt-
more stick, although it can be constructed, theoretically, for
trees of any size, cannot be read closely when applied to trees
of very large size.*

Foresters measure the diameter of standing trees at a height
of four feet, six inches from the ground, a point spoken of as
“‘breast-height.”” (Commonly abbreviated to “d.b.h.”’) If the
tree stands upon level ground the determination of breast-
height presents no difficulty; if, however, the tree stands upon a
slope, or if the ground at the base of the tree is very uneven,
the determination of breast-height is a matter for the exercise of
some care. The rule, under such circumstances, is to stand
in such a position that the feet are upon a contour line running
through the center of the tree. This secures an average measure-

* The limit of accuracy for the Biltmore stick is about 42 inches. See Jackson,

A. G.: “The Biltmore Stick,” Ferestry Quarterly, IX, page 406.
48
MEASUREMENT OF DIAMETER 49

ment and saves the time and labor of taking the mean of twe
measurements — one made from the upper side, and one from
the lower side of the tree.

Nearly all trees are more or less eccentric in cross-section;
this means that in careful work the calipers should be applied at
more than one position (all at breast-height, of course). The
easiest and quickest way to secure an average measurement of
breast-height diameter is as follows: in applying the calipers to
a tree, the jaws are opened, the caliper placed with the graduated
beam tangent to the tree, and then the jaws are pressed to-
gether until they both touch the tree. If the calipers are
revolved about, as this pressure is exerted, the sense of touch
will tell when the minimum diameter has been reached. This
can then be read from the graduated beam, and carried mentally
until the maximum diameter has been measured, which, in 9
times out of 10, will be found at right angles to the first position.
The mean of these two readings can usually be made mentally,
and represents the average diameter of the tree. This quantity
is the one that should be recorded, rather than a diameter
obtained by a single reading of the calipers, applied at random.
In some kinds of work, requiring extreme accuracy, for the pur-
pose of making future comparisons, both the maximum and the
minimum diameters are recorded. (See Article 75, Permanent
sample plots.)

Sources of error in measuring diameter are: (1) calipers not
adjusted correctly, (2) calipers not held at breast-height, (3)
calipers not held at right angles to the stem of the tree, (4) cali-
pers held so as to include some abnormality of form of the tree.
In order to guard against these errors, the calipers should be
inspected at frequent intervals, and corrected by the adjustment-
screws (see Article 15) if they need it. Elimination of errors
number 2 and number 3 can be obtained only by exercising
constant care. Error number 4 is not always easy to avoid;
if it is necessary to measure a tree with an abnormal form just
at breast-height, the mean of two readings, one above and one
below the deformity, should be taken. It is far better, however,
to measure only normal trees, unless the character of the work
50 THE MEASUREMENT OF STANDING TREES

requires that all trees be measured. Trees that fork should be
measured as two or more trees, even if the calipers have to be
held slightly above the regulation 43 feet above ground, for in
utilizing such trees, the lumbermen would probably “butt off”
the forked portion. Provision for other unusual abnormalities
or conditions can be made at the discretion of the man in charge
of the measurement.

28. Measurement of Height.— The measurement of the
height of standing trees is attended with no special difficulties.
The chief sources of error are: (1) incorrect measurement of the
base-line on sloping ground, (2) no allowance for the departure of
the stem from a perpendicular position, (3) failure to make the
observations on the very bottom and very top of the tree, (4)
lack of proper care in the use of the hypsometer, leading to in-
accurate readings.

These errors can be eliminated very largely by exercising care
in the manipulation of the hypsometer. The base-line should,
of course, be measured horizontally, and under no circumstances
along the surface of sloping ground. (See Article 3, page 6.) If
a tree leans, the observer with the hypsometer should take up
his position at right angles to the direction of inclination (e.g.,
if a tree leans to the north, make observations from a position
either due east, or due west). It is better, however, to measure
none but straight trees, for leaning trees are too apt to be ab-
normal in some respect. The third error is of frequent occur-
rence in dense stands, where the foliage may very easily obscure
the view. Often, the crowns of trees in a dense stand are diff-
cult to distinguish, one from another, and the greatest care must
be taken to avoid mistakes of this character. The temptation
to work constantly with a base-line of exactly 100 feet, thereby
saving computations, should be resisted, for very often a little
time spent in finding a place from which a clear view of both
the top and the bottom can be obtained, will be more than
offset by the danger of making doubtful observations at some
arbitrary point chosen simply because it would obviate the
necessity for mathematical computations. It is easier to meas-
ure a base-line through masses of intervening foliage and under-
FORM FACTORS 51

growth than it is to maké observations through similar
obstructions. Error number 4 — lack of care —is sometimes
more difficult of elimination in the presence of strong winds.
Some types of hypsometers are very difficult to operate
accurately if a strong wind is blowing, and all that can be done
is to wait for a quiet day. A windless day has the further
advantage that the trees themselves are not swaying, and it is
then much easier to obtain accurate readings with the hypsometer.

29. Measurement of Volume. — The volume of standing trees
can be obtained approximately by any one of five methods:
(1) Measure the diameter breast-high, and either the total
height, the merchantable height, or the number of logs of stand-
ard length that the tree will yield, and then refer to the ap-
propriate form of volume table for trees of the same locality.
(See Chapter VII.)

N(2) Measure the diameter at the base of the merchantable
stem, the total height, and the diameter at one-half the height
(this is done by the aid of a dendrometer). Then apply Schiffel’s
formula. (See Article 25.)

V(3) Measure the diameter at the base of the merchantable
stem, the height at which the diameter is exactly one-half of
this value (Hig. See Article 25), and then apply Pressler’s
formula.

t4) Measure the diameter at breast-height, the total height,
and then apply the method of form factors. (See Article 30.)

\(5) Measure the diameter at breast-height and estimate by
the eye the number and top diameters of logs of standard length,
scaling each log separately by any desired log rule. (See Article
44.)

30. Form Factors. — A form factor is the ratio, expressed
decimally, between the volume of a tree and the volume of a\-~
geometric solid (usually a cylinder) of equal height and basal
area. There are several kinds of form factors, depending on
how much of the tree is included in making the volume calcula-
tions, and at what point the diameter of the tree is measured.
In this country, it is generally understood that the diameter of
the tree is measured at breast-height, and that the volume of the
52 THE MEASUREMENT OF STANDING TREES

stem, exclusive of the branches, is used in comparison with the
volume of a cylinder. This is called the ‘‘breast-height stem
form factor,” or simply, the form factor. If, however, the vol-
ume is understood to include not only stem, but branches, it is
called the tree form factor; if only the merchantable portion of
the stem is included, then it is called the merchantable form
factor. In recent years other kinds of form factors have been
devised, as, for example, the so-called frustum form factor, com-
paring the board-foot contents of trees, within certain merchant-
able limits, with the board-foot contents of ideal frustums of
cones, in which the taper is regular.*

If the time ever comes when the cubic foot becomes a common
unit of measure in this country, it is quite probable that form
factors will be more generally used here. For the present, the
use of form factors will doubtless be confined rather closely to
theoretical investigations. The very fact that there is no con-
stant ratio between board feet and cubic feet makes it difficult
to use form factors in any practical way.

31. Use of Form Factors. — Once a complete table of form
factors has been constructed for trees of different species, and
growing under certain stated conditions, the computation of the
cubic-foot contents, either of single trees, or of whole stands,
becomes a relatively simple matter. The formula for finding
the contents of a tree by the method of form factors is

V=BxH*xFF

in which V = volume, B = basal area in square feet (see Ap-
pendix, page 231) and FF = the form factor. In the case of
whole stands, the total basal area of all the trees in the stand is
used, and this quantity, multiplied by the average height and the
forest form factor (i.¢., the average form factor for the whole

* See Forestry Quarterly, vol. X, pages 215-221. Bruce, D.: “A New Method
of Constructing Volume Tables.”

Other kinds of form factors, depending on where the base is measured, are:
(1) the absolute form factor, in which the base is measured level with the ground,
and (2) the normal form factor, in which the base is measured at a height above
the ground bearing a certain ratio to the total height of the tree. These form
factors are used chiefly in Europe, in theoretical work, and are practically unknown
in this country.
USE OF FORM FACTORS 53

stand) gives the contents of the stand. This method will yield
satisfactory results only in the case of pure, even-aged stands
of great regularity. The saving in labor and time is, of course,
very considerable, but at the present time there is a lack of
adequate tables of form factors, and the conditions in the forest
are so rarely favorable to the use of the method in this country,
that it is practically never used.
CHAPTER VII
VOLUME TABLES

32. Definition and Uses of Volume Tables. — A volume table
is a tabular statement showing for a given species | the average
contents of trees of different sizes. Volume tables may be made
for any desired unit of volume, as, for example, board feet, cords,
standards, cubic feet, ties, and so forth; the most commonly
employed units are board feet and cubic feet. With proper con-
verting factors it is possible to transform volume tables in cubic
feet to volume tables expressed in terms of cords, standards,
etc. Volume tables are used chiefly in connection with timber
estimating. After the tally of trees is complete, the appro-
priate volume tables are applied to obtain the estimate in terms
of the desired unit of measure. Used with due consideration
for the limits within which they will apply, accurate volume
tables may be relied upon when they are applied to a large
number of trees; but it is not to be expected, from the manner
of their construction, that they will apply to individual trees.
(See Article 38.)

33. Classification of Volume Tables. — According to the
manner in which the trees are classified, there are several kinds
of volume tables. The commonest in general use are as follows:

(1) Volume Tables Based on Diameter Only

In this form of table the trees are classified by diameter
breast-high only. No account is taken of the height or the
form of the tree; hence these tables are of little practical use
unless they are applied to trees of form and development similar
in all respects to the trees from which the tables were constructed.
This limits the use of these tables to restricted localities, and
unless there is a prospect of using them locally, it scarcely pays
to construct such volume tables. The locality in which the

54
CLASSIFICATION OF VOLUME TABLES sg

table was constructed, the limits within which it applies (es-
pecially the minimum diameter in the tops, and the average
height of stumps), the log rule used in scaling, and the average
dimensions of the lumber sawed from the logs, are also impor-
tant pieces of information which should be included in these, as
in all other volume tables. (See Article 23.) These data have
a special importance, however, in the case of volume tables of
this class, and tables lacking them should never be employed»

(2) Volume Tables Based on Diameter and Total Height

It has been pointed out in Article 31, where form factors were
discussed, that height and diameter are both important func-
tions of the volume of a tree. It needs but a moment’s reflection
to perceive that of two trees of equal diameter and of similar
form, but of different total height, the taller tree will have the
larger volume. This is not only true of the cubic contents, but
is even more emphatically true of the merchantable or board-
foot contents; for the taller tree has less taper, and will yield
more logs, each one slightly larger in diameter than the corre-
sponding log of the shorter tree, thus producing a total of board
feet considerably in excess of the product of the shorter tree.
In volume tables that show the average contents of trees classi-
fied both by diameter and height, it is therefore possible to
express the contents much more accurately. Moreover, such
tables are susceptible of a wider application, because the heights
of trees, even within a comparatively restricted geographical
range, will show marked differences, reflecting the differences in
quality of site. (See Chapter XI.) In constructing tables of
this kind it is customary to classify the trees, as to height, in
1o-foot classes. In other words, all trees 56 feet and over, up
to 65 feet, would be included in the 60-foot class; all trees from
66 feet to 75 feet inclusive would be thrown into the 70-foot
class, and so forth. A greater degree of refinement is scarcely
needed. An example of this form of volume table is shown in
the Appendix, page 232.
56 VOLUME TABLES

(3) Volume Tables Based on Diameter and Merchantable
Length

Tf it is true that the total height is such an important factor
in determining the volume of a tree, then the merchantable
length is even more important. By adopting this classification
of trees the greatest degree of accuracy in volume table con-
struction can be secured. Since common usage calls for logs in
multiples of two feet (7.¢., 8-foot logs, 10-foot logs, 12-foot logs,
etc.), it is necessary to recognize merchantable heights in the
same way, in order to meet any possible combination of log-
‘lengths. This means that a volume table constructed according
to this plan must have as many columns as will be necessary to
provide for all the possible merchantable lengths — often as
many as 30 or 4o columns. Such a table would be very com-
plicated and unwieldy; would occupy too much space; and would
be open to the objection that, in order to warrant its use, the
merchantable heights of the trees estimated must be judged
with great precision, — to be exact, within two feet, — a degree of
precision which in fact calls for the constant use of hypsometers.
This makes the work of cruising proceed very slowly and labori-
ously, and it is a question whether the time and money spent in
this meticulous manner can be justified by the results. After all,
a timber cruise is only an estimate, and there are limits beyond
which it will not pay to go. Tables of this form, therefore, are
rare; and the occasion for their use is very unusual. Under
conditions that demand some attention to the merchantable
length of the trees in a cruising operation, it will be found that a
classification of trees into groups by the number of logs of stand-
ard length will meet all the requirements, and the use of tables
of this kind is not only practicable, but is often the most satis-
factory when considering the two desirable features of efficient
timber estimating, namely, accuracy and reasonable cost.
Tables of this form will now be discussed.
CLASSIFICATION ‘OF VOLUME TABLES 57

(4) Volume Tables Based on Diameter and Number of Logs of
Standard Length

The standard log usually selected for tables of this form is the
sixteen-foot log. This length is, perhaps, the one most com-
monly used, and it is customary to recognize half-lengths (8 feet)
in the preparation of the volume tables. This provides for a
considerable degree of accuracy and at the same time the table is
of such proportions that it can be printed on a single page of a
hand-book or field-book. Moreover, a skillful cruiser needs no
instrument for measuring height, — his eye can be trained to
estimate log-lengths of this size with sufficient accuracy to
make tables of this form practicable. After a little practice in
judging merchantable lengths to the nearest 8 feet, the work
proceeds with great ease and rapidity. A further point to be
considered is this: the blank form in the cruising note-book is
not unduly wide, and the tallying process can be carried on
easily and quickly. All things considered, it seems safe to say
that when this method is followed, 7.e., trees estimated and
tallied according to log-lengths, recognizing units as small as 8
feet, the greatest degree of accuracy consistent with economy of
time and labor in the work of cruising, can be obtained. Tables
prepared according to this form are becoming more and more
common, and they have met with almost universal approval
by foresters and cruisers who are in the habit of doing careful,
accurate work.* A sample of this form of volume table is pre-
sented in the Appendix, page 233.

(5) Volume Tables Based on Diameter and Tree-class

For some kinds of work, particularly the estimating of cord-
wood, pulp-wood, or wood intended for a form of use where
actual cubic contents is of more consequence than the form of the
pieces, volume tables prepared for trees of different diameters

* As further evidence of the usefulness of tables in this form, it may be stated
that the U. S. Forest Service is now, and has been, for some time past, preparing

and publishing all its tables on this basis, using the 16-foot log as the standard,
and recognizing half-logs (8-foot lengths) in the tables.
.

58 VOLUME TABLES

and crown classes are useful. For example: A tree of large
diameter, growing in the open, or in an uncrowded stand, may
produce a very large, round-headed crown, composed of many
branches which are perfectly good as fuel, but worthless as
lumber. Such a tree compared with one of equal diameter,
but smaller crown, would yield a much greater quantity of cord-
wood. It will take a special form of volume table to show this
difference in volume. Again, certain species of trees adapted to
growing both in dense stands and in uncrowded or open stands
will display the greatest difference in form, and consequently
a difference in volume, depending on the situation in which
they are growing. Hard maple, grown in a dense stand, pro-
duces a long stem topped by a relatively small crown; in the
open it often attains a large diameter and good height, but the
stem almost invariably divides again and again, until a large,
round-headed crown is the result. This tree would yield per-
haps four or five cords of wood, but practically no saw-timber.
Under such conditions, the irregularity of tree form makes the
use of the ordinary volume table impossible; but if volume tables
based on diameter and tree form are available, the work of
estimating such timber can be done with considerable con-
fidence.

_ The classes of trees recognized in making tables of this kind
are usually based on crown development. A convenient form of
classification is as follows:

Crass A. Trees growing in the open, with large, spread-
ing crowns, occupying from 75 to go per cent or more of
the total height.

(Large oaks, maples, and hickories growing in old pas-
tures are good examples of this class of tree.)

Crass B. Trees in uncrowded stands, with irregular,
forked, and many-branched stems, the crown occupying
from 50 to 75 per cent of the total height.

(Maples in an old sugar bush, or irregular trees of inferior
form left after culling the best merchantable trees in a
stand, are common examples of this class of tree.)
TREES FROM WHICH VOLUME TABLES ARE CONSTRUCTED 59

Cuass C. Trees in crowded stands, with crowns occupy-
ing less than 20 per cent of the total vee and with
irregular, deformed, crooked stems.

(Trees badly oppressed, or totally suppressed, as a result
of insufficient light and growing space, are examples of
this class of tree.)

It will be noticed that this classification takes no account of
those trees the crowns of which occupy from 20 to 50 per cent of
the total height. Trees answering this description are more
than likely to be normal in form, and therefore the ordinary
form of volume table will be applicable, providing the trees are
straight enough to yield saw-logs.

Volume tables of this kind are sometimes very useful, but are
not common, since they are extremely limited in their range of
usefulness. They are generally prepared for restricted localities,
and are not applicable to stands outside those localities. They
apply to classes of trees which are, strictly speaking, abnormal,
and since the ordinary volume table should be constructed from
normal trees only (see Article 35), these tables are what might
be termed ‘‘exceptional.”’

34. Kinds of Trees from which Volume Tables are Con-
structed. — By definition (Article 32), volume tables show the
average contents of trees of different sizes. It is therefore
necessary to exercise great care in the selection of trees for meas-
urement, as the basis for constructing the table, and to use only
those trees that are found to be normal and representative of the
average for the locality. This means that trees of unusual pro-
portions must be excluded; it means that no crooked, diseased,
forked, or broken-topped trees shall be included; it means, in
short, that practically all trees described under Classes A, B, and
C in the preceding article, shall be excluded. For the very fact
that these trees have had to be classified as to form and crown
development means that they are not normal, average trees.
Grown under normal conditions in the forest, a tree will usually
produce one stem, which is rarely absolutely straight, and
practically never of perfect geometric form; nevertheless, the
average tree of a given species will approach rather closely a
60 VOLUME TABLES

certain, definite form which is quite constant for the species.
This has been proved conclusively by many thousands of
measurements on tzees grown under favorable silvicultural
conditions. It may not always be possible to tell by a superfi-
cial inspection whether or not a tree is of average, normal form;
but errors in judgment of this kind can generally be detected
when the trees have been properly classified preparatory to
constructing the tables. The methods usually followed are
described in the next Article.

35. Methods of Constructing Volume Tables. — (a) In the
Field. — If the cost of the work is to be kept within reasonable
limits, it is impossible to fell trees for the special purpose of
volume table construction. Moreover, such a course of action
-would be unnecessarily wasteful, unless the felled trees could be
utilized promptly. The usual custom is to follow the tree-
felling crews of a lumbering operation, and, as pointed out in
Article 22, use the trees that are cut by these crews, always ob-
serving, before the tree is cut down, whether or not it appears to
be normal, and obtaining the diameter breast-high measurement
while it is yet standing.* After the tree is felled and cut into
sections the measurements described in Article 23 may be re-
corded in the field book, together with such additional notes and
comments as the needs of the work dictate. The computations
mentioned in Article 24 are now made, not in the field where
such work is carried on at a disadvantage, but in the office,
where computing instruments make the work easy. This work
will now be described.

(b) In the Office. —TIf the field notes have been taken ac-
curately and the descriptions of the trees made with care, the
work of computing the contents of the trees measured in the field
progresses smoothly and rapidly. First, all the trees of the
same diameter-class and the same height-class are grouped
together; in doing this work, fractions of an inch in diameter
are considered as going to the nearest whole inch gbove if the
fraction is 0.6 or more, and to the nearest whole inch below if the

* It is possible to obtain the diameter breast-high of a felled tree, but the meas-
urement is not made so easily, and a liability of error always exists.
METHODS OF CONSTRUCTING VOLUME TABLES 61

fraction is 0.5 or less. The heights are classified as explained in
Article 33. The several logs of each tree of a given class are
then scaled by some acceptable log rule, and the total contents of
each tree obtained by adding together the contents of the sevéral
logs. When this has been done for all the trees of a specified
inch-class (i.e., diameter-class) the values are averaged together
to determine the mean value for all trees of that particular
class.

The following tabulated arrangement of the data is suggested
as being easy to work with, and it will further serve to enlighten
the text:

 

60-foot height-class

Average contents of trees of { 14-inch diameter-class

 

| rein NoOvoxee cistecmeeeaks 27 85 | 192 215 | 218 | 507 etc.
’D.b.h. (inches)........... 13.7| 14.2} 14.5|° 13.6} 14.1] 14.3] etc.
, Height (feet)............. 56.3] 61.4] 62.1] 60.1] 59.8) 64.7] etc.

 

 

Board feet by Scribner Rule.

 

 

 

 

 

 

 

 

 

 

First log..... Pomc duels 55 55 59 55 59 69
Second log............... 32 35 40 35 40 30
Third 10g. 2s es wateuuds 14 | 18 18 12 18 18
Totalegiscvercass swage tor | 108 | 117 | 102 | 117 | 117
Average diameter, breast-high................ 14.07 inches
Average height... .......... cece cece cece 60.7 feet
Average board-foot contents .................- 110 _ board feet

While there is naturally some difference between the values
for the several trees, the extremes — 101 and 117 — are not
very. far from the average, 110. This figure may therefore be
accepted. If, however, any large discrepancies had appeared,
it would have been wise to go over the figures again, to see if
any mistakes had been made. If the work were found correct,
then those trees which depart very widely from the general
average should be eliminated from the calculations, on the
ground that they are not normal. ,

After having averaged together the values for each class of
tree, the easiest and quickest way in which to construct a table
62 VOLUME TABLES

is to employ the graphic method.* For much of the work in
forestry, graphic methods are by far the best to employ be-
cause the dependent variable quantities, like height, volume,
diameter, rate per cent of growth, and so forth, are practically
always made functions of age —i.e., time, which is the in-
dependent variable quantity. Sometimes diameter, which is
closely associated with, and related to, age is made the independ-
ent variable, but even in such cases the graphic method can
usually be made to apply. In the case under discussion at
present, the contents in board feet (the dependent variable) of
all the trees of a particular height-class can be plotted on diam-
eter breast-high (the independent variable) and a curve can then
be drawn which represents the relation of board-foot contents
to diameter. The several points should be plotted on cross-
section paper, and a smooth curve should be drawn through
them. The same procedure is followed for trees of the next
height-class, and continued until the data for all the height-
classes have been plotted. The curves should then be com-
pared and harmonized,t so that the values for the several height-
classes progress smoothly and evenly. From these curves, the
appropriate values may then be read off and tabulated, showing
for each inch-class in diameter the corresponding volume in
board feet, each height-class being arranged in a vertical col-
umn by itself. See sample volume tables in the Appendix,
pages 232 and 233.

36. The Method by Taper Curves. — If tables are prepared to
show for different species and height-classes of trees the average
diameter measurements of the stems at specified heights above
the ground (inside bark),a means is thereby afforded for obtain-
ing the contents of-the trees by any desired log rule, since the
process is, in effect, a process of scaling on paper the logs of
normal, average trees. Such tables are called form tables, or
taper tables, and are constructed from taper curves, which in

* For an admirable discussion of all sorts of graphic presentation of data, see
Brinton, W. C.: “Graphic Methods,” New York, 1914, The Engineering Magazine
Co.

{ This can be done to best advantage by drawing all the curves on one sheet
of paper.
CHECKING VOLUME TABLES BY MILL SCALE STUDIES 63

turn have been drawn from the measurements of many normal,
felled trees. Good examples of taper tables may be found in
several of the recent Department of Agriculture Bulletins which
deal with the form and contents of commercial species of trees.*
The diameter measurements are usually made at stated intervals
up the stem of the tree, and are corrected to show diameter
inside bark, so that scaling can be done properly. The intervals
above ground are generally as follows: 1 foot, 2 feet, 3, 4, 4.5
(breast-height), 9.15, 17.3, 25.45, 33-6 feet, and so forth, progress-
ing by increments of 8.15 feet. In this way allowance is made
for a 1-foot stump, above which are half-logs of 8.15 feet, and
full logs of 16.3 feet. (The extra 0.15 foot and 0.3 foot are the
allowances for trimming.) To make a volume table for any
given species of tree from taper tables, the several logs, as shown
by the diameter values in the tables, are scaled to any desired
merchantable limit in the tops and by any preferred log rule.
In this way, it is possible not only to choose one’s own limits of
merchantability, but to select one’s own log rule; these ad-
vantages are obvious, since it may be necessary to vary the
merchantable limits in order to conform to local utilization
practices, or to use a particular log rule, which is in favor locally.
More and more of these taper tables are being published, and in
time there will be enough of them to make their general use
quite practicable. They are by far the most logical way in
which to attack the problem of preparing serviceable volume
tables.

Taper tables, or form tables, are constructed from a set of
harmonized curves, each set being drawn from the data secured
by measuring many trees of a given height-class, from which the
average dimensions are calculated.

37. Checking Volume Tables by Mill Scale Studies. — It is
often desirable, although not always possible, to check a volume
table by studies at the saw-mill, which include, first, scaling logs
which have been marked serially in the woods (see Article 23),
and secondly, following them through the mill to see what they

* See especially U. S. Dept. Agr. Bul. 285, ‘The Northern Hardwood Forest”
(1915), Tables 43, 44, 45 and 46. Others are listed on page 237 of the Appendix.
64 VOLUME TABLES

actually produce. If this work can be done for about one
hundred entire trees, of different size-classes, a fairly reliable
check on the volume table is obtained. It is especially desirable
that this work be done in cases where the trees are suspected of
hidden defect, or where they run very irregular in form.

38. Application of Volume Tables. — Now that the method of
constructing volume tables has been explained, it will be under-
stood why any one individual tree can hardly be expected to
yield the exact amount of lumber assigned to it by the appro-
priate value in the volume table. The chances are that not
more than one tree out of 100 trees of the same diameter- and
height-class would show a scaled volume the same as the volume
table value. If it is remembered, further, that a tree with a
merchantable length of, say 48 feet, can be scaled as three 16-
foot logs, or four 12-foot logs, or four 10-foot logs and one 8-foot
log, and so forth, it will be clear that the chances for an agree-
ment between the scaled value and the volume table value are
still more remote, because the results of the scale depend on the
way in which the tree is divided into logs. But when the vol-
ume table values are applied to a large number of trees, these
individual discrepancies disappear to a large extent; in other
words, the errors are compensating, and in the long run the use
of volume tables may be expected to yield satisfactory results,
provided, of course, that they are suited to the local conditions.
The more closely the tables are suited to the local conditions, —
the more closely the conditions of application and the conditions
of construction agree, — by just so much may the volume tables
be expected to give satisfactory results. If the limits of mer-
chantability are the same; if the log rule used is the same;
if the product sawed is of the same average dimensions; if the
same standards of soundness have been used in scaling and in
measuring the sawed product; then the reliability of suitable
tables, carefully constructed, should go unquestioned.
CHAPTER VIII
TIMBER ESTIMATING

39. Definition and General Remarks. — Timber estimating,
or timber cruising, as it is often called, is the art of determining
the approximate contents of trees, or stands of timber. It may
be done entirely by the eye, relying upon past experience to
guide the judgment, or instruments may be used to measure
the area of the land surface and the dimensions of the trees
standing thereon. In either case, it is always an estimate, for
no one can tell exactly what a stand of timber will yield in the
way of merchantable material until the trees have been cut
down and the logs sawed into lumber. The practices of half a
century ago, when timber and land were both relatively cheap
compared with the prevailing values today, were exceedingly
rough, and the estimates often fell wide of the mark — usually
erring on the safe side. In the present age of rising values and
closer utilization, the rough guesses of the early days are no
longer acceptable; the estimate must be accurate enough to
safeguard the investments made and the expensive equipment
now employed by large lumber companies. A difference in the
estimate of 10 per cent one way or the other, may be large
enough to be the deciding factor in a business venture, and the
purchasers of timber now expect a cruiser to submit an estimate
which will be within 10 per cent of the actual product. This
means that more refined methods of work must be employed.
Actual measurement of land surfaces must take the place of the
“guess” of the old-time cruiser, or even the maps which were
formerly thought to be good enough; * the diameters and heights

* Even the maps made by the U. S. Land Office forty or fifty years ago are not
above reproach; subsequent investigations have shown that many errors were
made, and that little confidence can be placed in maps made so long ago for remote
or inaccessible parts of the country.

65
66 TIMBER ESTIMATING

of trees must be measured with instruments, instead of being
judged by the eye; the trees must be counted and tallied in-
stead of merely guessing at the average number per acre; _cal-
culations based on sound mathematical principles must take the
place of ‘‘rules of thumb.” In other words, every possible
source of error must be eliminated, and the work conducted
with all the exactness and precision that time and money will
permit. At the best, it will still be an estimate; therefore
measurements, where they can be made, should be made accu-
rately, and so far as possible the element of personal choice
should be gotten rid of, in order that the results may be per-
fectly fair and unbiased.

The improved methods of timber estimating have been de-
vised to meet the more exacting demands of the market due to
changes in economic conditions which have followed the devel-
opment of the country at large. The vast forests of the North
and the West, once reckoned as inexhaustible, have been so
depleted by wasteful logging and forest fires that the end is in
sight; and with the inevitable rise in stumpage prices it has not
only been possible, but absolutely necessary, to conduct the
work of timber estimating in a more scientific manner. It has
thus grown to be an art, and a competent timber estimator no
longer relies upon a “‘sixth sense,” but bases his judgment on
cold, mathematical calculations. Modern, up-to-date timber
estimators employ methods of an entirely different kind than
those of the cruisers of fifty years ago.

40. Dependence of Methods on Objects of the Work. —A
further cause for greater refinement in the work of timber
estimating has been the progress of forestry, especially that
branch of forestry known as Forest Management. This term
has been defined as “the practice or application of forestry in
the conduct of the forest business.” * If the forest business
is to be conducted successfully it is necessary to know not
only the present stock in trade, but how fast that stock is |
increasing. In other words, while the timber cruisers of years
gone by concerned themselves only with the amount of mer-

* Terminology as adopted by the Society of American Foresters, 1917.
DEPENDENCE OF METHODS ON OBJECTS OF THE WORK 67

chantable timber which could then be cut from the stand,
present-day practices usually demand not only an inventory of
the merchantable stock, but an enumeration of the immature
stock, with a prediction of future growth based on careful studies
of the present rate of growth. The business of the forest has
assumed permanency; the two ideas of growth and future pro-
duction have called for data which can be supplied only by a
modern timber estimate, supplemented by studies of growth and
yield which foresters are in a position to conduct. Accordingly,
on these grounds, ‘it is possible to recognize two classes of timber
estimates, depending on the objects for which the work is done:

Crass I. Estimates which are the basis for the purchase
or sale of merchantable timber.

Crass II. Estimates which are the basis for a Forest Work-
ing Plan. (A working plan is the plan under which a
given forest property is to be continuously managed.
See Chapter XII.) On account of their greater detail,
these might perhaps be called ‘‘Forest Surveys.”

Estimates of Class I usually call for the following data:

(a) Amounts of merchantable timber (about 12 inches
d.b.h., and upward) classified by species and sizes (saw-
timber, poles, posts, ties, cordwood, pulp-wood, etc.).

(b) Location of the timber with reference to mill sites and
markets.

(c) Accessibility and estimated logging and milling costs.

(d) Market conditions, and estimated stumpage values, by
species. No attention is paid to the immature timber,
and the whole question of growth is ignored.

Estimates of Class II, or Forest Surveys, are much more
elaborate, and should include the following data:

(a) Amounts (and often grades) of merchantable timber
(12 inches and up) classified by species and sizes (saw-
timber, poles, posts, ties, cord-wood, pulpwood, etc.).

(6) Amounts of immature timber (less than 12 inches
diameter) classified by species and sizes, often going as
low as 4 inches, breast-high.
68 TIMBER ESTIMATING

(c) Detailed forest description for each type of forest
represented in the survey. Types are generally recog-
nized on a physical basis, where possible, and the estimates
for each type are kept separate by changing tally-sheets
wherever a change in type is encountered. (See Article .
48.) The forest description must be accurate, complete, :
but brief (for outline see Appendix, p. 243). bv

(d) A complete set of the volume tables used, with notes as
to local adaptations; or, ample references to standard
volume tables. .

(e) Studies of growth and yield for each commercial species
represented. (See Chapters X and XI.) These are
usually compiled in tabular form for easy reference.

(f) A complete map on a scale large enough to show every-
thing necessary. This will usually include the bound-
aries of the property, the several forest types, the topog-
raphy, streams, roads, trails, and cultural features.

(g) Location of important stands of timber with refgfen
to mill sites and markets. :

(h) Accessibility and estimated logging and ing costs.4

(zt) Market conditions and estimated st :
species.

  
  
   

Detailed instructions for the silvicultural treatment of the
several stands of timber and methods of regulating the cut are
matters which should be discussed in the Working Plan, and
have no place in the timber survey. (See Chapters XII and
XIII.) The forest survey should have as its object the com-
pilation of all the facts and figures upon which the working plan
is based.

Methods of timber estimating may be classified in another
way, 7.e., depending on the degree of accuracy with which they
are conducted. From this point of view, we may recognize
three general classes; and the several methods will be discussed
in the Articles as indicated:

I. Ocular methods. Distances and sizes judged by the eye.
Estimates based on the inspection of a very small per-
La OCULAR METHODS 69

centage of the total area — usually not more than 1 per
cent or 2 per cent.
See Article 41 for discussion.

II. Approximate methods. Distances paced; diameters and
heights judged by the eye, but checked by instruments.
Estimates based on the inspection of from 1} to 25 per

cent * of the total area.. ...............00. Article 42
(a) As applied to surveyed land.............. Article 43
(¢) Method of small plots.......... eiigiea Article 44

(#) Method of strips. . ietsneceeecs MCAS

(b) As applied to unsurveyed land, ru aor Article 46

III. Precise methods. Distances and areas measured with
instruments. Heights measured by hypsometer; diam-
eters measured by caliper or Biltmore stick. Estimates
based on 5, 10, or even 20 per cent of the total area.

These methods are further subdivided into

(a) Strip surveys............ LS pete pieese eau Article 47
A (i) Narrow strips.........77............ Article 48
4 ; (@2): Broad Strid. 0u.scpiwwe senawsessewos Article 49
aN (6) Accurately measured plots................ Article 50

41. Ocular Methods.— The methods of Class I (Ocular
methods) are often used when a very rapid reconnaissance of an
extensive area is wanted with the object, not of using the data
gathered for a working plan, nor even of using them as the basis
for a specific purchase or sale, byt merely to obtain reliable in-
formation regarding the location of stands of merchantable
timber, their composition, approximate age, condition, acces-
sibility, value, and the desirability of making more accurate
surveys later, which surveys would fall under Class II or-Class
Tlf. They are more in the nature of “exploration cruises,”
and might be called such. There are relatively few extensive
bodies of timber anywhere in this country that ‘have not been
cruised, so that the occasions when this method would be ap-
propriate are very rare indeed. For the few occasions that
might arise, the very best men obtainable should be employed,

* This large percentage of area is inspected only under special conditions, which
are described in Article 45.
7o TIMBER ESTIMATING

for good judgment, based on years of practical experience,
is essential to the success of the method.

42. Approximate Methods. When the work has for its
object the accumulation of sufficient data to determine an ap-
proximate stumpage value for the several species represented,
and such additional information as will enable the investigator
to arrive at a definite opinion regarding the value of the timber
as a business proposition, then the examination of the timber
must be more thorough, and methods of work furnishing these
data would be grouped under Class II — approximate methods.
There are many methods falling under this head, and in a book
of this kind there is not room to describe all of them. In fact
the methods are open to so many modifications, invented to suit
the tastes and the requirements of the individual estimator,
that any attempt at a complete enumeration of the methods
would be practically impossible. It will be sufficient, therefore,
to describe some of the standardized methods, which are typical.
Practically all of the methods aim to secure a reliable estimate of
the timber by species, sizes, classes of material, etc., and a map
which will be sufficiently accurate and detailed to plan the log-
ging operations. Descriptions of the stands, estimates of the
cost of logging, and other points of interest, are generally in-
cluded so that stumpage prices can be fixed; but no studies of
growth and yield aremade. The percentage of the area actually
covered may range from 1 or 2 to 5 per cent, and since a knowl-
edge of area is so essential to the success of any of these methods,
the logical way to classify them is according to whether or not
the land has been surveyed and the boundary lines permanently
marked. (Interior lines as well as exterior lines.)

43. Approximate Methods as Applied to Surveyed Land. —-
By surveyed land, in this connection, is meant land that has been
divided, by survey, into units six miles square (called townships),
and each township then subdivided into 36 square miles (called
sections) ,* all numbered and referred to certain established base-

* The townships of Maine and the Adirondacks, surveyed before Congress had
adopted the standard form of survey employed in the western states, have no
definite number of sections; and the system of numbering them differs from the
system used in the U. S. Land Office.
; :
APPROXIMATE METHODS AS APPLIED TO SURVEYED LAND 71

lines and meridians, according to methods prescribed by the
U. S. Public Land Office.* The establishment of permanent
corners on the ground, the blazing of trees along the lines, and
the sets of descriptive notes accompanying the sketch-maps, —
all done according to a uniform system provided for by the
government, — did much to make the work of orientation and
area determination easy; and where the marks of the original
surveys have not been obliterated orientation is still a com-
paratively simple matter. Contrasted with these rectangular
surveys are the ordinary surveys by metes and bounds, and
these are not nearly so readily handled by the timber estimator.
Unless the parcels of land are relatively small (z.e., 160 acres or
less), and unless the survey lines are plainly marked, both on the
ground and on the map, it is usually necessary to run some
preliminary lines before the work of timber estimating can be-
gin. Moreover, the lines of metes and bounds surveys are apt
to be so irregular, and the work of such questionable accuracy,
that it is frequently necessary not only to run a straight line as a
base-line, but to retrace the exterior lines, for the purpose of
securing the necessary control. All this work is superfluous
in country that has been subdivided into rectangles; the straight
lines running due north and south, or due east and west, furnish
admirable base-lines from which to start the cruising lines, and
also make it easy to keep a constant check on the work. Areas
are calculated with a minimum of trouble. Orientation is always
simple. The work can be planned and executed with com-
parative ease. In order to explain the methods applicable to
surveyed country, the following diagram of a township, with its
sections and subdivisions, is shown.

* For a complete treatise on the method of making these surveys, see “‘ Manual
of Instructions for the Survey of the Public Lands of the U. S.,” Washington, D. C.
A synopsis of the chief points which concern the woodsman will be found in
Part I, Section VIII, of Austin Cary’s “‘A Manual for Northern Woodsmen,”
Cambridge, Harvard University Press, 1918. Unfortunately, the field-work was
not always done with the required precision, and the descriptive notes are not
always as complete as they should have been.
72 / TIMBER ESTIMATING

N

 

°
{
ina}

 

S

be
3lm[=[e

 

8[-Je[=

 

 

LS |
°

 

 

© | @| ©
Onno
@©@/|O|e
®|@®|@|] ©} ©
®|@®/e@]e/]e

 

® | ®
®|®/®
® | ©

 

®|@®/|@)|®@

 

©
®
®
®
®
®

 

 

 

 

 

 

 

 

S
Fic. 11. Diagram of a Township.

1 township = 36 square miles = 23,040 acres.

1 section = 1 square mile = 640 acres.

1 “forty” = ps square mile = 40 acres.

(The small squares in Section 1, lettered alphabetically a to p, are each } mile
square and are called “ forties.””)

44, The Method of Small Plots. — The first thing to do is to
decide what proportion of the total area shall be inspected and
measured. This will depend on the character of the country,
the density of the timber, and the regularity of the stands. If
the topography is not too uneven, if the stands are open enough
to allow the estimator to see a distance of approximately 40
rods (3 mile) on either side of his line of travel, and if the stands
are quite regular, then it may be safe to base an estimate of this
character on the detailed examination of 1} per cent of the total
area. Such a percentage would be obtained by taking two
plots of } acre each, or one plot of 3 acre, in each forty-acre
THE METHOD OF SMALL PLOTS 73

subdivision. A more irregular stand, or one situated in rough
country, would make it necessary to increase the percentage
of area examined to 23 per cent, or a total of 1 acre in each forty.
Four {-acre plots so spaced that the estimator’s lines of travel
would not make it necessary for him to see more than 330 feet
(+ mile) on either side of his compass line, would then be
preferable. The plots mentioned may be measured with the
least delay and effort if they are circular in outline; this form of

I

©

©)
C

I

20 chains, 14 mile
Fic. 12. Method of Small Plots 13 Per Cent Estimate.

 

20 chains, }4 mile

 

 

 

 

plot can be measured easily by one man working unassisted,
and it is to be recommended as better for this kind of an estimate
than a rectangular plot.

If it has been determined that a 1} per cent estimate will be
sufficient the estimator will plan to travel once across the center
of each forty, as shown in Fig. 12. Two plots, a and 6, each
+ acre in area, and spaced + mile apart, or one plot } acre
in area c, located in the center of the forty, may then be
estimated.

If a 23 per cent estimate has been determined upon, then the
plots should preferably be 3 acre in size, and four of them dis-
tributed, equidistantly, as shown in Fig. 13.

In this case the forty is traversed twice, plots “a” and “b”
being established one-eighth mile apart on the first line run
74 TIMBER ESTIMATING

through the forty, and plots c and d established on the re-
turn line, which is } mile distant from the first line, and
parallel to it.

The work of estimating the timber on these circular plots
consists in tallying the trees by species and diameter-classes

| t
> ©
oO ©)

t

Fic. 13. Methods of Small Plots 23 Per Cent Estimate.

 

20 chains, 44 mile

 

 

 

 

(d.b.h.) on a form of tally-sheet prepared in advance.* The
form of tally-sheet employed depends on the method of work
being followed, and may be similar to the form shown in Fig. 14,

 

 

LOCAHON ise ssie.c.e a sstecienien td PLOUN 0s sssisie' od sista erat ccareigie'g siti
DGC sess 55 seen exeeaewes DY PC ins avcinces va Seeimemiles sacs.
Area of Plot...........00008 Name of Cruiser.............0.5
Diam. Species. Species. Etc. Etc. Etc. Etc. Ete.

6

7

8

Etc.

 

 

 

 

 

 

 

Fic. 14. Form of Tally-sheet to be used when Volume Tables are Available.

which is sufficient when reliable volume-tables are available;
or the tally-sheet may take the form shown in Fig. 15, which
is especially desirable when no reliable volume-tables exist.

* This is to save time in the field. Note-books can be prepared each night for
the work of the following day, thus avoiding delay.
THE METHOD OF SMALL PLOTS 75

 

 

 

 

 

 

 

 

 

 

Location, ...... 600008 PE NO sir. 8.ccecetdnes
Dales ia55 B05. sceeseie 8 8 PS Pere deste Woes cai ass ccna
Area of Plot......... Name of Crusser............
Species. Species. Species. Species. Etc.
Diam-
eters. n n n n a a a n
oO n oo vo n oO nm ob
| BP Se Hele sisi sei 2) eis
& 4 ~ BY A] we Le | A] ne YR | | me
= 1 '
5 = & &
& Ss is
4 & Oy ES)
3 en | ot
Ss Pa Pa
> po
7 a ag Oo |
od 3 wt
Met
® wo 3 2a
8 as Ls 23
“a 4! =0 a2
Pe | Sie | ee
2 ge | oS | 8
o5 Do of
Ba ° ze
Etc. u wy we

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fic. 15. Form of Tally-sheet to be used when Volume Tables are not
Available.

The measurement of diameters at breast-height is usually
done by eye, checked frequently by calipers or Biltmore stick.
The measurement of height is also by eye, but checked by
hypsometer occasionally. In the case of inexperienced men,
however, -the use of instruments should be required until a con-
siderable degree of proficiency in ocular judgment of sizes has
been acquired. While the diameter at breast-height, and the
total height, or height at the top of each merchantable log can
be measured with the aid of instruments, the estimation of the
top-diameters of the several logs is purely a matter of comparison
and judgment.* It is in this work that the skill and experience
of the estimator play such an important part. A careful study
of the taper of stems of fallen trees will aid materially in this
work of judging taper on standing trees, and such studies on
wind-thrown or felled trees are strongly recommended.

The absence of reliable volume tables makes it very desirable
to estimate in terms of logs of standard size, and for this work,
the tally-sheet shown in Fig. 15 should be used, and the trees
estimated in terms of the standard 16-foot log.

The advantages in using 16-foot logs are: (1) they are per-
haps the commonest of the standard length logs, and (2) the cor-

* Unless a dendrometer be used. See article 19.
76 TIMBER ESTIMATING

responding half-log (8 feet) is the smallest practicable unit for
estimating, and usually the smallest merchantable unit.

While it may seem that the estimating of log-lengths and
top-diameters in standing trees is a matter of so much guess-
work that the resulting figures will be inaccurate and of little
value, it should be pointed out that the method has the advan-
tage of allowing the exercise of considerable judgment as to the
division of the stem into merchantable logs (eliminating bad
crooks and defects, and providing for such occasional forms as
forked trees) and that unless the estimator’s eye is grossly
inaccurate, the results obtained will, in all probability, be better
than figures gotten by applying volume tables of questionable
accuracy. As in all timber-estimating, practice is very neces-
sary to insure accuracy and reliable results, and no opportuni-
ties should be lost to check up one’s judgment of taper, sizes,
diameters, etc.; for only by so doing can one expect to attain
a creditable degree of skill.

It will be noticed that the tally-sheet (Fig. 15) provides for
the entering of top-diameters outside bark. This means that a
deduction for bark must be made before scaling the logs to
determine their contents. For any particular region, it is gen-
erally advisable to make up a table showing the average thick-
ness of bark, according to species and diameter of log; then by
taking twice the average thickness of bark * a table can be con-
structed to show the average number of inches to be deducted
from a log-diameter, so as to give its proper scaling diameter.
Such a table might well take the form shown in Fig. 16, and

 

Species.

Deduct 1 inch.

Deduct 2 inches.

Deduct 3 inches.

 

Douglas fir....

Western yellow
pine

.| on logs from 6”
to 12’ d.o.b.

.| on logs from 6’
to 10’ d.o.b.
Etc.

 

 

on logs from 13"’
to 20’’ d.o.b.

on logs from 11’’
to 15" d.o.b.
Etc.

 

on logs above 21””
d.o.b.

on logs above 16’’
d.o.b.

Etc.

 

Fic. 16. Bark Deductions for Standard Logs.

* Twice the thickness of bark is taken because in measuring the diameter of a
log with the bark on, the bark is included at both ends of the diameter.
THE METHOD OF SMALL PLOTS 77

should in all cases be made up from measurements taken on
logs cut in the immediate locality.

This method of estimating the size of logs in the tree, then
making the appropriate bark allowances, in order to apply a log
rule, might be spoken of as “scaling on paper,” and it yields
figures which may then be totaled to show the contents of the
entire plot, by species.

The advantages of the small circular plot method of estimat-
ing timber may be stated as follows:

(1) One man can do the work unassisted, since there is no
need to establish corners, or run the boundary-lines of the plots.

(2) The trees can be counted and estimated, in many cases,
without moving from the center of the plot. It is therefore
rapid.

Care should be exercised to avoid the following sources of error:

(1) Misjudgment of the radius of the plot, with a consequent
overestimate or underestimate of the required area.

(2) Misjudgment of diameters and sizes. Frequent checking
with the calipers and hypsometer will help to reduce errors of
this kind.

The size of the circular plots should in all cases be chosen to
suit the character of the stand. In dense stands of great regu-
larity, the plots need not be larger than } acre (radius = 59
feet). In very open, ‘irregular stands (western yellow pine in
the Southwest, for example) it would be safer to take plots of 1
acre (radius = 118 feet). For stands of intermediate char-
acter, an area of 4 acre might be chosen (radius = 833 feet).
The frequency with which plots should be established along a
compass-line depends on the objects of the work and the degree
of accuracy required. Only in rare cases would more than
5 per cent of the total area be covered by the method; for if a
greater proportion of the area is to be covered, one of the strip
methods (see Article 47) would accomplish the work to better
advantage.

The addition of a few brief notes regarding the condition of
the timber on each plot is to be recommended, but the descrip-
tion should not be so detailed as outlined in Appendix (page 243).
78 TIMBER ESTIMATING

The method of small plots provides a simple means of getting
an estimate of the standing timber on small areas at intervals
along a compass line. It is necessary, however, to know the
character and distribution of the timber on the remainder of
the area, in order to be sure of securing a reliable estimate.
This is accomplished by mapping the stands of timber along the
compass-line according to type, each type being represented
by an appropriate color, cross-shading, or symbol. In this way,
all barrens, burns, parks, or other non-timbered areas are noted,
and if the estimator uses care and discrimination in the recogni-
tion and in the designation of types (not only on the plots but
also in the stands of timber he passes through, or observes
adjacent to his line), he may feel some degree of confidence that
the plots are fair samples of the stands. On the map, as drawn
later, the area of the several types can be determined accurately
with a planimeter and the total estimate figured as described in
Article 55.

45. Method of Strips. — Under certain conditions it may be
easier, quicker, and fully as accurate to count trees on strips,
instead of on circular plots, and then by the application of
volume tables, or the method of ocular division into logs just
described, make an estimate of the approximate contents of an
entire stand. The conditions under which this method is to be
recommended are as follows: (1) The stand of timber is irregular,
with open spaces too numerous to be mapped accurately by the
method of small plots, just described. (2) The stand of timber
is very open, with but few merchantable trees per acre. (3)
The estimate calls for data on one or more selected species, which
occur scattered through the stand irregularly.

It is obvious that the use of plots in these circumstances would
be unreliable, and therefore continuous strips, of a width to suit
the peculiarities of the case, are employed. These, by reason of
their continuity, will yield results much more likely to be repre-
sentative of the entire area.

The work can be done to good advantage by three men, one
of whom runs the line through the country by means of a compass,
and keeps track of the distance by pacing, while the other two
APPROXIMATE METHODS APPLIED TO UNSURVEYED LAND 79

count and tally trees for a stated distance on either side of the
line. Each estimator should carry a caliper or Biltmore stick
to check the ocular judgment of diameters, and he should use a
tally-sheet of the form shown in Figs. 14 or 15, according to
requirements, tallying the trees on his side of the line as he
progresses through the stand. The compass man usually carries
a barometer and makes a topographic and type map as he goes
along. The strips may be one chain wide, or two chains wide,
or even as much as 5 chains wide. In open yellow pine stands,
strips as wide as 5 chains have been found feasible, and the great
gain in area covered has more than offset any slight loss in
accuracy due to the somewhat difficult task of gauging the width
of the strip. Since each forty-acre subdivision is traversed at
least once, these strips will cover, according to their widths, a
percentage of the entire area as follows:

 

 

 

1 chain 2 chains 5 chains
| wide. wide. | wide.
Strips run } mile apart (= once
through each “‘forty’’).......... 5% 10% 25%

 

 

Variations of the strip method, as thus described, are numerous,
and may be devised to suit the needs of the particular type of
country and timber that is being traversed; or the methods may
be modified to meet the requirements imposed by the object of
the cruise. For some such variations the reader is referred to
“The Woodsman’s Handbook,” * pages 68 to 71 and “Forest
Mensuration,” } pages 191-201.

46. Approximate Methods as Applied to Unsurveyed Land. —
The problem presented here is first to find the area of the tract
of land to be estimated. Many old metes-and-bounds surveys
are decidely inaccurate; and in all cases where doubt exists as
to the reliability of the maps, or where the area is an unknown
quantity, a traverse must be run, as described in Article 3 and

* Bulletin 36, U. S. Forest Service, by Graves and Ziegler, roto.
} ‘(Forest Mensuration,” by H. S. Graves, N. Y., John Wiley and Sons, Inc.,
1906.
80 TIMBER ESTIMATING

the area computed or determined by planimeter. Once this is
done, a system of parallel traverse-lines can be laid out so as to
cross the tract at right angles to the ridges and streams, and the
method of small plots, or strips, can be applied as just described
(Articles 44 and 45). The parallel strips afford an opportunity
to map the topography and forest types, and the boundary-
survey will be a valuable control for both.

47. Strip Surveys. — Strip surveys constitute the first of the
two classes of precise methods of timber estimating mentioned
in Article 40. The distinguishing feature of these surveys is the
use of instruments for measuring distances, areas, and dimen-
sions of the trees. Nothing is left to estimation or judgment
except the width of the strip, and this should be checked fre-
quently by pacing. In cases involving the inclusion or exclusion
of a large tree, situated so close to the edge of the strip as to make
it impossible to tell without measuring, whether it belongs in
or out of the estimate, the distance from the center of the strip
to the edge of it should be measured with the chain (or tape), so
as to remove all doubt. If the tree in question is not within the
strip by half or more of its diameter, it should be excluded. Be-
sides using instruments to insure accuracy in measurements,
strip surveys generally cover a larger percentage of the total area
than do the plots of the approximate methods. Depending on
the density and regularity of the stands, 5 per cent, 10 per cent,
or even 20 per cent of the total area may be covered by the
strips. The commonest practice is to run parallel strips 10
chains (§ mile) apart, which will usually give the required degree
of control for topographic and type mapping. If the strips
themselves are 1 chain wide this means that a 10 per cent esti-
mate is secured.

Other modifications are:

(rt) 1-chain-wide strips (narrow strips), 20 chains apart;
5 per cent estimate.

(2) 2-chains-wide strips (broad strips), 20 chains apart;
Io per cent estimate.

(3) 2-chains-wide strips (broad strips), 10 chains apart;
20 per cent estimate.
NARROW STRIPS 81

The conditions under which these different methods are used
will be described in the following article. The organization of
the crew and the duties of each man in it will also be described
fully in their appropriate places.

48. Narrow Strips. — When the stands of timber to be esti-
mated lack the regularity of even-aged, or pure stands; when
they present many or frequent changes in forest type; or when
they are so dense as to make the judgment of a wide strip difficult,
and the visibility of the timber between strips impossible; then
the narrow strips (66 feet, or 1 chain) are to be recommended.
The mixed hardwood and coniferous forests of the Northeast,
or. the irregular forests of the Appalachian Mountains are good
examples of the kinds of stands to which the narrow strips apply.
If the topography is so broken and irregular as to make it im-
possible to see the country adjacent to the strips for as much as
330 feet, then it may even be necessary for one or more members
of the crew to make occasional excursions to the side, in order
to be sure that no important changes in type are being overlooked.
But generally speaking, a 10 per cent estimate conducted in this
manner will yield satisfactory results provided proper care is
exercised to avoid inaccuracies. The work is conducted as
follows:

Parties of three, four, or five men can do the work; where five
men can be used, the highest degree of efficiency will be secured,
and the duties may be distributed in the following manner: one
man, usually designated as the compass-man, handles the com-
pass and acts as head chainman. He also carries a note-book in
which the topography is sketched as he proceeds along the line
of travel. He keeps a tally of the distance run, and indicates on
the map not only the topography, but the boundaries of forest
types, streams, roads, fences, cabins, and other features the
location of which would be of value in a forest map. A second
man, who is generally designated as the tally-man, carries the
note-book in which the trees on the strip are recorded, by species
and diameter-classes, and in which the forest descriptions are
written (see Article 40). He also acts as rear chain-man, and
should keep a tally of the distance traveled as a check on the
82 TIMBER ESTIMATING

compass-man. The frequency with which mistakes occur
through omitting to tally the distance, especially in inexperienced
crews, makes this check almost indispensable. Two other men,
called caliper-men, work on either side of the chain (or tape) and
measure the diameter of all trees (within specified diameter
limits) that stand within 33 feet (} chain) of the center line of
the strip, which can always be identified by the position of the
chain on the ground. The accuracy of the estimate depends
largely on the care with which the caliper-men perform their
tasks; if they are careless in measuring the diameters of the
trees, or if they misjudge the limits of the strip, or call in trees
by the wrong name, large errors may result. Therefore, while
this part of the work is admittedly the most mechanical and
monotonous, it is extremely important that errors here shall be
guarded against, and for this reason the work of the caliper-men
should be constantly supervised by the man in charge of the
party, — the captain, — who is the fifth man in the crew. He
should assume the responsibility of the work of the entire party,
and besides this supervisory work, he should make observations
on the silvicultural condition of the stands, the physical condi-
tions of the site, and should be ready to dictate to the tally-man
the data which constitute the forest description. (See Appen-
dix, page 243.) The forest description should be written for
each type passed through, or, if conditions warrant it, even for
each acre tallied. This task, although likely to become some-
what monotonous, should never be done in a perfunctory man-
ner, for it is of great importance.

Where five men are not available, it is possible to conduct the
work fairly well with a crew of four. In this case, the duties of
captain devolve upon the tally-man, who must then take time
to supervise the work of the caliper-men. The caliper-men, if
they have had sufficient training and experience to qualify them
for the work of forest description, can render valuable assistance
by reporting to the tally-man the silvicultural descriptions.
The thoroughness with which the caliper-men cover the ground
should enable them to perform this task very satisfactorily, but
it sometimes happens that they have not had the requisite train-
BROAD STRIPS 83

ing for this kind of work. With four men the strip-running
progresses not quite so rapidly as with five, but it may safely be
done by this number of experienced men. Reducing the number
to three, by which the compass-man is overloaded, since he must
generally assume the work of tallying the trees, seriously impairs
the efficiency of the crew. It means that the caliper-men are
idle while the compass-tally-man is getting his line of sight with
the compass, and that this one man has far more than his share
of work to do. Under some circumstances (i.e., where the trees
are so scattered that the caliper-men tally their own trees, or
where no map is necessary) it may be possible to get along
with three men, in which case one of the caliper-men should act
as rear chain-man; but it should be employed only as a last resort.

The work of chaining the distance in these strips should always
be done carefully, and surface measurement of sloping ground is
to be strictly avoided.* This means that in hilly country a
plumb-bob is a necessary appurtenance, to be used by the rear
chain-man in going up hill, and by the head chain-man in going
down hill.

49. Broad Strips. — Where the stands of timber are sufficiently
open to warrant it, and especially when experienced caliper-men
are employed, who can judge with precision the width of strips
up to 2, 4, or 5 chains, broad strips may sometimes be used to
advantage. As pointed out in Article 45, the gain in area
covered will frequently more than offset the slight errors due to
misjudging the correct width of the strip. The method here
described differs from that in Article 45 in that the length of the
strip is measured with chain, or tape, and the crew is composed
of four or five men; the trees are calipered, and practically all
the work is done with a greater degree of refinement. The
method is employed in open country or scattered timber where
the necessity for an accurate map is of prime importance. The
details of the method are similar in all respects to those already
described for narrow strips.

* If desired, distances can be measured along the surface of the ground, and
automatically corrected for slope, by means of a “‘slope tape,” so graduated that
the necessary corrections can be applied when the per cent of grade is known.
84 TIMBER ESTIMATING

50. Accurately Measured Plats. — If the several stands in the
timber to be estimated are very uniform and regular in character,
and present no special difficulty to the problem of selecting a few
sample acres that shall be in all respects representative and aver-
age, then the method of accurately measured plots may be used.
As the name implies the plots are measured carefully; and the
calculation of the volume of timber on the plots is done with as
much care as the measurement of the area of the plot. In addi-
tion to being used in even-aged stands of great regularity, this
method may be employed as a check on the estimates made by
the strip method, in which case a few sample plots are established
in each forest type. The ablest man in the party should make
the selection of the plots, for it requires a nicety of judgment and
a skilful eye to select a plot which will be a fair average of con-
ditions over an extensive area.

The size of the plots should correspond to the density of the
stand; in lodgepole pine, or eastern spruce, an area of one acre
will suffice, but in more open stands, like southern yellow pine, '
or western yellow pine, a plot should be large enough to insure
average conditions, and plots as large as 2, 5, or even ro acres
may be necessary. It should be said by way of warning, how-
ever, that if the.stands are so open and scattered as to require a
very large plot, the usefulness of the method becomes open to
question. Plots of one acre are standard, and the shape of the
plot may be square or rectangular, to suit the needs of individual
cases. If laid out with a tape graduated in feet and tenths, a
square plot (208.7 feet on a side) is very satisfactory; if a chain
be used, then a rectangular plot 4.0x 2.5 chains is acceptable.
Great care should be used to have the area exact; the lines
should intersect at the corners exactly at right angles and a
compass or a staff-head will be found indispensable to this work.
Corner stakes are usually set, sometimes temporarily, some-
times permanently, if for any reason it may be necessary to return
to the plot again for future measurements. To prevent tallying
trees outside the boundaries of the plot, a string or cord may be
stretched from one corner-stake to the next, or the outside tree
may be blazed or otherwise marked in a distinctive way.
ACCURATELY MEASURED PLOTS 85

The trees are measured carefully at breast-height, and recorded
according to species, diameter, and sometimes according to
height-classes. Instead of tallying only the merchantable trees,
it is customary to record all trees that will fall in the 4-inch class,
and upward; or, if deemed necessary, the record may include
trees of 2 inches in diameter and upward. The saplings and
seedlings are counted on one or more smaller plots, which may
be cone square rod in area, and established within the large one.
A very careful forest description * is then written, as a guide in
determining the details of silvicultural treatment of the stands.

If the carefully measured plots are established for the sole
purpose of checking the strips, then the average stand per acre
as determined for a given type by the strip method is compared
with the average stand per acre as obtained on the plots, and
any marked differences noted. If such differences indicate
inconsistencies and disparities which affect the total number of
trees per acre or the distribution of the diameter-classes, it may
be sufficient cause to question the accuracy of the work done on
the strips. It will then be advisable to re-run one or more strips,
as a check on the work, taking more than usual precautions to
secure accuracy. Or it may be desirable to select other plots,
with a view to detecting just where the inconsistencies lie, and
to what factors they are due. In either case, the work should be
investigated until a satisfactory conclusion is reached by the
man in charge of the work, and the estimates should be adjusted
accordingly.

If the plots are established for the additional purpose of volume
determination and growth studies, then one of the several
methods of volume calculation, described in standard texts on
Forest Mensuration,t may be applied. There are several of
these methods, but since most of them are of purely academic
interest to the American forester, only two of them will be
described here. The first one, called the Mean Sample Tree
method, is applicable to stands of even-age and great regularity;

* See Appendix, page 243, for the points to be covered in this description.
+ See H. S. Graves, “Forest Mensuration,” Chapter 14, N. Y., John Wiley
and Sons, Inc., 1906.
86 TIMBER ESTIMATING

the second one, called the Volume Curve Method, can be used to
good advantage where the conditions are not so uniform.

51. The Method of the Mean Sample Tree. — The trees on
the plot are measured and tallied by species and diameter-classes
of even inches. Then, since the volumes of trees of approxi-
mately the same age and height (conditions under which this
method is reliable) vary very nearly as their basal area, the basal
area for each diameter-class is computed, and the total basal area
for the entire plot is determined. (See example in Fig. 17.)
If more than one species is being studied, then the mean sample

 

 

 

Locality..........004. EY DC 27 sisolambiga van bx aheaewgy ees a4
DGG sstisar sis chaste ae os No. of Plot.......... Area........
No. of trees, by species. Sample trees.
D.b.h.
Spruce. Basal area. (Other species). D.b.h. Vol.
8 I5 Etc.
9 aI Etc.
Io 32
II 24
12 7
13 2
Total...... 101
Mean......]...........-

 

 

 

 

 

 

Total vol. (by species) on plot ..............
Fic. 17. Volume Determination by the Mean Sample Tree Method.

tree for each species must be determined separately. The total
basal area, divided by the number of trees of that species on the
plot gives the average basal area, from which the corresponding
diameter can then be determined. Three or more trees of this
diameter are then selected, care being taken to choose trees
which represent average development as to stem, crown, and
general condition; these trees are felled, and divided up into
sections; the volumes are computed by applying the appropriate
formule (see Article 25), and averaged together to obtain the
volume of the average, or mean, tree. This figure, multiplied by
the number of trees on the plot (of that species), will give the
total volume of all such trees on the plot.
THE VOLUME CURVE METHOD 87

The presence of more than one species complicates the work,
since the volume has to be worked out separately for each
species, and the method is, therefore, not recommended where
several species are represented.

It is not always practicable to find sample trees of exactly the
required diameter. The average diameter will usually work out
to be a number with a fractional part of an inch, and it is neces-
sary, in selecting the sample trees, to get diameters of exactly
this size, if possible; but if impossible, trees should be selected
that fulfil the requirements as nearly as may be, and then the
calculations adjusted in the following manner:

Let B = the basal area of entire plot.

sa b = the basal area of the sample trees.
V = the volume of the trees on the entire plot.
v = the volume of the sample trees.

Then 93:V=0:B

vB
and V= c

cc

“cc

For a full discussion of this method, and the conditions under
which it may be applied see Graves, loc. cit.

52. The Volume Curve Method.— Where the range of
diameters on the sample plot is large (more than six or eight
inch-classes) as would be the case in a stand which is uneven-
aged, the following method devised by H. S. Graves, and de-
scribed in his text-book already referred to, will be found useful.

Tally the trees by species and diameter-classes. Then, accord-
ing to the number of the trees and their range in sizes, select
arbitrarily from 5 to 7 sample trees, and distribute them so as to
represent some of the small diameter-classes, some of the large
diameter-classes, and some of the intermediate diameter-classes.
(See example worked out in Fig. 18.) Fell these trees which, of
course, should each be representative and normal, so far as can
be judged, and compute their volumes by the application of the
appropriate formula. Then, on codrdinate paper, plot the
volumes of these trees, using the diameter-classes as the abscissx
88 TIMBER ESTIMATING

 

 

 

Locality............ TYDEC. 5 cin ewrwore sien
Dale sun 3c nes No. of Plot.......... Area..... A
No. of trees by species. Sample trees.
D.b.h.
Pine. Basal area. Other species. D.b.h. Vol.
6 4 etc. 7.2
7 2 etc. 10.9
8 8 etc. 14.2
9 6 17.8
10 12 20.1
ee
2r I
etc.
Total.... 35

 

 

 

 

 

 

Fic. 18. Volume Determination by the Volume Curve Method.

(horizontal scale) and the volume as the ordinates (vertical
scale). Draw a smooth curve through the points thus ob-
tained, and from it may be read the volume-values for trees
of all diameter-classes. The number of trees of each diameter-
class multiplied by its appropriate volume-value gives the volume
of each diameter-class; these, in turn, added together, will give
the total volume of all trees of that particular species on the plot.

This method has the following features to recommend it: (1)
It involves no laborious calculation of mean sample trees, but
enables the direct and immediate choice of such trees. (2) Any
errors in judgment and selection of sample trees can be detected °
automatically when the volumes are plotted on codrdinate paper.

The sample trees felled on plots thus measured afford an
excellent opportunity to study growth; in fact it would scarcely
be worth while to employ the method of sample trees for the sole
purpose of volume determination. In most cases where an
estimate is being made as the basis of a working-plan, however,
a knowledge of growth is fully as important as a determination
of the volume, and the usefulness of these methods will appear
—

THE COST OF TIMBER ESTIMATING 89

more clearly when the subject of growth is treated. (Chapter
X.) To lay out plots, fell the sample trees, and compute the
volumes, is costly and time-consuming work; and the need for
it should be urgent and well-considered before undertaking it.

53. Factors Affecting the Accuracy of Timber Estimates. —
The chief factors affecting the accuracy of timber estimates
made by any of the methods described, are herewith enumerated
in order that the man in charge of such work may know what
to guard against.

(1) The percentage of the area covered by strips, or plots.

(2) The accuracy in chaining distance, and in estimating
the width of the strip.

(3) The accuracy in measuring the trees.

(4) The elimination of dead and worthless trees (visible
defect).

(5) Allowance for unsound trees (hidden defect).

(6) Applicability and accuracy of the volume tables used

in computing the contents of the trees tallied.

(7) Care in distinction of types.

(8) The accuracy of the map on which types are plotted
and from which areas are calculated.

(9) Misnaming species of trees.

The means to be used in guarding against errors will readily
suggest themselves, and it is the duty of the captain of the crew
to keep a watchful eye on all the operations of the men in his
charge.

54. The Cost of Timber Estimating. — Any work which is
susceptible of so many variations, as just explained in the pre-
ceding paragraphs, will naturally exhibit a wide range in costs.
In fact, timber estimating can be made to cost almost any figure,
above the irreducible minimum of a hasty ocular estimate, and
as a matter of fact the method of timber estimating employed
will be determined, at least in commercial work, by the amount
of money which can be expended upon it. In these days of
rising costs of labor, food and supplies, it is almost impossible to
give any definite figures; but the following table, based on sub-
go TIMBER ESTIMATING

sistence at $1.00 per day, unprofessional or ordinary labor at
$2.50 per day, professional service $5.00 per day, with additional
cost of camp maintenance and moving camp, may be accepted
as approximately correct for prevailing conditions.

Cost oF TIMBER ESTIMATING

(Exclusive of the Computations and Maps)

 

 

Class of estimate. Approx. cost per acre.
rt. Ocular estimates............... Variable; from $0.001 to $0.01
2. Small plots 1} per cent of area... | from $0.01 to $o.015
3. Small plots, 2} per cent of area. . ‘“ $o.015 to $0.02
4. Strips (approximate method).... ‘$0.05 to $0.07
5. Strips (precise; 10 per cent of area) ‘$0.12 to $0.15
6. Accurate plots.................. Cost per plot from $5.00 to $10.00

depending on size of plot, density
of stand, and number of sample
trees cut.

 

 

55. Computing the Volume of Stands from the Tally-sheets. —
There are two methods of doing this work, both of which call for
suitable volume tables: (1) The volume tables may be applied
directly, and the contents in board feet, cubic feet, or other unit
obtained for each tally-sheet (acre or fractional part) by species
and diameter-classes. This involves a large number of com-
putations and unless there is some special reason why each
individual acre should be so worked out, the second method is
easier and quicker. (2) All the acres tallied are classified
according to the forest types recognized; then all trees of the
same species and the same diameter-class are added together,
and divided by the total number of acres of that particular type,
with the result that a table can be constructed showing the
average number of trees per acre, by species and diameter-classes.
Such a table is called a stand table. The next step is to multiply
the stand-table values by the appropriate volume-table values,
with the result that a stock table, so-called, is obtained. Stand
tables and stock tables, being in terms of a unit of area (usually
the acre in this country), are of special value when it is desired
to make comparisons of one type with another, or to study the
COMPUTING THE VOLUME OF STANDS gI

relative distribution of the size-classes; and they are, therefore,
to be recommended. From stock tables, the merchantable
stand for the entire type can readily be computed, and by adding
together the totals for the types the grand total for the entire
tract is obtainable.

The methods employed in working up the tally-sheets should
always be chosen so as to fulfil to the best advantage the purposes
for which the survey was conducted. If the working plan calls
for any unusual classifications of merchantable material, due
regard to these requirements must be had at the time of making
the computations. This kind of work is best done by a corps of
expert mathematicians, who have the necessary adding machines,
slide rules, and comptometers to perform the task quickly and
accurately. The need for accurate, complete, lucid field-notes
and descriptions must now be apparent, for the men who do the
computing cannot be expected to interpret ambiguous notes
satisfactorily.
CHAPTER IX

THE AGE OF TREES AND STANDS

56. Practical Value of a Knowledge of Age. — The element of
time has an extremely important bearing on many of the problems
of forest management. It is very necessary to know at what
age certain species of trees mature and it is also very desirable
to know at what age the products of intermediate cuttings
(thinnings) may be expected to yield some financial returns.
The time element is of special importance to the forest owner
because it takes a long period of years (30 to 80 years or more)
for the timber crop to mature. The farmer sows in the spring
and reaps a harvest in the fall, and turns over his money once a
year; the merchant and manufacturer buy and sell constantly,
turning over their money at least once a year, and sometimes
much more frequently. But the timber owner, whether he owns
a large tract or a small tract of timber, must reckon in terms of
decades; and in a growing number of instances the investments
of the present are being made for long terms. As the supply of
standing timber in the country diminishes, an increasing number
of lumber companies are retaining possession of their lands, and
they are figuring on a second cut within 10 or 20 years and
repeated cuts thereafter. This is particularly true of pulp-wood
owners in the North, and owners of yellow pine lands in the
South. The length of time during which money must be in-
vested in standing timber, until it becomes of merchantable size,
is, therefore, one of great importance; and it is closely related
to the whole subject of the age of trees and stands.

57. Age of Seedlings. — Seedlings, because of their small size
and the ease with which their ages may be determined, will be
discussed first. They also have an important relation to other
age-problems (see Article 59), making it necessary to begin with
them.

g2
AGE OF FELLED TREES 93

In the case of seedlings of coniferous trees (pines, firs, spruces,
etc.), the age may be determined quite accurately by counting
the whorls of branches, since under normal conditions each
whorl represents one year’s growth. Even when the branches
are not present, there are frequently marks or scars to indicate
where they once grew, so that the age of trees of considerable
size may be ascertained approximately by this method. Seed-
lings of the broadleaf trees (oaks, maples, birches, etc.), do not
display the same regularity in their branching habits, and after
the third or fourth year it may indeed be almost impossible to
tell the age of such seedlings without resorting to other methods,
soon to be described. If age only is wanted, it will suffice to
uproot the seedling and make a clean cut with a sharp knife at
the root-collar; the number of annual rings of growth can then
be counted, beginning at the pith and counting outward on a
radius, to the bark. If further information be needed, such as
rate of height-growth, additional cross-cuts and measurements
will be necessary (see Article 58).

58. Age of Felled Trees.—It is a comparatively simple
matter to determine the age of a felled tree, provided the stump
is sound and it shows the annual rings of growth distinctly. The
counting of the annual rings is not always easy, especially if the
growth be extremely slow, or if the species be one in which the
differentiation between spring wood and summer wood is not
clear.* A sharp knife that will make a clean cut is absolutely
essential, and a magnifying glass is often a great help, especially
in counting the rings of spruce, hemlock, maple, and other species
of slow growth. To determine the age of a felled tree it is neces-
sary to know not only the number of annual rings represented
on the surface of the stump, but also the number of years re-
quired to reach the height of the stump. This will vary not only
with the species, but even with the individual tree; fortunately,
in most studies of age, an approximation will be sufficient;

* Annual growth rings show up clearly in most conifers because of the larger
amount of resin. present in the summer wood, as contrasted with the spring wood.
The rings of the so-called “ring-porous” woods among the broadleafed species
(oaks, hickories, ashes, etc.) also show up clearly. The rings of the so-called
“‘diffuse-porous” woods (maples, gums, etc.) are frequently very difficult to count.
94 THE AGE OF TREES AND STANDS

therefore, to the age as shown by the number of rings on the
stump, is added a certain number of years to account for the
time required to reach stump-height. This number may be
determined by the following procedure: A large number * of
seedlings of heights from 6 inches up to 3 feet or more f are
gathered, and sections are made by cutting with a sharp knife at
the root-collar, and at 6-inch intervals up the stem. The
number of rings at each level is then counted, and the data
entered on a form as follows:

Under (a) is shown number of rings appearing on section of stem at height
indicated.

Under (b) is shown number of years required to reach the height indi-
cated, which is simply the number of rings at that section subtracted from
the number of rings at ground level (or the total age).

 

 

 

 

 

SPCCS sores ncea cece aseeids Ve Locality.......... Date.......
Seed: | Ground Level. | o.5ft.high. | roft.high. | rsft. high. | 20ft. high. | Etc.
No. (2) (0) (@) (0) (a) (6) (a) (0) (a) (6)
I 4 ° 3 | 1 2 | 2 I 3
2 5 ° 3 | 2 2 13 I 4
3 8 ° 6 [2 4 |4 5 1/7
4 4 ° 2 |2 1 |3
5 5 ° 3 ]2 1/14
4 ° a | E i |3
Etc.
Average of
values un-
der (b).... ° 1.66 3.16 4.0 7.0

 

 

 

 

 

 

 

 

 

 

 

Fic. 19. Tabulation of Data to Show Relation Between Age and Height
of Seedlings.

The average values of (6) may now be plotted on codrdinate
paper and a smooth curve drawn, from which values may be
tabulated for reference; or the values may be read directly from
the curve itself. A separate curve should, of course, be drawn
for each species studied. The completed table should show the

* 50 to 100 should be taken, if possible.

{ The upper limit of height should be determined by the average height of the

largest stumps that will be measured. Exceptionally high stumps may be excluded
from the field study.
STUMP-TAPER CURVES 95

average height of seedlings at ages of 1, 2, 3, etc., years, or, con-
versely, the age of seedlings at specified heights above ground.
The latter form of table is most useful in this particular study of
age.

With the above information, it is now possible to select, for
any height of stump measured, the approximate number of years
to be added to the rings counted on the stump, in order to obtain
the total age of the tree.

If the felled tree is lying in position as it fell, the diameter
breast-high should be obtained. To do this the stump-height
should be subtracted from 4.5 feet (breast-height) and the
remainder will then be the distance from the butt of the first log
at which the d.b-h. is to be measured.* It is extremely important
that the diameter breast-high be obtained; for ‘“‘d.b.h.” is the
almost universal dimension for classifying trees, and if this
measurement be lacking, figures are of less value. If for any
reason it is necessary to make studies of age on stumps after the
lumbermen have removed the logs, it is still possible to carry on
the work, for the rings on the stumps can be counted, the appro-
priate number of years can be added to account for stump-height,
and the stumps can be assigned to their proper d.b.h. classes by
the method of stump-taper curves, which will now be explained.

59. Stump-taper Curves. -- These curves are to show the
average taper of tree trunks from the ground up to 5 feet, classi-
fied by diameters at breast-height. Their use is to refer stumps
to their corresponding d.b.h. classes; and the field-work consists
in measuring the diameters of the trunks of standing trees at in-
tervals of one foot from the ground up to five feet. In practice,
one man, equipped with a s-foot stick graduated to 1, 2, 3, 4, 4.5,
and 5 feet, and a pair of calipers, measures the diameters of the
trees at the intervals mentioned, while a second man records the
values (read to the nearest tenth-inch) in a note-book appro-
priately ruled. A large number of trees should be measured —
at least ro in each diameter-class from 6 up to the highest com-

* If d.b.h. can be measured while the tree is still standing, it should be done at
that time. Measurements made after cutting are liable to error, especially if the
cross-cut at the stump is at all uneven or irregular.
96 THE AGE OF TREES AND STANDS

mon merchantable size. When the field measurements are
completed, all trees of the same breast-height diameter-class *
are thrown together; the diameter values for the level of 1 foot
are then averaged together, those for the level of 2 feet are aver-
aged together, and so on, for the 3-foot level, the 4-foot level,
the 4.5-foot level (d.b.h.) and the 5-foot level. As a result, there
are obtained the average diameters of trees of a specified d.b.h.
class at heights above the ground of 1 foot, 2 feet, 3 feet, 4 feet,

D.B.H. 6 7 8 9 10 lt 1 1 4 %W 1 17 +18 +19 «+O 2 2

! Hit Ui AAA
|

1 \ 4
\
Th
\ AM

1

\

\

\

 

>

 

 

 

 

 

 

 

 

 

 

 

 

 

wo

 

\
\
\
\
\
\
\

p=
aoe

ey

\
thn X s
\ \ \ Wy \
VV x \ WN
\ \\ K

\

+A =
VI \

\ UNS

\

 

ey
a
=
=
ae
ea
_——
_

Distance above Ground ~ Feet

_

oo 6
nN

—— |
=_-
a
_—
bee
Le
eo.

\ \ \
\ wait \ s.. \ NL ms :
' : \ \ - \ \ \ ie I Slee
\ \ N =
WAIAWARAR A AN AAIADBINSINGN
20 2

6 7 8 9 10 it 122 128 UW BG 16 1 18 #19
Diameter - Inches

 

 

 

 

 

 

 

 

 

oo
oe

 

 

 

 

 

 

 

 

 

 

 

 

Fic. 20. Showing Stump-taper Curves Harmonized.
Note: Dotted lines show actual averages, as determined from a large number

of field measurements. Solid lines show harmonized curves, dividing the cross-
section paper into diameter classes.

43 feet, and 5 feet. From these figures, computed similarly for all
the different diameter-classes, a set of harmonized curves is drawn
on coérdinate-paper, observing the rule that although the average
of the d.b.h. measurements for any particular class might not
have come out in terms of an even inch (7.e., with no decimals) the
final, harmonized curves must be drawn so that they intersect
the 43-foot ordinate at even inch-classes. (See Fig. 20, in which

* When measuring to tenths of inches, all those values having a decimal of
more than 0.5 are thrown into the class above; those with o.5 or less are thrown into

the class below; i.e., 8.6 inches is considered as belonging to the 9 inch-class; and
8.5 inches to the 8-inch class, etc.
CORRELATION OF AGE WITH DIAMETER, HEIGHT, VOLUME 97

the dotted lines are the original curves, the solid lines are the
final, harmonized curves, forming inch-classes at breast-height.)

From these curves, a set of which is prepared for each species
studied, it is possible to assign any stump to its appropriate
d.b.h. class. For example, it is desired to throw a stump of
spruce, measuring 18.2 inches outside bark, into its proper d.b.h.
class. The average height of the stump is 1.2 feet, at which
point its average diameter is 18.2 inches. Going to the vertical
scale and following out the level of the ordinate for 1.2 (the
height of the stump), the point is located at which it intersects
the abscissa for 18.2 inches; this point is found to fall within
the taper curves for a 15-inch tree, breast-high. It, therefore,
belongs in that diameter-class.

60. Age of Standing Trees. — To solve the second part of the
problem — namely, the average age of trees of a given diameter
— the ages of all trees of a given diameter-class, as determined
by counts of rings on stumps, are averaged together, and the
results plotted on codrdinate-paper; a smooth curve is then
drawn through these points, and from this curve the required
relation between total age and diameter breast-high is obtained.
This, in effect, yields a table from which the average age of
standing trees of different diameters may be obtained. Such a
table is of the greatest practical utility, since it renders possible
the solution of many of the problems of management mentioned
in Article 56.

61. Correlation of Age with Diameter, Height and Volume. —
Age, in trees, is more closely related to diameter than to height
or volume. Two trees of the same diameter may not agree at all
in height or in volume; for rate of growth in height is influenced
to a great extent by the fertility of the soil, and volume depends
chiefly on the form of the tree. But even in the relation between
age and diameter, there is a great lack of definiteness, or uni-
formity, because the density of the stand, the tolerance of the
tree, and the fertility of the soil all affect the rate of growth in
diameter. It may, therefore, be stated that while age is more
closely related to diameter than it is to height or volume, it is
impossible to do more than draw very general conclusions from
98 THE AGE OF TREES AND STANDS

such relationship. Where reliable estimates of age are required,
they should be obtained by examining stumps, felled trees, or
by the use of an increment borer, and should not be based upon
the indefinite relation of diameter to age.

62. Age of Stands. — There are two distinct problems pre-
sented in determining the age of stands: (1) The age of a so-
called ‘‘even-aged stand” may be determined with considerable
accuracy, for in such a stand the trees are all of the same age,
or very nearly so;* (2) the age of uneven-aged stands can be
represented only as the average or mean of the ages of the several
age-classes which occur in that particular stand. Where such
age-classes — generally recognized as occurring in 20-year
periods, as 1-20, 21-40, 41-60, etc. — are well marked, as is the
case in many stands of yellow pine in the southern and western
states, the problem of obtaining the average age is susceptible
of at least an approximate solution. But in stands where the
trees cannot be grouped into well-defined classes, the ages of which
can be determined by measurement, the term “average” means
but little, and in fact would have no practical application. Such
stands are properly called “‘selection forests,” through all parts
of which many (or theoretically, all) age-classes are represented.

In the first case, the age of the class can be determined by
selecting a tree of average proportions (the mean sample tree
of Article 51) and ascertaining its age, either by felling it or by
using the increment borer (practicable only in trees of small
diameter). In the second case, where a number of age-classes
are represented, the average age can be determined by making
use of the familiar arithmetical formula for obtaining averages.
Let a be the age of class 1, a, the age of class 2, and a3 the age of
class 3, etc., and let 1, Nz, N3, etc., be the number of trees in
the respective classes. Then the average age (A) of all classes
can be determined by applying the following formula:

ee a,N, + a,N2 + a3N3 + etc., etc.
M + Nz + N3 + etc., etc.
* According to the definition accepted in “Forest Terminology ” (Soc. Am. For.,
1917) differences in young stands “should not be more than ro or 20 years: in

mature stands, not more than 30 or 4o years.” It will be observed, therefore,
that the term “even-aged” is merely a relative term.
AGE OF STANDS 99

Example. —

Class 1, No. of trees 80 X age17 = 1360
Class 2, No. of trees 150 X age 35 = 5250
Class 3, No. of trees 480 X age 55 = 26,400
Class 4, No. of trees 420 X age 64 = 26,880

59,890

A = GLX 80) + (35 150) + (55 X 480) + (64 X 420)
80 + 150 + 480 + 420
— 59,890 |
T1130

 

A = 53, the average age.

The practical application of the average age of stands, found
according to the above formula, is limited to certain problems
in forest management; it is always more or less artificial, and of
more theoretical value than practical, but serves in some cases
to answer, at least approximately, questions that would other-
wise have to remain unanswered.
CHAPTER X

GROWTH OF INDIVIDUAL TREES

63. Importance of a Knowledge of Growth. — Growth in
forest trees or stands is usually spoken of as accretion or incre-
ment, the former term being used for those quantities which are
directly measurable and the latter for those quantities which
must be calculated. Thus diameter and height, or length, can
be measured instrumentally, and even cross-sectional area by
means of tables of basal area (see Appendix, page 231), can be
obtained directly when the diameter is known; but volume must
be computed by the application of appropriate formule after
certain measurements have been taken, and it is common to
speak of growth in volume, whether of individual trees or of
whole stands, as increment. The use of this term has recently
become standardized * and it will, therefore, be used in the dis-
cussion that follows. ;

Increase in volume generally means increase in value; in the
case of forest trees, the rate of increase in value often becomes
accelerated towards maturity, or slightly after maturity is
reached; hence a knowledge of increment has an extremely
important bearing on both the financial and the technical man-
agement of the forest. (See the general subject of Rotation, in
Chapter XII.) Such questions as the proper age at which to
cut a stand of timber so as to secure the greatest financial
returns; the choice of species for planting, — either one species
alone or two or more species planted together; the length of
time required to produce a given proportion of a certain size or
grade of timber, and so forth; these and many other questions
even more complicated can be answered satisfactorily only
when the laws of growth which determine increment of forests

* See “Forest Terminology,” Soc. Am. For., 1917. Published in “Journal of

Forestry,” January, 1917.
100
THE SEVERAL KINDS OF INCREMENT IOI

are understood, and they affect commercial interests fully as
much as they do the strictly technical interests.

64. The Several Kinds of Increment. — Trees grow most
noticeably in height. After a period of comparatively slow |
growth as a seedling many species of trees exhibit quite a rapid
rate of height-growth in the sapling and pole stages. White
pine in these stages often grows in height from 18 to 24 inches
per year in favorable seasons and maintains an average of 1 foot
per year over long periods. Scotch pine also grows in height
with great rapidity; but the spruce and fir are not so rapid.
Among the broadleaf trees, cottonwood, poplar, locust, willow,
chestnut, catalpa, ash, and some of the oaks may, under favorable
conditions, show extremely rapid growth in height; but much
depends upon the quality of the soil and the abundance of light
and moisture received.

Height-growth can be measured, as explained in Article 57,
by counting the successive whorls of branches, wherever these
are sufficiently distinct. But this method is practicable only in
the conifers and in a few of the hardwoods which are marked by
great regularity of growth. A more reliable way is to sectionize
the stem at regular intervals, after which it is possible, by count-
ing the annual rings of growth, to ascertain mathematically or
graphically the rate of growth in height. This method is dis-
cussed fully in Article 65.

Diameter-growth may be studied to best advantage by mak-
ing a cross-section of the stem at the desired point. It is
customary to make ring-counts at the stump and at the top of
each log cut by the lumbermen, from which it is possible to
investigate the rate of growth at breast-height or at any other
point on the stem by interpolation, or by the method already
described in Article 58.

Growth in volume can be studied satisfactorily only by the
method of stem analysis, described in Article 65. Growth in
quality and value are, of course, quite dependent on volume,
and are, therefore, susceptible of satisfactory investigation only
after a detailed knowledge of volume increment has been ob-
tained.
102 GROWTH OF INDIVIDUAL TREES

There remain three other special kinds of increment to be
defined, namely:

Current annual increment (abbreviated to c.a.i.), which is the
increase in volume, quality or value of a tree or a stand for a
Specific year.

- Mean annual increment (abbreviated to m.a.i.), which is the
total volume of a tree or a stand divided by its age.

Periodic annual increment, which is the increment of a tree or
‘a stand for a specified period divided by the number of years in

“ the period.

Since the growth for one specified year (c.a.i.) is generally:
very small, and is liable to fluctuations from year to year which
are usually without any particular significance other than a
reflection of the kind of a growing season which obtained for that
year, current annual increment (c.a.i.) is generally nothing more
nor less than periodic annual increment. It so appears in the
majority of yield tables, and is frequently to be interpreted as
such when met with elsewhere. In some instances the literal
c.a.i. may be indicated, but the intention for such interpretation
is generally stated clearly.

65. Methods of Studying Increment. — Increment may be
studied by making repeated observations on the same tree (or
trees) at regular intervals of years, but the objection to this
method is, of course, that it takes too long to obtain results; it
is used, therefore, mainly in problems where there are so many
factors of uncertain or unknown influence, that it is the only
geliable method which can be applied. (See Article 75.) By
far the most satisfactory way to study increment is to cut the
, Stem of the tree into a number of sections, and analyze the growth
at each cross-cut. In this way, measurements can be obtained
which permit the computation of the volume at any particular
year, and at the same time the dimensions of the tree, both in
height and in diameter, may be read directly from the data sheet,
or from a graph which can be drawn very readily from the in-
formation on the data sheet. Such an analysis is called a stem
analysis, and may be defined as the measurement of stated cross-
sections of a tree to determine its increment at different periods
METHODS OF STUDYING INCREMENT 103

of its life. A stem analysis may be either partial or complete,
depending on whether the measurements include only a portion
of the stem, or all of it.

Methods of analyzing the stem of a tree have been described
in foreign textbooks * and in Bulletin 20, Forest Service, U. S.
Department of Agriculture; { also in Graves’ “Forest Mensura-
tion,” pages 290-293. The method to be described here is
based on the same principle, but has certain mechanical advan-
tages, tending to eliminate errors, and was made the subject of an
article by one of the authors of the present volume, in 1914.$

A felled tree should be prepared for analysis by making clean
cross-cuts with a. well-fitted saw, at intervals up the stem. To
save expense and time, the trees cut by lumbermen on a logging
operation are generally used in securing the necessary measure-
ments; but if opportunity offers, it is preferable to have the
stump-heights, log-lengths, and divisions of the bole into sec-
tions as uniform as possible. In other words, if all stumps could
be cut to the uniform height of 1 foot above the ground; if all
log-lengths could be ro feet, or 12 feet; and if the top could be
cut into sections of 4 feet each (suitable for cordwood), the
computation of volume would not only be easier, but the results
would be susceptible of more satisfactory compilation.§

For the sake of a common example, it will be assumed that an
analysis is to be made of one of a number of trees just felled and
cut into logs of standard length by lumbermen. ‘To quote from
the article referred to above:

On page 105 is shown a form filled in with data from a white
pine, in which the usual measurements are recorded, together
with a few additional ones which will render the computations
in the office less liable to error. For convenience, the spaces in
which the measurements are recorded are both named and

* See, for example, Lorey’s ‘“‘Handbuch der Forstwissenschaft,” 3d edit.,
Tiibingen, 1912.

+ ‘“Measuring the Forest Crop,” by A. K. Mlodziansky. Bul. 20, U. S. Forest
Service (1912).

t Bentley, John, Jr.: “Stem Analyses,” Forestry Quarterly, XII, pages 158-166
(1914).

§ See Article 36 on taper curves and Article 66 on a useful method for shorten-
ing the work of stem analyses on a large number of trees.
104 GROWTH OF INDIVIDUAL TREES

lettered to correspond with the following list; and in the discus-
sion which follows the several columns will be referred to by
letter.

(a) The number of the section; the stump being considered
No. 1, the top of the first log section No. 2, etc.
(6) The age of the section, i.e., the age up to that section,
and the number of annual rings on that section.
(c) The length of the section, expressed in feet and tenths.
(d) The diameter, outside bark, of each section, in inches and
tenths.
(e) The diameter, inside bark, of each section, in inches and
tenths.
(f) The width of the bark at each section.
(g) The width of the sapwood at each section.
(h) The average diameter of the several sections, by decades,
as explained in the following paragraphs.
(j) The diameter, breast-high.
(k) The total age, obtained as explained in the following para-
graphs.
() Clear length.
(m) Used length.
(n) Merchantable length.

It must be remembered that the object of stem analyses is
to secure figures of volume growth for a given species which will
enable us, after compiling a large number of values and averag-
ing them together, to construct a table showing the average in-
crease in volume by decades. That is, it is desired to know what
the volume of White Pine, or any other species, will be, under
average conditions, at an age of 10 years, and again at 20 years,
30 years, 40 years, etc. Since the age at the stump (cross-
section 1) is always slightly less than the true age of the tree
(from 2 to 10 years, often, depending on the stump-height, and
the rate of growth of the seedling of the species), and a number
of years — usually determined by a study of seedlings — has
to be added arbitrarily to secure the total age of the tree, it is
suggested that these years be added before the stem analysis is
105

METHODS OF STUDYING INCREMENT

(uv) phteeereseeesceecceees cua Bual a[qequeyjIoyy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(uw) RSE Steen gisinnnne ie e PO ee s+ a BEST DOS)
(2) EPG RE RR Ow ww ee “aq suey reg[9
a be og
a o+Sg (doy)
ze 61 vo I'r I'o Ze vz ov g1+69 6
ov |g | Si zr Io [or jar jor 1z+t9 3
gs {zs |o€ | go Sr ro | gS | gS jor gz+d$ L
vel rl | €S | gz Sr [zo |r. | gl Jor c€4z2S 9
06 | £8 1 9°9 I'v | 6:0 gt |Sz'o | o6 | S'6 } car gt+ly s
gir] S'rr |} 26 | gd rs |g 1 gil £o | gur | beer | azr gv4+le v
fpr | ovr | S-zr | gor | gl L'v |go gr fo | br | 6 br | zor gS+6z £
flr | redr | zgt | ght | ozr | z'6 [gS |r-z Sr | vo | €-dr | rgr | zor ol+S1 z
S-oz | €-0z | 6°gt | g'91 | O' Hr | Gor |g'g |g°f \E-1] S-xr | or S-oz | S:zz | or og+S I
5g
‘oyq «| «IL | Cor 6 3 L 9 s v € z I 7
es. | gate yo | ta. | | 88 “(2) wor,
des Jo | y1eq jo| . ih eat qgu: *(q@) O38 #098 10 ‘0
“sapeoap Aq ‘SUO1}0aS JO JajaeIp e8elaay (y) TAPEM | WPM ey tere ase
(4) Sg aay (/ nie ‘Had (aug 37M) savags* ee m eter ee ee wens ‘aqpq° Bee eee we ee *&414D90T

ANVIg SISAIVNY WEIS 4O WAOY FMVS
106 GROWTH OF INDIVIDUAL TREES

recorded, instead of afterward, thereby making it possible to
secure results which can ultimately be averaged together with a
smaller degree of error. For example, it is known that White
Pine seedlings attain an average height of one foot at an age of
5 years; a height of 24 feet at an age of 6 years, etc.*; if the
stump of the White Pine being analysed is one foot high, it is
then determined that 5 years must be added to the age of the
stump to secure the total age of the tree, which is entered on the
blank form at (), the space provided for it.

Now, as each section is analysed, the rings are counted back-
ward from the bark to the center, beginning at the outside and
designating the outermost ring with its proper number, wz., the
total age of the tree, and not the number of rings which happen
to be found on that section. Thus, if the total number of rings
at the stump is 80, and 5 years are to be added for a stump one
foot high, then the outermost ring on the stump will be counted
“85” and the next one inside ‘‘84,” etc., counting backward, and
placing a mark at the even decades, 80, 70, 60, 50, etc. In like
manner, the outermost ring on all subsequent sections will be
called ‘‘85,” and the counting proceed backward, until the center
is reached, marking each decade as before.

In the column marked ‘“ Age” (column 6) the age should be
entered as composed of two values, the first expressing the number
of years required to grow to the height of that particular section,
and the second, the number of annual rings on that section.

This method of entering the age enables the reader of the
form to determine the rate of height-growth very quickly, by
simply glancing at columns lettered 6 and c, respectively.

The form, it will be noticed, is practically the same as that
formerly in use. The method of entering the values under h,

* Values are taken from U. S. Forest Service Bulletin 22, “The White Pine,” by
V. M. Spalding and B. E. Fernow, page 28.

} If it is preferred by some to count from the center outward, the number of
rings on the section can be subtracted from the total age, and the counting begun
at the age obtained. For example, on section 5 there are 38 annual rings; this
subtracted from 85 = An and the counting may begin at the pith (center), count-
ing “48,” “49,” “50,” etc., and a mark placed on the even decades, 50, 60, etc.

This cook es precisely ‘the same result, and obviates the necessity of counting
backward, which may be objectionable to some.
METHODS OF STUDYING INCREMENT 107

however, is quite different from that generally described in text-
books, in this respect —- the measurements for all the sections at
a corresponding age of the tree fall in the same column. That is,
if the tree is 85 years old, showing 80 rings at the stump, the
last measured diameter,* representing the size of that section in
1914,} will fall in column 9, and the size at 80 years of age, in
column 8. This is entirely logical, for the measurements of
each decade’s growth fall in the column bearing the correspond-
ing number. The measurement of the odd years, representing
an incomplete decade, fall in the /ast column, instead of in the first
column, as was the case in the method formerly used. If the
number of annual rings at the top of the first log (Section No. 2)
is 70, the age at that section will be expressed as ‘‘15 + 70,”
in column 6, and the last measured diameter will be placed, not
in column 7, but in column g, directly under the corresponding
measurement for section 1. Similarly, the measurements for the
last section, although it shows only 15 annual rings, will be en-
tered so that the diameter of the stem at that point in the year
1914 will fall in column g. To find the volume of the tree in
the year 1914, the dimensions of the several sections are read
directly from column 9, where they appear one under the other
in their logical order. There is now no chance of selecting the
wrong pairs of values in computing the volumes of the several
sections, and no chance for errors in doubling the radii, for di-
ameters have been recorded directly. It would appear that one
of the great stumbling-blocks in computing volumes from stem
analyses could thus be removed by tabulating the data in the
manner described. The advantages of recording the data and
measurements in this form are obvious, and at the same time the
whole arrangement is much more logical, since the measurements
for any particular decade all fall in the same column.

Having made and recorded a complete stem analysis as de-
scribed, it is now possible to compute the volume of the tree at
the age of 10 years, 20 years, 30 years, etc., for as many decades
as may be needed in the investigation under way. The volume

* Diameters are recorded instead of radii.
{ The year the measurement was made.
108 GROWTH OF INDIVIDUAL TREES

is generally calculated in terms of cubic feet, and the formule
used, which are applied to the several sections of the tree, have
already been described in Article 25. Unless great precision is
required, the logs of a tree are usually considered as frustums of
paraboloids, the stump as a cylinder, and the top is regarded as
acone. For convenience in these computations, tables of basal
areas, in which the areas of circles are given in terms of square
feet, are included in most books on Forest Mensuration. See
Appendix, page 231, for such a table.

66. Stem Analysis as applied to a Large Number of Trees. —
It is a very laborious piece of work to make all the measurements
and computations of volume called for in a complete stem
analysis, particularly if the tree be of great age and of large size.
When a large number of trees are to be analyzed, the amount of
work involved is often too great for economy, and it therefore
becomes advisable to shorten the computations as much as
possible. This can be done to best advantage when the trees
are all sectionized at the same heights above the ground, as
suggested on page 103. Under these conditions, a method has
been described which requires just as many field measurements,
but the work of computation is reduced to a minimum.* This
method consists in averaging together the measurements of
diameter-growth made at certain specified heights above ground
on trees belonging to the,same crown-class, from which curves
are drawn which show the average growth in diameter, by
decades, at each of the specified levels. From these curves, the
dimensions of an ideal tree (the average for the class) are deter-
mined, and the volume of this ideal tree computed. In other
words, the measurements of diameter are averaged together, and
one volume computation made for all trees of a class, instead of
averaging together the computed volumes for all the trees of
that class. Since the most laborious and time-consuming part
of the work of stem analyses consists in the mathematical cal-
culations which must be made, anything which eliminates a
large part of this work effects a big saving in time and cost.

* See U. S. Dept. Agr. Forest Service Bul. 20, ‘Measuring the Forest Crop,”’
by Mlodziansky, A.K.; and Graves, H. S.: “Forest Mensuration,” pages 294-298.
INCREMENT PER CENT 109

A further shortening of this kind of work can be effected by
combining the average diameter-growth curves for the several
sections of the trees on one single sheet of codrdinate paper, as
described by Graves.* This affords a graphic representation of
the rate of growth of a class of trees which answers many questions
at a glance, besides lending itself admirably to the reduction of
the computations necessary tor volume studies. The dimensions
of the average tree can be read off the curves, and the computa-
tions of volume can then be made once for the entire group or class.

67. Increment Per Cent.— A very convenient way in which
to express increment is in terms of percentage. To the average
business man, the statement that a pure stand of red pine at
35 years of age is growing at the rate of 13 per cent per year is
likely to mean more than to tell him that it is increasing in volume
at the rate of 40 cubic feet per acre per year. Unless he happens
to be familiar with the increment and yield of red pine, the
figures would probably mean little or nothing to him. But
practically all people can understand increment if it is expressed
in terms of percentage; hence the usefulness of formule which
express increment in such terms.

The most accurate way to express increment per cent is to
consider the volume of the tree at a specified year as the Base,
or the Principal; the current annual increment, or the periodic
annual increment as determined usually for a short period of
years (corresponding to the interest on the Principal for one
year), is then divided by the Principal, and the result is the Rate
per cent. The method of arriving at this rate per cent may be
explained as follows:

Let: V = the present volume of a tree,
v = the volume » years ago.
Then V — v = the increment for years,
and ra ” = the increment for one year
and let p = the rate per cent.

* Graves, H. S.: “Forest Mensuration,” page 295.

{ Although this is, strictly speaking, the periodic annual increment, it is fre-
quently regarded as the current annual increment. See definitions, and explanation
of this apparent inconsistency on page 102.
110 GROWTH OF INDIVIDUAL TREES

Then, depending on whether V or » be considered the base,
or principal, two formule are developed as follows:

 

 

 

 

 

V: y-. 100: p,
yee)
whence p = 100 (G3 ,
v: = t= 100: p,
m= 100 (~ i *);
whence p = 100 (— *) (2)

Difference of opinion as to which of these two formule is to
be preferred, led to the derivation of a third described in the
next article.

68. Pressler’s Formula. — Since it might be argued that
either V or v could be used as the base (although in most interest
calculations, it would be customary to regard z as the principal)
Pressler * developed a formula in which the mean of the two
quantities, V and 2, is used-as follows:

 

 

Pe FOS
Dt mF 100: Bs
2 ee
whence p= (4 aca aa (3)

As a matter of fact, this formula (3) is regarded as yielding
the most satisfactory results. If the length of time required to
grow from one inch-class (d.b.h.) to the next above it be known,
then the figures in any carefully constructed, reliable volume
table may be used for the corresponding values of V and 2,
respectively, in a practical application.

* M.R. Pressler, 1815-1886. Contributed largely to that part of forestry deal-
ing with mathematics.
oe SCHNEIDER’S FORMULA III

; 69. Schneider’s Formula. — By an ingenious application of
the formula for the volume of a tree in which the form factor F
is used * Schneider developed a formula which is extremely
simple, and gives fairly good results when applied to trees in
which the height-growth is practically at a stand-still, z.e., in
mature trees. The formula is as follows:

=, 482
~ nD’
in which
nm = the number of rings in the last inch of the radius, at
breast-height,
D = the present diameter of the tree,
and
p = the volume increment per cent.

The number of rings in the last inch of radius can be ascer-
tained most conveniently by using an increment-borer (see
Article 18) on trees the wood of which is soft enough to permit
its use. On hardwoods, it would be necessary to make an
incision such that the annual rings of growth could be counted
and measured on a surface perpendicular to the stem of the tree.

Where the trees are not mature, and where height-growth is
still progressing at a moderate rate, better results can be obtained
if instead of 400, the quantity 500 is used as the numerator of the
fraction; and in cases of very vigorous height-growth, a numera-
tor of 600 gives approximately correct results. It should be
distinctly understood, however, that in no case can Schneider’s
formula be dépended upon to give such satisfactory results as
Pressler’s; it finds its legitimate use as a short, easily applied.
formula, giving results only roughly approximate, but sufficiently
accurate for preliminary estimates of increment. In its modified
form, it is still less to be relied upon.

* See Article 31 for the application of form factors.
CHAPTER XI
INCREMENT OF STANDS

70. Increment in Stands.— The study of increment in in-
dividual trees presents a number of problems, as has been
shown in the preceding chapter; increment in whole stands is
even more complex, for to the difficulties already encountered
in the problem for single trees there must be added the ever-
changing character of the stand, especially as to the number and
the sizes of the trees composing it. If the stand be pure and
even-aged, then the problem is presented in its simplest terms
and it can be solved as described in subsequent paragraphs (see
Article 72). The introduction of a number of different age-
classes complicates the problem to such an extent that no very
definite conclusions can be drawn; while if stands are both
uneven-aged and mixed (i.e., composed of more than one species)
there is little that can be done except by the method of per-
manent sample plots as described in Article 74. But the ob-
stacles in the way need not deter us from investigating the prob-
lems; and if we can but secure a good idea of the general rate of
volume increment in stands, it will be a great help in attacking
some of the questions of Forest Management.

The more important of these problems of increment may be
stated broadly as follows:

(1) Increment in Pure, Even-aged Stands. — Increment in
stands of this character is: best studied by laying out a large
number of plots and measuring the trees thereon. From these
measurements, yield tables are constructed. Yield tables are
defined in Article 71 and the method of constructing them for
pure, even-aged stands is described in Article 72.

(2) Increment in Pure, Many-aged Stands. — Increment in
many-aged stands may also be investigated by laying out a

number of plots, but the method differs in several respects from
112
YIELD TABLES II3

that just referred to, especially when the stand is of open char-
acter. The results of the investigation may be combined in a
so-called yield table, but special emphasis is placed upon the
determination of the current annual increment and the mean
annual increment. One of the methods employed in solving
this problem is outlined in Article 73.

(3) Increment in Mixed Stands of the Selection Form.* — In-
crement in stands of this character may be investigated in a
more or less approximate manner by any one of several methods
which have been evolved and elaborated by some foresters who
possess a mathematical turn of mind and a lively imagination;
but they all make use of measurements made at one point (or at
most, only two or three points) in the life-history of the stand —
usually the present — and attempt to predict future increment
in this stand when the composition of it and the rate of increment
in the several species are changing so as to render such predic-
tions nothing more than conjectural. In other words, there are
so many factors entering into the problem, — some of which
are little known or understood and others of which are not sus-
ceptible of exact measurement, — that it is practically impossible
to solve it except by the empirical method, requiring a long
period of years. (See Article 75.)

Since these problems differ considerably, they must be in-
vestigated by methods appropriate to the objects sought, and
they will be discussed separately in Articles 72, 73, and 74.
First, however, it will be advisable to take up the general subject
of Yield Tables, for the main object in the investigation of yield
is to gather data which can. be assembled and tabulated for
ready reference in the work of Forest Management.

71. Yield Tables. — A tabular statement of the periodic yields
attainable at different ages (usually in 10-year periods) per unit
of area (usually the acre) is called a yield table. Such tables are
constructed separately for given species, on different sites, under
specified systems of treatment, and are used as standards with
which to compare actual yields.

* A stand is said to be of the selection form when many or, theoretically, all age-
classes are represented, irregularly scattered through the stand.
II4 INCREMENT OF STANDS

A complete yield table contains a great deal of information,
and is made to show the following data: *

(x) Age. (By decades, from ro or 20 to 100 or more, depend-
ing on species.)

(2) Number of trees per unit area. (Acre in U. S.)

(3) Basal area in square feet.

(4) Diameter breast-high of the average tree.

(5) Height of average tree.

(6) Form factors (for the forest).

(a) Intermediate yields.

(7) Yield, (b) Total yield.

(8) Current Annual Increment (c.a.i )

(9) Mean Annual Increment (m.a.i.)

(10) Supplementary to items numbered (7), (8), and (9), there
is often a subdivision of the total yield into (a) merchantable
saw-timber, and (6) fuel wood.

Yield tables thus far prepared in this country are relatively
simple when compared with European tables, the data appear-
ing in items numbered (6), (7)(a), and (10) are often omitted,
and the table assumes a comparatively simple form.

The chief uses of yield tables are (1) to determine the approxi-
mate final yield of a stand of timber at any given rotation age,
when the quality of the site is known; and conversely (2) to
determine the quality of site occupied by a stand, when the vol-
ume per acre, age, and the density (judged by basal area) are
known; (3) to make comparisons between the actual c.a.i. or
m.a.i. of a given stand and the normal increments as shown in
the table; (4) to estimate the volume of a stand, knowing its
age and density (basal area). etc., etc.

Since yield tables represent ideal conditions which are rarely
if ever fulfilled over areas of any extent, it is generally necessary
to apply a reducing factor to the quantities as given in the table.
The ratio between the actual and the normal may be determined

* Arrangement of the Tables is generally in vertical columns, reading across
the page opposite the several age-classes, which appear as the extreme left-hand
column. See example of yield table in the Appendix, page 234.
YIELD TABLES FOR PURE, EVEN-AGED STANDS II5

approximately by comparing the basal area of the actual stand
with the basal area of the normal stand as given in the table; for
it has been found that the basal area is a very good index of the
relative volumes. For example, if the basal area of a 50-year-
old stand of white pine, on quality II site, is given in a reliable
yield table as 232 square feet, and a stand under investigation,
of the same age and on the same quality of soil, is found to have
a basal area of only 190 square feet, then the volumes may be’
expected to show approximately the same relation, or

volume of actual _ 190
——_——__———_ = = = 0 82.
volume of normal 232

72. Construction of Yield Tables for Pure, Even-aged Stands.
— This problem is the least difficult of any, and will, therefore,
be described first. The work consists of measurements in the
field and computations in the office, and the following steps may
be recognized:

(x) Select a number of pure, even-aged stands representing
as many different ages and site qualities as possible. The
number of plots should be as large as possible consistent with
the amount of money available for the study and may be any-
where from 30 to several hundred. Most yield tables show
data for at least 10 age-classes, by intervals of 10 years from 20
to 110 or more,* and since at least three different qualities of
site should be recognized, this means that at least 30 stands should
be selected in which conditions of growth are as uniform and
even as possible. The stands in each instance should be fully
stocked (i.e., there should be no open spaces, but the crowns of
the trees composing the stand should touch one another) and
they should also be normal,} so far as can be judged.

(2) In each stand, lay out a plot, either square or rectangular,
and number it. The plots should be one acre in area if possible,
but if plots of 0.5 acre (or even o.1 acre in young stands) can be
found where the conditions are quite uniform, they are to be
preferred to larger plots which do not exhibit the desired degree
of uniformity.

* See example of Yield Table in Appendix, page 234.
+ For an explanation of this term, see Chapter XII.
16 INCREMENT OF STANDS

(3) Measure the diameter breast-high of all trees within the
plot. (On plots of young trees, 2 inches may be taken as the
minimum diameter.) Record these by diameter-classes of
individual inches. Ascertain also the average height of the
stand, with the aid of the hypsometer.

Determine the mean sample tree, by the method explained in
Article 51 and fell at least three such trees on the plot which
shall be normal, representative trees, and which fulfil the re-
quirements as to average diameter and height.

(4) Make complete stem analyses of these trees, if possible;
or if time does not permit this, determine at least the exact
volume, age, and rate per cent of the increment for the last
decade. Then apply the method of the mean sample tree to
determine the volume of the entire stand, in cubic feet. The
cubic foot is used as being more applicable to young stands, and
as being more truly indicative of the actual increment taking
place. (See Article 9.)

(5) If some of the plots have been other than 1.0 acre in area,
reduce all the figures of volume to terms of 1.0 acre.

(6) Taking a sheet of codrdinate paper, with age as the
horizontal scale (abscisse) and volume as the vertical scale
(ordinates), plot the volume of each sample plot, and identify
it with its appropriate plot number.

(7) If in the selection of stands, wide ranges in age and in
quality of site have been observed, it should now be possible to
draw a maximum volume curve and a minimum volume curve,
representing the extremes. Any values which seem to be
abnormal, by reason of their marked departure from the general
average should be discarded, and omitted from the calculations.
Depending on the number of site qualities * to be recognized,
intermediate curves should be drawn, which will harmonize with
the maximum and minimum curves, and which will make the
breadth of the “bands” resulting approximately equal fqr a
given age. (See Fig. 21.) The bands now show graphically
the division into site quality, and those plots (by number) which

* In the United States it is customary to recognize three qualities, designated
I, 11, IIL.
ae TABLES FOR UNEVEN-AGED STANDS 117

are found situated in the uppermost band will belong to Quality
I (best); those in the lowest band will be classed as Quality IIT
(poorest); and those in the intermediate band will be classed as
Quality II (medium). Three curves may now be drawn, one in
the center of each band, which will represent the average for the
particular band in which it appears.

(8) The last step is to tabulate the figures read from the
curves in the center of the bands, as just described, one table

Quality I. Band

Quality
II.
Band

Quality
III.
Band

 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ete
Age (Years)
Fic. 21. Diagram to Illustrate the “ Band” Method of Determining
Site Quality.

being prepared for each site quality separately as shown in the
sample form of yield table in the Appendix, page 234.

The yield table now brings together in convenient, usable
form. the results of the investigations, and is an indispensable
help in the solution of the various problems of forest management.

73. Construction of Yield Tables for Uneven-aged Stands. —
It must be quite apparent from the foregoing discussion that the
three great essentials in any study of yield are a knowledge of
volume, area, and age. In other words, what is desired is a state-
ment of the volume per acre at a given age, in fully stocked
stands which are growing on forest soils of Quality I, Quality IT,
and Quality III. The problem presented by uneven-aged
118 INCREMENT OF STANDS

stands is not easy of solution, and since the results are generally
compiled in the form of a table similar to tables for even-aged
stands, it should be explained and understood that the applica-
tion of these tables cannot be direct. The tables are useful,
however, in that they show the rates of the increments (both
current annual increment and mean annual increment), which
are so necessary in deciding questions of policy in management.
The problem has been studied by a number of foresters of this
country, with the result that many papers have been published
in the technical journals.* The essential steps in the process,
as worked out by some of these authors, are as follows:

1. Select pure stands as nearly fully stocked as possible, and
representing conditions typical of the region. The degree to
which the stands are stocked (z.e., the density of the stands) will
vary a great deal according to the species of tree, the climatic
conditions, and the soil quality; and great care should be exer-
cised to keep separate and distinct the stands which represent
the three site-qualities.

2. In these stands, lay out plots, or run strips, on which trees
of all sizes from two inches up are calipered. The tally of trees
generally should be by individual inch-classes, although in some
of the methods used, certain broader classes are also made use of.
Depending on conditions, the plots may be anywhere from 1 or

* See especially articles by the following authors, who have contributed largely
to our present knowledge of the subject:

(1) CHapman, H. H.: “A Method of Investigating Yields per Acre in Many-aged
Stands,” For. Quart., Vol. 10, page 458.

(2) Cuapman, H. H.: “The Measurement of Increment on All-aged Stands,”
Proc., Soc., Am. For., Vol. 9, page 189.

(3) Carter, E. E.: “The Use of Yield Tables in Predicting Growth,” Proc. Soc.
Am. For., Vol. 9, page 177.

(4) Moors, B.: ‘Yield in Uneven-aged Stands,” Proc. Soc. Am. For., Vol. 9,
page 216.

(5) Wootsey, T. S., Jr.: “Yield Table Method for Arizona and New Mexico,”
Proc. Soc. Am. For., Vol. 9, page 207.

(6) AsHE, W. W.: “Determination of Stocking in Uneven-aged Stands,” Proc.

Soc. Am. For., Vol. 9, page 204.

(7) Muncer, T. T.: “A Formula for Normal Growing Stock in Selection-System
Forests,” Proc. Soc. Am. For., Vol. 10, page 18.

(8) Morr, W. J.: “Method for Regulating the Yield in Selection Forests,’
For. Quart., Vol. 11, page 21.
YIELD TABLES FOR UNEVEN-AGED STANDS 119g

2 acres up to 20, or even 40 acres, the larger sizes being em-
ployed only in stands of open character, such as Western yellow
pine in the Southwest. The seedlings and saplings are: usually
studied intensively on small plots (0.01 acre to 1.0 acre) located
within the large ones. Under certain conditions, the tally-sheets
of regular timber-cruises may be used, provided the site-qualities
can be distinguished with a fair degree of precision. This work
enables the preparation of stand tables for each of the forest
types and site qualities. These are to be used in step number
6(c).

3. Next, make a study of the crowns of the trees of the several
size-classes, with the object of determining just how much
growing space is required for a tree of a given size-class. Moore
(see reference number 4 on page 118) recommends the following
method of procedure for this step:

“Crown measurements may be made in one of two ways: (a)
One man stands off from the tree, where he can see both sides of
the crown; he then lines in the second man under one edge of the
crown, has him measure across under the crown at right angles
to his (the first man’s) line of sight, then stops him under the far
side of the crown. The measurer calls out the distance, and the
first man records it opposite the proper diameter, which has
already been measured and recorded. (b) Each man works
alone, lining himself in under one side, measuring across under
the crown, and then lining himself in under the other side. This
is, I believe, less accurate than the first method, unless the men
have previously practiced lining each other in as under (a), but
is more rapid, especially where two diameters are required for
most trees.”

Moore recommends measuring about 20 trees in each diameter-
class, representing all crown-classes of trees and keeping the
records distinct for the different site-classes.

4. The crown area may be computed by squaring the diameter
of the crown. This gives more than the true crown area (area
of circle = 0.7854 D*), but the crowns do not touch on all sides,
and by squaring the diameter, the author believes results are
obtained which agree more closely with conditions as they
120 INCREMENT OF STANDS

actually exist. The results are plotted on cross-section paper,
the crown areas being the vertical scale, and diameter-classes
(d.b.h.) being the horizontal scale; a curve is drawn which is at
least a good index of the relative growing space required by each
diameter-class, if not the actual growing space.

5. The average rate of growth in diameter is obtained from
about too stump counts of each species, for each type and site
quality represented. This work may be done as described in
Article 60. The average age of trees of each diameter is
wanted, therefore the points for the curve should be balanced
horizontally, if such balancing is necessary.

6. Considering each diameter-class as an age-class, the follow-
ing computations should next be made:

(a) Volume: Apply appropriate volume tables, using cubic
feet as the unit wherever possible.

(b) Age: The average age for the diameter-class can be
obtained from the curves drawn as described under step
No. 5.

(c) Area: The area occupied by each age-class (= diameter-
class) can be computed by obtaining the product of the
number of trees as shown in the stand table (step No. 2)
multiplied by the crown area of the class, as shown by the
curve obtained in step No. 4.

7. Convert the volume for each size-class, as found by the
process described under 6(a), to the basis of one acre, by dividing
by the area (decimal part of an acre) as determined under 6(c).
This now gives the data necessary for the final step.

8. Construct a simple yield table by plotting on cross-section
paper the volume per acre as found in step No. 7 on the average
age as found in step No. 5. A smooth curve should be drawn
through the points obtained from which may be read the volumes
at even 10-year intervals, thus giving a part of the data required
for a complete yield table. The table may be completed by
making calculations to show number of trees per acre, basal area
per acre, the mean annual increment, and the current annual
increment.
THE STUDY OF INCREMENT IN MIXED STANDS 121

The method as described above is not without its weak points,
and in the application of the results it is quite essential to keep
in mind the limitations and the shortcomings of the method.
Some of the difficulties are as follows:

(1) The table represents conditions as they might occur in
fully stocked, even-aged stands. As a matter of fact the actual
stands are rarely fully stocked, and are not even-aged. The
climate, the soil conditions, the site factors, and indeed the
inherent silvical character of the species may combine to make a
fully stocked stand impossible in fact. In interpreting the
table, therefore, these points should be borne in mind.

(2) The method of using crown area to determine the factor
of area is not always safe. In very old, decadent trees the crown
is quite likely to be smaller than it was at the time of the tree’s
best growth, and hence the space at present occupied is not a
true indication of how much space has been occupied in the past,
to accomplish the growth. In very young trees a similar diff-
culty is encountered, inasmuch as seedlings and saplings may
grow for a time under the shade of the older trees,* and hence the
same space (crown area, as projected on the surface of the
ground) may be occupied by the two classes of trees —- the
mature and the immature. This naturally leads to what would
appear to be an abnormal over-crowding; but in uneven-aged
stands of tolerant species, this condition may be perfectly normal.

With slight modifications as to details, other writers have
described methods of studying increment in uneven-aged stands
which are similar to the foregoing. The age-classes recognized
may be broader than individual inch-classes, and the method of
determining the area occupied by each age-class may be modified
to suit special conditions; but in one way or another any method,
to be at all useful, must take account of the three factors already
mentioned — age, volume, and area.

74. The Study of Increment in Mixed Stands.— When a
stand is composed of a number of species growing together
indiscriminately, it is impossible to construct a yield table which

* Trees that are capable of growing under more or less shade are spoken of as
“tolerant”; those that cannot endure shade are spoken of as “intolerant.”
122 INCREMENT OF STANDS

is such in the true sense of the term as already defined. The
proportionate representation of species in the mixture is con-
stantly changing because of differences in tolerance, differences
in rate of growth, and differences in reaction to the physical factors
of site. Moreover, the same species may exhibit a behavior in
one mixture totally different from its behavior in another mix-
ture. The problem is so complicated that the only thing that
can be done is to make repeated observations on selected areas
at definite intervals of time, recording with great care the meas-
urements and descriptions of the stand for future comparisons.
Studies of this kind are best made by establishing permanent
sample plots, which are the subject of the next article.

75. Permanent Sample Plots. — The establishment and study
of sample plots in Europe was begun about sixty years ago, but
in this country no effort was made to establish permanent plots
until 1904, when the then Bureau of Forestry initiated such a
policy. The purposes of permanent sample plots are to afford
opportunities to study increment in trees and stands, and to
observe the effects of applying certain definite systems of silvi-
cultural practice.* The effects of thinnings, cuttings, fires,
grazing by animals, etc., may be observed in sample plots —
in short, the effect of all influences combined can be observed
and interpreted in the light of the known history of the stand, as
disclosed by the records.

Depending on the density of the stand and the specific objects
of the investigation, permanent sample plots may be from a
square rod up to several acres in area. For purposes of in-
vestigating increment and yield, plots are generally of 1 acre or
one-half acre in dense stands, but may be as much as 5 acres,
10 acres, or even 40 acres in very open stands. Each tree on
the plot receives a serial number, and its diameter is carefully
measured at a definite point. Since painted numbers are likely

* See Graves, H. S.: “Forest Mensuration,” N. Y., John Wiley & Sons, Inc.,
1906, page 345.

Sterrett, W. D.: “Objects and Methods of Establishing Permanent Sample
Plots,” Proc. Soc. Am. For., II (1907), page 63.

Moncer, T. T.: “ Five Years’ Growth on Douglas Fir Sample Plots,” Proc. Soc.
Am. For., X (1915), page 423.
PERMANENT SAMPLE PLOTS 123

to weather off, numbers may be stamped on copper or zinc tags,
and these attached to the tree by nails. If care is exercised to
drive the nails at exactly breast-height, and if the diameter is
measured with a circumference tape, it will be possible to re-
measure the trees on the plots at intervals of 5 or 10 years with
the positive assurance that the re-measurement is being made at
precisely the same spot as was the original measurement — a
matter of the highest importance.

Besides numbering and measuring the diameter of all trees on
the plot, a number of representative trees are measured as to
height and crown development; very careful descriptions are
written; and numerous photographs are taken from designated
spots, so that the changes taking place can be photographed and
compared at leisure, at any time in the future. While the lapse
of a long period of years is necessary before any definite infor-
mation can be obtained, this method of permanent sample plots
is the only reliable one, when increment in mixed stands com-
posed of trees of all ages is being investigated. By establishing
plots in well-defined forest types in many localities, and conduct-
ing the work according to a definite plan of operations, there
will gradually become available a mass of information concern-
ing the life-history, development, and increment in mixed stands
of all ages, which will be invaluable to foresters and lumbermen
in solving the intricate problems of forest management. It is
gratifying to know that such studies are being made,* and that
in the course of time reliable statistics of increment in stands of
the selection form will be available.

* See Wootsey, T. S., JR.: “Permanent Sample Plots,”’ For. Quart., Vol. X,

No. 1, pp. 38-44. ‘‘ Plan for Permanent Sample Plots in the Adirondacks,” Jour.
For., Vol. XVI, No. 8, pp. 922-927.
CHAPTER XII

FOREST ORGANIZATION

76. Definition. — Forest organization concerns itself with the
organization of a forest property for management and its main-
tenance, ordering in time and place the most advantageous use
of the property, with the ultimate aim of securing a sustained
yield. The term forest regulation covers the same idea, but,
since it suggests police and administrative prescriptions, seems
less desirable except for that part of organizing a forest which
concerns itself with regulating the cut.

In order to have a definite scheme for the conduct of operations
on a tract so as to secure most effectively the objects desired by
the owner, a working plan is formulated. This may be defined
as the plan or plans under which a given forest property is to be
continuously managed.

77. Sustained Yield. — By sustained yield is understood the
yield or cut of timber from a forest which is managed in such a
way as to permit the removal of an approximately equal volume
of timber, annually or periodically, i to the increment.
(See Chapter XI.)

The five requisites for a sustained yield management are:

1. Enough, accessible forest.
2. A forest of the right character so that it will pay to cut
it for repeated crops.
J 3. Adequate fire protection.
4. Equitable taxation.
5. Good markets for products.

Wherever these conditions obtain, intensive forestry is practic-
able.
78. The Normal Forest. — The normal forest is a standard

with which to compare an actual forest to bring out its deficien-
124
THE NORMAL FOREST 128

cies for sustained yield management; the conception of an ideally
regulated or organized forest. The term ‘‘normal” is here used
in the sense of conforming to a standard, rule, or principle — a
model. Such a forest does not actually exist anywhere.

The normal forest has three attributes: normal increment, normal
age-classes in size and distribution, and normal growing stock.

(1) By normal increment is understood the best average in-
crement attainable by given species on given sites.

(2) To understand normal age-classes requires first an explana-
tion of what is meant by an age-class. All the trees in a stand
or forest whose age falls within stated limits are spoken of as
being in the same age-class. Age-classes are usually divided into
twenty year periods, so that a stand in which the trees fall
between the age of 1 to 20 years would be referred to as Age-
Class I. Age-classes are stated in extent of area or in percentage
of the whole stand, or, in selection forest (that is, a forest through
all parts of which many different age-classes are represented) by
number of trees.

Distribution of age-classes refers to either the local distribution
of age-classes or to the percentic or absolute representation of
the different age-classes in area or amount, or (in selection forest)
in number of trees.

Normal agé-class distribution in the strict sense of actual
location, means such distribution of the age-classes as will permit
annual or periodic fellings to be made without damage to adjoin-
ing stands. In the broader sense of extent of area or amount,
it means that each age-class is equally represented in per cent or
in absolute area, that is, the presence of a complete series of age-
classes corresponding to the rotation. It is in this latter sense
that the term is usually used in describing the normal forest.

(3) The third and last attribute of the normal forest, normal
growing stock, means the amount of material represented by the
stands in a normal forest.*

* Practically, it is the contents of the normal age-classes as represented in
normal yield tables (see Chapter XI). The statements of a normal yield table are
derived as an average from the best producing, fully stocked areas for given species
and sites. If a normal forest were not merely an idea, but actually attainable, the
normal yield table would represent its productivity and growing stock.
126 FOREST ORGANIZATION

Normality in (1) and (2) always results in normality in (3),
but the reverse is by no means true. A normal growing stock
may exist in a forest with only a single age-class, as is shown in
Fig. 22.

Nevertheless, as Flury says,* “the normal growing stock is

rea in Years F

 

Volume
Fic. 22.

the best, most pregnant, numerical expression of sustained yield
management. To attempt an approach to normal stock condi-
tions in some way, must be the aim of the manager for sustained
yield.”

* “Grésse und Aufbau des Normalvorrates im Hochwalde,” Mitteilungen der
Schweiz. Centralanstalt fiir das Forstliche Versuchswesen, XI, 1, 1914, pages

97-148.
DETERMINATION OF THE NORMAL GROWING STOCK 127

The actual growing stock is the volume of material which is
present on a given forest. This is obtained by timber estimating
(see Chapter VIII). But how can the normal growing stock be
determined?

79. Determination of the Normal Growing Stock. — The
normal growing stock (NV) is obtained (1) by formula (2) from
yield tables.

(x) The normal growing stock is expressed by the formula

NV = . where NV = normal volume of growing stock, r =

rotation, and 7 = the mean annual increment.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A B
a
g 4
a} S| $s} 8] 8] 2] a] & al 4 gs} 8] &
a
2 g : es
=25 < 7
a. 2) |e) el at
>| : : : _
& ; : : 2
2 zg : 3 z 2 :
—3|_g\_g1_8|_8\_af_g|_3|_81_ 8} 41 s1 314)
6) CU) CS kok] oso] oso] os] oS
zi 4
ae
A)
a b é d e@ h a j k 1 m
é f |g j ‘Alp
10 2 #8 4 #50 6 70 480 9 100 110 120 130 14
Age iu Years
Fic. 23.

(2) NV can also be determined directly from yield tables

constructed by measurements of fully stocked stands. sg ae
w
NV then equals W(a +6 + ¢ ce +25} = mame
ber of years in each age-class (step of the yield table) and a, }, c,
. . . M= the volume per acre given in the table for each age-class.

The method and correctness of finding NV (1) by formula, (2)
by summation from yield table, is illustrated in Fig. 23. For
128 FOREST ORGANIZATION

the values as given in this diagram, which is based on a yield
table for white pine constructed by W. J. McCarthy, M.F., in
the vicinity of Ithaca, N. Y., the normal growing stock would
be as follows, assuming a forest of 1000 acres:

(x) NV = < r

rotation = 140 years,
7 = mean annual increment per acre =
281.64 board feet.
WV = 140 X 281.64 aerate:

2
19,715 X 1000 = 19,715,000 board feet.

(2) NV = N(a+b+e oe +¥).

N = number of years in each step of yield table = 10.

a, b,c, . . . are volumes per acre in each step of yield

table. M is volume per acre at the rotation age (140
years).

NV = 10 (3580 + 8600 + 12,580 +++ + soxd30)

1000 2,996,950,000
— 6, ea 2 =
2,990,950 140 yts. 140 21,407,000
board feet.

Many authors have busied themselves with the problem of
how to determine the normal growing stock most accurately
and have suggested certain departures. Thus Flury* claims

that the formula NV = . to be more generally correct should

read: NV =c Xr Xi in which c is a variable constant. To
determine this constant, normal yield tables are necessary which
may be summed up by the formula

wv=N(ato+e--- +¥)a5,
then since
cxXxrxi=S,
— Ss .
rXt

* “Schweizerische Zeitschrift fiir Forstwesen;” March, 1913, briefed For.
Quart., Vol. XIII, No. 1, pages 108-113. :

 

c
DETERMINATION OF THE NORMAL GROWING STOCK 129

Applying Flury’s constant C to McCarthy’s white pine
yields as given above, the factor is as follows: for rotation of
30 years, C = 0.306; for 40 years, 0.365; for 50 years, 0.378;
for 60 years, 0.421; for 70 years, 0.452; for 80 years, 0.475; for
go years, 0.493; for 100 years, 0.507; for 110 years, 0.518; for
120 years, 0.525; for 130 years, 0.536; and for 140 years, 0.542.

Thus the value for 140 years given above as 19,715,000 board
feet would be corrected as follows:

NV =cXrxXi=0.542 X 140 X 281.64
= 0.542 X 39,430 X I000 (acres) = 21,371,000 board feet.

which compares closely with the value 21,407,000 board feet
found by summation of the yield table.

It is obvious that where the constant C is approximately 0.5
the error in finding NV by the formula method is least, since

WV =" =05Xxrxi.

To further illustrate the workings of C the average value
of C has been found by and applied to the white pine yields
as given in table 6, Bulletin 13, U. S. Dept. of Agriculture, for
site quality II, 7.e., medium site quality. The values by formula,
with and without use of C and by summation of yield table,
are also given.

AVERAGE VALUE OF CONSTANT C IN WHITE Pine, Site Quatiry II,
BasepD oN TABLE 6, U. S. Dept. oF AGRic., BUL. 13.

 

 

 

 

 

 

 

 

ee. oe nage i Pence
: ; =cxXrxXt. etween

peg C. NV = > de gvaungs *) a 2 columns.

Feet, Board measure, per acre.
40 0.227 11,750 51337-5 51334-5 3
50 0.280 18,300 10,280 10,248 32
60 0.330 23,450 15,525 15,477 48
7o 0.368 28,050 20,764 20,644 120
80 0.399 32,000 25,588 25,536 52
go 0.426 351430 30,239 30,203 36
100 0.449 38,500 34,610 345573 37
I10 0.465 41,600 38,745 38,771 26
120 0.484 44,050 42,654 42,650 4
130 0.506 45,750 46,280 46,299 19
140 0.549 47,050 51,604 51,660 56
Ave....... 39-4

 

~ Note. — Values over 100 years from prolonged curves.
130 FOREST ORGANIZATION

Munger * has devised a formula for determining normal
growing stock in selection forests. Munger conceives of the
normal growing stock as consisting of the reserve left after
cutting multiplied by the area, plus one-half the growth which
takes place on the entire forest for the entire cutting cycle.
Expressed as a formula:

NV = Exe -++ reserve for the entire forest,
2
where i = the current annual increment on the entire forest and
cc = the cutting cycle (interval between cuts).

Example. — If for 50 acres i = 5000 board feet, cc = 50 years,
that is, one-quarter of the 200-year rotation, and reserve =
200,000 board feet, then,

NV = S -++ reserve
= a 5° + 200,000

= 258,009 + 200,000
= 325,000 board feet for the entire fifty acres
= 6500 board feet per average acre.

Using the formula NV = “and the same premises, VV would

figure out as 10,000 board feet per acre.

Munger’s formula is undoubtedly well adapted for selection
forest.

80. Comparison of Actual with Normal Distribution of Age-
Classes. — In even-aged forests the degree of approach toward
normality may be judged by comparing the actual and the
normal age-class distribution. This comparison may be done
graphically as shown in Fig. 25. Of the two methods, the one
by rectangular blocks is to be preferred, since it is clearer and
can be kept posted by decades so as to reveal the progress of the
management towards the goal of normality.

* Proceedings Society of American Foresters, Vol; X, No. 1, pages 18-21. The
325,000

5°

example which Munger gives on page 20 is for 50 acres since = 6500.
100

   
  

Agein Years
an eo
oO oS

>
o

10

185 Acres
Fic. 24.

Acres
30,000

 

Fic. 25. ( 133)
132 FOREST ORGANIZATION

81. Division of the Area. — In order to facilitate the manage-
ment of a forest it is systematically divided into units of area.
A forest may be divided from various points of view into units,
either localized in the field or differentiated in the working plan,
or both,

The usual subdivisions of a forest are:

(1) Working unit: (Syn.: working plan unit.) A forest
area managed under one working plan. It may or may
not coincide with the administrative unit.

(2) Working group: (Syn.: management class, working
block; working circle, working section.) An organization
or working plan unit, comprising an aggregate of compart-
ments or stands to be managed under the same silvi-
cultural method and rotation. (The terms compartment,
silvicultural method, and rotation will be made clear in this
chapter; stand is.a general descriptive term referring to
an aggregation of trees, standing on a limited area, of
more or less uniformity of composition and condition, or
of age.)

(3) Block: A major division of the working unit, inter-
mediate in size between the working unit and a compart-
ment. A block is usually based on topography and com-
prises a main logging unit or group of logging units. A
single block may contain many thousand acres.

(4) Compartment: A unit of forest organization for purposes
of orientation, administrative, and silvicultural opera-
tions. It may or may not coincide with the public land
survey. There may be an indefinite number of compart-
ments in a block. The limits of a compartment are
rectilinear in the plains and follow topographic features
in hill and mountain country. The area of a compart-
ment varies with the intensity of management and seldom
exceeds 500 acres. In a forest under complete manage-
ment, the compartment boundaries are shown on the

‘forest maps and are permanently marked on the ground
by blazed lines, durable monuments, posting, roads,
trails, streams, or other well-defined natural features.
BOUNDARIES OF DIVISIONS 133

(5) Lot: (Syn.: Sub-compartment.) A small sub-division
of a compartment differing in composition, age, or char-
acter, requiring different treatment from the main body
of the compartment; impermanent if due to accidental;
permanent if due to site conditions.

82. Designation of Divisions. — Working units and blocks are
given names and blocks are sometimes numbered as well; com-
partments are numbered; sub-compartments are lettered. E.g.,
a paper-birch thicket in a spruce compartment on the lower
slopes of Mount Tecumseh block in the Waterville, N. H., basin,
would be designated as 29a, Tecumseh Block, Waterville
Unit.

83. Boundaries of Divisions. — Before designating the bound-
aries of any working-plan divisions, either in the field or on the
map, the forest organizer, in consultation with the owner and
the administrator of the forest, or both, should decide just what
divisions are to be made and on what basis. The determination
of working units is a sine qua non, but whether blocks, compart-
ments, and sub-compartments are also to be segregated depends
entirely on the specific needs of the forest. Large forests should
almost always be divided into blocks. The further sub-divisions
into compartments and sub-compartments is necessary only
where intensive working plans are practicable.

Having decided just how far to go in the matter of divisions,
the forest organizer keeps this in mind during his preliminary
reconnaissance and during the entire progress of the field work.
The detail of forest description and the unit described depend on
the extent of sub-division. That is, if blocks are the minimum
divisions possible, the organizer needs only the briefest descrip-
tions by sections or other survey units and a more detailed general
description by watersheds or other appropriate logging units.
Tf, on the other hand, the refinements of compartments and sub-
compartments are possible, the unit of description must be the
stand, and the forest description of each stand must be sufficiently
detailed so that the forest organizer can determine therefrom
whether to make it a sub-compartment, and its function in regu-
lating the cut.
134 FOREST ORGANIZATION

Obviously, therefore, the provisional boundaries of the mini-
mum unit of division decided upon must be noted in the progress
of the forest survey and noted on the map.

As the work of gathering the data progresses, the forest
organizer keeps always in mind the possible division of the
forest, and, map in hand, goes through the area to determine
its most advantageous arrangement. His task will be the
easier if the forest description data are well and carefully

gathered.
On the map the boundary of the working unit is marked by
heavy dot and dash —. —. —.—.; the blocks by dashes

maar ; the compartments by a dotted line ...........5
and the sub- dom partatents by a thin, unbroken line

84. Working Plan Conference. — Before organizing a forest
for management, a consultation, known as the working plan
conference, should be had between the owner or administrator
and the forester who is to make the working plan. This con-
ference should decide, first of all, the wishes and purpose of the
owner or administrator regarding the tract. Next it should
determine, with reference to the forest survey, what data are
requisite and what methods shall be used in securing these
data, and in how much detail the work is to be done, in-
cluding the division of the area into blocks, compartments,
etc. The permissible cost of the field-work should also be
decided.

It is well if the results of this conference are put in writing and
the document signed by-each of the participants.

After the fundamental wishes and purposes of the owner and
the essentials of the field-work have been fixed, then further
points must be decided. These are:

1. The objects of management to be attained.
2. The silvicultural methods to be used.
3. The rotations to be employed.

These will be considered in the order named.

* References: Roru, “Forest Regulation,” pages 34-43; Inzicx, “The Sub-
division of Forests,” For. Quart., Vol. XIII, 2, pages 183-198.
SILVICULTURAL METHODS 135

85. Objects of Management.— At the working-plan confer-
ence the objects for which the forest is to be managed must be
decided, z.e., whether:

(a) For sustained yield.

(6) For exploitation.

(c) For protection (watershed protection).

(d) For esthetic purposes.

(e) For a game preserve, or how far each or all of these or
any other consideration is to govern.

If the forest is to be a continuously productive one, the next
point to decide is the class of product desired, such as: saw-
timber, cordwood, mining timber, turpentine, etc.

86. Silvicultural Methods. — The conference should determine
whether the forest is to be managed as:

(a) High forest, i.e., a forest originating from seed.

(b) Coppice forest, i.e., a forest consisting wholly or mainly
of sprouts.

(c) Coppice with standards, i.e., a forest in which both
seedlings and sprouts are used in reproduction,
the seedling growth forming the standards. This
is known as composite forest.

If high forest is chosen, the method of reproduction must ‘be
determined provisionally. A method of reproduction is an
orderly procedure or process by which a forest is renewed or
established, either naturally (by self-sown seeds) or artificially
(by direct seeding or planting). The following methods are
distinguished:

1. Clearcutting, artificial reproduction.
2. Clearcutting, natural reproduction.
3. Seed tree method.
4. Selection method.
5. Shelterwood method.
These methods are defined and explained as follows:

1. Clearcutting with Artificial Reproduction. — Removal of the
entire stand in one cut with artificial reproduction or reforesta-
tion by direct seeding or by planting.

G., Kahlschlagwirtschaft. F., Méthode par coupe unique.
136 FOREST ORGANIZATION

2. Clearcutting with Natural Reproduction. — Removal of the
entire stand in one cutting, reproduction taking place by seed
from the marginal stand or seed in the ground. Differentiation
may be made according to the form of cutting area into strip
and group method. Strip method: (G., Saumhieb, F., Coupe
par bandes.) Cutting a strip, and when regeneration has taken
place by marginal seeding, seaming an additional strip and pro-
ceeding in this manner from year to year or period to period. A
variant called strip method in echelons (G., Kulissenhieb, Spring-
schlag. F., Coupe par bandes alternes) opens strips in several
places at the same time and then proceeds similarly by seaming.
The group method (G., Kesselhieb, Lécherhieb; F., Coupes par
trouées) proceeds by removing groups of trees making more or
less irregular openings and enlarging these until the entire stand
is removed.

3. Seed Tree Method. — Removal of the entire stand at one
cut, but leaving a small number of seed trees singly or in small
groups, to be eventually removed If the seed trees are held
over for another rotation, this may be called reserve tree method.

4. Selection Method. — That method of cutting in which
single trees, usually the largest, or small groups of such trees,
are removed and reproduction secured under the remaining
stand and in the openings. When groups of trees are taken, it
is termed group selection method, G., Plenterbetrieb, Femelbe-
trieb. F., jardinage, régime de la futaie jardinée.

A special form of the selection method is termed selection
border cutting or strip selection when selection cuttings are
made in narrow strips, in most instances beginning on the north
border and progressing southward, followed by clearcutting
when young growth is fairly established, with the expectation of
additional marginal seeding. The resulting forest is uneven-
aged in narrow lines. G., Blendersaumschlag.

5. Shelterwood Method. — A method of securing natural re-
production under the temporary shelter of the seed tree crown
cover, by means of a series of cuttings throughout the stand,
aimed to admit a gradually increasing supply of light to the
seedlings. The principle of the method lies in the protection
Prate II.

 

Forét de la Haye near Nancy, France. The forest officer is a

Coppice with Standards.

District Ranger or ‘ Brigadier.”
SILVICULTURAL METHGDS 137

(shelter) which the seed trees (nurse trees) afford the young
growth during its youth. G., Schirmschlagbetrieb (Gayer &
Lorey), in part Femelschlagbetrieb (Lorey). F., régime de la
futaie reguliére. The number and severity of the cuttings and
hence the duration of the entire removal period, depends upon
the rate of establishment and the need of light by the young
growth. In theory the sequence of cuttings is divided into four
parts as follows:

Preparatory cuttings fit the stand for its reproduction by the
removal of dead, dying, or defective trees and undesirable
species, and prepare the ground for the seed-bed and encourage
seed production. A stand in which one or more preparatory
cuttings have been made is in the preparatory stage. G., Vor-
bereitungschlag. F., coupe préparatoire.

Seed Cutting. — A further opening of the stand, before seeding
takes place, to secure the amount of light which the expected
seedlings will require. A stand in which one or more seed cut-
tings have been made is in the seeding stage. G., Besamungs-
chlag. F., coupe d’ensemencement.

Removal cuttings gradually remove the mature stand, which
would otherwise retard the development of the young trees.
A stand in which one or more removal cuttings have been
made is in the removal stage. G., Lichtschlag. F., coupe
claire.

The final cutting is the last of the removal cuttings, in which
all of the old stand still remaining is cut. (G., Abtriebsschlag,
Endhieb. F., coupe définitive.) In practice a two-cut shelter-
wood method may be used, including the seed cutting and final
cutting stages. The shelterwood method may be applied to a
stand in narrow strips, from the leeward side, at such intervals
that reproduction cuttings are generally going on in three strips
at one time, one strip being in the removal stage, one in the
seeding stage, and one in the preparatory stage. This manner
of application is termed shelterwood strip method.

Another modification of the shelterwood method of reproduc-
tion is that in which groups of valuable advance growth, if
present, form the starting points for the cutting which radiates
138 FOREST ORGANIZATION

from these centers. Such an application is termed shelterwood
group method. ;

The specific application of these various methods to given
conditions is the province of silviculture and is fully described
in books on that subject. The choice of methods must always
depend upon conditions on the ground. A brief discussion of
the applicability of the chief methods may, however, prove
helpful in reaching such a decision. The accompanying chart
shows the possible methods of reproducing the most important
species.

87. The Clearcutting Methods.* — All methods of natural
reproduction from seed trees not standing on the area to be
reproduced are much more uncertain than either the selection or
shelterwood methods. When the area is clearcut or denuded
by fire or other causes, soil deterioration is likely to occur and
the ground to become covered with a more or less dense growth
of herbage, making reproduction more and more difficult the
longer it is delayed. Clearcutting methods, because of the
difficulties and uncertainties in attaining natural reproduction,
usually result in artificial reproduction being required at least
to supplement the natural seeding and the new stand is estab-
lished at once. Artificial reproduction is often advantageous
because it is more certain of success. Furthermore only the
species desired are reproduced.

The strip method of clearcutting depends for effectiveness
upon the width of the strips, z.e., the narrower the strips the
more abundant and uniform the distribution of the seed, and,
under favorable soil conditions, the better the reproduction.
The success of this method depends also upon the points of
attack, z.e., the direction of the strips in reference to the pre-
vailing wind and the shade cast by the remaining stand.

The group method of clearcutting requires small openings.
The smaller the openings are, the better and more uniform the
reproduction and the closer the approach to the selection or

* The following four articles are adapted from ‘Seeding and Planting in the
Practice of Forestry,” by J. W. Toumey, John Wiley & Sons, Inc., New York,
1916.
-pisuoo uo Ajiseuid peseq st poyjeur suo Aue jo Ayyiqeoydde eyy, ‘sopeds 343
-qnd uo paseq st jieyp eyy, “spueys aind ur se jam sv ‘salads poyersosse 043 YI

 

 

 

 

“spoujeur oyes “480107 ‘Qasead
i

ureyunoyy 43904 ox
Ww smofo OST wf ‘sw
- NN
“spoyqjour x ag -ysol0gT
4sBop ggtoed
ul ey osTy

 

 

 

‘8 A ‘81 «1198 woppeqs ware 9 loys deeya|

  

 

 

Got TT ITA “20g JY “ag OO BOTT
ctajodpaeys peNyinoy Ate oT wlory Ng,
exo sqq} G8noyy uede ‘zwoTo yee oq soso!
Sout “ray Agony on UF 1G seIsNOG:

 

‘BPOYJOUI OUIBY “480107
98800 ppbed
Uy} BmMopo OSTY

 

 

“‘spoqjeur ole “48010

98800 puped 8 Joes

‘Ssarags Ad NOIL

 

 

 

 

 

 

 

 

 

 

 

 

 

RERUN eG ET A
Fold out
THE SHELTERWOOD METHOD 139

shelterwood methods. In the practice of this method, advan-
tage is usually taken of openings already existing in the stand
due to windfall or other causes, and their area is gradually in-
creased with the progress of reproduction. This method applies
best to uneven-aged stands of wind-resistant species.

88. The Seed Tree Method.— This method can seldom be
depended upon to attain satisfactory reproduction. Except
with the most wind-resistant species, the seed trees left are liable
to be blown over. The species must produce seed having great
carrying power, the soil must be receptive, and the reproduction
must be attained quickly or the.growth of herbage will prevent.
The seed tree methods have proved most useful abroad when:
used in connection with artificial reproduction. The scattered
seed trees are of other species which through natural reproduc-
tion introduce age variety, as well as variety in species, into the
otherwise even-aged artificial stand.

89. The Selection Method. — Natural reproduction is most
easily attained in forests managed by the selection method,
although in such forests it is often difficult to regulate the com-
position. The selection method is applicable to stands repre-
sented by trees of all ages. In such stands, trees are taken out
here and there as they mature while the younger trees remain
standing. Only a small percentage of the entire stand is cut at
one time. The openings made by the removal of single trees or
small groups of trees are always small. Because of the ‘abun-
dance of nearby seed trees and the protection afforded the soil,
the openings are quickly filled with young trees in vigorous
growth. Reproduction in a selection forest most nearly ap-
proaches that of a virgin forest, the chief difference being that in
the selection forest the small openings are made by the removal
of mature trees, while in the virgin forest the openings are made
through the death and decay of the overmature trees.

90. The Shelterwood Method. — The shelterwood method is
applicable to relatively even-aged stands. The mature crop is
removed gradually by a series of cuttings. From to to 15 years
usually intervene between the first cutting and the removal of
the last of the crop. During this interval reproduction takes
140 FOREST ORGANIZATION

place. From the standpoint of reproduction, this method has
many advantages. The cuttings leave a large number of seed
trees more or less uniformly distributed. The shelter of the
trees left protects the soil and the young seedlings and retards
the growth of weeds, grass, and brush. The seed is provided in
abundance and is well distributed. As the new growth is estab-
lished before the last of the old trees is removed, the soil is not
exposed as is the case in clearcutting.

91. Rotation. — By rotation is meant the predetermined time
period during which it is intended to cut over a working group;
the predetermined, approximate felling age of stands. Rotation
refers to the forest as a whole and is expressed not by a definite
year, but a period of ten to twenty years; felling age refers to a
stand and a definite year.

Rotations are determined by (1) technical, (2) economic, and
(3) financial considerations, silvicultural considerations exercis-
ing a limiting influence. They are designated accordingly.

92. Technical Rotations.— These attempt to produce the
maximum amount of material suitable for a certain purpose, such
as railroad ties, mine timbers, saw logs of given size and the like.

For example, railroad ties cannot be made from trees less than
ten inches in diameter at breast-high. If, therefore, an owner in
southern Connecticut desired to grow chestnut sprouts for this
purpose it would require 50 * years for the average tree to reach
10 inches d.b.h., on the best sites. At this age | there would be
435 standard ties produced per acre besides 35 cords of cord-
wood.

Another example may be taken from the Pacific Coast. To
produce suitable saw-timber from Douglas fir, the trees should be
at least 16 inches d.b.h. If, therefore, an owner in western
Washington desired to grow Douglas fir for this purpose it would
require { 70 years for the average tree to reach 16 inches d.b.h.
on the best sites. At this age§ there would be 56,500 feet,

* According to Table 17 of Bul. 96, Forest Service, U. S. Dept. of Agriculture,
“Second Growth Hardwoods in Connecticut.”

t Table 28, ibid.

t Table 1, For. Quart., Vol. XII, page 442.

§ Ibid.
ECONOMIC ROTATIONS I4I

board measure, produced per acre. For further examples, see
pages 238 to 242 in the Appendix.

This rotation is the one most commonly used in the United
States. It is easily applied, and, if conservatively chosen, will
give satisfactory results. In this, as in all rotations, the silvi-
cultural considerations exercise a limiting influence. For ex-
ample, where reproduction is by natural methods, such as the
shelterwood method, some of the trees will have to be left be-
yond the rotation age in order that the seed from them may
re-stock the area cut. This space of time required for the re-
newal of a stand constitutes the reproduction period and must be
added to the rotation age.

93. Economic Rotations. — These attempt to secure either the
maximum average volume production, or the maximum average
value production.

The higher the average yearly production of a piece of wood-
land, the greater, of course, will be its continuous producing
value if cut over repeatedly. For example, in the second-
growth hardwoods in Connecticut * the average annual growth
in cubic feet and cords culminates as follows:

Chestnut type: best sites and medium sites............ 35 years
Chestnut type: poorest sites... .......-. 6. eee e eee eens 40 years
Oak-chestnut type: best sites and medium sites......... 30 years
Oak-chestnut type: poorest sites........--.. ee eee ee eee 35 years
Oak type: best sites and medium sites..............+- 35 years
Oak type: poorest sites... ... cscs eeees D evacevaionecngbar MO 40 years

These lengths of rotation are so nearly similar that it is safe to
place the cordwood rotation for second-growth hardwood stands
at from 30 to 4o years. To illustrate how silviculture enters in
as a limiting factor, the rotation for stands containing much red,
black, or scarlet oak should be 30 or even 25 years in order to
secure successful sprout reproduction of these species.

Another example of the economic rotation may be taken from
Douglas fir on the Pacific Coast. According to published
tables ¢ the economic rotation for cubic volumes and board-foot

* Bul. 96, Forest Service, U. S. Dept. of Agri., Tables 30, 32, and 33.
} For. Quart., Vol. XII, page 447, table 6.
142 FOREST ORGANIZATION

volumes for best, medium, and poor sites, in western Washington
and Oregon is as follows:

 

 

 

Cubic volume. Board-foot volume.
Site quality.
Rotation, | Yield per | Rotation, | Yield per
years. | acre, cu. ft. years. acre, bd. ft.
BOSH autniles daa paw wacaimmne nantes 52 go50 110 100,000
MEGiitti ss itt a kan tong nbaln-nnaten 55 8110 110 74,000
POOLs4» duis eee ae Ree he eae 52 5650 IIS 58,000

 

 

 

A rotation of from 50 to 55 years could safely be chosen for
maximum production in cubic contents and of 110 to 115 years
for maximum production in board-foot contents.

Unlike the technical rotation, this rotation finds but little
application today, since it usually takes quantity of material as
the goal. It is satisfactory from the silvicultural standpoint,
hence it is sometimes spoken of as a “silvicultural rotation.”

94. Financial Rotations. — These introduce considerations of
cost and attempt to secure either the maximum forest rent or
maximum soil rent.

Forest rent is the net income from a forest organized for sus-
tained yield, without interest charges on the forest capital —
the forest, z.e., soil with a stand or growing stock, being conceived
as the forest capital, and the rent as the total interest earned
by it.

In other words, it is “‘a mere bookkeeper’s balance of income
and outgo, under annual management, without consideration of
time of income or outgo, forest and soil representing the capital
producing the rent as an annual receipt, like a house and lot
producing the annual rent.” *

The Norway spruce will serve as an example of financial
rotation based on forest rent. According to European tables
(Endres, after Schwappach) the gross income, expenses, and net
income per acre for different decades is as follows for medium
sites.t

* From letter by Dr. B. E. Fernow, to one of the authors, under date of Febru-

ary 23, 1914.
t Taken from “Forest Valuation,” Roth, Ann Arbor, Mich., 1916.
FINANCIAL ROTATIONS 143

 

 

 

Expenses per acre. Net income per acre.
¥, Gross income
ears. per acre. 3 Current
Initial
(planting). mee Rouen Total. Average.
$ $ $ $ $ $

30 87 12 27 39 48 1.60
4o 210 12 36 48 163 4.00
50 402 12 45 57 354 6.90
60 654 I2 54 66 588 9.80
7° 923 12 63 75 848 12.10
80 1212 12 72 84 1129 14.10
go 1474 12 81 93 1382 15.30
100 1710 12 go 102 1609 16.00
110 1919 12 99 Ili 1808 16.40
120 2087 12 108 120 1967 16.30

 

 

 

 

 

 

 

From this table it is evident that the highest net income occurs
at 110 years and this, accordingly, would be the financial rota-
tion chosen on the basis of forest rent.

Soil rent is that part of the income (or balance) from a managed
forest which remains as interest on the soil capital alone after all
expenses with compound interest have been deducted, the soil
alone being conceived as the capital.

In other words it ‘considers the soil alone as capital, the
forest stand representing the accumulated interest on that
capital. It is, therefore, based on intermittent returns and hence
requires a compound interest calculation; it is a financier’s
balance as compared with a bookkeeper’s balance.” *

A good example of financial rotation based on soil rent is
found in European tables. The following figures are taken from
Endres’ “Valuation” and Schwappach’s “Tables of Growth.”
Assuming an interest rate of 3 per cent compounded, the income
value per acre for different decades and different species is as
follows: ¢

* Letter from Dr. Fernow.
+ Taken from “Forest Valuation,” Roth, Ann Arbor, Michigan, 1916.
144 FOREST ORGANIZATION

 

 

 

 

Norway spruce. White fir. Scotch pine. Beech.
Years Best Medium Poor | Best | Poor | Best Poor | Best Poor
: sites. sites. sites. | sites. | sites. sites. | sites. | sites. | sites.
Dollars per acre.

30 5st 10 —14 ; —1I0 | —30 | 43 =3 4 —I19
40 100 47 13 67/— 5] 59 7 25 4
50 139 77 38 | 134 25 | 66 13 | 32 6
60 159 98 53 | 156 38 | 67 13| 35 7
70 166 105 59 | 156 44| 64 13 | 35 7
80 161 105 59 | 145 44] 59 10 | 34 4
go 151 99 56 | 130 41 53 8} 31 2
100 138 gt 51 114 36 | 48 5 27 2
IIo 126 83 46 99 30 | 43 4 | 24 —2
120 117 15 41 86 25 40 2 21 —aA

 

 

 

 

 

 

 

 

 

 

From this table it is evident that for Norway spruce, medium
sites, the financial rotation chosen on the basis of soil rent would
be 70 or 80 years; for white fir 70 years; for Scotch pine 60
years; and for beech 60 or 70 years.

The financial rotation will undoubtedly be used more and
more in the future especially as the necessary data become
available. ‘In any ordinary forest business the aim is to keep
the forest and land in best possible condition and at the same
time make the largest income. Assuming the silvicultural con-
ditions cared for, the best rotation is the one furnishing the best
income for the longest time. There are two distinct ways of
judging this income.

“(z) ... the largest net income per acre of established
forest.” (Forest Rent.)
“(2) . . . the largest per cent on the money invested in the

forest.”” (Soil Rent.)*

95. Choice of Rotation. — The kind of rotation to adopt de-
pends on matters of policy, to wit:

1. Conditions of ownership, wishes, and purpose of owner.
2. The market and logging conditions.
3. The site.
4. The character of the stand.
* “Forest Valuation,” Roth, page 85.
CHOICE OF ROTATION 145

1. The state can afford a higher rotation than can the private
owner; furthermore, it is the duty of the state to grow timber
not only for profit, but to supply future demand, especially in
sizes requiring long rotations.

2. The market conditions influence the rotation, inasmuch as
good markets and easy accessibility permit shorter rotations,
whereas forests further from market and more difficult of access
necessitate a longer rotation to make logging at all profitable.
The decreasing area of virgin forests and the rapidly increasing
population justify the consideration of future as well as present
market conditions. It is reasonable to expect that the price of
larger timber will increase proportionately more than that of
smaller sizes, and hence it may be good economy, in view of
future market prices, to adopt a longer rotation and plan to grow
larger sizes of timber than present market prices would warrant.

3. The more the site is adapted to a certain species, the longer
can the rotation be. Conversely the more rapid growth on good
sites will often tend to shorten the rotation.

4. The character of the stands influences the rotation in
respect to their quality and species. The better the quality of
the stand, the longer can the rotation be; the less thrifty stands
will often have to be cut before the regular rotation age. The
species in mixed stands can usually be worked on the same rota-
tion unless they mature at different ages or are markedly differ-
ent in value, e.g., a mixed forest of Engelmann spruce and white
fir (A. concolor) will often require a higher rotation for the spruce
than for the fir; because the fir deteriorates at an earlier age and
becomes almost valueless at a time when the spruce is just fully
matured.

In conclusion, as Roth says,* ‘“‘rotation should be chosen no
longer than is necessary to produce desired material, a good
income from the land, with full assurance that the fertility of
the land is not impaired.”

* 6

* “Forest Regulation,” Roth, Ann Arbor, Michigan, 1914, page 117.
CHAPTER XIII

REGULATION OF THE CUT

96. Definition. — By regulation of the cut, or, as it is some-
times called, regulation of felling budget, or regulation of yield,
cut, which in the normal forest 7 would be equivalent to ‘0 the annual
growth. “The regulation of cut is necessarily preceded by a
determination of the amount to be cut and by the location of the
areas to be cut over. The regulation of cut finds its expression
in the general and annual cutting plans. (See Article 106.)

97. Determination of Cut.— Of the many* methods for
determining the allowable annual cut —i.e., the cut which will
not be in excess of the sustained yield, only the simplest and most
useful ones need be given here. In general, these methods are
based either (1) on area, or (2) on volume, or (3) on area and
volume.

The most important single factor in deciding on a method of
determining the cut is the silvicultural method chosen, especially
as to whether it results in an even-aged forest or in an uneven-
aged (selection) forest. The clearcutting, the seed tree, the
shelterwood, and the coppice methods all result in an even-aged
forest. The selection method results in an uneven-aged forest.
Methods applicable to each form of forest will be given according
as the basis is area, or volume, or both.

98. Determination of Cut in Even-aged Forests. By Area —
(a) Description of Method. --- The forest is divided into a number
of cutting areas (annual or periodic) corresponding to the rota-
tion age. These annual or periodic cutting areas are marked on
the ground; annually or periodically, a cutting area is logged.
The size of the cutting areas is either exactly the same or else is

* Eighteen distinct methods are described in “Forest Working Plans,” Reck-

nagel, John Wiley & Sons, Inc., N. Y., 2nd Edition, 1917, pages 67-124.
146
DETERMINATION OF CUT IN EVEN-AGED FORESTS 147

equal to the reduced area corresponding to the varying site
qualities.

(b) Example.— A forest of white pine contains 1800 acres.
It is to be managed on a rotation of 60 years. The annual

cutting area = a = —— = 30 acres. If the cutting period is

20 years, then the periodic cutting area will be 30 x 20 = 600
acres.

By reduced area the results would be as follows: Each site
quality produces for a fully-stocked stand a varying volume at
the rotation age. For white pine it has been determined * that
the maximum yield (Site I) for a 60-year rotation is 60,200 board
feet per acre, the minimum (Site IIT) 33,600 board feet per
acre, the average (Site II) 46,900 board feet per acre.

As compared with Site I, Site IT yields 78 per cent and Site ITI,
56 per cent. These are the factors of reduction to the common
site quality (I).

If, in the above instance, the actual area of 1800 acres was
composed equally of each site quality, then the reduced area
would be:

Site I, original 600 acres, reduced 600 acres.
Site II, original 600 acres, reduced 468 acres.
Site ITI, original 600 acres, reduced 336 acres.
Total, original 1800 acres, reduced 1404 acres.

The annual or the periodic cutting area is, therefore, varied
according to the site quality or qualities in the area allotted.
For example, the annual cutting area = pcuted ates areé = 04 =

rotation 60
23.4 acres. Similarly, the periodic cutting area = 23.4 X 20 =
468 acres.

If the annual cut of 23.4 acres was all to be taken from Site III
stands, it would actually require: 23.4 X 1.79 = 41.9 acres; for,
from the above percentages, it requires: 1.28 acres of Site IT to
equal 1 acre of Site I, and 1.79 acres of Site IIT to equal 1 acre of
Site I.

* Table 6, Bul. 13, U. S. Dept. of Agric., “White Pine under Forest Manage-
ment.”
148 REGULATION OF THE CUT

(c) Value and Application. — This is the oldest and simplest
method of determining the cut. It is useful in coppice forests
and as an “‘area check” on results secured by other methods.

99. Determination of Cut in Selection Forests. By Area —
(a) Description of Method. — In the management of the selection
forest the cutting cycle —i.e., the planned interval between
fellings or cuts on the same forest area — is of more real import-
ance than the rotation. The cutting cycle, in turn, depends on
the time required for reproduction and on the growth so that it
may pay to log the same area again. The allowed annual cut-

ting area is nee , therefore, but th eee and the
r cc cutting cycle

volume to be cut is found by multiplying-by the amount to be

removed per acre.

(b) Example. — A tract of 1730 acres of hardwoods forest in
the Catskill Mountains is to be managed under the selection
method. Careful studies indicate a cutting cycle of 40 years;
of the 5090 board feet per acre present on the tract today, 3400
board feet per acre are to be removed in the selection cutting.
The allowed annual cut for the first cutting cycle therefore is:

4 X volume to be removed per acre.
ray X 3400 board feet = 147,050 board feet.

(c) Value and Application. — As in the even-aged forest, the
determination of the cut by area is chiefly to be used as a check
on determinations of the cut by other methods.

100, Determination of Cut in Both Even-aged and Selection
Forests. By Volume.— Two methods will be given: Von
Mantel’s and Heyer’s.

I. Von Mantel’s Method. (a) Description of Method. -— Von
Mantel bases his method on the conception of a normal forest
in which, as explained in the previous chapter (Article 79), the

‘ rx b ;
growing stock = = that is, the mean annual increment

multiplied by half of the rotation.
CUT IN BOTH EVEN-AGED AND SELECTION FORESTS 149

Since, as was shown in Fig. 22, the volume present in any
forest in any one year (NV in normal forest) equals one-half of
the total volume produced during the entire rotation (r x 7);
therefore the annual cut = volume present + by half the num-

ber of years in the rotation. In normal forest NV = — and z

(the annual cut) = “st , or, as Von Mantel writes it:

2

Annual cut =

slr

(b) Example. — A forest of 100 acres of white pine near
Ithaca, N. Y., is to be managed on a rotation of 80 years. The
area and volume of the age-classes are as follows (see Article 79
and Fig. 23):

I ( 1-20 years)....... 20 acres...... negligible volume
II (21-40 years) ....... go acres...... 258,000 board feet
III (41-60 years)....... 23 acres...... 408,250 board feet
IV (61-80 years)....... 27 acres...... 642,060 board feet
Ioo acres.... 1,308,310 board feet
V _ 1,308,310 1,308,310
The annual cut = — = ~SC2st0 _ 2:30°,370 _ 32,708 board feet
£ 80 40
2 2

An example of the application of this method in selection
forests can be given by using the data in Article 99. The
rotation is taken as 160 years.

Rae ie _ 5090 X 1730 acres _ 8,805,700
r 160 80

2 2
= 110,071 board feet

(c) Value and Application.— This has been termed the
method of ‘‘glorious simplicity,” because it requires no other
data than the volume of the growing stock and the rotation.
However, it is based on the premise of a normal forest and the
correctness of its results varies with the degree of approach to

 
150 REGULATION OF THE CUT

normal. Since most of our forests are far from normal the
results may be misleading. Its use is, therefore, restricted to
determining the cut provisionally before detailed data can be
obtained and as a check on the results obtained by other methods.
II. Hever’s Method. (a) Description of Method. — Heyer
writes his formula:

 
 
 

   

7 Annual cut = Fhe) ay

a e
in which V is the actual growing stock, 7 is the actual mean
annual increment, NV is the normal growing stock and « is the
period of years over which the surplus of V over NV (or the
deficit if NV >V) is to be distributed. A simpler way to write
the formula is: annual cut = 7 + nA The period x can
be determined only with regard to local exigencies (markets,
etc.); it must be developed out of a general plan of management
which is in consonance with the wishes of the owner.

(b) Example. — Taking the data given above for the example
of Von Mantel’s Method in even-aged forests, the mean annual
increment can be determined by taking the volumes given for
each age-class and dividing by the average age, thus:

Age-class I, M.a.1. = negligible vol.
Age-class II, m.a.1. = re = 8600 board feet.

_ 408,250

Age-class III, m.a.1. = 8165 board feet.

642,060

Age-class IV, ma. = = 9172 board feet.

M.A.I. Total = 25,937 board feet.
rt 80X 2
NV = ae eee aoe = 1,037,480 board feet.*
V = 1,308,310 board feet.
* Tf the normal M.A.I. for 80 years is used as read from the yield table given in

Fig. 23, NV ee ag ee board feet per acre, or for 100 acres =
1,320,000 board feet. However, the actual rather than the normal M.A.I. is com-
monly used.
CUT IN BOTH EVEN-AGED AND SELECTION FORESTS I51

Let x = 20 years (the first working period).
Annual cut = 7 + fat At = 25,037 + pose = 1,037,480

= 25,937 + 270s830 = 25,937 + 13,542 = 39,479 board feet.

An example of this method in selection forests can be given
by using the data given in Articles 99 and 100 for 1730 acres of
hardwoods forest in the Catskill Mountains. The increment
(current annual, which may be used in place of M.a.1. in the
selection forest) is as follows, for 1730 acres.*

Hemllckis 5.400 fected Vaiss 884 cae 8,055 board feet
BeGcht: 2220s basse 40an ivi tae abe Bae oie wee 15,996 board feet
BiChivcicaccaa ec saw ead qusivereaae nue 42,913 board feet
Maples sia taal: ec ge tee ne ruee aes 25,506 board feet
Miscellaneous. ..............6- hte tailor 21,484 board feet

Otel 2 Ss Sinks seal eee senes 113,954 board feet

r, the rotation = 160 years.
NV, the normal growing stock = = aes = 54
= 9,116,320 board feet.
V, the actual growing stock =8,805,700 board feet. (A deficit).
x, the period of distribution = 40 years (the first cutting cycle).

Then the annual cut = i — ara?
=I1 a 9,116, 20 — 8,80: 1400
= 113,954 jes
ae _ 310,620
= 113,954 i.

113,954 — 7766 = 106,188 board feet.

(c) Value and Application. —Heyer’s Method is directly
applicable to the majority of American forests, especially to
those where, as in virgin forests, the actual growing stock is far
in excess of the normal growing stock and a reduction to normal
is of prime importance. It is a very desirable method to use

* See “A Practical Application of Pressler’s Formula,” For. Quart., Vol. XIV,
No. 2, pages 260-267.
152 REGULATION OF THE CUT

and furnishes a good comparison with the allowable cut ‘as
determined by other means.

101. Determination of Cut in Selection Forests, by Volume. —

Two methods will be given: The Swiss and Hufnagl’s.
(a) Description of Method. — The Swiss
Method is described in an anonymous article on selection forest
management in the Swiss Forestry Periodical for 1913, briefed
in ‘‘Forestry Quarterly,” Vol. XIII, No. 2, pages 260-262, as
follows :*

“Divide the volume of the oldest size classes by the annual
increment of the entire stand. This will give the number of
years during which the volume of the oldest size classes must
last. If this be forty-five (45) years, then the cut for the next
decade would be from one-fifth to one-quarter of the volume of
the largest size classes.”

Expressed mathematically:

     
 

 

Let X = the volume of the size classes below the diameter
limit.
Xi = the current annual increment thereon.

Y = the volume of the size classes above the diameter
limit but within a satisfactory current annual
increment of, at least, 1 per cent.

Yz = the current annual increment thereon.

N
lI

the volume of the size classes beyond a satisfac-
tory current annual increment of, at least, 1
per cent — that is overmature timber — sur-
plus growing stock.

Zi = the current annual increment thereon.

CC = the cutting cycle.

vag
Th =
oe ee XitVi+Zi'
V+Z
And 1 cut aa.
nd annual cu CC

* See also “A Practical Application of Pressler’s Formula,” For. Quart., Vol.
XIV, No. 2, pages 260-267, especially pages 264-267.
DETERMINATION OF CUT IN SELECTION FORESTS me

This is the strict interpretation of the method as described,
but since Z is surplus growing stock it should play no part in
determining CC. Nor should the increment thereon (Z7).

Y
Then COs Xia Va
Y+Z *
1 Us = 2
And annual cut CC ;

(6) Example. — Using the data given in Article oo for the
1730 acres of hardwoods forest in the Catskills, it appears that
the current annual increment for the hemlock, for example, is
made up as follows:

 

 

 

 

 

 

 

 

 

 

C.A.L.
D.B.H., Vol i
inches. recane WP tBreck tabled C.A.I. per acre.
Per Cent Board Feet. Board Feet.
7 7.19 6.80 0.488
8 4.30 6.41 0.276
9 4.00 12.18 0.487 |,
10 2.69 17.98 x 0.484 Xi
Il 2.68 24.09 0.645
12 2.26 28 .83 0.652
Diameter limit.
13 2.08 26.68 0.555
14 1.75 21.45 0.376
15 1.55 15.48 0.240
16 1.69 18.36} Y 0.310 } Vz
17 1.48 22.23 0.329
18 1.24 20.51 ©.254
19 1.10 13.60 ©.150
Maturity limit.
20 0.97 7.78} er rs
21 0.89 17.56 Z 0.156 Zi
continued in stock table 5.478
(Table 5, Bul. 11, N. ‘Y's
Conservation Commis-
sion.)

 

 

 

 

The same thing should usually be done for each species, and,
of course, separately for each type.
154 REGULATION OF THE CUT

Using the data given above and a 12-inch d.b.h. limit, the cut
for hemlock figured by this method would be as follows:

Y = 138.31 board feet per acre.
Z = 168.48 board feet per acre.
Y + Z = 306.79 board feet per acre.
Xi = 3.032 board feet per acre.
Yi = 2.214 board feet per acre.
Zi = 0.232 board feet per acre.
Xi + Yi+ Zi = 5.478 board feet per acre.

eee Y+Z 306.79
= = = 56 d th
Substituting, CC Vie. cae 56 years and the

annual cut = t+ = a = 5.478 board feet, or, for the
1730 acres in the slope type = 9477 board feet of hemlock.
Eliminating Z and Zi in figuring CC:

Ys 138.31 — 138.31

oi Xi+ Vi 3.032 +2.214 5.246

 

= 26 years.

_V+Z _ 306.79 _
Annual cut = TC ee 11.797 board feet,

or, for the 1730 acres on the slope type = 20,409 board feet of
hemlock.

For the other species in the Catskills, the cut, to a diameter
limit of 16” b.h. figures out as follows including Z and Zi:

Beech......... 10.878 board feet per acre; 18,819 board feet for 1730 acres
Birch......... 29.183 board feet per acre; 50,487 board feet for 1730 acres
Maple........ 17.345 board feet per acre; 30,007 board feet for 1730 acres
Others........ 14.610 board feet per acre; 25,275 board feet for 1730 acres

These volumes must, however, be reduced 15 per cent for
local defect in the timber. The reduced values are:

Hlemlock:. i.e cccciieies «sao dead 8,055 board feet
BeOChi oii. cies eanarues es sacneaw 15,996 board feet
BleChisvaiy a coulndees alee sia gees 42,913 board feet
Maples c% cseama dh ere3 ckaen 25,506 board feet
Miscellaneous.............0.0 21,484 board feet

TOtalies ieee aiccseioaes 113,954 board feet
DETERMINATION OF CUT IN SELECTION FORESTS 155

(c) Value and Application. — This method is well adapted to
finding the allowed annual cut in a selection forest. It should
be used, however, in conjunction with some other methods, such
as that next to be described (Hufnagl’s) or Von Mantel’s or
Heyer’s, and with an area check.

Il. Hufnagl’s Method. (a) Description of Method. — The pre-
requisites of this method are (1) a stand table, that is, a tabu-
lar enumeration showing separately for each diameter-class and
species, the number of trees on a given unit of area, usually an
average acre. (2) A volume table, that is, a tabular statement
showing, for a given species, the average contents of trees of
different sizes. (3) A diameter growth table, that is, a tabular
statement showing the age of the average tree at various diam-
eters. Such tables commonly result from a complete forest
survey. The data for stand tables must be gathered locally but
published.data may be adapted for volume and growth tables.

Next it must be determined at what diameter and upward the
trees are most merchantable. It follows that all trees of this
diameter and larger are merchantable and should, other things
being equal, be cut in the near future, z.e., during the time
required for the next lowest diameter-class or classes to produce
an equal number of merchantable stems.

To express this numerically, let N equal the number of trees
in any diameter-class as found in stand table (usually put in
groups of 3 inches, to make calculations simple), let V equal the
volume of the average tree of any diameter-class (found in vol-
ume table), and let A equal the age of the average tree of any
diameter-class (found in growth table).

Let Ni, V; and A; represent the values for the diameter-class
just below the chosen diameter limit of cutting. Let N2, V2, and
A, represent the values of the next higher class and so on up to__
the maximum diameter limit, that is, the maximum diameter of
trees which it is practicable to produce.* This usually leaves a
surplus of still larger trees produced under virgin conditions.
This surplus may well be distributed over the cutting cycle (¢.e.,
the time required for the maturity limit class to be replaced by

* F. H. Millen has aptly named this the “Maturity Limit.”
156 REGULATION OF THE CUT

the one next below it) or disposed of more rapidly or more slowly
as seems best in view of local conditions.
Expressed as a formula:

Nz N3 —N, — Ny,
= ———V. V:
the allowed annual cut ae aa 4+ —+__= aa, 2 +po re i
N,—N2
+————- A= A; Vi.

(b) Example. — The stand table for the hardwood forest in
the Catskills * shows considerable hemlock present. Hemlock
becomes merchantable at about 12” d.b.h. and, considering
3-inch classes, the minimum diameter may be taken to include
trees 11’’-13”” d.b.h., the maximum diameter which it is practic-
able to produce is taken as 18” d.b.h. class (17’-19”), since
trees 20” and over have too slow a growth. (The c.a.i. = 1.10
per cent at 19”; 0.97 per cent at 20” d.b.h.)

The 3-inch classes, the number of trees in each, the volume of
the average tree, and the years required to grow from one class
to the next are as follows:

 

 

Number of trees per Years required to grow
D.B.H. cl Vol tree, board feet.
inches. | (Tables, Bul. 3.) | ¢qhvere®ger,, » | {tom one class to the
9 42 (Vi) 0.91 (M1) 27 (Ax — Ai)
12 93 (V2) 0.87 (Na) 32 (As — Aa)
15 172 (Va) 0.33 (Ns) 35 (Aa — As)
18 293 (Va) ©:20 (Na) | sh erea ey atau

 

 

 

 

+ Based on increment borings, see ‘‘A Practical Application of Pressler's Formula,” For
Quart., Vol. XIV, No. 2, table 1, page 261.

Applying the formula, the annual cut =

Zs A; V4= aS X 293 = 1.674 board feet per acre +
ae =4" Va= "S. X 172 = 0.637 board feet per acre +

i
:
=
u

fe

X 93 = 1.569 board feet per acre +
As—A> a
M—My _ 0.04 = gas
Ad Y= 2 X 42 = 0.062 board feet per acre.

Total 3.942 board feet per acre.

* See Table 4, Bul. 11, “Forest Survey of a Parcel of State Land,” Conservation
Commission, Albany, N. Y., rors.
DETERMINATION OF CUT IN EVEN-AGED FORESTS 157

The tables show that trees 20” and over have a volume of
168.48 board feet per average acre. This is surplus stock and
may be disposed of in the next cutting cycle. Taking the cutting
cycle as = A, — A; = 35 years and cutting 1/35 of this surplus
each year = 4.814 board feet per acre, to be added to the 3.942
board feet already determined, making a total of 8.756 board
feet per acre, or, for 1730 acres, 15,148 board feet of hemlock.

The cut for the other species, figured in the same way but with
a 16” diameter limit, is as follows:

 

 

Board Feet. Reduced for Defect
Board Feet.
Beeehi. vias vhietaats = 29,756 25,203
Biri cscs wiaeiern noone = 62,242 52,906
Maple...............04. = 77,591 65,952
Miscellaneous*......... = 8,926 71587
Hemlock............... = 15,148 12,876
Totals: snag creatine sca agyss 164,614

 

 

 

 

* Using an average cutting cycle of 35 years for removing all over 16” d.b.h

(c) Value and Application. — This method is perhaps the
most practical yet devised for use in irregular selection forests.

102. Determination of Cut in Even-aged Forests. By Area
and Volume. — (a) Description of Method. — For even-aged for-
ests Hufnagl has shown that the allowed cut can be determined
directly if the, volume and the increment of the stands which
now are more than half the rotation age are known. This method
requires a tabulation of the volumes and areas of all stands over

7 years old. To this volume is to be added the increment of the=

years old stands in the next : years; for, since the area of these

stands diminishes each year, the increment can only apply, on
an average, to half the area.

V+(axix ‘)
4).

r

2
(6) Example. — Using the data in Article 100, the rotation,

 

Expressed as a formula, the annual cut =

r = 8o years, = = 40 years, ; = 20 years. The area of the
158 REGULATION OF THE CUT

r ‘
stands — years and over = 50 acres, their volume = 1,050,310
2

board feet. From the example of Heyer’s method, the mean
annual increment of the stands of the III age-class (a x 7) is
8165 board feet; of the IV age-class it is 9172 board feet; a total
increment of 17,337 board feet. Then, by formula,

 

‘ rT
ye (ox ex 4
the cut = 4/ _ 1,050,310 + (17,337 X 20)
r 40
2
ae = 40.140 34,926 board feet.

(c) Value and Application,— This is a very simple and
accurate method of gauging the allowed cut in even-aged forests
of only moderate tegularity, the very conditions so frequently
encountered in America. Hufnagl suggests that current annual
increment can be used in place of mean annual increment in the
calculations, but the latter is the more conservative and hence
its use is to be preferred. Where yield tables are lacking, the
mean annual increment can be approximated by measuring
average stocked sample stands whose age is close to 7 years.
This method combines area and volume, and, if supplemented
by a careful cutting plan, will serve every purpose of regulation.

103. Summary of Results by Different Methods. — Using the
samepremises for computations, the allowed annual cutisas follows:

 

 

 

Article. Method. Premise. Premise.
White pine forest even-aged. | Hardwood forest uneven-aged.
Number. Area = Iooacres. Rotation = | Area = 1730 acres. Rotation
80 years. = 160 years.
98 Area 1.25 acres (not ex- | 43.25 acres =147,050
99 pressed in board feet.) board feet.
too | Von Mantel 32,708 board feet 110,071 board feet
too | Heyer 39,479 board feet 106,188 board feet
IOI SWISS | wakeup hadae eee ea vege 113,954 board feet
tor | Hufnagl =s_ | sa... ce eee eee eee it 164,614 board feet
toz2 | Area and vol-| 34,926 boardfeet «$s |... cee eee eee eee
ume (Huf-
nagl)

Average 35,704 board feet 128,375 board feet

 

 

 

 
CUTTING SERIES 159

104. Selection of Stands to be Cut.— A hundred years ago,
Cotta, one of the greatest of all foresters, said: ‘A proper
division of area, orderly sequence in cutting, and frequent
revision of the working plan, are far more important than a mere
calculation of the permissible amount of timber to cut.” This
is as true today as it was a century ago. Division of area has
been dealt with in Article 81. Revision of the working plan will
be, in Article 110. There remains the sequence of cutting, that
is, the selection of stands to be cut, which, in its highest form,
leads to the establishment of cutting series.

The conditions which govern the selection of stands to be
cut are: market, maturity, damage (insects, fungi, etc.), wind-
fall, fire, and the like.

Under market are contained all the manifold considerations of
logging accessibility, of profit in cutting and marketing, and the
sizes and species which can be logged. For example, a spruce
stand on top of an isolated mountain like Mt. Graham in Arizona
may be fully mature and in need of cutting, but unless there are
adequate logging devices which can market the timber at a rea-
sonable profit, it is useless to designate this as the sole cutting
area of the next working period, that is, the period of years during
which the working plan is intended to apply.

105. Cutting Series. — A cutting series, or felling series, is an
aggregation of stands into a proposed or actual sequence of
felling areas — that is, areas on which the trees have been cut or
are to be cut. The object of such a series is a distribution of
felling areas for administrative reasons or to secure a final
satisfactory distribution or location of age-classes, especially to
avoid damage by windfall and insects due to uniformity of stand
and size of felling area. It is intended to interrupt a regular
sequence of age-classes. It is quite generally used abroad in
spruce to prevent windfall and in pine to prevent insect damage.
It is not used in broadleaf forests or in any selection forest.

An example of cutting series is shown in the frontispiece.
Cutting series must be planned decades in advance, and require
careful thought and accurate judgment. The cutting of such a
series requires many years and early mistakes are difficult to
160 REGULATION OF THE CUT

correct. Although cutting series find but little application in
American practice today, the underlying principle can be
utilized now.

106. Plan of Cutting. — Having determined “how much”
and “where” to cut during the ensuing working period, this is
reduced to documentary form in the plan of cutting.

Two kinds of cutting plans are generally prepared: a general
cutting plan for the entire working period — i.e., for the period
of years during which the working plan is intended to apply,
usually 10 years; and an annual cutting plan for the ensuing year.

The general cutting plan provides cutting areas sufficient to
yield (if the working period be ten years) at least ten times the
volume of the allowed annual cut, or ten times the area, as the
case may be. It should, however, provide for somewhat more,
so as to furnish additional cutting areas in case it proves to be
impracticable to cut certain areas or in case a higher cut is
possible than was originally intended.

For the annual cutting plan, the administrator, through his
intimate knowledge of the forest and of local conditions of
logging, market, etc., selects from out the general cutting plan
those areas which, in his judgment, should be cut during the
ensuing year.

As an example of the plan of cutting, the selection forest of
hardwoods in the Catskills will serve. According to Article 103,
the allowed annual cut, on the 1730 acres of slope type, figured
by five different methods, averages 128,375 board feet. Assum-
ing a working period of ten years, this would allow a cut of
1,283,750 board feet in the next decade. In order to be con-
servative, the cut for the decade would be set at 1250 M. feet.,
b.m., which should not be exceeded by more than 10 per cent.
This fixes the “how much;” the “where” is determined by a
careful examination of the individual blocks and shows that
cutting should begin in Cascade Block.* The block description
for Cascade shows a total stand of 3,212,288 board feet, of which
67 per cent is over the assumed limit of 16” d.b.h.ft and hence to

* See map facing page 166.
t Table 5, Bul. 11, Conservation Commission, Albany, N. Y.
PLAN OF PLANTING 161

be cut. This would make available 2,152,233 board feet, more
than enough for the cut during the first decade. It is neither
necessary nor advisable to consider any -additional increment
which may accrue during the working period; such corrections
may best be left to frequent revisions of the working plan at
regular intervals. In this case, at the end of the decade a
thorough revision of the working plan and new growth data will
doubtless warrant a largely increased annual cut.

107. Plan of Planting. Some planting operations are neces-
sary in every well-regulated forest, whether it be to eke out a too
scanty natural reproduction. or to re-stock former forest areas
where natural reproduction is out of the question.

Just as a general cutting plan is drawn up for the intended
cuttings in the ensuing working period, so a general planting
plan is drawn up to cover all the operations of artificial reproduc-
tion which are contemplated during the ensuing working period.
From out this general planting plan the man in charge of the
forest selects those areas whose re-stocking he deems of the most
immediate importance and incorporates them into an annual
planting plan which becomes the planting schedule for the
ensuing year.

As a preamble to the general planting plan there should be a
general discussion of the areas needing artificial reproduction,
the extent to which it is expedient to go in re-planting com-
mensurate with the results to be-obtained, and other phases of
the policy to be pursued in the choice of areas. This should be
followed by a full discussion of the species and the methods of
seeding or planting to be employed. First the results of past
plantings and sowings, accentuating the reasons for failure or
success, and then the policy for future planting and sowing.
The source of plant material — seeds, seedlings, and transplants
should be considered; the seed should be shown to be from
reliable and appropriate sources (sources suitable to the climatic
and site conditions), and the planting stock preferably grown in
nurseries on the forest or else secured from outside nurseries
whose site corresponds approximately to that of the intended
planting area. If there are to be nurseries on the forest, the
162 REGULATION OF THE CUT

preamble of the general planting plan gives full provisions for
their location, creation; and maintenance, and should contain
the area thereof in seed-beds and their capacity, the area thereof
in transplant beds and their capacity, and the proposed annual
production by species and classes of stock.*

The area which it is intended to plant or sow during the
coming working period should be indicated on the working map
of the forest either by color or shading or symbols.

* For details of practice see “Seeding and Planting in the Practice of Forestry,”
J. W. Toumey, John Wiley &-Sons, Inc., 1916. For a Planting Plan Outline, see
the Appendix, page 244.
CHAPTER XIV

THE WORKING-PLAN DOCUMENT

108. Contents and Form. — The working-plan document is the
vehicle for recording the salient features of a forest bearing on
its organization and the detailed prescriptions of that organiza-
tion for the next working period. Simplicity and brevity are
the key-notes. The descriptive portion is usually confined to
such short statements as suffice to bring to the trained forester’s
eye the picture of the forest as it is in its essentials, but, occasion-
ally, a more detailed description is warranted so as to make the
plan comprehensible to a layman, e.g., where the plan is to be
executed by a layman-owner.

In the interests of clearness and brevity data should be tabu-
lated wherever possible, e.g., estimates, stand tables, age-class
tables, etc. Maps, also, are a powerful aid in graphic pre-
sentation of the data.

The working-plan document may be confined to the silvi-
cultural management, or it may cover all the activities of a
forest such as general administration, grazing management,
permanent improvements, forest protection, and use of forest
land; in other words, be a complete forest plan. The desir-
ability of including these sundry subjects depends on their
importance and the purpose of the plan. National forests
usually require complete plans. Where other subjects than that
of silvicultural management are to be included, the descriptive
data preceding the plan proper must be amplified accordingly.

These essentials may be presented in various forms, varying
with the needs and desires of the administrative officers. The
form of the working-plan document is comparatively unimpor-
tant. It may be typewritten or not, bound or unbound. If
typewritten it can be manifolded more easily; if plainly bound it

resists handling better, and the working-plan document is meant
163
164 THE WORKING-PLAN DOCUMENT

to be used constantly, not put away on a library shelf for the
admiration of visitors. To facilitate this use a 2-inch margin
should be left at the side of the text throughout the document,
excepting tables, for the purpose of allowing notes to be made
from time to time by persons charged with the execution of the
plan. This simple device keeps a plan alive and up to date and
greatly facilitates the work of revision.

The field-work in connection with forest organization often
results in the collection of many interesting and valuable silvi-
cal and other data which, while germane to the working plan,
are not a cognate part thereof. Such data, including volume,
growth, and yield tables, silvical notes, notes on climate, geology,
soil, etc., should be placed in the appendix or elsewhere conven-
ient, in order that everything in the plan may be confined to
the actual scheme of management for the forest.

109. Outline for Working Plan. —

1. Introduction.
a. Location and size of forest (working unit).
b. History of forest with important changes.
(r) Past and present ownership (status).
(2) Boundaries. Interior surveys.
(3) Past object of management and general adminis-
tration.
(4) Past revenues and expenditures.
c. Physiographic features.
(1) Topography.
(2) Drainage.
(3) Geology (formation).
(4) Soils (depth, fertility, etc.).
(5) Climate (maximum, minimum, and average tem-
perature, rainfall, prevailing wind direction).
d. Social and industrial features.
(z) Population. Dependence on forest for work and
fuel and timber supply.
(2) Labor supply.
(3) Local conditions — lumbering, grazing, mining,
agriculture, etc. Interrelation with forest.
OUTLINE FOR WORKING PLAN 165

Notes to amplify and explain outline:
I. Intropucrion

(a) Location and Size. — The briefest mention suffices.

(b) History of Forest with Important Changes. — Past and present owner-
ship and administration, boundaries, past object of management, past revenues
and expenditures.

(c) Physiographic Features. —The physiographic features include topography,
drainage, geology, soils, and climate. Detailed observations and statistics should
be reserved for the appendix, and only the salient characteristics which influence
the forest organization stated briefly.

(d) Social and Industrial Features. — The social and industrial features
include population, labor supply, local industries such as lumbering, grazing,
mining, agriculture, etc., all in their bearing on the problems of forest organization.
For it is evident that without adequate labor no forest resources can be developed,
without lumbering facilities no regulation of the cut can be maintained or executed,
and the very term “‘accessible” is modified by the degree of skill exercised in logging
and the kinds of appliances used to get the timber. Again, the need of the local
population for timber is the root of the theory of sustained yield. These funda-
mental phases require no detailed discussion, but brief statements of conditions in
explanation of the plan proper.

e. Digest of working-plan conference.

jf. Time, method, and personnel of field-work. Cost, if
desired.

2. Foundation.

a. Growing stock (estimates). Tabulation. (Stand and
stock tables if uneven-aged.)

b. Increment per acre or per cent or both.

c. Distribution of the age-classes. Tabulation. (Diam-
eter-classes if uneven-aged.)

d. General stand table. Tabulation.

(e) Digest of Working Plan Conference. — If a conference was had between
the forest organizer and the owner or administrator of the forest, as suggested in
Article 84, this should be digested and added to the working-plan document with
the names of the participants.

(f) Time, Method, and Personnel of Forest Survey and Organization. —
These statements should be exceedingly brief —a tabular form is advisable for
time and personnel, since they are of purely historical interest. The method used
should, however, be set forth in sufficient detail so that there can be no question
as to how much weight attaches to the accuracy of maps and estimates.

2. FOUNDATION

(a) Growing Stock (Estimates). — The estimates should be in form of a table
by species and classes of timber, either separate stand and stock tables or as part
of the general stand table. The details of this estimate table depend on the in-
166 THE WORKING-PLAN DOCUMENT

tensity of the entire plan. It will usually suffice to give the totals by compart-
ments (if any) and blocks, or else by survey units such as sections, or even town-
ships. Separate estimates may be given for each forest type. The estimate for
the entire working unit must always be given. It must also be stated to what
minimum diameter trees were estimated and, if available, what average deduction
must be made for defect. LEstimates in greater detail, ¢.g., section sheets showing
the stand on each “forty,” should be reserved for the appendix or for the files.
Volume tables should be placed in the appendix.

(b) Increment. — The increment, either current or mean annual, or else both,
is given, and is expressed either in increment per acre or as a per cent or both.
Growth and yield tables on which the calculation of increment may be based should
be included in the appendix.

(c) Distribution of the Age-Classes. — If the stand is even-aged or approxi-
mately so, a table of age-class distribution, like Fig. 25, should be included. Not
only does such a table show at a glance the relation of young, mature, and over-
mature timber, but, in the revisions of the working plan, it shows by means of
graphs or blocks what progress has been made toward the attainment of normality
in this direction.

(d) General Stand Table. — This should be included as a convenient tabular
summary of areas, volumes, and conditions of timber.

e. Maps. Statement of maps prepared. The maps
themselves should go in the back of the plan or else
be kept on file separately.

(e) Maps can be elaborated to almost any extent according to the kind and
importance of the data to be shown thereon. The following are the most im-
portant:

(1) A topographic map showing topography in contours, seldom hachures; roads,
trails, railroads, saw-mills, and all other “culture;” drainage. This map is the
“base” and should be of a convenient scale, such as 3, 1, 2; 4, of even more inches
to the mile, depending on the size of the tract and the amount of detail to be shown.
It should be drawn so as to permit of being manifolded in order that all officers
charged with the administration of the forest and the execution of the working
plan may be furnished with copies. On this “base” can be added any or all of the
following special data in so far as the wealth of detail will not confuse the whole.

(2) Boundary map showing the ownership (status), the forest boundary or
boundaries; survey lines, if any; boundary or boundaries of the working units,
blocks, compartments, and sub-compartments.

(3) Forest-type map, showing the various forest types, also cut-over areas,
burns, open “parks,” etc.

(4) Age-class map, showing the distribution of the various age-classes on the
ground.

(5) Site-quality map, showing the distribution of the various site qualities.

(6) Soil map, showing the various soils and geologic formations of the forest.

(7) Reproduction map, showing areas of good, fair, and poor reproduction.

(8) Cutting map, to accompany the general cutting plan, showing areas to be
cut over within the next working period, also those already cut over.
“SHPO OFUr yfun ued Supyiom jo uoystaip pue ‘sadé ‘satepunog ‘AydesZodo} Suimoys — doy quamasounyy ysosog

 

 

¥ L01'H09 °2°S 9

 

LS3N SQUIG ONIONYH A

gavosvo AI woous Aud IT
qHSNe IT] >NISHBAAN T
sn9018

aN 490718 ~7*" «ANI 3dAL—————

adAL 3001N Ss nune &
Baal ad01s (77) wano 109 FA

anaoa

 

     

ST*FI6T

ALISYSAINN 3ANYOD “AWePHS *
Ayses04 jo yuauysedag fq pasederg

*S$‘D'S'N wos poydepe sydesBodos
ont 0006 0 000 0003

4334 40 J1vO9

AYOA MAN-ALNNOD YaLSTIN

N3SXVONVHS JO NMOL
LoVe NOLSONIAIT

€ NOISIAIC + GNV ‘€'Z ‘LS1LO7 GNV Z NOISIAIG € LOT
AAUNSSAUd LSAYOI TIASLVYS

HLUON anu

suit \
4dO NOILYOd BaI3A110

 

‘TI ALlvIg

 
OUTLINE FOR WORKING PLAN 167

(9) Planting map, to accompany the general planting plan, showing areas to be
re-stocked artificially during the next working period, and areas already planted or
sown, all nurseries and proposed nursery sites.

(10) Fire map, to accompany the fire plan showing all lookout points, watch
towers, lines of patrol, ranger headquarters, fire-guard stations, location of fire-
fighting tools, and places whence assistance in fighting fire may be obtained. The
base should be maps 1 and 3 combined.

(11) Permanent improvement map, to accompany the permanent improvement
plan showing all improvements, existing or proposed, such as ranger stations, fire
cabins, telephone lines, etc.

(12) Grazing map, to accompany the grazing plan showing the grazing types,
condition of the range, the portions grazed (and by what class of stock) or un-
grazed, the winter, summer, or year-long range, corrals, pastures, drift fences, water
tanks, etc.

Lest too many data be placed on one map, it is better to have separate maps
than to combine too much and cause confusion.

Detailed maps of survey units or of small areas which it is desired to show in
greater detail should be placed in the appendix, as should also special maps showing
areas of insect or fungus attacks, etc.

f. Forest description. (For outline see Appendix, page
243.)

g. Division of area. Working unit, block, compartment,
sub-compartment. Working group if necessary.

3. Recommendation.

a. Object of management. Wishes and purpose of the
owner (policy, if national or state forest). Exploita-
tion or sustained yield (annual, periodic). Produc-
tion of cordwood, saw-timber, pulp-wood, turpen-
tine, etc.

b. Practical restrictions. Market, logging accessibility,
special danger from fire, erosion, avalanches, etc.

(f) Forest Description. — Must be concise and free from burdensome details.
Silvical details, methods and costs of logging and milling, etc., had better be placed
in the appendix or in a special file. The forest description of the entire working
unit should be a careful summary of the description for each block. The aim is to
present a lucid picture of the forest as it is in the essential silvical factors bearing
on the plan of management adopted. The description must be ample reason for
the provisions of the working plan. The description is the premise; the recom-
mended management the logical deduction from that premise.

(g) Division of Area. — On the basis of the forest description, the division
of area should be so evidently logical as to require very little special justification.
However, it is well to explain briefly what considerations governed in the choice of
working unit, block, compartment, and sub-compartment, in so far as this was not
168 THE WORKING-PLAN DOCUMENT

already covered in the digest of the working-plan conference. Since the working
unit usually has a sustained yield, its adequacy from this viewpoint should be
considered along the broad lines already laid down.

3. RECOMMENDATION

The recommended management should be the logical sequel of the data given
under “Introduction” and “Foundation.” The basic considerations of object of
management, of silvicultural method of management, and of rotation are con-
tained in Chapter XII. This part of the working-plan document should review
the governing conditions which determine the recommended management. These
are:

(a) Object of Management. —i.e., the wishes and purpose of the owner (in so
far as not already contained in the digest of the working-plan conference).

(b) Practical Restrictions of market, logging accessibility, fire danger, erosion
danger, etc.

c. Silvicultural method of management.
(1) Silvicultural method or methods, their proposed
application.
(2) Rotation (period of reproduction, cutting cycle,
etc.).
(3) Marking rules.
(4) Rules for brush disposal.

(c) Silvicultural Method of Management which can best fulfill the object of
management with the given silvical conditions and under the practical restrictions
imposed. Past management and its mistakes and lessons should be reviewed and
the proposed method of management given in detail. The best silviculture is not
always possible under existing conditions, and the organizer must seek to combine
the three divergent factors of object of management, practical restrictions, and
silvical requirements into a harmonious scheme of management. This should
cover: :

(1) Silvicultural method for each type with brief description thereof.

(2) Rotation chosen, with reasons for its adoption. The period of reproduction,
cutting cycles, etc., should be given and made entirely clear.

(3) Marking rul.s to be followed in the execution of the cuttings for natural
reproduction. They should be clear and concise, simply put so as to be readily
intelligible to the non-technical man charged with their execution, sufficiently
elastic to cover all cases. Good marking rules will do much toward insuring the
actual execution of the silvicultural method decided upon, especially when backed
by sample areas marked by the forest organizer as a concrete illustration.

(4) Brush disposal rules are a necessary concomitant of the marking rules.
Here too actual examples of what is desired should reinforce the written rules.

4. Regulation.
a. Determination of cut.
b. Distribution of out. Formation of cutting series, etc.
OUTLINE FOR WORKING PLAN 169

c. General cutting plan for working period.
d. General planting plan for working period.
5. Administrative plan.
a. Scheme of field administration.
(1) Administrative districts and area.
(2) Field and office force, year-long and temporary.
b. Forecast of receipts and expenditures and net income
for working period.

4. REGULATION

As the recommended management (3) is the logical outgrowth of the data given
under Introduction (1) and Foundation (2), so the regulation of the cut itself is but
the carrying out of the Recommendation (3).

The chief phases of regulation are:

(a) Determination of the allowable cut by one or more of the methods already
described. Where working groups are formed, each requires a separate determina-
tion of the cut.

(b) Distribution of the Allowable Cut. — Selection of stands to be cut, for-
mation of cutting series, etc., with concise reason for the choice; cutting policy in
so far as not covered already in the digest of the working-plan conference.

(c) General Cutting Plan for the next working period. It should contain
recommendations in regard to stumpage rates, methods of logging, rules of cutting
to prevent waste, and other features of practical utilization such as probable pur-
chasers, uses and markets, etc. An annual cutting plan for the ensuing year is
usually drawn up by the administrative officer in charge of the forest, and does
not, as a rule, form a part of the working-plan document.

(d) General Planting Plan for the next working period according to the outline
given in the Appendix (page 244). A description of the methods and cost of nur-
sery, planting, and seeding practice to be employed. An annual planting plan for
the ensuing year is usually drawn up by the administrative officer in charge of the
forest, and does not, as a rule, form a part of the working-plan document.

5. ADMINISTRATION

(These and subsequent notations are taken from the U. S. Forest Service outline
for Working Plans.)
Administrative districts. Number, area, and relative importance or amount
of work. (Tabulate.)
Force. Office and field and assignment. Salaries.
Also a brief forecast of future requirements. (Tabulate.)
Permanent, statutory.
Semi-permanent and temporary.
General administrative policy of forest. (General relation of important lines
of work. Include also points not already covered; fully and briefly in 1, 2,
and 3 order.)
170 THE WORKING-PLAN DOCUMENT

Receipts and expenditures and results. By lines of work for fiscal years, past
and estimated future.
Administrative provisions for increasing receipts or reducing expenditures.
Map, boundaries of administrative, or other districts.

6. Grazing plan.

a. Description of forage types and condition of range.

6. Protection and development of range.
(rt) Range improvements. Watering facilities.
(2) Treatment of overgrazed and partly stocked areas.
(3) Measures for fuller use of range.
(4) Control and eradication of poisonous plants.
(5) Control and extermination of predatory animals,

prairie dogs, and other pests.
c. Grazing control. Capacity of range. Grazing dis-
tricts and allotments.

6. GRAZING
Range Management:

Types. (Concise descriptions of each.)

Names of important and characteristic forage plants.

Accurate data on seasons of growth.

Accurate data on forage value.

Acreage. Withforage. Waste. (Tabulated.)

Carrying capacity. Present. Possible. Brief descriptions. By allotments or
divisions. (Tabulated.)

Demand and other local conditions in the live-stock industry which affect grazing
on the forest. Relation to silviculture.

Allotments.

Arrangement. (Division of the range between cattle and sheep, grazing
districts, and individual allotments to be shown on map. Guiding
principles, or necessary comment in the discussion.) To secure:

Best division between cattle and sheep.

Full and equal utilization.

Best division of types and early and late ranges.
Best division of watering places.

Proper silvicultural and watershed protection.

Number and kind of stock grazed. By allotments or divisions. Number of
permits by classes.

Seasons. (To secure full utilization of the forage without seriously inter-
fering with the natural requirements of plant growth, each portion of
the range should occasionally, every few years, be grazed only during
the last half of the natural growing period in order to keep the plant
constitutions strong and allow some actual reseeding. So far as is con-
sistent with this principle, the green tender feed should be available for
the stock during as much of the season as is practicable. This is essential,
OUTLINE FOR WORKING PLAN I7I

especially for sheep. This plan may be considered a variation of seasons
or a division of allotment.)

Fees. By classes of stock and season. (Tabulated.)

Methods of handling stock.

Cattle. (Salting and necessary riding by permittees to secure equal utiliza-
tion of range and prevent congregation along streams and water holes,
with resulting destruction of plant growth and poor development of
stock.)

Sheep.

Size of bands.

Herding. (Develop open quiet herding and avoid driving back to camp.)

Salting. (Encourage abundant use of salt, it means easier herding,
less danger from poison and disease, and less damage to the range.)

Other stock. (When special provisions are required.)

Range improvements:

(Permanent improvements in the improvement section.)

Re-seeding either with cultivated plants or by restricting grazing for natural
te-seeding, posting poisonous areas, changes or improvement in stock
driveways, extermination of predatory animals, prevention of erosion
by proper handling of stock.

Policy and administration.

General principles of policy not already covered. Protective and maxi-
mum limits, new owners, advisory boards, etc.
Administration. Extermination of predatory animals, counting stock,
or other special phases of the work. Special force required. Costs.
Investigations: im
Proper seasons, carrying capacity, poisonous plants, artificial re-seeding,
demonstration tests of proper utilization, effect of grazing upon
reproduction, and most efficient systems of grazing management to
climinate damage. Herbarium with necessary notes.
Map or maps, showing types, water, fences, corrals, topography, grazing dis-
tricts, allotments, reserved areas, driveways, or other factors or features
which influence or illustrate the handling of the stock.

7. Permanent-improvement plan.
a. General.
b. Telephone.
c. Look-out towers.
d. Fire cabins and tool-boxes.
e. Roads and trails.
jf. Ranger stations.
8. Forest-protection plan.
a. Fire control.
(x) Nature of fire problem.
(2) Past fires. Bearing on the plan.
(3) Hazards. Danger zones, extra fire risks, necessity
of special measures.
172 THE WORKING-PLAN DOCUMENT

(4) Codperation. Desirable and proposed cooperation.
(5) Scheme of protection.
(a) Primary control by look-outs.
(b) Secondary control by patrol and actual combat.
(6) Organization. Look-outs and patrolmen. Action
in case of fire.
(7) Mobilization.
(a) Fire-fighters, regular and volunteer, available.
(6) Transportation. Logging railroads, pack-
trains, teams, etc.
(c) Tools, equipment, and supplies. Location of
tool-boxes. Bases of supplies.
(8) Improvements. Additional headquarters, tele-
phone lines, trails, etc., required.

7. PERMANENT IMPROVEMENTS

Improvements. Comprehensive plan of the improvements needed. Location,
brief description, estimated costs, indicate those which should be undertaken
within the next five years. (Tabulated form.)

Roads, trails, telephone lines; fire lines, administrative fences, stock fences,
including the fencing of poisonous areas and bog holes, bridges, corrals,
dwellings, other buildings, water development, stream improvement,
dams to prevent erosion, other projects.

Maintenance, as above.

Policy and administration.

Improvement policy of the forest. (Concisely by lines of work such as silvi-
culture, grazing, protection, general administration, etc.)

Administrative provisions. Special force needed. Costs, exclusive of the
costs of individual projects.

Map showing all improvements constructed and planned, with a sufficient amount
of other data to make intelligible.

8. PROTECTION

Fire: (By divisions or geographical subdivisions, if advisable.)

Liability. Statement of value of destructible resources by classes, and for
districts or regions.
Timber, expectation value of young growth, forage.
Arbitrary value per acre of watershed protection. (Possible money

damage. Tabulate.)

Hazard or risk. Statement by types or regions based upon character of
stand, danger of fires starting, and difficulty and cost of suppression.
(Should be based in part upon a study of past experience.)
OUTLINE FOR WORKING PLAN 173

Protection required. (Principles which sum up on the basis of liability
and hazard; the relative amount of protection needed in specified parts
of the forest.)

Control.

Improvements available. By districts. (Brief description, tabulate if
map is not sufficient.)

Communication. Telephone, etc.

Transportation. Railroads, roads, trails, pack trains, etc.
Fire lines.
Look-out stations.

Supplies and tools. (Distribution or how they are to be purchased, etc.
Tabulate.)

Coéperation.

Adjoining forests, between ranger districts, State associations, cor-
porations, individuals, etc.

Organization and administration.

For look-out stations and patrol. Numbers of men and duties by
" districts. (Tabulate so far as possible.)
For fighting fires. (Tabulate if possible.)
Regular and temporary force.
Codperation, labor, including users.
Outside labor. .
Costs.

Specific and detailed instructions to rangers based on the above, and
resulting in its direct application should be issued to all forest officers
engaged in fire protection.

Map showing types, topography, improvements, and as much of above
information as is possible and advisable. Copies to accompany
letters of instruction.

6. Insect control 2and other special problems warrant-
c. Fungus control ing inclusion.
g. Uses of forest land.
a. Settlement.
(1) Classification of lands, whether of relatively greater
value for agriculture or for forest purposes.
(2) Sale prices of land. Comparative land values.
(3) Cost of clearing land for agriculture and probable
profits of agriculture thereon.
b. Special uses.
c. Water-power sites. Present and future development.

Stream measurements.
Insects:
Extent of infestation and damage.
Control, administrative measures, methods. Special force needed. Costs.
174 THE WORKING-PLAN DOCUMENT

Other damages:
Extent. Amount of damages.
Control, administrative measures. (As under Insects.)

Game:
Policy and administrative measures.
Investigations:
9. Lanps
Settlement:

Soils. (Classification with brief description and a statement of compara-
tive agricultural and forest value of each class based upon land values,
forest expectation values, etc.)

Demand for agricultural lands. Past, present, and future.

Policy. (In 1, 2, and 3 order, application of policy based upon the pre-
ceding classification, results of past policy, service policy, and any other
principles as a guide to examiners. Practicability of detailed classifica-
tion of certain districts in advance of application.)

Map, showing soil classification, if data is available.
Uses and Easements:

Resources.

Demand. Past, present, and future.

Policy. (Special features which are important by kinds of uses or ease-

ments. Include charges compared with value to users.)
Water-power:

Resources. Streams, sites, power. Cost and market data and stream
measurements. (Tabulate.)

Demand. Past, present, and future.

Policy. (Special features.)

Administrative sites:

Sites, rights of way, etc., withdrawn, or still needed and to be withdrawn.
Include comprehensive plan of rights of way needed for future sales
and other uses as well as sites and rights of way required in administra-
tion. (Tabulate or show on map.)

Administration:
Special force needed. Other administrative questions.
Costs.
Investigation:
Map or maps showing status, location of uses, easements, water-power projects,
administrative sites, etc.

10. Appendix (observations not properly a part of the main
working plan).
a. General data — geology, soils, climate, occurrence and
protection of fish and game.
6. Silvical data.
(1) Volume, growth, and yield tables.
(2) List of component species.
CONTROL AND REVISION 175

(3) Silvical characteristics of component species.
(a) Soil and moisture requirements.
(6) Influence of elevation and aspect.
(c) Tolerance.
(d) Reproduction.
(e) Injuries: fire, storm, frost, drought, fungus,
insects, etc.
c. Detailed estimates, maps, forest descriptions, etc., of
survey units or other units, unless filed elsewhere for
greater convenience.

10, APPENDIX

Material which should be preserved in connection with the plan, but which will
be used infrequently in actual forest administration.

List of species.

Details of methods used in the collection of data, costs, and areas covered.

Tables, growth, volume, etc., when it is reasonably certain that they will be
used infrequently.

Details of method for regulating the cut.

Detailed silvical discussions upon which conclusions and principles outlined
in the plan are based, if preservation seems necessary or advisable.

General notes upon which the conclusions in the plan were based.

Inventory of existing improvements, if desired. (Tabulate.)

Note. —In addition to the general working plan, annual or periodic plans
may be based on the general working plan and may refer to any specified class
of work, as the annual cutting, planting, protection, grazing or administration
and improvement plan. Such annual plans may be either mere schedules or may
contain more or less detail, explanations, estimates of cost and results, as seems
desirable.

110. Control and Revision.— No working plan can remain
alive and useful unless it is revised at frequent, more or less
regular intervals. These revisions incorporate all the changes
which have taken place during the working period. Such
renewals may be made at fixed intervals of say ten years or at
irregular intervals as is commonly the case where revised data or
changes in prevailing market conditions, etc., necessitate modi-
fication of the original plan.

Since the working period is usually ten years, the working-
plan document is usually revised every decade. But under
very intensive conditions more frequent revision may be justi-
176 THE WORKING-PLAN DOCUMENT

fied, even to the extent of every five years. On the other hand,
a plan should not, ordinarily, go without revision for more than a
decade, even though the working period be longer.

Especially under the kaleidoscopically changing conditions
in most parts of America is it desirable to have frequent revisions
so that the working plan may really “work” and not become
obsolete within the working period. Special revisions before the
end of the working period are, of course, necessitated when-
ever, through storm, purchase, or the like, a substantial change
is caused in the size, character, or composition of the forest.

The record of the progress of the work on the forest as out-
lined by the working plan is called the working-plan control.
This control operates as a check on the execution of the working
plan. In European practice these records are kept by maps
and books. The entries are made periodically or at the time
of completing each of the various projects. The books (called
“control books”) may conveniently be divided into two parts:
I, the cutting and planting record; II, the general or “‘history”’
book. ,

It is obvious that this part I of the control book is built up
from the annual cutting and planting plans. It embodies their
essentials in convenient form as a permanent record. It can, of
course, be extended to cover all the activities of the forest
besides “timber,” e.g., grazing.

A separate page is kept for each convenient unit — be it block
or compartment, township or section, depending on the needs of
the administration.

All areas cut or planted are to be entered on the map of the
forest.

Part II, the “history” book, contains convenient headings
for a general record of the various forest activities. Such are:

1. Forest survey and boundaries: a running record of the
forest surveys made and proposed, be it for timber, grazing, or
what not, and of the changes in boundaries and the demarca-
tion in the field of the boundaries.*

» This may also include the Status Records, that is, records showing the owner-
ship of newly acquired lands. Complete status records will show in detail the
CONTROL AND REVISION 177

2. Methods of cutting and planting: a running record of
silvical observations in natural and artificial reproduction.

3. Forest protection: a running record of all important forest
menaces; the method and success of the combat with them.
Such are:

(a) Fire.

(b) Storm.

(c) Frost.

(d) Drought.

(e) Fungi.

(f) Insects, etc.

4. Administration.

5. Grazing.

6. Permanent improvements

7. Uses of forest land.

8. Utilization of forest products.

(a) Methods and costs of logging.

(6) Methods and costs of saw-milling.

(c) Markets and prices of stumpage and lumber or
other products.

(d) Utilization of by-products.

(ce) Impregnation of wood (wood preservation), etc.,
ad lib.

9. Fish, game and-the-chase:~

10. Money returns of management.

(a) Gross income and expense.
(b) Net income.

11. Personnel relations.

12. Miscellaneous data.

Such a control book, together with the summarized annual
cutting and planting plans, corrected maps, and the marginal
notes and corrections in the plan itself, forms a perfectly ade-
quate basis for undertaking the periodic revision.

\

chain of title for each parcel of land and also all servitudes and easements attaching
to the land. In addition, they usually show the location and extent of all qualified
or temporary alienations such as unpatented mineral claims, leased areas, or lands
otherwise specifically under permit or affected by outstanding contracts, as for the
sale of timber, etc.
178 THE WORKING-PLAN DOCUMENT

The thoroughness of the revision depends on the correctness
of the original plan. Only rarely should it be necessary to
re-write the entire plan. Those portions which come under
“introduction,” such as physiographic features, social and indus-
trial features, and under ‘“‘foundation,” such as forest descrip-
tion, division of area, etc., can either be incorporated directly
in the new working plan, or else reference made to the original
working plan covering these subjects in detail.

In matters of determination and distribution of the cut as
embodied in the general cutting and planting plans, the revision
is essentially a re-calculation and re-allotment..

The preliminary of every revision should be a working-plan
conference to review the plan for the working period just passed
and to make suggestions for the ensuing period. The digest of
this conference should be incorporated in the revised working
plan.
CHAPTER XV

FOREST FINANCE

111. Definition. — Forest finance is that part of forest manage-
ment which relates to the forest as an investment. It includes
two distinct subjects: forest valuation and forest statics; the
first concerns itself with valuations of soil and growing stock,
increment and damage; the second concerns itself with a com-
parison of the financial results of different methods of treatment
and other questions of profitableness and financial effects.

Forest finance calculations require a clear understanding of
the terms: Value, Capital, Cost, and Income.

112. Value. — The following values may be differentiated:

Investment value. — The purchase price or the actual expendi-
ture or investments that have been made in acquiring or creating
the property with interest, less incomes actually derived from it,
with interest.

Cost value.—- An investment value based on production.
This may be differentiated into — Subjective cost value if based
on actual expenditures, and Objective cost value if based on esti-
mated cost of replacement of the property (as in damage
suits).

Sale or Exchange value. — The market price based on statis-
‘tics of actual sales; a special kind of sale value is the forced sale
or wrecking value that can be obtained by exploitation of saleable
parts.

Stock or Stumpage value. — Based on sale. value of material
ready for immediate utilization.

Expectancy value. — The present worth of all estimated or
expected future net earnings (discounted value); the capitalized
net income value.

Rent or Yield value. — A value, determined by capitalizing,
with a demanded rate of interest, the yearly or intermittent net

179
180 FOREST FINANCE

return possible to be derived from a managed property. See
Forest Rent and Soil Rent, Article 94.

113. Capital. — This factor of production in the forestry busi-
ness is variously figured according to what parts of the investment
are referred to and what basis of valuation is applied.

Fixed capital — refers to such kinds of capital as are not used
up in production, like the soil.

Working or operating capital — refers to money capital needed
to supply current expenses in operating a forest.

Soil capital —- refers to the value of the soil figured in various
ways.

Stock capital — refers to the value represented by the wood
material of all stands comprising a forest or working unit.

Forest capital—refers to soil capital and stock capital combined.

Base capital — may be used for the combined soil and working
capital.

These capitals may be based upon various kinds of values,
and to secure a definite meaning, the term must be qualified by
the method by which its value was determined.

There are four sources of capital which may in a greater or less
degree be relied upon for Jarge scale forest production, viz.:

The nation.

The state.

The municipality.
The large corporation.

bh wb H

114. Cost. — In Article 77 it was pointed out that the require- ~
ments for a sustained yield management are five-fold.* So are ~
the costs per acre of growing timber dependent on five main “
factors:

1. Interest on the value of the land.
2. The cost of stocking it with young trees and interest on
this amount from time of stocking to maturity.

Enough, accessible forest. .

. A forest of the right character so that it will pay to cut it for repeated crops.
. Adequate fire protection.

. Equitable taxation.

Good markets for products.

APwnday
COST 181

3- The annual expenses for administration and protection
and interest on each annual expense from time of
expenditure to time of maturity of timber.

4. The annual taxes and interest on each annual tax from
time of payment to maturity of timber.

5. (Last but not least!) The rate of interest.

How do these factors affect various classes of owners?

Certain owners might save all or portions of certain costs, or
find them properly chargeable to other lines of business which
they conduct. Thus a coal mining company might find it
necessary to hold a large area of coal lands, the surface of which
is unsuited to agriculture or any other use except forestry. In
this case it would be fair to charge all the land value to the coal,
thus removing the heavy interest cost on land value from the
forestry costs. This would enable a company of this sort to
produce timber as cheaply as the state.

In municipal forestry, a city finding it necessary to own land
for watershed protection might practice forestry without charg-
ing interest on land value to it, and might also charge a large
part of the actual administration cost to the water department
because sanitary patrol is necessary anyway. (Example: area
around Ashokan Reservoir, New York.)

The large corporation can practice forestry because of its
relatively low interest rate and the economies in administration
and protection due to the ownership of large areas. Where it
has holdings in several localities its fire losses will not exceed the
average losses of the community.

Railroads have three additional advantages which would make
it profitable for them to engage in forest production on lands
already owned. These are:

1. They are large consumers and the cheapest possible supply
of timber is of enormous importance to their construction and
maintenance departments.

2. Since they are large consumers, practically all selling costs
would be saved to their forestry departments.

3. Railroads depend on adjacent territory for tonnage. Land
adapted only to forestry will vield little tonnage any other way,

ea]
182 ae FOREST FINANCE

“ but supposing land under management will yield 500 feet b.m.
per acre per year. This would mean to the railroad from 1500
to 2000 pounds of freight for each year that the forest crop is
maintained.

Small Owner. — As already stated, the small owner, either
corporate or individual, can seldom afford to practice forestry
except in the case of the farm woodlot owner. The farmer con-
sumes most of the product of his own forest, thus saving all
selling costs, middleman’s profits, and transportation to a dis-
tance. To this strong economic position as to markets, may be
added three other advantages:

1. Protection and administration costs nearly disappear.

2. Because of the small cutting areas necessary in the farm
woodlot, reproduction will in nearly every case come naturally,
without extra expense, provided grazing is properly restricted.

3. Though the farmer pays high interest rates when he
borrows, he works principally on his own capital, on which, as
a rule, he makes a very low rate of interest.

All elements of cost are profoundly influenced by the interest
rate. Individuals, states, and the nation have to pay different
rates. The.elements of cost in a given case, Douglas fir, medium
quality site on the Pacific Coast, as related to the interest rates,
are proportionately as follows: *

 

Interest Rate (Compound.)

 

3per | 4per | 44 per} Sper | 6per | 7 per
cent. cent. cent. cent. cent. cent.

 

Per cent of total due to each item.

 

First cost of stocking and annual
charges excepting taxes........ 15 8.6, 6.4) 5§5.4| 3.3] 2.0
Compound interest on land value
on cost of planting and adminis-

 

 

tion charges (60 yr. total)....... 60 | 66.4] 68.6) 74.6] 81.0] 85.6
Taxes and interest thereon........ 25 | 25 25 20 15.7| 12.4
Total nic. scx ase Gerace: 100 | 100 100 100 100 100

 

 

 

 

 

 

 

* “The Cost of Growing Timber in the Pacific Northwest, as related to the
interest rates available to various forest owners,” B. P. Kirkland, University of
Washington, Forest Club Annual, Volume III, 1915, pages 16-38. Reprinted in
1915. Article 114 is drawn directly from Kirkland’s paper.
INCOME 183

From the foregoing it appears that the production of timber,
z.e., the practice of forestry, is mainly a question of the invest-
ment of capital, either by the nation, state, individual, or some
other owner. Those owners who must pay or can get high
interest rates for the use of capital, cannot wisely undertake the
production of timber as an investment, even if they were content
with such long term investments, which is seldom the case.

Costs of Production per Cubic Foot, by Steps, in Germany. —
Eberbach * shows that the total cost of producing 100 cubic feet
(about 623 board feet) is $4.17 of which:

$1.31 or 32 per cent = personnel of the administration.

$1.50 or 36 per cent = cutting and marketing.

$o.246 or 6 per cent = planting.

$0.64 or 15 per cent = roads, new construction and maintenance.
$0.474 or I1 per cent = general expenses, labor, etc.

Total $4.170 = 100 per cent.

115. Income. — In forest finance, the gross income represents
money returns from which no expenses have been deducted; net
income results by deducting all actual expenses charged in book
account, including interest on borrowed capital, but not the
calculated interest on investment, which enters in determining
profit.

Final income — returns from final harvest.

Intermediate income — returns from stands not yet mature.

In considering the advisability of forestry for any particular
area or species, the important thing is to determine what interest
rate on the capital invested can be realized on such an enterprise.

116. Compound Interest Formule. — There are certain prob-
lems in forest valuation for whose solution compound interest
is necessary.

a. The future value of a present sum.
To compute the total cost of investment up to a definite date.
b. The present value, by discount, of a future sum.

To appraise the value of property on the basis of future in-
come.

c. The rate of interest earned by an investment.

* Forstwissenschaftliches Centralblatt, July, 1911, pages 357-377; Oct., 1911,
pages 541-542.
184 FOREST FINANCE

For determining the ratio which income bears to the capital
invested, with full recognition of the element of time.
For comparison of investments.
d. The future value of temporary annual rentals.
e. The present value of temporary annual rentals.
For these the following compound interest formula have been
developed:

a. For determining the accumulation of cost on an invest-
ment.
Interest rate = p.
Principal plus one year’s interest = 1 + p.

Interest expressed as per cent = - = 0.0 p.

p is here an arithmetical, not an algebraic, quantity.

Principal plus interest = 1 + 0.0 p = 1.0.

At end of first year, interest is added to principal. Prin-
cipal at beginning of second year = 1.0 p.

Principal plus interest, end second year = 1.0p X (1 +
0.0 p) =10pX10p=1.0 Pp’.

By same process, at third year, 1.0 p? (1 + 0.0 p) = 1.0 p*.
And in year n, 1.0 p? =1.0 p*™1(1 + 0.0).

1.0 p” is the ratio which gives the future value of a pres-
ent sum at p percent compound interest for years.

Present value of capital or principal = C.

Value at p per cent in ” years
aCX reps] Cn... «2.4 «2 » «4 (Formula J)

6. For discount in the valuation of assets.

Discount is the process of determining the present equiva-
lent of a future value.

Let C,, = future sum = 1.

C, =C X1.0 p" from above example.

C = present equivalent at p per cent.
Cn I

1.0p" 10p""

 

 

(Formula IT)

 

i , : ;

oe is the discount factor or multiple, a decimal,
which gives present value of a future sum.

c. For rate of interest earned.
COMPOUND INTEREST FORMULA 185

As Chapman ™* points out: “the rate of interest, p per cent,
is accepted as a fixed standard in computing cost (Formula I);
or in discounting for value (Formula II). But when both cost,
or investment, and income are known, the ratio of this income
to cost represents the earnings of the capital invested, or divi-
dends. A rate of interest can be found by which the discounted
value of income is made to exactly equal cost, or the accumu-
lated costs to just balance income. This rate is the per cent
earned by the investment.

“To distinguish this rate from the rate of interest », the
term x will be used.”

The formula is: Vu

1.007 = Voc (Formula ITI)
in which x is the rate per cent of income earned, Vn the gross
income, and Vo the value of all costs and charges at compound
interest up to the time of cutting 7.

Instead of solving these various equations, the compound
interest tables in the Appendix may be used wherein Column I
corresponds to Formula I, Column II to Formula II and the
value of 1.0 x" may be found by interpolation in Column I.

d. For future value of temporary annual rentals.
Last payment = e.
Previous payment = e X 1.0 P.
Third last payment = e X 1.0 p”.
First payment = e X 1.0 p71
In all, 2 payments, the sum of which forms an increas-
ing geometric series of n terms, with a ratio of 1.0 p. For
this, use formula:
First term (Ratio" — 1)_
Ratio — 1
Substituting e for first term and 1.0 for ratio, gives:
e (1. arr =—2) 2Gep= 1)
1.0 “p =I 0.0 p
pt op*—1). . (Formula IV)

Sum =

 

* Chapman, H. H., “Forest ae John Wiley and Sons, Inc., N. Y.,
IgI5, page 66.
186 FOREST FINANCE

Since =o paves the capital value of e, it represents
0.0

the sum which would earn e as interest annually at p
per cent.

Let E = —“- = capital value of e.

0.0 p

Then cost of annual expenses = E (1.0 p* — 1), or
Ex10p*—E.

This last form emphasizes the fact that E is never
expended, but, only the compound interest upon
the value represented by E.

e. For present value of temporary annual rentals.
Each rental may be discounted to the present by using Formula
I, but the same result is more easily obtained by discounting the
final future value of the sum of these rentals to the present,
using Formule II and IV for this purpose.
By Formula IV the future value of these temporary annual

e (1.0 p* — 1)
°.

rentals = which may be discounted to the present

I
1.0 p”

 

by multiplying by as shown in Formula II. Hence,
e (1.0 p" — 1) isos (1.0 p" — 1) (Formula ¥)
0.0 p 10p" oopX1.0p"

The values for Formule IV and V are given in Columns ITI
and IV, respectively, of the compound interest tables in the
Appendix. (See pages 246 to 260.)

Additional formule of compound interest will be found in
Chapter V of Chapman: “Forest Valuation” or in Chapter II
of Roth: ‘Forest Valuation.” *

117. Rate of Interest.— The rate of interest is especially
important in long time investments -— such as forestry — whose
income is deferred. The interest rate is determined primarily
by the use of money in loans. This rate is influenced by the
following factors:

* Roth, F., “Forest Valuation,” Ann Arbor, Mich., 1916.
RATE OF INTEREST 187

a. Risk, or danger of loss of interest or principal.
b. Cost of collection of interest.

c. Duration of the investment.

d. Rising prices.

In order to determine the rate of interest that should be
charged for forest investments as compared with other forms of
investment, the following factors should be taken into account:

a. Since forest investments actually tie up funds for long
periods, even where the enterprise as a whole may pay
annual returns, comparison on basis of annual interest
cannot be made.

b. Investments for long periods as savings banks, and life
insurance, pay 3 to 4 per cent, compound interest, up
to approximately 20 years.

c. Business investments which do not pay annual interest
are not usually computed by investors on basis of
compound interest, though they should be. Such in-
vestments are considered satisfactory if after periods
of 20 years they return 4 per cent compound interest.

d. The best short time investments in growing timber may
pay 4 to 6 per cent compound.

e. For investments over 50 years, no existing money or
business investments. can be compared. One must
gauge the rate by comparison with shorter investments
since the comparatively enormous increase of com-
pound interest over simple interest, for high rates and
long periods, causes conditions which are impossible
of fulfilment. Forests will actually earn 2 to 3 per
cent compound, for very long periods.

Writers differ on the rate of interest to adopt for forest in-
vestments. Roth * is a strong believer in an interest rate of not
to exceed 3 per cent. Fairchild,} on the other hand, holds that

* Loc. cit., pages 24-29, 55, and “Business Rate of Interest and Rate Made
by the Forest,” For. Quart., Vol. XIV, No. 2, pages 255-259.

+ Fairchild, F. R., “Taxation of Timber Lands,” in Report of National Conser-
vation Commission, 1908, page 616 ff.
188 FOREST FINANCE

“these rates are too low, at least for American conditions. To
mention only two reasons for this belief: In the first place, the
risk of fire is so great that no insurance company will accept it.
In the second place, forestry is peculiar in the long interval of
time which must generally elapse before the investment begins
to yield an income. It is a well-known psychological fact that
such an income will be discounted at a higher rate of interest
than those whose enjoyment is less remote.

““Without mentioning other reasons for a high rate, the writer
is convinced that, as compared with ordinary investments, forest
investments must be capitalized at a relatively high rate of
interest. Five per cent is certainly not too high. It is very
probably too low.”

In European forestry, Pilz * has shown, conclusively, that the
following rates of interest are earned on the capital invested.

I. Government forest: Per Cent
Saw-timber over 100 years old, deciduous... 1
Saw-timber under 100 years old, deciduous.. 2
Saw-timber up to 100 years old, conifers.... 2

. Coppice, pulp-wood, €te.o 5.542 aeees Sede
II. Large, corporately owned forest:
Add one-quarter per cent to above rates.
III. Small, corporately owned, and private forest:
Deciduous saw-timber................-.-. 23
Coniferous saw-timber and deciduous coppice. 3

i
2

NS
tele

118. Calculation of Costs. —In order to determine the true
economic relation of cost and expenses to income, cost accounts
must be kept. In proprietary accounts the element of time is
wholly neglected, and it is this inconsistency that the cost
account eliminates. This is accomplished by the adoption of a
rate of interest by which all expenditures are computed forward
to the year when the income, for which the cost was incurred,
is finally received.

The calculation of costs in forest production results in one side
of the equation for securing an economic forecast in forestry.

* Allgemeine Forst- und Jagd- Zeitung, January, ror4,
CALCULATION OF COSTS 189

This economic forecast consists of balancing past cost with
compound interest to date, against future income discounted to
date as represented by the expectation value of assets. A com-
parison of past net outlay and future net income for any specific
year, will show the exact economic status for that year.

Costs incurred in forest production are of three principal kinds
and may be grouped as follows:

I. Investments or permanent outlay.
II. Initial expenditures.
III. Annual expenditures.

The various items with which most investments in forest
production are concerned, fall within these groups as follows:
Group I:
Land.
Permanent improvements.
Group II:
Standing timber.
Reforestation expenses.
Groups IIT:
Silviculture and protection.
Taxes.*

Let S = cost of land.
C = initial costs of reforesting.
e = annual protection expenses.
nm = number of years in period.

lI

Using these letters, the following formule of compound
interest are employed to calculate the costs of forest production.

Group I. Let land (S) serve as an example.
Total costs = S (1.0 p") — S.
Group II. Let costs of re-forestation (C) serve here as an
example.
Total costs = C (1.0 p").
* Under the general property tax, this cost will be an annuity. Under some
form of taxation whereby land and timber are taxed separately, the tax on land

would be an annuity, while the tax on timber would, in all probability, be a yield
tax into which no interest costs would enter.
Igo FOREST FINANCE

Group ITI. Let e—the annual expense of protection —-

 

 

serve here.
Total costs = 5 (1.0 p» — 1) (see Formula IV, Article
0.0
116),
or
ge
0.0 p

and

Total costs = E (1.0 p* — 1).

- It will be unnecessary to go through the mathematics of ©
working out by logarithms each value desired; results can be
secured from Column III of the interest tables in the Appendix.*

Using the formule given above, the total costs would be
equal to

S (1.0 p") —-S+C 2p") + E (1.0 p* — 1)

or
(s+ ron) —(S+£).. . . . (Formula VI)

Where cost is incurred in a year a after the time at which the
investment started, but previous to the year 7, when the final
returns are secured, this cost must be carried forward for (n — a)
years and the amount added to the total of other costs. In like
manner, income received in a year a, must be carried forward
for (n — a) years and the amount added to the gross returns.

The following practical considerations enter into the cost of
growing timber crops:

a. Comparison of cost of artificial crop production with
native grown timber, and the prospects for the future.
Advisability of plantations now must be judged by
markets fifty years from date.

6. Cost of securing reproduction by leaving seed trees.
Net cost depends on whether these survive; in which
case it equals C x 1.0" —C, where C = original
value and C, = final value of trees.

* See Article 116, “Compound Interest Formule” and Appendix pages 246
to 260.
DETERMINATION OF PROFITS I9I

c. Cost of disposal of slash after logging.
It is a measure of initial fire protection expenses.
As such it should be calculated per acre and charged
against the new crop.
In practice it is charged against the standing timber
reducing the proceeds from the sale of stumpage.
d. Costs incurred in leaving a large percentage of the stand
' for a second cut.
1. Marking timber for removal.
2. Precautions to prevent injury to standing timber, ¢.g.,
brush disposal.
3. Increased cost per M. feet of transportation charges.

These items are a charge against the second crop, on
the basis of the stand or M. feet per acre at time
of returning.

Total actual cost of leaving part of the stand for a
second crop is the present value of timber left, plus
total expenses incurred, including taxation: and
interest on land, or (C + S + E) 1.0 p" — (S + E)
when C = value of timber and initial costs.

119. Determination of Profits. — Knowing the total cost of the
investment, this can be subtracted from the future stumpage
value (see Article 121 for determination of stumpage values),
and thus the profit determined. The following table * shows
for a wide range of yields and stumpage prices, the net profit and
corresponding compound interest rate on a number of different
initial investments. This is the rate of interest actually earned,
as explained under c in Article 116.

* Sterrett, W. D. and Barrows, W. B., “Tables for Determining Profits in
Forestry,” For. Quart., Vol. XIII, No. 1, pages 12-14.
192

Rates or INTEREST ON DIFFERENT INITIAL INVESTMENTS IN TIMBER GROWING CALCULATED FOR VARIOUS YIELDS, STUMPAGE VALUES,

AGES, AND Costs oF LAND AND ESTABLISHMENT.
Yield per Acre — Board Feet; and Stumpage Values per M. Feet.

FOREST FINANCE

  

 

 

 

 

   

 

 

 

 

 

 

     

 

 

 

 

   

 

 

 

 

  

 

 

 

  

 

 

   

 

  

 

 

 

   

 

 

  

 

 

 

 

 

 

 

 

 

. z MO MO HOH 1 Hho MHI rg
8 |: : a
gf € |: ft [ons Eran ese mmee nds) 3 3
*| 3 To RHO FANO MOHO MAN TOO MB 2 ‘a
ae 5 Pb ibis it igo reso misuurounds/E 33
ae = : MON HOOHON ND THTRARS 8 > g
aS Hobs irs AH HGSVNS HHT SHOE g >
& eg Bea DIAAMATHARH HO. “|B & »
OG eee oe ees MONTEMOKNEMO iS: < EI 8
Z . TAI TS ONO HAC MRR RAR SMMONES 8 o 3
g| a : GHG ACG Son RRS ROS MNES Md a/8 1 @
cts ®
| s 7 ROO ARO TNATONADHOHODD OO MH! b yn aA
wel ow LIA GAWD EGO MGKKOSS MNT HHS Sm a &
oe — >
ae iz “ne MEAS OHO OMR NN ME MORONDA |S 3 3
£5 a DTH RKO ArooHMrENTT TONG 1g 3 g
2 2 7 |p MOWRAOSTAGMETOORA: HMI: g 2 8
a : 1 AROMA THRHTEHMHTHM > - i: os
: MOHONNE NOON EO TUWATO AAO 00000 OO} HOO § 2 a
eg] 4 EEOUH ONC Ona roo rcoONoE MU dO MNT TMS g g
o
¢ °° NO OH SS OS TOMS OME TOMO MAMA TON F > 2
2 3 BORGG An awd roanros unre vndto ot TOM a 3s ¢€
= ~ (COMPOS ROR AMO TAAMOTEOENOMOTON © of 8 &
oe) & TUNG AWA CO roo NNO HHTTONT SE HMMTIM | 13 4 §
s
a & loroanbranamnnonne . TSO 4 5
A [Rares Hoc Uudemondm | Pibiem se & Ss 3
» [SA DMR ONS HRNOOMOOMHMHMOMOHONDA |g eg
Slo (MPEP Aad der rwe ares HHEwS HITTITE HIM ‘| 2 = 8
o = a
o 6 SOMTS OD RH ROMS TOONS TRURAONN TOA art ko 2 2g
ial 8 TUG AGH Co roo noonndssHsdIMHSHM § &o¢
st +>
os % [OSORNO MRHOTOAMRTOORN mn 12 8 e
86) & [OGarrvarcsuvdruddmmndam fs 5 oe
2 4G
é & |wouneRenonnn wHo..:0- tl @ Bg
A [orweussrusmm Mem isl Phebe bls 7 &
, [OTA ANMINS UERHOTAOMRIOORN. nH... -\9 g =
g] 2 [pg anrrweareunerundcemmMndas i) q Qo
@| 8 laraan nna Ramneane - \e € a
iB b [panrcc vas hd emoude | 3 8 s
; hs i
ze ® TANTRA HOME 8 tl Z
28) & [oreuscrudcam See eee. 38 a 8
ee anion Teeles ani
A jews: tine | ee e 2 28
e [TOM TRA MOURA OHO IO: bs BE oe
g| BG [greudsrndam Mdm slit: q “sé
3 Soda eg ; a
°| § Re TTROwS wR ae 3 1 82
4) 2 lacuemmw sm 5 5 oa
so) & 2 2 |< op
ino} “S PROS se es ee Ss es
ml as feSaeee bbs Bs Ge Dee
SG i a . e <¥
e o |- . ee 3 at 8
By ire ee as pees BN &
lol of
*; a §8
© CONNHHNTTHOEraAaeE 5 aie]
g BZSSSVSAN GATS RRSESRASSSSZS ARABS E CN]
GB Ler HMMA DAANMHWD MMAR SS Ao *
G [PURER RARRSSRRSIBBBBARSSSSeeaggy 8 E
ae HRA iT
g < 56
ale & ae
q >
o d = ~ ae
w on
B| € jpeveraverensveanguavensuavergnald 2 Bs
8) & q ie
2 8 he
a On % ; = ~
a € f 2 va
a (848 onngoMoOMNEOwHOMMEOMOMNEOMOMMOO N/E a bo
‘3 ae wt ae AA ot ete 3s > 2
a Da
is R8 B 32
J By 3 ‘a
% [oesauermagunerceruevgeryemgauules 2 Ey
o8 3 1g
3 ws
: me 2
a <
88 (8 2 2 8 2 CE om be
<q
a

bee
DETERMINATION OF PROFITS 193

This table may be practically applied as follows:

McCarthy’s yield table for white pine near Ithaca, N. Y. (see
Article 79, Fig. 23), shows about 20 M. feet, b. m., per acre at
60 years. If the land is worth $10.00 an acre, planting costs
$10.00 an acre, and annual administration expenses and taxes
are 5 cents per acre per annum for administration and fire pro-
tection and 1 cent on the dollar annually for taxes with compound
interest at 6 per cent, what rate of interest may be expected
if the stumpage value in 60 years from now is $10.00 per M.?

Using the table, the answer = 3.2 per cent.

If the stumpage value were $15.00 the answer would be = 4.3
per cent. With money at 5 per cent there would here be no
enterpriser’s profit. (The enterpriser is the one who under-
takes — the ‘‘entrepreneur.”’)

The gaps in the table may be filled by interpolation. Thus,
other factors being equal, the interest rate for a stand in which
the initial investment is $12.00 per acre, would be between the
rates for $10.00 and $15.00 investments. Similarly, the interest
rate for a stand containing 25 M. board feet per acre would be
intermediate between one of 20 M. and one of 30 M. per acre.
Thus, in the first example, the yield table (Article 79, Fig. 23),
shows 20,920 board feet per acre at 60 years; this is practically
21 M. The interest rate, as shown, is 3.2 per cent for 20 M.
per acre; it is 4.2 per cent for 30 M. per acre, for 21 M. it is
one-tenth of the difference, or 3.3 per cent.

The interest rates earned by white pine stands on medium
quality sites, using the values given in table 6 of U.S. Dept. of
Agriculture Bul. 13, ‘‘White Pine under Forest Management,”
are as follows:

 

 

 

Stumpage value per M. feet, board measure.
Rotation, Volume acre, feet,
years. board measure. $10 $15
Interest per cent Interest per cent

earned. earned.
30 9,600 5.4 6.9
40 23,500 5-9 7-1
50 36,600 5.8 5-7
60 46,900 Sur 6.0
70 56,100 4.4 5.2

 

 

 
104 FOREST FINANCE

With money at 5 per cent there would be an enterpriser’s
profit in all but one instance; at 6 per cent in only two in-
stances.

From the data in tables 15, 16 and 17 of Bul. 13, it appears
that, under optimum conditions, the net profit, per acre per
annum, from growing white pine is as follows:

Money at 4 per cent compound...... $5.20 net profit per acre per year.
Money at 5 per cent compound...... $4.42 net profit per acre per year.
Money at 6 per cent compound...... $4.22 net profit per acre per year.

The maximum income, per acre per annum, from the State
forests of Germany has been as follows:*

 

. : . Average of net
Wiirttemberg. Saxony. Bavaria. Prussia. returns.

 

Gross. Net. | Gross.}| Net. | Gross. | Net. Gross. | Net.

 

 

 

$ $ $ $ $ $. $ $ $
10.90 7.47 | 9.60 | 6.17 | 6.30 | 3.30] 5.19 | 2.98 | 4.98*

 

 

 

 

 

 

* By using the values for several years and by taking into account the acreage of forest in each
country, the average net returns per acre per annum are as follows:

Wiirttemberg............ 490,000 acres ....... $6.64.........606 1905 to 1909 incl.
Saxony......-....-.e eee -431,000 acres........ BSG ard aceon 1905 to 1911 incl.
BaVarldiscsiieics oc stueduin se 2,330,000 acres. ....... QFE tesa hievnialein's 1905 to 1909 incl.
PHiSSIA isis dass eeeneene: 6,796,000 acres........ O: 33 sss setae 1905 to 1911 incl.
Proportioned average for 10,047,000 acres....... $2.7617 = Net annual revenue per acre.

120. Financial Advantages of Sustained Annual Yield. — The
advantages of a sustained annual yield (see Article 77) over a
single yield once in a long period of years (called “intermittent
management”) are well illustrated by the following comparison
of the two adapted from Roth: “Forest Valuation.” ¢

* Adapted from Roth, “Forest Valuation,” page 138.
{ “Forest Valuation,” F, Roth, Ann Arbor, Mich., 1916, page 83.
STUMPAGE VALUES 195

COMPARISON OF YEARLY AND INTERMITTENT WORKING

Premises. — Area 1000 acres; rotation, 80 years; interest rate, 3 per cent;
value of timber at rotation age, $400 per acre; land cost $10 per acre; m.a.i.
= 1 cord per acre; value per cord, $4.00; cost of planting, $10.00 per acre;
current expenses, $1.00 per acre. Thinnings omitted.

 

Property with yearly cut
and yearly income.

Property with a cut and
Income every 80 years.

 

1. Growing stock at begin-

2. Growth of merchantable
material during the 80
VATS?» ji+4 awieha ea fea ka es

3. Growing stock at end of 80
VOATS aces ease haces nae
4. Value of property at begin-
MING 0-5 oe ee nanan ae ‘

5. Income during the 80
CAT Shas hay HS Gedveremcriseanrasonen ©
6. Income at 80, 7.e., in last
CAT acs 5 cere eeemna mine

 

40,000 cords

80,000 cords

40,000 cords

$10,000 for land and
about $60,000 for
growing stock.

$320,000 plus inter-
est.

$4000
Has earned:
Per year:
Income: $4000
Expenses:
Rent $335
Tax and care $1000
Planting $125
Total expense $1460
Net income per year
$2540
Net income for 20
ears (fos)
Vee Ss
or about
$68,250

 

None

80,000 cords

80,000 cords

$10,000 for land
nothing for growing
stock; might  in-
clude value of plan-
tation.

None, thinnings not
considered.

$320,000
In debt:
Expenses per year:
Rent $335
Tax and care $1000
Total $1335
For 20 years expenses

(1.03% —1)
7335 1.03 —1I re
$35,871

For planting $10,000
Plus interest or
10,000 (1.03)
18,000
Total expenses for 20
years: $53,871

 

121. Stumpage Values. — Chapman ™* defines stumpage value
as “the sale value of merchantable standing timber — its value
on the stump previous to felling and removal.” This value

may be determined:

I. As lump sum: this may be per acre or for entire tract.
II. Per unit of product:
(a) Based on actual sales in the vicinity.
(b) Based on appraised value:
(1) According toper cents of grades and gradeprices.
(2) According to mill run selling price.
* “Forest Valuation,” Chap. XI.
196 FOREST FINANCE

Of these the last named is the one most commonly used. The
appraised value is more reliable than a figure based on precedent
or a lump sum.

The appraisal of stumpage value is based on costs of logging
and milling (O) on selling price (S), and on a fair profit (p) in the
investment. These three factors must be determined for every
prospective operation.

The main items of costs entering into lumbering operations
are as follows, per M. feet, board measure:

d = investment charge (sinking fund or depreciation).
2 = interest on investment.
¢ = operating costs — stump to f.o.b. cars.*
m= maintenance of plant and equipment unless included
in c.
= office charges, taxes, insurance (overhead expenses).
additional cost of logging under forest management
(see Article 118).
w = wrecking value of d at end of operation — to be de-
ducted from d.

The item d should, as a rule, include all of the initial in-
vestment in mills, yards, railroads, tramways, livestock, logging
equipment, etc., necessary to put the finished product on the
market in the logical manner indicated by local conditions, minus
the estimated cash value of the plant and equipment at the end
of the operation. The item may generally be handled in the
following manner: Suppose the purchaser of 10,000,000 feet of
timber under a five-year contract is required to invest $20,000
in a plant and equipment. Presuming that the average annual
cut will be 2,000,000 feet, the investment charge amounts to
$4000 per annum (if it is considered that the plant and equipment
will have no actual sale value at the end of the operation), and
this sum prorated over the 2,000,000 feet handled annually
makes the item d equivalent to $2.00 per M. If, however, it
is estimated that the plant and equipment will have an actual

* For outline of logging and milling costs see: Recknagel, A. B., “Theory and
Practice of Working Plans,” 2nd. edit., John Wiley and Sons, Inc,. N. Y., 1917,

pages 33-36

2 e
|
STUMPAGE VALUES 197

sale value of $10,000 at the end of the operation, the item d is
reduced to $1.00 per M.

In computing the item 7, it should be considered that half of
the full initial investment has been retired at the expiration of
one-half of the contract period. Therefore, it is permissible to
reverse this assumption and, for the sake of simplicity, to allow
interest on the full investment for one-half of the contract
period, and the item 7 should be so computed at six per cent
simple interest. In the above assumed case as an example,
simple interest on $20,000 at six per cent would be figured for
2} years, amounting to a total of $3000. This amount prorated
over the total cut of 10,000,000 feet makes the item 7 equivalent
to $0.30 per M. It should be noted that this item is not de-
creased if a wrecking value is calculated, since the $20,000 is
invested for the full period of the operation and interest should
be allowed regardless of any amounts which may be returned
through the sale value of the equipment at the end of the operation.

The item m should not be confused with the investment
or depreciation charge. It covers the amount expended solely
for the purpose of keeping the plant and equipment in working
efficiency during the operation. That is, it represents the cost
of necessary repairs and replacements only. ;

Under item ¢ should be included wagon roads, since such
roads will be an investment for which there are no appreciable
assets at the end of the operation. Such roads will usually have
to be abandoned or will become county roads at a future date.

In charging against the item 7,* consideration should be
given to such factors as brush disposal, cutting of snags and
dead trees, utilization of small or inferior material which can be
handled at little or no profit, and the amount of stumpage
handled per acre. This latter point will be governed largely
by the recommended system of marking, 7.e., the percentage of
the merchantable stand marked for removal. It should be
borne in mind that, other conditions being equal, the cost of
logging is about proportional to the amount of timber handled
per acre.

* See Chapman, “Forest Valuation,” Article 107, page 81.
198 FOREST FINANCE

The item w should be handled with great care. It should
be limited in all cases to the estimated cash value of the plant
and equipment at the end of an operation.

The total cost, exclusive of stumpage, should be summarized in
the above manner and the average mill run selling price f.o.b.
cars, or other point of sale, should be determined as accurately
as is feasible. The operating costs and average mill run selling
price, together with the per cent of operating profit to be allowed
the purchaser, having been determined, the true value of the
stumpage may be found by the three following formule in which

x = unknown stumpage value.

s = average selling price.

o = operating costs = (d—w) t}iteotm+tot+r.
p = per cent of operating profit.

Formula A, known as the forester’s formula, was first promul-
gated by the U. S. Forest Service in January, 1912 and reads:

x =s—o—p(o)— p(x),

 

or, in abbreviated form (by algebraic reduction): sie
s rai
a — 0.
I+ p

This formula allows a percentage of profit on the stumpage price
as being one of the operating costs and “‘ was formerly advocated
by the Forest Service for use in small sales where but little

capital is invested but has been set aside” * in favor of formula B.
Formula B reads:

x=s—o—p(o).
“The computation of profits as a per cent of operating costs, if
based on the results of individual operations, would place a
premium on extravagance. But when gauged by average costs
of well-conducted operations of similar size, and applied in deter-
mining appraisals in advance of cutting, no such objection can
be urged.” *
Formula C reads:
x=¢q (s = 0) ’

* Chapman, “Forest Valuation,” page 183.

Ci
STUMPAGE VALUES 199

in which g is the per cent of net income taken for stumpage
value — it shares the profit between the owner of the stumpage
and the operator. ‘‘Such a plan requires complete confidence
in the integrity of the operator or a right to inspect his books,
and is not generally practiced, though one of the most equitable
of methods.” *

In using formule A and B it is necessary to take into account
the over-run of mill scale over log scale. ‘‘All log scales in
extensive commercial use give less than the contents ordinarily
sawed from logs, and this discrepancy increases as utilization
becomes closer. The excess of manufactured lumber over the
contents measured by the log scale is termed over-run.” t

The stumpage value per thousand feet of sawed lumber
multiplied by 1+ the percentage of over-run will give the correct
stumpage value per thousand feet, log scale.

Examples of Stumpage Determination. — In a given operation
in New York State t the operating costs (0) were as follows:

 

Cutting............ $1.50 per M. feet, b. m.
Skidding........... 1.75 per M. feet, b. m.
Sawing..........-.. 3-50 per M. feet, b. m.
Piling.............. 1.00 per M. feet, b. m
Hauling............ 5.00 per M. feet, b. m.
Total. cee vane $12.75 per M. feet, b. m.

The average mil] run selling price (s) was $25.00 per M., and the
per cent of operating profit (p) was 25 per cent. The over-run
of mill scale over log scale was 15 per cent, that is, each thousand
feet log scale produced 1150 board feet of lumber.

By using formule A and B, the results are per M. feet, b. m.,
as follows:

 

 

 

Without over-run. With over-run.
Item.
Formula A.|Formula B.|Formula A.|Formula B.
$ $ $ $
Stumpage value.............-6555 7.25 9.06 8.34 10.42
Profit per Mi <4 dvsceeseeoesces oe 5.00 3.19 3.91 1.83

 

 

 

 

* Chapman, “Forest Valuation,” page 184.
+ Chapman, “Forest Valuation,” page 187. See above Chapter IT, Article 12.
¢ Bul. 9, N. Y. State Conservation Commission, st. edit., pages 95-08, 2d. edit.,

page 57-
200 FOREST FINANCE

By using formula C and assuming that g, the per cent of net
income taken for stumpage value, is 50 per cent the result is,
per M. feet, b. m , as follows:

x = q(s—o) = 0.50 (25.00 — 12.75) = 0.50 (12.25)
= $6.125 = stumpage value.

Stumpage values in Germany and other European countries
are as follows:

Good Scotch pine, Germany and France, $12-$24 per M.*
Dr. House { gives for Scotch pine in Eberstadt near Darmstadt a
stumpage price of $60 per M. feet, b. m.

In general, stumpage prices in Europe for timber of moderate
accessibility and of such species as Scotch pine, Norway spruce,
etc., vary from $15 to $35 per M. The spruce and fir in the
Black Forest bring an average stumpage price of $24 per M.

For stumpage values in America, Roth} says: ‘“‘Stumpage
prices today vary not only for species but vary with market,
railway facilities, habit of the people of the district, etc. Aver-
age figures for stumpage have little value, they vary chiefly
between $3 and $7, go as high as $20 and as low as $1, and
generally make from 10 to 30 per cent of the value of the lumber
at the mill.”

Note. — For further details regarding Stumpage Values and Methods of
Stumpage Appraisal, see: Chapman, “Forest Valuation,’ Chapters XI and XIV;
Roth, “Forest Valuation,” Chapter VI; and U. S. Department of Agriculture,
Forest Service, ‘Manual of Stumpage Appraisals,” Nov., 1914.

122. Appraisal of Damages. — Chapman § lists the following
principles underlying the appraisal of damages to forest property:

(a) Damages are payable in money — compensation, not
restoration.

(b) Difference in value before and after damages is the basis.

(c) Sale value is an important index but is not a final standard
of value.

* U.S. Dept. of Agric., Bul. 139, “Norway Pine in the Lake States.”
t Report of the New York State Botanist, 1913, page 4.

t Roth, “Forest Valuation,” page 91.

§ Chapman, “Forest Valuation,” Chapter LX.
APPRAISAL OF DAMAGES 201

(d) Value set by owner must have commercial, rather than
personal, basis.*

(e) Prospective income, if reasonably certain, is accepted, but
not when based on speculative or contingent factors.

(f) Cost of restoration is the basis if less than the present
value.

(g) Average costs or income, rather than individual or ex-
ceptional figures, are accepted.

(hk) Damages must be proved with reasonable certainty.

Based on these principles, the U. S. Forest Service, on Febru-
ary 6, 1914, issued ‘‘Standard Instructions for the Determina-
tion of Fire Damages.”’ These instructions make no attempt,
for the present, to estimate the loss in soil productivity due to
the destruction of humus and litter and to changes in the physical
characteristics of the soil, or to the increased danger from insects
and disease, although it is recognized that these may frequently
represent real and important damages. Soil rental (see Article
94) is also to be omitted from calculations of expectation and
replacement values, since under present conditions it is so
‘difficult to determine, is to a large extent offset by other factors,
and unnecessarily complicates the problem.

The government’s detailed instructions for calculating fire
damages are given below:

I. TmBER
Definition of ma- 1. Mature Timber. — This includes all timber which is of
ture timber. sufficient size to be ready for cutting according to the general

lumbering practice of the region. Burns in mature timber will
fall into three general classes:

(a) Where the entire stand is killed and rendered unmer-
chantable by the fire. In this case the damage will be assessed
at the full stumpage value of the timber, both live and dead,

Entire stand ren- immediately before the fire, determined according to the usual
dered unmer- method of appraising stumpage for timber sales. Other products
chantable. than lumber, such as poles, ties, mining props, fencing, fuel, etc.,

for which there is a market, should be included in determining

* Ibid., p. 121: “ Aésthetic values, or the value of ‘legitimate gratification,’
must ‘be recognized whenever based on elements generally accepted by the public
at large. Sentimental value peculiar to the owner cannot be admitted.” And on
page 139 he says: “the esthetic values destroyed may frequently be gauged
roughly by the loss in sale value of the entire property.”
202

Inaccessible
stands.

Stand killed but
in part mer-
chantable.

Stand only partly
kille4.

Definition of im-
mature timber.

Stands approach- .

ing merchant-
ability.

Expectation value
formula.

Stumpage value.

FOREST FINANCE

the value of the stand. When the stand destroyed is so
inaccessible as to be at present unmerchantable, its stumpage
value will be taken as the minimum rate for the Forest.

(b) Where the entire stand is killed, or so damaged that it
will die in a few years as a direct result of the fire, but where
some of the timber is still merchantable. In this case the timber
should be advertised for sale with or without naming a minimum
price, depending on the circumstances in each case. If sold,
the damage would be the difference between the appraised
stumpage value of the timber before the fire and the selling price.
If not sold, the damage should be taken as the full appraised value
before the fire.

(c) Where part of the stand is killed and part left undamaged,
either in the form of single trees or solid blocks. In this case
the damage would be the difference between the appraised
stumpage value of the entire stand before the fire and the ap-
praised value of the remaining merchantable stand after the fire,
or its sale value if an immediate sale is practicable. The stump-
age value of the undamaged timber would ordinarily be less after
the fire than before, as a result of the increased cost,of logging
due to the destruction of part of the stand.

_z. Immature Timber. — This includes all timber not yet mer-
chantable, that is, timber which is still too small to be ready
for cutting according to the general lumbering practice of the
region. Stands of immature timber will fall into two general
classes:

(a) Stands which are approaching merchantability. The
lower age-limit for this class is the age at which the trees have
obviously passed the stage of being mere “reproduction.” This
will ordinarily be at from one-third to one-half the length of the
rotation, depending upon the species and market conditions.
The upper age-limit is the age at which the trees are obviously
ready for cutting according to the general lumbering practice of
the region.

The damage to stands of this character will be taken as their
expectation value. This is merely their estimated value at the
end of the rotation, reduced by the cost of protection during the
intervening period, and discounted to the present at compound
interest. It may be determined by the formula

ra (1.0 p"-™ — 1),
G= -op
1.op"—"
where

G = expectation value of the young stand.

Y = stumpage value of the stand at the end of the rotation,
based on present stumpage prices. The yield per acre at the
end of the rotation should be estimated as accurately as possible
Yield tables.

APPRAISAL OF DAMAGES 203

by means of empirical or normal yield tables. Empirical yield
tables, giving the average cut at different ages for the region in
general, will ordinarily be most satisfactory, particularly in
irregular stands. Where normal yield tables are available,
however, they may often be used to advantage, particularly in
regular, well-stocked stands, making due allowance of course for

.the normality of the particular stand in question.

Annual expenses.

Rate of interest.

Length of rotation.

Age of stand.
Stands only par-
tially destroyed.

Practical examples.

é = annual expenses for fire protection. These should be as
nearly as possible the average amount actually spent by the
Forest Service for protection in the same general region, and will
necessarily vary according to the topography and character of

the stand. = is the capitalized value of the annual expenses,

and is sometimes represented by the single symbol E.

.op = rate of interest. This will be taken uniformly as 3
per cent.

2 = length of rotation. This will vary according to the
species, and should be the rotation which the Service actu-
ally plans to use for the species and locality under con-
sideration.

m = present age of stand.

Where only part of the stand has been destroyed, the amount
of the damage is the difference between the expectation value of
the stand before and’after the fire. This may be determined by
the formula

y—YyY’
damage = 10pm
where

Y’ = stumpage value at the end of the rotation of that part
of the stand remaining after the fire.

A 50-year-old fully-stocked stand of Douglas fir is destroyed
by fire. Yield tables show that such a stand will yield 80 thous-
and board feet per acre in 100 years worth $1.50 per thousand at
present stumpage prices. The cost of fire protection is 3 cents
per acre per year. The expectation value of the stand per acre,
and consequently the amount of the damage suffered is therefore:

oe yY- pn 1)

1.0 p™—™

— 2:93 100-50 _.
80°X 1.50 a (1.03 1)

1.031040

 

120 — (4.3839 — 1)
4.3839
116.6161

= ——— = $26.60.
4.3839
204 FOREST FINANCE

Tf the stand were only partly destroyed, so as to reduce the
yield at the end of the 1oo-year rotation to 40 thousand board
feet, the damage per acre would then be:

yY-—Y’
Damage = lope pom
__ 80 X 1.50 — 40 X 1.50
Ga 1.031060
__ 120 — 60
4.3839
= $13.68.

Very young stands. (b) Stands which would generally be classed as “reproduc-
tion,” and which obviously cannot be considered merchantable
for some time to come. This will ordinarily include stands with
ages up to one-third or one-half the length of the rotation.

Replacement value The damage to stands of this character will be taken as the

formula. cost of replacement. This is merely the cost of planting or
seeding the area plus the cost of fire protection, both items being
calculated at compound interest for the number of years neces-
sary to replace the stand destroyed. It may be determined

 

by the formula:
e
R=CX1.0p"+ cope p” —1),
where

R = cost of replacement of stand.

Cost of stocking. C = cost of planting or seeding. That method of reforesta-
tion should be adopted which gives the most assurance of success
under the given conditions of species, soil, climate, etc. Reason-
able figures for cost should be used based on previous experience
by the Service in similar situations.

Sufficient stock should be planted or sufficient seed sown to
establish a stand which at the end of the rotation will produce as
nearly as possible the same yield as would have been produced
by that destroyed.

Rate of interest. 0.0 p = rate of interest. This should be taken uniformly as
3 per cent.

m = number of years necessary to replace the stand. Or-
dinarily this will be the same as the age of the stand destroyed.
Where, however, growth has been abnormally slow, as a result
of overstocking or suppression, interest charges should be cal-
culated only for the number of years which would normally be
necessary to produce a stand of the size of that destroyed.

Annual expenses. e = annual expenses for fire protection. These should be as
nearly as possible the average amount actually spent by the
Service for protection in the same general region, and will neces-
sarily vary according to the topography and character of the

stand. — is the capitalized value of the annual expenses,
and is sometimes represented by the single symbol E.
Where natural re-
production may
be depended on.

Practical examples.

APPRAISAL OF DAMAGES 205

In burns where reproduction in sufficient quantities is already
coming in naturally after a fire, or where it is certain that it will
come in naturally within a reasonable time, no charge should be
made for planting or seeding. In other words, C in the formula
equals 0; and the cost of replacement is simply the cost of
protection, at compound interest, for the number of years
necessary to replace the stand destroyed. Where natural
reproduction may be counted upon to come in slowly but surely
after a fire, as with western yellow pine, this period may be
considerably longer than the age of the stand destroyed, in order
to allow a reasonable time for the reproduction to become estab-
lished. In all cases where it is doubtful as to whether natural
reproduction can be depended on, the cost of planting or seeding
should be included.

A to-year-old stand of Douglas fir is destroyed by fire.
Natural reproduction is out of the question, but a similar stand
can be replaced in ten years by planting at a cost of $6 per acre.
The cost of fire protection is 3 cents per acre per year. The cost
of replacement per acre, and consequently the amount of the
damage suffered, is therefore:

é

R=CX HOR? Tap

 

(1.0 p™ — 1)

= 10 1. 2:03 10 _
6 X 1.03! + 05 (1.03 1)

= 6 X 1.3439 + (1.3439 — 1)
= $8.41.

A xo-year-old stand of lodgepole pine is destroyed by fire.
Natural reproduction takes place immediately and can be
counted on to produce in ten years a stand as good as that
destroyed. The cost of fire protection meanwhile is 3 cents per
acre per year. The cost of replacement per acre, and conse-
quently the amount of the damage suffered, is therefore:

R=CX 1.09" + 5 (10 9"— 9)

© X 1.03! + ar (1.03°— 1)

= 0 + (1.3439 — 1)
= $0.34.

A to-year-old stand of western yellow pine is destroyed by
fire. Natural-reproduction can be depended on to take place,
but owing to the slowness with which the young growth comes in,
30 years will be required to replace a stand similar to that de-
stroyed. The cost of fire protection is 3 cents per acre per year.
The cost of replacement, and consequently the amount of the
damage suffered, is therefore:
200

Reasons for using
both  expecta-
tion value and
cost of replace-
ment value.

Mature and im-
mature timber
on same area.

Two-storied
forests.

Selection forests.

FOREST FINANCE

é

RSC Anee tes

 

(1.0 p™ — 1)

= 30 4. 2:03 20

o X 1.03% + are (1.03 1)
= 0 + (2.4273 — 1)
= $1.43.

The use of both expectation value and cost of replacement
value in the case of immature timber is necessitated by the fact
that present stumpage prices bear no relation to the cost of
timber production. Expectation value is the fairest to use with
stands approaching merchantability since it can be determined
with considerable accuracy and gives reasonable results, while
cost of replacement value for such stands appears unreasonably
high because of the present low stumpage prices. For very
young stands, on the other hand, expectation value cannot be
determined accurately because of the difficulty of predicting
future yields so far in advance; furthermore, it is unreasonably
low since it must be based on present stumpage prices, while as
a matter of fact it is almost certain that stumpage prices will
be considerably higher by the time the timber is mature. For
such stands, therefore, cost of replacement value is preferable
because it can be more accurately determined and gives more
reasonable results. As stumpage prices approach the cost of
growing the timber, expectation value and cost of replacement
value also approach each other until they are the same for any
given age when the stumpage price is exactly equal to the net
cost of production.

3. Mature and Immature Timber on the Same Area. — Stands
of this character fall into two general classes:

(a) Where the immature timber occurs in approximately
even-aged stands as an understory beneath the mature timber.
In this case the value of the mature and immature timber should
be computed separately as provided for under 1 and 2, and the
sum of these values taken as the damage to the stand. This is
on the assumption that the reproduction already present would
actually be used to re-stock the ground in case of a timber sale.
If this is not true, that portion of the immature timber which
would not be made use of after a timber sale should be disregarded
in the calculation. In determining the value of the immature
timber it should be borne in mind that unless the entire stand is
destroyed, natural reproduction can usually be depended on to
take place from seed trees left after the fire.

(b) Where the mature and immature timber occurs irregu-
larly over the area in the form of a selection forest. In this case
the value of the mature timber should be determined as already
outlined. The value of the immature timber should be deter-
mined either (1) by ascertaining its average age and finding the
Acreage _ basis;
private rates.

Carrying capac-
ity.

Injury lasting sev-
eral years.

Unmerchantable
stands.

APPRAISAL OF DAMAGES 207

expectation or replacement value of a stand of this age and
degree of stocking; or, (2) by dividing the young growth into a
small number of age-classes, and finding the expectation or
replacement value of each of these. In determining the value of
the younger age-classes in the immature timber it should be
borne in mind that, unless the entire stand is destroyed, natural
reproduction can usually be depended on to take place after the
fire.

II. Forace

Damage to forage will be estimated on an acreage basis at the
current rates paid for grazing privileges on private land of similar
carrying capacity. Thus, if 500 acres of range are burned over
so as to be useless for grazing purposes for a full season of six
months, and private land of similar carrying capacity rents for
$64 per section, or 10 cents per acre, for an equivalent season,
the damage would be 500 X $0.10, or $50. If the carrying
capacity of the National Forest Range is less than that of the
private land, or if the grazing season is shorter, or if the damage
is such as not to prevent the use of the range for a full season, a
corresponding reduction would be necessary in the value of the
forage destroyed.

If it can be conclusively established that the severity of the
injury is such as to prevent the use of the range for a certain
number of years, the value of the forage should be calculated for
each year in the same manner. Unless the number of years can
be determined with reasonable certainty, however, the estimate
of damage should include only the value of the forage actually
destroyed.

III. Protection

When a stand is destroyed which never would be merchantable
but which still has a value for watershed protection, its value
will be taken as the cost of replacing a stand sufficient to exert
the same amount of protection, as determined by the formula

R=CX 109" + 5 (1.0 9" — 0).

For the present, however, the value of C will be taken uniformly
as 0, on the assumption that in all such cases natural reproduction
can be relied upon to re-stock the area.* The amount of the
damage, will, therefore, be merely the cost of fire protection, at
compound interest, for the number of years until the new stand
can be considered to afford the same amount of protection as that

* Chapman, “Forest Valuation,” page 138, favors using “‘ the cost of re-estab-
lishing the protective cover, either by natural or artificial means, and of protect-
ing this area from fire until it reaches the same state of effectiveness as that
which was removed.”
208

Merchantable
stands, brush,
and grass covers.

FOREST FINANCE

destroyed. Wherever a considerable period will be necessary
for the reproduction to become established, this fact should be
taken into consideration in determining the value of m in the
formula.

For the present the value of merchantable stands which also
exert a protective influence will be calculated as previously
provided for, and no attempt made to charge for loss in protec-
tion during the period in which a new stand is being established.
Similarly, no charge will for the present be made for the pro-
tective value of brush or grass covers.

IV. ImprovEMENTS

The value of all improvements destroyed, such as cabins,
barns, fences, telephone lines, etc., should be included in estimates
of fire damages. This value should be based wherever possible
on the original cost of construction, and where this is impossible
on the cost of replacement. In either case an allowance should
be made for depreciation of the improvements, in order to
determine their actual value at the time of destruction.

V. Fire FIGHTING

Full damages should be collected from the trespasser for the
cost of extinguishing the fire, including salaries and expenses of
Forest officers, wages of temporary labor, supplies, tools, teams,
and miscellaneous items.

These instructions, though intended specifically for fire dam-
ages, will apply with equal force in gauging other forms of damage
to forest property. Further details regarding the appraisal of
damages will be found in Chapman, “Forest Valuation,” Chapter
IX; Roth, ‘Forest Valuation,” Chapter VII; and Fernow,
“Considerations in Appraising Damage to Forest Property,”
Forestry Quarterly, Vol. III, pages 119-142.

In all cases

. a thorough field examination and careful estimate

of the extent of the damage is essential. It is advisable to have
this work supervised by some one of experience who can later
qualify in court as an expert.
CHAPTER XVI
FOREST ADMINISTRATION

123. Introduction. — Forest administration deals with the
principles of business conduct and the methods employed in the
administration of forest properties. It divides into two parts:
I. Whose are the duties of forest administration? J.e., organ-
ization of forest staff. II. What are the duties of forest adminis-
tration? J.e., business practice. Only the first of these is
within the scope of this book.

124. Organization of Forest Staff. — Here the task is to secure
the best possible arrangement of human labor with respect to
the work to be done in the forest. It varies according to char-
acter of owner (federal, state, communal, private), size of property,
and intensity of management. With changing conditions, the
ideal is constantly changing hence one must consider what,
under a given set of conditions, is the best form of adminis-
tration.

The subject of organization of forest staff may be divided into
(A) functions and grades, (B) distribution according to area,
and (C) personnel relations. These will be considered seriatim.

125. Functions and Grades. — The activities of a forest staff
may be classified as: (1) directive, (2) inspective, (3) executive,
(4) protective, and (5) special detail. These will be taken up
in the order named; the organization of the U. S. Forest Service
as shown in the accompanying chart will be used as an example.

126. Direction. — This may be handled in one of two ways.
Either Bureaucratically by means of a Director or Collegially by
means of a majority vote of the Committee or Commission
directing the work. The former is of advantage where quick
decisions are to be reached and matters pushed vigorously. In
it, the responsibility is fixed upon the individual. The latter
is of advantage where long and careful consideration must be

209
FOREST ADMINISTRATION

210

‘QZ ‘OLY

u3DNVE
asauod

wOSIAUadNS
4gau0s

DNIAVUDNa AHEVEDOLOHA gyqiy ONILIVED gaanune
SABAENG

anv
WBMOd YaLYA eave sovou

—_—__4—_____

ONIUASNIONS
:UO|JeZjULBIO BujMojjo}, ey
UUM YoURIg azezeEdas & epew
uaeq souls sey Bujsoou/Bug 4

   

 

         

    

    

S$i83u03
WNOLLYN
sob

YaINIONA LOYL8IC
4N39DV WWosid
431934Os LOINLSIC

BNOlLVLG
SNA Sox

   

 

   

             

6301940 LOWLSIC £

 

  

NOLLYuag009
avis

Nov4vaad009
wWwiz0m

ae fssmone]
193803
SNOLLTBLLS3ANI e210n4s O1LLYHASINING
Twiwisnon 1say03 CELIFS
} Houv3say | BYNLINDIATS

L ]

 

AaNvdno30

| Seg cuy H- ouineas | | erua Led siuvannoe | |

| OULNOD } | Noravoraissy19 [ [vaNnoswag any
waaay | Buln ee SAaAUNB b own ™| JONVNBLNIVR cee |
4. YaSNION] 43IHD

ONIZVED | sanv1 | NOILvuad0
¥O.LIGg

83183404 ALVIOOSSY
¥3.1S3y403

     

  

 

 

 

 

ONVSSIvNNOOaY
‘w3OMiL ONY
SNYId ONIHOM

 

BSABAUND

     
 

 

 

 

 

 

  

NOILISINDOV

 

 

 

SLNNOD0V

 

 

 

9161 ‘1 AaNNP ‘Z0IAN3S LS3yNOs 40 NOILVZINVOHO ONIMOHS LYVHO
INSPECTION 211

given, e.g., in mapping out a program of research work, in legal
matters, in judging complaints against subordinates, etc.

The individual assignment of the directive work, i.e., jurisdic-
tion, may be according to area or according to subject. In the
former, the official handles all cases in his particular area; in the
latter all cases in his particular line of work. In practice, routine
direction and inspection are according to area; law, fiscal
matters, forest organization, according to subject. The former
has the advantage of exact acquaintance with local conditions;
the latter exact acquaintance with the field of activity. The
larger the area and the more diverse the conditions encountered,
the more is the area division to be recommended. However,
specialized subjects are better handled by one man —e.g.,
forest organization — for the whole District.

127. Inspection. — Is secured either by (1) the appointment of
special inspectors or by (2) the district officers doing the inspect-
ing themselves.

The District Inspector system is one of Centralization, e.g.,
all handled from Washington, with long distance correspondence.
The inspectors have no authority to correct things on the ground;
they merely report — usually at great length.

The District Forester system is one of Decentralization. Its
advantages are: -(1) greater local knowledge on the part of those
called to decide. (2) The results of inspection can be applied
directly by the inspector, himself and watched by him. (3)
Diminished correspondence and “paper work.” The only dis-
advantages are that personal prejudice may enter into decisions
and that the inspecting officer may not be quite so capable.
The District Forester system is, with us, still according to
subject. Each Assistant District Forester covers his subject for
the entire area of the District. This is inevitable with present
specialization —i.e., the Assistant District Forester in charge
of Grazing is scarcely in a position to decide Timber Sale ques-
tions and vice versa. However, an area assignment is the ideal
towards which to strive. It has been attained abroad, where
each Assistant District Forester is directly responsible for a
group of forests and must visit them at least twice a year.
212 FOREST ADMINISTRATION

128. Execution. — This is the most important part of the
whole administrative organization; for it involves the direct
execution of the policies formulated by the higher officers and is
also the first point of direct contact with the users of the forest.
An administration stands or falls according to the caliber of its
men on the ground. It is useless to formulate elaborate rules and
regulations, to issue stimulating circular letters, etc., if the
executive personnel is not developed to carry them out. From
the business standpoint too, the profitableness of a forest depends,
in large measure, upon the enterprise of the executive in charge.

The supervisor must not be overloaded — this refers not only
to his technical duties, but also to the malpractice of making the
supervisor a policeman as well.* This is the reason why super-
visors and rangers should not be deputy sheriffs. Another reason
is because they may not receive any pay for extra-federal services.

The supervisor should, obviously, be a technically trained
man in order to do justice to his position and its possibilities.

The supervisor must not be burdened with purely mechanical
work, 7.e., he must have adequate clerical assistance to take care
of correspondence, records, accounts, etc.

One of the most important parts of forest administration is
the carrying out of the working plan and taking care of its
control and revision. This needs, on the part of the supervisor,
a knowledge (1) of local conditions, (2) of methods of forest
organization. The former is achieved by every supervisor.
The latter is asking too much — the field is too specialized, and
means too much extra work for the supervisor, to be done by
him without adequate assistance. Hence forest organization is
properly the task of a central office with a corps of trained men.

Where there is no special office for forest organization, there
should be, at least, certain higher officers especially entrusted
with the direction of forest organization, with a staff of helpers
to do the necessary field-work.

The deputy supervisor, the forest examiner and even the forest
assistant, all assist in the executive work under the supervisor’s
immediate direction.

* See “Administration of a Prussian Forest,” For. Quart., Vol. XI, No. 1.
PROTECTION 213

129. Protection. — The protective service comprises the rangers
and their assistants. At first the rangers were chiefly occupied
in preventing poaching (‘‘King’s Foresters”), fire, theft of wood,
etc. Gradually, technical duties have devolved upon them.
The work which they perform varies greatly in different countries
and under different conditions and with the training and ability
of the individual. The ranger must at least be able to execute
the technical directions of the supervisor and to judge when
these are insufficient and further directions must be obtained.

The larger the ranger district and the more extensive the
management, the more independent and responsible is the posi-
tion of the ranger until it may approach that of the true head
ranger, who is a supervisor-in-parvo. ‘The increasing education
of the ranger has led, abroad, to the placing of additional responsi-
bility on him and to increasing the size of his district — as far
as is compatible with the intensity of management.

Under the District Ranger scheme the proper education of the
incumbent officers is essential. This means efficiency. It also
means increased expense for better salaries. Hence, the employ-
ment of mere woodsmen, untrained in technical lines, is cheaper.
This is known as the Forest Guard system, and is what we find
today in the U. S. Forest Service — disregarding the slight
training at “Ranger Schools” which some of our rangers have
enjoyed. The efficiency of this system depends directly upon
the personal equation.

In Europe, the District Ranger system is increasing because
of the increasing intensity of management. Even those states
where the other system still exists are planning for a change to
the former, by providing for the education of men already in the
Service.

Only in small administrative units is this system of untrained
rangers desirable since the supervisor or his technical assistant
cannot, as a rule, give their personal attention to the details of
a ranger’s work. It is also indicated under very extensive
management; indeed, with respect to the low income usual
under such conditions, it is often necessitated there in order to
keep down expenses.
214 FOREST ADMINISTRATION

Various combinations of the two systems are found. Thus,
in France, the well-educated ranger has untrained assistants.
We, too, have this. The District Ranger is assisted by guards —
chiefly, however, for fire patrol and improvement work (roads,
trails, telephone, cabins, etc.).

Rangers, then, should not be over-burdened with executive
work, especially not with such executive work as is beyond their
capacity and training; but they should be trained to perform
the simpler executive functions which are their proper sphere
and which they can perform more economically than anyone
else.

130. Special Detail. — This includes certain lines of work
which, in their very nature, require the use of specially trained
men. Such work cannot be efficiently executed by the regular
personnel and it becomes necessary, therefore, to detail men
especially to it. The attempt to have untrained men handle
this work may be seemingly more economical but in reality it is
more expensive; for the work must, in many cases, be done over
by a trained personnel.

Among the many kinds of work requiring special detail for
efficient execution may be cited:

(a) Survey and improvement work of a technical character.

(b) Working plans. Forest organization is a technical subject
requiring special training and capabilities. This is true even of
the field-work of forest organization — forest surveys. Experi-
ence has shown that for good results the work must be done by
special parties, mot as a part of the ranger’s district work —
however alluring this may seem from the standpoint of economy.
Both here and abroad the preparation of working plans is being
placed pretty generally in the hands of especially detailed men.
However, the supervisor has general control of the party while
they are on his forest. He maintains, or should maintain, an
active advisory and coéperative attitude which is the more
important, since, without it, the party is deprived of his valuable
local knowledge and experience.

The same is true of the ranger in whose district the party may
be at work; indeed, the district ranger is often assigned to the
DISTRIBUTION ACCORDING TO AREA 215

party — frequently at his own request—in order to gain
familiarity with forest survey methods.

(c) Investigations or Research.— The research work on the
forests must be coérdinated and this involves centralized control.
The district office issues the necessary instructions for this most
important work. Usually, the experiment stations are the foci
of investigative activity in the district.* These have, of course,
their own specially trained personnel and operate under an
annual program formulated by the District Investigative Com-
mittee and approved by the Central Investigative Committee in
Washington. In addition, forest assistants or forest examiners
attached to certain forests may pursue research work independ-
ently of the experiment station. Experience has shown that
here, too, routine work often impedes research and seriously
reduces in value the results secured.t Investigative work
requires, for its full fruition, special details. Ambitious officers
should, however, be encouraged to do work along these lines as
they have time and opportunity or where such work is urgently
needed.

131. Distribution According to Area. — The activities of the
administrative units must be delineated not only according to
the subject of work but also according to area. A conflict in
area is just as much to be avoided as one in subject. The area
is ‘to be sufficient so as to require the full working ability of an
average man; temporary increase in the amount of work can be
met: ‘

(a) By temporarily increased activity on the part of the
forest officer.

(6) By assignment of temporary assistants.

The central office invariably comprises the whole country and
is located at the capital. The districts usually coincide with
the political boundaries of certain states or groups of states.

Where the district officers act as inspectors, each of a certain

* See Pearson, G. A., “‘The Administration of a Forest Experiment Station,”
For. Quart., Vol. XII, No. 2, pages 211-222.

+ A good example of this is the gathering of data for volume, growth, stand,
and yield tables. For such data local executive officers can seldom be depended

upon.
216 FOREST ADMINISTRATION

group of forests, the whole district is not made larger than the
personnel can cover; figuring that each district officer shall visit
each forest within his group several times a year, besides hand-
ling his routine work in the district office. Means of communi-
cation and the size and accessibility of the individual forest play
an important part in deciding upon the size of districts. Size
and accessibility tend to counterbalance each other inasmuch as
mountain forests which by reason of their topography are more
inaccessible and hence justify smaller districts are, at the same
time, less intensively managed, allowing larger sized districts.

In Europe the district of each inspecting assistant district
forester comprises about 60,000 acres. Within the district
proper there are usually 300,000 acres, depending upon the
number of inspecting assistants. ,

In the United States, the seven districts, on June 30, 1918,
comprised 152 National Forests with a total net area of
155,374,002 acres. This is an average of about 22,000,000
acres in each district.

Considerations similar to those given for districts, govern in
determining the area of the individual executive unit, and, in
addition, the following:

(a) Does the supervisor or head-ranger system exist on the
forest?

(b) Of what caliber are the executives and what preparatory
training have they had?

(c) What is the nature of the business, e.g., small business —
small timber sales, many grazing permittees, greatly increase
the amount of routine.

The proper area of an executive unit is to be so determined
with reference to these and the aforementioned considerations,
that the executive may be fully responsible for his administra-
tion in all its details and may be independent of his subordinates’
judgment in passing upon the efficiency of the work on every
part of his forest. The deputy forest supervisor is not to be
considered a subordinate in this respect. When the work on a
forest is very complex, men may be assigned to assist the super-
visor in special lines — e.g., timber sales, grazing; in their par-
DISTRIBUTION ACCORDING TO AREA 217

ticular lines they represent the supervisor’s office whenever they
go in the field and speak with his authority, though they are, of
course, responsible to him.

In Europe the size of the average executive unit is about
6000 acres. In the United States the 152 National Forests
average 1,022,200 acres each.

In Europe increasing intensity of management has made for
decreased size of executive units. However, experience has
taught that there is a distinct limit in this direction, beyond
which further reduction in area is uneconomical. It is poor
policy to have a high-priced official doing work which a cheaper
subordinate is equally capable of performing. The tendency in
European forest administration is towards a better training of
the ranger force, the assigning of adequate clerical assistance and
the fullest possible utilization of all modern means of communi-
cation (automobiles!). This tendency, will, undoubtedly, lead
to an increase in the size of the executive units. Even now, a
forest of less than 5000 acres is considered uneconomically small
unless the forest is very much split up. Schwappach* says:
“7200 acres can, other things being equal, be quite intensively
administered by a single executive, and, under simple conditions,
in level country, an area of 12,000 acres is not too large.”

The choice of headquarters is a very important matter. It
must be centrally located with respect to the forest, and, at the
same time, be accessible to forest users and offer to the super-
visor’s family opportunities for social and religious intercourse
and for the proper education of children. However much the
young bachelor may revel in the freedom of a headquarters
remote from civilization, he will be more than likely to change
his opinion when married and with a family to bring up.

In deciding upon the area of ranger districts the following
conditions govern:

(1) The topography and the kind of timber, i.¢., open or
dense, softwood or hardwood, etc.
(2) The geography of the forest, 7.e., configuration.
(3) Intensity of management and degree of settlement.
* In Lorey, “Handbuch der Forstwissenschaft,”’ Vol. III, 3rd edit., 1912.
218 FOREST ADMINISTRATION

(4) Fire danger.
(5) Training of the ranger.
(6) Whether the district ranger scheme is in effect or not.

In Europe the average size of a ranger district is about 1440
acres. In the United States proper, it approximates 60,000
acres. Rangers should be stationed in or close to their districts;
with them the demands for an agreeable social environment are
not so pressing. A district ranger can handle a larger area than
the unassisted ranger. In certain districts winter work is out
of the question. All but the regular rangers are laid off during
the winter; in the summer they are given adequate assistance to
handle their districts which are usually larger than is the case
where field-work is possible the year round.

132. Personnel Relations. — Under this heading come (z)
appointment, (2) promotions, and (3) pay. The subject of
qualifications might be added but it will suffice to quote Dr.
Schenck’s famous definition of what a forester should be. “A ~
forester,” he said, ‘‘should stand the life in the woods like a
tree and should stand the knocks in the mill like a log, lest he go
to waste with the culls.” *

133. Appointment. — There are two possible ways of recruiting
personnel in forest administration. (a) By examination. (6)
By arbitrary appointment. The former, exemplified by the
system of civil service of which the federal forest service is a part,
safeguards the employees from political influence and ensures
stability regardless of changes in the party in power. The
arbitrary appointment may result in higher efficiency but, in
complex organizations, such as the national forest administra-
tion, employing over 3000 men, it is apt to be bound up with
injustice to the individual, with party politics, and even with
graft.

Admission to the government service is, with the rare excep-
tions of experts, dependent upon the passing of examinations.

* See also, Pinchot, G., “The Training of a Forester,” J. B. Lippincott, Phila-
delphia, Pa., 1914, especially pages 63-71. Also Redington, P. G., “The Place
of a Forest Supervisor in the Community,” American Forestry, March, 1914,
pages 182-184.
APPOINTMENT 219

For the United States Forest Service these are held by the
Civil Service Commission and are subject to its rules and
regulations. The most general entrance examination is that
of forest assistant. The passing of this single examination
enables promotion to any position in the service. The papers
are prepared and marked by officers of the service, chiefly in
Washington.

In Europe, three examinations are generally requisite for
entrance into the administrative service. At government
forest schools the professors (who are also government forest
officers) themselves conduct the preliminary examinations. In
some cases * the examinations are held by a commission com-
posed of higher officers. It has been found that these higher
officers are not as well qualified to judge the technical
knowledge of the applicants as are the professors, who, in
the nature of things, are more conversant with important tech-
nical developments. Furthermore, the examination must, in a
measure, be based upon the ground covered in the school’s
curriculum.

The final examinations t are always conducted by higher
officials of the service.

Examinations for the ranger service are, in the United States,
also conducted by the Civil Service Commission (assistant
forest ranger examination). The papers are prepared in Wash-
ington but are marked by the respective district forester and his
assistants.

In Europe an examination is omitted where the forest guard
system obtains.{ Where there are ranger schools § an examina-
tion is held at the completion of the course. In certain European
states, examinations are also required for the attainment of
ranger positions in communal and private forests.

Admission to the government forest service is by no means a
guarantee of employment. This is true both here and abroad.*

* See “The Prussian Forest Service,” Part I, For. Quart., Vol. XI, No. 1,
pages 42-53.

t See For. Quart., Vol. XI, No. 1, page 47.

¢ See Article 129.

§ See For. Quart., Vol. XI, No. 1, pages 50-53.
220 FOREST ADMINISTRATION

The forest assistant in the Forest Service of the United States
enters upon a two-year apprenticeship under an experienced ranger.
134. Promotion. — In the interest of the service and of the
forest officers, it is necessary that promotion to higher positions
be according to a just and equitable system which avoids even
the semblance of arbitrariness and nepotism.
Three main methods of judging fitness for promotion are:

(1) The results of examinations.
(2) Length of service or seniority.
(3) Special qualifications within and without the service.

The first method — that of examinations— although it con-
stitutes a fairly good basis for judging the knowledge of the
applicant, is not an index as to whether the candidate is really
qualified for the demands of the position; this drawback becomes
more pronounced the longer the time since the examination was
passed. :

From the pedagogic standpoint it is hardly necessary to point
out the unsatisfactory index to ability furnished by examinations
—even in highly theoretical subjects. How much more so is
this true of a subject like forestry, combining in a rare degree
high technical and practical qualifications!

The scheme of requiring an examination before promotion to
a higher position, or at least to certain higher positions, has been
tried in forest administration (Hannover) but without satis-
factory results since, in the first place, formal examinations are
scarcely suitable for men of advancing years, smacking, as they
do, of the classroom; and, in the second place, it is.exceedingly
difficult to combine the multiplicity of demands made upon a
higher administrative position into a single suitable examination.
A better test would seem to be the incumbent’s record in the
position held. His incumbency will, ordinarily, furnish abundant
evidence as to his fitness for a higher office. The stimulus for
further study which examination for promotion furnishes is not
sufficiently advantageous to offset the disadvantages mentioned.
The right kind of man will continue to study and improve himself
anyway.
PROMOTION 221

(2) Promotion according to length of service is based on the
presumption that those who have been in the service the longest
time have gathered the greatest store of experience and hence are
best fitted for promotion; that, furthermore, they aré more
entitled to it than are newer incumbents. The method avoids
any seeming arbitrariness in promotions and accords with the
view that after a certain length of service a man deserves advance-
ment. The great disadvantage of this method lies in the facts
that:

(a) The higher positions demand certain extra qualifications
which are apt to be lacking in the majority of men who reach the
intermediate places.

(6) Promotion by seniority is apt to postpone the reaching of
higher, positions to an age when the incumbents may lack the
mental freshness and initiative so necessary for constructive
work, and, perhaps, the bodily vigor requisite for arduous field-
inspection duty. By basing promotion to high positions on
seniority the incumbents are apt to change too frequently for
the good of the service — that is, they seek retirement just when
they have “learned the ropes.”

This method, therefore, will not suffice in all cases.

(3) Where special qualifications of an incumbent are made the
basis of promotion, it is necessarily according to the judgment of
some superior officers. It may be entirely arbitrary, as in the
reputed “one-man” methods of the late James Hill in the per-
sonnel of the Great Northern Railway. Usually, however, a
committee of superior officers will, periodically, consider the
qualifications of all subordinates and make a “‘slate” for pro-
motion. At the same time, this review serves as a basis of
judging whether incumbents are satisfactorily filling their
present positions or whether demotion or even dismissal (or
forced resignation) are in order.

Modern methods of efficiency demand that incumbents be
informed not only of satisfactory work but also of shortcomings
in order that they may be given the chance to overcome their
deficiencies. Needless to say the communication of such adverse
findings requires the greatest tact. The “slate” for promotion
222 FOREST ADMINISTRATION

is published in France (tableau d’avancement) and the committee
charged with promotions (conseil d’avancement) consists in part
of subordinate officers, two representatives being chosen for each
subordinate position up to and including the brigadiers (rangers) ;
’ within their own rank these representatives can vote, for other
ranks only advise. ;

The very highest positions and also the positions of especial
difficulty are always filled by direct appointment of particularly
well qualified men.

In conclusion it would seem expedient to:

(a) Follow the method of examination for filling the sub-
ordinate positions; grading the men according to the marks
achieved in the examination and appointing them in that order.

(b) Promote to intermediary positions (executive, protective,
etc.) according to seniority of service.

(c) Promote to higher positions (inspective) according to
promotion ‘‘slates’” drawn up by a committee of higher officers.

(d) Promote to highest positions (directive) by special ap-
pointment (e.g., the position of Forester in the Forest Service
is filled by presidential appointment, although the incumbent
must have passed a civil service examination).

Transfer from one post to another, where the move is in the
nature of a promotion, should never be without the consent of
the promoted except where it is necessary ‘‘for the good of the
service.”

135. Pay.— Certain general principles of remuneration for
services may be formulated. These, rather than the presenta-
tion of statistics of actual salaries paid, are the object of this
article.*

In the first place, the time of initial employment without
compensation should be as short as possible, preferably zero.
Second, there should be a proper relation in the pay of the differ-
ent positions. Third, the salary paid should be sufficient so that
the incumbent and his family may live thereon in a manner

* Woolsey, T. S., Jr., in “Forest Service Revenue and Organization,” For.
Quart., Vol. XIV, No. 2, pages 188-235, gives on page 207, a “Comparative
Table of Main Titles and Salaries” in the United States, France, Austria,
PAY 223

commensurate with the dignity of the position and of the organ-
ization which they represent. He should be able to live with-
out enforced recourse to private means, and to educate his
children properly. Fourth, the forest officer should, before too
advanced an age, attain the right of retirement on an adequate
pension. ;

One man does not make a forest service but the whole service
is often judged by the individual representative encountered.
If through insufficient salary he is forced into a penurious form
of living it may react unfavorably on the service.

For the government service a fifth condition should be added;
the pay should approximate that received for similar services in
private employ. So far our government technical services have
been a procession. Men enter, are trained to efficiency and then
accept more lucrative positions elsewhere. This is false economy
disguised as an apparent saving. Though the salary roll may be
lower, how about the costly mistakes made by inexperienced
men, the loss in prestige and efficiency due to constantly chang-
ing personnel? ‘‘No man,” says Carlyle, ‘‘works save under
conditions.” To the young unmarried man, the forest assist-
ant’s initial $1200 a year seems bounteous. Ten years later, with
wife and one or more children, he finds that he cannot live on
his salary — and for his family’s sake he leaves the service for
a more lucrative position, hard as the change may be. Surely,
this is not good for the ésprit de corps for which the United States
Forest Service is justly famous. Why should the French Forest

British India and Prussia. The following salaries are given for the U. S. Forest
Service:

Forester............ $5000 per annum
I. Washington Office } Assistant Forester......... 3000-3500 WN. B. Since
Forest Inspector.......... 2700-3200 July 1, 1977,
i all salaries
District Forester.......... 3000-3200 from $1200 to
Salty ssistant District Forester.. 2700- $1800 per an-
II. District Office Hecsias A é num have been
Forest Examiner.......... 1400-1800 in pee
Forest Assistant.......... 1200-1400 cent, all those
4 under $1200
Supervisor... Waters ee ees 1800-2400 lave Been ee
Deputy Supervisor........ 1400-1800

creased ro per

AT: -Natonsl, Roses Forest Ranger............ 1200-1500 cent.
224 FOREST ADMINISTRATION

Service, for example, command the services of the best foresters
in the country and maintain them on its rolls throughout their
active lives? Is our patriotism less pure; is our ideal of service
less high? The American Forest Service of today is too largely
a training ground —a costly one if efficiency and progressive
work count in government as well as in private enterprise.

Two systems of increasing pay are possible aside from arbitrary
increases or ‘‘promotions.” In one, the advance to higher
salary is automatic upon completing a certain term of service
or reaching a certain rank. In the other, only a certain per-
centage of the incumbents of each position are entitled to the
increased pay, and vacancies occur only through promotion.

Forest officers of the executive and protective service are, from
the nature of their occupation, required to live in small communi-
ties or even remote from other habitations. It is necessary,
therefore, that they be furnished by the service with proper
dwellings and places of business. This has been recognized by
our forest service in the construction of ranger cabins. Super-
visors are but rarely furnished with houses; in fact, only when
suitable dwellings cannot be rented by them. Rangers should
be given free pasturage (in addition to forage allowance) and it
is expedient to have some arable land in connection with the
ranger stations for the production of garden truck. Where
fodder is raised by rangers in considerable quantities, propor-
tionate deduction is made from the forage allowance.

A source of increased expense arises from the frequent neces-
sity of providing for the education of the children by means of
private tutors if schools are too distant. In certain cases this
has led to a supervisor seeking transfer from an otherwise very
desirable post. Medical help, also, is more difficult of access,
more expensive and less efficient; finally, many zsthetic enjoy-
ments, such as theatres and concerts, must be foregone as well
as agreeable social intercourse. There is, further, very little
opportunity for participation in religious exercises. These
considerations have led, in Europe, to the granting of additional
emoluments in the form of free dwellings, arable land, free con-
veyance, free fuel, and certain incomes from fish and game.
PAY 225

These emoluments, in part, are still in force; however, the modern
money-basis of life, the necessity of equality in pay of different
posts of the same grade, is putting them in abeyance. More
and more the old system of making emoluments a part of the
salary is being displaced by granting pay to the full value of the
emoluments and charging the incumbent rent for house, arable
‘land, etc. In return, he is granted reimbursement for upkeep
of wagon or automobile (mileage for the latter) and subsistence
when away from his official station.
APPENDIX

TABLE 1
SuRvEyor’s MEAsSvRE (LINEAR)
rt link = 0.01 chain = 0.66 foot = 7.92 inches.
roo links = 1.00 chain = 4rods = 66 feet.
80 chains = 1.0 mile = 320 rods = 5280 feet.
TABLE 2
SURVEYor’s MEASURE (SQUARE)
1 acre = 160 sq. rods = 10 sq. chains = 43,560 sq. feet.
40 acres = a square the side of which is } mile.
640 acres = 1 sq. mile, or section.
36 sections = 1 township = 23,040 acres.
TABLE 3
Area of triangle = 3 base X altitude.
Area of circle = rr? = 3.1416 7?
= a = 0.7854 D*.

Radius of circle whose area = 1 acre = 118 feet (approx.)
Radius of circle whose area = 3 acre = 83 feet (approx.)
Radius of circle whose area = } acre = 509 feet (approx.)

TABLE 4
USEFUL EQUIVALENTS AND CONVERTING Factors *

1 cord (fuel wood averaging 5” or less in middle

diameter) size of pile 4’ X 4’ X 8’ = 333% bd. feet
1 cord (fuel wood averaging 6” or more in middle
diameter) size of pile 4’ x 4’ x 8’ = 500 “
1 cord of spruce pulp-wood =560 “
1 telephone pole 7” X 30’ = 60 “
1 telephone pole 9” x 30’ =100 “
1 standard tie 6” x 8” x 8! = jo
1 tie 7" X90" XxX 8 = 35 *
1 post 6" x 7 = 7 «
1 cubic foot (round timber) = 6 *

* Taken from “ The National Forest Manual,” Silviculture Section, p. 64, 1915..
226
 

 

 

 

 

 

APPENDIX 227
TABLE 5
VOLUME OF SOLID Woop IN STACKS
4 ft. high, 8 ft. long, and ro in., 12 in., 14 in., etc. wide
Ist class: 2nd class: 3rd class: sidend ard
Wick. | sal citer] small diameter | small ameter | clases mised. | cases mid
Cusic Fest.
Inches.

10 19.50 17.50 14.00 18.50 15.75
12 23.50 21.00 16.00 22.25 18.50
14 27.32 24.50 19.00 25.91 21.75
16 31.00 28.50 21.50 29.75 25.00.
18 35.00 32.00 24.30 33-50 28.15
20 37-50 35.00 27.00 36.25 31.00
22 42.20 39.00 30.00 40.60 34.50
24 46.02 42.00 32.70 44.01 37-35
26 50.00 46.00 35.20 48 .00 40.60
28 53.21 ° 49.00 38.00 51.11 43-50
30 57.00 53.00 41.00 55.00 47.00
Feet.

3 68.50 63.00 50.00 65.75 56.50

4 88 .g2 82.42 63.62 85.67 73.02

5 108 .50 IOI .50 78.00 105.00 89.75

6 128.50 120.00 92.30 124.25 106.15

7 149.55 138.05 106.41 143 .80 122.23

8 170.00 165.00 119.90 167.50 142.45

9 190.00 175.00 133.50 182.50 154.25
Io 211.00 193.00 147.50 201 .00 170.25
II 230.00 210.50 161.20 220.25 185.85
12 250.00 228 .00 175.00 239.00 201.50
13 269.00 245.50 189 .0o 257.25 217.25
14 287.50 262.50 203 .00 275.00 232.75

 

 

 

 

 

 

Raphael Zon in For. Quart., Vol. I, No. 4, page 133.
228 APPENDIX

TABLE 6

ScRIBNER LoG RuLe!

(Decimal ‘'C’’)?

 

 

 

 

Length in feet.
Diameter Diameter
in 6 8 Io 12 14 16 : in
inches. : inches.
Contents in board feet.

6 0.5 0.5 I I I 2 6
7 0.5 I I 2 2 3 7
8 I I 2 2 2 3 8
9 I 2 3 3 3 4 9
10 2 3 3 3 4 6 10
- I 2 3 4 4 5 7 11
12 3 4 5 6 7 8 12
13 4 5 6 7 8 10 13
14 4 6 7 9 Io II 14
15 5 7 9 II 12 14- 15
16 6 8 10 12 14 16 16
17 7 9 12 14 16 18 17
18 8 IL 13 16 19 aI 18
19 9 is I5 18 21 24 19
20 II 14 17 21 24 28 20
21 12 15 19 23 27 30 2I
22 13 17 21 25 29 33 22
23 14 19 23 28 33 38 23
24 I5 21 25 30 35 40 24
25 17 23 29 34 40 46 25
26 19 25 31 37 44 5° 26
27 2r 27 34 41 48 55 27
28 22 29 36 44 5I 58 28
29 23 31 38 46 53 61 29
30 25 33 4l 49 57 66 30
31 27 36 44 53 62 71 3r
32 28 37 46 55 64 74 32
33 29 39 49 59 69 78 33
34 30 40 50 60 70 80 34
35 33 44 55 66 77 88 35
36 35 46 58 69 81 92 36

 

 

 

 

 

 

 

 

1 Taken from “The Woodsman’s Handbook.”

2 The total scale is obtained by multiplying the figures in this table by 10. Thus the contents of a
6-inch 8-foot log are given as 0.5, so the total scale is 5 board feet. A 30-inch caine log is given
as 66, or a total scale of 660 board feet.
 

 

 

 

 

 

 

 

APPENDIX 229
TABLE 7
CrarRK’s INTERNATIONAL LoG RULE}
Length in feet.
Diam-
eter in| 8 9 Io Ir 12 13 14 15 16 17 | 18 | 19 | 20
inches.
Contents in board feet.?
Vv
6 Io| ro] ro} 15] 45} 15} 20] 20) 20) 25 25 30 30
7 I5} 5} XS} 20) 20) 25) 25; 30) 30] 35 35 40 45
8 20; 20) 25) 25) 30) 35) 35) 40] 45) 45 5° 55 60
9 25| 30} 30] 35] 40] 45] 50] 50] 55| 60 65 7° 75
1o | 30) 35} 40] 45] 50) 55] 60) 65| 7o) 75 85 99] 95
Ir 40] 45] 50) 55! 65} 70) 75] 80! go} 95 105 110 | 115
12 50} 55] 65] 70] 75| 85] go| roo] 105] 315 | 125 | 130] 140
13 60} 65] 75} 85] go} roo} 110] 120} 130) 140 145 155 165
14 70| 80] go} 100] 110] 120] 130] 140] 150] 160 175 185 195
15 80] go] 105) 115] 125] 140] 150] 160] 175| 185 200 | 215 225
16 95| 105} 120] 130] 145] 160] 170! 185] 200] 215 230 | 245 | 260
7 | 105] 120) 135] 150] 165) 180] 195] 210] 225) 245 260 275 205
18 | 120] 135] 155] 170) 185] 205] 220) 240] 255) 275 295 | 310] 330
19 | 135] 155] 175] 190] 210] 230) 250] 270] 290| 310} 330] 350 | 370
20 | 150] 170] 195/ 215] 235] 255] 275] 300] 320] 345 | 365 |} 390 | 410
21 | 170| 190] 215] 235] 260/ 285) 305] 330) 355] 380 | 405 | 430] 455
22 185] 210] 235] 260] 285] 315] 340] 365] 390} 425°; 445 475 500
23 | 205, 230] 260] 285) 315] 345] 370] 400] 430/ 460 | 490] 520] 550
24 | 225] 255] 285] 315] 345] 375] 405] 440] 470] 500] 535 | 565 | 600
25 | 245] 275| 310] 345| 375] 410] 445] 475] 5t0| 545 | 580 | 615 | 650
26 | 265) 300] 335] 370] 405] -445| 480] 520] 555] 595 | 630°} 670} 705
27 290] 325] 365] 405] 440] 480] 520] 560] 600] 640 | 680 725 765
28 | 310] 350] 395] 435| 475| 520] 560] 605] 645) 690 | 735 | 780 | 825
29 | 335] 380] 425] 470] 510] 560] 605] 650] 695) 740 | 790 | 835 | 885
30 | 360] 405] 455] 500] 550] Goo] 645] 695] 745] 705 | 845 | 895 | 95°
31 | 385] 435] 485] 540] 590] 640] 695] 745] 800] 850 | 905 | Q60 | IoI5
32 | 410] 465| 520] 575] 630] 685] 740] 795] 850] 910 | 965 | 1025 | 1080
33 | 449} 495] 555] 610) 670] 730) 790) 850) 905} 970 | 1030 | IO9O | II50
34 | 470) 530] 590] 650] 715] 775] 840} 900] 965/ 1030 | 1095 | 1160 | 1225
35 | 495] 560] 625] 690] 755] 825] 890] 9551025] 1095 | 1160 | 1230 | 1300
36 | 525] 595] 665) 735| 800] 875] 945)1015/1085] 1160 | 1230 | 1305 | 1375
37. | 560} 630] 705] 775] 850] g25|1000|1075|1150] 1225 | 1300 | 1380 | 1455
38 | 590) 665] 745] 820] 895) 975)1055]1135|1210) 1295 | 1375 | 1455 | 1535
39 | 620] 705| 785] 865] 945|r030/1110/1195|1280| 1365 | 1450 | 1535 | 1620
40 | 655| 740] 825] g10| 995|1085|1170|1260|1345| 1435 | 1525 | 1615 | 1705
41 690} 780] 870| g60/1050/1140]1230/1325/1415| 1510 | 1605 | 1700 | 1705
42 725] 820] 915|1010|1100|1 200|1295|1390|1490| 1585 | 1685 | 1785 1885
43 760| 860] 960|1060|1155]1260/1360|1460|1560] 1665 | 1770 | 1870 | 1975
44 | 800} goo|1005|1110/1215|1320/1425|1530|1635| 1745 | 1855 | 1960 | 2070
45 | 835] 945|1055|1160/1270|1380/1490|1600|1715) 1825 | 1940 | 2050 | 2165
46 875] gg0|1100|1215|1330|1445|1560|1675|1790) IgIO | 2030 | 2145 2265
47 | 915|1035]1150|1270/1390|1510/1630|1750|1870| 1995 | 2120 | 2240 | 2365
48 | 955|1080]1205/1325|1450|1575|1700|1830|1955| 2085 | 2210 | 2340 | 2470

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t By permission of Judson F, Clark.
2 The contents are tor logs sawn with band saws cutting one-eighth inch kerf.
230 APPENDIX

TABLE 8

ScaLE VALUES FOR BILTMORE STICK *
(6 to 30 inches)

d(a—-t)

Va(d+a)
d = the diameter of the tree, a= arm’s length, ¢ = thickness of the stick.

Calculated from the formula S = in which S = the scale value,

 

Values for S, when ¢ = } inch.

 

 

Diameter. @ = 23 inches. @ = 24 inches. @ = 25 inches. @ = 26 inches.
6 5.28 5.31 5.34 5.36
7 6.06 6.09 6.13 6.15
8 6.82 6.85 6.90 6.93
9 7-54 7-59 7.64 7-71

10 8.25 8.31 8.36 8.41
II 8.904 9.01 9.07 g.12
12 9.62 9.69 9.76 9.83
13 10.28 10.35 10.42 10.51
14 10.92 II .00 Ir .08 Il.17
15 11.54 Ir .63 II.72 11.82
16 12.15 12.25 12.36 12.46
17 12.75 12.86 12.98 13.08
18 13.33 13.46 13.59 13.70
19 13.90 14.04 14.18 14.30
20 14.46 14.61 14.75 14.89
21 15.01 15.17 15.32 15.47
22 15.55 15.72 15.87 16.05
23 16.09 16.26 16.42 16.60
24 16.62 16.79 16.95 17.14
25 17.13 17.31 17.48 17.67
26 17.62 17.82 17.99 18.20
27 18.11 18.32 18.52 18.72
28 18.60 18.81 19.04 19.24
29 19.08 19.30 19.54 19.74
30 19.56 19.78 20.03 20.22

 

 

 

 

 

* Calculated by Slide Rule (and hence correct only to nearest 0.02-inch).
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDIX 231
TABLE 9
AREA OF CIRCLES IN SQUARE FEET
TENTHS OF INCHES.
Diam- 2.0 0.1 0.2 0.3 0.4 05 0.6 °.
eter, R is \ . i : 7 0.8 0.9
AREA — SQUARE FEET.
Inches.
I 0.006} 0.007| 0.008] 0.009] 0.011! 0.012] 0.014] 0.016] 0.018] 0.020
2 0.022] 0.024] 0.026] 0,929] 0.031} 0.034] 0.037| 0.040] 0.043] 0.046
3 ©.049] 0.052) 0.056] 0.059} 0.063| 0.067] 0.071] 0.075] 0,079] 0.083
4 0.087] 0.092] 0.096] 0.101) 0.106) 0.111] 0.115] 0.121] 0.126) 0.131
5 0.136] 0.142] 0.147] 0.153] 0,159] 0.165) 0.171] 0.177] 0.184] 0.190
6 0.196] 0.203] 0.210) 0,216] 0.223] 0.230] 0.238) 0.245] 0.252] 0.260
7 0.267] 0.275) 0.283] 0.2911 0.299] 0.307] 0.315] 0.323] 0.332] 0.340
8 0.349 0.358 0.367} 0.376) 0.385] 0.394] 0.403] 0.413] 0.422] 0.432
9 0.442] 0.452] 0.462] 0.472) 0.482] 0.492] 0.503] 0.513] 0.524] 0. 35
Io 0.545] 0.556] 0.568) 0.579] 0.590] 0.601] 0.613) 0.625] 0.636 ar
ILI 0.660] 0.672) 0.684) 0.697/ 0.709] 0.721] 0.734] 0.747] 0.760) 0.772
12 0.785| 0.799] 0.812] 0.825] 0.839] 0.852] 0.866) 0.880] 0.894] 0.908
13 0.922] 0.936] 0.950] 0.965] 0.979] 0.994] 1.009] 1.024] 1.039] 1.054
14. | 1.069] 1.084] 1.100] 1.115] 1.131] 1.147] 1-163] 1.179] 4.195] 1.211
15 1.227]. 1.244] 1.260] 1.277| 1.294] 1.310] 1.327) 1.344] 1.362] 1.379
16. 4 | 1,396) 1.414] 1.431| 1.449] 1.467] 1.485] 1.503} 1.521] 1.539] 1.558
17 1.576] 1.595] 1.614) 1.632) 1.651] 1.670] 1.689] 1.700] 1.728] 1.748
18 1.767] 1.787] 1.807| 1.827| 1.847] 1.867] 1.887] 1.907] 1.928] 1.948
19 1.969] 1.990] 2.011] 2.032] 2.053] 2.074} 2.095] 2.117] 2.138] 2.160
20 2.181) 2.204) 2.226] 2.248) 2.270] 2.292] 2.315] 2.337] 2.360] 2.383
21 2.405] 2.428] 2.451] 2.475] 2.498] 2.521] 2.545] 2.568] 2.592) 2.616
22 2.640) 2.664) 2.688] 2.712] 2.737] 2.761] 2.786] 2.810] 2.835] 2.860
23 2.885} 2.910] 2.936] 2.961] 2.986] 3.012] 3.038] 3.064] 3.089] 3.115
24 3-142] 3.168) 3.194] 3.221] 3.247] 3.275] 3.301] 3.328] 3.355) 3.382
Diam | Area, |} Diam | Area. || Diam | Area. || Diam | Area. || Diam | area
Inches. | Sq. ft. || Inches. | Sq. ft. || Inches. | Sq. ft. || Inches. | Sq. ft. Inches. | Sq. ft.
25. | 3-41 32 | 5-59 39 | 8.30 46 | 311.54]/ 53 | 15.32
26 | 3.69 33 | $-94 40 | 8.73 47 | 12.05|/ 54 | 15.90
27 3.98 34 6.30 41 9.17 48 12.57 55 16.50
28 | 4.28 35 | 6.68 42 | 9.62 49 | 13.10 56 | 17.10
29 | 4.59 36 7.07 43 [10.08 50 13.64 57 17.72
30 | 4.91 37 | 7-47 44 |10.56 5t | 14.19 58 | 18.35
3 | 5.24 38 | 7.88 45 |I1.04 52 | 14.75 59 | 18.99

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

232 APPENDIX
TABLE 10
SaMPLE VoLuME TABLE FoR WHITE Pine IN NEw HAMPSHIRE
(From the ‘‘ Woodsman's Handbook,"’ Table No. 12.)
Height of tree (feet).
Breast- .
eee 30 | 40 | 50 60 70 80 go too | 110 | 120 (on
(in.).
Volume in board feet.

5 8] 12] 15 aie |) aes 7

6 | 13 | 20] 23] 27] 29 41

7 | 18) 28] 34] 39] 44 75

8 241 36] 45 53 62]... 128

9 | 32} 441 56] 69] 81 93 |... 156
Io | 41 | 53 7o | 85 | 102 | 119 | 138 177
II -. | 63 | 84 | 103 | 126 | 147 | 168] ... |... 164
12 73 | 1oo | 125 | 151 | 177 | 200 | 228 | 245 146
13 84 | 117 | 148 | 180 | 210 | 238 | 270 | 293 137
14 95 | 137 | 173 | 210 | 243 | 277 | 312 | 348 gI
15 105 | 158 | 200 | 241 | 282 | 321 | 362 | 406 61
16. .. | 181 | 230 | 277 | 323 | 370 | 415 1 470 88
17° 209 | 261 | 313 | 368 | gaz | 471 | 540]... 70
18 238 | 297 | 352 | 411 | 475 | 531 | 610 | 688 68
19 270 | 336 | 393 | 460 | 530 | 598 | 682 | 763 44
20 302 | 379 | 436 | 506 | 583 | 660 | 750 | 840 35
21 425 | 480 | 553 | 634 | 720 | 820 | 918 23
22 -++ | 522 | 597 | 681 | 779 | 887 | g90 16
23 «++ | 566 | 639 | 727 | 834 | 958 |1065 19
24 ..» | 674 | 769 | 889 |1030 |1135 9
25 706 | 809 | 942 [1105 | ... 12
26 737 | 846 | 994 |1180 II
27 sue | sev [TO4G | oes peace
1578

 

 

 

 

 

 

 

 

 

 

 

 

 

The volume given is actual saw cut. Sixty per cent was round-edged, and forty per cent

squared; seventy per cent, one-inch boards, and thirty per cent, 2}-inch plank.
APPENDIX

TABLE 11

233

SAMPLE VOLUME TABLE FOR YELLOW BircH IN NEw HAMPSHIRE

Volume in Board Feet

 

 

 

 

 

 

 

“ Number of 16-foot logs. Diam-
Diss - eter | gt,
Breast |} (ep | eae [a Tat inside | fevgnt. | Bass
ae Volume — board feet in tens. of top.
Inches. : Inches.| Feet. | Trees.
7 I I 2 3 le stand oped eaatiae 6 2.1 2
8 I 2 2 3 4: || sete aalcaineets 6 Qua 8
9 I 2 3 4 5 looms es|esewae 7 2.2] 24
10 2 Ji 4 5 6. hued vain 7 2.2] 43
Ir 2 4 5 6 Bl oeceasvese Paes aac 8 2.21) 44
12 3 5 6 8 Q Iaiawanfe care ee 8 2.2] 45
13 3 6 8 9 TE, pease ientstens 9 2.2 | 36
14 4 7 9 II 13 TA: lessees 9 2.3 | 35
1s 4 8 II 13 15 ID fectisiies 10 2.3) 47
16 5 10 13 15 17 TS! py steaiss II 2.3 | 40
17 6 II 15 18 20 OT Nsapeae II 2.4 | 32
18 7 13 17 20 23 2G Pacsueieiss 12 z.4] 38
19 8 14 20 23 26 28. Veen 13 2.4) 36
20 9 16 22 26 30 33 36 13 2.5} 39
21 10 18 25 30 34 37 41 14 2.5] 28
22 Il 20 27 33 38 42 47 15 2.6] 22
23 13 23 30 | 36 | 42 48 53 15 2.6] 24
24 14 25 33 40 | 47 53 59 16 2.7 | 21
25 15 27 36 44 51 53 64 16 2.7 | 23
26 |...... 30 40 48 56 63 7o 17 2.8 | 17
OT. Ws ieaes 33 44 52 61 69 76 18 2.9 14
28 A scoas 36 48 57 66 74 82 18 2.9] 17
20) Ye saceieas asad 52 62 71 80 88 19 3.0 7
BO We araturaa | aa. eacees 57 67 77 86 95 20 B./0i) ao
BT Laas eset et aaees.s 72 82 92 IOI 20 3-1 5
BS? [siarsiasced] oars’ at sua macss eee 78 88 98 | 108 21 3.1 5
651

 

 

 

 

 

 

 

 

 

Logs scaled as cut, 10 to 16 feet long, by Scribner Decimal C rule. Utilization as close as form

of tree allowed.

Taken from U. S. Dept. Agric. Bul. 285, ‘The Northern Hardwood Forest,” etc., by E. H.

Frothingham.
234 APPENDIX

TABLE 12
SAMPLE YIELD TABLE FOR WHITE PinB!

Yield per Acre for Pure, Even-aged, Second-growth Stands

 

 

 

 

 

 

 

 

Quality I.
3. | ee u et ps g
° & g 9 Og ah o
gi |fe) £,) = | s ai) ge] .| 2] s
go je] se] & | = ge | fe ise] & | 3
&| “a }se! ua ee & | “¢ gs Os ms
<| 98 jes! 3, | § a i<| se | 23 ]g5| # g
pe ecl B| 3 | & pe} ee |e") g | &
eS |Ad > 8 aad
ae |AS| 2 3 av |Aaal2 | 2
Yrs. | Feet. | Ins. Sq. ft. | Cu. ft. |] Yrs. | Feet. Ins. Sq. ft. | Cu. ft.
10 7.2 | 1.7] 1728 29 | 800 || 60 | 85.5 | 12.8 | 311 278 | 10,500
15 | 14.5 | 2.9] 1520 68 | 1400 || 65 | 90.5 | 13.7 | 279 286 | 11,300
20 | 24.5 | 4.0] 1322| 115 | 2100 |] 70 | 94.5 | 14.7 | 249 | 293 | 11,900
25 | 34.5 | 5.2] 1115] 162 | 3000 Il 75 | 98.0 | 15.6 | 226 | 300 | 12,500
30 | 44.0 | 6.4) 879 196 | 4000 |] 80 |1ro1.5 | 16.5 | 207 307 | 13,000
35 | 53-0 | 7.5] 710 218 | 5200 || 85 j105.0 | 17.4 | 190 313 | 13,500
4o | 61.0 | 8.6) 583 | 235 | 6500 |] go j108.0 | 18.2 | 177 | 319 | 14,000
45 | 68.0 | 9.7] 485 | 249 | 7700 || 95 |1r0.5 | 19.0 | 165 | 324 | 14,400
50 | 74.5 |10.8] 408] 260 | 8800 |iroo |113.0 | 19.8 | 154 | 330 | 14,700
55 | 80.5 {11.8} 354] 269 | 9700 ]....J......[.... fee ee eee eee fee cee
Quality I.
Io | 6.0] 1.4] 2015 20 | 650 || 60 | 74.5 | 10.7 | 397 248 | 8,500
I5 | 12.0 | 2.2! 1834 50 | 1150 || 65 | 79.0] 11.6 | 348 |, 255 | 9,200
20 | 19.5 | 3.2] 1626 go | 1750 || 70 | 83.0 | 12.4 | 311 261 | 9,840
25 | 28.0 | 4.1] 1420] 131 | 2420 || 75 | 86.5 | 13.3 | 277 267 | 10,400
30 | 36.5 | 5.1| 1192] 169 | 3250 || 80 | 90.0 | 14.1 | 251 272 | 10,930
35 | 44.5 | 6.11 950] 193 | 4180 |! 85 | 93.0 | 14.9 | 229 277 | 11,400
40} 51.5 | 7-1] 760] 209 | 5130 || 90 | 95.5 | 15.7 | 210] 282 | 11,850
45 | 58.0 | 8.0] 633] 221 | 6100 |] 95 | 98.0 | 16.4 | 195 286 | 12,250
50 | 64.0 | 8.9] 537] 232 | 7000 |I100 |100.0 | 17.1 | 182 290 | 12,630
55 | 69.5 | 9.8] 460] 241 | 7800 |/....f.... 0 fee fee ee ede ee ee ede eee eee
Quality III.
Io | 4.0] 1.0] 2408 14 | 530 || 60 | 64.0] 8.6] 543} 219 | 6,530
15 | 9.0 | 1.6] 2234 33 | goo || 65 | 68.0 | 9.4] 465 224 | 7,160
20 | 14.5 | 2.3] 2060 60 | 1350 || 70 | 71.5 | 10.1 | 412 | 229] 7,760
25 | 21.0 | 3.1] 1886 98 | 1850 || 75 | 75.0 | 10.9 | 361 234 | 8,320
30 | 28.5 | 3.9] 1676] 139 | 2450 || 80 | 78.0 | 11.7 | 318 | 238 | 8,820
35 | 36.0 | 4.7] 1400] 167 | 3100 || 85 | 81.0 | 12.4 | 288 242 | 9,300
40 | 42.5 | 5.5] 1118] 183 | 3780 |! 90 | 83.0 | 13.2 | 258 245 | 9,750
45 | 48.5 | 6.3] 900} 194 | 4500 || 95 | 85.5 | 13.8 | 239 | 248 | 10,150
50 | 54.0 | 7.0] 764] 204 | 5200 |]100 | 87.0 | 14.5 | 219 251 | 10,530
55 | 58.0] 7.8! 639] 212 | 5870 |]... J... fee pee ee el ee dee ee

 

 

 

 

 

 

 

 

 

 

 

 

 

1 Taken from ‘‘ White Pine Under Forest Management,’’ by E. H. Frothingham, U. S. Dept. of
Agr., Bul. No. 13.
APPENDIX 235

INDEX TO SELECTED VOLUME TABLES

Ash (black). — U.S. D. A., Bul. 299, pp. 85-86 (cu. feet), p. 86 (cords), p. 87 (bd.
feet).

‘Ash (green). — U.S. D. A., Bul. 299, pp. 81-82 (cu. feet), p. 83 (cords), pp. 84-85
(bd. feet).

Ash (white). — U.S. D. A., Bul. 299, p. 78 (cu. feet), p. 79 (cords), pp. 80-81 (bd.
feet).

Ash (white). — (Second growth) Vermont Agr. Ex. Sta., Bul. 176, p. 81 (cu. feet).

Aspen. —} U: S. D. A., Forest Service, Bul. 93, p. 34 (cu. feet), p. 35 (cords).

Aspen. —? U.S. D. A., Forest Service, Bul. 36, p. 113.

Balsam Fir. —+ U.S. D.A., Bul. 55, p. 50 (cu. feet), p. 51 (cords), pp. 54-55 (bd.
feet).

Balsam Fir. —* For. Quart., Vol. IX, p. 593.

Basswood. —! U.S. D. A., Bul. 285, pp. 55-57 (bd. feet), p. 61 (cu. feet).

Beech. —} U.S. D. A., Bul. 285, pp. 49-51 (bd. feet), p. 59 (cu. feet).

Beech. —* (Second growth), Vermont Agr. Exp. Sta., Bul. 176, p. 81 (cu. feet).

Birch (white or paper). —U. S. D. A., Forest Service, Circ. 163 (1909), pp. 31-32
(cu. feet).

Birch (yellow). — U.S. D. A., Bul. 285, pp. 47-49 (bd. feet), p. 58 (cu. feet).

Birch (yellow). — (Second growth), Vermont Agr. Exp. Sta., Bul. 176, p. 80 (cu.
feet).

Cedar (western red). — ‘Western Red Cedar in the Pacific Northwest” by J. B.
Knapp and A. G. Jackson. Reprint from “ West Coast Lumberman,” Feb. 1,
1914 and Mar. 1, 1914, by the U. S. Forest Service.

Chestnut. — U.S. D. A., Forest Service, Bul. 96, p. 64 (cords), p. 65 (bd. feet).

Chestnut. — U. S. D. A., Forest Service, Bul. 36, ‘‘ The Woodsman’s Handbook,”
p. 128.

Chestnut Oak. — See Oak.

Cypress (southern). — U.S. D. A., Bul. 272, pp. 70-72 (bd. feet).

Douglas Fir. — U. S. Forest Service, Bul. 36, pp. 154-161.

Gum (sweet, or red). —! U. S. Forest Service, Bul. 36, p. 148.

Gum (sweet, or red). —? U.S. Forest Service, Bul. 58, p. 31.

Hemlock (eastern). — U.S. D. A., Bul. 152, pp- 31-34 (bd. feet), p. 35 (cu. feet),
pp. 36-37 (bark, in cords).

Hemlock (eastern). — Vt. Agr. Exp. Sta., Bul. 161, “‘ Hemlock in Vt.,” p. 5.

Hemlock (eastern). — For. Quart., Vol. IV, p. 292.

Hemlock (western). — U.S. D. A., Forest Service, Bul. 33, p. 31-

Hemlock (western). — ‘Western Hemlock” by E. J. Hanzlik and H. B. Oakleaf.
Reprint by U. S. Forest Service, from “ Timberman” of October, 1914. (p.
unnumbered.) (last page of reprint.)

Hickory. — U. S. Forest Service, Bul. 36, pp. 132-133 (cu. feet).

Hickory. — U. S. Forest Service, Bul. 80, p. 35 (cu. feet).

Incense cedar. — U. S. D. A., Bul. 604, p. 37 (cu. feet), pp. 38-40 (bd. feet).

Juniper. — See Cedar.

Larch (western). — U. S. Forest Service, Bul. 36, pp. 166-169.

Maple (sugar, or hard). —U.S.D. A., Bul. 285, pp. 52-54 (bd. ft.), p. 60 (cu. ft.).

Maple (red, or soft). — U.S. D. A., Bul. 285, p. 61 (cu. feet), p. 62 (cords).
236 APPENDIX

Oak (black). — U.S. D. A., Forest Service, Bul. 96, p. 62, p. 65.

Oak (chestnut). — U.S. D. A., Forest Service, Bul. 96, p. 63, p. 66.

Oak (red). — U.S. D. A., Forest Service, Bul. 96, p. 62, p. 65.

Oak (white). — U.S. D. A., Forest Service, Bul. 96, p. 63, p. 66.

Pine (bull, or western yellow). — U.S. D. A., Bul. 418, p. 43 (bd. feet), pp. 44-45 (bd.
ft.).

Pine (bull, or western yellow). — For. Quart., Vol. VIII, p. 177.

Pine (loblolly). — U.S. D. A., Bul. 11, pp. 53-54 (cu. feet), pp. 54-57 (bd. feet).

Pine (loblolly). — N. C. Geol. Surv., Bul. 24.

Pine (lodge pole). — U.S. Forest Service, Bul. 36, pp. 170, 171.

Pine (long-leaf). — U.S. Forest Service, Bul. 36, p. 151.

Pine (Norway or red). — U.S. D.A., Bul. 139, pp. 34-35 (bd. feet), p. 36 (cu. feet).

Pine (pitch). — For. Quart., Vol. ITI, p. 16.

Pine (short-leaf). — U.S. D. A., Bul. 308, pp. 56-59 (bd. feet and cu. feet).

Pine (sugar). — U.S. D. A., Bul. 426, pp. 37-38 (bd. feet).

Pine (white, eastern). — U.S. D. A., Bul. 13, pp. 64-65 (bd. feet), p. 67 (cu. feet),
p. 68 (cords).

Pine (white, eastern). — For. Quart., Vol. IX, p. 594.

Pine (white, western). — U.S. Forest Service, Bul. 36, pp. 176, 177, 178.

Poplar (yellow). —U. S. Forest Service, Bul. 36, pp. 139, 140, 141.

Redwood. — U. S. Forest Service, Bul. 38, p. 23 (d. b. h. 14-27” only).

Spruce (eastern red). — U.S. Forest Service, Bul. 36, p. 126 (cu. feet).

Spruce (castern red). —U.S. D. A., Bul. 544, pp. 69-79 (bd. feet and standards),
pp. 79-81 (cu. feet), pp. 82-83 (cords).

Spruce (eastern white). — For. Quart., Vol. IX, pp. 590-592.

Spruce (Engelmann). — U. S. Forest Service, Bul. 36, pp. 184-186.

Tamarack. — See Larch. :

Willow (black). — U.S. D. A., Bul. 316, pp. 14-18 (bd. feet), p. 19 (cu. ft.)

In addition to the above, a large number of volume tables for trees of all parts
of the United States is published in U. S. D. A., Forest Service, Bulletin 36, “The
Woodsman’s Handbook” by Graves and Ziegler.

INDEX TO SELECTED YIELD TABLES

Birch (paper, or white). — U.S. D. A., Forest Service, Circ. 163, p. 36.
Cottonwood. — U.S. D. A., Bul. 24, p. 24.

Douglas Fir. — For. Quart., Vol. XII (1914), pp. 440-451.
Pine (loblolly). — U.S. D. A., Bul. rz, pp. 46-47.

Pine (lodgepole). — U.S. D. A., Bul. 154, pp. 29-34.

Pine (short-leaf). — U.S. D. A., Bul. 244, pp. 40-43.

Pine (short-leaf). — U.S. D. A., Bul. 308, pp. 29-32 (cu. feet).
Pine (short-leaf), —U.S. D. A., Bul. 308, p. 44 (cords).

Pine (red, or Norway). — U.S. D. A., Bul. 139, pp. 21-24.
Pine (sugar). — U.S. D. A., Bul. 426, p. 29.

Pine (eastern white). — U.S. D. A., Bul. 13, pp. 69-70.
Spruce (eustern red). —U.S. D. A., Bul. 544, p. 43.

Spruce (Norway).— U.S. D. A., Bul. 544, p. 44.

Willow (black). — U.S. D. A., Bul. 316, p. 25.
APPENDIX 237

INDEX TO TAPER, OR FORM TABLES

Ash (white, green, and black). — U.S. D. A., Bul. 299, pp. 53-77.

Balsam fir.— U.S. D. A., Bul. 55, pp. 42-49.

Basswood. — U.S. D. A., Bul. 285, pp. 75-79.

Beech. — U.S. D. A., Bul. 285, pp. 69-71.

Birch (yellow). — U.S. D. A., Bul. 285, pp. 67-68.

Birch (paper, or white). — U.S. D. A., Forest Service, Circ. 163, p. 33.

Hemlock (eastern). — U.S. D. A., Bul. 152, pp. 37-43.

Hickory. — U. S. Forest Service, Bul. 80, p. 37 (diam. outside bark).

Maple (sugar, or hard). — U.S. D. A., Bul. 285, pp. 72-74.

Pine (loblolly). — U.S. D. A., Bul. 11, pp. 57-59.

Pine (red, or Norway). — U. S. D. A., Bul. 139, pp. 38-41.

Pine (short-leaf). — U.S. D. A., Bul. 308, pp. 60-65.

Spruce (eastern red). —U.S.D. A., Bul. 544, pp. 84-93.

Western Red Cedar. —“‘ Western Red Cedar in the Pacific N-W.” by J. B. Knapp
and A.G. Jackson. Reprint by U. S. Forest Service from “‘ West Coast Lum-
berman,”’ Feb. 1, 1914 and March 1, 1914.

Willow (black). — U.S. D. A., Bul. 316, pp. 21-24.
APPENDIX

238

CEL aqey ‘FPS ‘Ing "VY 'd"S$'Q) ‘sieved SS ur SoYOUT IT pue ‘sea SE Ul SaYOUT g ‘sIeaA Sz UT SayUT g Yowes [[IM soNIds AeMION JO spurys paquelg

C21 aIqey ‘vrs "Ing “y °C “Ss ‘N)

“ays a4}

uo Zurpuadap ‘ssea4 06 03 SP WO] UT SayoUT g pus SIBdA Of 0} OF LOI] UT SAYSUT g YO¥aL |] Sainysed plo uo aonids Jo spueys YAMOIZ pUodses 'pur[suq Man UT

«SIVA COI 0} OF WO] UT SaYOUT ZI YOwaL 0} aonads IO} a[qissod st 41 ‘sulOIyIpUOD sjquIOA] Jopuy)
SIvad Ogi adeIIAB UF UO SalINbal 41 sHOepUOIIPY oy} UT ,, (ZI “d) Shes ‘II6I “A “N “OUT ‘Sud % AdTIM ,,‘SpUe[POoM Bul[pueFy jo sad

*SoYOU! ZI JO JayaUIEIp & YIeeI 0} Bonds & JO}

OUI ,, SY Ut SPABID ,

 

 

 

 

 

 

 

 

 

S6 of of III eus
Sg 99 or of II PHS
o'ng ‘sas ‘al $2 ss SP of oz JT ous oureyy joo (ajddog) uedsy
‘U'asv) |= (sor Sgr Ser Sor Sgr || oe Reha sees STIEys1e9Q
UW ‘dq ‘Vv o6r Sgr Corr oe eee Pataca | see se ea ee syoepuolipy
‘Laiqey ‘SgzIng'y'a'’s'n|. S1z oLt obi oI 06) | eta “SIM BUST Jo aide se3ng
‘Wa vi: ogr Svr oz 06 OL, ef apna tee sqItysyeg
Si ‘g ‘Vv o61 oSt o6 aeeeee | wee sew | ste ee Oe se syoepuolipy
Latqe ‘Sgz ‘mg‘y'a's'n o61 Sr Ser Sor Sg a bherarsar ates: a) a: “SIM BUSA | Yosig MOTAA.
‘Wa yi S6z o0z oSt oz COL, |) Sr eaeee S[ItyszeO
UW ‘gd ‘Vv Cee Sgr oStI eee ee | Hee eee | cen ed ee we syoepuolpy
“Cr aqeL «cc ‘Ing'v'a's na ofz ogt ori OIL 06 a Pai ees ee “SIM xa “UDI SPRORER ARS oR ew yqooog
Sraqel ‘SS Ing-ya'‘s’nl o$i IaAo Sor of ss sodA} [IV auleyy
o$t 1aA0} Sor SL dureag
“er oSt 06 09 +eLA
atqeL “Ss macy a stnl sort? | Here Szr 0g ss adots P.Ap.H a NT, [ees aa Ily wesjeg
‘II pue or Sor Sg of ss 4 ‘CAM
soiqe ‘brS -Ing'ya‘s'n| S&1 S6 og Sg SS i ee Soeert es syoepuolipy jot » sonidsg pey
‘g2Iqel ‘6f1‘ng-'yaq's'n| olf SZ ss, ov OF Sess "STM [ote se autg AeMION
OOI I3aA0 $6 SZ ss Sv III 21S (spueys
S_¢ oor IaA0 0g 09 Sv se II 2S pase-uaae oind)
soqqe ‘fr'Ing‘y'a's‘n| 06 $9 oS se of I eS "AN: ese auld eM
ISduO] NUFHLYON
“sIvaé “sreoh “seek “stead “sieaA
‘(taqulty *(seqod) * (sary) ‘(djnd‘3*a)| ‘(sysod) :
“AV OYINY nes) Yq'P]  “Y *q "p i ie Bs Ua "Pp | “4a "Pp “AVTEIOT “setoadg
your-gi your-br Yyour-Ir yout-g your-9
yovel OF youal oy youss OF yowaloy | yoeal oy

 

 

 

 

 

 

 

 

 

SadIOddS LNVLYOdWI dO SNOILVLOY TVOINHOUL
239

APPENDIX

 

 

 

 

 

 

 

“€9 a1geL
‘gt ‘Ing ‘S ‘d ‘Ss a cer a wwe Hae Be. waves So os 4% ae eee eon “SSTPAL jnuIsxSOP
eee eee || w armas DR ae ea ae cr of synoidg ‘AY x» ‘pul oe ‘yreqseys
eee ee Pw ee ee we fw ew te we St ge sqnosdg “AM xy ‘pul avee “qnusig
RITA 0g 09 SP of Y}MOIZ pz “AY BY “puy | “ynusszyig
‘gpuetsaqep jo yc Sg °9 Sv YyMois pz “AY ‘pul | “yreqseys
‘0g ‘Ing ‘Ss ‘a ‘'S ‘aA eee fe ee ee Sg So gs yyMois pz “LY 29 ‘pul vee qnustg : AIOWOUT
“£9 aIqeL eee eee | wea ee |) ae ees Sz oz y}Mo1s pz ‘eA
‘gf ng S ‘ad Ss n Olt. © jn PS ee bse ants Cp FOL ee ee ee ed ee ee ‘uuay ee iejdog MOTPA
[tos Aeyo 03
662 ‘ING-yoaq‘s‘n|o Sor 04 Sg | $4 03 OS | OS 07 SE | SE 04 Sz | Ureo] Apues ‘ACN
6 pue g solqey, ozI S6 SZ 09 OSE) 4h, Se eee ea sen ‘uuaL
'66z Ma-veas‘s‘nalooc fo 0g ol og, || #kewteisese “pur [nies Ysy ovum
Pe eR, PS ae eee ate bares GL IOAO og-SS Ill ays ‘uu0d (spueys
Sz-€z saqey of cc pt SZ 1aa0 09 oP II 211g ‘uuod | Inoids pase-u9A0)
‘96 Ing ‘Ss ‘a Ss aA eee eee | new ee ol or ce I ays “uu0d see *paxIyl
ogI og op ce sw ee ee “AY se eee aTIUM
“9 a1geL oor or of cz wwe eee ‘AY be ne eee pew
‘gf ‘ng ‘S ‘a S “aA ofl of ce cz ee ee ee ‘AM ee) yorlg :SyVO
eee al Peary doace SL IaA0 09 Sy III 231g ‘au0g (spueys
“6I-AIsaqqey fo} SZ os se TI 991g ‘auuodg | ynoids pese-uaaa)
‘96 ‘Ing ‘S ‘a ‘Ss Sy | eee eee: | eaters 09 or of I azs ‘uu0d eee eee i
gt ng ‘S “a ‘S ‘a Sg cs ov cz Oz: | See Ras eRe ‘PIN ERS SAI BKRSS & qnuyseya
ISauO J
aqoomMauvy] TWaLNad
_ Sae0k *svak “sread. ss1eak “steak *
(aque | s(sojod) | (son) | «(and 2) | «(s1s0d)
*Aquoyny qap | Yar | wap | wap | wap, “AYTEOOT] “sajoedg
OUI-gE your-v1 Youl-11 your-g yout-9
ese Or | WeOL | yeasoy | yoearoy | yovaroy

 

 

 

 

 

 

 

 

 

(panuyuod) —SHIOAdS LNVLYOdWI JO SNOILVLOU TVOINHOAL
APPENDIX

240

 

 

 

 

 

 

‘CI pue It olt Sz1 06 S9 OS: | eee eT :
soqe ‘zZzIng-y'q's'n Sg S9 oS se of yyMo1s pz ‘PIN | “sseadA-— usayynog
“60+ ‘d 6 we Pw ee ee Pw ee ee os of WINUILUIAL
‘ON ‘IX ‘TOA “Og ‘Joury o$ JaA0 ov Sz oz 04 Sr | Sr 04 oF UMUINXe]A[
‘205 *D0Ig UL u00}}e]Y peewee Pee e cane Sv Sz oz aseloAy ‘eld foc *-auIg yse[s
eee og I9AO 09 ce eee Ill aug
“QI og 1aAo SZ oS 09 SY OER” | 4] setae II 941g
aTI2L ‘808 "ING “Vv "d'S 'N | Og 4ea0 99 ov 04 SE Of I evs “IV
wee eee Pe ee eee og I3A0 ¢g¢ se III ays
SPL) psorrens 0g 1aA0 $9 ov Sz JI ous
arqeL ‘sof Ing-v-a‘s'n | ‘7° oL of of oz I 9231S ‘O'N
+4 ene og I2A0 os of 62 | Bee ees ae sree “ry “N
‘oI aqeL ‘bbz ‘Mmayv'a's’a ozit ol or of Of of, DF eee wees “yIV “Mm
*€9 alge ‘9f "Ing ‘casa oft oor SL SG ff weet ete | a ete eee ary [Ores aut jeef-340q9
*“SspApy
*IIIX Sg Sb s¢ Sz oz U}IM poxty
aqqeL ‘v9 ‘Ing ‘sS‘a'S'o Sy SE 04 OF | OF 03 Sz | Sz 04 oz | oz 04 SI | spueys ong “xOL
ww we ee Fw ew we ee Fee ee os of III aug
were ee | nee eae o§ JaAo0 se Sz 04 oz TI e71S
‘aqqeL mg vasa} yp sv oe oe 1 21S “PW
teens 0g ss se oz III erg
“gl aque ‘bz "Ing OOI JaAO Sg sy of 03 Sz fortes II eH19
‘AVAING “OW "JO92D ‘ON Sg ss ov Seo pe siees Teus ‘ON
“£9 aqeL ‘gf ng ‘'S ‘a 'S ‘a ol gs ov Sz GZ | | he eee sees *r) ‘S sees oulg ATIOTGO"T
“ysolOg [BUOTZEN
eplio[g ‘ued SuryloM sees Sgr ozt CL GG | Rea eee ea hae “ely
“fg a[GeL ‘gf ‘has ‘a °S ‘a ofr CoOL cL wee eee Pw eee eee Fw ew ee ee ee “2 ‘Ss Settee ould jeojsuo'T
Issuoq NYGHLNOS
‘ sei “svat “seat “sive
(eau | seajoa) | Gon) [cine | «ceisod)
“AYOyINY ‘4'q"P ‘4'q'p ‘y"d'P “4a "P ‘q"q"P “Aqre00] *seyoadg
OUT-gI yout-h1 your-11 your-g yout-9
wen OL yovel oy, yoval oy, yoval oy yoral oy

 

 

 

 

 

 

 

 

 

(panuyuod) —SAIOUdS LNVLYOdWI JO SNOILVLOY TVOINHOGL
241

APPENDIX

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TE Tp eae a ey Sf 13900 Sz oz » duings ‘Z11Y (OS
‘lr aqel sqnoids
‘loz ‘ONID“'S “A'S ‘TD 06 of ss ob of Aimfuy ‘auy og | ‘oryroQ Arowq
‘o161 ‘ploy goypem | op 00z I9A0| ogi oft — |fadéy sadtun{ “xOT "N |" aadrunf “yl 479087
‘orl ‘psoynyy royem | oc oz 1aA0 oLI ozr uoulg ‘MOIN N POU aut would
"S a1qeL a
‘161 ‘OIG S ‘ad ‘S “aA wee ee Pe eee ee olt oz1 o6 uodo ul ‘Z1uy ete eee Jodrunf{ yen
ue sur
-4I0 M “JOW “JEN YOOID S11 06 0g $9 9.0 = Rees ‘ay | 90nidg uuewelsuq
ue[q sur 3
-YIO MA “JO “FEN YOoID oor of ss ob So. trees eee eae ‘ZW
ee ee o0z csr ozI ool ee ‘o[OE
of -d afqeL Olt Szz oor SL SO) Ah oars ee qein
‘OSI "9D *S “A'S ‘OD oz 06 SZ 09 oS eee ‘epy |" ‘coat sepsnog
Mog
eee 00z 19A0 S61 Szz Sg sUIDIpey “OAM
Sie 00% I3A0 oft SZ sg uloysig ‘oAM
+ eee” 00zZ I9A0 S61 oz Sg asvloAy “quO|,
“€ pure z sarqeL Sool],
‘vS1 ‘Ing “Vv ‘Cd ‘Ss ‘fp | 002 Joao Sgr Szx 0g ss queurwi0 *‘quoy] [°° *” (aUtg ejodespo'T
oor Soi cL ¢ cp aa “9109
‘eI aIqeL 00z 1aA0 of! oor of ss PERE Te “quo!
‘Ler ‘wg Sa SA} S61 ofr 06 ol serene . “xeq *S “++ *QUTg MOTIPA “SOM
Str Sor SZ s$ OR [reer ess ‘xOP NY 'ZUNy
‘II pue or ‘6 sajqeL oor of ss ov of oel yor ,, ‘Z1Ly
‘lol "Ng ‘S ‘4 ‘S ‘O ogt oil og og 07 SS sv auld MoTyad,, ‘2Iny |''" ‘aU MOTTAA “sam
IsHAOY “LY AM0Y
es “s1eak “steak “s1eak “seo
oquan | (joa) | eon) | cand) “(3500)
“AyUOyNY qaqp | Wa‘ | aap | wap | da'p *AqIEOO'T *sapoadg
OUI-gl your-br Youl-11 your-g youl-9
es By | weezeL | yvatoy | yoearoy, | yororoy,

 

(panuyuo)) — SAIOddS LNVLUYOdWI dO SNOILVLOW TVOINHOUL
APPENDIX

242

 

“CyzueH) — 6 aqey
‘€€ -d ‘AT ‘JOA ‘Tenuuy

 

 

 

 

 

 

 

 

 

quid “10g “YSeM jo “AlUp) . we Pw eee 06 09 cy Be eee ‘210 sees auld ajodespo’]
OI aIquL
‘gzv ‘ing ‘yeaqsssa oz oor Sg of og ft yeo peers Jeped ssusouy
"9aTqeL ‘of Ings a's'n | 06 99 se oz 1931S ‘epl | auld SHUM ‘SOM
‘Eg atqey, ‘gf [ng ‘sas'a Czr see ol os es ed “ySeM wee yoo wey “SOM
‘Eg atqe ‘gf ‘Ing ‘Ss ‘ad ‘Ss ‘a ovr PeRpeine et Fe ews ee cL commen | tee ee eS, TeD eee ee lg ayUuM
“€gatqey ‘of -Ing's"a's'n of of s¢ Sz oz sqnoidg SLRS eS poompoey
‘tI ajqeL
‘421 ‘ONIQ ‘GS ‘a ‘S ‘fn Szr S6 ol os ob || Stee “YSeM
‘€gatqeL ‘of Ing‘s‘a's'n og ss SY se Se | [seein ‘Ted
‘OI
atqey ‘giving 'v'a's‘n ol Sg 03 09 | 09 03 SS } SS 03 of oS |e seers ‘219 [°° OUTG MOTIOA ‘SOM
“Eg aTqey ‘gf [ng ‘S ‘a $a OOT |). esa Sg oS ob eee eee TeO
“41
aqeL ‘ozv ‘ng ‘Vv ‘ad S a Oor Sg ol og ss sete ae TeQ eee we . ‘OUI zeang
soqIs ][e
Orr SL ss ob of { ave ae
‘Soy rsaqey ‘ISb-obb Jott oll of of ob III ous “4SoM pue
soseq “€°ON ‘TIX ‘IOA ott ol ss ov of TI 211g u0sa19
‘“qren() ‘Jog ul ylzuey og 09 sv S€ Sz J a4IS
‘of ‘d ‘aiqey
‘oSi ‘og ‘S ‘a 'S ‘A ol oS ov of Sz Re “ys@M Ula}seM fo “cca sepgnoq
IsadO] LSvOD d14lovg
“steoA e a “ .
oe -@oqot) | “eon) | (end #) | “ers09)
“Aquoqiny ‘"'q"P ‘Y'q'P “qa"p da 'p “aap *AIITEOOT ssetoadg,
OUT-gi Yyour-rr Your-1r youl-g yout-9
Woes OL yowaroy | yovaloy | youaloy | yoraroy

 

 

 

 

 

 

 

 

 

(panusju0y) —SAIOddS INVLYOdWI dO SNOILVLOY TIVOINHOaL
APPENDIX 243

Outline for Forest Description

A. General (for the whole tract).

1. Situation and altitude. Reference to mountains, ridges,
streams, camps, etc. Elevation above sea level, if
possible.

2. Topography.

(a) General character — level, hilly, or mountainous. Per-
centage of level land and steep slopes.

(6) Height of the hills above the local streams.

(c) Drainage. Size of streams; navigable or drivable.

3. Rock. Outcrops. Quantity and size of boulders.
B. Specific (for each forest type).
1. Slope and aspect (aspect = exposure).

(a) Slope:
Level oto spercent.. o to 3. degrees
Gentle sto 15 “ .. 3 to 83 Se
Medium 15to 30 “ .. 8% to 163 7
Steep 30 to so “ . 163 to 263
Very steep sotor1co “ . .263 to 45 =
Precipitous over 100 “ ..over 45 .

(b) Aspect:
Eight principal points of the compass. (N, N-E, S,

S-E, etc.)
2. Soil.

(a) Physical composition. (Gravel, sand, loam, clay and
intermediate forms.)

(b) Depth:
Very shallow = less than 6 inches
Shallow =6 to 12 “
Moderate = 12 to 2 “
Deep = 24 to 36 “
Very Deep = 36 inches +

(c) Color and consistency.
(d) Moisture. (Wet, moist, fresh, dry or very dry.)
(e) Agricultural value.
244

3:

APPENDIX

Forest floor. (Vegetable matter on the ground.)

(a) Litter (the upper, only slightly decomposed portion of

the forest floor). Deep, moderate, scanty, etc.

(6) Humus (well decomposed). Depth in inches.

4. Ground cover. (All small plants, except trees.) Her-

baceous, woody, grass, ferns, etc. Give amounts.
Underbrush. (All large woody plants which are not trees.)
Reproduction. (Trees less than 10 feet high; from sprouts
or from self-sown seeds.) State whether the reproduc-
tion is from seeds or from sprouts, and the relative abun-
dance of it.

Stand. Any special features not apparent from an exam-
ination of the tally sheets, should here be mentioned.
Density of crown cover, form of trees, and apparent
vigor of growth, etc.

Merchantable condition. Damage by fire, grazing animals,
insects, fungi, and atmospheric agents.

Site class. (Forest-producing power of the locality.)
Usually expressed in qualities, as I, II, and III. See
Chapter XI.

Outline for a Planting Plan

Prepared by S. N. Spring, Professor of Silviculture at Cornell University.

Title.

Introduction.

General description of tract giving broadly also the purpose

and usefulness of planting, mentioning species and stating

reasons for choice.

Planting sites (each designated by a number or letter).

(a) Area.

(b) Description.

(c) Species recommended.

(d) Spacing of trees (make diagram).

(e) Number of trees required (or quantity of seed if direct
seeding).

(f) Special instructions.
APPENDIX 245

5. Summary of recommendations for sites (tabular form showing
sites, area, species, number of trees).

6. Annual plantings. (A schedule by years to indicate sug-

gested sequence of annual planting operations.)

Source of stock or seed. (Nursery plan if required.)

Preparation of the sites and preliminary protective measures.

9. Planting instructions. Full details pertaining to methods

of planting and local conditions governing the execution of
the plan.

10. Future treatmeat (protection, cleanings, etc., during first
decade).

11. Financial considerations.

12. Appendix — maps and photographs.

com

COMPOUND INTEREST TABLES

Note. — These tables are taken from Chapman: “‘ Forest Valuation,” John Wiley
and Sons, Inc., N. Y., 1915, pp. 249-264. The period of years, », appears in the
left-hand column.

Column I, Formula I = Future value of $1 at end of m years. (See page
184.)

“Tl, «II = Present value of $1 due in 7 years. (See page 184.)
“ II, “IV = Future value at end of ” years of an annual rental
of $1 payable m times. (See page 185.)

Column IV, Formula V = Present value of an annual rental of $1 payable x

times. (See page 186.)
246 . APPENDIX

 

 

 

 

 

 

3 PER CENT
n years. I. II. Ill. Iv.
1 1.0050 -9950 1.0000 -9950
2 1.0100 -QQOI 2.0050 1.9851
3 1.0151 -9851 3.0150 2.9702
4 1.0202 -9802 4.0301 3-9505
5 1.0253 +9754 5.0503 4.9259
6 1.0304 +9705 6.0755 5.8964
7 1.0355 -9057 7.1059 6.8621
8 1.0407 -9609 8.1414 7.8230
9 1.0459 -95601 9.1821 8.7791
10 1.0511 +9513 10.2280 9.7304
11 1.0564 -9466 IL.2792 10.6770
12 1.0617 -9419 12.3356 11.6189
13 1.0670 +9372 13.3972 12.5562
14 1.0723 +9326 14.4042 13.4887
15 1.0777 -9279 15.5365 14.4166
16 1.0831 -9233 16.6142 15.3309
17 1.0885 -9187 17.6073 16.2586
18 1.0939 -Q141 18.7858 17.1728
19 1.09004 -9096 19.8707 18.0824
20 1.1049 -QO51 20.9791 18.9874
21 I. 1104 .9oo6 22.0840 19.8880
22 1.1160 - 8961 23-1044 20.7841
23 1.1216 -8916 24.3104 21.6756
24 1.1272 -8872 25.4320 22.5629
26 1.1328 -8828 26.5501 23.4456
26 1.1385 -8784 27.6919 24.3240
27 1.1442 .8740 28.8304 25.1980
28 1.1499 .8607 290.9745 26.0677
29 1.1556 -8653 31.1244 26.9330
80 1.1614 .8610 32.2800 27.7941
$1 1.1672 .8567 33-4414 28.6508
32 1.1730 -8525 34.6086 29.5033
33 1.1789 8482 35.7817 30.3515
84 1.1848 - 8440 36.9606 31.1955
85 1.1907 - 8308 38.1454 32.0354
36 1.1967 .8356 39.3361 32.8710
37 1.2027 - 8315 40.5328 33-7025
38 1.2087 -8274 41.7354. 34-5209
89 1.2147 -8232 42.9441 35.3531
40 1.2208 - 8191 44.1588 36.1722
41 1.2269 - 8151 45.3796 36.9873
42 1.2330 .8110 46.6065 37-7983
43 1.2392 .8070 47.8306 38.6053
a4 1.2454 . 8030 49.0788 39.4082
45 1.2516 - 7990 50.3242 40.2072
46 1.2579 -7950 51.5758 41.0022
47 1.2642 -7910 52.8337 41.7932
48 1.2705 -7871 54.0978 42.5803
49 1.2768 «7832 55.3683 43-3635
60 1.2832 -7793 56.6452 44.1428
55 1.3156 - 7601 63.1200 47.9782
60 1.3488 +7414 69.7600 51.7020
66 1.3829 +7231 76.5800 55.2764
70 1.4178 +7053 83.5600 58.9364
75 1.4536 -6879 90.7200 62.4745
80 1.4903 .6710 98.0600 65.7988
85 1.5280 -6545 105 .6000 69.1099
90 1.5665 -6383 113.3000 72.3268
95 1.6061 -6226 121.2200 75.4747
100 1.6467 -6073 129.3400 78.5449
106 1.6882 +5923 137.6400 81.5306
100 1.7309 aS777 146.1800 84.4531.
115 1.7746 - 5635 1§4.9200 87.2085
120 1.8194 +5406 163 .8800 90.0736

 
 

 

 

 

 

 

APPENDIX 247
1 PER CENT
n years. 1. II. Itt. IV.

1 1.0100 -QQOI 1.0000 -QQOI
2 1.0201 .9803- 2.0100 1.9704
3 1.0303 -9706 3.0301 2.9410
4 1.0406 .9610 4.0604 3.9020
5 1.0510 -9O515 5.1010 4.8534
6 1.0615 -9420 6.1520 5.7955
7 1.0721 -9327 7.2135 6.7282
8 1.0829 -9235 8.2857 7.6517
9 1.0937 -9143 9.3685 8.5660
10 1.1046 +9053 10.4622 9.4713
11 1.1157 -8063 11. 5668 10.3676
12 1.1268 -8874 12.6825 tk 2555
18 1.1381 -8787 13.8093 12.1337
14 1.1495 .8700 14.9474 13.0037
15 1.1610 -8613 16.0969 13.8651
16 1.1726 -8528 17.2579 14.7179
17 1.1843 -8444 18.4304 15.5622
18 1.1961 . 8360 19.6147 16.3983
19 1.2081 -8277 20.8109 17.2260
20 1.2202 -8195 22,0190 18.0456
21 1.2324 8114 23.2392 18.8570
22 1.2447 -8034 24.4716 19.6604
23 1.2572 -7954 25.7163 20.4558
24 1.2097 -7876 26.0735 21.2434
25 1.2824 -7798 28.2432 22.0232
26 1.2053 +7720 29.5256 22.7052
27 1.3082 - 7644 30.8209 23.5596
28 1.3213 -7568 32.1291 24.3164
29 1.3345 -7493 33-4504 25.0658
30 1.3478 +7419 34.7849 25.8077
31 1.3613 -7346 36.1327 26.5423
32 1.3749 +7273 37-4941 27.2006
33 1.3887 -7201 38.8690 27.9807
34 1.4026 -7130 40.2577 28.7027
35 1.4166 -7059 41.6603 29.4086
386 1.4308 . 6989 43.0769 30.1075
387 1.4451 .6920 44.5076 30.7905
38 1.4595 6852 45.9527 31.4847
39 1.4741 -6784 47.4123 32.1630
40 1.4889 .6717 48.8864 32.8347
41 1.5038 6650 50.3752 33-4907
42 1.5188 -6584 51.8790 34-1581
43 1.5340 -6519 53-3978 34.8100
Sd 1.5493 -0454. 54.9318 35-4554
45 1.5648 - 6391 56.4811 36.0045
46 1.5805 -6327 58.0459 36.7272
47 1.5063 -6265 59.6263 37-3537
48 1.6122 .6203 61.2226 37-9740
49 1.6283 -6141 62.8348 38.5881
60. 1.6446 .6080 64.4632 39-1961
55 1.7284 -5786 72.8400 42.1430
60 1.8166 +5505 81.6600 44.9521
65 1.9093 +5238 90.9300 47.6247
70 2.0066 -4983 100.6600 50.1644
15 2.1090 “4742 I1I0.g000 52.5841
80 2.2166 +4500 121.6600 54.8858
85 2.32096 +4292 132.9600 57.0742
90 2.4485 -4084 144.8500 59.1750
95 2.5733 «3886 157.3300 61.1304
100 2.7046 - 3697 170.4600 63.0259
105 2.8425 «3518 184.2500 64.8107
110 2.9875 +3347 198.7500 66.5272
116 3.1399 «3185 213.9900 68.1518
120 3.3001 «3030 230.0100 69.6979

 
2448

APPENDIX

13 PER CENT

 

 

 

 

 

 

n years. be II. III. IV.

1 1.0150 -9852 1.0000 -9852
2 1.0302 +9707 2.0150 1.9559
3 1.0457 -9563 3-0452 2.9122
4 1.0614 +0422 4.0909 3.8544
5 1.0773 -9283 5.1523 4.7826
6 1.0934 -O145 6.2290 5.6972
7 1.1098 -QOIO 7.3230 6.5082
8 1.1265 -8877 8.4328 7.4859
9 1.1434 8746 9.5593 8.3605
10 1.1605 .8617 10.9027 9.2222
11 1.1779 -8489 11.8633 10.07II
12 1.1959 -8364 13.0412 10.9075
13 1.2130 .8240 14.2368 11.7315
4 1.2318 -8118 15.4504 12.5434
15 1.2502 -7999 16.6821 13.3432
16 1.2690 - 7880 17.9324 14.1313
17 1.2880 -7764 19.2014 14.9076
18 1.3073 -7649 20.4804 15.6726
19 1.3270 +7536 21.7967 16.4262
20 1.3469 -7425 23.1237 17.1686
21 1.3671 +7315 24.4705 17 .QOOT
22 1.3876 .7207 25.8376 18.6208
23 1.4084 - 7100 27.2251 19.3309
24 1.4205 -6905 28.6335 20.0304
26 1.4509 -6892 30.0630 20.7196
26 1.4727 -6790 31.5140 21.3986
at 1.4048 .6690 32.9867 22.0676
28 1.5172 -6501 34.4815 22.7267
29 1.5400 6404 35-9987 23.3761
80 1.5631 .6398 37-5387 24.0158
$1 1.5865 -6303 39.1018 24.6461
32 1.6103 -6210 40.6883 25.2671
33 1.6345 .6118 42.2086 25.8790
34 1.6590 .6028 43.9331 26.4817
35 1.6839 -5939 45.5921 27.0756
86 I.7OQI - 5851 47.2760 27.6607
87 1.7348 -5764 48.9851 28.2371
88 1.7608 -5679 50.7199 28.8051
39 1.7872 +5595 52.4807 29.3646
40 1.8140 +5513 54.2679 29.9158
41 1.8412 +5431 56.0819 30.4590
42 1.8688 -5352 57.9231 30.9940
43 1.8969 -5272 59.7920 31.5212
44 - 1.9253 -5104 61.6889 32.0406
45 1.9542 ~5117 63.6142 32.5523
46 1.9835 ~5042 65.5684 33-0565
47 2.0133 4967 67.5519 33.5532
48 2.0435 -4894 69.5652 34.0426
49 2.0741 -4821 71.6087 34.5247
60 2.1052 -4750 73.6828 34-9907
55 2.2679 -4409 84.5206 37-2715
60 2.4432 +4093 96.2147 39.3803
65 2.6320 -3799 108 . 8000 41.3373
70 2.8355 +3527 122.3640 43-1549
16 3.0546 +3274 136.9670 44.8409
80 3.2907 +3039 152.7110 46.4073
85 3-5450 . 2821 ' 169.6600 47.8603
90 3.8189 -2618 187.9300 49-2009
95 4-1141 .2431 207 .6000 50.4618
100 4.4320 -2256 228.8030 51.6247
105 4.7746 - 20904 251.6330 52.7036
110 5.1436 -1044 276.2380 53.7055
115 5.5411 «1805 302.7330 54.6351
120 5.9093 -1675 331.2880 55.4085

 
APPENDIX 249

 

 

 

 

 

2 PER CENT
n years. iT IL. III. IV.

1 1.0200 -9804 1.0000 «9804
2 1.0404 -9612 2.0200 1.9416
3 1.0612 +0423 3.0604 2.8839
4 1.0824 -9238 4.1216 3.8077
5 1.1041 -9056 5.2040 4.7135
6 1.1262 -8880 6.3081 5.6014
7 1.1487 -8706 7-4343 6.4720
8 1.1717 -8535 8.5830 7.3255
9 I.IQ51 - 8368 9.7546 8.1622
10 1.2190 - 8203 10.9497 8.9826
11 1.2434 -8043 12.1687 9.7868
12 1.2682 - 7885 13.4121 10.5753
18 1.2936 -7730 14.6803 11.3484
14 1.31905 -7579 15.9739 12.1062
15 1.3459 +7430 17.2034- 12.8403
16 1.3728 -7284 18.6393 13.5777
17 1.4002 = 7142 20.0121 14.2019
18 1.4282 «7002 21.4123 14.9920
19 1.4568 6864 22.8406 15.6785
20 1.4859 -6730 24.2074 16.3514
a1 1.5157 -6508 25.7833 17.0112
22 1.5460 -6468 27.2990 17.6580
23 1.5769 -6342 28.8450 18.2922
24 1.6084 -6217 30.4219 18.9139
25 1.6406 6095 32.0303 19.5235
26 1.6734 -5976 33.6709 20.1210
27 1.7069 -5859 35-3443 20.7069
28 1.7410 5744 37.0512 21.2813
29 1.7758 - 5631 38.7922 21.8444
30 1.8114 - 5521 40.5681 22.3965
31 1.8476 .5412 42.3704 22.0377
32 1.8845 - 5306 44.2270 23.4683
ss 1.9222 «5202 40.1116 23.9886
$4 1.9607 . 5100 48.0338 24.4986
35 1.9999 - 5000 49.9045 24.9986
36 2.0309 - 4902 51.9044 25.4888
87 2.0807 - 4806 54.0343 25.9605
38 2.1223 -4712 50.1149 26.4406
39 2.1647 -4619 58.2372 26.9026
40 2.2080 -4529 60.4020 27.3555
41 2.2522 -4440 62.6100 27.7905
42 2.2972 +4353. 64.8622 28.2348
43 2.3432 -4268 67.1505 28.6616
44 2.3901 4184 69.5027 29.0800
45 2.4379 +4102 71.8927 29,4902
46 2.4866 -4022 74.3306 29.8923
47 2.5363 +3943 76.8172 30.2866
48 2.5871 - 3865 79.3535 30.6731
49 2.6388 +3790 81.9406 31.0521
50 4 2.6916 -3715 84.5794 31.4236
55 2.90717 -3365 98.5865 33-1748
60 3.2810 «3048 114.0520 34.7609
65 3.6225 .2760 131.1250 36.1073
70 3.9995 2500 149.9780 37-4986
16 4.4158 -2265 170.7900 38.6763
80 4.8754 +2051 193.7720 39.7445
85 5.3828 +1858 219.1400 40.7111
90 5.9431 - 1683 247.1570 41.5869
95 6.5617 -1524 278.0850 42.3800
100 7.2446 .1380 312.2320 43-0984
105 7-9987 +1250 349.9300 43.7489
110 8.8312 1132 301.5590 44.3382
115 9.7503 -1026 437-5150 44.8719
120 10.7652 -0929 i 488.2580 45-3554

 

 
 

 

 

 

 

 

25250 APPENDIX
2} PER CENT

n years L II. III. Iv.
1 1.0250 -9756 1.0000 -9756
2 1.0506 -9518 2.0250 1.0274
8 1.0769 -9286 3.0756 2.8560
4 1.1038 .9060 4.1525 3.7620
5 1.1314 - 8830 5.25603 4.6458
6 1.1597 8623 6.3877 5.5081
7 1.1887 8413 7-5474 6.3494
8 1.2184 .8207 8.7361 7.1701
9 - 248: - 800' 9.9545 7.9709
10 oe ee II. 2034 8.7521
11 1.3121 . 7621 12.4835 9.5142
12 1.3449 -7436 13.7056 10.2578
13 1.3785 -7254 es ay
14 1.4130 -7077 16.
15 I “a8 ee 17 he oe
16 I. 3 19.3802 -
17 oo ae 20.8647 13.7122
18 1.5597 -6412 22.3863 14.3534
19 I 5087 <peas 23 cane : 3 he
20 1.63 - 6103 25.544 15.

1.6796 7 27.1833 16.1845
s I ee ee 28.8629 16.7654
23 1.7646 . 5667 30.5844 17.3321
24 Te +5529 oe et
5 Le : 34.15 -
o see Stee 36.0117 18.9506
27 1.9478 - 5134 37.9120 19.4640
28 1.9965 - 5009 39.8598 19.9649
29 2.0464 -4887 41.8563 20.4535
30 2.0976 -4767 43-9027 20.9303
2.1500 -4651 46.0003 21.3054

a 2. sone ak 48.1503 21.8492
33 2.2589 -4427 50.3540 22.2919
34 2.3153 +4319 52.6129 22.7238
35 2.3732 -4214 54.9282 23.1452
86 2.4325 -411I 57-3014 23.5563
37 2.4933 4011 59.7339 23.9573
38 2.5557 -3913 62.2273 24.3486
39 2.6196 .3817 64.7830 24.7303
40 2.6851 +3724 67.4026 25.1028
41 2.7522 - 3633 70.0876 25.4661
42 2.8210 -3545 72.8398 25.8206
43 2.8915 -3458 75.6608 26.1664
44 2.9638 +3374 78.5523 26.5038
465 3.0379 +3292 81.5161 26.8330
46 3.1139 +3211 84.5540 27.1542
47 3-1917 3133 87.6679 27.4675
48 3.2715 +3057 90.8506 27.7732
49 3.3533 .2982 oe fee
50 3.4371 +2909 97 4943 .
55 3.8888 -2571 TI5.551 29.7140
60 4.3998 +2273 135.992 30.9087
65 4.9780 +2009 159.120 31.963
70 5.6321 +1775 185.284 32.898
76 6.3722 -1569 214.888 33-645
80 720 ter a 383 ee.
85 -1570 +122 286.280 c
90 9.2280 - 1084 329.154 35.666
96 10.4416 -0958 377-664 36.171

100 11.8137 .0846 432-549 36.614

105 13.3661 .0748 494.644 37.007

110 15.1226 .0661 564.902 37.355

115 17.1098 10584 644.392 37.664

120 19.3581 +0517 734.326 37-934

 
 

 

 

 

 

 

APPENDIX 251
3 PER CENT
n years. I. IL. III. IV.
1 1.0300" +9709 1.0000 -9709
2 1.0609 -9426 2.0300 1.0135
3 1.0927 -QOI5I 3 2.8286
4 1.1255 8885 4.1836 3.7171
5 1.1593 8626 5.3001 4.5797
6 1.1941 -8375 6.4684 5-4172
7 1.2299 - 8131 7.0625 6.2303
8 1.2668 - 7804 8.8923 7.0197
9 1.3048 - 7664. 10.1591 7.7861
10 1.3439 -7441 11.4639 8.5302
11 1.3842 -7224 12.8075 9.2526
12 1.4258 -7O14 14.1920 9.9540
13 1.4685 .6810 15.6178 10.6350
14 1.5126 6611 17.0863 11.2961
15 1.5580 -6419 18.5089 I1.9379
16 1.6047 .6232 20.1569 12.5611
17 1.6528 .6050 21.7616 13.1661
18 1.7024 5874 23.4144 13.7535
19 1.7535 +5703 25.1169 14.3238
20 1.8061 +5537 26.8704 14.8775
21 1.8603 +5375 28.6765 15.4150
22 1.9161 -5219 30.5368 15.9369
22 1.9736 - 5067 32.4529 16.4436
24 2.0328 -4919 34.4265 16.9325
26 2.0938 4776 36.4503 17-4131
26 2.1566 -4637 38.5530 17.8768
27 2.2213 +4502 40.7006 18.3270
28 2.2879 -4371 42.9309 18.7641
29 2.3566 +4243 45.2189 19.1885
30 2.4273 +4120 47-5754 19.6004
31 2.5001 -4000 50.0027 20.0004
82 2.5751 «3883 52.5028 20.3888
33 2.6523 +3770 55-0778 20.7658
34 2.7319 - 3660 57.7302 21.1318
35 2.8139 +3554 60.4621 21.4872
386 2.8983 +3450 63.2750 21.8323
37 2.9852 +3350 66.1742 22.1672
38 3.0748 -3252 69.1504 22.4025
89 3.1670 -3158 72.2342 22.8082
40 3.2620 - 3066 75.4013 23.1148
41 3.3599 2976 78.6633 23.4124
42 3.4607 . 2890 82.0232 23.7014
43 3.5645 . 2805 85.4830 23.9819
44 3.6715 | 62724 89.0484 24.2543
45 3.7816 - 2644 92.7100 24.5187
46 3.8950 2507 96.5015 24.7754
47 4.0119 +2493 100.3965 25.0247
48 4.1323 -2420 104.4084 25.2667
49 4.2562 «2350 108.5406 25.5017
60 4.3839 .2281 112.7969 25.7208
55 5.0821 -1968 136.072 26.7744
60 5.8916 «1697 163.053 27.6756
66 6.8300 -1464 194.333 28.452
70 7.9178 +1263 230.504 29.123
75 9.1789 - 1089 272.630 29.702
80 10.6409 -0940 321.363 30.201
85 12.3357 -O81I 377-857 30.701
90 14.3005 -0699 443-349 31.002
95 16.5782 -0603 519.273 31.323
100 19.2186 -0520 607.288 31-590
105 22.2707 -0449 709 .323 31.838
110 25.8282 -0387 827.608 32.043
116 29.9420 -0334 964.733 32.220
120 34.7110 -0288 1123.70 32.373

 
 

 

 

 

 

 

25 252 APPENDIX
3} PER CENT
n years. i II. III. Iv.

1 1.0350 -9662 I.0000 -9662

2 1.0712 +9335 2.0350 1.8997
3 1.1087 -QOI9 3.1062 2.8016
4 1.1475 -8714 4.2149 3.6731
5 1.1877 «8420 5 -3625 4.5151
6 1.2293 -8135 6.5502 5.3286

7 1.2723 -7860 7-7794 6.1145

8 1.3168 +7594 Q.O517 6.8740
9 1.3629 +7337 10.3685 7.6077
10 1.4106 - 7089 11.7314 8.3166
11 1.4600 -6849 13.1420 9.0016
12 I.5111 -6618 14.6020 9.6633
13 1.5640 -6304 16.1130 10,3027
14 1.6187 6178 17.6770 10.9205
15 1.6753 -5969 19.2057 IL.5174
16 1.7340 -5707 20.9710 12.0941
17 1.7947 -5572 22.7050 12.6513
18 1.8575 +5384 24.4907 13.1897
19 1.9225 «5202 26.3572 13.7008
20 1.9898 «5026 28.2797 14.2124
21 2.0504 -4856 30.2605 14.6980
22 2.1315 -4692 32.3289 15.1671
23 2.2061 +4533 34.4604 15.6204
24 2.2833 -4380 36.6665 16.0574
25 2.3632 +4231 38.9499 16.4815
26 2.4460 -4088 41.3131 16.8904
27 2.5316 +3950 43-7591 17.2854
28 2.6202 -3817 46.2 17.6670
29 2.7119 - 3687 48.9108 18.0358
80 2.8068 +3563 51.6227 18.3920
81 2.9050 +3442 54-4205 18.7363
82 3.0067 +3326 57-3345 19.0689
33 3.1119 +3213 60.3412 19.3902
34 3.2209 +3105 63-4532 19.7007
35 3.3336 3000 66.6740 20.0007
36 3.4503 - 2898 70.0076 20.2905
37 3-5710 . 2800 73-4579 20.5705
38 3.6960 -2706 77.0289 20.8411
39 3.8254 - 2014 80.7249 21.1025
40 3-9593 +2526 84.5503 21.3551
41 4.09078 +2440 88. 5005 21.5991
42 4.2413 2358 92.6074 21.8349
43 4.3807 2278 096.8487 22.0627
44 4.5433 2201 IOI. 2383 22.2828
45 4.7024 2127 105.7817 22.4955
46 4.8669 2055 110.4840 22,7009
47 5.0373 1985 115.3510 22.8904
48 5.2136 1918 120.3883 23.0912
49 5.3061 1853 125.6018 23.2766
50 5.5849 1791 130.9979 23.4556
55 6.6331 +1508 160.947 24.2641
60 7.8781 .1269 196.517 24.9447
65 9.3567 - 1069 238.763 25.5168
70 11.1128 - 0900 288.938 26.0004
16 13.1986 .0758 348.531 26.4067
80 15.6757 0638 419.307 26.7488
85 18.6179 0537 503.368. 27.0368
90 22.1122 +0452 603.205 27.2793
96 26.2623 -0381 721.780 27.4708
100 31.1914 .0321 862.612 27.6554
105 37.0456 0270 1029.874 27,8002
110 43-9986 0227 1228.53 27.9221
116 52.2565 OIgI 1464.471 28.0247
120 62.0643 o161 1744.69 28.1111

 
 

 

APPENDIX 253
4 PER CENT
n years. L IL. Ill. Iv.

1 1.0400 -9615 1.0000 -9615

2 1.0861 -9246 2.0400 1.8861

8 1.1249 - 8890 3.1216 2.7751

4 1.1699 -8548 4.2465 3.6299

5 1.2167 .8219 5.4163 4.4518

6 1. 2653 +7903 6.6330 5.2422

7 1.3159 +7599 7.8983 6.0025

8 1.3686 +7307 9.2142 6.7327

9 1.4233 - 7026 10, 5828 7.4353
10 1.4802 -6756 12.0061 8.1109
11 1.5305 -6406 13.4864 8.7605
12 1.6010 -6246 15.0258 9.3851
13 1.6651 - 6006 16.6268 9.9856
14 1.7315 +5775 18.2919 10.5631
15 1.8009 +5553 20.0236 11.1184
16 1.8730 +5339 21.8245 Ir.6523
17 1.9479 +5134 23.6075 12.1657
18 2.0258 -4036 25.6454 12.6503
19 2.1068 +4746 27.6712 13.1339
20 2.1911 -4504 29.7781 13-5903
21 2.2788 -4388 31.9692 14.0292
22 2.3699 +4220 34.2480 14.4511
23 2.4047 -4057 36.6179 14.8568
24 2.5633 + 390I 39.0826 15.2470
25 2.6658 «3751 41.6450 15.6221
26 2.7725 -3607 44.3117 15.9828
27 2.8834 +3468 47.0842 16.3206
28 2.9987 +3335 49.9676 16.6631
29 3.1187 +3207 52.9663 16.9837
30 3-2434 +3083 56.0849 17.2920
81 3.3731 - 2065 59.3283 17.5885
32 3.5081 . 2851 62.7015 17.8736
33 3.6484 - 2741 66.2005 18.1476
34 3-7943 = 2636 69.8579 18.4112
35 3.9401 +2534. 73.6522 18.6646
36 4.1039 2437 77-5983 18.9083
387 4.2681 +2343 81.7022 19.1426
38 4.4388 +2253 85.7903 19.3679
39 4.6164 - 2166 90.4001 19.5845
40 4.8010 - 2083 95.0255 19.7928
41 4.9931 - 2003 99.8265 19.9031
42 5.1928 -1926 104.8200 20.1856
43 5.4005 -1852 II0.0124 20.3708
44 5.6165 .1780 115.4129 20.5488
45 5.8412 -1712 121.0294 20.7200
46 6.0748 -1646 126.8706 20.8847
47 6.3178 -1583 132.0454 21.0429
48 6.5705 -1522 139.2632 21.1951
49 6.8333 +1463 145.8337 21.3415
50 7.1067 -1407 152.6671 21.4822
55 8.6464 «1157 IQI.I59 22.1086
60 10.5196 .OQ5I 237.0901 22.6235
65 12.7987 .0781 294.967 23.0466
70 15.5716 -0642 364.290 23.3045
15 18.9453 .0528 448.642 23.6281
80 23.0498 +0434 551.245 23.0154
85 28.0436 -0357 676.090 24.1085
90 34.1193 -0203 827.983 24.2673
95 4.5114 -0241 1012.785 24.3077
100 50.5049 -O198 1237.622 24.5050
105 61.4470 -0163 I51l.175 24.5931
110 74.7597 -0134 1843 .992 24.6656
115 90.9566 -OIIO 2248.915 24.7251
120 110.663 . 0090 2741.558 24.7741

 

 

 

 

 
 

 

 

 

 

 

25 254 APPENDIX
43 PER CENT

n years. I. II. Ill. IV.
1 1.0450 -9569 1.0000 -9569
2 1.0920 -O157 2.0450 1.8727
3 1.1412 -8765 3.1370 2.7490
4 1.1925 - 8386 4.2782 3.5875
5 1.2462 .8022 5.4707 4.3900
6 1.3023 - 7679 6.7169 5.1579
7 1.3609 ©7348 8.0192 5.8927
8 1.4221 -7032 9.3800 6.5959
9 1.4861 .6729 10.8021 7.2688
10 1.5530 -6439 12,2882 7.9125
11 1.6229 .6162 13.8412 8.5289
12 1.6959 -4807 15.4640 9.1186
13 1.7722 +5643 17.1599 9.6829
14 1.8519 «5400 18.9321 10.2229
15 1.0353 -5167 20.7841 10.7395
16 2.0224 -4945 22.7193 I1.2340
17 2.1134 -4732 ' 24.7417 11.7072
18 2.2085 -4528 26.8551 12.1600
19 2.3079 -4333 29.0634 12.5033
20 2.4117 -4146 31.3716 13.0079
21 2.5202 - 3968 33-7831 13.4047
22 2.6337 -3797 36.3034 13.7844
23 2.7522 -3634 38.9370 14.1478
24 2.8760 -3477 41.6892 14.4955
25 3.0054 +3327 44.5652 14.8282
26 3.1407 «3184 47-5700 15.1466
27 3.2820 = 3047 50.7113 15.4513
28 3-4279 -2916 53-9933 15.7429
29 3.5840 -2790 57-4230 16.0219
80 3-7453 . 2670 61.0071 16.2889
81 3.9130 +2555 64.7524 16.5444
82 4.0900 -2445 68.6662 16.7889
33 4.2740 + +2340 72.7562 17.0220
34 4.4664 +2239 77 .0303 17.2468
365 4.6673 »2143 81.4966 17.4610
86 4.8774 / . 2050 86.1640 17.6660
37 5.0969 -1962 Q1.0413 17.8622
38 5.3262 -1878 96.1382 18.0500
39 5.5659 -1707 IOI. 4644 18.2207
40 5.8164 -1719 107 .0303 18.4016
41 6.0781 - 1645 112.8467 18.5661
42 6.3516 -1574 118.9248 18.7235
43 6.6374 “1507 125.2764 18.8742
“4 6.9361 -1442 131.9138 19.0184
45 7.2482 . 1380 138.8500 19.1563
46 17-5744 .1320 146.0982 19.2884
47 7.9153 .1263 153-6726 19.4147
48 8.2715 .1209 161.5879 19.5356
a9 8.6437 - 1157 169.8504 19.6513
50 9.0326 - 1107 178.5030 19.7620
65 11.2563 -0888 227.9180 20.2480
60 14.0274 .0713 289.4980 20.6380
65 17.4807 10572 366.2380 20.9509
70 21.7841 -0459 461.8700 21.2021
16 27.1470 .0368 581.2670 21.4118
80 33.8301 -0296 729.5580 21.5653
85 42.1585 -0237 914.6330 21.6951
90 52.5371 -O190 I145.2700 21.7902
95 65.4708 .O153 1432.6840 21.8828
100 81.5885 .O123 1790. 8600 21.9499
105 101.674 .0098 2237. 2000 22.0036
110 126.704 .0079 2793 .4300 22.0468
115 157.807 .0063 3486 . Go0o 22.0815
Saag 120 196.768 .OO51 4350.4000 22.1003

 
an

t

.
¥

4 Pa e we

. .

 

 

flee Oe ate
te as APPENDIX .- 4 255 5
’ cS oy mo
5s PERCENT ,.

n years. I. IL. Il. Iv. :
1 1.0500 -9524 1.0000 +9524
2 1.1025 -9070 2.0500 1.8504
8 1.1576 -8638 3.1525 2.7232
4 1.2155 . 8227 4.3101 3.5460
5 1.2763 +7835 5 +5256 4.3205
6 1.3401 -7462 6.8019 5.0757
7 1.4071 - 7107 8.1420 5.7864
8 1.4775 -6768 9.5491 6.4632
9 1.5513 -6446 11.0266 7.1078

10 1.6289 -6139 ‘22.5990 7.9217
11 1.7103 -5847 14.2068 8.3064
12 1.7959 +5568 15.9171 8.8623
13 1.8856 +5303 17.7130 9.3936
14 1.9799 «5051 19.5986 9.8986
15 2.0789 -4810 21.5786 10.3797
16 2.1829 -4581 23.6575 10.8378
17 2.2920 4363 25.8404 11.2741
18 2.4066 -4155 28.1324 11.6896
19 2.5270 +3957 30.5390 12.0853
20 2.6533 +3769 33.0660 12.4622
21 2.7860 +3589 35.7193 12,8212
22 2.9253 -3418 38.5052 13.1630
33 3.0715 +3256 41.4305 + 13.4886
24 3.2251 «3101 44.5020 13.7986
25 3-3864 +2953 47-7273 14.0939
26 3-5557 . 2812 51.1135 14.3752
27 3-7335 - 2678 54.6601 14.6430
28 3.9201 +2551 58.4026 14.8981
29 4.1161 +2420 62.3227 15.1411
380 4.3219 +2314 66.4388 15.3725
31 4.5380 «2204 70.7608 15.5928
383 4.7649 +2099 75.2988 15.8027
33 5.0032 - 1999 80.0638 16.0025
84 5.2533 +1904 85.0670 16.1929
35 5.5160 +1813. gO. 3203" 16.3742
36 5.7918 +1727 95.8363 16.5469
37 6.0814 -1644 101.6281 16.7113
38 6.3855 -1566 107.7005 16.8679
39 6.7048 - 1491 114.0950 17.0170
40 7.0400 «1420 120.7998 17.1591
41 7.3920 -1353 127.8398 17.2044
42 7.7616 -1288 135.2318 17.4232
48 8.1407 -1227 142.9033 17.5459
44 8.5572 ~1169 151.1430 17.6628
45 8.9850 «IIT3 159-7002 17.7741
46 9-4343 . 1060 168.6852 17.8801
47 9.9060 . 1009 178.1194 17.9810
48 10.4013 -0961 188.0254 18.0772
49 10.9213 .0916 198.4267 18.1687
50 11.4674 .0872 209.3480 18.2550
55 14.6356 . -0683 272.7130, 18.6335
60 18.6792 -0535 353-5840 18.9293
65 23.8309 .O419 456.7980 IQ.119r
70 30.4264 -0329 588.5200 19.3427
16 38.8327 -0257 756.6540 19.4849
80 49.5614 -0202 971.2290 19.5965
85 63.2544 .0158 1245 .0880 19.6838
90 80.7304 -O124 1594.6100 19.7523
95 103.035 +0097 2040. 7000 19.8058
100 131.501 .0076 2610.0300 19.8479
105 167.833 .0060 3336. 6600 19.8808
110 214.202 +0047 4264.0300 19.9066
115 273.382 .0037 5447 .6400 19.9268
220 348.012 -0029 6958. 2400 19.9427

 

 

 

 

 
25 256

APPENDIX

53 PER CENT

 

 

 

 

 

 

n years. I. II. Ill. IV.
1 1.0550 -9479 1.0000 -9479
2 1.1130 - 8085 2.0550 1.8463
8 1.1742 .8516 3.1680 2.6979
4 1.2388 -8072 4.3423 3.5052
5 1.3070 - 7651 5.5811 4.2703
6 1.3788 -7252 6.8881 4.9955
7 1.4547 -6854 8.2669 5.6830
8 1.5347 -6516 9.7216 6.3346
9 1.6191 -6176 11.2563 6.9522
10 1.7081 5854 12.8754 7.5376
11 1.8021 +5549 14.5835 8.0925
12 1.9012 -5200 16.3856 8.6185
13 2.0058 -4986 18.2868 9.1171
14 2.1161 -4726 20.2926 9.5806
15 2.2325 -4479 22.4087 10.0376
16 2.3553 -4246 24.0411 10.4622
\17 2.4848 -4024 26.9964 10.8646
18 2.6215 -3815 29.4812 11.2461
19 2.76056 .3616 32.1027 11.6077
20 2.9178 +3427 34.8683 II.9504
21 3.0782 «3249 37.7861 12.2752
22 3.2275 -3079 40.8643 12.5832
23 3.4262 -2919 44.1118 12.8750
24 3.6146 -2767 47.5380 13.1517
25 3-8134 -2622 51.1526 13.4139
26 4.0231 2486 54.9660 13.6625
a7 4.2444 2356 58.9891 13.8981
28 4.4778 2233 63.2335 14.1214
29 4.7241 -2117 67.7114 14.3331
30 4.9840 - 2006 71-4355 14.5337
31 5.2581 . 1902 77.4194 14.7239
32 5.5473 - 1803 82.6775 14.9042
83 5.8524 .1709 88.2248 15.0751
34 6.1742 -1620 94.0771 15.2370
36 6.5138 -1535 100.2514 15.3
36 6.8721 +1455 106.7652 15.5361
37 7.2501 -1379 113.6373 15.6740
38 7.6488 .1307 120.8873 15.8047
39 8.0605 .1239 128.5361 15.9287
40 8.5133 «1175 136.6056 16.0461
41 8.9815 1113 145.1189 16.1575
42 9-4755 -1055 154.1005 16.2630
43 9.9967 . 1000 163.5760 16.3630
“4 10.5465 0948 - 173-5727 16.4579
46 11.1266 .0899 184.1192 16.5477
46 11.7385 .0852 195.2457 16.6329
47 12.3841 .0807 206.9842 16.7137
48 1310653 .0765 219.3684 16.7902
49 13.7838 -0725, 232.4336 16,8628
50 14.5420 .0688, 246.2175 16.9315
55 19.0046 .0526 327.3563 17.2251
60 24.8381 +0403 433-4200 17.449
65 32.4623 .0308 572.0364 17.6216
70 43-4150 .0230 771.1818 17.7630
15 56.7414 .0176 1,013 .4800 17.8614
80 72.4703 .0138 1,299 .4600 17.9309
85 04.7152 -0106 1,703 .9127 17.9898
90 123.7883 .0081 2,232.5145 18.0349
95 161.7855 .0062 2,923 .3727 18.0694
100 211.4463 -0047 3,826. 2963 18.0958
105 276.3503 .0036 §,006. 3691 18.1160
110 361.2768 .0028 6,550.4873 18.1315
115 472.0413 .0021 8,564. 3873 18,1433
120 616.0357 .0016 18.1523

 

11,198.8309
 

 

 

 

 

APPENDIX 257
6 PER CENT
n years. I. II. III. Iv.

1 1.0600 +9434 1.0000 -9434

2 1.1236 .8900 2.0600 1.8334

3 1.1910 -8396 3.1836 2.6730

4 1.2625 +7921 4.3746 3.4051

5 1.3382 -7473 5.6371 4.2124

6 1.4185 +7950 6.9753 4-9173

7 1.5036 -6651 8.3938 5.5824

8 1.5938 -6274 9.8075 6.2008

9 1.6895 «5919 IL.4913 6.8017
10 1.7908 +5584 13.1808 7.3601
11 1.8983 -5268 14.9716 7.8869
12 2.0122 «4970 16.8699 8.3838
13 2.1329 -4688 18.8821 8.8527
14 2.2609 +4423 21.0151 9.2950
15 2.3966 -4173 23.2760 9.7122
16 2.5404 -3936 25.6725 10.1059
17 2.6928 -3714 28.2129 10.4772
18 2.8543 «3503 30.9057 10.8276
19 3.0256 = 3305 33.7600 Ir. 1581
20 3.2071 -3118 36.7856 11.4699
21 3-3996 - 2942 39.9927 11.7641
22 3.6035 +2775 43-3023 12.0416
23 3.81907 -2618 46.9958 12.3034
24 4.0489 -2470 50.8156 12.5504
25 4.2919 - 2330 54.8645 12.7834
26 4-5494 - 2198 59.1564 13.0032
27 4.8223 -2074 63.7058 13-2105
28 5.1117 -1956 68.5281 13.4062
39 5.4184 -1846 73-6308 13 - 5907
30 5-7435 1741 79.0582 13-7648
31 6.0881 -1643 84.8017 13.9291
32 6.4534 .1550 90.8898 14.0840
33 6.8406 -1462 97-3432 14.2302
34 7.2510 -1379 104.1838 14.3681
$85 7.6861 . 1301 IIIT. 4348 14.4982
36 8.1473 -1227 119.1209 14.6210
87 8.6361 -1158 127.2681 14.7368
38 9.1543 - 1092 135.9042 14.8460
89 9.7035 - 1031 145.0585 14.9491
40 10.2857 -0972 154.7620 15.0463
41 10.9029 -OO17 165.0477 15.1380
42 II.5570 .0865 175.9505 15.2245
43 12.2505 .0816 187.5076 15.3062
“4 12.9855 .0770 199.7580 15.3832
45 13.7646 .0727 212.7435 15-4558
46 14.5905 -0685 226.5081 15.5244
47 15.4659 -0647 241.0985 15.5890
48 16.3939 .0610 256.5645 15.6500
49 17-3775 0575 272.9584 15.7076
60 18.4202 -0543 290.3359 15.7619
55 24.6507 .0406 304.1783 15.9905
60 32.9883 -0303 533-1383 16.1611
65 44.1458 .0226 719.0966 16.2891
70 59.0772 -0169 967.9533 16.3845
16 79.0587 -0126 1,300.9783 16.4558
80 105.7985 - 0005 1,746.6416 16.5091
85 141.5287 .007I 2,343 -0450 16.5489
90 189.4698 .0053 3,141. 1633 16.5787
95 253-5538 -0039 4,209 . 2300 16.6009
100 339-3125 .0029 5,638. 5416 16.6175
105 454.0770 -0022 7,551 .2833 16.6299
110 607.6591 -0016 I0,1T0.9850 16.6392
115 813.1867 -OO12 13,536.4450 16.6461
120 1088. 2280 . 0009 18,120.4667 16.6513

 

 
 

 

 

 

 

 

25 258 APPENDIX
7 PER CENT
n years. I. IL. III. IV.

1 1.0700 -9346 I .0000 +9328
2 1.1449 -8736 2.0700 1.8043
8 1.2250 8163 3.2142 2.6228
4 1.3108 -7629 4.4400 3.3857
5 1.4026 «7130 5.7514 4.0986
6 1.5007 6663 7-3529 4.7657
7 1.6058 -6227 8.6542 5.3886
8 1.7182 - 5820 10, 2600 5.9700
9 1.8385 +5439 11.9786 6.5143
10 1.9671 - 5083 13.8159 7.0228
11 2.1049 +4751 15.7843 7.4971
12 2.2522 -4440 17.8886 7.9414
13 2.4008 +4150 20.1400 8.3557
14 2.5785 -3878 22.5500 8.7442
15 2.7590 -3624 25.1286 9.1071
16 2.9522 -3387 27.8886 9.4457
17 3-1588 -3161 30.8400 9.7686
18 3.3800 +2959 34.0000 10.0571
19 3.6165 .2765 37-3786 10.3343
20 3-8697 .2584 40.9528 10.5928
21 4.1406 +2415 44.8657 10.8343

22 4-4304 2257 49.0057 Il.
23 4-7405 - 2109 53-4343 II.2714
24 5.0724 -1971 55-3200 11.4685
26 5.4275 - 1842 63.2500 11.6528
26 5.8075 .1722 68.6786 11.8242
27 6.2140 - 1609 74.4857 11.9857
28 6.6490 «1504 80.7000 12.1357
29 7.1144 «1406 87.3346 12.2757
80 7.6124 +1314 94.4628 12.4071
81 8.1452 .1228 102.0742 12.5300
32 8.7154 «1147 110.2700 12.6457
, 33 9.3255 -1072 118.9500 12.7528
84 9.9783 . 1002 128.2618 12.8528
35 10.6768 -0937 138.2400 12.0457
86 Il.4241 -0875 148.9157 13.0343
87 12.2239 .0818 160.3414 13.1157
38 13.0795 .0765 172.5642 13.1914
39 13.9950 -0715 185.6428 13.2628
40 14.9747 .0668 199.6386 13.3300
41 16.0230 .0624 214.6143 13.3928
42 17.1446 -0583 230.6371 13.4514
43 18.3448 +0545 247.7828 13.5057
“4 19.6290 +0509 206.1428 13.5571
45 21.0030 .0476 285.7571 13.6043
46 22.4332 -O445 306.1886 13.6485

47 24.0463 .0416 329.2328 13.
48 25.7888 .0387 354.1257 13.7314
49 27.5306 .0363 379.0086 13.7657
60 29.4577 +0339 406.5386 13.8000
65 41.3162 .0242 575.9458 13.9385
60 57.9482 .0173 813.5458 14.0371
65 81.2755 .0123 1,146.7928 14.1085
70 113.9929 7 1,614.1844 14.1585
76 159.8823 -0062 2,141.1757 14.1959
80 224.2440 -0045 2,260.7471 14.2200
85 314.5138 .0032 3,160.6285 14.2385
90 441.1230 .0023 4,478. 7682 14.2514
95 618.7000 -0016 6,287 .4714 14.2614
100 867.7600 -OOIL 8,824. 2857 14.2685
106 1217.0812 .0008 12,382.2855 14.2728
110 1707 .0235 .0006 17,372 .5886 14.2757
116 2304.1978 +0004 24,371 .7642 14.2785
= 120 3357-9023 -0003 34,188. 5400 14.2800

 
 

 

 

 

 

 

APPENDIX 259
8 PER CENT
n years. I. IL. III. Iv.

1 1.0800 -9259 1.0000 -9250
2 1.1664 -8573 2.0800 1.7825
3 1.2507 -7938 3.2463 2.5762
4 1.3605 - 7350 4.5062 3.3112
5 1.4693 - 6806 5.8366 3.9912
6 1.5869 -6302 7.3362 4.6212
7 1.7138 - 5840 8.9225 5.1987
8 1.8509 +5403 10.6363 5.7450
9 1.9990 +5002 12.4875 6.2462
10 2.1589 -4032 14.4862 6.7087
11 2.3317 -4289 16 6463 7.1375
12 2.5182 -3971 18.9775 7.5350
13 2.7196 -3676 21.4950 7.9037
14 2.0372 +3405 24.2150 8.2425
15 3.1722 -3152 27.1525 8.5587
16 3.4260 -2919 30.3250 8.8513
17 3.7000 -2703 33-7500 9.1200
18 3.9960 - 2502 37-4500 9.3712
19 4.3157 +2317 41.4463 9.6025
20 4.6610 - 2145 45-7025 9.8175
21 5.0339 - 1987 50.4237 10.0150
22 5.4366 - 1839 . 55-4575 I0. 2000
23 5.8716 - 1703 60.8950 10.3700
24 6.3413 -1577 66.7663 10.5275
25 6.8486 - 1460 73-1075 10.6737
26 7.3964 +1352 79.9800 10. 8087
27 7.9882 «1252 87.3525 10.0337
28 8.6272 - 1159 95.3400 II.0500
29 9.3174 +1073 103.9675 11.1575
380 10.0629 -0904 113.2862 Il.2562
31 10.8678 .0920 123.3475 11.3487
32 1I.7371 .0852 134.2138 11.4337
83 12.6763 -0789 145.9537 II. 5125
34 13.6904 +0730 158.6300 11.5862
35 14.7853 .0676 172.3163 11.6537
36 15.9684 -0626 187.1050 11.7162
87 17.2460 -0580 203.0750 11.7737
38 18.6249 -0537 220.3113 11.8275
39 20.1159 -0407 238.9488 11.8775
40 21.7250 .0460 259.0625 Il .0237
41 23.4630 .0426 280.7875 11.9662
42 25.3400 -0395 304.2500 12.0050
43 27.3072 -0365 329.5900 12.0425
44 29.5567 -0338 356.9588 12.0762
45 31.9213 -0313 386.5163 12.1075
46 34.4750 +0290 418.4375 12.1362
47 37.2330 .0269 452.9125 12,1625
48 40.2117 -0249 490.1463 12.1875
49 43.4207 +0230 530.2588 12.2112
50 46.9029 .0213, 573-7863 12.2325
55 68.9160 -O145 848.9500 12.3175
60 101.2605 . 0099 1,253.2563 12.3750
65 148.7849 .0067 1,847 .3113 12.4150
70 218.6150 -0046 2,720. 1875 12.4412
75 321.2177 -0031 4,002.7213 12.4600
80 471.9761 -002I 5,887 . 2013 12.4725
85 693 .4888 .OO14 8,656. 1100 12.4812
90 1,018.9649 . 0010 12,724. 5613 12.4862
95 1,497 . 1093 - 0007 18,702. 4913 12.4900
100 2,199. 8838 - 0005 27,486 .0475 12.4925
105 3,232.3656 .0003 40,392.0700 12.4950
110 4:749.4130 +0002 59,355 .1025 12.4962
115 6,978.4677 .O00I 87,218 .3463 12.4075
130 10,253.6792 .O001 128,1§8.4900 12.4989

 
 

 

 

 

 

 

26 260 APPENDIX
= to PER CENT
n years. L Il. III. Iv.
1 1.1000 -QOQI 1.0000 0.908
2 1.2100 -8264 2.1000 1.735
3 1.3310 +7513 3.3100 2.486
4 1.4641 -6830 4.6410 3.169
5 1.6105 -6209 6.1050 3-790
6 1.7716 - 5045 7.7160 4-354
7 1.9487 +5132 9.4870 4.867
8 2.1436 -4665 11.4360 5-334
9 2.3580 +4241 13.5800 5-758
10 2.5938 +3855 15.9380 6.144
11 2.8531 +3505 18.5310 6.494
12 3-1385 «3186 21.3850 6.813
18 3-4523 - 2807 24.5230 7.102
14 3.7976 +2633 27.9760 7.366
15 4.1773 +2304 31.7730 7.605
16 4-5950 2176 35.9500 7.823
17 5.0545 -1978 49.5450 8.021
18 5.5600 -1799 45 8.200
19 6.1160 -1635 51.1600 8.364
20 6.7276 -1486 57.2760 8.513
21 7.4004 +1351 64.0040 8.648
22 8.1404 -1228 71.4040 8.771
23 8.9545 -II17 79-5450 8.882
24 9.8500 - 1015 88. 5000 8.984
26 10.8349 +0923 98.3490 9.076
26 11.9184 -0839 109.1840 9.160
27 13.1103 +0763 121.1030 9.236
28 14.4213 -0693 134.2130 9.306
29 15.8634 -0630 148.6340 9.369
30 17.4498 +0573 164.4980 9.426
81 19.1948 -O521 181.9480 9.478
32 21.1143 -O474 201.1430 9.525
33 23.2257 +0431 222.2570 9.568
34 25.5483 -0391 245.4830 9.608
35 28.1032 +0356 271.0320 9.643
36 30.9135 +0324 299.1350 9.675
87 34.0049 +0294 330.0490 9.705
38 37-4054 -0273 364.0540 9.726
89 41.1460 -0243 401.4600 9.756
40 45.2605 +0221 442.6050 9.778
41 49.7866 «0201 487.8660 9.798
42 54-7655 -0183, 537-6550 9.816
43 60.2420 -0166 592.4200 9.833
“4 66.2662 -OI51 652.6620 9.848
45 72.8928 .O137 718.9280 9.862
46 80.1822 -O125 791.8220 9.874
47 88.2004 -O113 872.0040 9.886
48 97.0207 -O103 960.2070 9.806
49 106.7228 -0004 1,057.2280 9.905
60 117.3926 .0085 1,163 .9260 9.914
55 189.0668 -0053 1,880. 6680 9.946
60 304.4944 +0033 3,034.9440 9.966
65 490.3932 -0020 4,893 .9320 9.979
70 789.7876 -0013 7,887 .8760 9.986
75 1,271.9648 -0008, 12,709.6480 9-991
80 2,048. 5188 -0005 20,475 .1880 9.904
85 3,209.1742 -0003 32,981.7420 9.906
90 5,313-3659 0002 53,123 .6590 9.907
95 8,557.2549 +O001 85,562.5490 9.998
100 13,781 .6139 -00007 137,806.1390 9-9992
105 22,195.5102 »00005 221,945. 1020 9.9004
110 35,746.1983 - 90003 357.451.9830 9.9996
115 57,509.8666 .00002 575,088. 6660 9.9997
as 120 92,717 .0213 .Q0001 927,160, 2130 9.9998

 
261

APPENDIX

“sqjue} pue

“syjuay pure saqour ur wrerp doy, |

goo} UL WIBUST

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

al] 2] a] a] | B |] Dg fmta/aeued] De [wea jaseet “pe | Beta a8007|| De | pwrera|.us097 ae
EVEL ELRLELE Elie]?
— — = ‘°
z . 5 x e & soqe 01q +(9) Boy pak *(q) 30] puz *(D) Boy 4st & a eS
elele)a)e] a pie |?
+ s BF Pl 3 g *s8O] JO aTeos pu suorsuauntcqT 3

sds Qataites b-w Sevraica ie Seiseliee Sos 20g ORS RRR SRS eres Pe lg Dammoey oa eee teteteeeeeeee ener Cgp20T

ATIVL FZIVOS DOT GNV SLNANATANSVAW FZAAL
INDEX

Acres, reduction of square chains to................0ceeeeee
(table) sushi: ving attrac oS rec mnhakcunene 2 eda eas Mawes eeaare
Age, average, meaning of.............. 0.00 ccc een eee eeeeeee
Age-classes, defined... 1.1... cece cece ccc cence cence ees
comparison of actual with normal................2..20005
distribution of: 4 ss scesa deus ees cda eeene eee eased atineen

Barrows, W. B., quoted.......... 2.0 cece cece eect eet eeeeeee
Biltmore Stick. 5 uss ocicec ale cavaaesarnensus eeaasade aMewes
references to (footnote)... 2.2.0.0... 0. cece cece eee eee ee
table of values fOr ses 3 ses siseecee svcd s eetieseeee eure ss
Block, defined. ............ 000 ceeeeeees ere SRB aR ace cake
Board-foot contents, rule for............ 0. ese cence eee ee ee
Gehnition Ob. ec, aac eg cus sus a eae Somoewanee ees

Chain SUPVEyOr’S ois.2. 5.5.5.5 jesus e rtineomenwaeheadnaiamaceeort
Chapman, H. H., quoted............ 0: cece cece cece e eee ees

(footnote) <5. cswsacee ses uh caas cater Seas nes

(tables) cca vevswiebana heeives pewesees cezeseu eds
Circles, area of in square feet (table)................000 eevee
Clark, J. F., quoted... 0... . cece cece cece ree nn cert tees
Compartment, defined. ............ 0b eee e eee nent e eens
Compass, staff. ..1052 5000s ceasnwede cece es same e ee eke ee eees
Compound interest, formula............6. 0-2 e eee e eee eee

Conference of Forest Schools, quoted. ...........--0.000 eee
Control books (see working plan, control and revision of).
Converting factors, tables of...... 2.0.0... . esses veer eee eeee

ARTICLE PAGE

15
113
135

116
121

122
122

12
81

116

2
226
98
125
130
125
218
12
12

Ig
38
39

230

132
15
15
ar
16

31
180
223

2
185
195
198
199
200
207
245
231

27
132

2

183
245-260
x1

226
264 : INDEX

Cord, definition of.............. cece eens

short, defined... 2. ccseasesccacevawes ness
Costs, calculation of. ..............0c cee

main factors of, in forest finance.........
Cotta, H., quoted... .... 2... cece cece ee ees
Cubic foot, defined. ................00000
Cutting cycle, defined................005-
Cutting, plans of... 0.0... ccc cece eee eee

Cutting series, defined....................

Damages, appraisal of...............0.005

instructions for determination of
Dendrometeb os... oxcvx sce gee suier ere vewes ¢
Departure (latitude and departure).........
Diameter, breast-high (= d.b.h.), defined. . .

Economic rotation (see rotation).
Error of closure, to eliminate..............

Fairchild, F. R., quoted...............046.
Felling age, defined. ................0000 .
Felling series (see cutting series).

Fernow, B. E., quoted...............000

Financial rotation (see rotation).
Flury (Swiss forester), quoted .............

Forest administration, defined.............
Forest description... .........0...05
outline:for ss i422ccsessmees eos s ramen
Forest economy, defined...................
Forest finance, defined...............00005
Forest management, defined...............
Forest mensuration, defined...............
Forest organization, defined...............
in forest administration...............
Forest regulation (see forest organization).
Forest rent, defined.................0000

Demet we mete eee

ee we we eres

eee weer eer e eens

rr rr

Cece e ere eee eee

new wee ene

106
106

122
122
19
ii
83

82
81

117

94
94
78

123
40

159

148
146
160
159

200
201
38

21
48
133

133
132

187
140

142
143

126
128
209

68
243

179
66

14
124
214

142
143

210
INDEX 265

ArTIcLE PAGE

Forest Service, salaries in (footnote)..............eeeeeeee 135 223
U.S. Dept. of Agriculture, quoted.................0005 109 169
, 122 201
Forest staff, organization of... .........0 00 0c cece cece cence 124 209
Forest statics, defined... 0.0... 0. ccc ccc eect eee neces 111 179
Forest valuation, defined. ............ 0.00 cece ee nee neeeeeee 111 179
Form factor, defined... 0.2... 0.0 o ccc cece eee eee eees 30 51
USE Ole cis nari tend eee a eons CORR Ree a 31 52
Form tables (see taper tables).
Formule, compound interest... ........... 00 cc eeee eee eeeee 116 183
for calculating expectation value...................-- 122 202
for calculating profit (footnote)................ 2. eee 119 192
for calculating replacement value.................005 122 204
for stumpage values..... Yoo lariensr aly shasta) ddnacl'e otartapie eieteliee 121 198
geometric solids, contents.............0cece eee eee ee 25 44
Pressler’s (for volume)... .......- 00000 ee cece ee eee es 26 46
Schiffel’s (for volume)... 2.0.00... 0... c cece eee eens 26 46
Graves) H.S:, quoted ).gs0 ge ca eecasd theeseenerceig 4 omen oe 11 22
(footnote) og oy cae os eee A Ge gu a vo ac eed saecedad oateees 238
Hanzlik, E. J., quoted. . 0... 0... cece cece ence eee ee 242
Height, measurement of............. cc cece eee e eee eee 28 50
Heyer’s method of regulating cut...............0- ee eee eee 100 150
Horizontal measurement of distance............-...0-- eee 3 6
House; H...D); Quoted .2): ccaceeee cape Wea eae her eaag Shiels 121 200
Hufnagl’s method of regulating cut................2.00 eee 101 155
102 157
Hypsometers 2accccesasidesesucees i beeesae der sees xaueee es 16 32
Income, in forest finance... ..... 0.0... eee eee e eee 115 183
State forests of Germany............. 0.0. e ee eee eee eee 119 194
Increment; borers sw ssa s+ akan ee sees x Ree EME HES et od oat 18 38
Increment current annual ............. 0.0... c cee eee eee eee 64 102
denned > gedic sad ode ac ealelaWaa dase Naquad aud yamemod cue 63 100
mean annual.................-05. “pastes RRA NATE a egal 64 102
Per Cents asicew evs peaee sme s sweearaeaies YY eee RAEN 67 109
pericdicianntial .. ois scscudens de oenes Dawe be oaeeveced eee 64 102
Interest rate, in forest finance...... 0.0.0... ese e eee e eee 117 187
Instruments, used in survey of area. ...... 20... eee eee eee 2 2
Kirkland, B. P., quoted. ....... 0... c cece eee cece eee e eens 114 180
Latitude (latitude and departure)... ............. 0 cece enone 4
Linear foot, definition and application of..................6- 9 19
Log rules, application Of............. 0.0. eee renee ees ss aranitl 13 28
Clark’s International (table)................0e cece eee ee 220

COMMENt ON wccs Ss sawn eae baw ca lelsiggamiee see ay eA 14 28
266 INDEX

Log rules, definition of......... 00... c cece eee eee
description of specific rules..................00005
methods of constructing............... 00.0 eee eee
Scribner (Decimal “C”’), (table)...............045

Management class (see working group).

Mapping, methods of... ......... 0. cc cece eee ee eee

McCarthy, W. J., yield table for white pine............
McKenzie, H. E., quoted... 0.2.02... 0. cee eee eee eee
Mean sample tree, method of............-..----00 00+
Merchantable length. .............. 0 eee esse eee eee
Moore, B., quoted. ........... 00. cece eee eee eee ees
Mulford, Walter, quoted... ............ 2c eee e eee eee
Munger, T. T., quoted. ...... 2.0... cece eee ee eee eee

Normal growing stock, defined..................2.005,
how determined.............. 0.0. e cece ees
Normal increment, defined...............00eeeeeeeeee

Poles, dimensions of

Regulation of cut, defined. ............cc eee eer eee eees
MEthOdS OE iss cc Set ga ee ewes y ope Ranta Ae eee pia
Regulation of felling budget (see regulation of cut).

Regulation of yield (see regulation of cut).

Research, in forest administration.........0.eeeeeee eee eees é

permanent sample..............- 2. cece cece eee eee
Plumb-bob, use for... 0.0.0.0... 06.0 e eee ees
Posts, dimensions of. .......... 00.000 ccc cee eee eeeeeee
Pressler’s formula (increment per cent)................
Profits, determination of, in forest finance..............
Promotion, in forest administration...................

MB favi Ce isa es sb a eis scas a SEG Sos DESOTO AS

ARTICLE PAGE
11 22
14 28
12 22

228

81 133
4 8

4 7

4 7
79 127-128
12 26
61 86
23 42
73 119
241

79 130
131 216
131 217
8 14
xT

78 125
18 124
18 125
79 127
78 125
244

107 161
50 84
44 72
50 84
75 122
3 6

9 19

9 19
68 110
119 Ig
134 220
134 222
96 146

97-103 147-158

130

215
INDEX 267

ARTICLE PAGE

Rotation, choice of........... 0... c ccc cee cece eeseeeaes 95 144
Mehndi sfc icteadconganonc an seine aeioulenesdexs pea hace 91 140
ECONOMIC A Ae eilan we vnhuieene ss bed eitidadee ted 98 141
financials i osc0v 3 aesieageed occas tdeise ns cash anita a eae s 94 142
silvicultural (see rotation, economic).
technical i535 oy aisckiven 6 wxnaaeoaeeene ee Gan abla ke Gs 92 140

238-242

Roth, Fi,:quoted). sera sas dasa oon wees 054 Wales ee bees 94 144

95 145
119 194
120 195
121 200

Scale-stick!vicvcwaidasil cet eeadioaiuns okeaniaawaee we bnr oe 17 37
GENE ise croliainted ca ae yynue codes hee See ae ieey 11 22

Schenck, A., quoted. ..... 0... cece cece cence eee eee eenee 1382 218

Schneider’s formula (increment per cent)...............0.005 69 11r

Schwappach, A., quoted.................04. $iedseGhinw ee: 131 217

Seedlings; AGO scale: sein cad sagaaatlear aes Renu ee eHaN 57 92

Silvicultural methods, defined.....................0..00000- 86 135

Silvicultural rotation (see rotation).

Site, quality of, as applied to yield tables... . cart earenenat 72 116

Soil ‘rerit; Cefitied.. yyw ho ae ei cndiniameness Heber eee Ree ade 94 143
exemplified) iat cc ponnic Dimemewas poe ed wade ae ale tae 94 144

Spring, S. N., quoted (chart)............. 0... eee e eee eee 138

(outline) se22 23 6s dewerts oeecese seknesawe tes ea ees 244

Standard (unit of measure)............... cece eee eee eens 9 17

Stands; Age Of oscar d se ng cont Aatmieulen 24 a ealneethe oa he 62 98
defined 204 on he a tenaalotg ex as SOs Chace eowaae heed 81 132
INCremen tity «2004 team eda e wionsauR eae eae 70 I12
mixed, study of increment in......................00008- 14 121
pure, study of increment in.............. 0... e cece eee 12 IIs

Stem analysis, defined... ......... 0... cece eee ener eens 65 102

Sterrett, W. D., quoted......... 0... cece eee eee ee eee 119 19gl

Strips, broad (as applied in timber estimating)............... 49 83
narrow (as applied in timber estimating).................. 48 8r
number of men required for strip survey.................. 48 81
width of, for different percentage of area covered........... 45 79

Stumpage values, defined... 2.0.0.6... . eee eee cece een eee 121 195
examples Of 0s isiacce « seduigace var ee ei eee ees e Kaew 121 200
formittla: for’... sce tae teeeiaa ees aes Newer ese names 121 198

Sub-compartment (see lot).

Survey; COStiOfs a vssnsngaade sss ca pndnewes see Namen Phas 7 13
fOTeSty cise kv 4A AWG es Soe eS eae a RRS e eRe OMe Bee 40 67
form of notes for... 2... eee cece cere cece e nett et eeeeee 3 4
in forest administration. .......... 0000s e cece ence erent eee 130 214
methods Of... 0... sc ce cece cree cece teen e erence eeneenee 3 3

1 I

necessity Of........0.05 iaetled eter aida we ge oa ccate as
268 INDEX

Agticte Pace

Surveyor’s measures, tables Of ............sccseeecseeeeeeee
Sustained yield, defined... 2.2.0... cc cece ceed eee e eevee eens TT
financial advantage Of... 2.6... . cece eee ee eee renee 120
Sustained yield management, requisites for.................- TT
114
Swiss method, of regulating cut........... 0... cece ee ee ewee 101
Tally-sheet forms of, for timber estimating.................. 44
Tape, Steelic..: sinc ger agamehies sles sea eowhinke cease mamens 2
Taper curves, as applied in constructing volume tables........ 36
as applied to stumpS............ 2... c cece cece eee e eee 69
Taper tables (= form tables) ........... cece eeee een e ene 36

MGERHG 25 canescens iqaee ede eaa noe netdan ee Hees

Technical rotation (see rotation).

of important species... 0.2... cc cece eee cece teen e eee
Ties, railroad, dimensions of... ..........00c cc cee cece ee eees 9
Timber: GStima tes. fo) 5. dca dio. ya sivlaniivecs Hee ¢ dead scaksenetd aye dod Gees 39
Timber estimates, accuracy Of............ccceeeeeec enna 53
COSE Olan cays 2 gesncann, AU naa. Ve oe emi 54
methods of computing. ........... 0... cece eee e eee ee 55
Timber estimating, methods of............... 00. e cece eee 40
Toumey, J. W., quoted... 2... cee cece cece e eee ens 87-90
Townships, diagram Of... 0.2... . eee cece eee eee eee eens 43
Traverse, definition Of............ 0.0 c cece cece cere scenes 3
AP Fees: f OFMAOL 225, sce ccsasroneaelats ame ule apres eib wards tee Ue Is os 26
Trees, felled; age Of) siias. coves cusses saeseee es eye e424 cares ex y 58
Measurement Of......... 2c cece cece cece eee eeeeeeeeee 21
23
Trees, standing, age Of... 12... . cece cece eee eee eee 60
MeCasurementiOl...anuasee uae eenenees Ge vameoamndins 27

form for recording........ 0... ccc ccc e cece cece eeeees
Units Of Measures. sie saecsiGd sauenenhand ince beeenngaaeres 9
Values, in forest finance............ cece eee eee eee e ee eet eens 112

Volume, of solid wood in stacks (table)................0.00008
measurement? Of s s.i50.. somes oss Mea eewaN Ee Cede oie s 29
Volume tables, application of ............... 0 cece eee Reeds 38
Classification Ofs sic. ccakwoersciweosaseysggees tenaas ee 33
CODSERUCEION Obie. oo Acute Varese gga vdectaapeeeusinnss 36

examples Of juidew. ses ia denotes os Sg aewe We NEO

for white pine:.:.3...5 928444. exe scan imate wn cate aeies

for’ yellow birch s. 2 eco. ec sce 5 sieceaasisse naeunnioanrameleesalee areas

BOER CO ioc excxcncr cating ee rewis ene pared SARs RATE pe eG SRR
Von Mantel’s method of regulating cut.................2005 100
Woolsey, T. S., Jr., quoted (footnote)... 0... .... cece eee eee 135

Working block (see working group).

226
124
194
124
180
152

74-75

62
95
62

237

238
19
65:
89
go
go
68

138-140
72

3

43

93

40

4r

97

48

261

15

179
227
51
64
54
60
232-233
232
233
235
148

222
INDEX

Working circle (see working group).

Working group, defined... ..........0.0 0.0 ccc cece eee eens

Working plan, conference........... 2... .0ec eee eeee eee ees
control and revision.......... 0.60. c eee eee ee eens

Working plan unit (see working unit).
Working section (see working group).
Working unit, defined............ 0... cece eee eee eee eee

Xylometric methods (for determining contents of solids).......

Yield table, application of................ 0c c cece cece e eee
CODSEIUCHION OF 6. gis ca Pee ee eAiiandwinnaien dhats elena
GERDICION OF 5 cosine d oa Rola ana dae RMR R AGS
CxaMpleOb ic.a24 cededuneahd aes Ce woe eae heres
for white pines. s--6.2: caches nese s wales as acon auc
index tO: ses oerisges inners es et tad Ce Nate Os Ne ae foe caters

ARTICLE

110

76
108
130
109

209

PacE

132
134
175
124
163
214
164

132

47

II4
115-122
113
234
234
236
125
114
 

 

Subjects Related to this Volume

For convenience a list of the Wiley Special Subject Catalogues,
envelope size, has been printed. These are arranged in groups
—each catalogue having a key symbol. (See Special Subject
List Below). To obtain any of these catalogues, send a
postal using the key symbols of the Catalogues desired.

List of Wiley Special Subject Catalogues

1—Agriculture. Animal Husbandry. Dairying. Industrial
Canning and Preserving.

2—Architecture. Building. Masonry.

3—Business Administration and Management. Law.
Industrial Processes: Canning and Preserving; Oil and Gas
Production; Paint; Printing; Sugar Manufacture; Textile.

CHEMISTRY
4a General; Analytical, Qualitative and Quantitative; Inorganic;
Organic.

4b Electro- and Physical; Food and Water; Industrial; Medical
and Pharmaceutical; Sugar.

CIVIL ENGINEERING

5a Unclassified and Structural Engineering.

5b Materials and Mechanics of Construction, including; Cement
and Concrete; Excavation and Earthwork; Foundations;
Masonry.

5c Railroads; Surveying.

5d Dams; Hydraulic Engineering; Pumping and Hydraulics; Irri-
gation Engineering; River and Harbor Engineering; Water

Supply.
(Over)

 

 
 

 

CIVIL ENGINEERING—Continued
5e Highways; Municipal Engineering; Sanitary Engineering;
Water Supply. Forestry. Horticulture, Botany and
Landscape Gardening.

6—Design. Decoration. Drawing: General; Descriptive
Geometry; Kinematics; Mechanical.

ELECTRICAL ENGINEERING—PHYSICS
7—General and Unclassified; Batteries; Central Station Practice;
Distribution and Transmission; Dynamo-Electro Machinery;
Electro-Chemistry and Metallurgy; Measuring Instruments
and Miscellaneous Apparatus.

8—Astronomy. Meteorology. Explosives. Marine and
Naval Engineering. Military. Miscellaneous Books.

MATHEMATICS

9—General; Algebra; Analytic and Plane Geometry; Calculus;
Trigonometry; Vector Analysis.

MECHANICAL ENGINEERING
10a General and Unclassified; Foundry Practice; Shop Practice.
10b Gas Power and Internal Combustion Engines; Heating and
Ventilation; Refrigeration.
10c Machine Design and Mechanism; Power Transmission; Steam
Power and Power Plants; Thermodynamics and Heat Power.
11—Mechanics.

12—Medicine. Pharmacy. Medical and Pharmaceutical Chem-
istry. Sanitary Science and Engineering. Bacteriology and
Biology.
MINING ENGINEERING
13—General; Assaying; Excavation, Earthwork, Tunneling, Etc.;
Explosives; Geology; Metallurgy; Mineralogy; Prospecting;
Ventilation.

 

 
.

eae
Recess

fae
eas
Stenaee

Me BALE
Seu fea a
igeeneeattad

eet
Bie.
nee:

i
pa

ae