SCH Lien's

ANUALOF Forestry

ANAGEMENT

W. SCHLICH

m]t ^. 31. Itll pbraru

JJortlj (Carolma ;Steti; College

SD371

534
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SCHLICH'S
MANUxlL OF P^ORESTRY.

X<)ti\ — Strictl}- speaking, this is the second edition
of Volume III., but as the first edition consisted of a
larger number of copies than those of Volume 11. ,
and in order to bring this volume into line with
Volume II., it has been issued as the third edition.

SCHLICH'S

MANUAL OF FOKESTEY.

VOLUME III.

FOREST MANAGEMENT.

W. SCHLICH, Ph.D.,

CLE.. F.K.8.. F.L.i?..

PRINCIPAL PROFESSOR OF FORESTRY AT THE ROYAL INDIAN ENGINEERING COLLEGE,
COOPERS HILL ; LATE INSPECTOR-GENERAL OF FORESTS TO THE GOVERN-
MENT OF INDIA; HONOR.VRY PROFESSOR OF FORESTRY AT THE ROYAL
AGRICULTURAL COLLEGE, CIRENCESTER.

TIIIllD EDITIOX. REVISED.

WITH 58 ILLUSTRATIONS.

LONDOX :

BliADBlEY, AGNEW, ^^^ CO. Lu., 10, BOUVEKIE STEEET.

1905.

BRADBURY, AONEW, & CO. LD., PRINTERS,
LONDON AND TONBRIDGE.

PREFACE.

A NEW edition of this volume having become necessary,
I have made various changes, so as to render some of the
mathematical problems more easily understood. I have also
simplified and shortened some of the calculations.

The appendices have been considerably altered. Some of
those contained in the former edition have been shortened,
while I have added a set of complete yield tables for oak,
beech, Scotch pine, spruce and silver fir, and preliminary
tables for several other species. The former are the result
of many years' labour on the part of the German Association
for the collection of forest statistics. They give the progress
of development of the several species in Germany, more
particularly in the northern part of it. The data contained
in yield tables enable the forester to determine the quantity
of timber and firewood produced on lands of varying yield
capacity under the supposition, that the progress of the woods
has not suffered from any extraneous interference. Hence,
they serve to determine the yield, which may be expected, and
to gauge the financial results of the industry, if the land is
planted with one or the other species. I have satisfied myself,
that the tables apply, in a general way, to the conditions found
in the South of England, and also in the Midland Counties.

It has been suggested, elsewhere, that such tables should be
altogether rejected, because the statistics, upon which they
are based, were collected on the Continent, but I cannot accept
such a view. To construct tables, based upon data collected
in this country, will take many years, and, surely, it is more
sensible to use the tables now given than none at all. In
the latter case, we should continue to grope in the ^i^CO^'^

considerable period of years, and the financial aspect of
forestry in this countr}^ would remain as obscure as it has
been in the past.

It has been said, that British forestry is a thing apart.
That, no doubt, is so in its present condition ; but the question,
whether it is desirable to afforest additional areas and to
work them on economic principles, depends first and foremost
on the financial aspect. Hence, if we discard the information
supplied by adjoining countries, no substantial progress can
be made for a generation or so.

There is an important point yet to be mentioned. My
object in publishing the Manual of Forestry was to give a
clear picture of economic forestry. That picture was to serve,
in the first place, in the education of candidates for the
Indian Forest Department and only incidentally for the
instruction of those, who take an interest in the development
of forest management in this country. Hence, I took my
illustrations from the country, where economic forestry has
been most highly developed, and not from Britain. In this
country, statistical data, which bear upon the economic aspect
of forestry, are as yet extremel}' rare, and it would have been
absolutely impossible to deal with the general aspect of the
subject without more complete statistics, even if they are
stamped with the well-known mark " Made in Germany." As
soon as we can boast of our own data, we shall be only too
pleased to put on one side those collected abroad.

As the bulk of British forests are in the hands of private
proprietors, we must rely chiefly on the limited areas belonging
to the Crown, which are under the management of the Com-
missioners of Woods. Several of these areas have now been
placed under systematic management, and it may be expected,
that, year by year, useful data will become available, which
can ultimately be tabulated and made available for general
use in this country. At any rate, the most urgent need of
British forestry is the collection of statistics, which will enable
the proprietor and his forester to gauge the economic value of

Vll

forest operations. Let us hope, that good progress will be
made in this direction in the immediate futm-e. This being
so, I need hardly point out, that a fully equipped forester must
have, in addition to l)eing a Sylviculturist, a mathematical
mind, so as to do full justice to the financial aspect of the
industry. This branch of a forester's education is in no way
of less importance than the study of natural history, which,
in the past, has only ton often been mistaken for the sole basis
of forestry by specialists, who had not succeeded in grasping
the true objects aimed at l)y the forest industry conducted on
economic lines.

Before concluding, I desire to offer my thanks to Mr. L.
Gisboriie Smith, late of the Indian Forest Department, for
his assistance in passing this volume through the press.

W. SCHLICH.

Coopers Hill,
\st Jannari/, 1905.

TABLE OF CONTENTS.

INTEODUCTION

PART I.— FOREST MENSURATION 3

Chapter I. — Instkuments used ix Forest Mensuration . . . 6

1. Instruments for the INIeasurement of the Girth . . 6

2. Instruments for the Measurement of the Diameber . 7

3. Instruments for the ]\teasurement of the Diameter

Increment ......-• 12

4. Instruments for the Measurement of the Length of

Felled Trees and Logs 14

5. Instruments for the Measurement of the Height of

Standing Trees 14

6. Instruments for the direct Measurement of the

Volume 26

Chapter II. — SIeasueement of Felled Trees . . .28

1. Volume of the Stem 28

2. Volume of Branch and Root Wood . . . .32

3. Volume of the Bark 34

Chapter III. — Measurement of Standing Trees . . . .35

1. Ocular Estimate 35

2. Estimate of Volume by means of Form Factors . 36

3. Estimate of Volume by means of Volume Tables . . 39

4. Measurement of Standing Trees by Sections . 40
Chapter IV. — Determination of the Volume of Whole Woods . 43

Section I. — Measurements Extending over the Whole Wood . 43

A. Measurement of all Trees 43

B. Determination of Volume by means of Sample, or Type,

Trees 43

I. The Height is a Function of the Diameter . . . 45

1. Description of the General Method . . . .45

2. Modifications of the General Method . . . 52

a. Draudfs Method 54

1). Urich's :\rethod > . . .... 57

c. Robert Hartig's IMethod 59

3. Determination of Volume by means of Form Factors

and Volume Tables 61

4. Comparative Accuracy of the Several IMethods . 63
IL The Height is not a Function of the Diameter . 64

X TAULE OF CONTENTS.

Chapter IV. — continued. i-agf.

Section IJ.— Determination of Volume by means of Sample Plots 66

1. General 66

2. Selection of Sample Plots 67

3. Extent and Shape of Sample Plots . .68

4. Measurement of Volume of Sample Plots . . . 68

5. Merits of the Method of Sample Plots . . .69

Section III. — Determination of the Volume by Estimate . . 69

1. Estimating the Volume of the Wood as a Whole . . 69

2. Estimating by Trees 70

3. Estimating according to the Results of Past Fellings 70

4. Estimating the Volume by means of Yield Tables . 70

Chapter V. — The Age of Teees and Woods 72

1. Determination of the Age of Single Trees . . . 72

2. Determination of the Age of Whole Woods . . . 74

Chapter VI. — Determination of the Increment . . . .78

Section I. — Determination of the Increment of Single Trees . . 79

1. Height Increment 79

2. Diameter Increment 80

3. Area Increment ........ 82

4. Volume Increment 82

Section II. — Determination of the Increment of Whole Woods . 92

A. Determination of the Increment according to the IMean

Annual Increment of the Past 93

B. Determination of the Increment by means of Yield Tables 93

I. Of Yield Tables Generally 93

1. Definition of Yield Table 93

2. Objects and Contents of Yield Tables . . . . 94

3. Local and General Yield Tables . . . .95

4. Quality Classes 95

5. Methods of Constructing Yield Tables . . .97

II. Determination of the Increment by means of Y'ield

Tables 104

PART II.— FOREST VALUATION 109

Chapter I.— Preliminary Matters 112

Section I. — Value of Property Generally 112

Section II. — Choice of Rate of Interest 113

Section III. — Formula; of Compound Interest .... 116
&'<;c^io)i 7 v.— Estimate of Receipts and Expenses . . . .118

1. Receipts 118

2. Expenses 119

3. Examples of Money Yield Table.-, . . .120

TABLE OF CONTENTS. XI

PAGE

Chapter II. — Valuation of Forest Soil 122

Section I. — The Expectation Value of Forest Soil . . . 122

Section JJ.— The Cost Value 130

Section III.— The Sale Value 131

Chapter III. —Valuation of the Growing Stock . . . . 133
Section J.— Value of the Growing Stock of a Single Wood . . 133

1. The Expectation Value 133

2. The Cost Value 137

3. The Sale, or Utilisation, Value 139

4. Eelation between the Expectation and Cost Values . 140

5. Relation between the Expectation and Cost Values

on the one hand, and the Utilisation Value on the

other 141

Section II. — Value of the Growing Stock of a Normal Series of

Age Gradations 141

Chapter IV. — Valuation op Whole Woods or Forests . . . 144

1. The Expectation Value 144

2. The Cost Value 147

3. The Sale Value 148

4. The Rental Value 148

Chapter V. — Determination of the Rental of Forests . . 149

Chapter VI. — The Financial Results of Foresty . . . . 151

Section I. — The Methods of Calculating the Financial Results . 151

1. Determination of the Profit of Forestry . . . 152

2. Determination of the Rate of Interest j-ielded by

Capital invested in Forestry 157

Section II. — The Financial Test applied to the Methods of Treat-
ment 163

PART III.— THE FOUNDATIONS OF FOREST MANAGEMENT 1G7

Chapter I. — The Increment I74.

Section I. — Volume Increment I74

1. Progress of Volume Increment 174

2. Volume Increment Per Cent 183

Section II. — Quality Increment .... . . 186

Section III. — Price Increment ...... 189

Section IF.— The Forest—, or Indicating, Per Cent. . . . 190

Chapter II.— The Rotation I94

1. The Financial Rotation 194

2. Rotation of the Highest Income .... 200

3. Rotation of the Greatest Production of Volume . . 202

4. The Technical Rotation 203

5. The Physical Rotation 203

6. Choice of Rotation 204

Xll TABLE OF CONTENTS.

PAGE

Chapter III.— The Normal Age Classes 206

1. The Annual Coupe 207

2. Size of the Age Classes 209

8. Distribution of the Age Classes over the Forest . 220

Chapter IV. — The Normal Growing Stock 225

1. Calculation of the Volume 226

2. Calculation of the Financial Value . . . . 232
Chapter V.— The Normal Yield 233

1. The Yield determined by Area and Volume . . . 233
•2. The Financial Value of the Yield .... 237
Chapter VI. — Relations between Increment, Growing Stock

and Yield 238

1. Allotment of Increment during a Rotation . . 238

2. Relation between Normal Y''ield and Normal Growing

Stock 239

Chapter VII. — The Real Forest compared with the Normal

Forest 240

PART IV.— PREPARATION OF FOREST WORKING PLANS . 243

Chapter I. — Collection op Statistics 248

Scctimi I. — Survey and Demarcation of Areas . . . . 248

Section II. — Description of each Wood or Compartment . . 250

1. The Locality 250

2. The Growing Stock 251

3. Determination of the Quality of each NYood . . . 256

4. Notes regarding Future Treatment .... 263
Section III. — Past Yields, Receipts and Expenses . . . . 264
Section IV. — General Conditions in and around the Forest . 266
Section V. — The Statistical Report 268

1. Register of Boundaries 268

2. Table of Areas 268

3. Description of Compartments 269

4. Table of Qualities of Locality 269

5. Table of Age Classes 271

6. Table of Past Yields 272

7. Maps 273

Chapter II. — Division and Allotment op the Forest Area . 276

1. The Working Circle 276

2. The Compartment 277

3. The Sub-compartment 278

4. The Working Section 278

5. The Cutting Series 281

6. Severance Cuttings . ...... 282

7. The System of Roads and Rides 284

8. Demarcation of the Divisions of a Forest . . . 288

9. Naming and Numbering of the Divisions of a Forest 288

TABLE OF CONTENTS. Xlll

PAGE

Chapter III. — Determination of the ^^Iethod of Treatment . 290

1. Choice of Species . 291

2. Sylvicultural System 291

3. Method of Formation 293

4. ^Method of Tending 294

5. The Eotation 294

Chapter IV. — Determination and Regulation of the Yield . 295

Section I. — Selection of Woods for cutting in accordance with
Sylvicultural Requirements and the Objects of
Management (Judeich's Method) . . . . 296

1. Clear Cutting in High Forest and the Shelter-wood

Compartment System 297

2. Coppice Woods 302

3. Coppice with Standards 303

4. The Selection Forest 304

5. Change from one System to another, called a Con-

version 305

Section II. — Other Methods of Determining and Regulating the

Yield 310

A. Division of Forest into Fixed Annual Coupes . . 311

B. Allotment of Woods to the Periods of One Rotation . . 311

1. The Method of Periods by Area 312

2. The Method of Periods by Volume 314

3. The Method of Periods by Area and Volume combined 316

C. Regulation of Yield according to Increment and Growing

Stock 316

1. The Austrian Method 317

2. Hundeshagen's Method 320

3. von Mantel's Method 323

4. Brandis' Method 324

D. Regulation of Yield according to Increment and Growing

Stock combined with the Allotment of Areas to Periods

(Heyer's Method) 326

Chapter V. — Control of Execution and Renewal of Working

Plans 330

1. Record of Changes 330

2. Record of Works 331

3. Renewal of Working Plans 331

APPENDICES.

Appendix 1 335

A. Area of Circles for Diameters of 1 inch to GO inches . 336

B. Table of the sum of Circles and of the Volumes of

Cylinders 338

Appendix II.— Tables of Compound Interest 340

XIV TABLE OF CONTEXTS.

PAGE

Appendix III. — Yield Tables 345

Yield Tables for High Forest of Oak . . . . 346

Yield Tables for High Forest of Beech . . .356

Yield Tables for High Forest of Scotch Pine . . . 362
Yield Tables for High Forest of Spruce . . . .368
Yield Tables for High Forest of Silver Fir . . . 374

Preliminary Yield Tables for High Forest of Larch,

Alder and Birch 380

Yield Tables for Coppice Woods 380

Appendix IV. — Geneeal Workixg Plans for the Method of

Allotment of Woods to Periods .... 381

A. Allotment according to Area 382

B. Allotment according to Volmnc 3SS

Appendix V.— Cteneral Working Plan for the Austrian ^Method 390
Appendix VI. —Notes on the Formul.^^ for Compound Interest 307

INDEX 401

FOREST MANAGEMENT

INTEODUCTION.

The management of forests depends, apart from local
conditions, on the objects, which it is proposed to realise.
These differ considerably according to circumstances, but,
whatever they may be, they can be brought under one of the
following two headings : —

(1.) The realisation of indirect effects, such as landscape
beauty, preservation or amelioration of the climate,
regulation of moisture, prevention of erosion, landslips
and avalanches, preservation of game, etc.
(2.) The management of the forest on economic principles,
such as the production of a definite class of produce,
or the greatest possible quantity of produce, or the
best financial results.
It rests with the owner of the forest, in so far as his choice
is not limited by the laws of the country, to determine in each
case, what the objects of management shall be, and it then
becomes the dutj' of the forester to see, that these objects are
realised to the fullest extent and in the most economic
manner.

In some cases the realisation of indirect effects requires a
special and distinct management, but in the majority of cases
they can be produced in combination with economic working.
The present volume deals with the economic aspect of forest
management.

The economic working, whether it aims at the production
of a special class, or the greatest quantity of produce, or the
F.ir. B

Library

2 INTRODUCTION.

best financial results, must be based on the yield of the forest.
In order to determine thi§, the forester must study the laws,
which govern production ; he must be able to measure the
produce and the increment accruing annually or periodically,
to determine the capital invested in the forest, to regulate the
yield according to time and locality, and to organise the
systematic conduct of the business.

Accordingly, Forest Management may be divided into the
following parts : —

Part I. — Forest Mensuration, dealing with the determina-
tion of the dimensions of trees, the volume of
trees and whole woods, their age and increment.

,, II.— Forest Valuation, dealing with the determination
of the capital employed in forestry, and the
financial results produced by it.

,, III. — The Foundations of Forest Management.

,, IV. PRIiPARATION OF FoREST WoRKING PlANS.

PAET I.

FOREST MENSURATION.

b2

FOREST MENSUEATION.

Forest Mensuration deals with the determination]! of the
dimensions, vohime, age and increment of single trees and
whole woods.

These determinations are required for the calculation of the
material standing on a given area, the yield which a wood can
give, and the value of single trees, whole woods and forests.
They serve also as the hasis for the calculation of the effects
of different methods of treatment.

As a rule, the units of measurement employed in Britain
and India are the foot, square foot, and cul)ic foot.

The subject has been divided into the following chapters: —

Chapter I. — Of the Instruments used in Forest Men-
suration.

,, II. — Of the Measurement of Felled Trees.

,, III. — Of the Measurement of Standing Trees.

,, IV. — Of the Measurement of Whole Woods.

,, V. — Determination of the Age of Single Treks
AND Whole Woods.

,, \l. — Determination of the Increment of Single
Trees and Whole Woods.

CHAPTER I.

INSTRUMENTS USED IN FOREST MENSURATION.

Instrujjknts are required to measure the circumference or
diameter of logs and trees, the length of logs, the height of
trees and the increment. Such measurements have for their
ohject, either to ascertain the various dimensions, or to
calculate from them the volume ; in the latter case the
measurement of the girth or diameter is used to calculate the
area of the cross-cut section, on the assumption that it forms
a circle. This is generallj^ called the sectional or basal area.

The instruments may be classified as follows : —

1, Instruments for the Measurement of the Girth.

The girth may be measured with a tape, or with a string
and tape.

The tape consists of a band, about half an inch in
breadth, so constructed that it alters its length as little
as possible when moist. It is divided on one side into
feet, inches and, if necessary, decimals of inches ; on the
other side the sectional areas corresponding to the length of
girth are sometimes noted. It is useful to have a small
hook on one end, which can be pressed into the bark when
the girth exceeds 5 feet. Long tapes are rolled up in cases,
which are made of leather, wood', or metal. Of late years,
flexible steel tapes have come much into use.

The advantages of the tape are, that it is easy to handle
and convenient to carry. Measurements with it are, how^ever,
subject to various sources of inaccuracy, amongst which the
following deserve to be mentioned : —

(a.) The sections of most trees are not circles.

MEASUREMENT OF THE DIAMETEK.

(b.) Owing to the presence of a rough bark, the measured

girth is too large,
(c.) Irregularities in the tree are difficult to avoid.
(d.) The tape is frequently not applied at right angles to the

axis of the tree.
In order to avoid some of the disadvantages of tape measure-
ments, a thin string is sometimes used, which is then held
parallel to a graduated tape or rule. In this way more
accurate results may he obtained, but the procedure takes

Vertical Section of ilovable
i Arm.

Fig. 1. — Friedrich's Calliper.

more time, and is therefore not employed, where large numbers
of trees have to be measured.

2. Instruments for the JSIeasurcment of the Diameter.
The diameter of sections of trees is measured with an
ordinary rule or a tape ; in all other cases the calliper is used,
or sometimes the tree compass.

a. Tlte Callqier, or Diameter Gauge.
It consists of a graduated rule and two arms. Of the latter,
one is fixed at one end at right angles to the rule, so that its

8 INSTRUMENTS USED TN MENSURATION.

inner plane lies in the starting point of the graduated scale ;
the other arm moves along the rule, parallel to the fixed arm.

In using the calliper, the tree is brought between the two
arms, until it touches the rule, then the fixed arm is pressed
against the tree on one side and the movable arm shifted,
until it touches the tree on the other side. The diameter can
then be read off on the rule (see Fig. 1).

The length of the rule and of the arms depends on the size

li!!!!ll!!l!!|!ilil!lil!

l^|iiii|l!iii

of the trees to be measured ; each arm should be at least half
the length of the rule. Callipers exceeding 4 feet in length
are rarely used. The rule is divided into units, which depend
on the desired degree of accuracy. Ordinarily they will be
inches or two inches ; in some cases half inches, and for very
accurate measurements decimals of inches.

T\'here large numbers of trees are to be measured, it is
desirable to round off the limits of each unit ; for instance, if
the rule is divided into intervals of inches, the first division
line is placed at ^ inch from zero, the second at 1^, the third
at '2h, and so on (Fig. 2). In this way all trees measuring from

[EASUKEMENT OF THE DIAMETER.

^ to 1^ inches are recorded as having a diameter of 1 inch,
those from 1^ to 2J inches as 2 inches, and so on.

A good calHper must fulfil the following conditions : —

(1.) It must be sufficiently light, so as not to fatigue the
labourer, and yet sufficiently strong to resist the wear
and tear, to which it is likely to be subjected.

(2.) The two arms must be at right angles to the rule, or at
least parallel to each other, when pressed on to the tree.

(3.) The movable arm must move with sufficient ease along
the rule.

Callipers of iron would be too heavy and too cold in winter.
The former objection has been removed by making the in-
strument of aluminium. However, up-to-date callipers are
generally made of wood. As wood alters with the degree of
humidity, the movable arm is liable to jam at one time, or to
move too easily at others. To avoid this drawback, various
constructions have been adopted, resulting in a number
of callipers, of which the following two deserve to be specially
mentioned : —

Giistav Heyer's Calliper. — The distinguishing feature of
this instrument is, that the rule
is given, in section, the shape
of a trapezium, and that it
is pressed up or down in the
movable arm by means of a
wedge, so as to counteract the
swelling or shrinking of the
wood. In Fig. 3, a represents
the cross- section of the rule,
h the wedge, and c the section of
the movable arm. The wedge
is fastened to a screw, which
can be moved by a key at (/.
On moving the wedge from
left to right, it presses the rule
upwards and thus tightens it ; ^.,^_ 3._iieyei's CaUiper.

10 INSTKUMENTS USED IN MENSURATION.

on moving the wedge from right to left, it releases the rule,
and enables it to move more freely. To force the rule to
follow the backward movement of the wedge, a spring is
fastened at e, which pushes it from right to left, so that it
always must be in touch with the wedge.

Fricdrich's Calliper. — In this instrument the section of the
rule has the shape of a rectangle, while the opening of the
movable arm is larger than the section of the rule, and
placed slanting towards it. At the same time it is so shaped,
that, on being pressed against the tree, it assumes a position,
which is at right angles to the rule (Fig. 1). In this position
the arm rests on the two points, a (below) and h (above). As
these points are liable to wear away, thus causing the arm to
assume a position, which is no longer at right angles to the
rule, Bohmerle has added a spring at h, which can be moved
by a screw, until the true position of the arm is established.

h. Accuranj of Measuremenla wilh tlie CaJJiper.
To insure the greatest possible accuracy, the following
precautions must be taken : —

(1.) Moss, creepers, etc., found on the tree must be removed

before measurement.
(2.) In the case of an abnormal swelling or indenture, the

measurement must be taken above or below it, or both,

and the average taken.
(3.) In the case of eccentric or elliptic trees, two diameters

at right angles to each other must be measured and

the mean taken.
(4.) The height fixed for the measurement must be strictly

adhered to.
(5.) In the case of a tr&e which is divided into two or more

limbs below the fixed height of measurement, each

limb must be measured and recorded as a sejtarate

tree.
(6.) The calliper must be placed at right angles to the axis

of the tree, and the rule must touch the tree.

MEASUREMENT OF THE DIAMETER. 11

(7.) The reading must be taken while the caUiper rests on
the tree, and not after it has been withdrawn.

r. The Tree Compass.

The shape of this instrument will be understood on reference
to Fig. 4. The diameter of the tree or log is taken by the
two points r and d, while it can be read off at // on the are/, g.

In order to produce sufficient stiffness in the arms of the
compass, they have to be made of
metal, which makes the instrument
very heavy and unsuited for con-
tinued use.

ih Dendromcfrrs.

In some cases certain dendro-
meters are used to measure the
diameter of trees at some height
from the ground. The theory is
this : —

The angle which is formed by
two rays running to the two sides
of the tree is measured, as well as
the distance of the eye of the
observer from the tree. From
these data the diameter is calcu- pig. 4._Tiie Tree Compass.
lated. Instead of the angle, the

distance ah between the two lines of sight can be measured,
in which case the diameter is obtained in the following way
(Fig. 5 on next page) :—

C A : C a = AB : a h,
and

AB = %^Xa h.
C a

If, therefore, the instrument gives a h and (' (/, and the dis-
tance C A has been measured, the diameter can be calculated.
So far, instruments of this class have not obtained a footing

12

INSTRT'MKNTS USED IN MENSURATION.

ill practice, because those at present available either do not
Mork \Yith sufficient accuracy, or take too much time.

3. Instruments for tlie Measurement of the Diameter Inerement.

The diameter increment of prepared sections is measured
with an ordinar}- rule, or with a pair of compasses and a rule.
Such rules are made of metal or wood, and are sufficiently
sub-divided.

If no section is available, as in the case of standing trees,
the measurements are made with Pressler's Increment Borer
(Fig. 6). This instrument extracts a cylinder of wood from
the stem, and it consists of the following parts : —

(a.) A hollow borer, A, which is slightly conical from the

handle towards the point.
(b.) A handle, B, which serves as a lever when the instru-
ment is in use. It is hollow and serves to receive the
borer, wedge and cradle, when the instrument is not in
use (see E in figure),
(c.) A wedge, C, which has a scale marked on one side
wherewith to measure the breadth of the concentric

MEASUREMENT OF THE DIAMETER INCREMENT.

13

rings ; it is roughly toothed on the other side to assist
in extracting the cylinder of wood.
(d.) A cradle, D, into which the cylinder of wood is placed,

after extraction, to prevent its breaking.

The borer is used in the following way : —

It is screwed in a radial direction into the tree, at right

angles to its axis, to the desired depth, whereby a cylindrical

column of wood enters the hollow borer, and is severed from

the tree except at its base ; then the wedge is inserted between

Fiff. 6. — Pressler's Increment Borer,

the column of wood and the inner wall of the borer, with its
toothed side towards the former, and firmly pressed in. This
prevents the cylinder from turning round inside the borer
during the following operation. The borer is now screwed
backward one or two turns, whereby the cylinder of wood
is severed at its base from the tree. The borer is now screwed
further in, w'hich causes the severed cylinder of wood to be
pushed back, until it can easily be withdrawn and placed
into the cradle. In this way a column of wood is obtained
of about '2 inches diameter and from 2 to 6 inches long
according to the length of the borer. The breadth of the

14 INSTRUMENTS USED IN MENSURATION.

concentric rings is then measured. If the rings are not distinct,
a smooth surface maj^ be prepared with a sharp knife.

4. IiistriLincnfs for the Measurement of the Length of FclleJ

Trees and Logs.

The length of felled trees and logs is measured with the
tape or measuring staff. The former has already been
described. The staff varies in length up to about 15 feet; it
should be made of hard, straight-grained, well-seasoned wood,
and w^ell varnished to protect it against moisture. The ends
may usefully be capped with metal plates.

5. Instruments for the Measurement of the Height of Standing

Trees.

The instruments, which have been designed for measuring
the height of standing trees, are very numerous, but they are
all based upon one of two principles : either they determine
the height by means of similar triangles (geometrical height
measuring), or they serve to measure the angles of elevation
and depression (trigonometrical height measuring).

a. Geomelrical Height Pleasuring.
If a horizontal plane is drawn from the eye of the observer
to a tree, it will hit the same, according to the position of
the observer, either between the top and the foot of the tree,
thus dividing it into two parts, one of which is situated above
and the other Ijelow the horizontal plane ; or a])ove the top ;
or below the foot. If the observer holds a plumb-line at
some distance from his eye, it may be considered parallel
to the axis of the tree ; hence, by looking at the top and foot
of the tree, similar triangles are formed, which are used for
the determination of the height of the tree.
Let A B (Fig. 7) be the height of the tree.

D B, a. ray from the eye of the observer to the top of
the tree.

HEIGHT MEASURING.

15

Z> .4, a ray from the eye of the observer to the foot of

the tree.
D C, a horizontal hue.

a, h, and c, the points where the three rays hit the phimb
line. Then the heiojht is determined as follows : —

Fig. 7.

(1.) The horizontal line hits the tree between the top and
foot. Here the following equation holds good : —

B C :hc = DC '.Dc
and

B C = ^ ^' ^ ^ ^
D c
Again,

A C : ac = D C : D c
and

a c X D C

AC ^

D

Hence,

B C + AC = AB = height of tree = (^ ^ + « ^) x ^ <^' .
^ 1) c

or,

H = ah X

D C
Dc'

(2.) The horizontal plane passes below the foot of the tree.
In that case (Fig. 8) : —

H = BC-AC = ^^^^^^AR^ = ahx^^

D c

Dc'

16 INSTRUMENTS USED IN MENSURATION.

B

(3.) The horizontal plane passes above the top of the tree
(Fig. 9). Then—

Fiff. 9.

HEIGHT MEASUEING.

17

In each of the above three cases two measurements are
required, unless the foot of the tree happens to be at the same
level as the eye of the observer. The horizontal distance D C
must be measured, and a c, h c and D c are read off upon the
instrument.

The measurement of I) C can be avoided in the following
manner (Fig. 10) : —

A staff M X, of a laiown length = I, is placed alongside the
tree, so that both its ends can be seen. In this way the
plumb-line gives two further points, m and u, and the similar

B

B/

b

- ' "

n

M

Fig. 10.

triangles D C M and I) c m, as well as D C N and Den, so
that the following equations hold good : —

l> C : D c = A B : a h

and

hence,
and

D C : D c = M X : m n ;
A B : ah = M X : m n

A B = H

a h X .V A^ _a h X I

in n m ii

The indirect determination of the distance by means of a
staff is less accurate than measuring it on the ground, as it is
F.M. c

18

INSTRUMENTS USED IN MENSURATION.

difficult to read off m n with sufficient accuracy, owing to its
smallness and the necessarily primitive arrangement of the
height measuring instruments.

If the length oi ah = h can he read off at once, the business
becomes more simple, and may be expressed as follows : —

If two parallel objects are cut by diverging rays, then the
portions of the parallel objects, lying between the said rays,
are proportionate to the lengths of the rays.

Let 1) A = L (Fig. 11) be the length of ray from the eye of
the observer to the foot of the tree, D a = l that from the eye

1'j

4c

Fiff. 11.

to the plumb line, A B = H the height of tlie tree, and a h=]t
the length of the plumb line between two rays going from the
eye of the observer to the top and foot of the tree, then,

Da: D A = a h : A B, or, I : L = h : II

and

A B = 5-i X a h, or, II = ^x h.
D a I

In this case L can easily be measured following the surface of
the soil, whether it be level or slanting, while I and It are read
oft' on the instrument.

The number of hypsometers based upon the above theories
is very large ; some being used with stands, others without.

HEIGHT MEASURING.

19

Only the latter are really useful for forest operations. Most
in use are those by Faustman, Weise, and Christen. Others
are those by Hossfeld, Winkler, Bose, and Klaussner. A very
simple instrument is the measuring board by Konig.

Measurements made with the above-mentioned hypsometers
are liable to yield inaccurate results, owing to the following
causes : —

(1.) Inaccurate reading owing to the unsteadiness of the
plumb line in windy weather, or in consequence of a
shaky hand.

(•2.) Inaccurate measurement of the base line.

(8.) Slanting position of the tree.

Other things being equal, the most accurate results are
obtained, if the distance of the observer from the tree equals
the height of the tree.

The inaccuracy of the better hypsometers does not exceed
2 per cent, of the height of the tree.

h. T'rigonomctrical HelgJit Measuring.

This is based upon the measurement of the angles of eleva-
tion and depression indicated by rays running from the eye of

#:

■■X

Fi<?. 12.

-i

the observer to the top and foot of the tree. In /\ B C D
(Fig. 12)- BC = DCx tan. h.

c2

20

INSTRUMENTS USED IN MENSURATION.

and in a A C D

hence, ^^ C = DC X tau. a :

A C + B C = height = 11 = 1) (' (tan. a + tan. h).
If the horizontal h"ne of vision passes below the foot of the
tree, the above formula becomes —

H = D C (tan. h - tan. a).
If it passes above the tree —

H = D C {ta)i. a - tan. h).

B

#

^:: 1,- J -^.

In each of these cases the measuring of the horizontal line
D C can be avoided b}' placing a staff of known length along-
side the tree. In that case (Fig. 13) —

and

hence,

M C = D C X tan. m ; K C = 1> C X tan. n
M X = 1 = I) C {fan. m + tan. n) ;
I

DC =

tan. ni -\- tan. n'

WEISE S HYPSOMETER. 31

B}^ introdacing this value into the former equation, the
height is obtained as —

H

_ I X {tan, a -|- tan, h)
tan. m + tan. n

All instruments which measure vertical angles are suited
for trigonometrical height measuring. For practical purposes
it is desirable that the instrument should not require a stand,
and that, besides the angles, the corresponding tangents
should be marked on it.

c. Description of some of the more imful Instruments.

Weise's Instrument. — It consists of (1) a tube T with an
objective in the shape of a cross at one end 0 and an eye-

Fig. 14. — Weise's Hypsometer.

piece E at the other. (2) A scale fastened longitudinally to
the tube (called the height scale, H, Fig. 14) ; it is toothed on
one side, and has the zero point some distance from its end.
(3) A second scale, D, moving at the zero point of the height
scale and at right angles to it (called the distance scale).
From the upper, or zero, point of this scale depends a plumb
line P.

When not used, the distance scale and plumb line are kept
in the tube.

2a

INSTRT'MENTS T'SED IN IMENSUKATIOK.

In using the iiistrnment, a position is chosen, from which
both the top and foot of the tree can be seen ; then the
horizontal distance from the point of observation to the tree
is measured, and the distance scale drawn out, until it indicates
at the zero point of the height scale the number of units in
the distance ; then the tube is raised and directed towards the
top of the tree, taking care that the up and down line of the
objective keeps a vertical position. As soon as the horizontal
line of tlie cross covers the top of the tree, the tube is gently
turned from left to right, thereby causing the plumb line,
which hitherto swung free, to be caught by the toothed edge

i.

:>?l^'^:-

Fig. 15.

of the height scale. The instrument is then taken down
and the number of units, from the zero point to the point
where the plumb line was arrested, read oft". This number
gives the number of feet (or yards, as the case may be) from
the horizontal of the eye of the observer to the top of the tree.
To this must be added (or deducted) the difference in height
between the eye of tlie observer and the foot of the tree,
whicl) is obtained in the same way, by directing the tube
towards the foot of the tree, and reading the lieight on the
prolongation of the scale to^^ards O. An improvement of
the instrument would be the addition of a guide for tlie
plumb line.

The theory of the instrument rests upon the similarity of

CHRISTEN S HYPSOMETER.

23

the triangles with the sides 11 II D and /• // d ; that is to say,
the followino; equation holds good : —

and

d:h=D:H

Fig. 16. — Christen's Hypsometer.

If, therefore, the units of the scales, which give h and d, are
of the same size, and d is so fixed that its units are the same
number as the units of the measured distance D, it follows,
that the above formula gives the height.

Christen's Instrument. — It consists of a piece of metal (see
Fig. 16) with protruding upper and lower edges (see a and 1))

24 INSTRUMENTS USED IN MENSURATION.

The instrument is based upon the theory explained on page
17, which avoids the measurement of a base line. A staff of
known length = /, say 4 3'ards, is placed alongside the foot of
the tree. The instrument is then held in a vertical position
at some distance from the observer, and moved backward and
forward, until the top of the tree is seen along the upper edge
a, and the foot along the lower edge }> ; then the point is
marked on the instrument, where a ray from the eye to the
top of the staff hits the instrument at e. In this way
similar triangles are formed, in which the following equation
holds good : —

he A B

If now ah = 12 inches, and / = 4 yards, and successive values
for A B = height of tree, are introduced, corresponding values
oih c are obtained and can be marked on the instrument. In
this way the heights can be read off straight on the instrument.
For convenience sake, the marks on the instrument are cuts, so
that the place on the scale, where the top of the staff cuts in,
may be more easily seen.

The instrument has the disadvantage that the marks are
very close one to another for heights over 30 yards. This
might be obviated to some extent by lengthening the instru-
ment and making it with a clasp in the middle, so that it
could be folded together when out of use.

It is evident that, instead of using a staff 4 yards long, one
of, say, 2 yards can be used. In that case the height read
off on the instrument must be divided by 2.

The instrument works well up to heights of 25, or at the
outside of 30, yards ; for higher trees it cannot be recommended
in its present shape.

Brandis' Hiipsometer (Fig. 17) is based upon the trigono-
metrical method of height measuring. It consists of a tube
with an objective, 0, at one end and an eye-piece, e, in the shape
of a horizontal slit, at the other. Attached to this tube is a

I'ibrarv

BRANDIS HYPSOMETER.

25

wheel, which is weighted on one side and swings between two
pivots, so that it always maintains the same position when at
rest. Oscillations can be ai-rested by a stop (see at s in figure).
That point of the wheel, which corresponds with the horizontal
line of vision, is marked as zero, and from this point the wheel
is graduated to 60^ up and down. A lens is fastened along-
side the eye-piece, to facilitate the reading of the angle on the
wheel. By directing the tube to any point, the angle can be
easily read off on the wheel, which preserves the same position
while the instrument is being raised or lowered. The wheel
is placed in a firm metal case.

Fig. 17. — Branditi' Ilypsonieter and Clinometer.
(The front lid I'enioved, so as to show the wheel,)

In using the instrument, any convenient position, where
the top and foot of the tree can be seen, is chosen, the angles
to the top and foot of the tree read off, and the distance from
the e^^e of the observer to the foot of the tree measured. The
height is then found by the formula (see Fig. 18) —

D A X sin. (u + 0 *

H =

COS. u

This formula is obtained in the following manner : —

Height - 11= I) CQaii. u + fun. I).
Since D O = D A x cii>'. I :
II = D A X vox. I [tan. u + tan. I)

H

B A X COS. I X

n'ni. n X COS. I + sin. I x cos.

COS. U X COS. I

-. . sin. (ji + 0

26

]NSTRT-:\rEXTS TSED IX MENSURATION.

For convenience sake, a little table accompanies the instru-
ment, in which the heights, corresponding to various distances
and upper plus lower angles, are given. In order to reduce
this table as much as possible, it gives only upper angles from
40° to 50° in intervals of 2°, and lower angles from 0° to 25° in
intervals of 5°. This necessitates placing a staff, on which
feet are marked by alternate colours, alongside the tree, so as
to read off the distance between the lower ray of the lower
angle and the foot of the tree, a distance which has to be
added to the height taken from the table.

The instrument is at tlie same time an admirable clino-
meter, with which the angles of slopes can be measured and

^ "

^ ^

7-

' ' "', "

--..-_.-.....

-v^i^

^^-^^W^^

y/Tz^

Fiff. 18.

roads laid out. The author has used the instrument exten-
sively, both for the measurement of the height of trees, and
for the laying out of forest roads ; he has arrived at the
conclusion, that it is decidedly the most useful of similar
instruments, which are known to him. The instrument works
accurately, and much quicker than the reader would imagine ;
besides, its strong const-ruction renders it admirably adapted
for forest work.

0. luHtrumentsfoy ihe Inrcct JSIeasurevK-nt of the Volnme.

For this purpose the xylometer, either alone or in com-
bination with a scale, is used. The method is based upon

MEASUREMENT OF VOLUME WITH THE XYI,OMETER. 27

the fact, that a sultmerged body displaces a vohime of water
equal to the volume of the body, and the instrument used is
called a xylometer. It consists of a graduated vessel, Fig. 19,
in which the wood is submerged. Before and after submersion,
the position of the water is noted, and the difference gives
directly the volume. The method is employed for the measure-
ment of irregular pieces, such as root wood and fagots. To
obviate the necessity of submergmg large quantities of wood,
the whole is first weighed, and only a portion submerged.
Let the weight of the whole be = W, that of the submerged

Fig. 20. Fig. 19.

portion = ir, the volume of the former = T', of the latter v,
W : ir = V : r

then :
and

T^ = - X ir.

w

Instead of having a graduated vessel, the latter may be
filled up to an opening, then the wood is submerged, the out-
flowing water caught in a separate vessel and measured
(Fig. 20).

Note. — Pressler's Increment Borer can be obtained from
Herr Moritz Perles, Verlagshandlung, Wien, Austria ; Brandis'
Hypsometer from Herr Max Wolz, Bonn, Germany. All the
other instruments can be procured through Herr Wilhelm
Spoerhase, 37, Stein Strasse, Giessen, Germany.

28

MEASUREMENT OF FELLED TREES.

CHAPTER 11.

MEASUREMENT OF FELLED TREES.

The methods of measuring the various dimensions of felled
trees have been explained in Chapter I. In this place the
measurement of the volume will be dealt with.

Each tree consists of a stem or trunk, branches and roots.
These have peculiar shapes of their own, which differ con-
siderably ; hence they must be considered separately.

1. Volume of the Stem.

If the stem, or trunk, of a tree had a regular or distinct shape,
its volume could be calculated direct by means
of a formula corresponding to that particular
shape. As a matter of fact, the stem shows
different shapes in different parts of the tree.
Again, the shape of trees differs widely
according to species, the ages of the trees,
and the conditions under which they have
grown up, whether in the open or in a crowded
wood. At the same time, trees of the same
species and age, which have grown under the
same conditions, generally show shapes, which
are nearly identical. Moreover, experience
has shown, that each part of the stem shows
approximately a constant form. Thus the
uppermost part, a (Fig. 21), of an undivided
stem has generally the shape of a cone, the
lowest part, c, that of a truncated semi-cubical
paraboloid, while the bulk between these
extremes approaches in shape a truncated
Appollonian paraboloid, or a cylinder.

VOLUME OF THE STEM.

29

If h = the height, or length,
*S' = the lower section,
s = the upper section, and
s.^^^ = the middle section (Fig. 22),
the volume of each of the above-mentioned
truncated solids is, according to Simpson's
rule —

6

X h.

This formula reduces —

For the cylinder to V = S X It

For the cone to V = ^^

^

S ■>',

/ \

Sm

Fis. 22

And for the truncated Ap. paraboloid to T

■ = '^xh,ov,

By means of these formulae it would be possible to calculate
the volume of each part of the stem, provided its particular
shape had first been ascertained. This, however, would be a
tedious business, and it is necessary to search for a more
simple procedure.

It has been found, that by far the greater portion of the
stem approaches in shape that of a paraboloid, and that, if
the stem is divided into a number of pieces of moderate
length, each can, without committing any appreciable error,
be considered as a truncated paraboloid, the volume of
which is —

V =i S,n X h.

Of these two formula, the latter is the more convenient, and
experience has shown, that it is even more accurate than the
former.

30

MEASUREMENT OF FELLED TREES.

Accoi-ding to this method the V(jhime of the whole stem is
obtained by means of the following formula (see Fig. 23) : —

Volume of stem = si Iti + ^._i /',) + «:j /'3 + • • -5

where si, s^, s^ . . . are the sectional areas taken in the middle
of successive paraboloids, and lii, Jio, //3 . . . the corresponding
heights or lengths. If the pieces are made of equal length,
the above formula changes into the following : —

h.

Fig. 23.

Volume of stem = (si + so + .S3 + . . .) h.

This formula is used in all scientific investigations, and the
degree of accuracy, with which it works, depends on the length
of the pieces.

For the purposes of determining the yield of woods and
for the sale of logs, the formula is further simplified by con-
sidering each log as one paraboloid, in other words, the
volume is calculated from the middle section of the log
multiplied by its length, according to the formula —

where H„, represents the area of the circle, or sectional area,
in the middle, and H the total length of the log. Experience
has shown this formula to give sufficiently accurate results
for all practical purposes.

The sectional area is obtained, either by measuring the
girth, or the diameter. If ry==girth, and fZ=diameter, the
section is —

S =

47r

•07 9G X >f,

and

VOLUME OF THE STEM. 31

S = ~= -780 X d- {= r X tt),

V = -0796 X 'f X //,

or

V = -785 X cl' X H {= r X vr x H).

In practical work, the sectional areas are taken from specially
prepared tables ; there are also tables which give directly the
volume of logs according to their mean girth and length, or their
mean diameter and length. (See Appendix I., page 335.)

All these calculations are made on the assumption, that the
section represents a circle. This is, however, rarely the case.
As a rule, the degree of divergence from the circular shape
depends on : —

(1.) The part of the stem; the lowest and uppermost parts

differ most.
(2.) The age of the tree ; young trees are more regularly

shaped than old ones.
(3.) The species.

(4.) The conditions under which the tree has grown up ; in

crowded woods the shape is more regular, than in the

case of trees grown in the open ; exposure to strong

winds, slanting position and the nature of the soil also

affect the shape.

Generally, the sections of trees approach the shape of an

ellipse, the greater axis of which lies, in the same locality, as a

rule in a constant direction. Where trees are much exposed

to wind, the greater axis lies generally in the direction of the

prevailing wind : in Western Europe, therefore, from west to

east or from south-w^est to north-east.

The inaccuracy caused by measuring the girth, and calcu-
lating therefrom the sectional area, has been found to amount,
on an average, to about 7 per cent. ; w4iere only one diameter
is measured, the error may be the same or even more ; where
two diameters at riLrht angles are measured aud the mean

32 MEASUREMENT OF FELLED TREES.

taken, the error generally does not exceed 2 per cent, of the
true value.

In Britain and in India, the sectional area in the middle is
calculated hy the method of the quarter girth, that is to say,
by the formula —

,S = (|)^ = -0625 X[f.

In comparing this with the real sectional area = "0796 X^r,
it is found, that the quarter girth method gives only 78i per
cent, of the true volume, omitting 21^ per cent. The method is
based upon the assumption, that this amount represents the
waste incurred in squaring the timber. Quantities calculated
by the exact method can be converted into the quantities cor-
responding to the other, by deducting 21|^ per cent, of the
volume. If the bark has been omitted in the measurements
in both cases, no further correction is required. In measure-
ments according to the quarter girth, it is usual to deduct for
the bark one inch out of every t\Yelve of the quarter girth,
before the latter is squared. Hence the deduction on account
of bark comes to 12 X 12 — 11 X 11 = 144 — 121 = 23 square
inches out of every 144. In other words, a reduction of
16 per cent, is made on account of bark. This may be too
much in some cases and too little in others. It is a much
better plan, in the case of felled logs, to take off a ring of
bark, so as to measure the girth over the wood only.

Generally speaking, it may be said, that the volume calcu-
lated according to the quarter girth method is equal to three-
fourths of the volume in the round.

2. Volume of Branch and Root Wood.

In some cases, pieces of branch and root wood are of a
sufficiently regular shape to measure and calculate their
volume in the manner given above. As a general rule, how-
ever, such wood requires a different treatment* Its volume is
ascertained by shaping it according to custom and stacking

VOLUME OF BRANCH AND ROOT WOOD. 33

it in a space of regular geometrical form. The volume of this
space is ascertained, as well as the quantity of solid wood of a
particular description, which can be stacked in it.

Taking, for instance, a space of 100 cubic feet, the quantity
of solid wood, which can be stacked in it, is ascertained,
according to whether the material consists of split wood,
round billets, branch wood, fagots or root wood. This can be
done by measuring each piece separately, an operation of
considerable difficulty, and one which takes much time. A
more expeditious way is, to submerge the material in a xylo-
meter and ascertain the volume by measuring the quantity
of the displaced water. From the data thus obtained, aver-
age coefficients are calculated and used on all subsequent
occasions.

It is evident, that different descriptions of wood give different
coefficients. The solid contents of stacked wood depend on
many things, amongst which may be mentioned : —

(1.) Shape and nature of the pieces ; thick, smooth and
straight pieces give more solid contents than thin,
bent, uneven pieces.
(2.) Length of pieces ; short pieces pack better than long
ones; hence, they give a higher percentage of solid
contents.
(3.) Method of stacking ; careful stacking causes the per-
centage of solid wood to be considerably increased.
Under these circumstances, no absolutely average data can
be given. By way of illustration it may be mentioned, that
the coefficients, which are officially recognised in Hesse-
Darmstadt as representing averages, are the following : —

Split firewood = "7

Round firewood billets under 5" diameter = '6
Eoot and stump wood . . . . = '5
Fagot wood stacked (not bound) . . = "2

That is to say, 100 cubic feet of stacked split firewood
contain 70 cubic feet of solid wood and 30 cubic feet of air, etc,

F.3I. D

34 MKASUREMENT OF FELLED TREES.

3. Vohune of flic Bark.

In many cases it is desirable to ascertain the volume
of the bark, especiall}' when it is sold separatel}' as in the
case of tanning bark. This can be done stereometrically or
xylometrically. In the former case the pieces of wood are
measured before and after barking, the difference giving the
volume of the l)ark. If a xylometer is used, the bark can be
measured separately, or the pieces of wood are measured
before and after barking.

According to species, age and locality, the bark comprises
from 6 to '10 per cent, of the total volume. Schwappach
found on a limited number of trees the following results : —

Oak

. = 1 5—20%

Alder .

. = 16—19%

Ash

. =12-14

Lime

. = 16—19

Elm

. = 9—11

Aspen

.= 9—18

Birch .

. = 13—17

Scotch Pine

. = 10—16

Tanning bark is usually sold by weight ; other bark is sold
according to measurement, like firewood.

85

CHAPTEK III.

MEASUREMENT OF STANDING TREES.

1. Ocular Estimate.

Originally, the volume of standing trees was estimated.
Such an estimate takes into consideration the special shape or
form of each tree, and fixes the volume accordingly. The
accuracy of purely ocular estimates depends entirely on the
person, who makes them. To be only approximately correct,
the estimator requires great practice and occasional oppor-
tunities to compare his estimates with actual measurements,
after the trees have been felled. Even then the results are
subject to considerable errors, unless the estimator practises
his art constantly. Mistakes of 25 per cent, are of common
occurrence, and they may reach up to 100 per cent, in the
case of an inexperienced estimator.

The uncertainty of purely ocular estimates led to the
measurement of diameter (or girth) and height; this done,
the basal area near the ground can be calculated, multiplied
by the height and an estimate made of the actual volume of
the tree. It stands to reason, that such an estimate is less
dependent on the individuality of the estimator, than that
mentioned above, since he has only to estimate the proportion,
which exists between the actual volume and that of an
imaginary body constructed out of the height and the sectional
area at the base, a matter which he must decide according to
the peculiar shape of the tree. By degrees it was considered
desirable to collect data regarding the form of various trees,
which might be utilised in subsequent estimates, and thus
foresters arrived at the method next to be described.

n 9.

36 MEASFEKMENT OF STANDING T«EES.

2. Estimate of Volume hy means of Form Factors,
a. DefiniUon and Classification of Form Factors.

By " form factor " is understood the proportion, which exists
between the vohime of a tree and that of a regularly-shaped
body of the same base and height as the tree. The
form factor means, therefore, a coefficient, with which the
volume of the regularly-shaped (geometrical) body must be
multiplied in order to obtain the volume of the tree.

Any regularly-shaped body, the volume of which can easily
be calculated by means of a mathematical formula, is suited
for the above purpose. In practice, only the cone and cylinder
have been employed, and at the present time onh' the latter is
used. Let s be the area of the basal section of the tree, h its
height, / the form factor and r the volume, then —

Volume of cj-linder = s X h,
Volume of tree = v = s X h X /,
and

r

Form factor = f =

s X h

The volume of the stem of a tree by itself is always smaller
than that of the corresponding cylinder ; hence, the form factor
for the stem only is always smaller than 1. If the volume of
the branches is added, the form factor is sometimes greater
than 1, especially during the early youth of the tree.

Various kinds of form factors are used in forestry, of which
the following may be mentioned : —

(1.) Stem form factors, which refer only to the volume of

the stem above ground.
(2.) Tree form factors, which refer to stem and branches,

omitting root wood.
(3.) Timber form factors, which refer onl}' to the parts of
the tree classed as timber, whether they are taken
from the stem or branches, omitting all other
material.

ESTIMATE BY MEANS OF FOmi FACTORS.

87

Form factors for l)ranch wood, fagots, or root wood only are,
as a rule, not used ; their volume is ascertained by utilising
the results of actual fellings and determining their proportion
to the volume of timber.

As it would be highly inconvenient to measure the diameter,
or girth, of the tree close to the surface of the ground, where
it is usually cut, it has been agreed to take the measurement
at a convenient height.
According as to whether
that point is fixed or vari-
able, the following kinds
of form factors may be
distinguished : —

(1.) Absolute Form Fac-
tors. — The diameter (or
girth) is measured at any
convenient height above
the ground, and the form
factor refers only to the
part a of the tree above
that point (Fig. 24), while
the volume of the piece b
below it is ascertained by
separate measurement and
added to the rest. This
is evidently troublesome
and takes extra time.

(2.) True or Normal Form Factors. — The diameter (or girth)
is measured at a constant proportion of the height of the tree,
say, i\)th, 2^oth, etc. (Figs. 24 and 25). In this case the height
of the ideal cylinder is equal to the height of the tree. Such
form factors, it was believed, would have the advantage, that
all trees of the same shape would have the same form factor,
since they have been measured at a height, which bears in all
cases the same proportion to the total height. There are,
however, various drawbacks to the employment of these form

Fitr. '25.

3S MEASUREMENT OF RTANDTXa TREES.

factors. In the first place, the height of the tree ninst lie
determined, before the point of measurement can be fixed ;
secondly, the latter may he very inconvenient in the case of
very tall, as well as very short trees ; thirdly, it has been
found from actual measurements, that the factors thus
obtained are by no means so regular as had been supposed,
that is to say, trees of different heights show by no means
the same form factor if measured at a constant proportion
of the height.

(3.) Form Factors based on Measiiremejits made at Hchjht of
Chest, called Artificial Form Factors. — The diameter (or girth)
is measured at the most convenient height from the ground,
namely at chest-height of an ordinary man. (In Germany and
France now generally fixed at 1'3 meters = about 4 ft. 3 in.).
The height of the ideal cylinder is equal to the height of the
tree. Owing to the measurements being taken at an absolutely
constant height, the form factors of two trees, which show the
same shape but differ in height, cannot be the same. It follows,
that, in using such form factors for calculating the volume of
trees, the height of the latter must be taken into consideration.
Nevertheless, in practice, these are the only form factors
now used.

J). Delerminalion of Form Factors.

At first form factors were estimated, taking into considera-
tion all points which affect them, such as species of tree,
height, age, free or crowded position, etc. Such an operation
requires much skill and practice, and in fact it comes pretty
much to the same thing as estimating the volume direct.
To eliminate such uncertainty, tables have been prepared,
which give the form factors for different species, heights and
ages, such tables being based upon the results obtained by
the measurement of numerous felled trees. Of late years, it
has been recognised, that the variations due to age can be
omitted, except where great accuracy is required, as in
scientific investigations.

ESTIMATE BY MEANS OF VOLUME TABLES.

39

The follo^Ying table shows the form factors, taken from the
Yield Tables in Appendix III., on pages 345 to 379.

Height

Form Factors for Timber in the

FOKM

Factors for Timber

N THE

Height

of

ROUND DOWN TO 3 INCHES

ROUND AND FaGOTS (EXCLUSH'E OF

of

Tree

DIAMETER.

Root Wood).

Tree

or
Wood.

or
Wood.

Feet.
20

Oak.

Beech.

Scotch
Pine.

Spnice.

Silver
Fir.

Oak.

Beech.

Scotch
Pine.

Spruce.

Silver
Fir.

Feet.

•07

•19

•32

•36

•40

•84

•76

•86

102

110

20

30

•28

■33

•38

•48

•45

•67

•69

•72

•89

•82

30

40

■38

■41

•44

•52

•48

•62

•65

•64

•78

•69

40

.50

•4.5

•45

•46

•53

•49

•59

•61

•58

•71

•64

50

60

•48

•47

•47

•53

•50

•58

•60

•55

•66

•61

60

70

•.50

•4S

•47

•54

•50

•57

•59

•53

•62

•60

70

80

•51

•49

•47

•52

•51

•57

•58

•52

•59

•59

80

90

•.51

•49

•47

•51

•52

•57

•58

•51

•57

•58

90

100

•52

•.50

•46

•50

•51

•57

•59

•50

•55

•57

100

110

•52

•52

•46

•49

•51

•57

•60

•50

•.53

•56

110

120

•53

•54

•4(i

■49

•.50

•.-.8

•61

•49

•52

•55

120

130

•48

•50

•52

•55

130

140

•48

•50

•52

•55

140

i.-,o

•47

...

•51

...

1.50

In the case of quarter girth measurements, the form factors may be placed at
three-fourths of those for timber in the round. For instance, the form factor
for 70 feet high oak would be = •oO x f = ■37.

In using these tables, it must not be forgotten, that they
give the averages of numerous measurements ; hence, they do
not give reliable results in calculating the volume of a single
tree. Their application should be restricted to the calculation
of the volume of a number of trees — in other words, of whole
woods — where the differences between the several trees are
likely to compensate each other. (See example on pages 60
and 61.)

3. Estimate of Volume hi/ means of J'olume Tables.

If, instead of giving the form factors only, they are multi-
plied by the corresponding heights and basal areas, the
volumes of the trees are obtained, which can be arranged into
so-called " volume tables." The latter may be defined as tables,
which give the volume of single trees arranged according to
species, age, diameter and height of tree.

40 MEASUREMENT OF STANDING TREES.

These tables rest upon the assumption, that trees of the same
species, which have reached in the same time an equal height
and diameter, show also an equal volume, and that trees of the
same species, diameter, and height show volumes, which differ
with the age of the trees; in other words, the volume becomes
greater with advancing age, although the height and the dia-
meter at chest-height may be the same. Foresters say the
trees become less tapering, or more full bodied, or the point,
where the real tapering commences, moves higher up the tree
with advancing age.

In order to use such tables, it is necessary to ascertain the
diameter at chest-height, the total height and the approximate
age of the tree, when the volume corresponding to these data
can be obtained from the tables. It must, however, not be
forgotten, that the tables give only averages and consequently
only true results, if used for determining the volume of a
number of trees, or of whole woods.

Note. — The Bavarian volume tables are based upon the
measurement of 40,000 trees ; they give the volumes for
spruce, silver fir, larch, oak, beech and birch, arranged into
two age classes (up to 90 years, and above 90 years old),
the trees having been measured at a height of 4ft. Sin. above
the ground.

Volume tables are nowadays less used than form factors,
as the latter are more handy.

4. Measurement of Standing Trees hy Heetions.

Analogous to the measurement of felled trees b}^ sections,
the volume of standing trees can be ascertained by determining
the diameter (or girth) at various heights from the ground.
For this purpose, a man must be sent up the tree, which is a
cumbrous procedure, or the several diameters must be deter-
mined indirectly. The latter, as has been explained in
Chapter I. (page 11), is subject to great inaccuracies; hence,
the method is without practical value.

Where the diameter at half height is wanted, it is often

MEASUREMENT BY SECTIONS. 41

estimated from the diameter at height of chest. The method is
a rough one, but much used in Britain, France and Belgium.
As far as the author is aware, no uniform method of esti-
mating the girth or diameter at half height, from the girth
or diameter at, say, height of chest, has been recognised in
Britain. Consequently, the actual estimate depends on the
individuality of the estimator. No wonder, then, that different
estimators obtain different results. The calculation of the
volume by means of form factors, which represent the average
of numerous measurements of trees lying on the ground,
leaves no latitude to the estimator. He measures the dia-
meter of the tree at height of chest and the height ; he takes
the basal area and form factor out of a little table which he
carries in his pocket, and obtains the volume by a simple
multiplication.

Example. — An oak tree, grown in a fairly stocked wood, has
a diameter of 12 inches at height of chest and a total height
of 70 feet. On reference to the table on page 336, it is found
that the basal area, corresponding to a diameter of 12 inches,
is s = 0*7854, and on reference to page 39 the form factor for
a height of 70 feet will be found to amount to '50 for timber
in the round, or '37 (= | of "50) for quarter girth measurement.
Hence the volume V = "7854 X 70 X '50 = 27-5 cubic feet
in the round, or V = '7854 X 70 X '37 = 20-3 cubic feet
quarter-girth measurement. The product of '7854 X 70 can be
obtained from the table on page 338, without multiplication.

On the other hand, according to British custom, the esti-
mator has to do three things : (1.) to measure the girth at
height of chest, say, = 38 inches ; (2.) the length of service-
able timber, say 50 feet; and (3.) to estimate the girth at
25 feet from the ground. Supposing he estimates a decrease
of 20 per cent., then the girth at 25 feet comes to about
30 inches, and the volume, according to the quarter-girth
measurement, amounts to —

144

42 MEASUREMENT OF STANDING TREES.

If he estimates the decrease of the girth at 15 per cent., the
girth at 25 feet from the ground would l)e 32 inelies, and

T — \ , , — = 22*2 cubic feet.
144

If he estimates the decrease at 25 per cent., the girth at
25 feet comes to about 28 inches, and

r='^' J ]</'» = 17-0.

In fact, the vohime thus estimated would range from 17 to
22*2 cubic feet, and the only chance of obtaining the exact
amount depends on the skill of the estimator, thus intro-
ducing a factor of considerable uncertainty. Hence, the most
urgent need for the estimation of trees grown in fairly well-
stocked woods is the collection of data, from which form
factors can be calculated, whether for determining the volume
in the round, or according to quarter girth measurement.
Tbe method is, however, not applicable in the case of hedge-
row trees, or others grown under similar conditions. In the
latter case, each tree must be measured, or estimated,
separately.

48

CHAPTER lY.

DETERMINATION OF THE VOLUME OF WHOLE
WOODS.

This chapter mav be divided into three sections, according
to whether the measurements extend over the whole wood, or
over only a selected portion of it, or whether the volume is
estimated.

Sfxtion I. — Measurements extending over the Whole
Wood.

The method demands a uniform treatment of the whole
wood, but a distinction may be drawn between the measure-
ment of all trees and that of selected trees, called sample,
or type, trees.

A. Measurement of all Trees.

Each tree is measured separately and its volume ascertained
in one of the ways described in Chapter III. By adding up
the volumes of the several trees, that of the whole wood is
obtained.

As the method takes much time, it is, in practice, only
employed when the total number of trees is small, or when
the wood is of an irregular description. As a rule, the
following system is chosen, as it works more rapidly.

B. Determination of Volume by means of Sample, or

Type, Trees.
The volume of a wood consists of the sum of the volumes
of the individual trees. The volume of each tree is calculated
according to the formula —

r = s X Jt X ./,

44 MEAST^REMENT OF WHOLE WOODS.

where .s represents the l)asal area at a certain height, Ji the
total height and f the form factor of the tree. In all cases,
where s, h, and /differ from tree to tree, nothing remains but
to ascertain them separately for each tree as indicated under
A. In the case of regularly grown woods, however, there are
always a number of trees, which show, at any rate approximately,
the same basal area, height and form factor, so that they can
be thrown together and dealt with in a uniform manner ; in
other words, all trees of a wood, which show the same base,
height and form factor, are joined into one class ; the volume
of one tree (or of a few trees) is ascertained and the volume
of the whole class obtained by multiplying the former by the
number of trees in the class. If every class is dealt with in
the same way, the vokime of the whole wood is obtained by
adding together the volumes of the several classes.

So far, however, little or no advantage is gained, because it
would be necessary to ascertain the base, height and form
factor of each tree, in order to put it into its proper class, and
when this has been done, the volume of each tree may just as
well be calculated separately. Moreover, in crowded woods
the height is not always easy to measure, and the form factor
could only be estimated, unless it is taken from a table. Only
the basal area is easily ascertainable by measuring either
the diameter or the girth.

Here, experience had to be called in, which fortunately
showed, that, in regularly-grown crowded woods, the height
and form factor are approximately functions of the diameter
of the tree ; in other words, trees of the same diameter have
approximately the same height and form factor. At any
rate, this is found to hold good to a sufficient extent, so
as to justify a classification according to diameter classes
only.

In open woods, however, the height and form factor vary
within much wider limits, so that, besides diameter classes, at
any rate also height classes must be formed. Hence, the two
cases must be dealt with separately.

GENERAL METHOD OF SAMPLE TREES. 45

/. — The Height is a Function of the Diameter.

1. Descriptum of the General Method.

a. Fonnafion of Diameter Glasses.

The number of classes depends on the difference between
the largest and smallest trees of a wood and the desired degree
of accuracy. As a rule, all classes are given the same extent,
that is to say, either 1 inch, 2 inches, 3 inches, etc., or part of
an inch. For the purpose of forest working plans in Europe,
each class comprises 1 or 2 inches : in India frequently as
yet 6 inches.

The calliper, used in measuring the diameters, should have
a rounded-off scale, as described in Chapter I., that is to say, in
the case of inch classes, the first should comprise the space
from J to li inch; the second that from Ih to 2^ inches, etc.
For scientific investigations the classes may be further reduced
to a part of an inch.

h. Height and Manner of Measurement.

All trees must be measured at the same height, the latter
being so chosen, that the place of measurement falls above the
irregular swelling frequently observed near the foot of the tree;
at the same time, the height should not be so great, that it
becomes difficult for an ordinary-sized man to measure accu-
rately. Whenever practicable, the height should be the height
of chest of an average man.

In executing the measurement, all the precautions indicated
in Chapter I. must be duly taken, so as to obtain as accurate
results as possible. More especially, any irregularity in the
shape of the sections must be duly considered. "Where the
section differs systematically from that of a circle, either two
diameters at right angles must be measured, or the direction
of measurement changed from time to time. For instance,
after a certain number of stems have been measured with the
face of the measurer to the east, an equal number must then

46

MEASUREMENT OF WHOLE WOODS.

be measui-ed with the face of the measurer towards the north
or south. Or the change can be made at alternate trees. In
this manner average diameters are obtained.

r. The Boolciwi of ihe Measurements.

In measuring' the diameter, the gaugers call out each
measurement and in mixed woods also the species ; the book-
keeper enters each announcement, repeating it at the time, so
as to prevent mistakes.

A book-keeper may work with one or two gaugers, the
party taking a narrow strip of the wood at the time ; each tree
is marked as soon as measured, preferably with chalk.*

The booking can be done in a variety of ways, as the follow-
ing samples will show: —

Diameter
in Inches
measured
at 4' 3"
from the
Ground.

Species.

Number of Trees.

Beech. Gale.

Ash.

Beech.

Oah.

Ash.

Total.

'

fweeiii

IW.J!

1

18

9

3

30

9

iT 1 111 %'. if
111

m i III

mill

23

13

8

44

10

n:-

a

37

13

9

59

11

• •••••••'

.....

27

14

7

48
181

.....

1

Grand Total

105

49

27

The first two methods of booking are least liable to errors.

* In some parts of India it is customary to paste small pieces of paper on
the trees, each different coloirr representing a distinct class ; this method haa
for its object to facilitate the control exercised by the supervising officer. The
method was introduced by Mr. E. Ellis, Deputy-Conservator of Forests.

GENERAL METHOD OF SAMPLE TREES. 47

d. Sclertion and Number of Sample Trees.

As the volume of the whole class is to be calculated from
that of the sample tree, it is necessary to select for the latter
a tree, which represents the average of the class: in other
words, the sample tree should have the mean height, as near
as possible a circular section, a fairly straight and not a
forked stem and an average extent of crown. Even with the
greatest care, it is not always possible to avoid errors in the
selection ; hence, it is generally advisable to take several sample
trees for each class, and to ascertain the average of their
volume for the calculation of the volume of the class. The
actual number of sample trees depends on the desired degree
of accuracy and the total number of trees in the class. At
the same time, the felling of many sample trees is undesirable ;
hence, their number should be kept within reasonable limits.

A further requirement is, that the sample tree should show
a basal area, which corresponds exactly to the mean section of
the class. Such a tree is found only in exceptional cases ;
hence, it is necessary to take a tree as near as possible to the
true section, and to modify the volume in proportion of the
basal areas of the true and approximate, or false, sample trees.
Let r = volume of true sample tree, v' that of the approximate
sample tree, s and s the corresponding basal areas, then v is
found by the formula —

V xv' X s : s'

V = v'xt
s '

e. DelermimUion of the Volume of Sample Trees.

The volume of the sample trees is determined, either by
felling and measuring them on the ground, or by means of
form factors or volume tables.

If the trees are felled, the stem and all straight pieces of
branches, in fact all regularly shaped parts, are divided into
pieces of moderate length, from 8 to 10 feet, according to

48 MEASUREA1E>-T OF WHOLE WOODS.

the desired degree of accuracy, and the voUime of each section

is ascertained separatel}' by the formula : —

Volume = area of circle in the middle X by the length of

the section :

V = s,„ X h.

The volume of all irregular pieces, including root and
branch wood, is ascertained —

either by the xylometric method,
or by proportionate figures,

or by measuring their volume stacked, and multiplying
it by known reducing factors, if such are available.

The xylometric method has been explained in Chapter I.

Proportionate figures are obtained from actual fellings. If
it has been found, that in the felling of a wood every 100 cubic
feet of timber are accompanied by, say, 20 cubic feet of fire-
wood, that proportion can be applied to other woods of a
similar description.

The determination of the volume of sample trees by means
of form factors or volume tables can be highly recommended,
whenever suitable data are available, because they give
averages, and that is just what is wanted in this case. Ex-
perience has shown, that form factors and volume tables are
applicable for a considerable distance outside the locality, for
which they have been prepared.

/. Calculation of the Volvmes of the Classes and of the Whole Woo<l.

Here several cases may occur :

(1.) One sample tree has been measured in each class, the
dimensions of which are exactly the average of the class. In
that case, the volume of the class is obtained by multiplying
the volume of the sample tree by the number of trees in the
class. If —

T' = volume of whole wood,

I'lj y^, ^3 . . . = volumes of classes 1, 2, 8 . . .

GENERAL METHOD OF SAMPLE TREES. 49

''ij i':> ''3 . • . = volumes of mean sample trees of successive

classes,

Hi, Un, 113 . . . = numbers of trees in successive classes,

tlien

t 1= I'l X tii; \ 2= i'2 X ii.2 . . .
and

T^ = Ti + ^2 + Tg + • . • = '-1 X 111 + 1-2 X 11-2 + rg X //3 + . . .

(2.) The sample trees in the several classes differ in basal
area somewliat from the mean basal areas.

If the volumes of the approximate sample trees are r/, r^',
V3 . . . and the corresponding basal areas = s/, s.,', S3,
. . . . then
,. _ r/ X si y _ 1-2 X S2 . J. _ vs' X S3

\ 1 T X III , » 2 ^r X ^2 , ' 3 } X 113 . . .

Si S2 S3

■^^ SiXiii = 'S'l = total basal area of the first class,

S2X112 = So — total basal area of the second class, etc.,
the volume of the wood is :

y ^ v/XSt _^ V2^X S, _^ Va^X S3 _^

Sj Sg S3

(3.) Several sample trees are measured in each class. In
that case —

h' + Si" + Si'" + . . . ' " S2' + S2" + S2'" + • • •

etc., and

si + si" H- si'" + . . . sa' + S2" + S2'" + . . .

//. Cl'iihhing together several Clauses, leading to t//e Jletlod of the
ArilJnnetkal mean Saiiipte 7Vee.
In order to shorten the method described above and to

reduce the number of sample trees to be felled, several, or all,

classes may be clubbed together into a group.

Let

111, n.,, 7/3 ... be the numbers of trees in the several classes
si, S2, S3 . . . ., basal areas ,, ,, ,, ,,
hi, ]i2, /'3 • . . ,, heights ,, ,, ,, ,,

Ji,J2,h . • . ,, form factors ,, ,, ,, ,,

F.M. E

50 MEASUREMENT OF WHOLE WOODS.

and

s, It, J the basal area, height and form factoi' of the mean
tree of the classes thrown together,
then the following equation holds good : —

T^ = »1 X Si X h X./l + »2 X So X //2 X /o + . . .

= ("1 + "2 + • • •) X s X h X f.
If it is now assumed, that Iti Xf\ = ^o X J\ = h^ X f\ = . .
= // X /' then the a])Ove equation becomes :

"1 X Si + ;/2 X 6'2 + • • . = ("1 + "2 + • . .) s,

and

S = "1 X Sl + Ho X 6-0+ • • •_ ^
"1 + »2 + ■ • • A"

where S = basal area of all trees of the group, and
A" = total number of trees ,, ,,
In words, the basal area of the average tree is equal to
the arithmetical mean of the basal area of all trees contained in
the group.

The volume of the group is then :
T^ =- r X N,
where v represents the volume of the arithmetical mean sample
tree with a basal area = s.

If no tree can be found with the basal area s, "another as
near as possible to it is chosen of a section s', and the volume
of the group is obtained by the formula :

s' s'

since s x X = S = the basal area of all trees in the group.

If several approximately mean sample trees are taken, the
formula changes into the following : —

V^ (v^ + y" + y'" + . . .) X S
s' -I- s" + s'" ...

The above method rests on the assumption, that hifi =
^2 /2 = ^'3 .f3= • ■ ■ = It /• This, however, is not
absolutely correct, though it holds good approximately in

GENERAL METHOD OF SAMPLE TREES.

51

all regularly grown woods. It follows, that the degree of
accuracy decreases with the increase in the number of classes,
which are clubbed together into a group, the least accuracy
being obtained by joining all classes into one group. In
this latter case, the method is known as " the method of the
arithmetical mean sample tree."

Example. — In order to illustrate this and the methods to
be described hereafter, one acre of Scotch pine wood, 70 years
old, was measured, and twenty-four sample trees of various
diameters felled and measured. Only timber down to 3 in.
diameter at the small end has been included in the account.
The wood is situated at Caesar's Camp, on gravelly sand with
a fair layer of humus, showing a yield capacity of about
middling quality. The following list shows the dimensions
and the volume of the sample trees : — •

List of Twenty-Four Sample Trees.

Number.

Diameter.
Inches.

Height.
Feet.

Basal
Area.
Square

Feet.

Vohime.

Solid Cubic

Feet.

1

4-00

38

•087

1-80

2

.5-2.5

40

•1.50

3-27

3

6-40

45

•223

4-41

4

6-50

42

•230

4-52

.-,

7-50

49

•307

6-92

6

7-50

37

•307

6-62

7

8-50

44

•394

7-26

8

9-25

56

•467

1213

i)

9-40

46

•482

10-81

10

9 •(52

50

•503

11-65

11

lU-70

40

•624

12-37

12

10-70

64

•624

17-14

IH

11-00

57

•660

16-19

H

11-50

56

•721

17-43

15

11-60

58

•734

19-17

16

12-10

48

•798

20-41

17

12-10

62

•798

22-40

IS

13-10

63

•936

25-93

I'J

13-60

56

1-009

21-87

20

15-00

48

1-227

27^79

21

15 00

59

1-227

28-40

22

16-40

63

P467

38-53

23

17-00

64

1-576

39-50

24

17-.50

74

1-670

49-43

The subjoined statement illustrates the procedure, which has
just been described.

E 2

52

MEASUREMENT OF WHOLE WOODS.

Calculation of Volume by Inch Classes, Four Groui>s, and

FOE One Acre of Scotch

Diameter
in

Inches.

Number

of
Trees.

Basal
Area in
Square
Feet.

JlKl

HOD OF I

NCH Classes.

Mkthod of

Diameter

of
Sample
Tree.

Basal
Area of
Sample

Tree.

Volume

of
Sample
Tree in
Cubic
Feet.

Volume

of Class

in Cubic

Feet.

Number

of
Group.

Number

of
Trees in
Group.

Basal
Area of
Group.

Mean
Sample Tree.

Basal
Are^.

Diameter

4

4

•349

4-0

087 ■

1-80

7

^

5
6

12
26

1-637
5-104

5-25
6-4

150
223

3-27
4-41

36
101

- I.

83

18 047

•218

6-3

7

41

10-957

7-5

307

6-92

247

8

42

14-661

8-5

394

7-26

270

9

51

22-.")32

9-25

467

12-13

585

. TI.

144

65-010

•451

9-1

10

51

27-817

9-6

503

11-63

643

11

34

22-439

110

660

16-19

550

1

12

16

12-566

12-1

799

20-41

321

\ III.

59

43-301

•734

11-6

13

9

8-296

13-1

936

25-93

230

)

14

6

6-414

13-6

1

009

21-87

139

i

15
16

5
3

6 136
4-189

l.VO
16-4

1

1

227
467

28-40
38-53

142

110

1

1

16

19-892

1-243

15-1

17

2

3-153

17-0

1

576

39-50

79

Total...

302

146-250

3J60

2. Modifications of the General JMctlwd.

It 1ms been shown above, that the vokime of a ^YOod is
represented by the formula : —

Si S2 .s-3

It is obvious, that, as Ion" as the fractions — , '~,-^ . . .

,Si S2 S3

differ, the volunies of the sample trees in the several classes
must be measured separate!}'. In order to avoid this incon-

MODIFICATIONS OF THE GENERAL METHOD.

53

THE Arithmetical Meak Sampf^e Tree of the AVhole Wood
Pine Wood, 70 Years Old.

Four Groups.

Real Sample Trek.s.

Total

9-25
y-40

11-.-)

n-6

Total

15-0
15 0

Total

Basal
Area.

•223

•230

•1'41
4-52

•467

•482

•721
■734

1-227
1-227

S^93

12^13
10-81

17^43
1917

Volume

of
Gro\ij).

Mkthod of Arithmetical Mea^ Sample Tree.

Nunibei

of
Trees.

2-i54

27-79

28-40

302

Mean Sample Tree
of Wood.

Basal
Area.

RE.iL Sample Trees.

Volume

of
Wood.

9-25
9-40
9-60

Total

-467
-482
-503

12-13
10-81
1163

34-57

34^57 X 146-2.50

= 3,482 cubic feet.

venience, it has been proposed to fix the number of sample
trees in each class so, that

= a constant =

^=^ = ^^ =

Si 8.2 S3

when the above formula reduces to : —

V = (Vi + v._, + V3 + . . .) X c.

By following this method, it is not necessary to keep the
sample trees separate; they can be thrown together and

54 MEASUREMENT OF WHOLE WOODS.

measured in one lot. This is a great convenience and saves
much time. The vohmie of all sample trees multiplied by
the constant c gives the volume of the wood. In this way, a
modification of the general method has been elaborated, which
is known by the name of Draudt's method.

Draudt selects in each class the same percentage of sample
trees, thus ensuring, that —

-^ ^ '^2 ^ ^ ^ _ _
Si S2 S3

Let

T' = ri X »i + r2 X »2 + ''3 X »3 + • • •

If J) per cent, of the trees in each class are taken as sample
trees, the proportion of these to the total number of trees is

= J^ = -Op. By multiplying each term in the above

equation by this coefficient, the following equation is
obtained : —

T" X -Oj) = ri X )/i X -Op + V2 X 7/2 X -Op + /"a X U3 X 'Op -\- . . .

Here, vi x //i x '0^) represents the volume of the sample
trees in the first class, r^, X n^ x '^p that of second class, kc.
If the volume of all the sample trees, ?i x ;;i X "O;^ + v^, x »2
X -Oj) + . . . = r, then

I

X

■Op

=

r

I-

V

;

• X

100

and

•0^; p •

It happens generally, that the number of sample trees in
each class contains a fraction of one. Such fractions are
eliminated by considering '51 as a full sample tree and by

DRAUDT S METHOD. 55

neglecting '50 and under, tcaldng care, that the total number
of sample trees is as nearly as possible correct. The result
of this operation is, that the original proposition is no longer
absolutely maintained ; in other words, the volume of the
actual sample trees does no longer represent the true value

F X jj
100 *

To avoid this inaccuracy, Draudt introduces the basal

area of the whole wood = S and of the sample trees = s, by

Calculation of Volume according to Dbaudt"s Method.
Aiea=10 Acres.

1

Sample

Trees.

Diameter
Inches.

No.

of

Trees.

Basal 1
Area. 1

Square
feet.

Percentage

=1%

multiplied

by Number

of Trees.

Volume

of
Wood.

Cubic
feet.

Number
rounded

otr.

Basal
Area
should be.
Square
feet.

Basal

Area

really is.

^^tf^

Volume.

Cubic
feet.

i

40

3-49

-40

5

120

16-37

1-20

I

-136

■150

6

260

51-04

2-60

3

•588

•669

7

410

109-57

4-10

4

1-068

1-2-28

8

420

146-61

4-20

4

1-396

1-576

9

510

225-32

5-10

5

2-210

2-335

10

510

278-17

5-10

5

2-725

2-515

U

340

224-39

3-40

3

1-980

1-980

12

160

125-66

1-60

2

1-570

1-598

13

90

82-96

•90

1

•922

-936

14

60

64-14

•60

1

1-069

1009

n

50

61-36

•50

1

1-227

1-227

16

30

41-89

•30

17

1

20

31-53

•20

3020

1462-50

.30-20

30

14-891

15-223

357-60

34355

F

er Acre

== 3436

^_ 357-6(

) X 1462
15-223

^=343

55.

and

fxl

This formula is used to calculate, not only the whole volume,
but also that of timber and firewood separately.

be

MEASUREMENT OF AVHOLE WOODS.

The advantages of Draudt's method are : —

(1.) That the sample trees can all he worked up together ;

and
(2.) That it 3 ields a high degree of accuracy.
Its drawhacks are : —
(1.) That, in rounding off the numher of sample trees in each

class, inaccuracies are likely to he introduced ; and
(2.) That frequently no sample trees at all are taken

from classes, which contain only a small number of

trees.
The larger the wood, that is to say, the greater the number
of trees in the several classes, the more accurately the method
works.

Example. — The example on page 55 will further explain the
method. The data are the same as those used in the previous

Calculation of Volume,

Number

Groups.

IJasal Area.

Diameter.

of

Trees.

Diameter.
Indies.

4

Number of Trees.

Square Feet.

Detailed.

Total.

Detailed.

Total.

4

40

i

40

3-41)

5

120

, 1

.r,

120

16-37

6

2(iO

6

260

51-04

7

410

i

7

335

755

81)-53 160-43

^

420
510

9

(

7

75

20-04

10

nio

11.

s

420

146-61

11

840

• [

'.)

260

755

114-87

281-52

12

1 (50

18

1)0

111. -I

i)

250

110-45

14

60

10

505

755

275-44

385-89

15
16

50
30

10

5

2-73

17

20

IV. -

11

12
13

340
160
•10

224-39
125-66
82-96

14

00

64-14

ir,

50

61-36

It;

30

41-89

17

20

755

31-53

634-66

3,020

3,020

1462-60

URIC'H S METHOD.

57

example, but they have been multiplied by ten all round, in
order to obtain a larger number of trees.

h. Uriah's MetJwd.
In order to avoid the inaccuracy caused by rounding off
fractions of sample trees, Urich proposes to arrange the
trees in such groups, that each sample tree represents
the same number of trees. For this purpose he places the
same number of trees in each group and then calculates
the arithmetical mean sample tree for each. For the rest
he proceeds on tlie same lines as Draudt, so that he obtains
the volume of the whole wood by the same formula,
namely : —

K=,-X«.

ACCORDING TO URICH'S METHOD.

Mean- Sample Tree.

Real

Sample Tree.s.

Volume

of

Wood.

Cubic feet.

Basal Area.

Diameter.

N'limber.

Diameter.

Basal Area.

Volume.
Cubic feet.

Detailed.

Total.

•212

6-2

1
2

6^4
fi-o

•223
•230

•453

•701
•985

1-598

•373

8-2

3
4

7^5

8-0

•307
■394

•511

9-7

5
(i

9-4
9-6

•482
•503

■841

12-i

8

121
121

•799
•799

Total...

3-737

88-36
Per Acre.

34,580
= 3,458

58

meast:rement of whole woods.

Urich's method is thus a combination of Draudt's method
with that of the arithmetical mean sample tree for each
group.

The degree of accuracy depends on the number of groups,
which are formed, and on the number of sample trees
measured in each. Too large a number of groups is, however,
inconvenient, as it involves repeated separation of the original
diameter classes.

The method has the disadvantage, that the basal areas must
be calculated before the sample trees can be selected. Urich
proposes to avoid this by estimating the sizes of the sample
trees in the several groups, a procedure which may lead to
inaccuracies.

Example. ^^ee pages 56 and 57.

Measukement of Volume according

Diameter.
Inches.

Number

of

Trees.

Basal

Area.

Square
Feet.

Groups.

No.

Diameter

Number of Trees.

Ba.sal Area.

Detailed.

Total.

Detailed.

'I'otal.
;■ 365-52

1

4
5
6
7
8
9
10
11
12
13
14
15
16
17

40
120
260
410
420
510
510
340

i(;o

90
60
50
30
20

3-49

16-37

51 -04

109-57

146-61

225-32

278-17

224-39

125-66

82-96

64-14

61-36

41-89

81 -.50

1

4

6

7
8
9

40
120
260
410
420

87

1 1337

3-49
16 37

51-04
10957
146-61

38-44

"■\

9

10

423

328

1™

186-88
178-90

1 365-78

,„.)

10

11

12

182

340

53

t 575

99-27
224-39
41-63

' 365-29

\

^

12
13
14
15
16
17

107
90
60
50
30
20

1:

3020

84-03
82-96
64-14
61-36
41-89
31-53

V 365-91

Total...

3020

14(;2-50

1462-60

ROBERT HARTia S METHOD.

The volume is obtained by the formula :-

59

y ^ 88-36 X 1,462-51 ^ ^^ .^^
3-7B7

. r. Robert Hartig's 3fefkoiI.

In Draudt's and Urich's methods, each sample tree repre-
sents the same number of trees. As the volume increases
rapidly with the diameter, it follows, that a sample tree in a
class or group of small diameter represents a much smaller
volume than one in a class or group with a large diameter.
For this reason, Robert Hartig argues, that the number of
sample trees in each class or group should be proportionate to
the volume, which it contains, and not to the number of trees.

TO Robert Hartig's Method.

Mean Sample
Trees.

Real Sample Trees.

Volume
of

Groups
and of
whole
Wood.

8U(!0

8834
8638

8992

Remarks.
13-54 x36.5^52

Basal
Ai-ea.

Diametei

No.

Basal Area.

Volume.

Detailed.

Total.

•273

7^1

1
2

7^5
7^5

•307
•307

•614

•985

13^54

■614
8061 cubic feet.

Per Acre = 3402
cubic feet.

•487

d-i

3
4

y^4

9-6

•482
•503

22^44

•635

10-8

5
6

10^7
10^7

•(524
•624

1^248

2951

r025

13-7

7
8

13^1
13-6

•936

roo9

1-945

47^80

Total..

34024

60

MEASrRf]MENT OF WHOLE WOODS.

As the volume is fairly proportionate to the basal area, Robert
Hartig forms groups, which contain equal basal areas. He
divides the total basal area of the wood by the number of
groups, which he proposes to form ; this gives the basal area
to be allotted to each group. After having placed in each a
sufficient numl er of trees to give that basal area, he calculates
the mean sample tree for each group, and selects an equal
number of these for each.

The formula for E, Hartig's method is as follows : —

V=r,x''^' + r,X^' + rsX'^'-\-

As

^1 'S'2 *S'3

. are not equal the one to the other,

Si So S3

it follows, that the sample trees must be measured and the

Calclilation of Volume by

Height

Basal

According to Form Factors

Diametei

Xuinbei-
of

ISasal
Area.

S(iuare
feet.

ascer-
tained

Arva
multiijlieil

Height
c X d.

]J.v lucl

Classes.

By Four

Trees.

Sample
Trees.

Feet.

Form
Factors.

V'olume.

Basal
Area.

Basal Area
multiplierl
by Height.

a
4

b

C

"

e

/

ff

h

i

4

•349

38

13-26

-43

6

1

5

12

l-(537

40

65-48

-44

29

lS-()!7

77t-0')

6

26

5-104

42

214-37

-45

96

t t 0 Z^

7

41

10-957

44

482-11

•45

217

1

a

42

14-661

46

674-41

•46

310

9

51

22-532

48

1081-56

•46

498

65-UlO

3146-82

10

51

27-817

50

1390-85

•46

640

11

34

22-439

52

1166-83

-47

548

12

16

12-566

54

678-56

-47

319

■43-301

2309-97

13

9

8-296

56

464-58

-47

218

14

6

6-414

58

372-01

-47

175

15
16

5
3

6-136
4-189

60
62

368-16
259-72

•47
■47

173
122

1 19-892

1201-68

17

2

8-153

64

201-79

-47
Total...

95
3446

METHOD OF FORM FACTORS.

61

volume of each group calculated separately. By adding
together the volumes of the groups, the volume of the whole
wood is obtained. This makes the method more laborious
than those of Draudt and Urich.

The example on pages 58 and 59 will further explain the
method.

3. Determination of Volume hi/ means of Form Factors and
Volume Tables.

Instead of felling and measuring sample trees, their volume
can be ascertained by means of form factors, or taken from
volume tables. This applies to all the methods given above.
In all these cases the volume is ascertained according to the
general formula : —

V = S X H X F.

Means of Form Factors.

FOR n., OR

Average Quality (see page 39).

Groups.

By One Group.

Mean
Height i

Form
Factors.

Volume
h X fc X /.

Basal
Area.

Basal Area
multiplied
by Height.

Mean
Height -^

Form
Factor.

Volume
rt X JJ X (/.

n

I

m

n

0

J>

'I

7'

42-95

•45 =

349

48-45

•46 =

1448

\14G-25

7133-73

.50-83

•46 =

3420

53-35

•47 =

1086

CO-42

•47 =

565

Total...

3448

62 MEASUREMENT OF WHOLE WOODS.

How the basal areas of the trees of a class or a wood are
obtamed, has ah-eady been explained. The mean height of a
number of trees, or of a whole wood, is ascertained in the
following way : —

V=S xHx F = SiX hiX /i + .So X ho X f.2 + S3 X //3 X ^3 + . . .

hence ^^.siX/^iX./i + s.2 X //.2 X./2 + • • •

SXF

If it is assumed, that the form factors are the same through-
out, the above formula reduces to the following : —

^^ _ 81 X //I + g2 X //2 + • • • .

in words: "the mean height is equal to the total volume of
cylinders erected over the trees divided by the total basal
area." This formula holds good in the case of the several
trees of one class, as well as for calculating the mean height
of several classes, or of a whole wood.

If a somewhat smaller accuracy suffices, one of the following
methods may be adopted : — A number of trees are selected,
which show about an average diameter and height, their
heights are accurately measured and the mean taken, which
represents the mean height of the class, or wood. Or the
height of the tree with the average diameter (or basal area)
is taken as the mean height of the wood. It remains to be
noted, that the heights obtained by means of these simplified
methods are generally a foot or two smaller than those obtained
according to the formula : —

H =z ^i2^lA^ -\- SoX h.2-\- . . .

S

How the form factors of single trees are ascertained, has
been described above. Similarly, form factors for whole woods
can be determined according to the formula :—

r = sxiixF. 1-=^,

Example. — See pages 60 and 61.

COMPARATIVE ACCUEACY OF THE SEVERAL METHODS. 63

If volume tables are used, the calculation is made according

to the formula —

V = n X s X h X f.

Here s x h x f, equal to the volume of the mean tree, is
taken direct from the tables.

4. Comparative Accuracy of tlie several Methods.

Guided by investigations made by various authors, it may
be said, that, in the majority of cases, the difference between the
calculation made according to any one of the above-mentioned
methods and the results of actual fellings keeps within 2 per
cent., that -the maximum error in the case of the method of
the arithmetical mean sample tree may be placed at 10 per
cent, and in the case of all the other methods at 5 per cent.

If the results obtained in the examples used above are put
together, the following data are obtained : —

Method.
The general method —

Volume.
Cubic feet.

DifEerence

Each inch class calculated sepa-

rately

Inch classes arranged in four

^^

3460

groups .....
All inch classes thrown together

—

8471 .

. + -3

into one group
Draudt's method ....

8482 .
8436 .

. + -6
. - '1

Urich's method ....

=

3158 .

. - -06

Hartig's viethod ....

=

3402 .

. - 1-7

Calculation icith form factors —

According to inch classes .

=

8446 .

. - *-4

According to four groups .

All inch classes thrown together

=

3448 .
8420 .

. - -3

. - 1-2

These data show, that form factors for Scotch pine, obtained
from measurements in North Germany, are quite applicable to
woods in the South of England. Experience has also proved,

61 MEASUl{E:\rENT OF WHOLE WOODS.

that they are applicable to the Midland Counties, and prol)aljly
also to districts further north.

It will be seen, tbat, for the methods described above, the
greatest difference amounts to 1"7 per cent. Under these
circumstances it appears, that any of the methods meets
the requirements of measurements for the preparation of
working plans, and that much more depends on the care
bestowed upon the operation than on the particular method
followed. If the actual fellings show greater differences tlian
the calculations justify, they are frequently due to extraneous
causes, such as the felling of the trees at some distance above
the ground, careless working up of the material, inaccurate
measurement of the fall, theft of material, etc.

In all cases, where special accuracy is required, as for
instance for scientific investigation, or for the determination of
the sale value of woods, the classes, or groups, should be small
and the number of sample trees large. In this way greater
accuracy is likely to be obtained than by making a distinction
between the different methods, which have been described.
Above all, the utilisation of form factors is strongly recom-
mended, especially as there are now callipers to be had, which,
^^hen measuring the diameter, give the basal area of all the
trees, which have been measured. Of these, Wimmenauer's
calliper can be specially recommended. Where form factors
are not yet available, efforts should be made to collect the
necessary data for their preparation at the earliest possible
date. Their application obviates the cutting down of sample
trees, and the determination of the volume takes only a
fraction of the time required in the case of any other method.
In the absence of form factors, or volume tables, Urich's
method is the most useful.

11. — The Height is not a Function of the Diameter.

If it is found, that, in the case of equal diameters, the heights
differ considerably, then height classes must be formed in
addition to diameter classes.

METHOD OF SEVERAL HEICxHT CLASSED

6

In some cases it happens, that the different height cLasses
are separated according to area, for instance, where a marked
change in the qiiahty of the locality occurs, due to change in
the soil or subsoil, aspect, etc. In such cases, the wood is
divided into as many parts as different height classes appear,
and each is treated as a separate wood.

If the several height classes are mixed over the whole area,

Beech

Diameter

Totals.

Inches. 1 1

i 1

I. Height
Class.

n. Height
Class.

Total.

8

mmm r'mmw \ >»

12

30

mmm

M

18

52

1(1

tttt+ttfMM^+Wlli

"

33

80

11

mmwwm^mmmm

39

20

59

12

mmm : mm\

17

11

28

Grand Total ' 155

94

249

as in irregular selection forests, then the diameter and height
must be measured in each case. Where only two height
classes are adopted, the height may be estimated, while the
diameter is measured, and the tree placed in the one or the
other height class. Each of the latter is then considered as a
separate wood and its volume ascertained according to one of
the methods already described.

Cases, where more than two height classes, in addition to

F.M. F

66 MEASUREMENT OF WHOLE WOODS.

diameter classes, are called for, are very rare. Generall}-, the
distinction of height classes is a matter of considerable difficulty,
unless the heights are measured. It is necessary only where
a very high degree of accuracy is aimed at.

The example on the preceding page shows the manner of
booking in the case of two height classes.

Section II. — Determination of Volume by means of
Sample Plots.

1. General.

Instead of measuring all trees in a wood, a certain part of
the area may be selected, the volume on it ascertained and
from it the volume of the whole wood calculated. Such a part
is called a sample, or type, plot. It may be defined as a
portion of a wood, which contains an average volume of material
per unit of area.

Having ascertained the volume of the sample plot, that of
the whole wood can be calculated in two ways: either according
to area, or according to the number of trees on the sample
plot and in the \YOod.

Let A = area of wood,

a = area of sample plot,

V =^ volume of wood,

V = volume of sample plot,

then the following proportion is assumed to exist : —

V : V = a: A

and

V - ^ X A

a

Again, if

A^= number of trees in the wood,

n = number of trees on the sample plot,
then

v:V=n: X,
and

V = ^-^-^.

n

.■MRTHOD OF SA^FPLE PLOTS.

67

In the first case it is necessary to ascertain the areas, and
in the latter the number of trees, in both sample plot and wood.
As, however, the comiting of all trees gives hardly less trouble
than measuring them, the second method yields only a small
saving of labour ; it would be followed only, when the area of
the wood is not known, or cannot readily be ascertained.

2. Selection of Sample Plots.

The proportion given above will hold good only, if the sample
plot represents a fair average of the whole wood, so that it can
be considered as a model of it ; in other words, if a measure-

Fio-. 2:

ment of the trees on it yields an average basal area of stems
per unit of area, an average height and the same form factors.
Hence, the sample plots must be selected accordingly.
Here several cases must be distinguished : —
(a.) The quality of the wood is the same throughout the
area. In this case, the sample plot may be selected
anywhere, as long as the density of stocking represents
an average. In very large woods, it may become
desirable to take several sample plots and calculate
the mean.
{h.) Several qualities occur, which are clearly separated
according to area. Here each quality is treated
separately and one or more sample plot taken in each
part (Fig. 26).

f2

6S MEASUREMENT OF WHOLE WOODS.

(c.) Several tiualiLies exist, Nvliich change gradually from
one to the other. In this case, the sample plot may
take the shape of a strip, ^Yhich runs through the
whole wood, so as to include a due proportion of each
quality (Fig. 27). As this is difficult to accomplish,
it is generally hetter to follow the method given
under (/>), to divide the wood into several parts and
to take a sample plot in each.

(<^.) Several qualities prevail irregularly over the whole
wood. Here a sample plot of average stocking must
be selected, a matter frequently beset by great
difficulties.

3. Extent and Shape of Sample Plots.

The sample plot must be of sufficient extent, to contain the
different classes of trees in the same proportion as the wood.
Hence, its size depends on the degree of regularity of the
stocking; the more uniform this is, the smaller ma}^ be the
sample plot. It follows, that they may be made smaller in
young fully stocked, than in old irregularly stocked woods.

Very small sample plots have the disadvantage that propor-
tionately too many trees fall into the boundary lines.

The absolute extent of the sample plot depends on the
desired degree of accuracy. In mature woods, it should not be
less than 5 per cent, of the whole area, but in young \YOods it
may be much less.

The best shape would be that which includes the greatest
area as compared with the boundary, in other words, a circle.
As this is impracticable, it is usual to give to the sample plot
the shape of a square, or of a rectangle approaching a square.

4. JSIcasuremeiit of Valuvte on Sample Plots.

This can be done according to any one of the methods
described above. As here a conclusion is drawn from the
volume of a small area to that of the whole wood, it is desirable

ESTIMATING THE VOLUME. 69

to measure the volume on the sample plot as accurately as
possible.

5. Merits of the Method of Sample Plots.

The method of sample plots works quickly, and it affords
a great saving of time and expense as compared with the
measurement of whole woods. On the other hand, its accuracy
depends on the degree, to which the sample plot represents
an average of the whole wood. Hence, it only yields accurate
results in regular grown young and middle-aged woods, less
so in old- irregularly stocked areas, or where the (quality
changes frequently. The method is chiefly useful, where
extensive areas have to he assessed, or where the value of
the produce is small, in fact where a high degree of accuracy
is either impossible to attain, or not required. Where only
small areas have to be measured, or where the value of a
forest has to be ascertained for the purpose of sale — in fact,
when a high degree of accuracy is wanted— the whole wood
should be measured.

Section III. — DETEiniiNAXioN of the Volume by Estimate.

Instead of measuring the trees on the whole or a part of the
area, the volume can be estimated in various ways, of which
the following deserve to be mentioned : —

1. Estimating the Volume of the Wood as a Whole.

This method, being the oldest and roughest of all, consists
of going through the wood and estimating the volume, either
of the whole wood, or per unit of area, if the total area is
known. The estimator must consider differences in the density
of stocking, the average volume per tree, the differences in the
quality of the locality, and, if for the whole wood at once, its
area or number of trees. It stands to reason, that the method
requires great experience and practice on the part of the
estimator, and even then considerable mistakes may be made.

70 MEASUREMENT OF WHOLE WOODS.

2. Estimating by Trees.

Under this method each tree is estimated separately, the
volume of the wood being obtained bj^ adding together the
volumes of the several trees. "With great care, an experienced
estimator can obtain fairly accurate results, but, if done care-
fully, the operation takes almost as much time, as if the
diameters of all trees and the height of some of them are
measured ; in the latter case, the volume can be calculated by
means of form factors or volume tables, a procedure which
yields far more reliable results.

The method is only justified in open woods, consisting chiefly
of old trees, such as standards in high forest or in coppice with
standards, or where a low degree of accuracy meets the require-
ments of the case. In such cases, the estimate may extend
over the whole area, or over a sample plot only.

3. Estimating aceording to the Results of Past Fellings.

Where fellings have been made and the fall accurately
measured, the results can be used to estimate the standing
crop in similar woods. In such cases, it is necessary to
take into consideration any differences in the age, density of
stocking, height, etc.

Frequently fellings, made in strips clearing for roads or
rides, give useful data for estimating the crop of the adjoining
woods. In all such cases the estimate is based on the volume
per unit of area.

4. Estimating the Volume by means of Yield Tables.

In the same way as volume tables of single trees are con-
structed, which give the average volume of trees arranged
according to diameter, height, form factor and age, so tables
can be compiled, on the basis of extensive measurements,
which show the volume of whole woods according to species,
age, quality of locality, etc. (see Appendix III.).

METHOD OF YIELD TABLES. 7 J

If tables are available, which are suited to a particular part
of a country, it is necessary to ascertain in the wood to be
estimated —

(1.) The quality class of the locality.
(2.) The density of the crop.
(3.) The age of the crop.

The first is judged by the height of the trees; the second
by ascertaining the basal area of the trees on a sample plot ;
the third by counting the concentric rings on stumps or on
a few trees cut close to the ground, unless the age is known
from records. Based upon these data, the volume can be taken
from the yield table. If, for a certain age, the basal area given
in the table differs from that of the wood, the volume of the
table must be modified accordingly ; a second correction may
be necessary owing to a difference in the height.

The method just indicated is, however, not much used,
because, if basal area and mean height of the wood have
been ascertained, it is much shorter to calculate the volume
by means of form factors or volume tables. Yield tables are
better adapted for ascertaining the increment of woods ;
hence, the method of preparing them will be described in
Chapter VI.

72

CHAPTER V.

THE AGE OF TREES AND WOODS.

It is of importance to know, not only the actual dimensions
of the trees and their volume, but also the time, which has
been necessary to produce them. To solve this question, the
age of single trees, as well as that of whole woods, must be
ascertained.

1. Determination of the Age of Single Trees,
a. Standing Trees.
All trees increase annually in diameter and also by the
elongation of the leading shoots and branches, at any rate
up to a certain age. Tlie diameter increment produces
every year an additional concentric ring, and the new leading
shoot leaves marks, which are more or less distinguishable,
according to species and age. These facts yield data, by which
the age can be determined in the majority of cases, but not
in all, when no records are available, which give the age.
Accordingly, the following methods of determining the age
may be distinguished : —

i. Deteumination from existing Records.
Reliable records yield the best results, if they refer to
individual trees. In the case of trees, which form part of a
wood, they are not always accurate, as many woods are not
even-aged.

ii. Determinatkix r,Y Estimate.

As a general rule, it may be assumed, that the larger the
tree the older it is. Taking, therefore, into consideration the
conditions, under which a tree has grown up, its age can be

AGE OF SINGLE TREES. 73

estimated within 10 or 20 years, as long as height-growth
continues. In the case of very old trees, the limit of accuracy
is much wider. At all times, this method requires much practice
and experience, and even then it yields only approximately
correct results.

iii. Detekminatiox by the Number of Anntal Shoots.
In the case of species, which leave clear marks of the
successive annual shoots, the age can be ascertained by
counting these shoots from the top downwards and by adding
a proportionate number of years for the lowest part of the
stem, where the marks are no longer distinguishable. This
method is, in Europe, only applicable to the various species
of pine up to a certain age, less so in the case of firs and not
at all in that of larch or of the ordinary broad-leaved species.

iv. Deteumixatiox by means of Pressler's Increment Borer.
As explained in Chapter I., with this instrument a narrow
cylinder of wood can be extracted from the stem, on which the
concentric rings may be counted. The instrument does, how-
ever, not work satisfactorily beyond a depth of 6 inches, so
that the centre can only be reached, if the diameter of the tree
does not exceed 12 inches. Even then, it is frequently difficult
to hit off the centre, as the trees grow generally more or less

eccentric.

I. Felled Trees.

It is by far the best method to count the concentric rings on
a stump, and, if necessary, fell a tree for the purpose. At the
same time this is not always an easy operation, and in some
cases it is altogether impracticable. It is easiest in the so-
called ring-porey broad-leaved species and in conifers, which
produce a darker coloured summer, or autumn, wood than
that formed in spring. Frequently false rings appear. These
may be distinguished from true rings by finding, that they do
not run right round the tree (Hornbeam, Alder). In the case
of suppressed trees, the true rings are frequently so narrow,
either all round or in parts, that they are difficult to distinguish.

74 AGE OF TREES AND WOODS.

The business may be facilitated hj smoothing the surface,
making a slanting cut, or applying colouring matters (as
indigo, alizarine ink, Prussian blue, alcohol coloured with
aniline, sulphuric acid, etc.). Such colouring does, however,
not always facilitate the counting.

The number of rings thus counted represents only the age
of the tree above the place, where it has been cut. To the
number so obtained, the number of years, which the tree took
to reach that height, must be added. If absolute accuracy is
required, the stool must be split open along the centre and the
rings counted to the starting-point.

In this way, the x>lujsical age of the tree can be ascertained,
provided that each concentric ring represents a year's growth.
It is, however, by no means certain, whether this is always the
case, as temporary interruptions of growth may cause two
rings to be formed in one year. (For instance, the destruction
of the leaves by insects and the subsequent sending forth
of a second crop of leaves, fire running through a wood, or
even late frost.) Moreover, there are trees in the tropics,
on which the concentric rings do not exist, or cannot be
distinguished.

Another point is, that a distinction must be made between
the physical and economic age of a tree. B}' the latter is under-
stood the actual growing age, leaving out of consideration any
years, during which the tree may have been at a standstill,
owing for instance to heavy shade from above.

2. Determination of the Age oj Whole Woods.

a. Even-aged Woods.

If the age of such woods is not known from authentic
records, it can be ascertained by determining the age of a tree
by one of the methods indicated above. If a tree is felled for
the purpose of counting the concentric rings, it is desirable to
avoid exceptionally thick trees, as such trees may represent
former advance growth.

AGE OF WOODS. 75

As whole woods are rarely established in one year, owing to
failures and subsequent repairing, or, in the case of natural
regenerations, owing to two or more seed years being necessary
for the complete stocking of the area, it is generally desirable
to examine several trees and take the mean.

h. Uneven-aged Woods.

In many cases, woods are less even-aged, than has been
indicated above. The differences in the age of the several
component parts of the wood may be very considerable, as
regeneration may have extended over a long period. In such
cases the mean age must be ascertained.

By the " mean age " of an uneven-aged wocd is understood
that period, which an even-aged wood requires to produce the
same volume as the uneven-aged w'ood.

Let V be the volume of the wood ;
«!, ^2, «3, • • • the ages of the several age classes ;
■'"i, I'i, ''3) • • • the volumes of the several age classes ;
I, the mean annual increment of an even-aged wood of the

same volume as the uneven-aged one ;
A, the mean age, or the age of an even-aged wood of the same

volume as the uneven-aged one ;

Then, according to the above definition, the following
equation holds good : —

ri+r2+r3+. . . = IXA,
and

A — ^'1 + ^-'2 + ^3 + • • • _ V
^ 1 1'

As the even-aged and uneven-aged woods are assumed to
have the same volume, it follows that I must be equal to the
sum of the mean increments of the several age classes of the
uneven-aged wood, that is to say : —

z = £i + !J + ia+...

«! (t2 (f^

76 AGE OF TREES AND WOODS.

Bj' substituting this expression for I in the above equation
the latter becomes —

A _ ^1 + ^2 + V3 + . . .

^1 _|_ ^2 _^ _^3

(1.)

This formula is known as that of Smalian and C. Heyer. It
says in words: The mean age of a wood is obtained by dividing
the volume of the whole wood by the sum of the mean annual
increments of the several age classes. The method may be
simplified by assuming, that the age is approximately propor-
tionate to the diameter ; hence, the diameter classes may be
taken as the age classes. The above formula is chiefly used,
when the age classes are irregularly mixed over the area.

If the areas of the several age classes are represented by
y«i ; 7//2 ; ni-i) .... and the average annual increment
per acre by ii\ H', i^\ • • • • then formula (1.) can be
written in this way (after Gustav Heyer): —

J _ nil X /'i X (ii 4- ^^'2 X 12 X a.2 -\- ;»3 X /^ X ((^ -f" • • -

nil X h X ^'1 _|_ 111-2 X i-2 X a-2 , 'ij'i X i^ X ('3 1

or «i "2 «3

^ _ mi X ii X ai + ^2 X ia X aa H- "^3 X is X a3 -|- . . . .g )

mj X ii + ma X 12 + mg X ig + . . .

If it is now assumed, that —

'1 = '2 = 'y = • ■ •
the above formula reduces to the following :

. _ mi X ai + ma X aa + ma X aa +

- . (3.)

mi + mg + ma + . . .

This formula was first given by Giimpel. It holds good
only, if the differences in age are small and the age itself is
close to that, at which tlie increment culminates, as it then
changes but slowly.

Andre follows a yet different method. He bases the calcu-
lation upon the number of trees in the several age classes. If
they are Hi ; n^ ; »3 ; .... his formula would be:

A = -^ X^i + n^ X aa + na X ag + . . . . ^^ ^

^1 + 112 + 113 + /. r

AGE OF WOODS. 77

All these formulfe are somewhat trouhlesome. Formulae
(1) and (2) demand a knowledge of the volume and (2) besides
of the areas occupied by each age class. Formula (3) necessi-
tates also a knowledge of the areas, while for formula (4) the
numbers of trees in each age class must be ascertained. In
practice, the mean age is frequently taken as equal to the
average age of the sample trees, or of the age classes, according
to the formula —

^ ^ a, 4- a, + aa + . . • . . . (5.)
n

where n represents the number of sample trees, or age classes,
as the case may be.

Finally, the age of the arithmetical mean sample tree can
be taken as the mean age of the wood.

Example : —

Let

n = 4,000

(ti = 50

/;;i = 2 acres

7/1 = 1,500

ra = 9,000

a.2 = GO

»'2 = 'd „

No = 1,600

^3 = 7,000

((3 = 70

Vis = 2 „

7/3 = 800

Vi = 4,000

cci = 80

nii = 1 „

m = 300

Mean age acco]

:ding to formula : —

^ _ 4,000 + 9,000 + 7,000 + 4,000 _

. 24,000 _

^ ■ 4,000

, 9,000 ,

7,000 , 4,000
70 "^ 80

380 ■

50

"^ 60 "^"

Years.

(2) A -^X^QX50+3X 150X60 + 2X100X70+1X50X80

2 X 80+3 X 1 50+2 X 100+1 X 50

= 61-6

/ox f _ 2 X 50 + 3 X 60 + 2 X 70 + 1 X 80 ^^.^

^'^^'-- • 2 + 3 + 2 + 1 7 '='^'

.^s ^ _ 1,500X50+1,600X60+800X70+300X80 _ rn.o
1,500 + 1,600 + 800 + 300 '^

(5) A= . . . 50 + 60+70 + 80 ^ ^.

78

CHAPTER VI.

DETERMINATION OF THE INCREMENT.

During ever}' growing season, a tree increases by the elonga-
tion of the top shoot, side branches and roots and by the
laying on of a new layer of wood and bark throughout its
extent. Thus, the height and diameter (or basal area), as well
as the spread of the crown, increase constantly up to a certain
age, producing an increase of volume called the increment. By
adding up the increment of the several trees in a wood, that
of the whole is obtained.

The increment may refer to one or more growing seasons,
and accordingly a distinction must be made between —

(1.) The current annual increment, or that laid on in the

course of one year.
(2.) The periodic increment, or that laid on during a number

of years or period.
(3.) The total increment, or that laid on from the origin of
a tree or wood up to a certain age, frequently that when
the tree, or wood, is cut over.
(4.) The mean annual increment, or that which is obtained
by dividing the increment laid on during a given period
by the number of years in the period. If the mean
annual increment is calculated for a portion of the total
age, it is called the periodic mean annual increment, if
for the total, or final, age of the tree or wood, it is called
i\\Q; final mean annual increment.
In determining the increment of whole woods, it must be
remembered, that a certain number of trees disappear from
time to time owing to thinnings and natural causes. All such
removals must be taken into account in determining the total
increment laid on.

HEIGHT INCREMENT. /9

The determination of the increment may refer to the past
(backward), or to the future (forward). As the former deals
with actually existing quantities, the determination can be
made with a comparatively high degree of accuracy ; the latter,
on the other hand, is to a considerable extent based on specu-
lation, hence less reliable.

Section I. — Detekmination of the Increment of
Single Trees.

1. Height Increment,
a. Of the Past.

The height increment of standing trees can, in some cases,
be ascertained by the whorls formed in successive years. This,
however, refers to a limited number of species. In the majority
of cases, it is necessary to cut down a tree for the purpose of
investigating the height increment.

The height increment of the last few, say n, years can be
ascertained, in the case of some conifers, by measuring the
length of the last n shoots. In the case of all other species,
the height increment of the tree during the last n years is
ascertained by cutting off a certain length and counting the
rings ; if they are less than n in number, an additional piece
must be cut off and so on, until that spot has been found,
where the section shows n rings. If the section of the
first cut shows more than n rings, then another cut higher
up is made, until again the section shows n rings. The
length above that point gives the height growth of the
last n years.

In all cases, where a complete knowledge of the height
increment during the several periods of life is required, the
tree should be divided into a number of sections, the length
of which depends on the desired degree of accuracy. The con-
centric rings are then counted at the end of each section, and,
from the data thus obtained, the height of the tree at successive

so DETERMINATION OF THE INCREMENT.

periods of life can be ascertained, either by calculation, or
interpolation.

Generally, graphic interpolation gives the better results, as
it equalises accidental irregularities. In this case the abscissae
represent the ages and the ordinates the corresjDonding heights.
By connecting the points, thus indicated, by a steady curve,
the height at successive ages can easily be read off.

Example. — See analysis of a Scotch pine tree, at p. 83.

J). Height Tnrremmf of the Future.

The expected height increment for a number of years to
come can be estimated from the increment of the immediate
past. In doing this, the rate of increment during the past
must be studied and especially the time ascertained, when the
current annual increment of the species usually culminates.
If the increment immediately before the time of inquiry was
still rising, it may continue to do so or not, according to
whether the maximum has been reached or not. If it is
already falling, it will continue to do so, and in that case the
rate, at which it is likely to fall, must be estimated. In this
way, the probable increment for a limited number of years (say
10) can be estimated with satisfactory accuracy. This is best
done by constructing a height curve of the past, and elongating
it for the required period, so as to form a continuous curve.

2. Diameter Increment,
a. Of the Fast.

This can refer to wood and bark, or to wood only.

The increment of wood and bark, laid on by standing trees,
can be ascertained by repeated measurements of the same tree,
a certain number of years being allowed to pass between every
two measurements. The latter are made with the calliper,
care being taken to mark the place of measurement without
causing an unusual swelling at that part of the tree. Where
immediate results are required, the increment can be ascertained

DIAMETER INCREMENT. ^l

with Pressler's increment borer. The number of years, for
which it can be ascertained, depends on the length of the
cyHnder, which can be extracted, and on the rate of growth.
As most trees grow irregularly, it is necessary to ascertain the
increment at opposite sides, or at four sides, and to take the
mean. These investigations rest on the assumption, that the
concentric rings are distinguishable, and that each ring repre-
sents one year's growth.

The increment can be ascertained with much greater accuracy
by felling a tree and measuring the breadth of the desired
number of rings on the section, the latter being laid at right
angles to the axis of the stem. The measurements are made
with a scale subdivided to a sufficient degree. This is either
laid on the section and the breadths read oft", or the latter are
taken off with a pair of compasses, and the dimensions then
taken from the scale. In either case, care must be taken to
obtain averages by measuring along two, four, or more radii,
arranged at equal distances over the section, and then taking
the mean of the several readings.

In the case of standing trees, the increment can only be
ascertained for a limited number of years. If a tree is felled,
the increment can be ascertained for the several periods of its
life, sa}', for every live, ten, or more years. The result can be
graphically represented and a mean curve of increment con-
structed, from which the increment for any desired intervals
can easily be determined. By repeating the above operation
at successive heights from the ground, the increment can be
ascertained in the several parts of the stem.

h. Diameter Increment of the Future.

This is estimated from the increment of the immediately
preceding period, taking into consideration, how far the
future diameter increment may be affected by the method
of treatment, more especially the proposed degree of thin-
ning ; the stronger the latter, the greater is the increment
likely to be.

F.M G

82 DETERMINATION OF THE INCREMENT.

3. Area Increment.

The increment in basal area is calculated from that of the
diameter. Let D be the mean diameter of the whole section,
d the diameter of the same section // 3'ears ago, then

Basal increment ] _ />- X tt _ f/- X tt
during n years > "^ 4

= (^^-;^-^'=(/>=--/^, X-785.
4

The basal increment can be ascertained for a limited number
of years only, or for the several periods of the life of a tree.
An estimate of the future increment is based upon that of the
immediate past, taking into consideration the proposed treat-
ment, as in the case of the diameter increment.

4, Volume Increment.
a. Of /he Fast.
The past volume increment of a tree during a certain period
of years, n, is equal to the difference of volumes at the com-
mencement and end of the period. These volumes can be
ascertained by examining a series of sections at various heights
of the tree, or by basing the calculation upon measurements
made at the middle section, or by using form factors.

i. DETEnMINATION OF THR IXCKEMENT I!Y SECTIONS.

If the increment of only a limited number of years, n, is
desired, it can be ascertained by means of the increment borer.
The breadth of n rings is ascertained at regular intervals along
the stem and the differe)ice between the present volume and
that n. years ago calculated.

The investigation of the progress of increment throughout
the life of a tree is called a stem analysis. It consists of a
combination of a height and a diameter analysis.

VOLUME INCREMENT OF SINGLE TREES. S3

The tree having heen divided into a suitable number of
sections, each is cut through in the middle, the number of
concentric rings counted and the diameter at the several ages
measured. The measurements are best plotted, so that a
representation of a longitudinal section through the tree is
obtained. For this purpose, the heights of the several cross
sections from the ground are marked on a vertical line, which
represents the axis of the stem; also the heights which the
tree had obtained at successive periods of its life. Next, the
radii of the cross sections are marked on horizontal lines and
the points thus obtained connected by a series of lines, which
represent the stem curves at the several stages during the life
of the tree. From the data thus obtained, the increment
throughout the several periods of the life of the tree can be
calculated. As the thickness of the bark at former periods
cannot be ascertained, these investigations can refer only to
the increment in wood, exclusive of bark.

The following example will explain the procedure : —

Analysis of a Scotch Pine Tree.

The tree was cut up into nine pieces, which gave the
following ci'oss sections : —

Section I. taken at foot of tree, showing 97 concentric rings.
II. taken at 5 feet above fifround ,, 95 ,, ,,

III.

15 „

„ 89

IV.

25 „

„ 85

V.

85 „

„ 80

VI.

45 „

„ 72

VII.

55 „

„ 64

VIII.

G4 „

„ 34

IX.

68 „

„ 26

Top

= 9 feet long.

Total

height =

77 feet.

g2

84

DETERMINATION OF THE INCREMENT.

Number of Years

Height of

Xiiniber of

which the 'IVee

Section.

Kings.

took to reach

Fett.

tliat Height.

0

97

0

5

95

2

15

89

8

25

85

12

35

80

17

45

72

25

55

64

38

64

34

63

68

26

71

77

0

97

^

10

90 100

liO 40 £.0 00 70

A(iE, IN VEAH«.

Fig. 28. — Graphic representation of the IIei(j}it Increment

j\-„/^.._.Tlie tree grew in a veiy favouiable loeality. but it was overtopped by
other trees at the age of about 40 years ; hence tlie reducetl height growth
after that period.

ANALYSIS OF A SCOTCH PINE TREE.

85

Radius of Section I.

Radius

of Section II.

Radius of Section III.

Radius of Section IV.

at foot of tree,

at 6' fro

n the ground,

at 15' from the ground,

at 25' from the ground,

in Inches.

m

Inches.

in Inches.

in Inches.

Total = 11-50

Total

= 8-82

Total = 6-92

Total = 6-38

97 = 10-56

95

= 8-3-2

89 = 6-78

85 = 6-21

87 = 9-88

85

= 7-86

79 = 6-45

75 = 5-94

77 = 9-22

75

= 7-34

69 = 6-16

65 = 5-62

67 = 8-50

65

= 6-77

59 = 6-04

55 = 5-30

57 = 7-65

55

= 6-25

49 = 5-46

45 = 4-99

47 = 6-71

45

= 5-74

39 = 4-95

35 = 4-41

37 = 0-74

35

= 5-06

29 = 4-24

25 = 3-80

27 = 4-94

25

= 4-34

19 = 3-50

15 = 2-81

17 = 3-83

15

= 3-38

9 = 2-25

5 = 1-30

7 = 1-85

•>

= 1-30

Radius of Section V.

Radius of Section VI.

Radius of Section VII.

Uadius of Section VIII.

at 35' from the ground,

at 4 j' from the ground.

at 55' from the ground ,

at (34' from the ground.

in Inches.

m

Inches.

in Inches.

in Inches.

Total = 6-U3

Total

= 5-Sl

Total = 3-54

Total = 2-12

80 = 5-96

72

= 5-75

64 = 3-46

34 = 207

70 = 5-71

62

= 5-40

54 = 2-98

24 = 1-66

60 = 5-28

52

= 4-87

44 = 2-40

14 = -SS

50 == 4-80

42

= 4-31

34 = 1-85

4 = -24

40 = 4-37

32

= 3-74

24 = 1-40

30 = 3-85

= 3-05

14 = 1-03

20 = 2-95

12

= 1-90

4 - -41

Radius of Section IX.

10 = 1-35

2

= -35

at OS' from the ground,
in Inches.

Total = 1-43

26 = 1-39

16 = 1-02

6 = -50

Calculation op the Volume op the Tree at Different Ages.

Number

of
Section.

Dia-
meter,

Basal
Area, in
Square

Feet.

Length,
Feet.

Cubic
Feet.

Number

of
Section.

Basal
Area, in
Square

Feet.

Length,

in

Feet.

Cubic

Feet.

Whole Tree, includitig Bark
97 Years.
1
2
3
4

17-6

1-69

10

13-8

1-04

10

12-8

-89

10

12-1

•80

10

11-6

•73

10

7-1

•27

10

4-2

•10

8

16-9
10-4

S-9

Whole

Tree, to'tthout Bark
97 Yenr.'^.

16-6

1-50

10

13-6

1-01

10

12-4

•84

10

11-9

-77

10

11-5

•72

10

6-9

•26

10

4-1

-09

8

15-0
10^1
8-4
7-7
7-2
2^6
•7

Total Timber — 55-0
8 I 2-9 I -05 I r I -15

Total Timber and Fuel = 55-15

Total Timber
I 2-8 I •Ol I I

Total Timber and Fuel

51-7
•12

51 •82

* The top is considered as representing a cone, the volume of which
area x one-third of the height.

86

DETERMINATION OF THE INCREMENT.

Calculation of the A'^olume of the Tree at Difff.hknt Ages

Number

of
Section.

Dia-
meter,

Basal
Area, in
Square

Feet.

Length,
Feet.

Cubic
Feet.

Tree 87 Years

ou.

15-7

1-34

10

12-9

•91

10

11-9

•77

10

11-4

•71

10

10-8

•64

10

6-0

•20

10

3-3

•or,

s

13-4
9-1

7.7

7-1
6-4
2-0

Total Timber = 4fi-2
I 2-0 I -02 I I I -(IB

Total Timber and Fuel = 4r.-23

11-8
8-3

Tvl
5-1
1-3

Tree 7

Years

Old.

14-7

M8

10

12-3

•83

10

11-2

•68

10

10-6

•61

10

9-7

•51

10

4-8

•13

10

Total Timber
•02 I 8
•01 i

39-4
■16

Total Timber and Fuel = 39-r,(;

Tree 67

Years

om.

13-5

•99

10

12-1

■80

10

10-6

■61

10

9-6

■50

10

8-6

■40

10

3-7

•07

10

Total Timber = 33-7
2-0 I -02 I % I ^04

Total Timber and Fuel = 33-74

Tree 5

7 Years

Old.

12-5

■85

10

10-9

■65

10

10-0

■55

10

8-7

■41

10

7-5

•31

10

! % i

I'lital Timber =
■04 I 10 I
*'l I I I

Total Timber and Fuel = 28-11

Number

of
Section.

Dia- j JJasal , ,

! meter, | Area, in '■''^' S^":

I in I Square , v^\
Inches. Feet. ! '^•^''*'-

Tree 4

7 Years Old.

11-5

•12 1 10

9-9

•53 10

8-8

•42 10

•32 i 10

6-1

-20 1 10

2-1
-6

Total Timber =

S. 1 V' I

Total Tinilje

Tree 3

- Years

Old.

101

•56

10

8-5

•39

10

7-6

•32

10

5-9

•19

10

3-8

•OS

10

Total Timber =
2-4 I -03 I I I

7-2
5-3
4-2
3-2

2-0

2r9

•20

5-6
3-9
3-2

r9

•8

15-4

•07

Total Timber and Fuel = 15^47

8-7

•41

10

7-0

.97

10

5-6

•1-

10

Total Timl^er =
I 2-7 I -04 I 10 I

Total Timber and Fuel =
Tree 17 Year.-< Old.

6-8
4-5

8-5
•40
•02

Total Timber = 3^6
2-6 I -04 I 10 I -40
1-2 -01 I ^02

Total Timber and Fuel = 4-02

7 Years Old.

Total 'J'imber
I -(14 I 10

Total Timber and Fuel

00
•4
•01

0-41

ANALYSIS OF A SCOTCH PINE TREE.

87

^

14

.^

,
^

,^

^

10

^

^

y

/

/

f

/

AGE. 0 10 20 30 40 00 m 70 SO 00 100 AGE.
Fig. 29. — Graphic representation of the Biameter Increment
at 5 feet from the ffronud.

67 77
RADIUS, IN INCHES (EXAGGERATED).

Fig-. 30. — Graphic representation of a Trer An/ihj.<<i.<t (Yerticnl ppctinn
of one half of tlie Tree).

88

DETERMINATION OF THE INCREMENT

l\cc(q)iinlatu)n.
The stem of the tree had, at the age of 97 years

A total vohime of = HiVlH cul:)ic feet
Of this was

( = 55-15 - 51-82 = 3-33 cuhic feet

Bark

I = 6 per cent, of total volume.

Leaving

Timher (over 3" diameter) = 51-7 cul)ic feet.
Firewood . . . = "12 „ ,,

Total Timber and Firewood = 51*82 cubic feet.

CO

O 20

7

/-

/

/

/

/

/

J

/

/

y

/

0 10 20 ;!0 40 50 CI) 70 80 UO 100

AGE, IX YEARS.

Fig 31. — Graphic representutiou of tlie Volume.

BY THE MIDDLE SECTION.

89

By graphically representing the volume of wood at the several
ages, Fig. 31 is obtained, which, with the previous diagrams,
gives the following data : —

Diameter without

Volume witliout

Periodic Incre-
ment for every

Ten Year.s.

Cubic Feet.

Age of Tree.

Height, in Feet.

Bark, at 5' above

Bark, in

Ground, Iiiche.s.

Cubic Feet.

0

-

-

-

'• 1-8

10

20

4-0

1-8

[ 4-2

20

38

7-4

6-0

|- 6-0

30

51

'.)•!

12-0

[ 6-0

40

58

10-6

18-0

'• 6-0

50

fi2

11-9

24-0

[ 5-9

(50

CI

12-8

29-9

i 5-4

70

67

13-9

35-3

1 ^'^

80

70

lo-O

42-0

'■ 6-0

90

74

16-0

48-0

[ 3-8

y7

77

i6-(;

51-8
Total

51-8

ii. Determination of the Increment by the Middle Section.

If somewhat less accurate results suffice, the volumes can be

ascertained by multiplying the basal area in the middle by the

height. Let T^ be the volume of the tree at the present time,

V that n years ago, H and // the corresponding heights. Fig. 32,

and *S' and s the corresponding basal areas at -- and -', then
I = V- r = S X JI - s X h.

TT

The height and basal area at — can easily be measured ;

A
h is ascertained by cutting off a piece from the top downwards,
and repeating the operation, until the point has been ascer-
tained, where the basal area contains ii concentric rings.

90

DETERMINATION OF THE INCREMENT

Then the hasal area .s, at -^ , is ascertained, either In' makino; a

cross section at the sjDot, or hj ascertaining the breadth of the
last n rings with the increment borer, thus ascertaining the
diameter, which the tree had n years ago. In either case,

Fij?. 32.

the diameter increment must be measured in several places of
the circumference, so as to obtain the mean.

In order to simplify the operation, Pressler proposed to cut
off a length corresponding to n years' height growth in the
first place, and then to measure the basal area in both cases at

-. (See Fig. 33.) He ol)tains the increment according to the

A

formula :

7 = ,S X /( - .5 X // = (S - s) h.

The error due to omitting the top is said to be compensated

for l)y ,S' being taken somewhat below -.

BY FORM FACTORS.

91

iii. DlVlEliMINATION OK THE IXCHEMKNT liY FoRM FAnOKS.

Let S be the basal area of a tree taken at chest height; s the
basal area of the tree // years ago taken at the same height ;
H and h the corresponding heights, and F and ./' the corre-
sponding form factors, then the increment —

I = S X H X F - s X h X f.

In the case of a standing tree, H is measured with a height
measurer, h is estimated or taken from tables of height growth,
the proportion between the outer
and inner diameters being utilised
to determine //. S is obtained l)y
measuring the diameter with a cal-
liper, and s with the assistance of
an increment borer. F and / must
be taken out of form factor tables,
or estimated. If F is taken as = f,
the formula becomes :

I = {S X H - sx h) X F.

The method can give only approxi-
mately correct results, because h has
to be estimated. It must also
not be overlooked, that form factor
tables give only averages ; hence
the method is not adapted to the
measurement of a single tree, but
only to that of a large number of ti
case, the results can be only aj^proximately correct.

Z*. Vohoup Inrremeni of the Fuivre.
The increment, which a tree may be expected to lay on in
the future, can be estimated from its own past increment,
especially that of the immediate past.

The increment is represented by the formula:
7,^ = ,S' X 7/ X 7' - s X A X ./',

ees. Even in the latter

92 DETERMINATION OF THE INCREMENT

where s x // X/ represents the present voUime, and S X H
X F that to be expected after n years. The formula shows,
that, in order to obtain fairly accurate results, it is necessary
to estimate *S', // and F from s, h and/. How this should be
done as regards basal area and height has been explained
above. The form factor F may be obtained from tables, if
such are available ; otherwise it must be estimated, or it may
be taken as equal to/.

Instead of estimating the separate factors, the volume incre-
ment of the next n years may be estimated direct from that
laid on during the last n years, taking into consideration how
far the latter should be modified with regard to the age of
the tree, locality, future treatment of the wood, especially the
proposed degree of thinning, etc.

According to Pressler's method, the probable increment can
be ascertained by estimating the probable diameter increment
and then proceeding by the formula :

4 = (,S' - s) h,

where s represents the present section in the middle, ;S' the
expected section in the same spot after n j^ears and h the
present height. The method applies only to felled trees ;
hence it necessitates the felling of one or more sample trees.

Section II. — Determination of the Increment of Whole

Woods.
It has been shown, that, in the case of single trees, the
accumulation of the volume, as well as the increase of the
factors, which lead up to it, height, diameter, or basal area
increment, can be followed backwards with a considerable
degree of accuracy. This is not the case as regards whole
woods, because trees die or are taken away in thinnings.
Investigations, made on sample trees selected in a wood,
show only the gradual development of the individuals
existing at the time of examination, but they throw no light
on that of those trees, which have disappeared in course of

OF AVHOLE WOODS. 93

time, since the wood was created. Height growth alone makes
an exception. An analysis of a number of sample trees will
indicate the mean height of these trees during previous periods,
M'hich may be taken as the upper height of the wood at those
times. These would, of course, not represent the mean
heights at the several ages, because it may safely be assumed,
that the now existing trees were, as a rule, always the leading
trees. Investigations have proved, that the mean height of
woods can be deduced from the upper height. For instance,
in the case of the Scotch pine the difference ranges from
about 3 to 5 per cent, according to the age of the wood.
But no such relation has as yet been found as regards the
basal area or the volume, and to evolve the former amounts of
these out of the present quantities is more or less speculative.
Under these circumstances one of the two methods about to be
described may be followed.

A. Determination of the Future Increment according to
the Mean Annual Increment of the Past.

The present volume of the wood is ascertained and divided by
its age, the quotient giving the mean annual increment, calcu-
lated on the growing stock present at the time of measurement.
According to the age of the wood, it may be assumed, that the
mean annual increment will be laid on for a number of years
to come, or a somewhat diminished or increased increment.

The method gives fair results, if the calculation is made for
the time, when the mean annual increment culminates and even
for older woods; it is less accurate in the case of younger woods.
Moreover, it is only applicable for a limited number of years.

B. Determination of the Increment by means of

Yield Tables.

/.—Of Yield Tables Generally.

1. Befiniiion of Yield Tahles.

It has already been explained, that the progress of height,

diameter, basal area and volume increment can be rejn'e-

94 DETERMINATION OF THE INCREMENT

sented by curves constructed on the principle, that the succes-
sive ages are marked as abscissae, and that the corresponding
ordinates represent the height, diameter, basal area, or
volume. Such curves indicate the appropriate quantities for
any age up to a certain limit, generally the highest rotation
likely to be adopted. Instead of employing curves, the data,
which they represent, are read off and arranged in tables, and
these are called Yield Tables.

By a yield table is understood a tabular statement, which
gives the course of the development of a wood from early youth
up to a certain age, either from year to year, or for intervals
of a certain number of years.

2. 01>jeet and Contents of Yield Tahles.
Yield tables are used for a great variety of purposes, as :

{a.) Determination of the volume of woods.

(/>.) ., ,, ,, increment of woods.

(f.) ,, ,, ,, quality of localities or of the stock.

((/.) ,, ,, ,, most profttable species, method of

treatment and rotation.
{e.) ,, ,, ,, value of the soil, growing stock, or

both.
(/.) ,, ,, ., yield of forests.

In order to meet all these requirements, yield tables should
show, per unit of area (acre) :

(1.) The number of trees.
(2.) The mean diameter of trees.
(3.) The basal area of trees.
(4.) The height of the wood.

(5.) The volume, which may be found in a fully-stocked
wood at successive ages ; also the yield of thinnings.
(6.) The current annual and mean annual increment.
(7.) The form factors.

OF YIELD TABLES GENERALLY. 95

Separate yield tables must be prepared for

{a.) Each species.

(/>.) Each method of treatment, as high forest, coppice wood

and combination forest.
(t\) Each quality of locality.

The volume is given divided into the different classes of
wood, as timber, firewood, fagots, etc. The volume of thin-
nings, or intermediate yields generally, is entered separately
from that of final yields.

Yield tables are prepared only for "normal" woods, that is
to say, for woods, which are fully stocked, taking into considera-
tion the species, quality of locality, and the adopted method of
treatment. Such woods are produced, if no extraordinary
influences have interfered with their progress, such as natural
phenomena, faulty treatment, etc.

3. Local and General Yield Tables.

If a yield table has been prepared for a particular district of
limited extent, it is called a local yield table ; if for a whole
province or county, a gencrcd yield table.

The question, what territorial limits should be assigned to
the applicability of a yield table, is still under discussion, but
so much is certain, that, in the preparation of such tables, a
considerable extent of country can be thrown together without
incurring any appreciable inaccuracy. It has been proved, for
instance, that yield tables prepared for North-Germany are
quite applicable to the south and centre of England,

4. QucdiUj Classes.

Localities of different quality, or yield capacity, produce
woods, which follow in their development different laws. The
law of increment of the one cannot be evolved out of that of
the other. The preparation of each yield table should, there-
fore, be based on data obtained from localities of precisely the

96 DETERMINATION OF THE INCREMENT.

same quality. Asa rule, however, a large number of different
qualities exist ; hence, in practical forestr}', some concession
must be made, by being satisfied with a limited number.
These rarely exceed five, and frequently three are quite suffi-
cient. The best quality is generally designated as I. quality,
though the reverse would be better.

In proceeding to construct yield tables, it is obviously of the
first importance to have a ready method, by which the quality
of a locality may be indicated. It has been explained in
Sylviculture, that the several factors of the locality, such as
the chemical and physical conditions of the soil and subsoil,
the climate, etc., do not enable the forester to determine the
quality of the locality for forest purposes with any degree of
accuracy, and that tlie only satisfactory indication is given by
the wood which has been produced on it. In other words, a
locality which produces, in a given time, a large volume, is of
good quality ; one which produces a small volume, of inferior
quality. The volume, then, is in the first place the surest
indication of the quality of the locality.

As it is, however, a somewhat cumbrous process to ascertain
the volume, when searching for a certain quality, the question
arises, whether one or more of the elements, from which the
volume is calculated, would not do equally good service. It
has been shown above, that the volume is

V = s X h X /.

Of these three elements, the form factor moves between
comparatively narrow limits, and it is not suited for the
present purpose, apart from the fact, that the volume would
first have to be ascertained in order to determine the form
factor. Basal area and height together give a sure indication
of the quality, that is to say, two woods, which show the same
basal area and height, may safely be assumed to have the same
volume ; hence, the localities, which have produced them, would
be of the same quality.

If only one indicating element is used, the height is far

METHODS OF CONSTRUCTING YIELD TABLES. 97

preferable to the basal area. While two woods, of the same
species and equal basal areas, may have very different heights,
experience has shown, that two normal woods of the same
height have approximately equal basal areas. It follows,
that the height is, next to the volume itself, the best indi-
cator of the quality of the locality. Great height growth
means good quality, small height growth inferior quality of
locality.

Neither the mean diameter nor the number of trees can be
used for the above purpose, as they are not in due proportion
to the volume. Nor can the product of number of trees
multiplied by the mean diameter be used.

5. Methods of Constructing Yield Tables.

The following methods have been proposed : —

a. Annual or Periodical Measurement of the Grou'ing Stock of one
and the same Wood ; in the second case the Inteunediate Values
are found by Interjiolativn.

The method gives absolute certainty, that all figures of the
yield table are derived from the same quality class, but as the
preparation of the table would take a century and more,
the method has only theoretical value. Moreover, accidents
may happen which would render the wood unfit for further
observation.

l. Annual or Periodical MeasKremcnt of the Groicincj Stock of a
limited member of Woods of different Ages.

In order to save time, it has been proposed to select several
woods differing in age by a certain number of years, say 20,
and to obtain from the measurements of each, extending over
20 years, part of the yield table. To make sure, that the
quality of the several woods is the same, it is necessary, that
they should have the same volume at the same age ; in other
words, the wood now 40 years old should have had, when 20

F.M. H

98 DETERMINATION OF THE INCREMENT.

years old, the same volume as the present 20 years old wood
has ; again, the 60 years old wood the same volume, when it
was 40 3'ears old, as the present 40 years old wood, etc. Or,
to put the matter differently, the 20 years old wood should
have, when it becomes 40 years old, the same volume as the
40 years old wood has now, etc. In addition, the progress of
the increment should be steady throughout.

Although it is difficult to select localities on these lines,
which are of exactly the same quality, or woods which will
develop in the same manner, there can be no doubt, that
ultimately satisfactory yield tables can be obtained only by
observing and periodically measuring suitable woods for a
series of years. Hence, the method is actually followed. For
each quality class and age gradation several sample plots are
selected, and these are periodically measured and the mean
taken. In this way, yield tables will ultimately be obtained.
It is necessary to take several plots for each quality and age
gradation, so as to obtain average results, and because one or
other may become unfit for the purpose in consequence of
unforeseen events.

c. 3Ieasuremcni of a large number of Woods of different Ages once,
so that Yield Tables are obtained immediately.

Until yield tables, prepared as indicated under h, become
available, others for immediate use are required. These are
obtained by measuring fully stocked sample plots in a sufficient
number of woods, representing all ages with moderate intervals.
Out of the data thus obtained, steady curves and tables are
prepared. A separate set of woods is required for each quality
class, and the great difficulty consists in selecting for each set
localities of the same quality. For this purpose, various
methods have been suggested. Most of these start from
an indicating wood, while one, specially elaborated by Baur,*
starts from a different principle ; the latter will be dealt with
in detail further on, as it is the most practical method.

* Late Professor of Forestry at the University of Munich.

METHODS OF CONSTRUCTING YIELD TABLES. 99

i. Selection of "Woods for each QrALiTY Class by Means of an
iNDicATiNfj Wood.

The method is based upon the fact, that the older wood has
been evolved out of the younger, in other words, that the older
wood had at one time the same volume as the younger. Hence,
it should be possible, by analysing a number of sample trees,
to ascertain the volume, or the factors from which it is calcu-
lated, namely, basal area, height and form factor, which the
trees of a mature wood had at the several periods of their life.
Guided by the data thus obtained, woods are selected; the
dominant trees of which show the same dimensions as those,
which the mature trees had at the same age. Such woods are
assumed to give true representations of what the now mature
wood was at the same ages. When a sufficient number of
woods of various ages has been selected, sample plots with
normal stocking are measured in them, and the data worked
up into a yield table for the corresponding quality class.
The same procedure is followed for all other quality classes.

Various authors have gradually elaborated this system, first
Seutter as early as 1799, then Hossfeld in 1823. Huber, in
1847, was the first to give a regular method of working with
an indicating wood. He calculated the mean tree of a normal,
mature wood, analysed it and searched for younger normal
woods, the mean trees of which possess the same dimensions
as the mean tree of the mature wood had at the same ages.
His method is, however, wrong, because the mean tree of
the mature wood was not the mean tree at all former stages
of life.

Theodor Hartig, and afterwards Eobert Hartig, analysed
the largest trees of the mature wood, and then searched for
younger woods, an equal number of the largest trees of which
show the same dimensions as the largest trees of the mature
wood had at the same ages. Such woods are considered as
having been produced on localities of the same quality, so that
they can be used for the preparation of one yield table.

100

JlETER^nXATION OF THE IXCREMENT.

The system presupposes, that the largest trees of the
mature wood were amongst the largest trees at all previous
periods of the wood's life. Although this holds good generallj-,
exceptions occur. Besides, the method is very troublesome in
execution.

11,000

..U.-iA. .

1

y

^/

o.ooc

/

,' '„

L _

/

/ti

'' •

/"

S,000

i-

/

/

•' ^

/.

y]

!

y

/.«

/

/

''^

7,000

i

A

/

V

1^

1

/

,-

/

.'*

A

'

6,000

i 1

A,

"V

/"\

/

L'«

1

/

/

/A

/

,

'?>-

5,000

1

f /

■/

''

/

,*"*

v

ri —

i

/

K V *

y.

y

/

1

h

>}:'/

V

/

/

■'/vX', '

'?

1

3,000

A'

■AY -(A

"

■rf-'h

2,000

m

{'/

/

P'/iC'y

9

l.OOfi

I'JL

'/

i

£

1

I. QUALITY.

I. QUALITY.

ir. QUALITY.

0 10 20 bO 40 oO liO 70 bO <J0 100 110 12D

AGE, IX Y'EARS.

Fig. 35.— Graphic Representation of the Volume per Acre of 40 different "Woods nnd
their allotment to Three Quality Classes, according to Baur's method.

ii. Bau:

ilr.THOD OF rr.EPAKlXG YlF.LD TaUI.KS.

After a sufficient number of normal sample plots on all sorts
of qualities and ages have been carefully measured (at least 30
for each quality class), the volumes are marked as ordinates
over the corresponding ages as abscis::8B (see Fig. 35).

METHODS OF CONSTRUCTING YIELD TABLES.

01

Example of Preparing Yield Tables according to Baur's Method.

Scotch Pine : 3 Qiiility Classes to be distinguished.

Woods Measured as follows :—

Age.
Years.

No.

Ba.sal

Mean

Volume

Age.
\ears.

76

No.

Basal

Mean

Volume

No.

of

Area,

Height,

in solid

No.

of

Area,

Height,

in solid

Trees.

sq. ft.

feet.

cub. ft.
1800

21

Trees.

sq. ft.

feet.

cub. ft.

1

1.5

62

16

295

173

70

5500

2

17

60

14

1400

22

79

265

177

72

6300

3

IS

61

13

1100

23

81

245

192

86

7200

4

21

84

20

1700

24

85

290

156

62

5030

.5

27

1400

130

33

3300

25

94

190

196

93

9000

6

29

2400

99

25

2050

2''.

94

240

150

67

6000

7

31

1480

133

35

3250

27

94

218

177

80

7300

8

3.5

1670

113

32

2800

28

96

248

1.50

69

5300

!)

3.5

910

156

46

4450

29

97

200

176

82

6950

10

46

620

165

55

4800

30

99

170

194

93

8200

11

47

740

150

47

4230

31

104

160

192

94

9200

12

48

860

132

40

2900

32

106

169

177

86

7150

13

49

6S0

154

52

4700

38

106

220

160

69

5700 ;

U

50

750

132

44

3500

34

108

178

179

86

8100

15

54

450

182

69

6400

35

109

210

152

72

6700

16

62

450

169

65

4700

36

109

151

196

96

8500

17

62

869

184

73

6200

37

112

148

194

98

9700

18

68

420

148

56

4450

38

115

150

176

88

7500

19

74

270

192

83

7800

39

118

145

194

98

9000

20

74

350

146

61

4000

40

120

186

157

75

6000 !

Woods Separated into

Qualities. (See Fig. 35.)

No.

Age.

No.

of

Trees.

Basal
Area.

Mean
Height

Volume

No.

Age.

No.

of

Trees.

Basal
Aiea.

Mean
Height.

Volume

I. (,

7>nditii

13

49

680

154

52

4700

1

15

62

16

1800

16

62

450

169

65

4700

5

27

1400

130

33

3300

21

76

295

173

70

5500

9

85

910

1.56

46

4450

22

79

265

177

72

6300

10

46

620

165

55

48O0

27

94

218

177

80

7800

15

51

4.50

182

69

6400

29

97

200

176

82

6950

17

62

369

184

73

6200

32

106

169

177

86

7150

19

74

270

192

83

7800

34

108

173

179

86

8100

23

81

245

192

86

7200

38

115

150

176

88

7500

25
30

94
99

190
170

196
194

98
93

9000
8200

III.

(^ualUij.

81

104

160

192

94

9200

3

18

...

61

13

1100

86

109

151

196

96

8500

6

29

2400

99

2050

37

112

148

194

98

9700

12

48

860

132

40

2900

39

118

145

194

98

9000

14

50

750

132

44

3500

18

68

420

148

56

4450

II.

Qiiulifi/

20

74

350

146

61

4000

24

85

290

156

62

5030

2

17

60

14

1400

26

94

240

150

67

6000

4

21

84

20

1700

28

96

248

150

69

5800

7

34

1480

133

35

3250

33

106

220

160

69

5700

8

35

1670

113

32

2800

35

109

210

152

72

6700

11

47

740

150

47

4230

40

120

186

157

'' (

6000

102

Dl':TEt;MlXATION OF THE INCREMENT.

Next two curves are drawn, so that the lower touches the
lowest points, and the upper the highest points indicating these
volumes. Then the area thus confined is divided into as many
equal strips, as there are quality classes to be distinguished.
The woods falHng into each strip are considered as belongiii"

,700
,000
,500
,400
,300
,200
.100
,000
'JOO
800
700
600

—

\

I

\

\

\

V

\

\

\

\

300
■200
100

\

V

V,

"^

--

^^

30 40 50 60 70
AGE, IN YEARS.

liU 100 110

Fig. 30. — Giiiphiu llepreseutatiou of the Kumbcr of 2'rees per Acre.

to the same quality class. By drawing a mean curve through
each strip, the mean volume curve for the quality is obtained,
from which the volume table is prepared for successive years.
In a similar way, mean curves for the height, basal area and
number of trees are constructed for each quality class. The
method is of easy ap})lication, and it yields good results.

METHODS or CONSTRUCTING YIELD TABLES.

103

Baur's method, combined with that described under (Z>),has
been utihsed in the preparation of yield tables for Germany.

■iw

•^

^^

^^

*-*

-•i

ISU

/

X^

100

/

140

y

/-

lliU

/

100

f—

80

J

1:10

T

40

f

■JO

2

n

on

ia

40

10

tiO

-()

so—

90 :

00

ir, 1

AGE, IX YEARS.

Fig. o7.— Giapliic Eepreseutation of the Baud Areas per Acre.

90 100 110 120
Fig. 38.— Graphic Representation of the Height Groicth.

10 20 30 40 50 60 70
AGE, IN YEARS.

The work was commenced some thirty years ago on a pre-
arranged systematic plan, and has led to the compilation of a
number of tables. Those, which appeared best adapted for the

101.

DETERMINATIOX OF THE INCREMENT

conditions in Southern and Central England, will be found in
Appendix III. There is no pretence on the part of the Author
to maintain, that the tables absolutely apply to the conditions
found in the United Kingdom, but there is sufficient proof to
show, that the data given in them hold good approximately for
woods in the south and centre of England, and that they may
safely be used, until tables have been prepared based on data
collected in this country. It maj' be said, that the most
urgent need of British forestry is the collection of statistics,

Yield Table for the Scotch Pine, I. Quality.
Derived from the Curves ia Figs. 35, 36, 37 and 38.

Age.

Number

of
Trees.

Ba.sal Area.

Square Feet.

Mean

Height.
Feet.

Volume.

Cubic Feet,

solid. •

Increment.

Current

Annual.

Cubic Feet.

Mean

Annual.

Cubic Feet.

10
20
30
40

r,o

fiO
70

SO

90
100
110
120

2000
1200
770
o20
880
300
2r,()
200
160
1.50
140

30
92
133
160
175
186
190
192
193
194
194
194

10
23
40
54
64
73
80
86
90
94
97
100

900
2100
3300
4500
5400
6250
6950
7600
8200
8650
9100
9500

90
120
120
120
90
85
70
65
60
45
45
40

90
105
110
112
1(18
104
9SI
95
91
86
83
79

by means of which the financial results of the industry can be
estimated. Until such statistics become available, no sub-
stantial progress is likely to be made, unless the results
obtained elsewhere are temporarily admitted.

//. — Determination of the Increment of "Woods by Means
of Yield Tables.

If yield tables are available, and it is desired to estimate the
increment of a wood forward or backward, it is necessaiy to
decide in the first place, which of the quality classes of the
tal)les corresponds with that of the given wood ; in other

BY YIELD TABLES.

105

words, it must be ascertained, to which quality class the
wood belongs.

The best way of doing this is, to measure the volume of
a normal sample plot in the wood and compare it with the
volumes given in the tables for the same age and the different
quality classes. If it agrees with one of these volumes, the
two are of the same quality class, and the increment shown in
the table applies also to the wood in question.

If the volume of the wood does not agi-ee with any of the
volumes in the tables, then that quality class is selected which
comes nearest to it, and the increment is ascertained in pro-
portion to the two volumes. Let ?'« be the present volume of
the wood, V„ the nearest volume given in the table ; F« + n the
volume given in the same table for the year a -\- n ; and
Va + ,1 the desired volume of the wood in the year a + n, then
the following equation may be assumed to hold good (see
Fig. 39):-

and
and

t;, : i\, = y

Vu + a= Vu + n X ^

I = Increment in n years = r„ _, ,j — r„

V„ + n X V,

I = v,(_-"-l

1U6 DETERMINATION OF THE INCREMENT

This method rests upon the assumption, that the selected
yield table correctly represents the progressive increment of
the wood, of which the increment is to be ascertained. As
this is only approximately the case, the degree of accuracy of
the method depends —

(a.) On the degree to which r„ approaches Va,

(h.) On the difference of ages, that is to say, the difference
between a and a -\- n ; the smaller this is, the more
accurate will be the result.

In folluNving the above method, it is essential to measure the
volume on a " normal " sample plot, because only then can
the true qualit}^ class be ascertained by means of the volume.
If no fully stocked sample plot is available, that nearest to it
should be selected, and the proportion between the actual and
normal stocking ascertained. The actual volume must then be
augmented in the same proportion, before it is used for the
determination of the quality class and the selection of the
yield table. At the same time, this procedure is subject to
errors, as it is not always easy to determine correctly the
proportion between the actual and normal stocking.

Generally, the method is better adapted to woods, which
have passed middle age, than to younger woods, as in the
latter the factors of the locality have not in all cases found
full expression. In the case of very young woods, it is alto-
gether useless to measure the volume for the purpose of
selecting the proper yield table. For such woods, the quality
class must be determined by means of an older wood growing
in the vicinity on a locality of similar quality ; the same
procedure is followed in the case of blanks. If no such older
wood is available, the soil and climate must be examined and
the best possible estimate of the quality made accordingly.

As the measurement of the volume takes much time, and
as it is difficult to estimate the exact proportion between the
actual and normal stocking, it has been proposed to select the
proper yield table for a wood by means of one factor only of
the volume. It has already been explained, that of all, such

BY YIELD TABLES.

107

as number of trees, diameter, form factors, basal area and
height, the last is the most suitable. Indeed, actual investi-
gation has proved, that, in the case of all woods of middle age
and upwards, the volume of two woods, other conditions being
the same, is fairly proportionate to their mean heights. The
mean height is, therefore, an excellent indication of the
quality class ; it, as well as the age, is comparatively easy to
ascertain. In selecting the appropriate yield table, the mean
height is used in the same way, as has been described for the
volume. If the height agrees with one of the heights given
in the yield table for the same age, the increment can be
read off directly. If it differs, the nearest is selected and the
increment of the table modified in proportion to the difference
between the actual height and that given in the table. Should,
moreover, the wood not be fully stocked, then the increment
given in the table must be further modified in the manner
mdicated above.

The height by itself is no true indicator of the quality for
very young woods ; for such, as well as for blanks, other woods
growing in the vicinity must be utilised, or the soil and
climate examined.

Example: —

A Scotch pine wood has a height of 53 feet when 60 years
old, and a volume of 3,800 cubic feet ; find the probable
increment for the next ten years '?

Yield Tables.
(See Appendix IIL)

Quality.

Height.

Volume in tlie Volume in the
Year 60. Year 70.

I.
IL
IIL

52
30

6,960 —
4,660 ' O.070
2,170 —

The wood belongs to the II. Quality.

08 DETERMINATION OF THE INCREMENT.

Acconling to the formula —

/60-70 = (5,070 - 4,660) X 'g X J|'|^^ = 341 cul^ic feet.

109

PABT 11.

FOREST VALUATION.

Ill

FOREST VALUATION.

Forest Valuation deals with the determination of the value
of forest soil, the growing stock, the forest as a whole and
the rental derivable from the soil or the forest as a whole.

These values must be determined in all cases of sale, or for
the purpose of assessing forest property, or when it is pro-
posed to divide a property. Soil and growing stock also form
the capital invested in forestry, and their value must be ascer-
tained for the purpose of gauging the financial success of the
forest industry. The latter subject is generally dealt with
in a separate part called, " Forest Statics." In the present
instance it is proposed to compress that part into one chapter
and to add it to "Forest Valuation."

In order to deal with the matter here contemplated, it is
necessary to explain the various methods, according to which
the value of property may be ascertained, to determine the
rate of interest applicable to the forest industry, to give
certain formulae for calculating with compound interest, and
to explain the methods of estimating receipts and expenses.
All these matters will be dealt with in a preliminary chapter,
and the subjects here under consideration will be arranged as
follows : —

Chapter I. — Preliminary Matters.

II. — Valuation of Forest Soil.
III. — Valuation of the Growing- Stock.
IV. — Valuation of Whole Woods or Forests.
V. — Valuation of the Eental.
VI. — Methods of Calculating the Financial
Eesults of the Forest Industry and of
determining the Most Profitable Treat-
ment OF Forests.

112

CHAPTER I.

PRELIMINARY MATTERS.

Section I. — Value of Pkoperty Generally.

Property means an object which serves for the satisfaction
of a requirement. The degree of utility of a property hidicates
its value.

The value of property may present itself in various ways : —
A piece of property may possess value, because it can be used
for a certain purpose (as articles of food), or for the pro-
duction of another kind or class of property (as a set of
carpenters' tools, or raw materials).

Again, the value of a property may be general or special ;
the former is that, which a property has in the open market ;
the latter is that, which it has for a particular person (as a
piece of land situated in the middle of another estate), or
under special circumstances (as a loaf of bread in a famine-
stricken district).

By the price of a property is understood the amount of
another class of property, which is offered for it in exchange ;
the ordinary means of exchange is money.

The value of property can be ascertained in various ways,
of which four must be mentioned : —

(1.) The exj^ectation rahie, by which is understood the
present net value of all yields, which a property may
be able to give ; it is determined by discounting to the
present time all incomes derivable from the property,
and deducting from them the present value of all
expenses necessary for the realisation of the incomes.
(2.) The cost value, or the total outlay on the acquisition,
or production, of a property.

CHOICE OF RATE OF INTEREST. 118

(3.) TJic sale value, or the price which can be realised by
the sale of a property ; if the sale is open to general
competition, the sale value becomes the market price,
which depends on supply and demand.

(4.) The rental value, by which is understood the capital
corresponding to the rental, which the property is
capable of yielding. This value is ascertained by
capitalising the rental according to the formula: —

Rental X 100 11 X 100

Capital

rate per cent.

It is commonly expressed as "a certain number of years'
purchase."

In determining the value of a forest property, or indeed
any other property, all calculations must be made with com-
pound interest, as all money, whether principal or interest, is
capable of again yielding interest.

Section II. — Choice of Eate of Interest.

By rate of interest is understood the proportion between
the 3'early interest (/) and the capital (C) which has yielded
it, as represented by the formula : —

Eate of interest = — .
C

By rate per cent, or, shortly, per cent., is understood the
yearly interest yielded by a capital of 100 ; hence the per
cent. : —

p = 1 X 100.

c

The rate of interest, applicable to an industry, depends on
many things, of which the most important are : —

{(I.) The degree of security of the investment and the
safety, with which it yields a return. In a general
way, it may be said, that the rate of interest should be
inversely proportional to the safety of the investment.

F.M. I

114 PRELIMINARY MATTERS.

(I).) The supply and demand of capital, which change from

time to time and with the locality.
(c.) The general credit of the country, in which the in-
dustry is carried on, in other words, the interest
yielded by Government securities (called Consols in
Britain).
It follows, that the general rate of interest applicable to the
forest industry cannot be a fixed quantity, but that it changes
with the locality, time and a variety of other circumstances.

The question then arises, what rate of interest is applicable
to the forest industry under a given set of conditions ? In
attempting to answer this question, the following points must
be taken into consideration : —

(1.) The safety of capital invested in forests. The soil
offers (apart from changes in prices) almost absolute
security. The growing stock is subject to damage by
men, insects, fungi, wind, snow, rime and, above all,
by fire. The degree of danger from fire differs much
according to species, method of treatment, length of
rotation, climate, etc. ; in temperate climates the
damage keeps within narrow limits.
(2.) The price of forest produce is, on the whole, subject to

less sudden fluctuations than the value of money.
(3.) Investment in forest property possesses the great con-
venience of yielding a steady income.
(4.) Forests cannot easily be let on lease, as inroads on the
growing stock are difficult to control ; for the same
reason forests, beyond the value of the land, are not
well suited as security for loans.
(5.) Compared with the cultivation of field crops it must be
noted that : —

{a.) A forest once placed under systematic manage-
ment yields annually equal returns, or nearly
so, whilst those of fields differ much according
to the seasons.
(/;.) Forests require much less labour.

CHOICE OF RATE OF INTEREST. 115

(c.) Temporary high prices can be fully utilised by

cutting more than the normal yield for a time,

or vice versa.

(d.) As a rule, successful forest management requires

larger estates than the cultivation of field crops.

Bearing these matters in mind, attempts may be made to

determine the rate of interest for the forest industry in one of

the following ways : —

(1.) Determination based upon the rental and value of the
forest.

If the value, F, of a forest, so managed as to yield an
annual net return Ft, is known from a sale, which has taken
place, the per cent, would be : —

p = ^ X 100.
r

The conditions for the applicability of the method are : —

{a.) That the annual rental of the forest is accurately known.

{h.) That the forest is, at any rate approximately, in such a
condition, that it can yield a steady annual return.

(c.) That the price realised for the forest was the result of
genuine competition.

There is great difficulty in complying with all these con-
ditions, so that frequently this method is not of much
practical value.

(2.) Determination based upon the rate of interest obtain-
able in agriculture.

As indicated above, differences exist between the two methods
of using the soil, which are difficult to estimate. At the
same time, forestry and agriculture resemble each other in
many respects, so that the agricultural rate of interest can
frequently be applied to the forest industry.

(3.) Determination according to the rate of interest yielded
by Government securities.

The rate of interest of Consols may be too high in some
5, and too low in others, according to the general credit

i2

116 PRELnriNAHY MATTERS.

of the State and the nature of the forests. On the whole,
however, this is a safe way of determining the rate of interest
for the forest industry in all well regulated States.

The rate of interest generally adopted in the calculations
contained in the following chapters is that of British Consols,
that is to say, 2^ per cent.

Sectiok III. — Formulae of Compound Interest.*

The following formulae, based upon compound interest, are
required in forest valuation : —

1. Amount, or the Futun- Value, to uhleh a Capital
accumulates.
A capital C\ put out at p per cent, compound interest accu-
mulates in the course of n years to the value —

C'„ = C„ X I'Op- . . . (I.)
or log. (',, = log. t\ + » X log. I'Qp,

.here 10,, = 1£J-+J' and 10,," = (10,,," = C^^')-

2. Discount, or Determination 0/ Present Value.
The present value C, of a capital €„ to be realised n years
hence, is — ^,

('., = T^„ • • . . (H.)
1 07^"

log. C = log. ('„ — n X log. I'O^).

3. Snnwtatio)i of Rentals.
((. Futwe Value.
A rental H becomes due for the first lime after 111 years, and
is payable altogether ?? times at intervals of in years; its value
at the end of m X n years is —

(■-.. = ^^^^fr^' • • (HI.)

1 Oj/" — 1

* For the benefit of those who are not vciscd in calculations with compound
interest, the detaiLs, showing how the formulae have been obtained, are given in
Appendix VI.

formul.t: of compound interest. 117

A rental ;• is due at the end of each year, altogether n
times ; its value at the end of ii years is —

'Op

b. Prexent V'due.

A rental R becomes due for the first time after m years,
and is payable altogether n times after intervals of in. years ;
its present value is —

^ ija-or^-D

l-Ojf" il-Op'" - 1) ^ ^

A rental r is due at the end of ea -h year, altogether n
times ; its present value is —

^ r (l-0^>» - 1)

1-Oy' X -Op ■ • • ^vi.;

A rental r is due at the end of each year, for ever ; its
present value is —

<'o=TJr- ■ ■ ■ (VII.)

•Op

A rental B is due after ii years, and again every n years,
for ever^ its present value is —

'•■ = roi?^i • • •(^™->

A rental It is due after m years, and again every n years,
for ever ; its present value is —

1-Op'^ - 1 ^ ^

A rental It is due now, and again after every n years, for
ever ; its present value is —

_ It X ro/v-
^" - l-0/>" - 1 • • • ^^'^

118 PRELIMINARY MATTERS.

4. Conversion of an Intermittent into an Annual Rottal.

A rental li is due after n years, and again every n years for
ever ; it is equal to an annual rental of —

^ - X -O;) . . . (XL)

1-0/'

A rental 11 is due after m years, and then every n years for
ever; its value is equal to an annual rental of —

'■ = %^'x-o. . .,xii.)

A rental II is due now, and again every n years for ever ;
its value is equal to an annual rental of —

All the above calculations can be made with logarithms,
or by means of tables, ^Yhich give future or present values
for various rates of interest. The tables in Appendix II.,
page 340, which give the vahies for Formula I., II., YIIL,
and YL, suffice for all ordinary forest calculations ; they will
be utilised in the subsequent chapters.

Section IV. — Estimate of Eeceipts and Expenses.
1. Ilcceipts.

The receipts of forests are derived from a variety of pro-
duce, which are generally divided into two classes : Major, or
principal, produce and minor produce.

(I. J/ ajar J'rodiirc.

This comprises all yields of wood, that is to say, timber and
firewood. Bark is generally included; if it is severed from
the timber before disposal, it is sometimes classed as minor
produce.

ESTIMATE OF RECEIPTS AND EXPENSES. 119

INfajor produce is subdivided into that obtained from final
cuttings (final yield) and that from thinnings, etc. (inter-
mediate yields).

The value of major produce is ascertained by means of
money yield tables, which are calculated from volume yield
tables.

The preparation of volume yield tables and the selection of
the proper table have been explained in Forest Mensuration.
If tables are available, the age, volume and height of each
wood are ascertained, and these data are used in the selection
of the proper yield table. If the data do not agree with any
table, the nearest is selected, and its quantities are modified in
proportion to the volumes, or heights, as the case may be, of
the wood in question and those given in the yield table.

When the produce yield table has been determined, it is
converted into a money yield table, for which purpose the
local prices of the several classes of timber and firewood must
be ascertained. In doing this, it must be remembered, that the
average value of material per unit of measurement generally
rises with the rotation up to a certain age.

These tables refer to fully stocked or normal woods ; hence,
the quantities must be modified before use, in the same degree
as a particular wood differs from the normal condition. In
some cases, a further reduction is made as a kind of insurance
against future events. Some authors give 10 per cent, as a
proper reduction.

b. Minor Produce.

This comprises all yields, which do not consist of timber
and firewood ; their amounts and values must be locally
ascertained.

2. Exj^enses.

The expenses comprise the cost of administration, pro-
tection, formation, harvesting, construction of roads, slides,
houses, taxes, etc. The amounts must be locallv ascertained.

120

PRELIMINARY MATTERS.

3. Examples of Monei/ Yield Tables.

Subjoined follow two money yield tables. The first is for
Scotch pine and the second for beech, it being assumed that
the quality of the locality is about the same in both cases.

For simplicity's sake, it has been assumed that the thin-
nings are made at the end of every 10 years ; hence, column //
gives the values of the wood before the thinnings are made,
and column / the values which remain after the thinnings
have been executed.

Money Yield Table foe One ache of Scotch Pine Wood.
Calculated with English prices ; brushwood under 3 inches diameter omitted.

Age.

Yield in Cubic

Feet.

Net Value of Return.s.

Final.

Inter-
mediate.

Per Cubic Foot,
Pence.

Total, Shillings.

Final.

Inter-
mediate.

Final.

Inter-
mediate.

Total, Final
and Inter-
mediate.

h

a

h

c

d

e

./■

0

20

30

40

.50

60

70

80

90

100

110

120

130

140

fiOO
1,170
2,830
3,940
4,(590
.5,250
5,720
6,100
6.410
6,690
6.950
7.190
7.410

353
524

565
536
493
446
397
334
232
200
180

1-5

3-
4-
5-
6-

7'
8-
9-

lo-
ll-

12-

1-

1-5

2-

3-

3-5

4-

6-

8-
9-

75

195

590

985

1,563

2,187

2,860

3,558

4,273

5,017

5,792

6,591

7,410

44
87
118
134
144
149
165
167
135
133
135

75
20t)
634
1,072
1,681
2,321
3,004
3.707
4,438
5,184
5,927
6,724
7,545

Example. — In the year 60 the volume amounts to 4,690 +
565 = 5,255 cubic feet, of which 565 are taken out in the
thinning, leaving 4,690 cubic feet to go on with. These
increase during the next 10 years to 5,250 + 536 = 5,786
cubic feet. Similarly, of the total value in the year 60 =

:\rONEY YIELD TABLES.

121

1,681 shillings, 118 are taken out in the thinning, while
a value of 1,563 shillings remains. This increases during the
next 10 years to 2,187 + 134 = 2,321 shillings, and so on.

The Scotch pine wood is supposed to be grown on fairly
good soil, so that the returns stand about half way between
best and middling quality according to the yield tables in
Appendix III., page 362. The values per cubic foot are those
prevailing in the south and centre of England.

Money Yield Table for One Acre of Beech Wood.
Calculate I with English prices ; brushwood under 3 inches diameter omitted.

Age.

TiELD IN Cubic
Feet.

Net Value of Returns.

Final.

Inter-
mediate

^''^emcl°°'' Total, Shillings.

Final.

Inter-
mediate.

! Total,
p.;,,^. Inter- | ^'°^^
F'-'- m.diate. ,X.
j mediate.

a

b

c

d

-

/ ' ff h

30

40

50

60

70

80

90

100

110

120

130

140

86
943
2001
2915
3716
4430
5045
5573
6045
6460
6817
7117

86
272
329
357
400
414
400
400
386
372

2-
3-
4-5
6-

8-
9-

lo-
ll-

12-
13-

14-

3-

4-

4-5

5-

6-

8-

9-
10-
11-

14 — 14
236 — 236
750 21 771
1457 ' 91 1548
2167 1-23 2290
2953 149 ' 3102
3784 200 ' 3984
4644 241 4885
5541 267 5808
6460 300 6760
7385 322 7707
8303 , 341 8644

122

CHAPTER II.

VALUATION OF FOREST SOIL.

The soil can be utilised in U\o waj-s : —

Either by being used direct, as for mining, quarrying, con-
struction of dwellings, etc. ;

Or by letting it i^roduce other goods, as field or forest crops.

In each of these cases the soil may have a different value.
Forest valuation ascertains the value of the soil under the
supjDosition, thatit is used for the production of forest crops;
for this purpose it determines the expectation, cost and sale
value.

Section L — The Expectation Value of Fokest Soil.
1. Method of Calculation.

In conformity with the definition given at page 112, by
the expectation value of forest soil is understood the sum of
the present values of all returns expected from the soil in the
course of time, less the present value of all expenses, which
must be incurred to obtain those returns.

a. Frosent Value of Returns.
(1.) Final Yields. — Let the rotation contain r years, and let
the value of each final yield, less cost of harvesting, = ¥,., to
be realised every r years, then the present value of all final
yields for ever amounts, according to formula VIII. (page 117),
to:—

r..

Present value of all final yields

1-0//— 1'

(2.) Intermediate Cuttings, or Tliinninijs. — Let Ta, T,„ T^
. . 1\, represent the value of thinnings, less cost of

EXPECTATION VALUE. 123

q. Each of

these thmnings occurs durmg every rotation, that is to say,
every r years. Thus the first thinning occurs after a years,
again after a -\- r years, again after « + 2 X r years, and so
on ; hence, the present value of all these thinnings, according
to formula IX: —

_ T, X 1-0// -° T, X l-O;/" , , 1\ X VOp'-"

\-0f - 1 "*" VOp' - 1 ^ ■ • • "*" i-Qp'- - 1

= ^'g X VO}f-" + Tr> X VOf ' + > • • + T„ X 1-Oj/ "^
l-Oi/-l

(3.) Minor Produce. — These are dealt with in the same way
as thinnings, if they occur at regular intervals. Let il/„ Mt
. . . Ml be the values of minor produce occurring in the
years s, t . . . z, and again every /■ years, then their present
value is-^

_ M, X 1-0^'-^ + .V, X 1-Oy + ■ . . H- M, X l-Oy--'
l-Qf — 1

If items of minor produce, M, occur regularly every year, as
grazing fees, rent from shooting, etc., and of equal value year
after year, their present value amounts, according to formula

VII., to i^.
•0})

h. Prosenf Valve of E.rpen.^es.
(1.) Cost of Formation. — Assuming, that c represents the
(»ost of formation, whether artificial or natural, which has to
be incurred at the commencement of each rotation, then the
present value of all such expenses comes, according to formula
X, to :—

Total present value of cost of formation = /' X 1 Up

l-O^/ - 1

If the first cost differs from that on future occasions, and if
the latter is represented by c', then the total present value is -r-

e+ ^1 .

124 VALUATION OF FOREST SOIL.

(2.) Annnalhi Eecurnnfi Expenses. — Let e represent the
value of all annually recurring expenses, as cost of adminis-
tration, taxes, etc., then the total present value of all such
expenses comes to -f-

or the capitalised value of the annual expenses.

(3.) Periodically Occurring Expenses. — These are dealt with
as has been sho^Yn in the case of thinnings or items of minor
produce.

(4.) Expenses of Harvesting and of Collection of Revenue. —
These are alwaj^s deducted from the receipts, and they do not
appear in the account.

r. Formula for the Expertatioi Value cf Forest Soil.
This formula would be represented by an addition of all
the items enumerated under a less those under h. In order
to shorten the formula, without destroying its accuracy, it may
be assumed —

(1.) That T, , To . . . T,^ represent thinnings as well as

items of minor produce ;
(2.) That the expenses are reduced to the cost of formation

and the annually recurring expenses ;
(3.) That the cost of formation at the commencement of

each rotation comes to the same amount.
(4.) That e represents the difference between the annually
recurring expenses and the annually recurring receipts,
such as grazing fees, rent of shooting, etc. If the
latter are higher than the former, then e, respectively
E, would be positive.
The expectation value Se of the soil is then represented by
the formula —

S _ Yr+1'aXlOp''^ + - • • + T,xi-Op'' "-cXlOp'' -g
lOp-— 1

Example. — An acre of land is to be cultivated at once with
Scotch pine, and to be worked under a rotation of 80 years.

EXPECTATION VALUE. 125

It is expected to jaeld the returns given in the money yield
table at page 120. The expenses are expected to be as
follows : —

Cost of formation every 80 years = 60 shillings.
Annual expenses for administration, taxes, etc., less annually
recurring incomes = 3 shillings.
Interest = 2i per cent.

The expectation value of the soil will, in that case, amount
to^

Sc =

3,004 + 5 X 1-025^" + 44 X l-025^" + 87 X l'0253o
+ 118 X 1-025-Q + 134 X IO251" - 60 X l-025^''_ 3
1025«"' — 1 -025-

By using the tables in Appendix II., page 340, this value
becomes —

S, = (3,004 + 5 X 3-4371 + 44 X 2-6851 + 87 X 2-0976 +

118 X 1-6386 + 134 X 1-2801 - 60 X 7-2096) X '1610 - 120

S, = 3,254-1333 X "1610 - 120 = 403-9155 shillings,

or,

*S; = 404 shillings = i:20 4.s. OcL

This shows that, for land yielding the above returns and
involving the above expenses, the proprietor may pay i620 4s.
an acre, if he is satisfied with 2h per cent, compound interest
on his investment. It will be shown later on, that he must
obtain the land for less than =£20 4s., if he desires to get more
than 2-|- per cent, on his investment.

Assuming now, that the same acre of land is planted with
beech, that it yields the returns given in the money yield
table at page 121, and that all other conditions remain the
same, the expectation value of the soil will be-f-

3,102+21 X l-025-"+!)l X 1025-"+123 X l-0-25i"- 60 X 1-0-25^'''

1-025'^^ - 1
- 120

S. = 366 shillings = £18 6s. 0(/.

126 VALUATION OF FOREST SOIL.

It follows that, under the above conditions, it pays to plant
beech on such land if the latter can be purchased for £18 6s.
an acre or under, which is less than in the case of Scotch pine.
The highest expectation value of the soil in the case of beech
is obtained under a rotation of 90 years, when -S', = £18 15s.,
which is somewhat lower than that obtained in the case of
Scotch pine.

2, Matters which affect the Expectation Value of the Soil.

As indicated by the formula, the expectation value of the
soil depends on-f-

(a.) The absolute amount of receipts and expenses.

(b.) The length of the rotation.

(c.) The time when the intermediate returns are realised.

(d.) The time when the costs of production have to be

incurred.
(e.) The rate of interest with which the calculation is made.
Each of these matters must be further considered.

a. The ahsolute Amounts of Receipts and Expenses.
These are influenced, not only by careful management, but
also by the choice of species. If, for one and the same piece
of land, the calculation is made for different species, the
expectation values thus obtained are likely to differ consider-
ably; hence the importance of selecting the most suitable
species in each case.

h. The Length of Rotation.
As the growing stock has, in the majority of cases, very
little value during the first part of the life of a wood, so
that the yield would not even cover the cost of harvesting,
it follows, that the expectation value of the soil may, under
a very short rotation, be negative. With advancing age, the
value of the growing stock increases, so that the expectation
value of the soil becomes positive; it goes on augmenting,
until it reaches a maximum, after which time it falls

EXPECTATION VALUE. 127

again. A second maximum may occur owing to a sudden
heavy increase in the value of the growing stock. Under an
excessively high rotation, the expectation value of the soil
would again become negative.

Example. — Making the calculation for successive rotations
for a Scotch pine wood, with the same conditions as before,
the following amounts of the expectation value are obtained : —

S^ for a rotatic
Se „

Se „
Se „
S, „

Se .,

Se ,.

Se „

■ s, ,, ,, ..

The above data show, that, financially, the most favourable
rotation must be that, under which the expectation value
reaches its maximum ; in the above example a rotation of
about 80 years. The higher the rotation beyond 80 years,
the less favourable are the results.

c. The Time when the Intermediate Returns are Reatised.

The earlier the intermediate returns occur, other matters
being the same, the higher will be the expectation value.

Example. — The present value of a thinning, worth 86
shillings, made in the year 60, and again every 100 years, is =

86 X l-02o*«

30 years

. =

-

52 1

shillings.

•10 „

^

+

164

,,

50 ,,

. =

+

262

,,

60 „

. =

+

353

70 ,.

:=

+

394

,,

80 ,,

. =

+

404

90 .,

=

+

392

100 .,

. =

+

368

110 „

=

+

338

J,

120 „

=z

+

304

,,

1-0251

= 21 shillings.

If the same thinning were made in the year 30, and again
every 100 years, its present value would be =

86 X 1-025'" ,^ 1 ..y
1^25^00^1 =^'^^^^^^^^S-

12S VALUATION OF FOREST SOIL.

It follows, that strong thinnings, made at an early age, can
consideral)ly increase the expectation value of the soil. At
the same time it must not be overlooked, that the small
material obtained from early thinnings is not always sale-
able at remunerative rates; moreover, such thinnings may
disastrously affect the later returns, especially' the final yield,
so that the advantage, gained in the first instance, may be
more than counterbalanced by loss later on.

Early receipts from minor produce affect the expectation
value in the same way as those from thinnings ; hence they
are of great financial importance, as long as they do not
unduly aft'ect later returns.

d. The Time when Uie Cosh of Production have lo be Incurred.

This affects the expectation value in a manner the reverse
of that produced by early thinnings and incomes from minor
produce. Expenses, incurred during the early part of the
rotation, affect the expectation value unfavourably ; hence it is
important to keep the cost of formation as low as possible.

Example. — The present value of the cost of formation
amounting to 60 shillings, to be incurred at once and again
every 100 years, is =

1^025100 _ 1 =^^^ shillmgs.

If the cost amounted to 120 shillings each time, the present
value would be =

120 X l'025i^J^ ,0-, i-ir
1-02510" - 1 "" shillmgs.

Thus it Diay happen, that the expectation value is higher
under the system of natural regeneration than under the clear
cutting system with planting, provided that natural regenera-
tion is easy ; if it involves loss of time, it may be more profit-
able to regenerate artificially, so as to prevent the lengthening
of the rotation.

EXPECTATION VALUE.

29

e. The Rate of Iiitprfi<i with ivliich the Calculation is made
A high rate of interest gives a low expectation value of the
soil, and vice versa. The value is, however, not in inverse
proportion to the rate of interest ; the former rises more
rapidly than the latter falls.

Again, under a low rate of interest the expectation value
culminates later than under a high rate.

Example. — Taking the same data as above, and calculating
the expectation value of the soil with 2i, and again with 3,
and 4 per cent., the following values are obtained : —

Calculation- made with

Rotation.

Years.

i

2*%

3%

4%

1

.«.

s.

.'!.

.iO

262

43

fiO

.3.^3

2U

61

70

894

230

.56

SO

404

22.T

43

ltd j

392

IS.T

KtO

368

This example shows : —

(1.) By raising the per cent, from 2J to 3, the expectation
value, for a rotation of 80 years, falls from 404 to 225 shillings
and calculated with 4 per cent, to 43 shillings.

(2.) By making the calculation with 4 per cent., the expecta-
tion value becomes very small, and under a higher per cent,
it becomes negative.

(3.) The expectation value of the soil culminates : —

Calculated with 2J per cent, at about 80 years.
„ 3 • „ „ „ 70 „
„ 4 „ „ „ 60 „
(4.) If the proprietor is satisfied with 2| per cent, on his
investment, he can afford to pay ^£20 4s. per acre for the
land; if he expects 3 per cent., only ^011 lOs.; if 4 per cent.,
only £S Is.

130 VALUATION OF FOIJEST SOIL.

3. Merits of the Method of the Expectation Value.
The expectation value indicates the true economic value of
the soil for forest culture, because it is based upon the produc-
tive power of the land when used for the rearing of forest
crops. It gives the value, which corresponds to the net returns
calculated with the adopted rate of interest. On the other
hand, the method gives correct results only under the following
conditions : —

(«.) That all items of expected incomes and expenses are
accurately known. In order to comply with this con-
dition, accurate and suitable yield tables are required.
Moreover, future prices of produce and expenses must
be estimated on the basis of those at present prevailing,
a matter which introduces much uncertainty into the
calculation.
(h.) That the calculation is made with a suitable rate of
interest. It has been shown above, that this is a
matter beset by considerable difficulty,
(c.) That the rotation, corresponding to the maximum
expectation value of the soil, can be adopted and
retained without thereby lowering the price of forest
produce ; in other words, that the market can readily
absorb any extra cuttings, which may be necessary, in
order to introduce a rotation lower than that hitherto
followed.
Generally speaking, the expectation value of forest soil is not
a fixed quantity; it changes, not only in the ways indicated
above, but also with alterations in the price of forest i^roduce,
consequent on changes in the areas set aside for the production
of forest crops.

Section II. — The Cost Value of Forest Soil.

By the cost value of the soil is understood the sum of all
expenses incurred in acquiring the land and rendering it fit
for forest culture. These expenses consist of : —

(1.) The price paid for the land.

COST VALUE AND SALE VALUE. 131

(2.) The sum expended in rendering it fit for cultivation,
such as drainage or irrigation, levelling, fixation, etc.

(3.) The interest accumulated on the outlay mentioned
under (1.) and (2.) up to the date, when the first forest crop is
started.

Example. — An acre of land has been purchased for £10 ;
a sum of £5 has been expended at once in breaking through
an impermeable substratum in strips 6 feet apart ; a further
sum of £2 has been spent after the lapse of 3 years in
breaking up the intermediate strips ; the land was allowed to
lie fallow for another 2 years. The cost value of the land
at the end of 5 years, when it is planted, amounts, calculating
with 2i per cent., to

S,. =z (10 + 5) X 1-025^ + 2 X 1-025- = £19 Is. 5(7.

The cost value of the land may be accepted as the true
value : —

(1.) If the expectation value of the soil cannot be ascertained

with any degree of accuracy:
(2.) If the owner agrees to let the land go at the price, which
represents his own outlay on it
The cost value of the soil may be equal to, smaller, or larger
than the expectation value.

Section III. — The Sale Value of Forest Soil.

By the sale, or market, value of forest soil is understood
the value, which it realises in the open market. It represents
the true economic value only, if it agrees with the expectation
value.

In most localities a sale price has established itself, but this
represents in the majority of cases the value, which the land
has for other purposes, such as agriculture. It may differ
considerably from the value, which the land has, if used for
the production of forest crops, the sale value being generally
higher than the forest value in the case of good lands and
lower in the case of inferior lands, because the former yield

k2

]32 VALrATinx of forest soil.

a liiglier rental under field erops, and the latter under forest
crops.

The sale value of forest soil may he taken as expressmg the
true value : —

(1.) If forest soil is to he disposed of voluntarily for other

uses
(2.) In the case of forced sales, when the local value has to
he ascertained, rather than the forest value.

138

CHAPTER III.

VALUATION OP THE GROWING STOCK.

The value of the growing stock can, as in the case of the
soil, be determined as the expectation, cost, or sale value.
The valuation may refer to —
(1.) One particular wood.
(2.) A whole series of age gradations, representing the

normal growing stock of a working section, or of a

whole forest.

Section I. — Value of the Growing Stock of a Single
Wood.

1. lite Expectation Value.
The expectation value of the growing stock of a wood now
ta years old is ecjual to the present values of all incomes,
which may be expected from the wood, less the present value
of all expenses, which must be incurred between the year m
and the time when the wood is linally cut over.

a. Jlefhod of Calculatioi.

Starting from the same data as those given in the case of
the valuation of forest soil, the receipts consist of —

Y.

(1.) Final yield in the year /• = Y, ; present value = ...q ',._„,.

(2.) Intermediate yields, such as thinnings, to be realised in
the years n, o, p, and q ; their present value amounts to —

Thmnnig m the vear n =— — -!i — = '\ ^ i — .

i\ X vop'-"

,, ,, 0 . . = — — .

134 VALUATION OF THE GROWING STOCK.

Thinning in the vear p . . ^,^p X I'Op'-^

Expenses :

(1.) Annual expenses to be incurred from the year m to the
year r; their present value amounts to —

l-0/*"^T(V "^ • • • + i^->" = (ncfording to Formula YD

e
^ a-Gp^-"'-l) ^Op (l'Oi''^"-l) _ E (1-0//-'"- 1)
V02f-"'X 'Op ~ ' I'Op'-'" ~ I'Op'"'

(2.) "Rent of soil to he paid from the year di to the year r; its
annual amount may he denoted hy ,S' X •O;^ ; the total present
value of the rent of the soil during r — vi years amounts to —

.S' X -O;) S X -Op S X -Op S X -Op (l-OjV-"'-!)

1-Op + VOp^ + • • •+ 1-0^/— - i-Op'-'" X -O;)
_ ,s' (l-ox-"'-l)
l-Oj/-'"
The formula for the expectation value of a wood stands,
therefore, as follows: —

Y,+ T„XlOp'""+ ••■ + T^Xl-Op'^-'>-(S + E) (lOp*-"-!)
l-Op"-"

Example. — A fully-stocked Scotch pine wood, worked under
a rotation of 80 years, is feloniously burned when 45 years old;
what compensation per acre should be paid to the owner, if the
expected retuins are those indicated in the table at page 120?
Rate of interest = 2i per cent.
Value of soil = 404 shillings.
Annual expenses = 3 shillings, to 1 e incurred at the
end of each year : —

3,004 + 87 X 1-025=" + 118 X l-025~" + 134 X l-025i"
- (404 + 120) (1-025=^^— 1)

'(i. =

1-0253S
'^(i,, = l,liJ8 shilhnos = £59 13.s. 0,1.

EXPECTATION VALUE. 135

h. Notes 071 the Exjjectation Value of the Groiving Stock.

The expectation value of the growing stock depends on the
following matters : — •

i. The Absolute AiiorxT of Receipts and Expenses.

Regarding the value of the soil to be introduced into the
calculation, it should be noted, that the maximum expectation
value should be chosen (in the above example 404 shillings), if
the soil is again to be used for forest purposes ; if the soil can
be more profitably used for agriculture or other purposes, the
correspondingly increased value must be introduced into the
account.

ii. The Length of the Rotation.

In the case of fully-stocked, or normal, woods, the highest
expectation value is obtained for that rotation, for which the
expectation value of the soil culminates, provided that value
is introduced into the account. (In the above example, rota-
tion = 80 years and S^ = 404 shillings.) If a larger value of
soil is introduced, then the maximum expectation value of the
growing stock is obtained for a lower rotation, than that for
which the expectation value of the soil culminates, and vice
versa.

In the case of insufficiently stocked, or abnormal, woods, the
rotation, for which the highest expectation value of the growing
stock is obtained, can only be determined by experimental
calculations based upon the data of each special case.

Example. — Taking the same data as before,

For a rotation of 70 years 'Vi^ = 1,169 shillings,
„ 80 „ „ =1,193
„ 90 ,, „ =1,160
„ 100 ,, ,, = 1,092

The maximum value is obtained for a rotation of 80 years,
that is to say, the rotation under which the expectation value
of the soil culminates (see page 127).

136 VALUATION OF THE GKOWING STOCK.

AssuDiing now, that the wood has been injured by wind at a
previous period, so that no thinnings can be made before the
year 90, and that the growing stock would reaHse —

At an age of 70 years . . . = 1,800 shillings,
,, 80 „ . . . = 2,700
M 90 „ . . . =: 3,707

then the expectation value of the wood under these rotations
would be as follows : —
For a rotation of 70 years —

45/. _ 1,800-524 (1-02525-1) _,,„ , .,,.
<J"e -, '..,- '= 729 shiihngs.

For a rotation of 80 years —

i5r< - 2'700-524 (1-025--1) „.,„ , .,,.

<J"e = , ' ,- = 83o shiihngs.

l-02o-^' ^

For a rotation of 90 years —

45/' - 3,707-524 (1-025^^-1) ^^ i -ii-
(^e Ym^^ ^=868 shiihngs.

For a rotation of 100 years —

45/. _ 4,438+149x1-02510-524 (l-025"-l) ^,,, , .„.
O. ^^:^^555 = 801 shillings.

It will be observed, that the maximum expectation value of
the growing stock is, in this case, obtained under a rotation
of 90 years.

iii. TuE Age of the AVuod.
The expectation value of the growing stock rises (given a
fixed rotation) with the age of the wood, but not in exact
proportion. If the thinnings are made after regular intervals,
say every 10 years, it generally happens, that, immediately
before making thinnings, the expectation value is slightly
higher, than immediately after the thinning has been made.
For instance, if a thinning is made in the year 60, the
ex^Dectation value of the growing stock for the year 59 will
probably be higher than for the vear 61.

COST VALUE. 137

Immediately after the area has been stocked m the beginning
of the rotation, the expectation value of the growing stock is
equal to the cost of formation, and at the end of the rotation it
is equal to the value of the final yield.

iv. The Rate of Interest with which the Calculation is made.
A high rate of interest gives a low expectation value of the
growing stock, and vice versa, similar to what has been shown
for the expectation value of the soil.

2. Cost Value of tlie Groiv'uKj Stock of a Sin<jle Wood.

The cost value of the growing stock of a wood now m years
old is equal to the present value of all costs of production, less
the present value of all returns, which the wood has yielded
before the year m.

a. MetJwd of Calculuiion.
Costs of Production. — (1.) The present value of the rent of
the soil during m years comes to —

S X 1-0//" - ,S' = S {VOp"' — 1).

(2.) The present value of the annual expenses during m
years (see Formula lY.) —

= e X l-O^y-i + c X l-0y"-3 + . . . + c',

=^{i-Oir-i)=E{i'Qf^-i).

Op
(3.) Present value of cost of formation —
= c X l-Ojj'".

lieceipts. — These consist of all previous thinnings and items
of other incomes realised before the year m ; they may be
represented by T„, 7\ . . . 2\. Their present value is —
= r„ X 1-Oi/'-" + 2\ X VOp'"-' + ...-\-TiX 1-Oir-K

Should any items of income have occurred in annually equal
amounts, such as shooting, grazing, etc., they can be summed
up according to Formula IV., or, better still, be deducted
from the annually recurring expenses.

138 VALUATION OF THE GROWING STOCK.

The general formula for the cost value is, therefore —

"G-^ = (S + E) (1-Op™ — 1) + c X l-Op" — (T^ X l-Op™-^
+ Tb X 1-Op^-' + . . . + T, X 1-Op™-').

Here "'G<. still includes the thinning of the j^ear m. If the
calculation is made for what remains as final yield to go on
with, then the tliinning in the year m (= T,,^ ) must also be
deducted.

Example. — Taking the same data as before, the cost value
comes to — •

45(7, = (404 + 120) (l-0-25^-^- 1) - (5 X l-025i-^+ 44 X l-025'^).
^^Gc = 1,193 shillings, as in the case of the expectation value.

h. Notes on Ihf Cost Vatve.

The cost value of the growing stock depends on —

(1.) The ahsohite anwKnt of tJie reeeijits and expenses up to the
year m.

(2.) The Afie o/ the Wood. — The value rises with the age,
but temporary exceptions occur, as immediately after
a thinning the cost value may be smaller than imme-
diately before it.

At the commencement of the rotation, the cost value is equal
to the cost of formation.

At the end of the rotation, the cost value is equal to the
value of the final yield, provided that —

(a.) the calculation has been made with the expectation
value of the soil (404 shillings in the above case) ;

(h.) the receipts and expenses were of the normal amounts,

and
(c.) the wood is fully slocked, or normal, at the end of the
rotation.

Proof.— Let ni = r, then,

rQ, = (s + F.) vop' - ] ) + c X 1-op - en X i-o;/-" + . . .
+ 7; X 1-Op' ")•

HALE VALUE. 139

By introducing the expectation value of the soil, the above
equation becomes : —

rQ, = /^;+ T„ X i-07y-"+- • .4- n X roy-^-e X rOj/_^.^^A

X (1-0;/ - l)+cX I'Oi/ - (r„X l-O;/-" + . . . + T„ X VOif-'').
which, after reduction, leads to —

(3.) The Rate of Interest. — If the calculation is made with
the maximum expectation value of the soil and the receipts
and costs corresponding to it, then a higher rate of interest
yields a lower cost value, and rice rersd.

If the above assumptions do not hold good, it depends on
the value of the soil and the amounts of receipts and costs,
which are introduced into the calculation, whether a higher
rate of interest gives a greater or smaller cost value of the
growing stock. It would lead too far, to follow up in this place
this somewhat complicated subject.

3. Sale Value, or Utilisation Value, of the Groicing Stock

of a Siiu/le ]J'ood.
By the sale value of the growing stock of a wood is under-
stood that price, which it would realise, if offered for sale in the
open market.

The growing stock may be sold und^r one of two
conditions : —

(a.) The wood is allowed to grow on for a number of years.
In this case, the purchaser would have to rent the soil
for a number of years, and to meet certain other
expenses. Hence, the sale value should be equal to
the expectation value.
Ih.) The wood is to be cut down at once. In this case the
sale value would be the price, which the cut material
realises in the open market. It is ascertained by
determining the volume of the growing stock and
multiplying it by the net mean rate per unit of
measurement.

14-0 VALUATION OF THE GROWING STOCK.

The sale value of very young woods, under condition b, is
generally negative, until the receipts obtained by the sale of
the produce cover the cost of harvesting ; from that period it
becomes positive, rising at first slowly, then more rapidly,
reaching its maximum value far beyond the period at which
the mean annual increment culminates, in fact not until the
annual increase in the value per unit of measurement is no
longer sufficient to cover the falling off caused by thinning or
decay. This period occurs, generally speaking, earlier in the
case of light-demanding species, than in the case of shade-
bearing species, which maintain a full stocking for a longer
space of time.

4. Relation cxi^tiiKj heticeen the Expectation and Cost Values
of tlie Growing Stock of a Normal Wood.

Looking at the formulae for the expectation and cost values,
it will be observed, that the rental of the soil and annual
expenses appear in the negatvie form in the one and in the
positive form in the other ; again, the thinnings appear posi-
tive in the first and negative in the second. It follows, that
any change in these items affects the two values in opposite
directions ; what raises the one value reduces the other, and
vice versa. Nevertheless, the one value can become equal to
the other. This is the case, other items remaining the same
in both instances, if the calculation is made in either case
with the expectation value of the soil.

Proof. — Let '"'G^ = '"G,, immediately after the thinning in
the year m has been made, then,

y, + T,, X I'Oir" + • . ■ + ^^; X i-Op'-" - {S -f E) (i-Qy>'-"' - p

= {S + E) (l-O;/" - 1) + *' X I'Op"' - {1\, X 1-Oy/"-" + . . .

+ 1\ X 1-0^/"' + TJ.
After making the necessary reduction, it will be seen, that
this equation can hold good only, if —

^ ^ F, + 2\, X 1-0//'" + . . . + '/; X l-Oi/~" - ^ X 1-Qi>'_j^- .
l-Ojj' - 1

VALUE OF THE NORMAL GRO'WINrT STOCK. 141

in other words, if the expectation value of the soil is introduced
for S. Even then, the above holds good only in the case of
normally stocked woods. If a wood has been too thinly stocked
from early j^outh, so that both thinnings and final yield are
below the normal amounts, the cost value will be found to be
greater than the expectation value.

5. Relation existing between the Expectation and Cost Values of
the Gron-in(i Stock of a Normal Wood on the one hand,
and the Utilisation Vcdne on the other.

The utilisation value of the growing stock is equal to the
expectation or cost value at the end of the rotation, provided
the maximum expectation value of the soil is introduced into
the account, and the rotation is that, for which the expectation
value of the soil culminates. An equality can also occur at
a previous stage, according to the values introduced into the
account.

Generally speaking, the utilisation value of young woods is
smaller than the expectation or cost value. On approaching
the end of the rotation the difierence is small, and it is then
the safest plan to value the woods according to their utilisation
value, as the calculation of the expectation and cost values is
based upon more or less uncertain data.

Section II. — Value of the Growing Stock of a Normal
Series of Age Gradations. (Normal Growing Stock.)

If a forest is so managed, that it yields annually an equal
return, it must contain a regular series of woods of equal
yield capacity ranging in age from 1 year up to r years, with
one year's difference between every two successive gradations.
Whether these age gradations are found on separate areas, or
are mixed with each other, makes no difference. In either
case, every year the oldest age' gradation will be cut over,
giving a yield = 1\, and every year there will be thinnings in
the gradations, which have reached the ages of a, b . . . q

142 VALT'ATION OF THE GROWIXCt STOCK.

years ; at the same time, every year formation will cost
c shillings, while supervision will cost r X e shillings. It
is of interest to the forester to ascertain the value of the
growing stock in such a forest, the same being known as " the
growing stock of a normal series of age gradations."

The annual net return of a normal series of age gradations,
or a working section, forms the rental of the soil and normal
growing stock of that working section. Like the interest
yielded by any ordinary capital, that rental is produced w^ithin
the year, so that the growing stock at the end of the year
represents the capital plus one year's rental. Hence, the
capital alone is present immediately after the year's rental
has been removed. At that moment the oldest age gradation
is (r— 1) years old, the next (r— 2), etc., and the youngest
(which has just been cleared), is 0 years old.

Where cuttings are made in winter, the normal growing
stock is present in spring, before the trees have commenced to
lay on the new annual increment.

The simplest way of calculating the value of the normal
growing stock is to capitalise the annual net income and to
deduct from the amount the value of the soil.

The annual net income is represented by the expression —
Yr + 2'„ + . . . + r,, - (c + r X e) ;
hence, the value of the growing stock is equal to —

Y,. + T, + • • • + r. - (c + r X g) _ , X v

or for the unit of area

r. + 7; + . . . + r, - {<■ + r X r) _ ^
r X -Op

Example.— Taking the same data as before and a rotation
of 80 years, the normal growing stock standing on 80 acres is —

8O/7 _

^-^ normal

3,004+5 + 44+87 + 118+134-(60+80x3) Qnx/ mi
^25 -80X404

^-G„<,™^; = 91,360 shillings,

VALUE OF THE NORMAL GROWING STOCK. 148

and the average value of one age gradation
91,360

80

= 1,142.

The vaUie of the normal growing stock can also he obtained
by adding up either the expectation or cost values of all the
different age gradations running from 0 years up to /• — 1 years.
If the maximum soil exj^ectation value is introduced into
these values, then the result is exactly the same, as if the
annual net rental is capitalised and the maximum soil
expectation value deducted. If a different value for the soil is
introduced, the result will not be the same.

144

CHAPTER IV.

VALUATIOIf or WHOLE WOODS OR FORESTS.

The value of a wliole wood, or a forest, is equal to the
value of the soil plus the value of the growing stock ; hence,
it can be ascertained by adding together these two values. At
the same time, that value can also be determined direct out of
tlie returns and expenses, or from sales of forests, or it can be
calculated out of the rental, which the forest yields. The
present chapter shows how the forester proceeds in each of
these cases : —

1. Expectation Value of a Forest.
As this is based upon future returns and costs, which differ
under different methods of treatment and species, two cases
must be distinguished : —

a. Calnikdion itiuhr the Svppo^ition ihat the mme Species and System
of Management are retained, after the p-esent Crop has been
Harvested.
(1.) Thevalue of the forest is equal to the ex^Dectation value

of the soil plus the expectation value of the growing stock.

The greatest expectation value of the forest is obtained for

that rotation, under which the expectation value of the soil

culminates: — ,„„ ,„,-, , ,^,

Let tbe age of the existing growing stock = m, then the
expectation value of the forest is —

r, + 2',, X roj/-" 4- . . . + 7; X roy-

'"F - - ('-.s; + E) (i-Ojj'-"' - 1) , ,^

= :^;+^'»xi-Oj/-"+ • • • +r,xi-Oj/-''-j: (i-Oj/-"'-i)+'">^,.

EXPECTATION VALUE. 145

By introducing the value of ^S'^ —

the above formula becomes

10p'"('y,+T„x10p'--"+ . . . +TqXl-Op^-'' +

^^ iop^-1 ^-

If )n is smaller than a, that is to say, if the age of the wood
is less than the year, when the first thinning occurs, then the
above two formubie become respectively —

l-0^>'-'"
and

.nj, ^ I'Op- (F,+ r„Xl-Oy-"+ . ■ . -^T.Xl-Of-'-c) _
1-0^/ - 1

If m = 0, and cultivation has not yet taken place —

i;+ T„ X i-op'- -"+...+ 1; X i-op'' - '-c x vojf

oj^ -E (l-0;/-l)+'-6',

= — ^^ — ' ,, , — = S. = the soil expectation value.
l"Oj>'

(2.) The forest expectation value can also be calculated
direct out of the expected receipts and expenses, in which
case —

l-Oi?'- - 1 "^ l-Op'- - 1 ^ • • • "^ i-oy _ 1

i4t) VALUATION OF WHULE WOODS OH iOKESTS.

VOp- - 1

i^;

as before.

Example. — Determine the expectation value of a forest now
45 years old, if that forest yields the returns given in
the money yield table for the Scotch pine at page 120 ;
rotation = 80 years ; cost of formation = 60 shillings ; per
cent. = 2^ ; and annual costs per acre = 3 shillings.

1-025*^(^3,004 + 87 X 1-025^^" + 118 X 1025-"

_ + 1B4X 1-025^0 + p4. + 1-^.-^0) _
l-025«'^-l
^T, = 1,597 shillings = £79 17s. Od.

It was found before —

At page 125. ^'\S', = 404 shillings.

„ 134. ^G', = 1,193 „

Total . . = 1,597 „ = £79 17.s. 0(/.
as above.

In the case of the present growing stock being abnormal,
the corresponding values must be introduced into the account
(see page 136).

h. Calculation uinler Ihe Supposition that, after the cuttimj ouer of the
present Crop, another Species or another Jfethod of using the Soil
is introduced.

In this case, the value »S" of the soil, corresponding to
the new conditions, must be introduced into the account ;
then the rotation r' must be determined, under which the
expectation value of the present growing stock reaches its
maximum.

COST VALUE. 147

The value of the forest is then represented l)y the formula —
,. .V ^ r,- + T,, X l-O^/ -" -\- . . .-E (l-Ojj'-'-'" - 1) + ^'

If the present growing stock is abnormal, a further moditi-
cation is required, by substituting the abnormal for the normal
returns.

'2. Cost Value of a Forest.

a. The (Just Value of a Forest is equal to the Cos/ Value of the
.Soil plus that of the Crowiiuj Stock

(1.) For any soil value —

'-F = s+{S+E) (i-oy- i)+c X i-Oiy"-[r,x i-Oiy''-"+ • • •]

"Pe = (S + E+ c) l-Op« — [T^ X l-Op-"^^ + . . . + E] .

(2.) By introducing the expectation value of the soil, the
above becomes, for normal woods —

-F, = (^;+:/:,Xl-Op"+...-cXl-0;,_ £ _^ £ _j. \ i.Q „
V I'O;?' — 1 /

- [r.xroi/"- + ... + £]

1-0//

«^" --£.

This, it will be observed, is equal to the expectation value
of the forest.

h. The Cost Value ran he cakulated direct out of the Expenses
incurred.

The method is similar to that followed in calculating the
cost value of the growing stock, but the value of the soil is
added instead of the rental only ; hence —

"'F,= Sxl-02J"^-\-E{l-0p--l)+c X l'Op"'-{T„ X l'Op"'-"+ . . .)
= {S + E + a) 1-Op"^ - [T„, X I'Qp'"-" + . . . + Al

as before.

l2

148 VALUATION OF WHOLE WOODS OR FORESTS.

3. Sale Tabic of a Forest.

By the sale value of a forest is understood the value
estimated according to prices realised for forests of a similar
description. As it is difficult to estimate existing differences,
and, hence, to estimate the sale value, the latter is of
subordinate importance.

4. llental Value of a Forest.

By the rental value of a forest is understood the capitalised
rental, AYhich it is capable of yielding. If the annually equal
rental is = R, the rental value would be —

Eental value = — .

This method is only applicable in the case of a forest, which
can be so managed, that it yields an annually (or periodically)
equal rental. The rental is represented by —

y, -f r. + r,, + . . .j^t„-{c^ r x o,

and the rental value of the forest is —

_ r, + T„ +:/; + ... + T„ - (r + r X e)
■Op

149

CHAPTEK V.

DETERMINATION OP THE RENTAL OF FORESTS.

In order to convert any item of income, whether it occurs
once or after stated intervals, into an annual rental, it is
necessary to ascertain the capital value of the income and then
to multiply it by "O^j. For instance, the rental which corre-
sponds to the thinning in the year a, and its recurrence every r
years, is equal to —

The annual payment corresponding to the periodic cost of
cultivation, is expressed by —

1. Rental of the Soil.

By the rental of the soil is understood the annual net
return of the soil. It is represented by the difference between
the rentals of incomes and the annual payment of expenses of
a wood, hence : —

Soil rental R

. X

Op + ^'><^X\-Op + . . . + ^^X'x'Op

l-Op'-l ' 1-0/ -1 ' ' ' 1-0^/— 1

VOjf - 1

This rental, it will be observed, is the rental of the soil
expectation value. Soil rental = ''S^ X 'Op.

150 DETETtMTNATION OF THE REKTAT, OF FORESTS.

2. ncntnl of ihr Foreai.

The rental of the forest is equal to the net return yielded by
the forest (soil plus growing stock)- In the case of the
annual working, the forest rental is equal to —

B,= Y, + 1\, + . . . + 7; - (r + r X e).

151

CHAPTER VI,

THE FINANCIAL RESULTS OF FORESTRY.

The subjects, which will be treated in this chapter, belong
to that part of scientific forestry, which is called, on the con-
tinent, "Forest Statics"; that is to say, the science, which
weighs and considers the comparative merits of the different
methods of treatment, to which forests may be subjected. The
financial results, or the rent-yielding power, of an undertaking
are expressed by the proportion existing between the yield
and the capital, which produces it. Hence, when several
methods of treatment lead to the realisation of the otherwise
desired object, it should always be ascertained, which of them
does so in the most profitable manner; in other words, which of
them gives the highest rate of interest on the invested capital.

In the present instance, only the most necessary matters
will be given, namely the methods of calculating the financial
results of forestry and their application to a few of the more
important questions.

Section I. — The Methods of Calculating the Financial
Results or Forestry.

The financial results of forestry can be determined in one of
two ways : —

(1.) by ascertaining the " profit," that is to say, the surplus

of receipts over costs of production, allowing compound

interest at a certain rate on both ;
(2.) by ascertaining the rate of interest yielded by the

capital invested in forestry, here called the "forest

per cent."
Each of these two methods must be explained in detail.

152 THE FINANCIAL RESULTS OF FORESTRY.

1. Deter mination of tlie Profit of Forestry,
a. Calculaiion for fJie Infrnuiflent WorJciiif/.
In the case of a single wood, of approximately uniform age,
the returns and costs do not occur at the same time, but at
intervals of various duration ; hence, tliey must be calculated
for one and the same time. In the first place, that time shall
be the commencement of the rotation, when the are.i is about
to be planted, or sown, for the production of a forest crop.

i. Calculation for a Blank Area.

Let as before —

1'. be the final yield occurring in the year r and again in
2 X r, 3 X r, and so on for ever ;

Ta, T^ , . . J\, the thinnings occurring in the years
a . . . q, and again in a + r . . . q -\- r years,
again in a -\- 2 X r . . . q -\- '2 X r years and so on ;

Sc the cost value of soil ;

E the capitalised annual expenses = -^ ;

c the cost of formation expended now, and again every

r years ;

c X I'Od'

C the capitalised cost of formation = — ;

I'Ojf — 1

J) the per cent, at which mone^' can be made available for
investment in forestry', and at which money taken out
of the forest can be invested with equal security.

Then the present value of all returns is —

_ i; + r„ X 1-0/-" + • • • + r, X 1-Op-"

l-Ojf - 1
while the present value of all costs comes to —

Hence, the profit of forestry is expressed by the formula —
Profit = P = Y, + T,xrOp-- +^ . . + T, X I'Op-^

lop' — i

- (S, + E + C).

DETERMINATION OF THE PROFIT. 153

This formula can also be written as follows : —

^-[ 1-0/ -1 ~~ ^) '^"

It will be observed, that the part in brackets represents the
expectation value of the soil ; hence, the above formula re-
duces to —

P = Se - S,.

In words : the profit in the case of a blank area is equal to
the difference between the expectation and cost values of the
soil. From this fact the following conclusions can be
drawn : —

(1.) A profit is realised, if the soil has been acquired at a
lower rate than that indicated by the expectation value
of forest soil.
(2.) A profit is also realised, if, although S^ = S, at the
outset, the soil expectation value is afterwards increased,
either by higher returns or by smaller costs, or both ;
in other words, by improved and more economic
management.
(3.) The greatest profit is obtained by the adoption of the
rotation, species, and method of treatment, which give
the highest expectation value of the soil.
(4.) If the cost value of the soil is equal to the expectation
value, the profit is nil, and the capital invested in
the forest yields exactly j) per cent. If the cost value
is greater than the expectation value, the forest
industry involves a financial loss ; in that case it is
more profitable to take the capital out of the forest
and invest it otherwise, as long as in this way p per
cent, can be obtained with equal securit3\

ii. Calculation of the Piiofit fok a Wood xow m tears old.

It is assumed, that the returns and costs are of the normal
amount.

54 THE FINANCIAL REST^LTS OF FORESTRY.

The receipts consist of —

(a.) All items of income realised l)etween tlie formation of

the wood and the year in, with accumulated interest to

the year m : —

T„ X I'Ojf"-" + T,, X I'Op''-' + . . . r,„.

(/>.) All items of income to he realised hetween the year 7??
and the end of the present rotation r, discounted to the
year m : —

T„ X 1-Op'-" + . . . + r, X iw + Y,.

(c.) All items of income to l;e realised dnring suhseqnent
rotations, amounting to —

T„ X 1-07/"" + • ■ • + ^^. X 1-Ojf-^^ + Y,
{I'Of - 1) X l-0]f~"'

TJic costs are —

(a.) Past costs with compound interest to the year???: —

.S; X VOp'" + ^ (I'O/" - 1) + ^- X l-O;?"'.
(/?.) Costs to be incurred from the year ??? to the end of the
first rotation : —

E (l-O//-- '" - 1)

(c.) Costs to ])e incurred during future rotations : —
K , c X l'0]f

1-0/)' '" iVOp' — 1) X 1-Op'-'"

By deducting all costs from the receipts, the profit is obtained
and represented l)y the following formula : —

Profit P =

1; + T„ X 1-Oy/-" + . . . 4- r, X VOf - F. (1-0;/-'" - 1) ^y ^
1-0/-'"

I 1 ( Y,.± T,, xro;?'-" + .+7;xro/ "- c x i-O// _ ^ a ..

^i-Op'-'A i-0/?'-i V •

- [(sv + ii;) d'O/" - 1) + ^- X vop'"- T„ X i-oy/" "- ... - 7;,]

-,S: (III.)

DETERMINATION OF THE PROFIT. 155

In this formnlapart (11.) represents the expectation valne of the
soil discounted for r — m years, and the bracketed part of expres-
sion (III.) represents the cost value of the m 3'ears old growing;
stock ; hence, the above formula can be written as follows : —

p_r,.+r,,xi-Oj/-"+...+r,xi-o;/-^^+^s;-j^(i-Ojf-'"-i)

-(.S.+'^G,).

Here again, the positive part represents the expectation value
of the forest (see page 144), and the negative part the cost
value of the forest ; hence —

Profit P = "T^ — "F^ = (S3 — SJ X l-Op*".

It will be seen, that this formula agrees with tliat given for
a blank, because for the year 0 the expectation value of the
forest is equal to the expectation value of the soil, and the
same holds good for the cost values.

The conclusions drawn on page 153, headings (1.) to (4.),
with regard to the formula P = S^ - »SV, also hold good with
regard to the formula P = '"F, — '"F,.

h. C'ahmlaUon for the Annual Worlnni].
In this case the returns and costs occur regularly every
year. If the}' are of annually equal amounts, the returns are

= Yr+T„+ + T„

The costs consist every 3'ear of —

(1.) Interest on the value of the soil . = r x S, x "O^) ,-

(2.) Interest on the value of the normal

growing stock . . . . = /• x "Or X "0/) .-
(3.) The annually recurring cost of ad-
ministration, protection, taxes, etc. = r x c ;
(4.) The cost of formation . . . =^ ^ ;
hence, the annual profit —

P = Y..+ T.. + .. . + T- c- r X f - [r X *S',.+ r X "G,] X '0]) ;
or.

Annual P^i;+r„+. • . + T-c-rXr ^^.^^^ ^ ^ ^.^„^^^
•Op "Op

lofi THE FINANCIAL RESULTS OF FORESTRY,

Now: —
Annual P

■Op
y,+ r„ + . . .-^T-c-rXc

= capitalised value of annual profit = total profit ;
= the expectation value of the

■Op
forest under the annual Avorking = F\ ;

r X *S', + /• X "6r, = cost value of forest = F, ;

hence, total, or capital, value of profit of the whole forest : —

Total P = F^ — Fg.

In words, the profit is equal to the difference between the
expectation and cost values of a forest. For the rest, what
has been said as regards the intermittent working holds also
good in respect of the annual working, and vice versa, because
a series of age gradations may be considered as so many
separate woods of various ages ; the profit calculated for the
series as a whole must be equal to that obtained by adding
together the profits derived from the several age gradations,
each calculated for itself.

Examples. — Given the data as before, that is to say, the
returns to be those of the yield table on p. 120,

p = 2^ per cent. ; e =^3 shillings ; c ^ 60 shillings ;
r = 80 years.

(1.) Calculate the profit per blank acre, if the soil was
bought for 300s. —

From previous examples it is known, that *S'<; = 404s. ;
hence— p^.^^^ ^ ^^^ _ ^^^ ^ ^^^^^

(2.) Calculate the profit of a wood 45 years old, under the

same conditions.
It was found at page 146, that ^'"F^ = 1,597s., while
457^;. = (300 + 120 + 60) X l-025^-^ - [5 X l-025i ' +
44 X 1-025^ + 120]
45/y^, = 1,281 shillings; hence—

1> = ^U\ - '-'Fc = 1,597 — 1,281 = 316 shillings.

+ 134 (1-0251"- 1) Pi ^ -025 - 80 (300 + 120) ;

CUERENT RATE OF INTEREST. 157

But also P = {S- S,) I'Op'' = 104 X 1-025^5 ^ 31,- shillings.

(3.) Calculate the profit of a normal series of age grada-
tions, that is to say, for the strictly annual working.

Total Profit = """'""F, - '""-'""'F,.

Now, '""■"-' F, = S. + ™'G, = 80 X 404 +91,360 (see
page 142).

vormai-^^ _ 123,860 sMlUngs,
while

normal J^ Q _1_ normal ri .

S, = 80 X 300 = 24,000 shillings.

-'"■>'""G,= [(300 + 120 + 60) (1-025^"- 1) - 1 5 X (1-0255" - 1)

+ 44 (1-025^" - 1) + 87 (1-02530- 1) + 118 (1-025'-^^'- 1)

-Dp, ^-025 -80 (£

«'-""'VV, = 73,836 shillings,
hence —

normal j^.^^ 24,000 + 73,836 = 97,836 shillings,

and

Profit = 123,860 - 97,836 = 26,024 shillings.

2. Determination of the Rate of Interest yielded hy the Cajntal
invested in Forestry, called the Forest Per cent.

a. Ciilriilaiion for ihc Tnicrmittent WorJriiir/.
Under the intermittent working, the rate of interest changes
from year to year, because the capital, as well as the increment,
change with the advancing age of the wood ; hence, it is neces-
sary to distinguish between the current annual and the mean
(or average) annual rate of interest.

i. Current Annual Rate of Interest.

As indicated on page 113, the rate of interest is expressed
by the fraction

Kate of interest = — .
C

158 THE FINANCIAL RESULTS OF FOKESTUY.

where C represents the capital which has produced the amount
/ in the shape of interest. The per cent, is then

per cent, p = ,, X 100.

This formula is used in the case of forestry, and it remains
only to introduce the proper amounts for / and ( '. In other
words —

The current annual rate of interest is equal to the net
annual value increment of a wood divided by the cost value
of the wood at the commencement of the year in (juestion.
The current annual per cent, is equal to that quotient
multiplied by 100.

Let—

y„, be the utilisation value of a wood at the end of the year )ii,

y.u+i „ „ „ „ „ „ „ M "'+1,

then —

-* //I -r 1 -^ in

represents the increase in value, which has been produced during
the year iii -{- 1. Deducting from this e, the annual costs, the
net increase in value is equal to —

The cost value of the wood at the end of the year iii (or
beginning of the year in + 1) is represented by —

(a.) The value of the soil with compound interest to the
year in =^ .^ -, r^ , ,

{b.) The cost of formation with compound interest to the

y^"'' '" = .• X 1-Oir.

(c.) The value of the annual cosLs during in years with
compound interest calculated for the end of the
year in =

ia5C^) = ,:a-0;r-i).

'Op

CUERENT RATE OF INTEREST. 159

(d.) From these amounts must be deducted all returns
realised between the formation of the wood and the
end of the year in =

T„ X 1-0//'-" + T„ X VQir-' + ...+ '/', X l-Qp'"-' + T,,,.

The current forest per cent. ""'''' Pf, with which the invested
capital has worked during the year v/i+l, is, therefore,
expressed by the formula —

(F,„+i - F,, - e) 100 ^

0S<..+£ + c)xi-Oiy'^-(r«xi-o/"-" + nxi-OK^'+ . . . + ^».+ £)'

The denominator in the above formula can also be written
thus : —

0S'.+£) (l%"'-l) + cX l%"'-('i'„X l-Oi/"~" + . . . + 7'J+^',.

On reference to page 138, it will be seen, that this expression
represents the cost value of the growing stock immediately
after the thinning in the year m has been made, plus the cost
value of the soil ; hence the formula for the forest per cent,
reduces to—

curr. ^ (Y^^i-Y^-e)XlOO* ^ (Y^^i-Y^-e)XlOO
Sc + ^G, -Fe

By substituting the utilisation value of the growing stock
for its cost value, the formula becomes —

curr. ^ ^ (Y„^i - Y„ - e) X 100

Se"+Y„

The latter formula is used, when m is anywhere near the
end of the rotation.

* This formula differs from tliat usually giveu in coutinental works, which is
as follows : —

(F„. + i- F,„)i00

■Pf

It is easy to show, that this formula is correct only for the year, in which
""■'■• j^;|- = general per cent. ^;.

160 THE FINANCIAL RESULTS OF FORESTRY.

Example. — Let S =■ 404 shillings ; e = 3 shillings ; p = 2i
per cent. ; c- = 60 shillings ; data on page 120. Then : —

,0-51 (1,055- 985 - 3) 100 , ^ ,

^'■^= 404 + 985 =4-8percent.

Go-61,, ^ (1,639_-1,563 -^3) 100 ^
^' 404+1,563

;o-:i ^ ^ (2,269 - 2,187 - 3) 100 ^ ^.q
^'■' 404 + 2,187

80-81 ., ^ (2,944 - 2,860 - 3) 100 ^ ^-s
■' 404 + 2,860

,,„_,ip ^ (3,646 - 3,558 - 3) 100 ^ ^-i
404 + 3,558

It will be observed, that the forest per cent., from the 50th
year onwards, is at first large but falls with the advancing age
of the wood. At the year 80 — 81 it is equal to the general
per cent, p = 2J % ; after that time it is smaller than 2^ %.
Hence, the current annual forest per cent, is utilised to
ascertain the financial ripeness of a wood, a matter which
will be dealt with further on.

ii. Mean Annual Rate of Interest.

The mean (or average) rate of interest is ascertained by
converting all net returns into an equal annual rental and
dividing it by the producing capital. That quotient multiplied
by 100 gives the mean annual forest per cent.

The best time for making the calculation is the commence-
ment of the rotation. At that time, the annual net rental is
represented by the expression —

/r,.+ 7;,xro/-"+ . . . +r,xrOj/-^-cxi-oy_ .a .^

V I'Oi;'--! / ^"

The producing capital at the commencement of the
rotation is equal lu the cost value of the soil = be. lience,

MEAN RATE OF INTEREST. 161

the mean annual forest per cent, under the intermittent
working is —

^ X 100.

If >S'->N,, then""""^V>jj.

If the expectation vakie of the soil is equal to the cost
value, then the mean annual forest per cent, is equal to the
general per cent. ]), which proves the correctness of the above
formula.

The highest mean annual forest per cent, is obtained under
that rotation, foi' which the expectation value of the soil
culminates ; it is then equal to the current annual forest per
cent.

Example.— Given the same conditions as before —

,S', = 404.S.
If the cost value of the soil is also 404.s., then

404

4U4

equal to the general per cent, j), with which the value of Se has
been calculated.

If S, = 300 shillings, then
404

mean ,, ^v^ . , n " .t < j

Pf — OQQ X 2-0 = 3-4 per cent.

If S, = 500 shillings, then

404

'"-»«, = 5^ X 2-5 = 2-0 per cent.
^ ^ 500 ^

In the latter case money is lost ; hence the capital had
better be taken out of the forest, and invested elsewhere, if
at least 2J per cent, can be obtained with equal security.

F.M. M

162 THE FINANCIAL RESULTS OF FORESTRY.

h. Calculation for the Annual Working.

Under the annual working, with equal annual increment,
3'ield, and costs, the current annual forest per cent, is equal to
the mean annual forest per cent. In this case, the annual net
return of r units of area amounts to —

r, + 7',, + . . . + 7', - c - r X e,
and the producing capital to —

r X N.. + r X ""™""G, ;
hence —

..„. r + 7'+ +7:,-<.-,-x^ X 100.

■" )■ X S,+ r X "<i,

■^ c

By multi[)lying and dividing the enumerator in this formula
by 'Op, the following is obtained : —

C^-^^^+'-y-^-'-^Qxioox-o.

'-'Pf = ^ 77 '

or, as the part in brackets is equal to the expectation value of
the forest = F^ : —

mean p ^ ^e >< p_

This formula is identical with that obtained above for the
profit = Fe- F, :

If F,>i*',,then'"'""j>^>;,.

If F^ = F„ then """"p^ = p.

The highest mean annual forest per cent, under the annual
working is obtained for that rotation, under which the expecta-
tion value of the forest reaches its maximum ; in the above
example, about 80 years.

CHOICE BETWEEN FORESTRY AND AGRICULTURE. 163

Section II. — The Financial Test applied to the Method
OF Treatment.

If the profitableness of the method of treatment is to be
tested, or if several methods are to be compared, it must be
assumed, that in each case those conditions exist, which render
the method in itself as profitable as possible. In that case it
may be said, that the most advantageous method of treat-
ment from a financial point of view is that, which yields the
highest profit, or the highest mean annual forest per cent.,
provided, in the latter case, that the capital is the same under
each method. If the capitals differ, the following cases must
be distinguished :

(1.) The method employing the greater capital is the more

profitable, if it gives the higher forest per cent.
(2.) Tlie one with the smaller capital is the more profitable,
if it yields an equal or a greater amount of interest. If
it yields less interest and yet a higher forest per cent.,
it cannot be decided off-hand, whether it is the more
profitable or not, as the total profit depends on two
factors, namely, the rate of interest and the amount of
the invested capital ; hence it is necessary to calculate
the actual amount of profit for each case, and to compare
the one with the other.
The above-mentioned tests may be applied to all questions
connected with forest management. Of these the following
are the most prominent : —

1. Choice between Forestry and Agriculture as regards a
Piece of Land.

Of these two methods of using the land that is the more
profitable, which yields the highest net rental of the soil.
Rental of soil under forest =

[Y,-\- r, X roj/-" + . . . + r, X ro;/-^ - c x ro/ _^] ^ .q
L i-oy-i J ^'

m2

J 64- THE FINAXriAL RESULTS OF FORESTRY.

Pieiilal of soil under agriculture =

Annual gross rental — annual costs = net letting value.

The decision can also be based upon the profit in each case,
when the formula stands as follows :—

where Y' represents the annual gross income from agricul-
ture, e' the annual expenses under agriculture, and S' the cost
value of the soil.

2. Choice of Species and Sylricidttind Sijstem.
In l)Oth cases the choice is determined b}- the amount of
the expectation value of the soil for various species or sj'stems.
It depends chiefly on —

(a.) the value of the returns and the time when they occur.
(h.) the cost of formation and the amount of the aimual

expenses, if they differ for different species or different

sylvicultural systems,
(c.) the rate of interest.

3. Choice of Method of Formation.

The choice depends on the amount of the expectation
value of the soil under the various methods of formation, such
as planting, sowing, or natural regeneration.

4. Choice of JMctJiod of Tendiiifi, cspeciaUi/ in respect of
the Time and Styenffth of Tliiniiiiifis.

This is best efiected by calculating the expectation value of
the growing stock for the different methods of thinning, and
comparing them.

FINANCIAL RIPENESS OF WOODS. 165

5. Determination of the Financial Rotation.

The financial rotation, or that which gives the best financial
results, may be determined in various ways, as : —

(a.) The rotation which yields the highest expectation value

of the soil, or the highest soil rental.
(b.) The rotation which gives the highest net return for the

forest, allowing compound interest on all items,
(e.) The rotation which, taking a certain value of the soil,

gives the largest profit or the highest mean annual

forest per cent.

G. Determination of the Financial Ripeness of a Wood.

The financial ripeness of a wood, say m years old, is gauged
by means of the current annual forest per cent. As long as —

c...,, _ (iVi-i^.»-g)xioo

is greater than the general per cent, p, the wood is not ripe.
If '""'''"'''pf-= p, then the wood is just ripe. If ""'"''j)/ < p, then
the wood is past ripeness and, if left standing, a financial loss
is incurred.

The above short notes will sutfice for the present. The
application of these principles will be found in the next part
of this volume.

167

PART III.

THE FOUND A.TIONS OF FOREST MANAGEMENT.

169

THE FOUNDATIONS OF FOREST
MANAGEMENT.

Forest working plans regulate, according to time and locality,
the management of forests in such a manner, that the objects
of the industry are as fully as possible realised. As the latter
differ widely, it follows that working plans cannot be drawn
up according to any uniform pattern. The working plan for a
protection forest, or a park-like forest, is altogether different
from that of a forest, which is managed on economic principles.
In this volume only forests of the latter class will be considered,
that is to say, it wdll be explained, how forests should be
managed so as to produce the best financial results, or the
greatest volume, or the most suitable class of produce.

The yield (or the return) of a forest consists of major, or
principal, and minor produce. By the former, timber, fire-
wood and bark are understood. It is in the nature of things,
that forests should yield chiefly such articles ; at the same
time, articles of minor produce (such as turpentine, fodder,
grazing, fruits, caoutchouc, etc.) are frequently of considerable
importance, and demand modifications of that management,
which would be indicated by considering only the realisation of
major produce.

Major produce is derived from the final and intermediate
jdelds. The latter comprise the thinnings and other cuttings,
which are made from time to time during the course of the
life of a wood, while the former is the return yielded by the
final cutting of the wood, to be followed by a new crop, whether
the old crop is removed in one cutting or by a number of
successive cuttings, as in the case of natural regeneration
under a shelter wood.

170 THE FOUNDATIONS OF FOREST MANAGEMENT.

The major produce of forests, wood, is one of the mdispens-
able articles of life, but it is bulky and not adapted for a long
transport by land. Hence, it must in many cases be produced
locally. To this must be added, that long periods of time
elapse between the planting and harvesting of woods. Both
these matters make it desirable, that the yield of forests should
be continuous and brought into the market in annually equal
or approximately equal quantities, necessitating a management
based upon the principle of a sustained yield.

Generally speaking, a " sustained yield " is secured, if
all areas, which have been cleared, are re-stocked within a
reasonable time and the young woods, which spring up,
properly tended, so that the soil continues to produce crops
of wood. At the same time, a distinction must be made
between —

(1.) The intermittent working, if the successive final returns
are separated by a varying number of years.

(2.) The annual working, if final cuttings occur in each year.
If the latter are approximately equal in quantity year
by year, the method is called the " equalised annual
working."

The regulation of the yield of forests worked intermittently
is very simple. It is only necessary to ascertain the most
suitable rotation, taking into consideration the objects of
management and to make the intermediate cuttings, whenever
they are necessary. The matter becomes more difficult,
when an annually equal yield is expected.

Although the method of annual working, and especially of
the equalised annual working, is not an absolute necessity,
still it is in the majority of cases highly desirable, more espe-
cially where extensive areas are under treatment, or where a
steady market has to be regularly satisfied. Moreover, it has
considerable advantages, of which the following may be
mentioned : —

(1.) It is best adapted to meet the requirements of the market
and therefore favours the development of a regular

INTRODUCTOKY. 171

and steady demand, with a sustained competition of
purchasers.
(2.) It affords equal employment'year after year and enables
the administration to maintain a regular number of
workmen, and to instruct them thoroughly in their work.
(3.) It secures to the owner equal, or approximately equal,

annual incomes, and facilitates budget arrangements.
On the other hand the method has disadvantages, such as : —
(1.) It cannot be introduced without cutting certain woods
at an age differing from that, which is most desirable,
in all cases where a regular series of age gradations does
not exist, or where the age gradations are irregularly
distributed over the area.
(2.) Owing to the necessity of bringing annually the same
quantity of produce into the market, it interferes with
the complete utilisation of special demands for forest
produce, or the omission of cuttings, w'hen the demand
is slack.
These remarks show, that each of the two methods of
working possesses peculiar advantages, and that the choice
depends on circumstances. In the majority of cases, the
annual working will be found more suitable and profitable,
without, however, strictly adhering to it, when it w^ould involve
sacrifices out of proportion to the general advantages of the
method.

Correctly speaking, in order to have equal annual returns,
it would be necessary to regulate the intermediate cuttings as
well as the final returns. Against such an arrangement the
following reasons may be given : —

(1.) Areas, which yield equal final returns, do not always

give equal intermediate returns.
(2.) Thinnings depend much more, than final cuttings, on
the method of formation and tending ; they must be
made, when they are necessary, so that the time for
their execution can, in many cases, only be determined
a short time before they become necessary.

172 THE FOUNDATIONS OF FOREST MANAGEMENT,

(3.) The yield of intermediate cuttings depends frequently on
events, which do not occur regularly, or ^Yhich cannot
he foreseen, so that it is almost impossible to estimate
it correctly beforehand ; for instance, in the case of
wind-break, snow-break, death caused by disease or
insects, etc.

Hence, it is desirable to confine the regulation of the annual
yield to the final cuttings, and to be satisfied with an approxi-
mate equalisation of the intermediate returns, such as will
naturally happen, if the final cuttings are systematically
equalised ; provided always, that the thinnings are not made
so heavy as to affect the subsequent final returns.

If a forest is to yield a return, either annually or periodi-
cally, it must be in a certain state. In order to determine,
what this state should be under a given set of conditions, it is
useful to construct an ideal pattern, such as would be presented
by a forest, which has grown uj) uninfluenced by external
interfering circumstances. The ideal state difi'ers, of course,
for every different method of treatment, in accordance with
the objects at which the management aims. In all these cases,
a forest, which corresponds in every way to the objects of
management, is called a normal forest. It enables the forester
to study the laws, which must govern the management, and it
serves as an ideal to be aimed at, though it may never be
altogether reached, and at any rate not permanently maintained.

The normal state of a forest, under a given set of conditions,
depends chiefly on the presence in it of —

(1,) A normal increment,

(2.)- A normal distribution of the age classes,

(3,) A normal growing stock.

By noniud increment is understood that, which is possible,
given a certain locality, species and rotation. An abnormal
increment may be caused by faulty formation, faulty treatment,
injurious external influences and also, for the time being, by
a preponderance of certain age classes.

By a iionnal distribution of (Hjc elnsscs is understood a

INTRODUCTORY. 173

series of age gradations so arranged, that at all times, when
cuttings are to be made, woods of the normal age are available
in such a position, that no obstacles to their cutting exist.

The normal growing stock is that, which is present in a forest,
in which the age gradations are normally arranged and show
the normal increment. It can, however, also be present (in
quantity) in an abnormal forest, if the deficiency of some
woods is made good by a surplus in others.

For the strictly annual working and the clear cutting system,
a forest is, therefore, normal, if it consists of a series of fully
stocked woods equal in number to the number of years in the
rotation and of the same extent, so that each year a wood of
the normal age can be cut, and that the returns are equal, at
any rate in quantity if not in value.

From a financial point of view, the further condition must
be added, that there should be no woods in the forest,
the current per cent, of which has sunk below the general
per cent, jj (see p. 165).

In accordance with these definitions, the following matters
demand special attention : —

(1.) The increment.

(2.) The rotation, or the norma! age at which woods should
be cut over.

(3.) The normal age classes.

(4.) The normal growing stock.

(5.) The normal yield.

(6.) The relations which exist between increment, growing
stock and yield.

(7.) The real forest compared with the normal forest.

174

CHAPTER I.

THE INCREMENT.

Every tree or wood may lay on three different kinds of

increment, namely : —

(1.) Quantity or volume increment.

(2.) Quality increment.) ,, ,, w, , • .

^ . . >Also called the value nicrement.

(3.) Price increment. )

Section I. — Volume Increment.

By volume increment is understood the increase in the
volume caused hy the growth of a tree or a wood. It is
measured by the solid cubic foot, or the stacked cubic foot.
The different kinds of volume increment and the modes of
measuring them, have been explained in Forest Mensuration.
For the purpose of working plans, it must be added, that
for short periods, say 5-10 years, the periodic mean annual
increment can be put equal to the current annual increment
without any appreciable error.

The calculations of increment may refer to the final yield
only, or to the intermediate yields, or to both together. In the
tables in Appendix III., the various classes of increment
have been calculated separately for final, intermediate and
both yields together.

1. Pror/fc'ss of Volume Increment.

a. Of Single Trees.

The volume increment is produced by an annual extension

of the crown and roots, and by the addition of a new layer

between wood and bark all over the stem, branches and roots.

As a general rule, the stem, or trunk, is the most important

VOLUME INCREMENT.

175

part of the tree ; hence, the forester is specially interested in
the height and diameter growth.

It has been explained in Volume II. of this Manual, third
edition, p. 54, that the energy of height growth differs not
only according to species, but also, in the case of one and the
same species, according to the age of the tree, the productive
power of the locality and the method of treatment ; besides,
there is in this respect a great difference between seedlings
and coppice shoots.

The subjoined table exhibits the height growth for some

Heighv

IN Feet.

1

Age,
\ ears.

Spruce.

Silver Fir.

Scotch Pine.

Beech.

10

8

3

12

6

20

20

9

29

IS

30

35

IS

44

31

40

51

30

55

45

50

65

45

65

56

60

76

59

73

67

70

85

71

80

76

80

93

82

8ii

85

90

99

91

91

92

100

104

98

95

9^

110

109

101

99

104

120

112

109

103

107

of the more important species of Europe, taking in each
case a locality of good productive power and assuming, that
the trees have grown up in fully stocked woods (see Fig. 40).
The height growth of oak is similar to that of beech. It is
somewhat quicker during the first few years; later on oak
holds its own against beech in some localities, and it is
passed by it in others.

Generally speaking, in the case of aeedlings, the height
growth during earliest youth is, in temperate climates, com-
paratively slow ; it then increases rapidly, remains steady for
a time, then decreases and ceases altogether, or nearly so.

The periods, when the current annual and mean annual
height increment show their maxima, are of special interest

176 THE INCREMENT.

to the forester, but the data at present available give wide

1 -JO

^

^-

y

y\

A

/<^

f

-

/

7y^

y. (-,(,

''J

u

'/

r

n

{/

/

- 40
30

■'A

/

y

Y/

A

//

/

U

■A

y

r

AGE, IN YEARS.

Pig, 40, — Diagram illustrating the Relative Height Growth of Spruce, Silver Fir,
Eeech aud Scotch Pine on Localities of the First Quality.

limits for those periods. The following table gives the average
ages at which the current annual and mean annual height
growth culminate : —

Spkcies.

Current Annual Hkioht
Increment.

Mean Annual Height
Increment.

Average Year ulien
JIaximum occurs.

Average Y'ear when
Maximum occurs.

Scotch Pine ....

Spruce

Beech .....
Silver Fir ....

25
35
38
50

40
50
50

m

On the whole, the culmination occurs earlier —

(1.) In the case of light-demanding species, and
(2.) In the better localities.

VOLUME INCREMENT.

177

The latter point will be illustrated by giving the followin*
data referring to Scotch pine : —

Ar.K.

Height in FtET.

I. or Best

II. or Middling

III. or Lowest

Quality.

Quality.

Quality.

10

12

6

4

20

29

17

;»

30

44

29

14

-10

55

38

21

50

()5

46

26

60

73

52

;:o

70

85

58

34

f-0

Si;

63

38

HO

'.»1

68

41

1(10

95

72

44

110

99

76

47

120

1U3

79

—

The first quality culminates in the year 20.
The second ,, ,, ,, .,25.

The third ., ,, „ .,35.

In the case of teak, the current annual height increment
generally reaches its maximum during the first five years of
the tree's life, frequently in the second or third year. Deodar
shows a height growth similar to that of spruce. Sal shows,
as far as is known at present, a remarkably even rate of
height growth up to an age of 80 or 100 years.

Coppice shoots show, generally, the greatest height growth
during the first few^ years of their existence ; the rate of
increment begins to fall ofi' early, nor do such shoots, rare
cases excepted, reach the same ultimate height as seedling
trees.

The lateral increment of the trunk of a tree, i.e., diameter
or sectional area increment, depends on the surface of the leaf
canopy and on its activity. Hence, free growing trees increase
more rapidly in diameter than those grown in dense or crowded
woods. At the same time, the position of the leaf surface is
of importance. Trees with a crown coming close to the ground

F.il. N

17S THE INCREMENT.

are comparatively more tapering, while those with the crown
restricted to the upper part of the stem show a more cylindrical
shape. The form or shape of the stem depends, therefore, on
the distribution of the crown. If, with advancing age, the
crown of trees in crowded woods moves higher up the stem,
the difference in diameter increment between the lower and
upper part of the stem decreases, and this is accompanied by
what may be called the "form increment"; in other words,
the tree becomes less tapering. The forester expresses this,
as explained at p. 36, by the " form factor," or the co-efficient,
by which the volume of a cylinder of the same base and height
as the tree must be multiplied, in order to obtain the volume
of the stem of the tree.

It has been stated, at p. 38, that in practice only the form
factors based on a measurement of the base at height of
chest, or 4J feet above the ground, are used, and at p. 39 the
form factors for the following trees were given : —

Scotch pine, according to Schwappach.
Spruce, ,, ,, ,,

Silver fir, ,, ,, Lorey.

Beech ,, ,, Schwappach.

Oak ,, ,, Wimuienauer.

These factors refer to trees grown in fairly crowded woods.

In the case of trees grown in coppice with standards, form
factors are out of the question.

b. Volume Increment of Whole Woods.

The increment of a wood consists, during the first period of
life, of the full increment of the individual trees. As soon as
the trees close overhead, the extension of the crowns is inter-
fered with, followed by a decrease in the diameter increment.
As long as the degree of crowdedness is not too great, the
height growth is not reduced ; on the contrary, a moderate
degree of density of the leaf canopy encourages height growth.
Although, during this period, the individual tree has less

VOLUME INCREMENT.

\1^

increment, than it would have in a free position, the increment
of a fairly crowded wood can have, and generally has, a larger
increment per unit of area than an open wood, because the
total increment is equal to the mean increment per tree
multiplied by the number of trees. What degree of density
of a wood gives the maximum increment is a question which
awaits solution. In the meantime it must not be forgotten,
that a fairly crowded condition encourages height growth,
decreases the tapering of the stems, and kills off the lower
branches, thus producing most valuable trunks.

Age.

Current Annual Incrkment.
Cubic Feet per Acre.

Mean Annual Increment.
Cubic Feet per Acre.

Spruce.

Silver
Fir.

Scotch
Pine.

Beech.

Spruce.

Silver
Fir.

Scotch
Pine.

Beech.

10
•2(1
30
•10
50
tiO
70
SO

'.)()

100
110
120

50
100
370

327
297
273
241
210
185
165
117
130

10
3i)
i)9

u;(>

2-15
292
301
407
399
340
255
210

40

115

180

186

178

154

126

112

97

83

76

66

15
40
126
191
228
196
192
188
176
165
154
143

51

173
212
229
236
237
234
228
222
215
208

16
59
86
117
147
178
206
228
239
240
238

22
48
137
149
155
155
151
146
140
135
129
124

7

IS

60

93

120

133

142

148

151

1.52

152

152

While the loss of material is very small in trees grown in
the open, it becomes considerable in the case of fully stocked
woods. Not only do all the lower branches die off, but the
greater number of the trees, of which the wood originally
consisted, must be removed by degrees, because they are
gradually overtopped, suppressed and finally killed ; these
form, ordinarily, the material of which the thinnings consist.

In fully stocked woods, especially in those treated as high
forest, a distinction must be made between the dominant and
suppressed trees ; the former may be called the major or
primary part of the growing stock and the latter the minor or
secondary part. Not only the latter, but also a consideraljle
portion of the former will be removed in the thinnings, in

n2

180

THE INCREMENT.

the same degree as, with the advancing age of the wood, they
lose their dominant character and join the secondary part of
the growing stock.. Exceptions to this may occur, which have
been explained in Volume II.

The progress of the increment in whole woods has by no

400

"-^

C\

/

\

f

\

/

\

'

V

V

\

/"*N

\

\

\

'"i

^^

-\

«!>-.

f 7

\

^

/'
il

If
//
//

* V,

■ '^.

/

AGK, IN YEARS.
Fig. 41. — Diagram sbowing the Current Aiiuual Iiurcnieut.

means been determined for all important species, though
much material bearing on this question has l)een collected
of late years on the continent of Europe. In India, matters
are still more backward.

The data on page 179 refer to European species, taken from
woods growing on land of good productive power. They give the
total pruductiun of timber and luewuud in full} stocked woods.

VOLUME INCREMENT.

181

These tables and illastratioiis justify the following con-
clusions:—

(1.) The current annual increment rises rapidly after tin;
first 3^outh is passed, and reaches its maximum, in the
case of many species, about the time, when the height
growth culminates ; it then falls, and reaches zero at
the death of the wood. In the case of other species, the
maximum is reached some time after the culmination
of the height growth, as in the case of silver fir.

7<

^

/

— — ^B

/ /*
//*

7

*^ ^*

y

/

>

V

100

120

0 -20 40 60 SO

AGE, IN YEARS.

Fiff. 42. — Diagram showino: the Mean Aumial lucreraeut.

(2.) The mean annual increment keeps below the current
annual increment, until the two become equal ; after
that period, the mean annual increment is greater than
the current annual increment.

(3.) The mean annual increment reaches its maximum at
the precise moment, when it is equal to the current
annual increment.

(4.) When the mean annual increment culminates, the
current annual increment must, naturally, already be

182

THE INCREMENT

l^ast its maximum, and be falling : hence the former
culminates later than the latter. During the inter-
mediate period between the two culminations, the
mean annual increment is still rising, whereas the
cm-rent annual increment is already falling.
These points are further illustrated by the adjoining

diagram (Fig. 43), giving the current annual and mean

annual increment for Scotch pine.

Mean

Annual

Increment.

Cuirent
Annual
Increment.

AGE, IX YEARS.
Fi?. 43.

(5.) Whenever the object of management consists in the
realisation of the greatest return of volume, the rota-
tion must coincide with the year, in which the mean
annual increment culminates.
The following example will illustrate this : —
The current annual increment of spruce in the above
example culminates at 30 years, the mean annual increment
at 70 years. In the course of 210 years there would be seven
rotations of 30 years, or three rotations of 70 years. The

VOLUME I^X•REMENT PER CENT. 183

former would yield in each rotation 17B x 30 = 5,190 cubic
feet, and in seven rotations = 5,190 X 7 = 36,830 cubic feet.
The latter would yield in one rotation 237 X 70 = 16,590
cubic feet, and in three rotations = 16,590 X 3 = 49,770 cubic
feet, or 13,440 cubic feet more.

The maximum for final yield only occurs earlier than that
for final phis intermediate yield ; the difference may amount
to 10 and even 20 years.

2. Volume Increment Per coit.

So far the increment has been expressed in actual volume.
In addition, it is useful to ascertain the proportion, which
exists between the total volume of a tree or wood at a certain
age and the increment laid on during the year before or
the following year. In order to express this proportion
independently of the actual volume, it is usual to give it in
per cents., and to call it the "increment per cent." ; by this
is, therefore, understood the current annual increment, which
is laid on by every 100 units of volume.

If a capital, C, yields annually the interest E, then the
per cent., 2^, with which the capital has worked, is found by
the equation —

R ^^
C 100

and

p = y^X 100

In the same way it may be said, if v ■= the volume of a tree
or wood, / = the increment added during one year's growth,
and />„ = the per cent., with which the capital v has worked,
then the following equation holds good : —

and

r 100'

p, = 1 X 100

V

184 THE INCREMENT.

or, if i = V — V,

V — V
2\,=- -X 100.

V

The matter can be considered from a different point of
view, as follows : —

Pv _ i _ r — /•
100 ~7 J^'

or

and

'Op. = - - 1,

1-Oi). = -

V=:v X 1-Op,.

This means, that the volume at the end of one year, T^, may
be considered as having been produced by r working for one
year with j;„ per cent.

The increment per cent, is used, sometimes to calculate
from the present volume the increment, which is likelj' to
be laid on in the immediate future, but chiefly for the purpose
of testing the activity of the capital invested in forestry.

The increment per cent. 2\ i^ naturally very large during
the early youth of a tree or wood ; but as the volume increases
year by year, that is to say, the denominator in the above
equation, while the annual increment does not increase in
anything like the same proportion, and in fact begins to
decrease comparatively early, it follows, that the increment
per cent, becomes smaller year by year. Heavy thinnings
can temporarily produce an exception to the above rule, as
they may retard the sinking of the increment per cent, by
diminishing the producing capital.

As the determination of the increment of a single year is a
difficult and inaccurate operation, it is usual to determine
it for a number of years, 5, 10, or, generally, n years, and
to consider T' as the volume produced by placing r for n years
at compound interest, working with 2\ per cent. : —

V = vX {1-OpJ".

VOLUME INCREMENT PER CENT. 185

From tliis —

i-o,„y=':

/ V

and

and

or

and

p, = 100 (,^X - 1 ) , = 100 X y/- - lOQ,

100 + ih = 100 X :/r

\os V — log?-

log(100+7O = 2 +

It

In order to avoid the use of logarithms, several formulae
have been evolved, which give approximately accurate results.
Pressler obtained such a formula by assuming, that the
increment during the n years is laid on in annually equal
quantities, and b}^ comparing the increment with the volume,
which is present in the middle of the period of n years. He
thus obtains the proportion —

Capital : annual increment = 100 : 2)„

^'t-'^: 11^' -100 :iK

and

V - V 200

This formula gives j^z, somewhat too small; but the difference
is so slight, that it can be neglected for all practical purposes.
Example : —

Let r in the year 70 = 3,820 cubic feet ;
„ V in the year 80 = 4,260

186 THE INCREMENT.

then —

K. = 100 (v/^' - 1 ) = l^f' C\/t^!l - l) = l-01J6percent.

^' r+r // 4,2()0 + 8,820 10 ^

If any thinnings have been made during the » years, their
amount must be added to V, before the increment per cent,
is calculated. Supposing that in the above case 327 cubic feet
were cut between the years 60 and 70, then —

,,,= 100(;/t260_t827_,)^,.,„,,^„^„,^

or

4,260 + 327 - 3,820 ^ 200 . ^^^ ,

p, = ' — ^ X = l,82o i)er cent.

^ 4,260 + 327 + 3,820 10 ^

+ 327 +

It remains to add, that the formula for the increment
per cent, can be applied to height, diameter, or basal area
increment, as well as to volume increment.

The results of investigations made on the Continent have
led to the preparation of yield tables for a number of species,
an abstract of which will be found in Appendix III. An
examination of these tables will confirm the conclusions so
far drawn. The tables for oak refer only to the lowlands of
Germany ; the returns of oak on hilly ground are somewhat
lower than those given in the tables.

Section II. — Quality Increment.

By quality increment is understood the increase in the
value per unit of volume. It is produced, in the first place,
by larger pieces of timber frequently fetching higher prices
per unit of measurement, and secondly by a reduction of
the cost of harvesting per unit of measurement. Quality
increment is independent of any alteration in the general
price of forest produce.

QUALITY INCREMENT. 187

If, in the course of n years, the net vahie of the unit of
voUime rises from q to Q, then the quahty increment is
— Q — q^ and the corresponding per cent, is obtained by the
formula —

(J = q X l-Oj>,;' ;
and

or

logdOO +,>„) = 2 + '^^^^^'^

An approximately correct value for 2^q is obtained by the
formula —

The quality increment may be rising, falling, or its move-
ments may be more or less irregular ; hence, they must be
ascertained in each case.

Woods grown for firewood only show little or no quality
increment after middle age ; except, perhaps, in so far as the
percentage of stem- to branch wood increases. The latest
investigations seem to indicate even, that wood taken from
middle-aged trees has a higher heating power than wood taken
from older trees, although the latter may be perfectly sound.

Matters are different in the case of timber forests; here
the quality increment rises, in the majority of cases, to an
advanced age, because :

(1.) Trees of large dimensions are, on the whole, more
valuable per unit of volume than those of small dimen-
sions, though exceptions to this rule occur frequently.

(2.) The percentage of timber to firewood increases, at any
rate up to a certain age.

The quality increment per cent, sinks, on the whole, with
advancing age, though more or less irregularly; it can become
nil and even negative, if the timber commences to decay, while
the volume increment is still above zero.

1S8 THE INCREMENT.

Example. — A Scotch pine wood GO years old contains —

Timber = 3,300 culnc feet, worth 4(/. per cubic foot.
Firewoods 760 ,, ,, „ Id. „

Hence, mean quahty —

3,300 X 4 + 760 X 1 o. -,
q = ^ = 3 44 pence.

The same wood in the year 70 has —

Timber = 3,820 cubic feet, worth 5(1. a cubic foot.
Firewood =710 ,, ,, ,, Id.

Hence-

And

,. 3,820 X 5 + 710 X 1 ..o^

(J= -J^ =4-3. pence.

4-37 = 3-44 X l-O^^/"

loy(100 + 7V _ , ^^^

And

.) I log 4-37 — log 3 jl4
])^ = 2*42 per cent.

Approximate value —

4-37 - 3-44 ,, 200 ^ qq ,

What has been said above can also be applied to the inter-
mediate returns. Indeed, the quality increment of that part of
a wood, which yields the thinnings, can be very considerable,
especially while the wood is still young. Here, a few years'
extra growth may cause a great rise in the quality per unit of
measurement. On the other hand, if thinnings are kept over
too long, they interfere with the proper development of the
major part of the wood; hemje, extremes iu tliis respect must
be avoided.

PRICE INCREMENT. 189

Section III. — Price Increment.

By price increment is understood the increment caused by a
change in the price of forest produce generally, independent
of the accompanying quality increment. It can be positive,
nil, or negative.

Exanqjle. — A hitherto inaccessible forest ig brought into
communication with a large town by the construction of a rail-
way ; the increase in the prices of the produce of the forest
represents the price increment, which in this case is positive.

()r, owing to an increased import of forest produce, the
price of the home production falls generally ; this represents
a negative price increment.

The price increment depends partly on the forester and partly
on external causes, over which he has little or no control. Of
the former class of causes are, for instance, the construction
of good roads, development of industries, which consume forest
produce, improvement in the general management leading to
a higher net value per unit of measurement.

It is out of the question to construct a law showing the
changes in price. In some cases such changes afi'ect all
classes of produce, in others only certain kinds. Under any
circumstances, it is almost impossible to foresee them, except
in special definite cases. At the same time, the price increment
is of considerable importance, as it affects the financial ripe-
ness of woods and in this way influences the lines, upon which
the management of the forest should proceed.

The price increment is calculated in the same way as the
quality increment. If s represents the value of the unit of
measurement at the present time, and S the corresponding
value after n years, the price increment is = 6' — s, and

s = -s- X i-op:

Vs = 100

(^/^^).

iogaoo+,,, = -2 + '°«^':'°^".

190 THE INCRF,:\rp:NT.

Again, the approximate value —

S — s 200

Section IV. — Addition of the several Increment
Per Cents, leading to the Forest Per Cent.

Instead of calculating with the volume-, quality-, and price-
increments separately, it is more convenient to combine
them. The combined increment per cent, is determined in
the following manner : —

A forest, which has at present a value = ;r, increases during
the next year —

In volume by p^ per cent.
,, quality ,, p.^ ,, ,,
., price „ p, .,

Its value at the end of one year may be expressed by the
formula —

W= (V X VOp, X 1-Op.^ X 1-0^/,.

For convenience sake —

l-Op„ X l-O^^, X 1-Op, is placed = l-Q^v,

where p/ represents the combined effect of p„ p,„ and p. ; hence

JV=ir X l-O^v-

This formula could be used to determine the financial
activity of a wood at any time, if it were possible to determine
accurately the value increment of the wood for a single year.
This, however, is a very uncertain operation ; hence the
difference in the value of the crop produced during a series
of years must be ascertained, a difference due to the combined
effect of volume-, quality-, and price increment during, say,
II years.

THE FOREST PER CENT. 191

In that case,

the

vakie of the forest after n years is-
]V=ic X i-Op;.

Out of this,

and

™'p,-100(.\/^J-l).

This formula was introduced by Pressler, who called the
""'Pf thus obtained the imlkatiiui per cent. (Weiserprocent.).

The indicating per cent, (or current forest per cent.)
indicates the per cent., with which the capital, represented by
a wood, works at the various periods of the wood's life ; in
other words, it indicates at any time, whether a wood is
financially ripe or not. As long as the indicating per cent, is
larger than the general per cent, p, at which money can be
invested otherwise with equal security, or at which money
can be obtained for investment in forestry, the wood is
financially not ripe; when the indicating per cent, has become
smaller than p, the financial ripeness of the wood is past ;
the wood is financially ripe at the time, when the indicating
per cent, is equal to p.

It remains to substitute the proper values for ic and 11 •
The capital value w of the forest at the present time m is
represented by the value of the growing stock and soil,
correctly = "'6f, + *^'- As the formula is, as a rule, only used
in the case of woods, which are at or near maturity, the
utilisation value may be substituted for the cost value of the
growing stock, so that

ic = i;^ + ,s'.

192 THE INCREMENT.

This is the capital, which it is jiroposed to let work for
another n years. During that period, it increases to the value
of the forest in the year //) + ii, from which amount must he
deducted the annual costs during ;/ years with compound
interest, so that —

W= r,„^„ + S-E a-Op" - 1)
and

100

("\/^

Y^+S

— 1

If, between the years m and m + », a thinning has been
made, say in the year x, its value, with compound interest
to the year m + «, must be added to TF, so that the formula
becomes : —

cur ^loof A/Yn,+n + T.XrOp"+"-" + S-E(10p"-l)_^Y

In either case, the value S of the soil can be taken as the
cost value or as the expectation value.

If n is placed = 1, the above formula reduces to —

C-0-. ,. _ (r,„+i - r,„ - (') X 100

^' y::-rs '

agreeing with that given at page 165 for the current annual
forest per cent.

Example. — Taking the data in the table at page 120, and
putting j; = 2i per cent., S = 404 shillings, c = 3 shillings,
the following values of pj are obtained : —

For the period 70 — 80 years : —

log (100+;v) =

.^ I log (2.860 + 144 + 404 — 84) — log (1,H87 + 404)
"^ 10

^o-^"^),. = 2-G8.

* This i'oi'iimla ditfeis lioui that given by Presslur and Jiideich for the reasons
indicated in the footnote at jiage 159.

THE FOEEST PER CENT. l9^

For the period 80 — 90 years : —

log (100 + p,) =

.^ , log (3,558 + 149 + 404 - 34) - log (2,860 + ^0-^)
"'' 10

««->_^=2-25.

The current annual forest per cents, given in the table at
page 197 have been calculated in this way, and they show,
that the financial ripeness occurred during the period 70 to
90, or, more precisely, in the year 79.

194

CHAPTER 11.

THE ROTATION.

By rotation is understood that period of years, which elapses
between the formation of a w'ood and the time, when it is
finally cut over and regenerated.

The end of this period, that is to say, the age of the wood
when cut over, is called the " final age." If it coincides with
that, which is considered the one best suited to the system of
management, it is called the normal final age ; if a wood has,
for one reason or another, to be cut over at a difl'erent age,
the latter is called an abnormal final age.

The determination of the rotation is one of the most
important measures in forest management. At the same time,
the rotation depends entirely on the various objects of manage-
ment; hence, it difters with every change of conditions. In
economic forestry the following deserve to be distinguished : —

(1.) The financial rotation.

(2.) The rotation of the highest income.

(3.) The rotation of the greatest volume production.

(4.) The technical rotation.

(5.) The physical rotation.

Any one of these may be indicated by the objects of
management, and it is necessary to explain them in some
detail.

1. TJie Financial Rotation.

a. ('((In/h/fion of flic Finaneiat Unlation.

By the financial rotation is understood that, under which
a forest yields, if calculated with a given per cent, and

THE FINANCIAL ROTATION. 195

compound interest, the highest net return. The financial
rotation is, therefore, identical with that which —

(a.) Gives the maximum soil rental as expressed by the
formula —

Soil rental = SeX'Op

^ y,. + i\ X 1-Op'-" + . . . +z;x VOi/-' - c X l-Oj/ _ ,
l-Oj;'- - 1 ''

'Op
(See page 149.)

{b.) Or yields the highest profit : —

P = S^—Sc, respectively = F^—F,.

(See pages 153 and 155.)

(c.) Or yields the maximum mean annual forest per cent. : —

S /<'

"'"'"j9^. =: _5 X p, respectively = ^r X P-

(See pages 161 and 162.)

Of these, the first formula is the most convenient, and the
procedure is as follows : — In the forest (for which the finaiicial
rotation shall be determined), a number of typical woods are
examined and as many data as possible collected. These can
be augmented by data taken from suitable yield tables, if such
are available. Then the soil rental is calculated for various
rotations, and that, for which the rental becomes a maximum,
is the financial rotation.

In order to explain the method, the appended table has been
calculated from the money yield table for the Scotch pine
given at page 120. In calculating that table, it has been
assumed, that the cost of formation comes to 60 shillings, the
annually recurring costs to 3 shillings, and that the general
per cent, p = 2^ per cent. It has also been assumed, that the
thinnings during the several periods of ten years have been
made at the end of each period ; for instance, the thinnings

o 2

196

THE ROTATION.

l.VANCIAl. Yll^iLl) TABI.E FOK

IJiitii ill L'oliuim h iiud c taken

a

h c

. 1 .

Length of

Rotation.

Years.

Net Value of Yields, in
Shillings.

«um <.f Inler-

niediatu Yields

with Comi.ound

Interest to Date.

ShilliuKs

i> '' ■-"■''•

Total Yield to

Date {h + d).

Shillings.

Fimil.

[ntennediatc.

3U

11).-.

.-.

:.

200

40

.-/.lo

44

.-.0

t;4o

.-)()

1»<S.")

S7

ir.2

1.137

(iU

i..^(;;{

118

■M-i

1.87.-.

7..

2.1cS7

134

5h:5

2,720

,su

2..SH0

144

827

3.li87

IHJ

8.5.-.8

141)

1,207

4.7(;.-j

1(10

4,27H

1 (•..■.

1.710

.-.,983

110

5,017

I(i7

2.:5.-.(;

7,373

120

:,.V.

13.-.

:5.oi.-)

8,807

during the period of 40 — 50 are assumed to have been made
in the year 50.

This table shows that the linaneial rotation fahs between
the years 70 and 90. In order to ascertain the exact year, the
rentals given in cohimn h of the table have been plotted (see
Fig. 44). It will be seen, that the financial rotation falls
into the year 79, when the rental reaches its maximum.

In column / the current annual forest per cent, is given,
calculated according to the formula on page 192. These data
show, that the forest- or indicating per cent, passes from
above 2i per cent, to below "Ih per cent, between the years 75
and 85. By plotting the per cents, (see Fig. 45), it is found,
that the exact time falls into the year 79, that is to say, the
year, when the annual soil rental culminates. Hence the
wood was financially ripe in the year 79.

THE FINANCIAL ROTATION.

197

One Acre of Scotch Pixe Wood.
from the Table at page 120.

./■

!/

/,

i

k

/

Cost of Forma-

Soil.

Soil

Current

tion=60s.,\\'itli

Total Yield less

Value of

Gross Rental

Net Rental

Forest- or

Compound

cost of Forma-

l-025'--l

q

i - Annual

Indicating

Interest to

tion (e-/).

•025 ■

k

Shillings.

Expenses.
Shillings.

Per cent.

Date.
Shillings.

Shillings.

during ever>
10 years.

126

74

43-904

1-69

-1-31

5-30

161

479

67-404

7-11

+ 4-11 1

3-89

206

931

97-484

9-55

6-55 j

3-97

264

1,611

135-992

11-85

8-85 j
9-32 f

3-19

338

2,382

18.5-284

12-32

2-68

433

3,254

248-383

13-10

10-10 ]

2-25

->-A

4,211

329-1.54

12-79

9-79 ]

1-95

709

5.274

4.32-549

12-19

9-19 1

1-73

907

(•.,466

564-902

11-45

8-45

1-51

1,161

7.646

734-326

10-41

7-41 '

h. Noh^ on ilio F'mancUtl PiOiafioiK

Owing to the uncertainty of the data, upon which the calcu-
lation is hased, the financial rotation can only he determined
approximately ; moreover, it changes with every change of
conditions. Under these circumstances, it can only serve as a
general guide.

Of the several items, which appear in the formula for the
soil rental, the rate of interest is the most important. A low
rate gives a high financial rotation, and vice versa. x\n altera-
tion of 1 per cent, in the general per cent, p may cause the
financial rotation to rise or fall hy 10 to '20 years.

As has l)een explained on a previous occasion, the general
per cent, applicable to forest finance may, for Britain, at
present be placed at 2| per cent.

198

THE ROTATION.

Of the receipts, the final yield is hy far the most important
item. Its present value can easily be ascertained, but fore-
casts for the future are of a risky nature. If, in the future,
the proportion between thejprices of the different classes of
produce remains about the same, then a change in the financial
rotation does not necessarily follow ; but great changes can be
produced in the reverse case ; that is to say, if for instance
tnuber of small dimensions rises in price, while that of large

10
9

8

_,^-7

-^^

/

^

"1

\

s_

/

/

N^

V

/

\

/

r

/

/

1

'

1

W 100 110 120

AGE, IN YEARS.
Fio;. 44.

dimensions falls, or rice rcrsd. Such changes are difficult to
foresee. The experience of the last decades seemed to show
that timber of large dimensions is not unlikely to rise in price.
During the last few years, however, middle-sized timber has,
comparatively, risen in price ; still, on the whole, the selected
rotation should l)e rather above than below the financial
rotation.

The intermediate returns exercise a considerable intluence
upon the actual amount of the rental, but a comparatively

THE FINANCIAL ROTATION.

199

small effect upon its culminating point ; in other words, early
thinnings reduce the financial rotation only to a limited
extent, and if they are made so heavy, that they reduce the
value of the final return, they may have even the opposite effect.
Of the costs, th6 annual expenses do not affect the financial
rotation, unless they alter in amount with the rotation. The
cost of formation affects the rental to a considerable extent,
but its effect upon the financial rotation is small.

AGE, IN YEARS.
Fig. 4.5.

Taking all effects together, it may be said, that the financial
rotation is low —

(1.) in the case of localities, where only firewood is saleable,
that is to say, where an increase in quality per unit of
volume ceases at a comparatively early age ; in other
words, the financial rotation would approximately
coincide with that of the greatest volume production ;

(2.) if trees of small dimensions can be sold as timber,
for instance in mining districts, in hop-growing
countries, etc.

The financial rotation is JnijJi —

(] .) in localities with an unfavourable soil or climate, such
as high exposed situations, where the trees take a longer
time to reach marketable dimensions ;

200 THE ROTATION.

(2.) in thinly populated districts, where prices ojenerally
rule low for small dimensions, while large timl)er can
be exported to other better paying markets.

r. Correriion of ilic calnilaicd VhuDirlal Bniaiion.

The length of tlie financial rotation, as obtained by a first
calculation, is subject to correction, because it is based upon
certain rates obtainable for the various classes of produce,
whereas a change in the actual rotation may alter those rates.
If, for instance, the calculated financial rotation is lower than
that actually existing and the former is introduced, more
small and less large timber will be produced ; also the pro-
portion between timber and firewood will be altered. This
may produce a fall in the average price of produce. The
reverse effect would be produced, if tbe calculated financial
rotation were higher than the one actually existing. In either
case it must be taken into consideration, that a change in the
rotation is accompanied by a change in the growing stock,
and that either more or less material is l)rought into the
market, at any rate for a number of years.

It follows, that the first calculation is generally subject to
some correction in accordance with the alteration of prices,
which may be produced by a change in the rotation.

(i. T))h'odiiftion of ilie Financial Jlotalion.
Although every deviation from the financial rotation is
accompanied by a financial loss, yet it is very desirable, that,
if it has been decided to introduce that rotation, tbis should be
done with great caution, because, in the first place, it can only
be determined approximately, and, secondly, its introduction is
accompanied by a change in the existing growing stock. If a
true, or assumed, surplus of growing stock has been disposed
of, it would take much time to re-establish it, should further
experience indicate a higher rotation than that originally
calculated. Hence, it is desirable to keep always somewhat
above the theoretical financial rotation.

ROTATION OF THE HIGHEST INCOME. 201

If a change of rotation has been decided on, it can be carried
out at once, provided the forest is of small extent and the
demand for produce sufificientl_y large to absorl) the extra
supply of produce thrown upon the market, without causing
any appreciable change in prices. If the forest is, however,
of some extent and the demand for produce uncertain, it is
always desirable to make the change gradually, so as either
to spread the extra supply of produce over a number of years,
or to accumulate the extra growing stock gradually, thus
disturbing the market as little as possible.

2. Rotation of the Highest Income.

By this is understood the rotation, which yields the highest
income, calculated without interest and irrespective of the
time, when the items of income occur. The net income is
thus calculated according to the arithmetical mean of incomes
diminished by the costs. All items of income and costs during
one rotation are added up and the sum of the latter deducted
from the former ; the difference, divided by the num])er of
years in the rotation, represents the mean annual income.

Hence, the rotation in this sense is that, under which the
expression —

Annual income = y,- + T„ + T„ + . . + T,, - r - y x e

r
becomes a maximum.

This rotation falls, as a rule, a considerable number of years
beyond the financial rotation.

Example. — Taking the data contained in the table at page
120, the net annual income amounts to —

For a rotation of

Shi/Ji,)'

2,187 + 5 + 44+87 + 118 + 184-00-

70 years = '^^^ = 38

70

2,860 + 5 + 44+87 + 118+184 + 144-

80 years z. ^^'^^X^ =39

80

202 THE ROTATION.

RhilJings.

3,558+5 + 44+87+118+13-4+144+

on 149-60-90x3 .o

90 years = ^ = 43

4,273 + 5 + 44+87 + 118+134+144+

,^^ 149+165-60-100x3 .«

100 years = ' — — = 48

5,017 + 5+44+87 + 118+134+144+

,,^ 149+165+167-60-110x3 -.,

110 years = -^ ^Jo ^

5,792+5+44+87 + 118+134 + 144 +

,^^ 149+165+167+135-60-120x3 _ ^.
120 years = ^ -^ ^ — - 54

6,591 + 5+44+87 + 118 + 134 + 144 +

149+165 + 167 + 135 + 133-60-

lon 130x3 K7

130 years = ^^ = 57

7,410+5+44+87 + 118+134 + 144 +

149 + 165+167+135 + 133+135-

-, ,^ 60-140x3 ^n

140 years = -— = 60

It will be observed, that the annual income still rises under
a rotation of 120 years, and will continue to do so, until the
volume- and quality increment become so much reduced, that
they will cause a reduction in the average income. At the
same time, a rotation of 120 years would involve a financial
loss, because interest on the invested capital has been alto-
gether omitted. This can easily be seen by a reference to
cohnnn /,• of the financial yield table at page 196. The net
soil rental under a rotation of 120 years comes to 7'41 shillings,
and under one of 80 years to 10*10 shillings. This is due to
the fact, that the income under a rotation of 120 years repre-
sents the interest on a much larger capital invested in the
forest, than is the case under a rotation of 80 years.

THE TECHNICAL ROTATION. 203

3. Rotafiou of the Greatest Production of Volume.

This is the rotation, under which a forest yields the greatest
quantity of material per unit of area ; it coincides with the
year, in which the mean annual volume increment culminates.

Let volume of final yield = F,.
Volume of thinning in the year a = r„

„ " b = n

etc.,

then the rotation of the greatest production is that, in which

the value -''"'"'"' ^'' "^ ' ' ' ^^ hecomes a maximum.
r

The calculation can be made for timber and firewood, or for
timber only.

Example. — Taking, for instance, the data for total yield in
the table for Scotch pine medium quality, at page 364, for
timber only, the rotation of the greatest production would fall
al)out into the year 80, which is approximately the financial
rotation. For timber and firewood, the rotation would fall
into the year 60, which is considerably below the financial
rotation ; in this case a financial loss would be incurred.

4. The Techmeal Rotation.

By this is understood the rotation, under which a forest
yields the most suitable material for a certain fixed purpose ;
for instance, for construction generally, shipbuilding, railway
sleepers, telegrapli or hop poles, mining props, tanning bark,
fuel, etc.

As the objects of management and the purposes, for which
the material is required, differ very much, the technical rota-
tion may fall into any age, either before, after, or into the age
of the financial rotation. The loss occasioned by following it
depends on the difterence between the technical and financial
rotations.

204 THE ROTATION.

5. The PJii/Hical Hotatio)!.

By the physical rotation is generally understood that age,
which is most favourable for the natural regeneration of a
species, taking into consideration the conditions of the locality
and the sylvicultural system. It cannot be lower, in the case
of high forest, than the age, when the trees have commenced
to bear good seed in sufficient quantity, nor as high as the age,
when the production of good seed has ceased ; the best period
being that about the end of the principal height growth.

In the case of coppice woods, the age must be ))elow that, at,
which the trees cease to produce good healthy shoots, when
cut over.

Sometimes a second physical rotation is mentioned as that,
which coincides with the natural lease of life of the trees. It
is only of interest in the case of protection forests, parks, etc.

6. Choice of Botafion.

The choice of rotation, or the age at which a wood is to
be cut over, is, as already stated, one of the most important
questions in forest management. Many and varied are the
arguments, which have been advanced in favour of the one or
other rotation.

One party maintains, that the financial aspect should decide
the choice of rotation, since forests represent capital, which
should yield the highest possible interest. Another party
brings the general usefulness more into the foreground and
maintains, that other considerations are more important to the
general community than purely financial results, especially
in the case of State forests.

In the author's view, the "objects of management" should
determine the rotation. These frequently demand deviations
from the financial rotation. For instance, to begin wath an
extreme case, for protection forests generally a very high
rotation is indicated ; where a nation considers it necessary
to produce timber fit for naval construction, a rotation, which
lies far beyond the financial rotation, is called for ; where

CHOICE OF ROTATION. 205

hop-poles are wanted, a very low rotation would be advisable; in
cases where land is scarce, and yet a certain quantity of wood
is wanted for existing industries, the rotation of the highest
production of produce is indicated ; if a proprietor wishes
to invest capital, so as to obtain the highest annual income,
irrespective of the rate of interest, he would choose the rotation
under which that income culminates, etc.

There may be good reasons in all these cases for adopting
the one or other rotation. At the same time, the proprietor
should know, what financial sacrifice he brings for the realisa-
tion of his special object. Hence, the general procedure in
fixing the rotation may be described as follows : —

In the first place the financial rotation should be determined,
as it alone gives a true expression of the economic value of
the management ; then it should be ascertained, in how far the
objects of management demand a departure from the financial
rotation ; lastly, the financial loss involved in such a departure
should be determined, so that the proprietor may have a clear
conception of the payment, which he is called upon to make in
order to realise his special object.

It need hardly be pointed out, that the above procedure
suits all possible cases, which may come under consideration.
It should, however, never be overlooked, that very short rota-
tions may injuriously affect the future returns of the locality,
owing to the frequent exposure of the soil to deteriorating
atmospheric influences. Hence, purely financial considera-
tions, in the case of all but really fertile localities, should be
adopted only after a full inquiry into the effects likely to be
produced on the future yield capacity of the locality.

206

CHAPTEE III.

THE NORMAL AGE CLASSES.

When, under the system of working for a sustained annual
yield, the rotation has been fixed, it is necessary, that, year
after year, or period after period, the required mature woods
are forthcoming, so that the calculated annual yield may be
obtained. This involves the establishment of a normal series
of age gradation. By that term is, therefore, understood a
series of age gradations so arranged, that at all times, when
cuttings are to be made, mature woods of the normal age are
available and so situated, that no obstacles to their cutting
exist. This means, that each age class must be of the proper
extent, and that the several age classes must be properly
grouped, or distributed, over the forest.

If a forest is to be managed according to the system of a
sustained annual yield and the clear cutting system, it must
contain a series of age gradations equal to the number of years
in the rotation ; the oldest age gradation must, immediately
before cutting, have the age of the rotation, the youngest nuist
be one year old, with a dilierence of one year in the age of
every succeeding two gradations.

Example. — Assuming the rotation of a coppice wood to
be 20 years, and the height which the oldest wood reaches
in that time = 28 feet, then the 20 age gradations may be
represented as in the appended figure, 46.

If the annual returns are to be equal in volume and the
quality of the locality is the same throughout, then all age
gradations must be of the same extent ; if different qualities
occur, the areas of the coupes must be in inverse proportion
to the quality of the locality. A series of age gradations so
arranged is called a normal working section. This subject

THE ANNUAL COUPE.

207

will again be dealt with further on. For the present it is
assumed, that the quality of locality is the same throughout.

Frequently, a number of age gradations are thrown together
into an age class. The following questions thus arise : —
(1.) What is the area to be cut annually under the different

methods of treatment ?
(2.) What is the size, or extent, of the age classes ? and
(3.) How should the age classes be distributed over the
forest ?

••

r

Ifl

j2-

5
-it

»

i

AGE, IX YEARS.
Fisr. 46.

1. The Annual Coupe, or the Area to he eut Annually.

This differs according to the method of treatment. (For a
description of the latter, see page 89 of Volume II. third
edition.)

a. Coppice and Coppice with Standards.

The annual coupe is determined by dividing the total area
of the forest, or working section, by the number of years in
the rotation, under which the coppice is worked.

208 THE NORMAL AGE CLASSES.

Let total area = .1 ,
Rotation of the coppice = r,

then tile annual cutting area c = -~. This holds good for the

coppice with standards system, because the annual cutting
area is governed by the coppice only.

//. ('/ear Ciiffi/i// in. Hhjli Forest.

Here is again :

. ^ A
r '

if each clearing is at once re-stocked. It frequently happens,
however, that the cleared coupes lie fallow for one or more,
say s, years ; in that case :

A
r + s'

so that the forest consists, immediately before cutting, of a
series of age gradations from 1 to r years old and s blanks, or
altogether r + s coupes.

r. 2Vie >%elter-wood Co)npartmenf tiyslem.

Under this system, the regeneration of each coupe extends
over a number of years, say /// ; hence, it is necessary lo throw
//( annual coupes together into a regeneration coupe, the crop
on which, by gradual cuttings, is led over, in the course of
m years, into a young wood. The size of the regeneration

coupe is, therefore, = - X ^/;.

In this case the first of the successive cuttings towards
regeneration may be made —

Either in the year r, so that the trees removed at the end
of the regeneration period would be /• + m years old, and the

mean age r +— -' years ; in other words, the procedure would
lead to a raising of the rotation from r to ' H--^^- years ;

SIZE OF THE AGE CLASSES. 209

Or, the first cutting may be made in the year r — ~ and

A

the last in the year /• + - , so that the mean final age comes
'A

to r years.

In the present chapter the latter is assumed.

d. The Selection Sysiem.

Strictly speaking, the annual coupe is equal to the total
area of the forest. For convenience sake, however, the cuttings
of each year are restricted to a portion of the area, so that it
takes a number of years to go round the forest, and before
cuttings are again made on the same area. If that number
is /, then —

Annual cutting area = y.

Example. — In the beech forests of Buckinghamshire, which
are worked under the selection system, it is usual to go round
once in seven years ; in that case the annual cutting area

A

would be equal to — . In other cases, as in the Indian sal

and teak forests, / is longer, generally from 15 to 40 years.

2. Size of the Age Classes.
In forests of some extent, which are worked under a high
rotation, and especially those regenerated naturally, it is, as a
rule, impracticable to separate the annual cutting areas, so
that a regular series of age gradations, differing by one year
in age throughout, exists. In these cases, it is necessary to be
satisfied with larger groups, that is to say, to join a number
of age gradations into an "age class." The normal size of
such an age class depends on the area of the annual coupe
and the number of such coupes thrown together. If a class
contains n gradations, its area would be = n X c. The number

of age classes = — is variable.
u

210 THE NORMAL AGE CLASSES.

Another waj^ is to fix the number of age classes : in that
case n is variable, but this procedure is not to be recommended,
as it is likely to lead to confusion.

It is usual to take for » a round number, say 10, 20, or
even 30; in coppice woods, n is usually taken as = 5. The age
classes are numbered. It is best to call the youngest I., the
next youngest 11. , and so on ; for instance, if n = 20 —

First age class I., contains all \¥Oods up to 20 years old.
Second ,, II., ,, „ from 21 to 40 years old.

Third „ III., „ „ „ 41 to 60

And so on.

In this way the number of the age class indicates directly
the limit of ages of the woods contained in it. The reverse
method, of calling the oldest age class I., the next oldest II.,
etc., is less desirable, but unfortunately it has been largely
adopted.

The number of years included in an age class is called a
" period," and the area dealt with in the course of a period is
called a "periodic coupe" (French: "Affectation").

The area of the age classes under the several methods of
treatment will be as follows : —

a. Char ChiUinij w Hifih Forest.
The area of each age class, C, in a normal state, is —

C = n X c = )i X ~, or C = n x

r + s

according as to whether each clearing is at once re-stocked, or

allowed to lie fallow for .s years.

Example : —

Let area A =1,000 acres.

Rotation r = 100 years.

s = 0 „

11 = 20 „
Then,

Annual age gradation = ^ = -'— - =10 acres;

SIZE OF THE AGE CLASSES. 21 1

and the age-classes :

Blanks : none.

C'l ( 1— 20 years oM woods) =rXii = 10x'20= 200 acres.
C2 (21— 40 „ „)=„=„= 200 „

C'3 (41— 60 „ „)=„=„= 200 „

C4 (61— 80 „ „)=„=„= 200 „

C's (81—100 „ „)=,,= „= 200 „

^=1,000 acres.

//. Shellpr-ii'ooil Compartment Si/stfm.

As already explained, under this system the old crop is
gradually led over into a young wood in the course of a
number of years, which has been indicated by m. There is
always an area under regeneration, which contains a certain
number of old trees and young growth, and this may be called
the regeneration class = C\,; it wanders gradually through the
whole forest, until, at the beginning of the second rotation, it
is found in the original position. As regeneration in some cases
takes only a few, and in others more, years, it is impossible
to define its duration accurately, and least of all can m be
placed equal to n, the number of years in the period. Under
these circumstances, the arrangement of age classes can
be indicated only approximately, somewhat in the following
manner : —

Cuttings in the oldest age class commence, when the crop

is r — — years old, and the last cuttings occur, when the crop

is ?■ + ^ years old ; then the annual cutting area, as before,

= — , and the area of the regeneration class =— x w. If
r r

m<^)i, then the regeneration class contains areas as vet

blank, young trees from 1 to m yeai-s old, and the remaining

old trees up to r + - years old. It forms part of the

n

p2

212 THE NORMAL AGE CT,ASSES.

3^oungest age class, C'l. IS'ow, it may happen, that /// = ii ; in
that case the youngest age class does not exist hy itself ; but
is identical with C,. Again, it may occur, that m > n, in which
case Cv contains not only the youngest age class, but also
a portion, if not the whole, of the second age class. Hence,
the size of the several age classes may be expressed as follows,
assuming five age classes: —

(1.) m<in.

C. = "^ X ni
r

Ci = - {n - m)
r

Ca = - X n
r

Cg = - X n
r

C\ = - X //
r

C'5 = ^XH

r
Example : —

,;( = 15 ; a = 20 ; r = 100 ; A = 1,000 acres.

Then

C'„ =10X15= 150 acres.

Ci = 10 X 5 = 50 „

02=10x20= 200 „

Cg = 10 X 20 = 200 „

C4 = 10 X 20 = 200 „

C'5 = 10 X 20 = 200 „

Total = 1,000 acres.
(2.) VI = n.

Example : — m = n = 20.

C = — X m = 200 acres.
?•

Ci = - (n-m) =0 „
r

SIZE OF THE AGE CLASSES. 213

Ca = - X n
r

= 200 acres.

Cs = ^ X »

= 200 „

Ci = -X u

= 200 „

6'5 = ^ X »

Total

= 200 „

= 1,000 acres.

(3.) m>

u, but ;/( < 2 X ».

Example

; — in -

= 30.

C\ = - X in

V

= 300 acres.

C'l =

= 0 „

C2 = - (2 XH-

m) = 100 „

C'3 = -Xn
r

= 200 „

C\ = y X //

= 200 „

= 200 „

And so on.

Toi

tal = 1,000 acres.

It is obvious, that, for tlie shelter-wood sj'stem with natural
regeneration, the above allotment is only of an ideal character,
because the duration of regeneration is so uncertain. The
regeneration class, the oldest and youngest classes are subject
to modifications amongst themselves, so that they cannot
easily be separated the one from the other ; hence, they are
best thrown together. The important point in that case is,
that the middle-aged classes are of the proper size. The
allotment may then be represented as follows : —

Example : —

('.,= ' X II = 200 acres.

~14 THK NORMAL AGP] CLASSES.

Cs=^X n

= 200 acres.

( '4 = y X II

= 200 „

r

} X

")

= -100 ,,

r5 + r„ + (

r

Total = 1,000 acres.
Or again, if regeiiei-atioii extends over a still longer period :—

C-s=-^X II = 200 acres.

;•

C4=— X II = 200 „

r

C5 + C. + Ti + C2 =^{r - 2 X //) = 600 „

Total = 1,000 acres.

c. Coppice Woods.

As the rotation of coppice woods is short, it is usually

possible to mark the annual coupes on the ground, so that

grouping in age classes is not necessary. If the latter should,

nevertheless, be considered desirable, generally not more than

live gradations are thrown together, so that t'l comprises the

1- to 5-years-old gradations, (.'2 those from 6 to 10 years, etc.

Example : —

Area = 200 acres.

r = 20 years.

II = 5 ,,

The arrangement of age classes would be normal, if —

C'i=-^X 5 = 50 acres.

C.=^X^= 50 „

Total = 200 acres.

SIZE OF THE AGE CLASSES. 215

d. Coppice with Standards.

Here each coupe contains coppice (underwood) and standards
(overwood). As far as the underwood is concerned, the
arrangement is exactly the same as in the case of simple

coppice ; the annual age gradation is = — , and the age class,
if any, = ^ X n.

The distribution of the overwood, in its normal condition,
is somewhat peculiar, which may usefully be explained here,
though it is only of a theoretical value.

In the first place, it should be remembered, that cuttings, in
both the under- and overwood on the same area must be made
at the same time, or rather those in the overwood must be
made immediately after the underwood has been cut over, and
before the new coppice shoots appear ; hence, the rotation R of
the overwood must be a multiple of the rotation r of the under-
wood, say R = r X t.

In each annual coupe, when cutting comes round to it, a
certain portion of the underwood (chiefly seedling trees), is
left standing, to form the youngest age gradation of the over-
wood. That portion should occupy an area = ^, assuming,

that each age gradation of the overwood occupies the same
extent of ground. The area occupied by each age class of

overwood comes to = y, X r = —.
1\ t

Assuming now, that the youngest overwood class, 1 to /• years
old, though still forming part of the underwood, is already
counted as belonging to the overwood, then there are t over-
wood classes. The latter are not separated according to area,
as in the case of clear cutting or coppice, but t gradations are
standing mixed on each annual coupe, so that each of the

latter contains -th part of each overwood class.

21(

THE NORMAL AGE CLASSES.

Immediately before cutting, the arrangement would be as
follows : —

Uiuierwoofl, Age in Years.

1 2

3

3

r + 3
2r + 3

(^-l))- + 3

r-1

r

Overwood Age Class Ci age

;; :; :; S :;

Cr...

1
r + 1
•2 r + 1

(t-l)r + l

r-1

2 r-1

3 r-1

txr-l

r
2xr
3 xr

t X r

It will be seen, that a normal coppice with standards forest
must have an overwood, which consists of f X r = H age
gradations ranging from 1 year up to li years old.

Example. — A forest of 200 acres, worked under a rotation of
20 years for the underwood, and 100 years for the overwood,

has -— - = 5 overwood classes. On the 10 acres which are

zo

about to be cut, will be found —

Underwood = 20 years old

Overwood = 20, 40, 60, 80 and 100 years old.

The next oldest coupe contains —
Underwood := 19 years old
Overwood = 19, 89, 59, 79 and 99 years old.

The youngest coupe contains —
Underwood = 1 year old
Overwood = 1, 21, 41, 61 and 81 3'ears old.

The appended figure, 47, illustrates the distribution of the
several age gradations over the area.

The area occupied by each overwood class can be determined
only by assuming, that each gradation occupies an equal
extent of ground ; hence, the youngest gradation will have most
trees and the oldest least. Imagining now, that the age classes
of the overwood were not intermixed, but that the trees of each

SIZE OF THE AGE CLASSES.

217

class were brought together on sejiarate areas, then the over-
wood, apart from the coppice, would form an open hij^h forest.
Of these woods the youngest would contain the standards from
1 to r years, the next those from r + 1 to 2 r years, and so on.

-i^

Fig. 47.

By degrees, the youngest class passes through all tlie inter-
mediate stages, until it l)ecomes the oldest and is cut over in
the course of r years. At each annual cutting, therefore, an
equal area must be cut over, on which the new, that is the
youngest, gradation is started, either naturally or artificially.

218

THE NORMAL AGE CLASSES.

The annual coupe is c = — and yl = c x r.

The number of overwood classes is = — = f, hence-

t X r

Area of each age class on each annual couije = * =:^ — =-,
^ Ii tXr t

200 ^ -200
100 5 X 20

15
5

2 acres.

As the whole forest consists of r coupes, each overwood
class, consisting of /• gradations, contains, in a normal forest,

- X /• = — units of area, or *^^ = 40 acres. This shows,
t t 5

that, theoretically, the proportion of the age classes is the

same as in high forest, although the distribution is different.

Example. — Data as before.

A = 200 ; R = 100 ; /• = 20, number of overwood classes
t = 5.

Normal annual cutting area r = —

200
20
10

10 acres.

= z acres.

On each coupe each age gradation I

of overwood occupies . . ) ^ ^

The area and distribution of the several age classes is as
follows : —

Cotiix' Xo. 20, oldest :

Underwood = 10 acres = 20 years ol
Overwood on 2 ,, =20 ,, ,

2 „ = -iO „ ,

•2 „ = 60 „ ,

2 ,, z= 80 „

2 ,, = lOU „

Coupe Xo. 1, i/oiiiKjest :

Underwood = 10 acres = 1 year old.

Overwood on 2 ,, = 1 ,, ,,

,, ,, '2 ,, = 21 years ,,

SIZE OF THE AGE CLASSES. 219

Overwood on '2 acres = 41 years old.

'■i „ = 81 „ „

The normal state of the age classes in the case of coppice
with standards is of a still more ideal character, than in the
case of the shelter- wood compartment system ; it can only
serve as a mathematical guide for the treatment of such woods,
as it gives some idea of the relative number of trees, which
should be found in each class or gradation. Each of these
should occupy about the same area ; hence, the youngest class
must contain a large number of trees, which is gradually
reduced to a comparatively small number in the oldest age
class. The actual proportion in these numbers depends on
the species and the quality of the locality.

('. T/w /^eleriio/i Fares/.
If the annual cuttings extend over the whole area, then all
age classes are, theoretically speaking, represented in all parts
of the forest; if, on the other hand, the cuttings pass over the
forest in the course of a number of years, say /, then the age
classes will gradually become located similar to the distribution
of the overwood in a coppice with standards forest. The

number of age classes will, theoretically, be equal to -^.

Let A = 1,000 acres ; r — 100 ; Z — 20 ; then each annual

cutting area = y = ' = 50 acres, and the distribution

would approximately be as follows : —

Coupe No. 1 {yomujest). Coupe No. 2.

1 year old trees = 10 acres 2 year old trees == 10 acres
•21 „ „ „ = 10 „ 22 „ ,. ,, = 10 „

^1 M M „ = 10 „ ' 42 „ ,, ,, = 10 „

61 „ „ „ = 10 ,. ! 62 „ „ ,, == 10 „
«1 „ „ ,- = 10 „ 82 „ ,, ,, = 10 „

Total = 50 acres Total = 50 acres

■ZiO

THP] NORMAL A(4E CLASSES.

Coupe No. 19.
19 years old trees = 10 acres
39 ,, ,, ,, = 10 ..
59 „ „ ,, = 10 „
79 ,, „ „ = 10 „
99 „ „ „ = 10 ,.

Total = 50 acres

Coupe No. 20 {oldest).
20 yeai"s old trees = 10 acres
10 ., „ ,, =10 „
BO ,, „ „ = 10 „
HO „ ,, „ = 10 „
100 „ „ „ = 10 „

Total = 50 acres

Each year the 100 years old trees in the oldest coupe
would be cut, which should cover an area equal to one-fifth
of the coupe, equal to 10 acres, thus cuttin^:; once the whole
area of the forest in 100 years. It is needless to add,
that such regularity is never reached in practical forest
management.

3. Distribution of the Age Classes over the Forest.

By a normal distribution of the age classes is understood
that, which admits of a proper succession of cuttings, so that
each wood is cut at the proper age, and that the other woods
are protected against external dangers, in so far as this can be
done by careful management.

It has already been explained, that every deviation from the
normal age interferes with the full realisation of the objects of
management ; hence, the age classes should be so distributed,
that no such deviations are called for. Of special importance,
in this respect, are threatening dangers, such a's damage
by strong winds, dry air currents, danger from frost, fire,
insects, etc., and sometimes considerations for a successful
regeneration.

StroiKj u'iii(h or (/ales are a most important consideration.
Their prevailing direction must be ascertained, and cuttings
must proceed against it. Assuming, that the strong winds
generally blow from the west, the youngest age class should,
at the commencement, be situated at that side and the oldest

DISTKIBUTION OVER THE FOREKT.

221

oil the east, so that the cuttings proceed graduahy from east to
west. (See diagram. Fig. 48). In this case, the younger age

y/y//yy/////////////

,-^

'

— <■ \\\N\\\\\\\\\\\\\\\\

CUTTING DIRECTION.

rl

■'?

c.

~

. -J

A~

'"L

C■^

--

--i

X

['■_

Oi

--

--1

I
fTt

i.

»

1

a. 1 a-

a.

%

I

«. 1 e

-

■=-

t.a.

.lis

J-

;;

,*

^

Fig. 48.

classes break the force of the wind gradually, while the youngest
(in'the diagram) will gradually grow up exposed to the strong
wind ; its edge trees will develop strong root systems, and the
wood will then be able to resist the force of the wind, whenj]it
grows up to represent the oldest age gradation.

In determining the prevailing wind direction, it must not
be overlooked, that it is frequently changed in hilly and
mountainous tracts according to the direction of the valleys
and hill ranges.

Dry winds may frequently blow from a direction differing
from that of strong winds; in that case, the forester must
decide, which is the more important consideration of the two
and determine the'cutting direction accordingly. Frequently
the seeds of trees fall under the effect of a dry wdnd, so that

222 THE NORMAL AOK CI,ASSES.

the cleared areas, which are to l)e naturally regenerated, must
1)6 situated to the leeward of the seed-hearing trees, as, for
instance, under the strip system with regeneration by seed
fallen from trees standing on the adjoining area.

Large cJearingH in one place are generally objectionable,
because the soil is liable to dry up, and damage by frost is
more likely to occur : hence, in extensive forests the area to be
cut annually may have to be divided into a number of small
coupes situated in different parts of the forest.

Inserts and fire are likely to be most injurious, when several
cuttings made in consecutive years adjoin each other, because
the former wander from one coupe to the next, while fire
spreads more rapidly in young woods, than if they are
interrupted by older woods.

These circumstances demand in many cases, and especially
where clear cutting is practised in coniferous woods, that a
second cutting should not be made in any locality, until the
first coupe has been successfully re-stocked. This leads to the
splitting up of a working section, or a series of age gradations,
into several sub-divisions, which are called cutting series.
Supposing, in a forest worked under a rotation of 20 years, it
was considered necessary, not to cut in the locality adjoining
a previous cutting except after a lapse of 4 years, the series
of age gradations would be divided into four cutting series, of
which each would comprise five coupes. (See Fig. 49.)

Cutting

Series

A would comprise the coupes now 20, 1(), 12, 8, 4 years old.
B „ „ „ „ ., 19, 15, 11, 7, 3 ,, „

C „ „ ,, ,, ,, 18, 14, 10, 6, 2 „ „

D „ ,. ,. ., ., 17, 13, 9, 5, 1 „ „

As a general rule, a careful distribution of the age classes
over the area of the forest is of special importance in the case
of species, which are easily thrown by wind, liable to attacks
by insects, to danger from fire or frost, and also those Avhich

DISTRIBUTION OVER THE FOREST.

228

Eli

t fi 10.1^8

n

J

CUTTING DIRECTION.
Fiff. 49.

are difficult to regenerate naturally. In all these cases, a
distribution must be aimed at, which allows the cutting of each
wood when mature, without thereby endangering, on the one
hand, the adjoining woods, and, on the other, the successful
regeneration of the cleared area.

The above considerations must specially guide the forester
in the case of forests worked under the systems of clear-
cutting and also of the shelter-wood compartment system.
They are of less importance in coppice, coppice with standards
and selection forests ; but even here the cutting direction
should be carefully determined.

At the same time, the forester should not go to extremes, as
there is something to be said on both sides.

Eeasons for adjoining the annual coupes are : —

(1.) Best security against damage by storms.

(2.) Reduction to a minimum of damage by overhanging
trees.

(3.) Production of a larger percentage of high class of
timber.

(4.) Reduction of the cost of transport of forest produce.

•Z-H THE NORMA!. A(tK CLASSES.

Keasons against adjoining the annual coupes are : —

(1.) Increase of danger througli tire and insects.

(2.) Eeduced protection of young growth against raw or dry

winds.
The suhject will again he referred to in Part IV., when
dealing with the division and allotment of areas.

225

CHAPTER IV.

THE NORMAL GROWING STOCK.

It has been stated at page 173, that by the normal growing
stock is understood that present in a forest, which has a normal
proportion of age classes and a normal increment. This being
so, the forester need only see, that the age classes and incre-
ment are normal, and the normal growing stock will be present
as a natural consequence.

It happens, however, that, as far as quantity is concerned,
the normal growing stock may be present, if neither the
normal age classes or increment have been established ; for
instance, if the deficit in one age class is made good by a
surplus in another. If, in such a case, an annually equal
quantity of wood were cut, it would lead to a deviation from
the normal final age and consequently to loss. Indeed, the
normal growing stock, according to quantity, might be present,
if the whole forest consisted of only one uniform age class of
about half the normal final age. In that case, no ripe w^ood at
all would be found in the forest, and cuttings would have to
be suspended for a considerable number of years.

Under these circumstances, the normal growing stock by
itself is of subordinate importance in determining the yield of
a forest, and yet it is useful to look at its determination for
the following two reasons : —

(1.) Because the yield, taken out of a forest in the course of
a rotation, consists partly of the growing stock, which was
present at the beginning of the rotation, and partly of in-
crement added to that growing stock during the rotation.
(2.) Because several methods base the calculation of the
yield upon the difference between the normal and real
growing stock.

F.M. Q

226 THE NORMAL GROWING STOCK.

The amount of the normal growing stock depends on the
length of the rotation ; the higher the latter, the greater the
former for one and the same area.

In calculating the normal growing stock, only the principal
part of the woods, which gives the final yield, is taken into
account, because, as previously explained, the determination
of a sustained yield is, in the first place, based upon the final
yield only.

The normal growing stock can be looked at from the
volumetric or the financial point of view.

1. Calculation of the Normal Growing Stock as regards
its Vohinie.

a. Clear Cutting in High Forest.

It has already been explained on page 141, that, under the
system of clear cutting, the normal growing stock consists of a
series of age gradations ranging from 0 years old to ?' — 1 years
old, with a difference of one year between the ages of every
two succeeding age gradations ; this occurs in a temperate
climate, in spring, before the annual increment has been
laid on.

(1.) Calculation from Yield Tables. — If a yield table is
available for a forest, which gives the produce standing in it
from year to year, the normal growing stock is equal to the
sum of all the growing stocks given in that table from the
year 0 to the year r — 1 ; that sum would represent the normal
growing stock of r units of area for spring.

If the yield table, and this is generally the case, gives the
volumes only from period to period, say for every n years, then
the approximate amount of the normal growing stock can be
calculated (according to Pressler) by assuming, that the
volumes rise within each period of n years according to an
aritlnnetical series, that is to say, by adding the same number
of cubic feet each year.

CLEAR CUTTING IN HIGH FOREST. 227

Beginning with the calculation for autumn,

let be volume in the year 0 =0 cubic feet,
» = a „ „
^ X n = h „ „
S X )i = c „
■i X II = d „ „

then —

Total volume from year 0 to year n minus a=: (0+^0 X -^ a

n „ 2 X » minus h={a-\-b) X '^i^ — b

*A

„ 2 X n „ dXn minus c = {b-{-c) X '^- — c

„ 3XH „ 4XH ={c-\-d)x'^.

2

Total volume from 0 to 4 X » years =

'l±i (O + 2 a + 2 /. + 2 c + d) - (^a + b + c)

Normal Gr. Stock, &„ = n Ta + b + c + -") + -.

This is the calculation for autamn.

If the oldest age gradation is cut away during winter, the
normal growing stock in spring must be d cul)ic feet less than
that in autumn, that is to say : —

!■„ in Spring =.n(^-\-\)-\-c-{- j —

In spring the growing stock consists onh' of a series of
gradations running from 0 to (r— 1) years old. In the course
of the summer (the growing season), the series is brought up
again to one running from 1 to r years old. If, therefore,
the calculation is made for the middle of summer, it may be
assumed, that one-half of the annual increment has been laid

q2

228 THE NORMAL GROWING STOCK.

on ; in other words, that the growing stock is then equal to
the arithmetical mean of those in spring and autumn : —

Summer's middle Gn = nfa-fb + e4- -)•

Exanqile. — A forest of 100 acres, to which the data given in
the Table at page 120 apply, worked under a rotation of 100
3'ears, has the following normal growing stock : —

In autumn ^'^'G„,,„„,= 10 (100 + 600 + 1,170 + 2,830 + 3,940

+ 4,690 + 5,250 + 5,720 + 6,100 +

3,205) + 3,205

= 10x33,605+3,205 = 339,225 cubic feet.

In spring ^'''G,„,,„„^ = 10 X 33,605 - 3,205 = 332,845 cubic feet.

In summer i""G,„„,„,„, = 10 X 33,605 =336,050 cubic feet.

The same forest, if worked under a rotation of 80 years,
would have, for summer, the following growing stock : —

8"G„ = 10 (100 + 600 + 1,170 + 2,830 + 3,940 + 4,690 +

5,250 + 2,860) ^ = 10 X 21,440 X "^-^ = 268,000 cubic feet,
80 80

which is considerably less, than if the area is worked under a

rotation of 100 years.

(2.) Calridatio)! icitit tlic Mean A)iniial Incrciiiciif. — A shorter,
but less accurate, method of calculating the normal growing
stock is based upon the assumption, that the normal final
yield is produced in annually equal instalments ; in other
words, that the growing stock of the several age gradations
form an arithmetical series. Indicating one year's increment
by /, the growing stock in successive age gradations would be
in tlie

Year =1.2, ;5 . . /—]./•.

Growing- Stock = /. 2 X /, 3 X / . . (r — l) i, r i.

and their sum 0„ = (/ + r i) = + r i X — .

As r X i represents the growing stock of the oldest age
gradation and is also equal to the total increment, I, laid

SHELTER-WOOD COMPARTMENT SYSTEM.

229

on by all age gradation during one year, the above formula
may be written thus : —

This is the growing calculated for autumn. For spring it is

G

IX

~^, and for the middle of summer (r„ =

IX r

The growing stock calculated according to this formula is
larger than that calculated from yield tables for short, and
smaller for high rotations. The subjoined table shows
this.

Normal Growing Stock, for the Middle of Summer.

Leugth of

1

Rotation.

Calculated from a
Yield Table.
Cubic feet.

Calculated from the Excess of Calculation

Years.

Mean Aimual ftom Mean Annual
Increment. , Increment.

Cubic feet. Cubic feet.

30

12,850

1 7,550

+ 4,700

40

32,850 .-.(i,r,00

+ 23,7.50

50

<)6.700 98,50U

+ 31,800

60

109,850 140.700 j + 30,8.50

70

159,5.50 183.750 + 24,200

80

214,400 228,800 i + 14,400

90

273,500 274,500 ! + 1,000

100

336,050 320,500 - 15,550

110

401,550 367,950

- 33,600

120

469,750 1 417,000

- 52,750

h. Sheltcr-trood Coiii/iaiimenf Sijstem.

The normal growing stock is the same as for the clear
cutting system, provided the regeneration cuttings are so
arranged, that one-half are made before the year r, and the
other half after it. Strictly speaking, this is only correct, if
the timber in the regeneration class is removed in annually
equal quantities, and if regeneration takes place in the middle
of the period. In reality, this does only rarely occur, but the
deviations compensate each other in the long run ; anyhow a
more accurate determination is practically impossible.

230 THE NORMAL GROWING STOCK.

c. Cojvpice and Coppice wWt Standards.

The calculation for simple coppice is the same as in the
case of clear cutting in high forest.

For coppice with standards forest the calculation must be
made separately for under- and overwood, and the results
added together. The former is of small account, as the
presence of the overwood reduces the quantity of the under-
wood considerably.

The calculation of the normal growing stock of overwood
is a complicated and uncertain operation and at the best only
of theoretical value. It must be based upon the number of
trees and the average volume per tree in each age class,
somewhat in the following manner : —

If the normal number of trees in each of the /•, 2 r, 3 r . . .
old age gradation is known, and also the volume of the average
tree in each of these gradations, then it can be assumed, that
the trees increase in volume, within each class, according to
an arithmetical series ; this makes it possible to interpolate
the volume of the trees r -{- 1, 2 r -{- 1 . , . years old. In
that case, the normal growing stock of the first age class would
be expressed by —

K'- « + '■"•■>

where T',+, represents the volume of all trees r -f- 1 years old,
and V.>r that of all trees 2 r years old. In the same way the
next age class would be represented by —

|(.w. + n

and so on. Adding all positions together, the normal groAving
stock of overwood comes to —

G„ = '- (iWi + r„. + y-^.n + Vr.r + • • • + r,„_,,.+i + F„-).

This amount does not comprise the youngest age class of
all, which still forms part of the underwood.

SELECTION FOREST.

231

Example : —

Area of a coppice with standards forests = 100 acres.
Eotation of underwood = 20 years.
,, „ overwood = 100 ,,

Number of overwood classes = -— — = 5.
Area of each coupe = 5 acres.

Age of Gradation.

Number of Trees
in Gradation.

Mean Volume
per Tree.
Cubic feet.

Total Volume of
Gradation.
Cubic feet.

21
40
41
60
(31
80
81
100

200
200
130
130

80
80
40
40

•2
20
2-65

15-

15-7.5

30-

31-

50-

40-
400-
344-5
1950-
12U0-
2-100-
1240-
2000-

^(40+400+344-5 + 1,950+1,260+2,400+1,240+2,000

G,= 10x9,634-5=96,345 cubic feet, or per acre = 963 cubic
feet. In practice, such calculations are rarely made, but they
give a clear idea of the proportion, which ought to exist between
the several age classes.

d. The Selection Fcyrest.
The growing stock of a normal selection forest may be
placed equal to that of a forest under the clear cutting system,
as all the age gradations are represented in a similar way,
though differently arranged over the area ; hence, it can be
ascertained by summing up the quantities given in a yield table.
At the same time, the calculation is likely to be less accurate,
since the younger age gradations stand under the shade of the
older trees, and it is difficult to say, in how far the loss of
increment of the former is covered by an increased increment
of the latter.

232 THE NORMAL GROWING STOCK.

2. Calculation of the Financial Value of the Normal
Growing Stock.

The various methods of calculating the jfinancial value of the
normal growing stock have been explained at pages 141 to 143.
It has there been stated, that the same results are obtained,
whether the value is calculated as the cost value, expectation
value, or the capitalised rental of the growing stock, provided
the expectation value of the soil is introduced into the account.
In each of these cases the value is expressed, for r units of
area worked under a rotation of r years, by the formula: —

rx _ Y. + T, + ■ ■ ■ + T, - (c + r X e)

^n :^ rxb,,

in words, the normal growing stock is equal to the capitalised
annual net rental minus the expectation value of the soil. To
make that growing stock truly normal, it is necessary, that the
per cent., which the capital yields, should be exactly equal to
the general per cent. ^;. Every deviation from this leads to
loss. As it is impossible to keep a forest always in that con-
dition, it follows, that the financial normal growing stock has
only a theoretical value, which assists in the comprehension of
the working of the capital invested in forestry, but is of little
importance in determining the yield of forests.

233

CHAPTER V.

THE NORMAL YIELD.

By the normal yield is understood that, ^Yhich a normal
forest can permanently give. The yield may be annual, or
intermittent. Instead of determining the yield for each year,
or certain intermittent years, it can be ascertained for a num-
ber of years, in which case it is called the periodic yield.

The yield is composed of the final and intermediate returns.
The regulation of the yield deals principally with the former,
for reasons, which have been explained at page 171.

The yield of major produce is further sub-divided according
to the different classes of wood, such as timber, cord-wood,
fagots, root-wood, etc. In order to bring them into the account,
all the different classes of produce are reduced to one common
standard, that is " the solid cubic foot."

The yield can be determined by area and volume, or by its
financial value.

1. lite Yield determined hy Area or Volume.

a. Clear Cutiing in High Forest.

(1.) The Normal Final Yield is equal to the volume which

stands on the oldest age gradation.

4 A

The normal cutting area is c = — or = — , — , according as to
® r r -\- s

whether the cleared area is at once re-stocked or allowed to lie

fallow for s years (see page 208). The volume standing on c

must be equal to the volume of the oldest age gradation in a

normal series of age gradations, if it is to give the normal

yield.

The periodic normal coupe is = ^ X u, or = — -, — X n.

r r + s

234 THE NORMAL YIELD.

Example : —

Area of forest . = 1 ,000 acres
Flotation . . = 100 years

Annual cutting area = ' = 10 acres,

if the area is at once re-stocked.

The annual yield of final returns, according to the table at
page 120, amounts to 6,410 + 397 per acre = 6,807 cubic feet ;
for ten acres = 6,807 X 10 = 68,070 solid cubic feet. (Final
yield during every period of 20 years = 68,070 X 20 = 1,361,400
cubic feet.)

(2.) Intermediate Yields. — These consist of all the thinnings
which are made. Taking the same table, the following thin-
nings would be made in each year : —

In the coupe 30 years old = 10 acres, each giving 57c' = 570

40 „

„ = 10 „

„ 353c' = 3,530

50 „

„ = 10 „

„ 524c' = 5,240

60 „

„ = 10 „

„ 565c' = 5,650

70 ,,

, „ = 10 „

„ 536c' ==5,360

80 „

, „ = 10 „

„ 493c' = 4,930

90 „

„ = 10 „

„ 446c' = 4,460
Total = 29,740

(3.) Total Xormal Annual Yield = 68,070+29,740=97,810
cubic feet. The total normal annual yield must be equal to the
total annual increment. To cut less than that amount, leads
to a higher rotation, and rice rersd.

h. iS/ie/fer-u-ood Compartment System.

The calculation of the yield is the same as under the system
of clear cutting, as long as the rotation r is maintained. If

regeneration is commenced later than in the year r — -, the

rotation is increased, and the calculation must be made
accordingly. Supposing the lirst cutting is made in the year

DETERMINED BY AREA AND VOLUME. 235

/•, and the last in the year r + m, then the rotation = r -\-

and the mean annual cutting area =

, m

2'
A

Example : —

Let m = 20; then rotation = 110 years. Annual cutting

1,000

9"09 acres. Volume standing on an acre at

110

the age of 110 years = 6,690 + 334 = 7,024; hence annual
yield = 7,024 X 9*09 = 63,848 culnc feet.

The intermediate yields would amount to = 35,010 cubic feet,
and : —

Total annual yield = 97,558.

The raising of the rotation has led to a reduction of the
volume yield, because the mean annual increment began to
decrease before the year 100.

c. Scledion Forest.

If all trees, which are cut in one year, \Yere brought together

on a portion of the area, the latter should be = ^ : hence the

yield is practically the same as in the case of clear cutting.

Another way of looking at the matter is to determine the
area, on ^Yhich cuttings are made in each year ; this has been

placed above (page 219), = -. • Everything, which has to be

cut on this area, forms the normal annual yield.

Example : —

Area of a selection forest = 1,000 acres
Flotation . . . = 100 years
I . . = 20 years.
Then :

A 1,000 Kn
- = .^ = 50 acres.
20

236 THE NORMAL YIELD.

On these 50 acres, the following material is cut : —

(1.) All trees which have reached the age of 100 years.

(2.) A certain proportion of trees in the younger age classes,
so as to reduce their number gradually to that, which should
reach maturity at the age of 100 years.

These cuttings should give, theoretically speaking, the same
yield, as if the area were treated under the clear-cutting
system.

(1. ( 'oiipiri' and Coppire ivith Slanihtrds.

The normal yield of coppice woods is calculated in the same
way as for clear cutting in high forest. In this case, the

annual cutting area is = - and the volumetric yield is com-
posed of the material standing on that area, plus thinnings in
the younger age gradations.

In coppice with standards, the annual cutting area is
the same as in simple coppice. The normal annual yield
consists of : —

(1.) The underwood on the oldest age gradation, less those
trees which are left to grow into standards.

(2.) The contents of the oldest, B years old, age gradation of
the over wood.

(3.) The thinnings amongst the younger age gradations of
overwood standing on the annual coupe and occasionally hi
the younger underwood gradations.

Example : —

Taking the data given at page 231, the yield in overwood is
as follows : —

40 trees (mature) 100 years old, each = 50 c' = 2,000

40 „ 80 ,, ,, ,, = 80 c' = 1,200

50 „ 60 „ „ ,, - 15 c' = 750

70 „ 40 „ „ „ = 2 c' = 140

Total = 4,090 c',
to which the volume of the underwood has to be added.

THE FINANCIAL VALINE OF THE YIELD. 237

The normal annual yield of overwood must also be equal to
the annual increment laid on by all the overwood during one
year, or

7= 2-0 X 200+ (15 - 2) X 130+ (30 - 15) X 80+ (50 - 30) X 40,
7 = 4,090 cubic feet.

As ah'eady indicated, this calculation is only of theoretical
value.

2. The Financial Value of the Xormal Yield.

The financial value of the normal yield is that, which secures
interest on all capital invested in a forest exactly at the rate of
the general per cent, j), at which money can be obtained for
forestry, or at which money taken out of the forest can be in-
vested with equal security as in forestry. The financial yield
is realised, as long as a financial equilibrium on the above lines
exists in the forest, that is to say, when the forest per cent, is
equal to the general per cent. p. This occurs under a rotation
equal to that, for which the expectation value of the soil reaches
its maximum.

Example : —

Taking the data in the table at page 120, and a rotation of
80 years —

Soil expectation value for 80 units of area = shlgs.

80 X 404 = 32,320

Financial value of normal "rowing stock . = 91,360

Total = 123,680

Financial Normal Y = 123,680 X "025 = 3,092 shillings;
or 38*65 shillings for each acre of forest.

288

CHAPTEPi YI.

RELATIONS BETWEEN INCREMENT, GROWING
STOCK AND YIELD.

Between the increment, growing stock and yield of a normal
forest relations exist, which are of great importance in deter-
mining the yield. In order to hring them out clearly, the
system of clear cutting in high forest will be used as an illus-
tration.

1. Allotment of Increment during a Ilotation.

Every normal series of age gradations contains, afc the com-
mencement of the rotation, the normal growing stock. Every
year the oldest age gradation is cut over, which gives the normal
final annual yield, and this is replaced during the following
growing season by the laying on of the normal increment.
The latter is added, partly to the old growing stock and re-
moved with it during the first rotation ; but partly it accumu-
lates on the cleared areas, forming a new growing stock, which
is carried over into the second rotation. The question then is,
how the total increment of one rotation is divided between
the two.

Making the calculation for spring, the youngest age gradation
is 0 years old, and the oldest r — 1 years. The former grows
for ;• growing seasons, and is cut over during the last winter of
the first rotation, so that all its increment is removed during
the first rotation ; hence, all goes to the old growing stock and
nothing to the new stock. The gradation now one year old
grows for y— 1 years during the first rotation, when it is cut
over. All the increment laid on during these years goes to the
old growing stock ; but that laid on during the last year is not
cut, but goes over to the second rotation. The gradation, now

THE UTILISATION PER CENT. 239

two years old, grows for r — 2 years during the first rotation,
and the increment laid on during these years goes to the old
growing stock ; but the increment of the last 2 years of the
first rotation is carried over to the second rotation, and so on.
If the calculation is carried through on these lines, the following
division of the total increment laid on during each rotation will
be obtained : —

At the commencement of the first rotation the normal grow-
ing stock is assumed to be present ; it amounts, for an area of
100 acres and a rotation of 100 years, to 332,845 cubic feet (see
page 228). The total increment laid on during one rotation
amounts to 978,100 cubic feet (see page 234). x\s the normal
growing stock must again be present at the end of the first
rotation, it follows, that the total increment during each rota-
tion is divided as follows : —

Cut away with the old growing stock = 645,255 c'
Carried over into the second rotation = 332,845 c'

Total increment = 978,100 c'

2. Relation heticeen Noi-mal Yield and Xornial
Growing Stock.

If the normal yield (!',) is divided by the normal growing
stock {G,) and the quotient multiplied by 100, the result is
called the " utilisation per cent."

Utilisation per cent. = --/' X 100.

G,i

It gives the units of yield for every 100 units of growing
stock, just as the increment per cent, gives the units of incre-
ment for every 100 units of growing stock. As the increment
of a whole series of age gradations is equal to the yield of the
same, it follows that —

Utilisation per cent. = increment per cent, of the whole
series of age gradations.

The utilisation per cent, must fall with the increase of the
rotation, just as the increment per cent, has been shown to fall.

240

CHAPTER YII.

THE REAL rOREST COMPARED WITH THE
NORMAL FOREST.

Having drawn a picture of the normal, or ideal, forest, it
remains to compare it with what is found in realit}-. A forest,
which is in every respect in a normal condition, does not exist,
especially in the case of extensive areas treated under high
rotations; and if a forest should ever get into that state, greater
or smaller deviations are sure to occur again. The great
value of the normal forest consists in its serving as a standard,
towards which the forester must endeavour to lead the forest
under his management. How this is done, is laid down in
forest working plans.

Forests, which are worked for quantity or quality of produce
only, may be abnormal in respect of —
(1.) The increment.

(2.) The size and distribution of the age classes.
(3.) The growing stock.

From a financial point has to be added : —
(4.) There may be woods, which work with a forest per cent.

smaller than the general per cent. jj.
Either one, several, or all these conditions may be in an
abnormal state.

In determining the method, by which the abnormal condi-
tions are to be removed, it must be specially noted, that the
increment alone renders the growing stock an active capital ;
it replaces year by year that quantity of the growing stock,
which has been removed by fellings. Hence, it must be the
forester's first care, to bring the increment up to its normal
amount. This is accomplished by regulating the cuttings
in a suitable manner, followed by efficient regeneration and

REAL AND NORMAL FORESTS COMPARED. 24l

tending of the growing woods. More especially as regards the
regulation of cuttings, care must be taken that all woods,
which have a poor increment, are utilised at an early date
and replaced by vigorous young woods. Next, a proper
proportion and distribution of age classes must be aimed at,
so that each wood can be cut over when ripe, without endanger-
ing thereby other adjoining woods. Only in this way is it
possible to avoid loss of increment in the future, due to the
premature cutting of vigorous woods, or to the belated cutting
of incompletely stocked or diseased woods.

The establishment of a normal proportion amongst the
several age classes (or normal series of age gradations) fully
insures a regular sustained yield, provided the increment is
not interfered with. With these two conditions in the normal
state, the third, or growing stock, must also be normal. The
latter, in its numerical aspect, is valuable as a means to judge
the capacity of a forest to yield a fixed return for a certain
period of time ; but it seems a procedure of doubtful expediency,
to begin by establishing the numerically normal state of the
growing stock, because it can exist while the forest is highly
abnormal in other respects.

A forest, consisting of a normal series of age gradations and
worked according to the system of a sustained annual yield,
is, after all, nothing else but a number of age gradations, each
of which is worked under the system of intermittent yields ;
by adding together the intermittent yields of the several age
gradations, the sustained annual yield of the whole series is
obtained. It stands, therefore, to reason, that the best method
of regulating the management of a forest is that, which con-
siders first the special requirements of each wood and then
adds up the cuttings, which have been determined on during
this process. In this way, a healthy treatment can be insured
to every part of the forest, leading to a healthy treatment of
the whole. How this can be accomplished will be shown in
Part IT. of this volume.

•243

PART IV.

PREPARATION OF FOREST WORKING PLANS.

r2

244

PKEPAIIATIOX OF FOKEST WORKING
PLANS.

A FOREST ^Yu^ki^g plan has for its aim to lay down
the entire management of a forest, so that the objects, for
■which the forest is maintained, may be as fully as possible
realised. In order to be of any use, it must be based
upon an exact and detailed examination of the actual state
of the forest in all its component parts ; next, the forest
must be divided into divisions of workable size ; the lead-
ing principles of management must be indicated and the
yield calculated ; finally, arrangement must be made to
control the execution of the plans and to collect additional
information, so that every succeeding working plan may
Ije more accurate and the management become more and
more exact. The whole material is then brought together
in a working plan report.

The w^orking plan report is a document, which gives, in a
systematic manner, all the necessary information and describes
the system of management in such detail, as may be required
in each case. No general rule can be laid down in this
respect. For forests, which are of great value, and which
yield high returns, detailed iDlans should be drawn up ;
for forests, which give as j^et only small returns, and the
yield capacity of which exceeds the demand, simple plans
would be indicated.

By way of illustration the following arrangement is
given, but it must be understood, that in one case many

INTRODUCTOliY. 2 lo

of the headings may he omitted, while in another additional
information may he required : —

•Working Plan riepovt.

Introduction.

Chapter I. — General Description.

1. Name and situation of forest ; name of proprietor.

2. Boundaries.

3. Area.

4. Configuration of the ground.

5. Eock and general character of the soil.

6. Climate.

7. Legal position of forest, rights and privileges.

8. Surrounding population and its requirements.

9. Markets, lines of export.

10. Prices of the several classes of produce.

11. Cost of extraction and transport to markets ; supply of
labour.

12. General description of forest growth.

13. Injuries, to which the crop is exposed.

14. Eate of growth.

15. Yield tables, volume tables, form factors, reducing
co-efficients, etc., used in the calculation of the volume
and increment of the woods.

16. Organisation and strength of the forest staff.

Chapter II. — Detailed Description of Compartments.
Chapter III. — Division and Allotment of Areas.

Chapter IV. — Description of the Method of Treatment.

1. The objects of management.

2. Choice of species.

3. Choice of sylvicultural system.

4. Determination of the rotation.

5. General lines of treatment.

G. Determination and regulation of the yield.

246 PREPARATION OF WORTHING PLANS.

Chapter Y, — Special Working Plans.

1. Plans of utilisation.

a. Final cuttings.

h. Intermediate cuttings.

i\ Minor produce.

2. Plan of formation.

3. Plan of other ^YOl•ks.

4. ]\raps illustrating the condition of the forest and the

proposed treatment.

Chapter YI. — Miscellaneous.

1. Eeorganisation of the forest staff.

2. Financial forecast.

3. Proposals for the control of the execution of the working

plan.

4. Miscellaneous ohservations.

In discussing the several headings of the working plan
report, it will be convenient to arrange the remarks into the
following chapters : —

Chapter I. — Examination of the Forest, or Collection of

Statistics.
,, II. — Division and Allotment of the Area.

,, III. — Determination of the Method of Treatment

AND General Lines of Management.
,, lY. — ])eter:\[ination of the Yield.
„ Y. — Control of Execution and Pexewal of

Working Plans.

The sul)jects coming under I.. II. and III. are not easy to
separate, because these chapters overlap to some extent. In
practice, they are dealt with simultaneously, more especially
Chapters I. and II., but in dealing with them here, they must
be taken one after the other. It is not possible to put the
statistics together in proper order, without having divided the

INTRODUCTORY. 247

forest into a number of working units ; nor is it possible to
divide and allot the area to its several uses, without having
previously ascertained, what each part of the forest contains.
Again, the division and allotment of areas cannot be finally
arranged, until the method of treatment and the general lines
of management have been provisionally laid down. It is for
this reason, that the division and allotment have been placed
between the collection of statistics and the determination of
the method of treatment.

The preparation of the special plans, enumerated in
Chapter V. of the Working Plan Eeport, differs so much
according to local conditions, that no general patterns can be
given. Some examples will be found in Appendices IV.
and V.

At one time, it was the practice to prepare working plans of
high forests for long periods of time, even as much as a whole
rotation. Such a procedure is to be strongly deprecated,
because the conditions, which govern the working of a forest,
change from time to time. Although the general lines of
action must be determined for some time ahead, so as to
secure continuity of action, the detailed prescriptions for the
management should be laid down only for a short period, say,
10 or perhaps 20 years. This is especially desirable, where a
working plan is prepared for the first time, and where the
data, upon which it is based, are as yet incomplete. It is desir-
able, in such cases, to revise the existing arrangements in the
light of the experience gained during the actual working of
the forest for a limited period.

248

CHAPTEK I.

COLLECTION OP STATISTICS.

The collection of statistics is of the first importance, because
the whole fabric of the working plan rests upon the data, which
have been collected as regards the actual state of the forest
and the notes on the treatment, which should be applied to
each part. The statistics to be collected must refer, on the one
hand, to each wood, which forms part of the forest and, on the
other hand, to the general conditions in and around the forest
as a whole, which are likely to influence the management.

The data to be collected may, therefore, be arranged under
the following heads : —

I. Survey and determination of areas.
II. Description of each wood or compartment.

III. Past yields, receipts and expenses.

IV. General conditions in and around the forest.
V. The statistical report.

The data under II. must be collected separately for each
unit of working or compartment ; those under III. may be
given for each compartment, or each working section, or for
the whole forest, according to circumstances.

Section I. — Survey and Determination of Areas.

The survey yields the necessary data, from which maps can
be prepared and the area of the whole forest, as well as of its
several divisions, ascertained. It is not intended to describe
here the various methods of surveying, as this work must be
done by professional surveyors ; the following remarks refer
only to those points, in which the forester must participate.

SURVEY AND DETERMINATION OF AREAS. 219

Before the survey is commenced, various preliminary matters
must be attended to, such as : —

(1.) Eegulation and demarcation of the boundaries of .the
forest, and of those parts, which are subject to
servitudes.
(2.) Demarcation of all areas, which are not destined for the
production of wood, such as fields, meadows, pastures,
swamps, rocky parts and other areas unfit for growing
woods.
(3.) The laying out of a suitable system of roads and rides,
in so far as it can be done without a map, or with the
help of a sketch map. What cannot be done in this
respect before the commencement of the survey, should,
if possible, be done during its progress, that is to say,
as soon as the necessary data become available. If
any part cannot be done until a map becomes available,
an additional survey will be necessary.
(4.) Demarcation of the boundaries between woods of
difierent species, ages, or qualities. The latter is
necessary only in valuable forests.
The method of survey depends on the value of the forest, as
represented by its returns ; the higher the latter, the more
minute should be the survey. Generally speaking, all main
lines, such as the boundaries of the property and of the areas
subject to servitudes, the roads and principal rides, should be
surveyed with the theodolite and chain or measuring staft'.
The details, such as the limits of woods and of sub-compart-
ments, may be done with the plane table or prismatic compass.
The area of the whole forest and its main parts should be
ascertained by the method of co-ordinates ; the area of the
compartments or woods may be ascertained with the plani-
meter, or a network of squares, each of which represents
a fixed area.

Whenever practical, the survey should be based upon a
previous triangulation.

The preparation of the maps will be dealt with in the last

250 COLLECTION OF STATISTICS.

section of this chapter. Frequently, general maps of the area
are already available. If they are on a sufficiently large scale
and reliable, only the additional details, required for the
management of the forest, need be added.

Section II. — Desceiption of each Wood, or Compart:\ient.

The description of each wood, compartment, or other unit
of working, is of the first importance, because it gives informa-
tion, on which depends the whole management, viz. : —

(1.) The selection of species to be grown in the future.

(2.) The method of treatment of each wood and the deter-
mination of the rotation.

(3.) The degree of ripeness of each wood.

(4.) The yield capacity of each wood and of the whole
forest.

The minuteness of the investigation depends on the value
of the forest and the intensity of management. Where these
are high, a detailed examination and record are called for ;
where the returns are likely to be small, or where the demand
is considerably below the possible yield, a summary procedure
may be indicated. The forester must in each case determine
the actual procedure, which he considers to be in keeping
with the interests of the owner of the forest.

1. The Localit)/.

By locality is understood the soil (and sulisoil) and the
climate, the latter depending on the situation. The agencies,
which are at work in the soil and the overlying air, determine
the yield capacity or quality of the locality.

The details regarding locality in relation to forest vegetation
will be found in the third edition* of Volume II. of this Manual,
pages 7 — 51. From what has there been said, it will easily be
understood, that a description of the soil and climate must
form part of the basis, upon which a working plan rests.

* All references to \'olunie II. are incanf for the fliird eililion of that volume.

THE LOCALITY. 251

In describing the climate and soil, the following points
deserve attention : —

a. i'Umate.

(1.) The geographical position of the locality, as indicated
by latitude and in many cases also longitude, espe-
cially where the vicinity of the sea, large lakes, or high
mountains are likely to influence the climate.

(2.) The local peculiarities of the locality, such as altitude,
aspect, slope, temperature, moisture in the air, rainfall,
exposure to strong, cold, or dry winds, susceptibility to
late or early frosts, etc.

(3.) The surroundings of the locality, in so far as they are
likely to affect the local climate.

h. Soil.

(1.) The underlying rock.

(2.) The mineral composition of the soil.

(3.) The organic admixtures of the soil.

(4.) The depth of the soil.

(5.) The degree of porosity.

(6.) The degree of moisture.

(7.) The surface covering of the soil.

In forests situated on level ground, the above data may be
the same over a considerable portion or the whole of the area,
but in the hills they have frequently to be determined for each
compartment, or even portions of one compartment, especially
if it shows considerable differences of altitude, aspect, or slope.

All these factors combined produce a certain quality or
yield capacity of the locality. How this is determined has
been explained in Volume 11. , page 45, and in Forest
Mensuration. Some further remarks on the subject will be
found in the last part of this section.

2. Tlic Groiviiui StocI,-.

The growing wood, or the crop produced on an area, repre-
sents the results of the activity of the locality under a certain

252 COLLECTION OF STATISTICS.

treatment. All points, which have influenced the quantity and
quality of the results, must be ascertained, to enable the
forester to judge of the merits of the treatment hitherto
followed and the advisability or otherwise of any changes
in it.

a. Metliod of Treatment, or Si/lvicultural System.

The different methods of treatment have been described in
Volume II., page 89. In this place, the forester must ascertain
the system, under which the wood has actually been managed
in the past.

b. tSpecies.

Pure woods are indicated by giving the species. In the case
of mixed woods, the degree of mixture must also be given ;
this can be done, either by adjectives, such as " some," "a
few," or, preferably, by decimals, placing the whole as 1.
These decimals should have reference to the area occupied by
each species.

Example. — The following description —

Beech = '5
Oak = -3
Ash = -2
Maple = a few,

would mean, that one-half of the area is occupied by beech,
•3 by oak, and "2 by ash, with a few maples.

In the case of very valuable trees, such as old oaks, or teak
trees in Burma, it may be desirable to give their actual
number. The manner of admixture is expressed as " in
single trees, ■■ "in groups," "in strips," or "irregularly
distributed."

It is also necessary to state, whether the mixture is
permanent or temporary, whether it is of special sylvicultural
or financial importance, such as a shelter wood (or nurses)
over another tender species, a soil protection wood, standards
of valuable species, etc.

THE GROWING STOCK. 258

The undergrowth, shruhs, herbs, etc., should also be
described.

c. Density of the Growing Stoclc.

To every method of treatment, as determmed l)y the objects
of management, corresponds a normal density of the growing
stock. The degree of density may be defined as over-crowded,
crowded, open, very open, interrupted, irregular, etc. Such
terms are indefinite and subject to different interpretations.
It is better to place the normal density as equal to 1, and
express the actual stocking in decimals of it. The degree of
density can be determined by ocular estimate, or, more
accurately, by comparing the basal area of the stems with
that of a normally stocked wood, or, still more accurately,
by comparing the volume of the wood with that of a fully
stocked wood of the same age. When the density of stocking
is insufficient, it should be stated, whether the wood is
generally open, or whether the deficiency is due to greater
or smaller blanks.

By a blank is understood an area, which, though it belongs
to the wood producing area, has no trees on it, or so few, that
its complete re-stocking is necessary. Areas, which are not
destined for the production of trees, are not included here, as
they form part of the areas set aside for other purposes, such
as fields, meadows, etc., or are altogether unfit for the produc-
tion of trees, such as bare rocks, boulder drifts, swampy ground
which cannot be drained, etc. As regards the latter, it is not
always easy to draw the line between actual blanks and wood-
land, as they frequently have a thin stocking, which may give
a small return from time to time.

d. A(/e.

The methods of determining the age of trees and woods
have been given in Forest Mensuration.

An absolutely accurate determination of the age is neces-
sary on\j, when the data are required for the preparation of

254 C'OTJ-ECTION OF STATISTICS,

yield tables or other statistical purposes. Fairl}' approxiuiale
data suffice for the purposes of working plans.

In the case of even-aged, or nearly even-aged, woods, one or
more sample trees are examined. If considerable differences
of age exist in a wood, the limits should be given and the
wood placed into that age class, to which it belongs according
to its economic character. If some older or younger groups
exist, which are not of sufficient extent to be enumerated as
separate woods, this should be mentioned. The same holds
good for a limited number of standards, which are to be held
over for a second rotation, or for young growth, which has
sprung up in an old wood.

In the case of woods, which have been kept back in their
development, the economic and not the actual age must be
given. For instance, a young wood, which has stood under
heavy shelter and is now 80 years old, but of a development,
which is ordinarily reached in 10 years, must be entered as
10 years and not as 80 years old.

In the regeneration class, the age of the overwood and
underwood must be given separately.

In selection forests, it suffices to give the limits of the age
gradations, ^Yhich are frequently determined by the number of
years, during which cuttings go once round the forest.

In coppice with standards, the ages of the overwood and
underwood are given separately ; for the former, the limits of
the existing gradations are given.

The age of coppice can generally be easily ascertained from
the time, when the last cutting occurred.

(;. Oriij'm and Pad Treatnient.

Whenever the necessary data can be ascertained, a short
history of each wood should be prepared, giving the method
of formation, whether by natural or artificial means, planting
or sowing, the manner in which the wood has been tended,
cleanings, thinnings, pruning, natural phenomena, which have
affected the development, etc. Such a history is very useful

THE (IROWING STOCK. 255

in judging the results of the past method of treatment and in
determining the future treatment.

/. Volume.

All methods of determining the yield in material require a
measurement of the volume, but to a different extent. For
some, it is necessary to measure all woods, excepting only those
which are very young, and which are estimated, either direct,
or with the assistance of yield tables. For other methods,
only those woods require to be measured, which will come
under the axe during the immediate future of, say, 10 to 20
years.

Where a fine financial management is followed, all woods
which are close to ripeness, or of which the ripeness is
doubtful, must be accurately measured, so as to calculate the
per cent., with which the capital is working.

For the determination of the capital value, an accurate
measurement of the volume is indispensable.

The volume should be given separately for the difl'erent
species, if their value per unit of measurement difters con-
siderably. It is useful to give all volumes in the same measure,
as solid cubic feet. The proportion between the difierent
classes of produce need only be given for each working
section ; best according to local proportionate figures, if such
are available.

The difierent methods, according to which the volume can
be measured, have been described in Forest Mensuration.
The choice of the method of measurement depends on the
circumstances of each case.

g. Imrement, Capital Value, and Forest Per Cent.

These matters have already been dealt with in full detail.

The determination of the quantity increment is required
for the calculation of the yield. It must be done for all
woods, if the increment forms the principal basis for the
determination of the yield. In that case, both normal and

256 COLLECTION OF STATISTICS.

real increment must be ascertained. When the yield is iixed
for only a limited period, the current increment must be
ascertained for that number of years, or the mean annual
increment of the past is substituted for it.

For financial questions, the volume-, quality- and price-
increment must be determined, as well as the capital invested
in the forest, so as to calculate the indicating or forest per
cent. The latter is necessary only for Avoods, the financial
ripeness of which is doubtful, that is to say, for woods, which
are approaching the normal final age, and woods, which have
suft'ered by injurious agencies, such as wind, snow, fire,
insects, game, etc.

3. iJi'tcrmuiation of ihe Qaalitij of each Wood.
a. General.

It has already been explained, that by the quality of a wood
or compartment is understood its yield capacity, as expressed
by the quantity of produce, which can be derived from it.

The yield capacity depends, in the first place, on the
locality ; but injurious influences may have interfered \\\W\
the full development of the producing factors of the locality,
so that abnormal conditions may be the consequence. The
forester distinguishes, therefore, between normal and abnormal
quality. The quality is normal, if no extraordinary injurious
influences have affected the development of the wood.

A further distinction must be made between the quality of
the " locality" and of the " growing wood " or standing crop.
Either of the two can be normal or abnormal. The quality
of the locality may be abnormal in consequence of a variety
of causes, such as the long continued removal of litter, or
excessive exposure to the effects of sun and air currents, which
have impoverished the soil ; or in consequence of unfavourable
natural phenomena, for instance, if the ground has become
swampy, temporarily denuded, or covered with moving sand.
An abnormal condition of the growing wood may be produced

DETERMINATION OF THE QUALITY OF WOODS. 257

by faulty treatment, by injurious external agencies, such as
drought, frost, wind, fire, insects, diseases of the trees, cattle
grazing, etc.

For the preparation of working plans, only the actually
existing, or real, quality of the locality should be taken into
account, because the restoration of the normal quality is
generally a slow process, if it is at all practicable. As regards
the growing stock, both values are required, because the
normal quality represents the real quality of the locality, and
the real quality of the growing stock forms the basis for the
calculation of the yield, which the forest can at present give.

On page 46 of Volume II. it has been said, that the quality
of the locality can be ascertained —

(1.) By an assessment according to the several factors of
the locality ; or

(2.) By an assessment according to a crop of trees produced
on the area in question, or on a similar soil in the
vicinity.

It has also been stated, that the first of these two methods,
however carefully carried out, is always subject to grave
errors, because an examination of the chemical composition,
the physical properties of the soil and a determination of
the climate do not indicate the yield capacity of the locality
for forestry with any degree of certainty ; hence, it should be
used only as an auxiliary of the second method, or when the
latter is not available.

Thus it will be seen, that the determination of the quality
of the locality depends practically on an examination of the
existing wood, which it has produced. In fact, a normal
growing stock is the true expression for the real quality of the
locality ; the same investigation gives both the quality of the
locality and of the existing crop.

For the purpose of obtaining an actual figure, which repre-
sents the quality, the best way is to ascertain the volume of
the growing stock, including all thinnings, and the number of
years, in which it has been produced. In dividing the volume

F.M. s

258 COLLECTION OF STATISTICS.

by the age of the wood, the mean annual increment is obtained,
which indicates the quaKt3^

It is evident, that in reahtj' a multitude of different qualities
exist, but for practical work they are grouped into a few,
generally not more than five, quality classes, which are
numbered I. to Y. Of these I. should represent the lowest
and V. the best quality, but, unfortunately, the reverse
numbering has been largely introduced. A still more con-
venient way is to represent the best quality by 1 and the
others in decimals of 1. Each of these quality classes
represents a distinct yield capacity, which differs with the
species and method of treatment.

The quality can be determined with the help of yield tables ;
their preparation has been explained in Forest Mensuration.
Such tables represent the progress of volume, or increment,
throughout life for each quality class ; hence, assessing the
quality means, in this case, the selection of the proper yield
table. The difficulty is, that for every species and sylvicultural
system a different set of yield tables is required. It may even
be desirable to have different sets for different localities, so-
called local yield tables ; but such a procedure is likely to lead
to confusion, as different standards of the quality classes are
introduced into the account. Hence, general yield tables are
to be preferred, even if the same degree of accuracy is not
obtained as in the case of local tables. The difference is, how-
ever, not considerable, as experience has shown, that, within
reasonable limits, general tables give sufficiently accurate data
for the preparation of working plans. It has, for instance,
been proved, that the general yield tables for the Scotch pine,
prepared for North Germany, may safely be used for fairly
crowded woods grown in the south of England. The fact is,
that the sources of inaccurac}^ unavoidable in the best methods
of measuring the volume of a standing crop, are greater than
those caused by using general yield tables for any particular
locality.

Yield tables for oak, beech, Scotch pine, spruce and silver

DETER:\riNATION OF THE QUALITY OF WOODS. 259

fir will be found in Appendix III. In these tables only
three quality classes have been distinguished, I. representing
the best, III. the least favourable, and II. the average, or
middling, quality.

The quality of young woods cannot be judged by their
volume, since the factors of the locality may not yet have
found full expression in it ; here the quality must be estimated
by the general condition of the crop and especially its height
growth. Indeed, the latter may be used even in older woods,
especially as long as it has not ceased.

The determination of the quality from yield tables, in the
case of clear cutting in high forest and in coppice, is a simple
matter, as previously shown. The regeneration area under
the shelter-wood system gives some trouble, because it is no
longer fully stocked, so that the volume does not represent
the quality ; here the determination must be based upon an
investigation of the quality of the locality combined with the
condition of the shelter- wood and young growth. A similar
procedure is followed in the case of coppice with standards
and in selection forests. The quality of blanks is estimated
from the soil and climate, or from that of adjoining woods,
which have been produced on soil of a similar description.

b. Reduction to One QuaUtij.

Several methods of regulating the yield demand a reduction
of the areas of the several woods, or working sections, to one
quality, so as to enter into the account only areas of equal
yield capacity. Such a reduction to one quality may be made
as regards the locality, or the growing wood ; in each case as
regards the normal or real quality. The method of procedure
is the same in each case.

The reduction is made by means of the final mean annual
increment, or yield. It can be made under one of the two
following conditions : — Eitlier the total of the several reduced
areas shall be equal to the actual area of the working section ;
in other words, the calculation is made with the mean quality

s2

^HO COI.I.ECTTON f)F STATISTICS.

of the area ; o^, the above equality- is not recjuiretl, in which
case anj' quaUty can be used as the standard, frequently
that being chosen, which exists over the greater part of the
area.

Calriihdioii n-itJi ihc Mean (Jiialitii. — By mean quahty is
understood tliat. which, if it existed throughout the working
section, would produce the same total yield as that produced
by the several existing qualities in different parts of the
working section.

Let «i, (t-2, (i;i ... be the several areas,
M .'/b !i2, .'Is • • • the corresponding annual yields, or

increment, per unit of area,
,, Y the mean yield per unit of area, then

f'l X jfi + ((2 X ?/2 + ^'3 X //3 + • . • = (iiY -{- a.jY -\- ((3 r+ . . .
= Y {((1 + 02 + as. . .),
and

y _ a I j/i -\- a2 i/2 + as P3+ ■ • • _ total annual yield
cii + «2 + 03 + . . . ~ total area

Exitinplc : —

A working section of 1,000 acres contains —

Block (1) 200 acres with 60 cub. ft. average increment,

„ (2) 100 ,, „ 50 ,,
„ (3) 200 „ „ 40 „
,, (4) 500 ,, ,, 80 ,, ,, ,, tlien—

Menu quality

^ 200 X 60 + 100 X 50 + 200 X 40 + 500 X 80 ^ ^^ ^^^^^ ^^
~ 1,000

By reduced area is now understood that, which would
produce, with a uniform quality = Y, the same total yield as
the actually existing areas with their varying qualities. It is
obtained by applying, in each case, the inverse proportion of
that, which exists between the actual and the mean quality :

}'; // =z (I : X and reduced area ./• = — =^' ,

DETERMINATION OF THE QUALITY OF WOODS. 261

In the ahoce example —

Block (1) The proportion is 60 : 40 : hence the reduced area
■c is obtained by means of the equation —

40 : GO = '100 : r and r =: '-^^^^ ^^ = 800 acres.

,, (2) 40 : oO = 100 : r ,, .r = -^ — =l'2ij ,,

40

„ ^8) 40: 40 = 200 :.r „ ,r = :^-^='200 „

„ (4) 40 : 80 = 500 : r „ .r = '^-i^-^ = 375 „

40

Total = 1,000 acres.

If now the forest is to be divided into annual coupes of
equal yield capacity, the area to be placed in each is also
obtained by calculating with the inverse proportion of the
qualities.

Example. — The above forest shall be divided into ten
coupes of equal yield capacity ; then the reduced area of

each coupe is = — .-^ = 100 acres. The real area of a coupe

in each block is calculated as follows : —

Block (1) 60 : 40 = 100 : x and x = i^^l^ = 66-67 acres.

bO

„ (2)50:40=100:^- „ .r = ^^^^i^= SO'OO „

oO

„ (8) 40 : 40 = 100 : x „ x = ^^^><100 _ lOQ-OO „

„ (4) 80 : 40 = 100 : r „ .r = —^^-^^ = 188-88 „

80

or,

Coupe No. 1 = 66-67 = 66-67 acres

„ 2= 66-67 = 66-67 „

„ 'd=z 66-66 = 66-66 „

,,4= 80-00 = SO-00 ,, Fnnii l)luck Xo. 2.

Taken from block
No. 1.

•262 COLLECTION OF STATISTICS.

,, x^ . mi-- n-,.r. ' Partly froiii No. 2

Coupe rso. 0 = 20+ ^'j = i<;)"00 acres , , ^^

I and partly iSO. B.

„ G= 100 =100 ,, From block No. 3.

I Partly from No. 3

= 25 + 100=12;-

and partly No. 4.

8= 133-33 =133-33
9= 133-33 =133-33
10= 133-34 =133-34 ., '

I
9= 133-33 =133-33 ,, From hlock No. 4.

Total = 1,000 acres.

Calcidatioii aitli aiii/ Suitable (JiiaUti/. — In this case any
quality can be used, whether it exists on the area or not.

The total reduced area is obtained by multiplying the
several qualities by the corresponding areas and dividing the
product by the selected standard quality. It may be greater,
equal or smaller than the actual area, according to the size
of the standard quality : —

Reduced A = "^ ^ -'^^ ± "-2 X j,, + a^Xj,^.. .

The reduced areas of the several parts are obtained by the
inverse proportion of their qualities to the standard quality ;
thus : —

Reduced a, = '^-^J'\

Reduced a, = ^^ ^/^

etc.

ExamjAe, as ahore. — Let the standard quality = 50 cub. ft.,
then total reduced area =

200 X GO + 100 X 50 + 200 X 40 + 500 X 30 _ y, ,, . , ^ ,.^^

— ouu cities,

50

and for the several blocks : —
i)0

N0TE8 EEGAEDING FUTUEE TEEATMENT. 263

,.., 100 X 50 1^^

(2) — = 100 acres

50

(8)205^ = 160 „

(4)500X^ = 800 „

50

Total = 800 acres.
Eeduced area of annual coupe =^rTr = BO acres,
and the size of coupes in the several blocks : —

(1) 60 : 50 = 80 : x and x = ^^-^ = 06-67

bO

(2) 60 : 50 = 80 : x „ x = :^0x80 ^ ^^.^^

oO

(3) 40 : 50 = 80 : x .„ x = ^^ ^ ^^- = 100'

(4)30:50 = 80:^ „ a- =-^^ ^^ ^-= 133-33 ;

as before.

It is obvious, that the last mentioned method is the more
convenient of the two.

4. Notes regarding Future Treatment.

While dra^Ying up a description of each wood, it is very
desirable to note down an^^ observations, which may strike the
forester regarding the future treatment. Such notes are, of
course, only of a preliminary nature, because a final decision
on the future treatment to be followed can be arrived at only,
after the management of the whole forest, or working section,
has been laid down. Nevertheless, they are a great help
during the progress of the work.

It is not possible to give a complete list of the points, which
should be attended to, as they differ according to circum-
stances ; the following may, however, be enumerated : —

(a.) Filling up the existing wood ; if so, the area to be treated
and the species to be grown should be given ; also the
method of sowing, planting, or other cultural operations.

264 COLLECTION OF STATISTICB.

{h.) Cleanings, thinnings, or prunings during the period, for
which the working plan is prepared ; the volume to be
removed should be estimated.

{<:) Degree of ripeness of the principal or final crop, talcing
into consideration the objects of management; if the
latter are financial, the forest per cent, should be
calculated. If it appears advisable, that final cuttings
should be made, the method of cutting should be given,
as well as an estimate of the volume to be removed.

{(I.) Method of regeneration to be followed and the species
to be grown, if this should occur during the period, for
which the working plan is prepared.

{c.) Measures to be taken for the protection of the wood
against threatening dangers, especially fire.

if.) Other works to be undertaken, such as construction of
roads, draining, irrigation.

ig.) Utilisation of enclosures and improvement of boundaries,
where practicable.

(/(.) Proposals regarding the formation of sub-compartments,
or the abolishment of those which exist, with reasons
for such proposals.

Section III. — Past Yields, Receipts and Expenses.

There is no surer basis in estimating future returns than
those of the past ; hence, it is of importance to ascertain and
note down the yield in material, the cash receipts and costs
for as many years, as the available data admit. These data
will, however, only be forthcoming, if records have been kept
for some time past.

As far as may be practicable, past yields, receipts and costs
should be given for each unit of working, that is to say each
wood or compartment. If the records have not been kept in
sufficient detail, the data for each working section should be
given; the latter may also be quite sufficient, where the
management is as yet in a backward condition, or where the
receipts are small.

PAST YIf:LbS, RECEIPTS AND EXPENSES. 265

The following notes indicate the class of information which
may be required : —

1. Yield of Wood or Major Produce.

The yield should be given separately —

(a.) For the principal species.

(/>.) For the different classes of timber and firewood,
according to size or value.

(c.) For final and intermediate returns.

(d.) Of cash receipts should be given the total, and the
average price of the several classes of material,
separated according to species.

(e.) The areas, over which cuttings extended, should, if
•possible, also be given separately for final and inter-
mediate cuttings.

2. Minor Produce.

Under this heading, th-e quantity of each article of minor
produce, which has been removed, and the cash receipts
obtained for it, should be given.

Receipts derived from areas not used for the production
of "wood, such as fields, meadows, etc., should be separately
recorded .

3. Eu:2)eiises.

These should be recorded separately for —

(a.) Cost of administration and protection.

(h.) Taxes, rates, etc.

(c.) Formation of woods.

{d.) Tending and amelioration.

(e.) Maintenance of boundaries.

(/.) Construction of roads, drainage, irrigation, and other

works.
ig.) Cost of harvesting, separated according to major and

minor produce.

266 COLLECTION OF STATISTICS.

4. Generalhi.

For forests worked on financial lines, the receipts and expenses
should be so arranged, that it is possible to ascertain —

(a.) The current forest per cent, of each wood whenever
desirable.

(6.) The forest rental, being the difference between all
receipts and expenses. It is used to determine the
percentage, which the forest capital has 3'ielded.

(c.) The capital value of the forest, being the sum of the
value of the soil plus value of the growing stock. For
the preparation of working plans, based upon financial
principles, these values may be ascertained as follows :
the data of receipts and costs, collected for the several
woods, will enable the forester to calculate a series of
expectation values of the soil for the different qualities
of locality ; besides, all available data referring to actual
sales of land, similar to the forest lands in question,
should be carefully noted. By combining these data,
it will be possible to determine the value of the soil
with sufficient accuracy for the purpose of working plans.
The capital value of the growing stock is then deter-
mined as the cost value, calculated with the value of
the soil as determined above, or as the utilisation value
in the case of woods, which are near maturity.

Section IV. — General Conditions in and around the Forest.

The management of a forest depends, not only on the state
of its several parts, but also on the general conditions, which
exist in and around it. The latter must, therefore, be ascer-
tained at this early stage, and they should be used for a
general description of the forest, to be incorporated into the
working plan report.

The field of inquiry here indicated is of considerable extent ;
the following matters may be mentioned : —

(1.) Name and situation of forest, giving the latitude and
longitude where necessary.

CONDITIONS IN AND AROUND THE FOREST. 267

(2.) Description of boundaries and names of the adjoining
properties and their owners.

(3.) Topographical features of the locahty.

(4.) General description of the geology, soil and climate.

(5.) Former and present proprietors, financial position
of the latter, whether the funds for formation,
tending, administration, amelioration, etc., are avail-
able ; whether specially heavy cuttings must be made
to meet the demands of the proprietor.

(6.) Nature of proprietorship, whether full and unfettered
property, or whether servitudes and privileges rest on
it ; in the latter case their extent should be recorded.

(7.) Eights enjoyed by the proprietor of the forest elsewhere,
such as rights of way or floating, or rights over other
lands, etc.

(8.) Requirements of the surrounding population and con-
dition of the market for forest produce generally ;
special industries in the vicinity which require forest
produce, such as mines, smelting works, saw mills ;
imports which compete with the local supply ; sub-
stitutes for wood available in the vicinity.

(9.) Extent of forest offences, their causes, effect upon the
forest ; suggestions for their prevention.

(10.) Labour available in the vicinity ; rate of wages.

(11.) Past system of management; changes introduced from
time to time ; prescriptions of former working plans
and their effect upon the forest.

(12.) Natural phenomena which have affected the condition
of the forest, such as storms, snow, frost, fire, insects,
fungi, etc.

(13.) Conditions of game and cattle grazing ; their effect
upon the forest.

(14.) Past seed years of the more important species.

(15.) Opportunities for consolidating the property, either by
exchange or purchase ; conversion of fields, meadows,
etc., into forest, or tlie reverse.

(IG.) The staff" of the forest, its organisation and efficiency.

^68

COLLECTION OF J^TATISTTCS.

Section V. — The Statistical iiEPouT.
The data, which have been coHected in the manner indicated
in the previous four sections, must be brought together in a
statistical report, accompanied by maps to ilkistrate it. The
form of this report depends entirely on the circumstances of
each case. In one instance it will l)e necessary to go into
minute details, in another a more summary treatment is
indicated. The following documents will ordinarily form
part of the report.

1. Fu'ijister of Boundaries.
This should give —

(a.) The boundary marks in consecutive numbers.
(6.) The angles backwards and forwards at each point.
{(■.) The horizontal distance between every two boundary

marks.
(d.) The nature of the boundary line, whether a road, water-
course, waterparting, ditch, cleared line, etc.
(<?.) The names of adjoining properties and of their owners.
The value of the register of boundaries is considerably
enhanced, if its correctness has been acknowledged by the
adjoining owners before the proper court of law.

2. Table of Areas.

The following form of this table is given as an ilkistration ;
it serves as a summary of all areas, and shows, how each part
is utilised : —

LOCALITV.

Area usc> il
for the

Akea sot used kor the Prodiction
OP Wood. Ln- Acres.

Grand
Total.

In
Acres.

Woikin-

Sfctioii or

IJlock.

Produc-
tioa of
Wood.
Ill Acres.

Road.s
and
Hides.

FieMs.

.Ateadows.

Water,
etc.

Total.

Ciesai's
Camp .

1

11

Ltc.

20 -4

2-2

~

•6

3-2

29-2

KiiiiAKK.s. — The Ubc of the tieidb lorms part of the foresters emoluments.

THE STATISTICAL REPORT.

269

3. Desrri])tion <>f Conijiartmrnts.

This description may be drawn up in a tabular form, or
otherwise ; the former is preferable, as it presents a more
intelligible picture of the forest, and gives greater security
that nothing has been overlooked. It is quite impossible to
recommend any particular form for this table, but by way of
illustration the appended form is given, (See page 270.)

In this table the quality of locality indicates that, which
corresponds to the normal quality of the growing stock. The
real quality of the growing stock is given in decimals, the
normal quality being placed equal to 1.

If the forest is worked on financial principles, further columns
must be added for the quantity and quality increment, wherewith
to calculate the forest per cent, and the forest capital.

4. TaliU: of Qualities of L<ir(diti/.

I.OCAMTY.

Quality Classes of
Area in Acre

Locality.

s.

Total
Area.

Sylvicultural
System and

Sub-
com-

Working

Com-
part-
ment.

Acres.

Specie.s.

Section.

part-

I.

II.

ni.

nient.

Best.

Jlirtdliug.

Lowest.

C-jesar's

High forest of

Camp

1

rt

2(5

26

Scotch piue

1

h

U

14

with some

2

32

6

38

broad-leaved

3

17

17

trees here

4

16

1.5

31

and there.

5

12

17

4 -

33

6

2.-)

6

31

7

7

21 »

27

Etc.

Total

36

116

65

217

AYhenever a certain intensity of management has been
arrived at, it is useful to prepare this table, as it enables the
forester to calculate the total yield capacity of the area. In
this table each working section must be recorded separately,

270

COLLECTION OF STATISTICS.

Description of

Locality.

Area, ix Acres.

Boundaries.

Locality.

Working

Com-

Sub-
Cora-
part-
ment.

Section or

part-

.Stocked

Blank

Total

Block.

ment.

Csesar's

Camp

1

a

24

2

26

Xorth cS- East :

Eleration: 420 feet

Sir A. Haytpi's i above sea-level, slop-

land, ing towards the east,

with moderate gra-

■%ufh: Com- dient. down to iiSO

partments 13 feet.

and 12.

Gcolofi'tciil Foniifi-

West : Eoman

tio/i: Middle Bagshot

road.

sands.

Soil: Loamy sand,

j fairly good in upper

part and good in

lower part ; no pan

to 4 feet depth.

as the yield capacity depends on the species, sylvicultural
system and rotation.

Assuming, that the yield tables for Scotch pine, given in
Appendix III., apply to the woods in question, and that the
latter are worked under a rotation of 80 years, the normal
mean production j^er acre and year will be as follows : —
For the I. Quality class = 146 cubic feet,
n. ,. ,, = 90

III. ,. .. = 87

The mean annual increment, or the yield cai^acity, of tlie
area shown in the above table would therefore be —
Yield cai)acity =

3() X 146 + IK) X !)0 + 65 X 87 = 18,101 cubic feet,

18,101 , . ,

or average yield capacitv per acre = ,7,-^ = 83 cubic feet.

THE STATISTICAL REPORT.

271

COMPAUTMENTS.

Growing Stock. Quality of

Remarks, and Notes

regardiiif; P'uture

Treatment.

SvMcul
'tural
System.

Species.

Age,

in
Years.

Mean
Height

Feet.

Volume
in solid
Cubic
Feet.

Lo-
cality.

|l

High
Forest

Oak=-J

Chest-
nut =-2

Beech
= •1

Scotch
pine = -3

70

Oak,
Chest-
nut &
Beech

= 5-t

Scotch
pine
= 60

Broad -
leaved
= 34,000
Scotch
pine
= 28,800

II.

(or
mid-
dling)

•8

The mixture of species
is uneven ; the Scotch
pine is chiefly found in
the northern part and
the broad-leaved trees
in the South : northern
part is well-stocked,
southern part open ;
most of the oaks and
chestnuts are frost -
cracked.

Future Treatmeni :
Southern part is so
increment-poor, that it
should be cut over
during the next ten
years, leaving the best
oaks and chestnuts, and
underplauted, or sown,
with beech. In the
northern part only dead
or dying trees should
be removed during the
next ten years.

62,800

This figure represents the normal yield ; the real, or actual
yield depends on the quality of the growing stock and the ages
of the several woods. Assuming that the mean quality of all
woods were equal to '1, the actual yield would, for the present,
be equal to

18,101 X -7 = 12,671 cubic feet,

or 58 cubic feet per acre and year, w^hile measure would have
to be taken, to increase the yield capacity in the future, by
growing more completely stocked woods.

5. Table of Age Classes.

This table is of great importance, as it gives a correct idea
of the proportion of the different age classes, which affects the

372

COLI.ECTION OF STATISTICS.

(letei'miiialion of the ^ield in the immediate future. It may
be prei^ared in the following form : —

TaBLI-: of A«E C'LASSEi>.

Locality.

Present
Mean

Age.

Age Classes, Areas in Acre.s.

Working
Section.

Com-
part-
nient.

Sub-
com-
part-
nient.

I.

l--_'0.

31

n.

•Jl-4().

14
31

in.

4;-(io.

IV. 1 V.
>il-80. (-)verSO.

Hliiiiks.

Itegenc-
ratiou
{•la.s.s.

Caesar's
(•amp

1
1
2

I

5
6

a

h

70
3.-)
05
54
16
46
24
86

Total ...

17
33

24

32
27

2

i
1

31

45

50

24

5<)

8

6. Table of Past Yidds.
This table should give the past yields in produce for as
many years as possible, and the mean annual yield calculated

from these data.

Table of
Material Cut in Past Years,

1881

1882

181)0

Total in
10 Years..

Annual
Average..

7,200

7,600
7,760

Fire-
■\vooi.l.

16,400,94,000

tHUj

:ifi,400
3,640

Fire-
wood.

12,200
1,220

6,00(:

48,600
4,8GO

1 ,!10(

114,000
11.400

Fire-
■\vood.

3,050

28,600

2,860

14,050

142,600
14,260

Timber ..''i\" Total.

2,750
275

Fire-
wood,

2,600
260

5,350
535

Remarks. — The area set aside for the i^rocluction of wood amounted, in the
beginning of 1881, to 217 acres.

MAPS.

ns

The data should be separated, Nvhere practicable, according
to final and intermediate returns, the principal species and
the different classes of produce.

The accompanying table illustrates this.

Where specially valuable timber has been cut, like oak
standards, teak, etc., it can be entered separately.

7. Maps.

It is most useful to represent on maps the data required
for the preparation of a working plan, as far as this can be
done. Such maps give at a glance a clear picture of the
forest, which impresses itself more readily on the mind of the
forester than a lengthy description. As it is not possible to
represent everything on one map, it is usual to prepare
different sets, such as the —

(a.) Topographical map.

(/>.) Detailed map on a large scale.

{<:■.) Map showing the nature and age of the growing woods,
called the stock map.

Pa,st Yields.

in solid Cubic Feet.

Leaved Species.

Total.

Intermediate.

Total.

Final.

Intermediate.

Total.

Tim-
ber.

Fire-
wood.

Total.

Tim-
ber.

Fire-
wood.

Total.

Timber

Fire-
wood

Total.

Tim-
ber.

Fire-
wood.

Total.

Timber.

Fire-
wood.

Total.

750

1,650

2,400

750

1,650

2,400

7,200

1,750

8,950

5,450

2,950

8,400

12,650

4,700

17,3.50

1,350
135

2,100
210

3,450
345

4,100
410

4,700
470

8,800
880

80,350
8,035

19,000
1,900

99,350
9,935

37,750
3,775

14,300
1,430

52,050
5,205

118,100
11,810

33,300
3,330

151,400
15,140

The annual yield was fixed at 15,000 solid cubic feet : or
150,000 for the period of 10 years ; hence, the average cuttings
exceeded the fixed yield by 140 cubic feet annually.

371 COLLECTION OF STATISTICS,

(cL) Geological map.

(e.) Soil map.

(,/■) Map showing the working sections and cutting series.

(r/.) Detailed road map,

(//.) Map showing the qualities of localit3\

There is, however, no need for so manj^ separate maps, as
several of them can be combined into one. Ordinarily three
maps suffice, namelj' : —

a. The Geoloyical Map.

This map should show the geological formation of the upper
layers, on which the nature of the soil depends. In it can
also be shown the general topography of the area ; the various
qualities of locality can be entered by lines of a distinguishing
colour, into which the quality figure is written.

h. Thf' Delaihl Maji.

The scale of this map depends on circumstances. In India
the ordinary scale is 4 inches = 1 mile. In a few cases maps
on a scale of 8 inches = 1 mile, and in others of 2 inches = 1
mile, have been prepared.

The map should show, amongst other items : —

(1.) Name of forest and year of survey.

(2.) Boundaries, all boundary marks being indicated on the
map and numbered ; boundaries between free property
and parts subject to servitudes.

(3.) Names of adjoining properties and their owners.

(4.) Area, total, as well as of the main divisions.

(5.) Areas not used for the production of wood.

(6.) Contour lines, or height curves.

(7.) The system of roads and rides, watercourses and other
natural lines, with their names.

(8.) The boundaries of working sections, blocks, compart-
ments and sub- compartments, with their names and
numbers.

Fig. 50.
REPRESENTATIOX OF TWO CCTTING SERIES

(THE UPPKR CONSISTING OF 10 COMPABTMENTS, THE LOWER OI' 5).

CLTTINC |)IKK( TION.

~\\

I III n ■" ni f m

T .
H H ^^1

II ^1 ^r"

/. Agr Class 1 — 20 i/cars old [

II. „ „ 21—40 „ „ [

III. „ „ 41—60 „

IV. „ „ 61—80 „ „

V. „ ,, over 80 years old

lintafinii = 80 !/<'ars.
The mate Lines indicate the coupes to he cleared during the ne.rt 10 years.

[n

MAPS. 275

r. The S'forJr Map.

This has for its principal object to give a picture of the
manner, in which the area is stocked with wood ; a smaller
scale than 4 inches = 1 mile generally suffices for it. The
map should contain, apart from the necessarj' details, a
representation of the existing species, sylvicultural systems
and distribution of the age classes. This can be done in a
variety of ways, as for instance in the following : —

In high forest the principal species are shown by different
washes ; the age classes by different shades of the same wash,
the youngest being given the lightest, and the oldest the
darkest shade ; the regeneration class receives some distin-
guishing mark.

MLced woods may receive a separate wash, or they may be
distinguished ))y the addition of small trees or marks of
various colours.

Coppice tcoods may receive a separate wash, if shown on the
same sheet.

Coppice Lcith standards may be distinguished from coppice b}'
the addition of miniature trees.

Selection forest may be indicated by colouring it with the
wash of the principal species, and indicating other species by
special marks.

Blanks remain uncoloured.

The stock map should be renewed, whenever a new working
plan is prepared; if this is done, it gives, in the course of
time, an excellent representation of the history of the forest.

By way of illustration, the appended Fig. 50 is added. It
illustrates two cutting series, a number of these constituting
a working section, or a complete series of age gradations.

T 2

276

CHAPTEK 11.

DIVISION AND ALLOTMENT OF THE
FOREST AREA.

1. Thr U'orhiHci Circh'.

By a working circle is understood the area, which is managed
under the provisions of one and the same working plan.

The area of a working circle depends on local conditions.
Its minimum size would he the area of a property belonging
to the same owner; the maximum will ordinarily he the area
forming one executive charge or range.

The division of an extensive projjerty into ranges depends
chiefly on: —

(1.) The situation, and

(2.) The intensity of management.

In the case of scattered blocks, in hilly country, or where
means of rapid locomotion are wanting, a range will comprise
a smaller area, than if the property is consolidated, situated on
level ground, or where railways and other means of locomotion
enable the range officer to move rapidly from one part of his
charge to the other.

In forests, which yield a small return, the ranges may be
large ; where the money yield is high, it pays best to make the
ranges small, so that an intense and detailed management may
be possible.

In some cases, one range otiicer may manage several working
circles ; for instance, if the owners of several small properties
join in employing one ofiicer for the management of their
forest property. That case occurs frequently in many Euro-
pean States, where Government forest officers manage both
the forests of the State and of Communes.

THE COMPARTMENT. 277

Each working circle or range, as the case may be, must be
further divided. The unit of that division is the compartment.
A number of compartments are grouped together into cutting
series, and a number of the hitter form the working circle, or
a part of it called a working section. The whole of this division
is effected by utilising, in addition to the outer boundaries,
interior natural lines, such as water partings, watercourses,
precipices, etc., and artificial lines, as roads, already constructed
or projected, and rides.

Although the division of the working circle depends chiefly
on the system of roads and rides, it is desirable, before indica-
ting how it should be laid out, to explain more fully, what is
understood by compartment, sub-compartment, cutting series
and working section.

2. The Compart Dient.
By compartment is understood the unit of working ; it forms,
therefore, the unit of the division of the forest.

The above definition should never be lost sight of. If the
boundaries of a compartment can be made to coincide with
those of a wood showing a certain composition or age, so much
the better, but it is a mistake to insist upon such an arrange-
ment ; the main point is, that each compartment should be of
a certain size, so as to fulfil its objects as the unit of working.
If that area includes two or more different kinds of growing
woods, they may be distinguished as sub-compartments ; but
the boundaries of the compartment should never be twisted
out of shape for the sake of including only one kind of growing
stock in it.

The formation of compartments is necessary —

(1.) For general orientation, so as to enable the forester to

define accurately any particular part of the area.
(2.) To render all parts of the forest easily accessible, since
one or more sides of the compartment should abut on
roads or rides.
(3.) To assist in the prevention of fires, and to enable the
forester to stop any, which may have broken out.

•2 7'^ DIVISION A\T> ALLOTMENT OF TTIK FOUKST AKEA.

(4.) For the location of the annual oi- periodic coupes.

(5.) To facilitate the transport of forest produce.

(fi.) To obviate the necessity for repeated surveys of tlie
coupes.

(7.) In some eases, to facilitate hunting and shooting.

The boundaries of compartments are formed l^y roads and
rides, whenever natural lines are not available.

The shape of compartments depends on the configuration
of the ground. In the plains, a rectangular shape (with sides
2 : 1, or 3 : 2) is most suitable. On hilly ground, such a
shape is not always practicable ; but the actual shape should,
as far as possible, approach that of a rectangle.

The size of compartments cannot be laid down : it depends
on —

(1.) The size of the working circle.

(2.) The intensity of management.

(3.) The extent of danger from fire.

3. TJic Siih-cnnijiarfiiK'nt.

If, within the limits of a compartment, considerable
differences exist in respect of species, sylvicultural system,
age of growing stock, quality of locality, etc., it may be
divided into two or more sub-compartments ; the latter may
be temporary, if the differences will disappear after some time,
or permanent. Bub-compartments may l)e marked by shallow
ditches or other cheap boundary marks.

The forester should not go too far in the formation of sub-
compartments, as it is accompanied l)y additional expenditure.
As a rule, sub-compartments should be formed only, if the
additional income, derived from different treatment, at least
covers the additional expense involved thereby.

4. 77/ r ]Vi>r]n)i(j See f ion.

A part of a working circle, which forms a se])arate series of
age classes, is called a working section. If a working circle

THE WORKING SECTION. ^79

consists of only one series of age classes, it is identical with a
working section. In working circles of some extent, however,
different conditions may demand the establishment of two or
more series of age classes, or a division of the working circle
into two or more working sections. The principal causes,
which demand the formation of working sections, are the
following : —

a. Spenps.

When several species appear in a working circle as pure
woods, they must be placed into different working sections,
if they require essentially different treatment, or if a certain
quantity of material of each species has to be cut annually.
When, on the other hand, the several species appear in mixed
woods, such a separation is neither practicable nor necessary.

h. Sijlvicultural System.

Each sylvicultural system may demand the formation of a
separate working section. If, for instance, part of a high
forest is treated under the compartment system, and another
part as a selection forest, each part must be formed into a
separate working section. Coppice woods and coppice with
standards always must form separate working sections.

c. Rotation.

Even in the case of the same species and sylvicultural
system, areas worked under different rotations must be placed
into different working sections, whenever an even or approxi-
mately even annual yield is expected. Unless this is done,
it will happen, either that the annual yield is uneven, or, if
the same quantity is cut every year, that the different
rotations merge into one.

d. Servitudes.

If part of a working circle is subject to servitudes, it should
be placed into a separate working section; this is necessary to

280 DIVISION AND ALLOTMENT OF THE FOREST AREA.

protect the interests of the owner, as well as of the right
holder.

c. Differences in I he Qualilij of ihc Locality.

Differences in the quality of the locality cause the establish-
ment of different working sections, if they necessitate the
growing of different species, or the adoption of different
treatment or rotations.

/ Distrihtition of Cidtings.

If cuttings must be made annually in different parts of the
working circle, so as to supply local demands, it is often
advisable to form different working sections, though this is
not absolutely necessary.

g. Size of ilie WorJcin// Circle.

When the area of a working circle exceeds a certain limit,
it may be more convenient to divide it into several working
sections, although no difference in the character of the growing
stock and the management exists. In this way, better arrange-
ments can be made for the execution of the work.

//. Generalhj.

A working circle consisting of several working sections is
said to be normal, if each separate working section is in a
normal state.

Although the formation of working sections is in certain
cases unavoidable, the forester should not go to extremes in
this respect. A separate record must be kept for each working
section, and they cause extra trouble and expense in other
ways ; hence, moderate differences of Qonditions, especially in
the rotation, should not induce the forester to introduce
separate working sections.

The question may be asked, why a separate working plan
should not l)e drawn up for each working section, thus making
the latter alwavs identical with a working circle. Such a

THE CUTTING SERIES. 281

procedure is not desirable, because it involves extra labour
and repetitions in the working plan report. It is preferable,
whenever practicable, to have one working plan for each
executive charge, because the management of the different
working sections can be so arranged, that they supplement
each other, thus enabling the forester to provide for a proper
allotment of work amongst the staff and a proper distribution
of the yield. Where the areas managed on different lines are
mixed up with each other, the division of a working circle into
two or more working sections becomes an absolute necessity.
It need hardly be pointed out, that the areas belonging to one
working section need not form a consolidated block ; they may
be scattered amongst other areas forming another working
section.

5. Tlic Cutting Series.

A working section in its simplest shape should consist of a
series of age gradations equal to the number of years (or
periods) in the rotation, so arranged, that cuttings commence
in the oldest age gradation and proceed steadily towards the
youngest in the direction, which is determined by the circum-
stances of each case. It has, however, been pointed out on
page 222, that such a simple arrangement is, in the case of
high forest, not always admissible, and that every working
section in such a forest must be further divided into several
parts, which are called " cutting series." Only such a
further division gives the necessary order and elasticity to
the arrangement of the coupes.

Each cutting series should comprise a number of gradations,
the ages of which differ by a certain number of years (see
diagram on page 223) ; it can be regarded as a working
section, in which cuttings are made periodically instead of
annually; ordinarily, however, a certain number of cutting
series together form one complete series of age gradations, or
a working section.

The number of age gradations to be included into one

2H2 DTVTSTON AND AT,LOT:\rENT OF THF. FOP.EST ARFA.

cutting series depends on local circumstances. On the whole,
small cutting series are desirable, as each gives a point of
attack where cuttings can be made. Amongst the advantages
of small cutting series the following may be mentioned : —
(1.) The special requirements of each wood can be met at
the right time : if a cutting is desirable at a given
time, it can be made without interfering with the
safety of adjoining woods.
(2.) A suital)le change of coupes can be arranged, so as to
protect the forest against the dangers, which may make
themselves felt, if two or more annual coupes adjoin
each other.
(B.) The establishment of small cutting series assists the
forester in distributing the yield to meet local
demands.
In order to realise these advantages it is necessary, that
each cutting series should receive a shape and be so situated,
that the coupes can be suitably arranged, and that cutting in
one series does not interfere with the requirements of adjoin-
ing series; in other words, each cutting series must be
independent of its neighbour. Where these conditions do not
exist, they must be specially provided b}' the clearance of
broad rides between the cutting series, called severance
cuttings.

6. Sercrancr Ciitthuia.

By a severance cutting is understood a cleared strip of
varying breadth, by which two woods are separated in the
general direction of the cuttings, at a place where some time
afterwards regular cuttings are to commence.

Severance cuttings are necessary, whenever an existing
cutting series is too long, and when it is desirable to divide it
into two or more series. Their object is, to accustom the edge
trees of the wood on the leeward side to a free position, so that
they may develop into storm-firm trees, and be able to
witlistand the effects of strnnf' winds, when the wood on the

SEVERANCE CUTTINGS. 283

windward side has been cut. An example will explain this.
A wood comprising a and h (Fig. 51), is to l)e divided into
two cutting series I. and II. To prevent the trees in II. being
thrown by wind, when I. is cut, a strip <■ is cleared some time
before cuttings in I. are commenced, so that the edge trees
along the line d — c may become storm-firm.

Severance cuttings need not be straight ; they may, if
necessary, be curved, or run along two or three sides of a
wood. The latter is necessary, w^here the prevailing wind
direction is not constant, but oscillates, say, from north-west
to south-west. The breadth of severance cuttings difters
according to species, their height growth and the strength

-^-^^A^mi^w

PREVAILING

WIND

DIRECTION.

of threatening winds : it will ordinarily range between 30 and
()0 feet.

Severance cuttings must l)e made, while the wood to be
protected is still young and capable of developing firm edge
trees ; such a development is generally no longer possi])le, after
the trees have passed middle age. They must be made some
15 to 20 years before the regular cuttings in the windward
wood are commenced. "Where danger from w'indfalls is great,
it is desirable first to clear a narrow strip, and to widen it a
few years afterwards in one or more instalments, so as
gradually to accustom the edge trees to the efTects of strong
winds. If the severance cutting is not to form a road or ride,
it is at once re-stocked, so as to avoid loss of increment, and
because the existence of a young wood in front of that to

2S4 DIVISION AND ALLOTMENT OF THE FOREST ABEA.

be protected is an additional safeguard against windfalls.
When a severance cutting is made along an existing road or
ride, it is, of course, placed to the windward of it.

If the proper time for making a severance cutting is past,
and the wood to be protected is too old, it would be a
dangerous procedure to make such a cutting. In that case it
is better to make a series of thinnings in the strip along the
edge of the wood to be protected, before cuttings in the wind-
ward wood are commenced. Whether this measure will have
the desired effect is doubtful, but it is l)etter than to risk a
regular severance cutting.

7. Tlie Sj/steui of Roads and Bides.

As already indicated, working sections, cutting series and
compartments must be separated from each other by natural
or artificial lines. Apart from suitable natural boundary
lines, such as waterpartings, watercourses, precipices, fields,
meadows, etc., roads are the best boundaries of compartments
and cutting series, because they facilitate the transport of the
produce. It is, therefore, desirable that, in the first instance,
a suitable network of roads should be designed and marked on
the ground. Eoads alone, however, rarely suffice. In some
cases roads already exist, which are not suitable for boundaries,
in others even new roads must be so laid out, that they cannot
be used as boundaries, because they must lead in the direction
of the places of consumption. Besides, in hilly or swampy
ground, they often follow a direction, which renders them unfit
to serve as boundaries.

The missing division lines are provided by a system of
rides, that is to say, by cleared strips of various breadths. A
distinction is made between major and minor rides.

a. Major Haks.

In so far as roads or natural lines are not available, cutting
series, and in many cases working sections, should be bounded

THE SYSTEM OF ROADS AND RIDES. 385

by major rides. These should run m the dh'ectioii of the
cuttings, that is parallel to the prevailing wind direction,
whenever the configuration of the ground does not necessitate
deviations.

In coppice and coppice with standards, the major rides
need not be more than (3 to 8 feet broad, unless they are used
as roads for the transport of the material. In high forest,
they must be much broader, because they are used as
severance cuttings, to induce the edge trees of adjoining
woods to become wind firm and accustomed to other climatic
influences. In the case of woods, consisting of species which
are easily thrown l)y wind, they should not be less than
30 feet broad, and if the major ride is also used as a fire line,
it may be still broader.

The edges of the woods consisting of species easily
thrown by wind, if bordering on major rides, should be
strongly thinned from an early age onward, so as to produce
strongly developed trees.

Major rides may be utilised for stacking wood. Their area
is entered as non-productive of trees; in many cases, however,
they produce grass.

In young woods, the major rides should be cut at once,
while the edge trees are capable of producing a strong
root system ; in woods, which are over middle age, only
6 to 8 feet broad lines should be cleared in the first in-
stance, which are widened to the required breadth, when
the adjoining woods are cut over.

b. Minor Rides.

Minor rides should run more or less at right angles to
major rides ; they complete the delimitation of the compart-
ments. The annual coupes will, therefore, run parallel to the
minor rides and stand at right angles to the major rides.
Minor rides need not be more than 6 to 8 feet broad, unless
they are used as fire lines.

t86 DIVISION AND ALLOTMENT OF THE FOREST AREA.

r. The Xotirorh of llldt's.

Major and minor rides together form the network or system
of rides. The laying out of it depends, especially in the
ease of shallow rooted species, chiefly on the prevailing
wind direction. In the plains, the latter can generally be
determined without much trouble. In mountainous districts,

CUTTING DIRECTION.

PREVAILING WIND
DIRECTION.

the matter is frequently beset by dithculties, because the con-
figuration of the ground may produce a local direction, which
differs from the general direction. Xo rule can be laid down
for such deviations ; the question must be studied on the spot.
The direction can frequently be recognised by the shape of
the crowns of trees, by a slanting position of the stems and,
above all, by the direction in which trees have been thrown.
As regards the latter, it must not be overlooked, that local
storms sometimes throw trees in a direction, which differs
from the ordinary direction of gales. In many cases, reliable

THE NETWORK OF RIDES. 387

information can be obtained from local people, who have lived
for some time in the locality.

The laying out of the sj^stem of rides is of great import-
ance, because it is used in the protection of the woods against
natural phenomena, and it leads to order in the management.
These advantages outweigh the loss of productive area, which
is, after all, very limited. Eegular networks of rides, with
right angles, are practicable only in the plains ; on hilly
ground they must accommodate themselves to the configura-
tion of the ground. The example on the preceding page
will illustrate this. The forest occupies a ridge, the slope
of which is indicated b}^ dotted contour lines - - - - .
The top of the ridge, being much exposed, must be
treated as a separate working section under the selection
system ; it is separated from the rest by a major ride

f^\ The slopes are treated under the compartment

system, and they are divided into two parts by the major

ride

s rr^ (y^ and (^. The numbers M^ ^2^

. . . indicate the minor rides, and 1, 2, 8 . . . the
compartments. The prevailing wind blows from the west.

The division would probably be somewhat on the following
lines : —

WorMiKj Section I. = Compartment Si/stem.
Cutting Series A comprises compartments 1 i.l' 2

„ D „ „ 5 & 6

Working Section II. = Selection Si/stem.
Comprises compartments 7, 8, and 9.
The cutting direction would be from east to west, a direction
which is indicated by the numbering of the compartments.

288 DIVISION AND ALLOTMENT OF THK FOHKST AKKA.

The coupes in coiiijiartments 1 to (5 run at right angles to

the major rides (^j and f ^ j, ov up and down the hill

side, as it is generally objectionable to let the coupes run
horizontally, even from the top gradually downwards.

8. Dcniarcaiion of tlic Dirisions of a Forest.
It is generally desirable, that all interior boundary lines
should be demarcated by boundary marks, so that they can
be recognised, if they should have become obliterated in
consequence of cuttings, windfalls, etc. For this purpose,
boundary marks may be placed at all points, where rides
cross, or where they show an angle. If straight rides are
very long, it is useful to place intermediate marks at suitable
distances. Such marks are placed on one side of the rides, so
that they may not interfere with the transport of the produce;
it is useful to choose always the same side, say the north side
of the major rides, and the east side of the minor rides.

9. Namin[i and Numherintj of the Divisions of a Forest.

The methods of naming and numbering the divisions ditier
much, Judeich recommends the following : —

(a.) Working sections receive Eoman numbers = I.,II., . . .
(/>.) Cutting series receive names and slanting capital letters

= A,B...
(c.) Compartments receive Arabic numbers = 1, 2 . . .
(d.) Sub-compartments receive small Roman letters =

1. 1. . .

(e.) Major rides receive upright capital letters surrounded

by a circle = (aJ , Tb J . . .
(_/■.) Minor rides receive small Arabic figures surrounded by

a circle = f 1 ;> ( ^ )
(See illustration on page *28(i )

NAMING AND NUMBERING OF DIVISIONS. ^89

Sometimes a number of compartments are joined into a
" block ; " if so, the latter should receive a name.

The numbering of compartments must be consecutive
throughout the working circle ; it leads to confusion to have
a separate series for each working section. The numbering
should be done so as to indicate the cutting direction.

In the French State forests the following system of
numbering the divisions was prescribed until a short time
ago:—

Working sections are numbered = L, II., III., . . .

Periodic blocks ,, ,, = 1, 2, 3 . . .

Compartments ,, ,, = A, B, C . . . with

the addition of the number of the periodic block ;
thus IV. C2 means Working Section lY., compart-
ment C in the 2nd periodic block.

F.M.

290

CHAPTER III.

DETERMINATION OF THE METHOD OF
TREATMENT.

Before the yield can be calculated and the general plan of
operations laid down, the method of treatment must be deter-
mined. The questions here involved have already been
discussed in this and in Volume II. ; the following references
will be useful : —

(1.) For choice of species, see Volume II., page 116.

(2.) For choice of sylvicultural system, see Volume II.,

page 107.
(3.) For choice of method of formation, see Volume II.,

page 261.
(4.) For choice of method of tending, see Volume II.,

pages 278—306.
(5.) For choice of rotation, see pages 194 to 205 of this

volume.
(6.) The financial aspect of forestry has been explained at
pages 151 to 165 of this volume.

The determination of the method of treatment depends
chiefly on —

(a.) The objects of management.

(/>.) The locality.

(r.) The growing stock actually existing in the forest.

{<!.) The dangers, to which the growing stock and the soil

are exposed.
{('.) The conditions of demand and supply of forest produce.
(,/'.) The supply of labour.
{(/.) The legal position of the forest, existence of rights,

privileges, etc.

CHOICE OF SPECIES AND SYSTEM. 391

The nature of these determining factors sho^YS, that no
general rule can be laid down, but that the method of treat-
ment and the general lines of management must be determined
locally on the merits of each case. In the following pages
only a few general hints are given.

1. Choice of Species.

The first step should always be to examine carefully, how
far the existing species meet the objects of management and
suit the locality. If the existing species do not answer, then
the forester should not hesitate to change them. On the
other hand, the introduction of a new species should not be
lightly undertaken, as it generally involves some loss, and
frequently introduces uncertainty as to future results. Only
species, which have been tried within a reasonable distance
and succeeded, should be chosen. The cultivation of untried
species is, in the first place, justified only on a small scale.
Above all, personal fancies must be banished from the
forester's mind.

The formation of mixed woods is of the first importance,
and its advisability should always be considered. In this
respect attention is invited to pages 71 to 88 of Volume II.

2. Si/lriciiltiiral Si/steiii.

This depends, of course, on the species, which exist on the
area, or which have been selected for introduction.

IIi(/]i forest yields the greatest quantities and generally also
the most valuable classes of major produce, as well as various
kinds of minor produce ; it is, except in the case of clear
cutting, the best system for the preservation of the quality of
the locality. On the other hand, it requires, in the case of
broad-leaved species, at least fairly good soil ; it also requires
a greater capital than other systems, owing to its greater
growing stock, accompanied, in some cases, by a low mean
annual forest per cent. The growing stock is also exposed to
many dangers, such as snow, ice, wind, insects and fire. High

u 2

292 DETERMINATION OF THE METHOD OF TREATMENT.

forest must be adopted in the case of all species, which cannot
be regenerated by stool shoots or root suckers.

As to the different kinds of high forest, clear cutting, shelter-
wood compartment system, group system, selection forest, or
their modified forms, it should be remembered, that clear
cutting is most easy to carry out, and that the selection system
is most favourable for the protection of the quality of the
locality, while the modified forms stand between these two
extremes. Again, clear cutting exposes the growth most to
dangers ; at the same time, it is generally obligatory in the
case of light demanding species. Its drawbacks can, to some
extent, be reduced by making the coupes of small extent.
Still, it should only be followed in the case of hardy
species.

The question, as to which of the forms of high forest gives
the highest returns, has been much discussed. On the whole,
a carefully carried out system of clear cutting, with a suitable
species, may be expected to give the best financial results;
the ordinary shelter-wood system approaches it in this respect,
while even higher returns have been claimed for some of its
modifications, such as the group system, the two-storied
high forest, or the system of isolated trees in conjunction
with an underwood.

In how far a locality can, under the clear cutting system,
maintain the higher returns (if any), depends on the nature
of the soil and the climate. Where these are not favourable,
one of the shelter-wood systems is certainly to be preferred.
The latter are absolutely essential in the case of species, which
are tender during early youth.

CojJjnrr woods are only possible in the case of those species
which reproduce from the stool. To do well, they require a
fairly mild climate and protected position. Coppice woods
make smaller demands on the chemical and physical pro-
perties of the soil and give quicker returns ; they require a
much smaller capital ; owing to the shortness of the rotation,
the danger of damage from outside (excepting frost and deer)

METHOD OF FOR:\rATION. 293

is much smaller, and the whole management can be more
regular and safer than in the case of high forest. On the
other hand, coppice gives smaller quantities and lower quality,
except in special cases, as for instance where tanning bark,
hop-poles, or vine-stakes are produced. Until comparatively
recent times, coppice woods paid very well, but, owing to the
fall in prices of late years, this is no longer the case in
Europe; in fact, special cases excepted, they will have to be
converted into high forest.

Pollarding gives frequently fair returns, and it can be
carried on in conjunction with agriculture.

Coppice icitli standards holds an intermediate position
l)etween high forest and coppice woods as regards the pre-
servation of the quality of locality and the capital value of
the growing stock. The comparatively free-growing standards
reach a certain diameter in a shorter time than trees in high
forest ; on the other hand, the stems are shorter and less
clean than in regular high forest, and they are more subject
to frost cracks and scorching of the bark. The yield is smaller
than in high forest, but larger than in coppice ; financially, it
generally holds a position between the two.

3. Method of Formation.

This depends chiefly on the sylvicultural system, the species
and the nature of the locality.

Natural regeneration is cheaper in itself, and, if successful,
leads to fully stocked young woods ; but, in the case of high
forest, seed-years do not always come, when they are wanted,
so that a regular progress of the regeneration may be seriousl}-
disturbed ; the loss of time, and other accompanying disad-
vantages, may more than outweigh the smaller original outlay.
Natural regeneration must frequently be augmented by a certain
amount of planting or sowing. To conduct the process of natural
regeneration by seed demands the highest skill of the forester.

Artificial regeneration generally accompanies the system of
clear cutting in high forest, but sowing and planting may also

291 DETERMINATION OF THE METHOD OF TREATINFENT.

be done under shelter-woods ; it is necessary in the case of first
afforestations, or where a change of species is contemplated.

Whether direct sowing or planting is preferable, depends
cliiffiy on the species and local conditions.

4. MrfJiod of' Tnidiuij.

This must be laid down in detail, but, as the Bul)ject has
])een fully treated in Volume II., it would only lead to
repetition to refer to it further in this place.

5. Thf Rotation.

The rotation is chiefly governed by the species, sylvicultiiral
system and the objects of management. Though the fhiancial
aspect should never be lost sight of, there are many cases,
where a departure from the financial rotation is fully justified.
This occurs where short rotations interfere with the preserva-
tion of the quality of locality, where considerations for the
production of a certain class of produce or the dictates of
political economy are of paramount importance.

:o5

CHAPTER IV.

DETERMINATION" AND REGULATION OF THE
YIELD.

As long as the owner of a forest is satisfied with inter-
mittent returns, the regulation of the yield is chiefly governed
by sylvicultural considerations, that is to say, every wood is
cut over, when it is just ripe according to the objects of
management, while thinnings are made, when they are neces-
sary. If the owner demands a sustained annual yield of
equal, or nearly equal, quantity, although the forest is not in
a normal state, the various cuttings may have to be made at
other times. All such deviations demand certain sacrifices on
the part of the owner, which differ according to the actual
condition of the forest and the objects of management.

These sacrifices are due to the fact, that the final cuttings
must be made at an age other than the normal age, as
determined by the objects of management ; even thinnings
may have to be postponed, instead of Ijeing made when the
condition of the woods demand such cuttings. This deviation
may be brought about by a surplus or deficiency of mature
woods, or by their being so situated, that they cannot be cut
over at the proper time out of consideration for the safety
of adjoining woods.

• The task of the forester in such cases is to secure a
sustained annual yield and yet to lead the forest, with the
smallest possible loss to the owner, gradually over into the
normal state, as described in Part III. of this volume. Many
different methods have been elaborated with the view of
achieving that task, which approach the subject from various
points of view. All the older methods started by considering,
in the first place, the forest as a whole, determining the yield

290 DETERMINATION AND REGULATION OF THE YIELD.

and tlien seeing, in which parts of the forest it had best be
cut. Moreover, working plans were generally prepared for a
long period of time, usually a whole rotation. Gradually a
method, which considered, in the first place, each wood rather
than the whole, was developed. It is, according to the author's
views, the most rational of all methods, and it will, therefore,
l)e described first.

Section I. — Selection or Woods for cutting in accord-
ance WITH Sylvicultural Eequirements and the
Objects of Management.

The method now to be described has been gradually
developed, since Heinrich Cotta was called to Saxony in
1811 ; it advanced by steps, until it was finally put into a
precise form by Judeich ; hence, it is now known as " Judeich's
Bestaudstvirthschaft.'" The German word " Bestand " can be
rendered into English by the word " wood," meaning part of
a forest forming a unit of fairly the same description. The
main character of the method lies in the fact, that first of
all the requirements of each wood are considered, and that
the management of the whole forest represents a summing-
up of the treatment laid down for each wood.

The first step under Judeich's method is a suitable division
of the forest into units, called woods, or compartments; next,
a general plan is sketched, to indicate the manner in which a
normal arrangement of the age classes, both as regards size
and grouping, is to be effected ; then the treatment of each
wood is determined for a limited number of years, with due
consideration of its sylvicultural requirements ; the cuttings
thus indicated are added up, and they represent the yield
during the first, say, 10 years, unless considerations for a
sustained yield in the future demand certain modifications.

It will thus be seen, that the method chiefly aims at the
establishment of a full increment and a proper arrangement
of the age classes. Not a word is said about the normal

CLEAR CUTTING IN HIGH FOREST. 297

growing stock, because this must come of itself, if the other
two conditions of the normal state have been established.

Finally, an important part of the method is, to fix the
working only for a limited number of years, and to have
revisions at regularly recurring periods, when the require-
ments of each wood are reconsidered, with due regard to the
introduction of a suitable arrangement of the age classes and
especially the introduction of small cutting series. The latter
point is of great importance, because it secures a perfectly free
hand to the manager to take each wood in hand at the right
moment.

In describing the method, the author of this manual has,
however, introduced a few changes. Judeich bases the ripe-
ness of each wood upon financial considerations; he ascer-
tains the forest- or indicating per cent., and calls a wood ripe,
if that per cent, has sunk below the general per cent. p.
This, the author considers too narrow a view to take ; the
ripeness should, in his opinion, be determined by the " objects
of management," as laid down by the owner of the forest, of
which the financial ripeness may be one, or not.

1. Ap2)lication of the Method to Clear Cutting in Hir/li Forest
and the Shelter-n'ood Compartment System.

a. The General Plan of Operations.

This is represented by a plan, which gives the division of
the forest into units of working or compartments. The latter
are marked off by natural or artificial boundary lines, as
described in Chapter II. This plan enables the forester, to
determine, in a general way, the order and direction, in which
the cuttings should proceed and the grouping together of
compartments into suitable cutting series. The latter may
be a definite arrangement, but in many cases temporary
cutting series must be designed, which will, at the time of
subsequent revisions, be gradually led over into more per-
manent groupings.

3 OS DETET^MINATION AND RErrULATION OF THE YIET.D.

b. Determination, of the Final Yield.

The liist step is, to determine the rotation in accord-
ance with the objects to be aimed at, as laid do^Yn by
the owner of the forest. How this is done lias ah-eady been
explained.

The financial rotation is ascertained by calculating the soil
rental, and the forest per cent, for a number of characteristic
woods ; in this way it is possible to determine the financial
rotation within 10 or 20 years. The rotation actually decided
on, as determined by the objects of management, may then
be compared with the financial rotation, with a view of
bringing out the financial sacrifice involved in a departure
from the latter.

The next ste]:) is, to select, with due consideration of the
desired cutting direction and the estal)lishment of suitable
cutting series, the woods where final cuttings are called for
during the period, for which the working plan is to l)e pre-
pared, say, for the next 10 years. Special care is taken not
to put down for cutting any wood, the removal of which
would expose the adjoining woods to windfall ; or where difli-
culties of transport would be encountered. Subject to the
modifications caused by these considerations, the following
areas would be selected : —

(1.) All areas which must be cut to meet sylvicultural or
protective necessities, such as the establishment of
severance cuttings, woods which must be sacrificed in
order to work up to a proper grouping of age classes
and arrangement of cutting series.
(2.) All decidedly ripe or over-ripe w'oods ; the ripeness to
be determined by the objects of management. In the
case of a financial management, this would comprise
all woods, the current forest per cent, of which has
sunk below the general per cent. p.
(3.) All woods, the ripeness of which is more or less doubt-
ful, and which may be situated in the direction of the

CLEAR CTTTTINrx IN HiriH FOREST. 299

cuttings. This includes the woods which will become
ripe during the working plan period.

The sum total of the cuttings indicated under these three
headings represents the final yield to be assigned to the period,
for which the working plan is prepared.

For small forests, or those where a sustained annual or
periodic yield is not called for, nothing further is required. It
is different in the case of extensive areas especially those,
where considerations for a steady annual income, for the
regular supply of markets, or the occupation of the staff
and workmen necessitate an approximately even annual out-
turn. Here the yield, as determined above, must be subjected
to a modifying regulator, either as regards the area to be
cut or the volume to be removed during the working plan
period.

This regulator can take any suitable shape, such as the size
of the mean annual or periodic coupe, or the yield calculated
according to volume. Judeich prefers the mean annual
coupe, as obtained by dividing the total area by the fixed
rotation. If a forest has an area of 2,000 acres and is
worked under a general rotation of 80 years, the mean

annual coupe would be equal to ^^^— — = 25 acres. During a

80

working plan period of 10 jesn's the normal cutting area for it

would amount to 25 X 10 = 250 acres. In other words,

during a period of 10 years 250 acres should be cut over, and

the areas selected for cutting should be brought within that

limit. This, however, is only desirable, if the proportion of the

age classes is fairly normal. In all cases, where considerable

deviations from the normal proportion exist, such a narrow

limit cannot be drawn, because in some cases it is highly

desirable to cut more than the normal area ; if, for instance,

too large a proportion of old or defective woods exist. In other

cases, the cuttings should be below the normal area, if, for

instance, the area of mature woods is deficient. Hence, the

regulator should give merely the maximum and minimum

800 DETER^riXATTON AND RErxFLATTON OF THE YIELD.

area to be dealt with. In the above case the area might be
given as 200 to 300 acres, or 225 to 275 acres.

As long as the total area determined under (1.) to (3.) falls
between these limits, it may be accepted as the area to be
dealt with during the first 10 years. If it is larger than the
maximum, then some of the most suitable areas enumerated
under (3.) should be held over until the second period of
10 years ; if smaller than the minimum, then possibly some
further woods may be found, which could be added to those
already placed under (3.). In extreme cases, the yield may
be kept for a number of years below the proper minimum.

Example. — Let the age classes in the above example be as
follows : —

A.ee Class.

Normal Distribulinn
of Areas.

Acres.

Real Distribution

of Areas.

Acres.

1—20
21—40

- 500

- 500

*001 700
300(

41—60

- 500

™0l 1,300
600)

Over ()0

— 500

Total = 2,000 2,000

As there is a considerable excess of old woods, the area to be
cut, or taken under regeneration, every 10 years should be

more than ^— — = 250 acres. Indeed, for the next 20 years,

H

up to 300 acres might be cut during every 10 years. The
result would be as follows : —

After 10 Years.
Acres.

After 20 Years.
Acres.

1—20

= 500

= 550

21-40

= 350

= 425

41—60

= 500

= 425

Over 60

= 650

= 600

Ti

Dtal

= 2,000

i2,000

CLEAR CUTTING IN HIGH FOREST. 301

After that, 250 acres might be cut durmg every 10 years,
so that, at the end of 30 years in all, the distribution of the
age classes would be : —

After 3U Years
Age Class. Acres.

1-20 = 525K^^2

21—40 = 487]

41-60 = 425) ,^gg

Over 60 = 563 >

The deviations from the normal distribution still existing will
disappear by continuing to cut about 250 acres every 10 years.

r. The Iiitermediaic Yields.
The limit between final and intermediate yields is not
always quite clear. In a general way it may be said, that —

(1.) Final yields comprise —

(a.) All returns obtained from woods, which are put down
for regeneration during the first period.

(h.) All returns from other woods, which, in consequence of
unforeseen causes, are so large, that the regeneration of
the woods becomes necessary, whether the final cutting
9ver is done during the working plan period or
later on.

(2.) Intermediate i/ields comprise all other returns derived
from —

(a.) Cleanings.

(h.) Ordinary thinnings.

(c.) Pruning, cutting of standards, etc.

{d.) Accidental cuttings, such as dry wood cuttings, wind-
falls, etc., in so far as they do not occur in the areas
put down for regeneration during the working plan
period, or are of such extent that they come under
sub-head (1 b.), above.

The woods to be cleaned and thinned are put down according
to their areas. The quantity of intermediate yields is best

302 DETERMINATION AND REGULATION OF THE YIELD.

estimated according to past local experience with due con-
sideration of the condition of the several woods. Where the
necessary local data are not availa])le, the most suitable
average data obtained elsewhere must be used.

The question, whether the regulation of the yield should
refer to the final cuttings only, or include the intermediate
cuttings, has been much discussed. There can be no doubt,
that the systematic working of a forest should, in the hrst
place, be regulated by the final cuttings. At the same time
the intermediate yields may be utilised to equalise any
unavoidable inequalities of the final yield. Under any
circumstances, l)oth classes of yields must be estimated, so as
to ascertain the probable quantities of produce, which will be
placed upon the market, and to prepare the annual budgets.

iL Sqia ratio II of Yield info Classes of J 'nut lire.

The yield should be separated according to classes of
produce, as it is brought into the market, say as timber and
firewood, or large timber, poles, mining props, fagots, etc.,
each being given in solid cubic feet. This separation should
be based upon locally obtained proportional figures.

It is also desirable, to give separately the yield of the
important species, as for instance oak, other broad leaved
species, larch, other conifers, etc. In India, teak, sal, deodar
and some other valuable species should always be given
separately.

2. Coppice ]]'u()(h.

In the first place, the rotation must be determined. By
dividing the total area (real or reduced) by the rotation, the
size of the annual coupe is obtained.

Next, the area is divided into as many coupes as the rotation
contains years, taking into consideration all matters infiuenchig
a proper arrangement of the age gradations, more especially
the requirements of transport.

If a coppice forest is so extensive, that it is desirable to cut

COPPICE AND COPPICE WITH STANDARDS. 308

in several places in each year, while the rotation remains the
same throughout, equal to r, it is first divided into a corre-
sponding number of working sections and then each of the
latter into r annual coupes.

If the several working sections are treated under different
rotations, a separate account must be kept for each ; for
instance, oak coppice worked for bark alongside of coppice of
an entirel}^ different nature, such as alder coppice.

In order to obtain, as far as practicable, equal annual returns,
the calculations should be made with reduced areas, though
it is not necessary to go into very minute details. The
different coupes should be marked on the ground.

The final yield is ascertained by estimating the returns,
which may be expected from the areas to be cut over during
the working plan period.

Intermediate returns consist of all cuttings made on areas
not put down for cutting over during the working plan period.
As a rule, they are not of much importance. Their amount
should be estimated according to average local figures.

o. CuppifC tvitJt StandanU.

The first step is to lay down a division into annual coupes
in the same way as for simple coppice ; this division regulates
the yield of the underwood.

The normal yield in overwood, as given on page "236, can
serve only as a very general guide ; in reality, the management
of the overwood partakes of the character of forest gardening
or selection fellings. Hence, this sylvicultural system offers
considerable difficulties, if the areas are extensive. Any but
a very elastic method of fixing the yield would be out of place.

The determination of the final yield in overwood is effected
by estimating, on the areas to be dealt with during the working
plan period, the probable amount of material to be taken out.
In doing this, the forester is guided by sylvicultural considera-
tions, and the degree of ripeness of the several standards.
Whenever fairly equal annual, or periodic, returns are aimed

304 DETERMINATION AND REGULATION OF THE YIELD.

at, the forester should see, that not more is cut during the
working plan period, than is likely to be produced again by
increment during the same space of time, allowance being
made for any surplus or deficiency of growing stock.

The sum total of the quantity of overwood thus ascertained
and of the underwood makes up the expected yield during
the working plan period. The executive officer should, how-
ever, not be forced to abide absolutely by that estimate, but
be permitted to modify it within certain limits in accordance
with requirements, as they may become manifest in the course
of the period, for which the working plan is drawn up.

Intermediate cuttings occur on the areas not put down for
final cuttings. Their amount should be estimated in a sum-
mary way on the basis of local experience.

4. The Selection Forest.
The selection forest resembles the coppice with standard
forest, since the several age classes are mixed on the area in a
similar manner. In the case of selection forests, it is desirable
to go round the whole area within a moderate number of years,
that is to say, to select again trees for felling over the same
portion of the area after a moderate interval, thus avoiding
having to cut too much at one time.

The area to be taken in hand annually is obtained by
dividing the total area by the number of years, /, fixed as
above. By multiiDlying the quotient by 10, the area to be
dealt with during the next ten years is obtained. On the area
thus fixed, all mature trees are cut and the necessary thinnings
in the younger age classes made. The age of maturity, or the
rotation, is fixed as in the case of clear cutting in high forest
or the shelter-wood compartment system.
Example : —

Area of a selection forest = GOO acres,

Eotation = 120 years,

/ = 20 years,

Annual cutting area = — — = 30 acres.

CHANGE OF SYSTEM. 305

Area to be dealt with during the first ten j-ears = 300 acres.
On this area all 120 jenvs old trees are cut, as well as the
necessary number of younger trees, so as to reduce them to a
suitable proportion. As it is a laborious matter to ascertain
the age of the trees, the diameter (or girth) at maturity is sub-
stituted for the age. For instance, instead of an age of
120 years, it may be laid down, that trees with a diameter
of, say, 2 feet at chest-height above the ground shall be
considered mature. At the same time it must be remembered,
that some trees will never grow beyond a certain size. These
must be cut, even if they have not reached the minimum
diameter (or girth) laid down for mature trees.

The areas, to be dealt with in each period of, say, 10 j^ears,
should be marked off on the ground ; in some cases even the
annual coupes may be marked.

A distinction between final and intermediate returns is very
difficult in the case of selection forests.

To attempt a regulation of the expected returns by volume,
seems of doubtful utility. At any rate, to fix the yield in
material only, whether in cubic feet or number of trees, is a
risky procedure, which may lead either to over- or under-
working of the forest. By far the best plan is to fix the yield
by area, and to determine the minimum size of the mature
ti-ees to be cut. This area should not be exceeded. With this
reservation, the probable amount of final returns to be cut
may be estimated according to Brandis' or von Mantel's
methods to be described hereafter. The same precaution, as
in the case of coppice with standards, is here necessary ; care
must be taken not to cut more, than will be replaced by
increment, whenever fairly even annual or periodic returns
are expected.

5. Cliaiific front one Sylricultural System to another, called
a Concersion.

As a general rule, the returns during the period of con-
version are likely to be uneven in amount. If the new
F.:\i. X

30R DETERMINATION AND REGULATION OF THE YIELD.

system requires a higher rotation, than that to be abolished,
the returns will also be smaller, until the conversion has been
completed, and possibly even longer. Hence, before a change
of system is undertaken, it should be carefully considered,
whether the advantages expected from the change are likely
at least to compensate for the unavoidable disadvantages.

The number of conversions from one sylvicultural system
to another, which are conceivable, is considerable, and it is
impossible to give any general rules of procedure. Whatever
the nature of the conversion may be, the only sure basis for the
determination of the expected yield is the annual cutting area.
Hence, the consideration of a few special cases will bring out
the essential points to be considered in each conversion : —

a. Conversion of the High Forest Selection System into the High
Forest Compartment System.

This conversion necessitates the substitution of even aged
for uneven aged woods, and it frequently involves the cutting
over of trees at an age differing from that, which is most
advantageous. To justify this sacrifice the compartment
system must offer decided advantages over the selection
system.

It is usual to fix one rotation for the conversion, to divide
the rotation into periods of even lengths, and to allot to each
period a corresponding portion of the total area, with due
consideration of the condition of the several woods. As a rule,
the several age classes are not evenly distributed over a
selection forest; generally, more old wood is found in some
parts of the area, and more young wood in others. This
fact is taken advantage of in the allotment, that is to say,
Period I. receives those woods which contain most old trees,
especially those with little increment. Period H. receives
the woods which are richest in middle aged trees, and so on.
In effecting this allotment, a proper grouping of the future
age classes must not be overlooked.

£ra»ip/c. ^Assuming the rotation to be 120 years and the

CHANriE OF SYSTEM.

307

whole area allotted to three periods of 40 years each, the
^Yorking during the lirst rotation would be as follows: —

During Period I. — Part A, approximatel}' equal to one-third
of the total area, will be regenerated, either naturally or
artificially, or by a combined method. From part B any
over mature trees are removed by selection, the necessary
thinnings made and blanks, if any, stocked. In part C over
mature trees are removed, blanks stocked, incomplete young
woods filled up and others thinned.

Diiriufi Period II. — Part B will be regenerated. In part A
any remaining shelter trees will be removed and probably
thinnings commenced. In part C over mature trees will be
cut and thinnings made wherever necessarj'.

During Period III. — Part C will be regenerated. In
part B any remaining shelter trees will be cut and thinnings
commenced. In part A the necessary thinnings will be made.

The following table will farther illustrate the procedure : —

Period.

Part A.

Part B.

Parte.

I.
1—40
years.

lipfiP nr rated .

Over mature trees re-
moved.
Thinnings made.
Blanks stocked.

Over mature trees re-
moved.

Thinnings made.

Blanks stocked.

Incomplete woods
filled up.

II.

41—80
years.

Any shelter trees re-
moved.
Probably thinnings
' commenced.

Reqenerated .

Over mature trees re-
moved.
Thinnings made.

III.

81—120
years.

Thinnings made.

Any shelter trees re-
moved.

Probably thinnings
commenced.

liegenerated.

l. Co7iversion of Coj^pice iciih Slandards into thr Compaiimont
System.

This conversion is easiest effected by gradually growing so
much overwood in each coupe, that it represents a high,

x2

308 J)ETER:\riNATI()\ AND TSErJULATTON OF THE YIELD.

forest. For this purpose, the coppice ^Yith standard system
is continued for a time, but as little as possible overwood cut,
and as many poles as possible are left standing, until the area
is fully stocked with overwood. The poles thus left should,
if possible, be seedling trees and not stool shoots. Another
method is, to grow the high forest direct out of the underwood,
provided the latter contains a sufficient number of seedling
trees, and has not suffered by too much cover overhead. In
either case, a good deal of planting may be necessary-.

To prevent a great unevenness of returns during the first
rotation, the conversion will be effected only gradually, as
indicated under a.

Example. — If the future rotation of the high forest be 120
years, the work would be distributed as follows : —

Duriiui Period I., of, say, 40 years. — Convert one-third of
the area, cut very sparingly in the second part of the area.
Cut as usual in the third part.

Diiriiiy Period II., of -iO years. — Convert the second part,
cut sparingly in the third part. Thinnings will be commenced
in the first part.

During Period III., of 40 years. — Convert the third part.
Thinnings in the first part will be in full swing. Thinnings
will be commenced in the second part.

r. Conversion of a Forest of Broad-Jenrcd Sperios into a Forest of
Conifers.

An irregularly stocked forest of broad-leaved species, partly
coppice and partly coppice with standards, shall be converted
into a coniferous forest, a conversion which is indicated liy
the special conditions of the locality.

The first and most important step is, to divide the forest into
a suitable number of compartments, by laying out a system
of roads and rides suitable to the locality. These compart-
ments are then grouped into a suitable number of cutting
series, without taking into consideration the present conditions
of the several woods, but merely future requirements.

CHANGE OF SYSTEM. 309

It would be problematic to determine the rotation to be
adopted for the future coniferous forest. On the other hand,
the age should be determined, which the oldest coniferous
wood should have reached, when the conversion has been
concluded, so as to have, from that moment forward, woods of
sufficient age to cut and supply the market. This age
determines the period, during which the conversion is to be
effected, called the " conversion period." The latter must not
be too short, or else there would be no final cuttings for a
number of years, after the conversion had been completed.
Supposing 60 years were chosen for the period of conversion,
then at its close the oldest coniferous wood would have an age
of 60 years.

By dividing the total area by CO, the area is ascertained,
which should be converted annually.

In selecting the areas to be taken in hand year by year, two
considerations present themselves : —

(1.) A suitable arrangement of the future cutting series ;
and

(2.) To begin with cutting over the woods, which are poorest
in increment.

A consideration of both decides the allocation of the annual
coupes over the forest area.

Examph'. — A coppice with standard forest of 1,*200 acres
shall, in the course of 60 years, be converted into coniferous

forest. Every 10 years -— = 200 acres must be taken in

hand for conversion. In that case the yield during the first
10 years would consist oi —

(1.) The clearing of 200 acres ; and

(2.) The treatment of 1,000 acres as coppice with standards.
During the second 10 years —

(1.) The clearing of 200 acres ; and

(2.) The treatment of 800 acres as coppice wath standards.

During the third 10 years —
(1.) The clearhig of 200 acres ;

31 0 DETERMINATION AND REGULATION OF THE YIELD.

(2.) The treatment of 600 acres as coppice with standards ;

(3.) Thinnings in the oldest coniferous woods.
And so on.

It is evident, therefore, that the returns fall oft' from period
to period, in so far as the reduction is not made good by
thinnings in the young coniferous woods. This can to some
extent be modified, by not making any cuttings in the 200
acres of coppice with standards, which will come under con-
version during the next period of 10 3'ears ; in other words,
to let the material get 10 years older, than it otherwise would.

The expected yield is determined by estimating the returns
from the 200 acres to be converted and adding thereto the
necessary cuttings on the rest of the area ; the latter should
be sparingly done, so as to equalise the cuttings as much as
possible.

Section II. — Other Methods of Determining and Regu-
lating THE Yield of Forests.
The number of other methods is so large, that it is not
possible, or necessary, to describe them all in this place.
The most important ones may, according to their principal
characteristics, be grouped in the following manner: —

A. Division of the forest into fixed annual coupes.

B. Allotment of woods to the periods of a rotation.

1. According to area.

2. ,, ,, volume.

3. ,, ,, area and volume combined.

C. Regulation of the yield according to increment and

growing stock.

1. The Austrian method.

2. Hundeshagen's ,,

3. Von Mantel's ,,

4. Brandis' ,,

D. Regulation of the yield according to increment and

growing stock, combined with the allotment of areas to
the several periods of a rotation (Heyer's method).

ALLOTMENT OF WOODS TO PERIODS. 311

A. Division of Forest into Fixed Annual Coupes.

Under this method the area of the forest is divided into as
many annual coupes, as there are years in the rotation, and
each coupe marked on the ground. Every year one coupe is
cut over, giving the annual yield of final returns, to which
must be added the necessary thinnings in the other coupes.

The size of each annual coupe is =^, if the area is at once

re-stocked, or = —^, — , if each coupe lies fallow for s vears.

In either case, A may represent the actual or reduced area.

The merits of this method are small. It aims, more directly
than any other method, at the establishment of a regular series
of age gradations, which becomes normal after one rotation, if
the division of the area is based upon the reduced area of the
several parts ; but it achieves this object only by heavy
sacrifices, because the returns during the first rotation must
be very uneven, unless at the outset a proper proportion and
distribution of age classes existed. The method takes no
notice of disturbances, nor of the state of the market ; hence,
it is very rigid. Above all, it neglects to a considerable extent
the fundamental principle, that the most important measure
must always be the establishment of the normal increment
within the shortest possible period of time.

The method is applicable to coppice woods, coppice with
standards, and, with modifications, to selection forests. For
all other methods of high forests it is (|uite unsuited, except,
perhaps, for clear cutting with a very low rotation.

B. Allotment of Woods to the DiflPerent Periods of
One Rotation.

In order to remove the great rigidity of the fixed annual
coupes and to obtain a method, which is suitable for the treat-
ment of high forest, especially if managed under the shelter-
wood sj'stems, the several woods comprising a forest are

312 DETERMINATION AND REGULATION OF THE YIELD.

allotted to a number of periods. The latter are generally
from 3 to 6 in number, and each comprises from 10 to 30
annual coupes. In this way, the forest is divided into as
many lots, as there are periods in the rotation ; during each
period one of these lots is dealt with. Thus, operations
extend over the whole area once in each rotation. Devia-
tions from this arrangement occur occasionally, for instance,
if a subcompartment is not cut over, or twice cut over,
during the tirst rotation, in order to make the compartment
uniform.

It is evident, that during the first rotation the total yield is
represented by the growing stock, which happens to stand in
the forest at the commencement of operations, plus that part
of the increment which is added to it during the course of the
first rotation ; it may be equal to, smaller, or larger than the
normal yield.

An essential part uf this method of regulating the yield is
the preparation of a framework or general working plan, drawn
up for one rotation and divided into a number of periods,
showing during which period each wood is to be cut over. The
allotment can be made according to area, volume, or the two
combined, so that practically three different methods are
established, which must be described separatel}'.

1. llic Mt'tliod of Periods hi) Area,
a. Descriplion of the Method.

The woods of a forest are so allotted to the several periods
of one rotation, that each contains the same, or approximately
the same, area, called the periodic coupe.

Where few or no differences exist in the quality of the
locality in the different parts of the forest, the size of each

periodic coupe will be = — , where t represents the number of

periods in the rotation. If such differences exist, the areas
must be reduced to one common quality standard, and the size

METHOD OF PERIODS BY AREA. 313

of the periodic coupe becomes = '—^. Unless this is

done, the periodic yields in the second and follo^Ying■ rotations
will not be equal.

In allotting the woods to the several periods, that to be
dealt with first receives the oldest woods and those with the
most deficient increment, taking into consideration a suitable
arrangement of the cutting series ; the allotment to the other
periods is made according to the age of the woods, with due
consideration to a suitable grouping of the age classes. If
then the totals in the several periods differ, shiftings are made
by moving certain areas backward or forward, until each period
contains the same, or approximatel}^ the same, area.

The woods placed into the first period are measured, their
volume calculated, and the increment for half the number of

years in the period, ^, added. The total of the volume thus

obtained is divided by the number of years in the period //,
so as to obtain the average of the final annual yield during
the first period. To this amount the thinnings must be
added.

For an example see Appendix lY., A, at page 882, where the
working plan for the communal forest of Krumbach, a village
in Hesse-Darmstadt, has been given. This working plan is
being actually followed.

1). Jlerils of the Method.

The method is simple and can be applied by any intelligent
manager. It establishes the normal state within one rotation,
if no disturbing events occur. At the same time, it may yield
very uneven returns during the first rotation, though this can
be avoided to some extent by suitable shiftings. Although the
method is much less rigid than that of fixed annual coupes, it
is often difficult to produce during the first rotation a proper
grouping of the age classes.

Another disadvantage is, that a surplus of growing stock

311 DETERMINATION AND REGULATION OF THE YIELD.

may be dragged over a whole rotation, whereas it should-
be removed as quicldy as possible ; or, on the other hand,
it may take a whole rotation to make good any deficit of
growing stock.

For a financial management, the method is little adapted,
except in so far, that it introduces order into the management.
It gives only a limited latitude to the forester to hold over
vigorous woods, or to cut over those, which are deficient in
increment.

2. The MetJiod of Periods hi/ Volume.
II. Dcscripiioii of the Meihud.

The woods of a forest are so allotted to the several periods
of a rotation, that each yields the same, or approximately the
same, volume. In some cases only the final returns are thus
regulated ; in others the intermediate returns are utilised to
equalise the jdelds of the several periods.

The allotment is based upon the table of age classes ; then
shiftings are made, so as to bring woods, which have a poor
increment, early under the axe and establish, as far as prac-
ticable, a suitable grouping of age classes ; then further shift-
ings are made, so as to equalise the periodic returns. The
result represents the general working plan for the first rota-
tion. It will be observed that, in the majority of cases, the
areas placed into the several periods will be uneven, resulting
in uneven returns during the second rotation, unless a fresh
allotment is made.

Example. — In Appendix lY., B, page 388, only the final re-
turns have, for simplicity's sake, been equalised. The data
are those of the Krumbach communal forest given in
Appendix IV., A.

As the future returns have to be estimated for a whole rota-
tion, it is evident, that yield tables must be used ; accordingly,
the above general working plan has been based upon the data
for beech high forest, given at page 121. After making the

METHOD OF PERIODS BY VOLUME. 315

shiftings indicated in the general working plan, the volumes
.allotted to the several periods stand as follows : —

Periodic Yield. Annual Yield.

Period I. — 189,393 cubic feet. 9,470 cubic feet.

„ II. = 195,474 ,, ,, 9,774 „

,, 111.^173,919 ,, ,, 8,696 ,,

„ IV. = 188,240 „ „ 9,412 „

¥. = 194,845 ,, ,, 9,742 „

Total = 941,871 „ ,, 9,419

An attempt to equalise the returns further would necessitate
the cutting up of compartments, which is not desirable.
The areas placed into the several periods

Is are-
Period I. = 36"00 acres.
,, 11. = 34-02 ,,
„ III. = 27-30 „
,, lY. = 29-05 ,,
„ Y. = 33-78 ,,

Total =160-15 ,,
Mean periodic area = 32*03 ,,

It is evident, that fresh shiftings will have to be made later
on, so as to equalise the returns during the second rotation.

h. Merits of the JMhod
The method has this advantage over the method by area,
that it gives during the first rotation equal, or approximately
equal, periodic returns; it considers the interests of the present
generation more fully. On the other hand, the estimate of the
future returns is more or less problematic, so that the equali-
sation of the returns for a whole rotation ahead is a very
uncertain operation. It shares with the method by area the
disadvantage, that a proper grouping of age classes is generallj'
beset by difficulties. It also drags a surplus of growing
stock over a whole rotation.

316 DETERMINATION AND REGULATION OF THE YIELD.

Whereas the method by area estabhbhes the normal state of
the forest withm one rotation, the method b}' volume takes
several rotations to accomplish this.

As regards its financial aspect, it stands on about the same
footing as the method by area.

3. TJte Method nf Periods hjj Area and Vohuiu: condnned.

The woods of a forest are so allotted to the several periods
of a rotation, that each contains the same area and yields the
same, or approximatel}^ the same, volume.

The equalisation of the periodic areas and returns is effected,
either by adding columns for the volume to the general
working plan used for the method b}- area, or by adding
columns showing the reduced areas to the general working
plan used for the method by volume (see page 389). Shiftings
are made, until l)0th area and yield are the same, or approxi-
mately the same, in each period.

It will easily be understood, that such an equalisation is a
difficult operation, especially in a very abnormal forest; hence,
more than an approximate equalisation cannot be attempted.

The method shows some of the advantages and disadvan-
tages of the two previous methods, of which it is a combination.
Its principal disadvantage is, that a suitable grouping of age
classes is still more difficult than in the case of each of the two
component methods.

In practice, various modifications of the above three methods
have been evolved, which sometimes partake more of one and
sometimes more of another of the methods.

C. Regulation of the Yield according to Increment
and Growing Stock.

The methods coming under this heading calculate the yield
by means of a formula, which is leased on the increment laid
on and any difference, which may exist between the real and

THE AUSTRIAN METHOD. 317

normal growing stock. Having thus determined the yield, the
woods for cutting are selected from time to time in accord-
ance with sylvicnltural considerations. There is no necessity
for drawing up a general working plan for a longer period,
than suits the special requirements of each case.

Of a considerahle number of methods only the following
need be mentioned liere, as the others are of moderate
practical importance.

1. lite Anstriau Method.

{Dir Ooxtrrrr'icli^chc Camera} Ta.ratioi),')

(I. Description nf tJie Mettwd.

In the year 1788 (during the reign of the Emperor Joseph II.,
one of the most enhghtened sovereigns known in history) the
Austrian Government issued instructions regarding the as-
sessment of forests for the purpose of taxation. In these
instructions reference Avas made to the difference, wdiich may
exist between the real and normal growing stock of a forest.
This led to the knowledge, that a forest, which is expected
to give permanently an annually equal return of the normal
age and amount, must contain the normal growing stock
corresponding to the rotation and method of treatment.
Foresters speedily applied this principle to the regulation
of the yield of forests by saying, that, in order to lead an
abnormal forest over into the normal state, it is necessary to
establish the normal growing stock, in other words, to re-
move a surplus or to save up any deficit, as the case might
be. The method developed upon this basis is called the
Austrian assessment method. Authors differ as to the details
of the original method, but a general survey of the literature
on the subject gives the following rule for determining the
yield : —

" If the normal growing stock is present in a forest, then
the actual, or real, increment must be utilised ; if the real
growing stock is greater than the normal, more than the real

318 DETER:\rTX.\TTON AND REra'T,ATTO\ OF THE YTF.LD.

increment must be removed ; if the real growing stock is
smaller than the normal, less than the real increment must be
utilised, until the deficiency has been made good."

In carrying this excellent idea into effect, however, errors
were introduced, which are still upheld b}' some foresters of
the present day.

The procedure is described as follows : —
(1.) The increment is calculated as the mean annual incre-
ment of a series of years.
(2.) The normal growing stock is placed equal to the normal
final mean annual increment, corresponding to the nor-
mal rotation, muhiplied successively by the ages of all
age gradations ; the sum of all these products gives the

value G„ = / X 5, calculated for the middle of the

growing season. Here / represents the normal annual
increment of all age gradations, which is equal to the
volume of the oldest age gradation.

(3.) The real growing stock is obtained by multiplying the
real final mean annual increment by the present age of
each age gradation. For this purpose it is necessary
to determine for each wood the real final age and the
volume at that age.

(4.) The difference between the real and normal growing
stock is removed during such period as the owner, or
forester, may determine according to the circumstances
of each case.

(5.) The general formula for calculating the yield, if the
deficiency or surplus of growing stock is to be removed
in the course of a years, runs as follows : —

. 1 ^r. n IT , I real Gr. Stk.— norm. Gr. Stk.

Annual \ ield=:real Increment +

a

Y=l + ^"" ~ ^\
a

If Or<, (r,„ then the last position becomes negative.

THE AUSTRIAN METHOD. 319

b. Merits of the Method.

The method was the first, which hased the calculation of the
yield upon a knowledge of the increment and the growing
stock. It has the advantages over the previously described
methods, that —

(1.) It teaches the proportion between the real and normal
growing stock and enables the owner to remove any
surplus or deficiency at his pleasure.

(2.) It assures to the owner the utilisation of the full real
increment, whenever the normal growing stock is
present.

(3.) It distinguishes in the yield between increment and
growing stock; in other words, between the removal
of genuine annual increment and that of surplus
capital.

On the other hand, the method, as above described, has
serious drawbacks : —

(1.) The calculation of the real and normal growing stock,
based upon the final mean annual increment, is not
correct and not even safe. As, however, both are
calculated in the same manner, and one is deducted
from the other, the error is, to a great extent, elimi-
nated.

(2.) As the yield is determined by a formula, the method, if
applied rigidly, may lead to absurd results: for instance,
it may happen that a full increment takes place, that,
numerically, the real growing stock is equal to the normal
growing stock, and yet there may not be a single mature
wood in the forest tit to cut.

If the method is applied judiciously, that is to say, if —

(1.) the real growing stock is taken as that actually existing
in the forest, and the normal growing stock calculated
from a suitable yield table ;

(2.) the yield, as calculated with the formula, is modified to
suit the special conditions of each forest ;

320 DETERMINATION AND REGrLATION OE THE YIELD.

then the method is one of considerable merit. It enables the
forester to arrange the grouping of the age classes and cutting
series in the most desirable way and to do justice to all other
s^'lvicultural requirements, since it leaves him an entirely free
hand in the selection of the woods to be cut.

The method is applicable to all sylvicultural systems, but
the determination of the increment and growing stock involves
much labour. Under it, a forest is gradually led over into the
normal state, though perhaps not for a considerable period of
time ; the difference between the real and normal state will,
after the first rotation is passed, be so small, that it can be
neglected.

The sample working plan given in Appendix Y., page 890,
has been based upon the formula of this method.

2. Hundeshafjen's ISIcthod.

a. Drscripfion of the MelJ/o/I.
Hundeshagen's method of determining the yield is based
upon the idea, that the real yield must bear the same pro-
portion to the real growing stock, as that existing between the
normal yield and normal growing stock ; he thus obtains the
equation —

and

i; = G, X ~" .

In words, the real yield is equal to the real growing stock
multiplied by the normal yield and divided by the normal grow-

r,,

real growing stock is multiplied, the " utilisation per cent."
(More correctly this indicates only the rate of utilisation,

whereas the utilisation per cent, is -./^ X 100.)

L^,^

The normal yield is placed equal to the normal increment,
or equal to the contents of the oldest age gradation in a

HUNDESHAGEN S METHOD. 321

normal series of age classes. The normal growing stock is
obtained by adding up the volumes given in a suitable yield
table; by the real growing stock Hundeshagen understands
that, which is actually standing in the forest.

In applying the method, Hundeshagen does not ask for a
general working plan, except for a limited number of years ;
he is satisfied with determining the species, sylvicultural
system, general lines of management, the rotation and general
rules for the grouping of the age classes ; he leaves it to the
manager to select the woods for cutting from time to time, say
every five or ten years.

As the yield is determined by the growing stock which
happens to exist, and as this practically changes from year to
year, it would, theoretically speaking, be necessary to re-
measure the growing stock every year, but as the changes are
slow, Hundeshagen considers it sufficient, if the re-measuring
is done once every 20 or 30 years.

Hundeshagen determines, in the manner above described,
only the final returns ; he adds the intermediate returns,
estimated in a summary manner, or calculated according to
average data obtained locally.

h. Meritx of the Mpthdd.

The principal assumption of Hundeshagen is not quite
correct; at any rate there is no justification for maintaining,
that the real yield bears the same proportion to the real
growing stock as the normal yield to the normal growing
stock, because the rate of increment is not determined by the
quantity of growing stock, which stands in a forest. On the
contrary, a large growing stock, consisting of defective old
woods, may give a small increment, while a small growing
stock, consisting of vigorous young woods, may show a large
increment.

The method, if applied rigorously, may lead to absurd
measures, just in the same way as the Austrian method ;

YM. Y

822 1>ETEKML\AT10N AAD KEGULATlON OF THE YIELD.

it prescribes a definite annual yield, while not a single mature
wood may be present; or it prescribes too small a yield, when-
ever a considerable portion of the area is stocked with decrepit
old woods, which ought to be cut over as quickly as possible
and replaced by vigorous young woods. In all such cases, the
yield, as fixed by the formula, must be modified in accordance
with the requirements of each case.

The method does not distinguish in the yield between
increment and growing stock, and in this respect, it stands
below the Austrian method. Moreover, it may drag a
surplus of growing stock over even more than one
rotation.

Hundeshagen assumes, that, with the yield calculated
according to his method, the normal growing stock will be
established naturally, as the yield bears a fixed proportion to
the real growing stock; if the latter is greater than the normal
amount, more than the increment will be removed, and vice
versa. This is ordinarily the case, but not under all circum-
stances. If, for instance, both the increment and growing
stock are deficient, the yield may be greater than the incre-
ment, so that the growing stock is still further reduced, at any
rate for a time ; hence, the establishment of the normal state
may be considerably delayed.

On the other hand, Hundeshagen s method has this great
advantage, that the increment need not be determined, such
a determination being at all times beset by difficulties and
uncertainty. All that the method requires is a suitable yield
table, and the measurement of the growing stock actually
standing in the forest. Hence, the method is by no means to
be despised, if a general plan is added indicating the grouping
of the age classes to be aimed at. For the rest, it leaves a free
hand to the manager to shape the management in accordance
with the requirements of each case, as long as the volume
determined by the formula need not be rigorously cut. It
may reasonably be assumed, that Hundeshagen himself
expected this.

VON mantel's method. 333

3. Von ManteVs Method.
Von Mantel, in arranging for the speedy determination of
the yield of certain forests in Bavaria, laid it down, that this
should be done according to the formula —

Annual Yield = I^eal Growing stock of the forest _ G^„,
Half the numl)er of years in the rotation r

2"
This formula rests upon the same basis as Hundeshagen's
method, if for the latter the normal growing stock is calculated
with the final mean annual increment as in the Austrian
assessment method. Hundeshagen's formula —

Y

= G,,

■■"^k

'

goes,

ni

that

case, over ni

to—

Y = G,„

v

In

G,.,

I„

-I

r

2

The cutting of the yield according to Von Mantel's formula
will gradually lead to the establishment of the normal growing
stock, as the following considerations will show : —

Supposing the real growing stock, by which Von Mantel
understands that actually present in the forest, is equal to
the normal growing stock, then his formula goes over into —
rj<J

r
"2
The formula gives, therefore, the correct yield, provided the
increment is normal.

If the actual growing stock is smaller than the normal, say

G,,„i = — x, then the

A

Yield = ^ = / - '^-^^ = / - -,

r r J-

2 2

which means, that less than the increment is cut.

y2

324 DETERMINATION AND REGULATION OF THE YIELD.

Supposing, that the real growing stock is greater than the

r X /

normal : ^„r,,„, = — - — + ./• ; then.

r r

2 2

more than the increment will be cut, so that the surplus of
growing stock will gradually disappear.

All these assumptions depend, however, on the supposition
that the normal increment is laid on. If the increment is
deficient, the abnormal state may be further increased, until
the increment has reached its normal size.

The merits of the method are approximately those of
Hundeshagen's method. It introduces an additional inaccu-
racy by being based on the assumption, that the normal

I X r
growing stock is = — - — . On the other hand, the normal

A

growing stock and normal yield need not be determined ; in
other words, the method can do without yield tables. It is
only necessary to measure the growing stock, and to determine
the rotation.

The method is very simple, and it is specially suited for
determining the yield of selection forests.

4. Brandis' Method.

The method to be described under this head will be best
understood by indicating the circumstances, which lead to its
elaboration.

Doctor (now Sir Dietrich) Brandis, on being appointed
Superintendent of the Pegu forests in Burma in 1856, found
himself confronted by enormous areas of teak forests in
danger of being heavily overworked. These forests contained
teak in varying proportions, but on the whole to a limited
extent, which has since been ascertained to amount to perhaps
10 per cent., while about 90 per cent, of the growing stock

BRANDIS' METHOD. 325

consisted of species, which at that time had no market value.
Indeed, the latter were allowed to be removed free of charge
without let or hindrance. Moreover, even teak trees required
to be of a certain size to make their extraction really remunera-
tive. At that time it was considered desirable, that no teak
tree should be removed, unless it had reached a circumference
of 6 feet, or roughly a diameter of 2 feet, measured at 6 feet
from the ground. Trees of that girth and above were called
trees of the first class.

Under these circumstances, Brandis' object was to ascertain,
as quickly as possible, the number of first class teak trees,
which might be removed annually, without exposing the forests
to deterioration. For this purpose he designed a method, by
which he ascertained —

(1.) the number of first class trees in the forests ;

(2.) the time which it takes to replace them.

By dividing the number of first class trees ascertained under
(1.) by the number of 3'ears ascertained under (2.), he calculated
the maximum number of trees, which it was permissible to
cut annually.

It will thus be seen, that the volume of marketable growing
stock was ascertained, and that this was removed at such a
rate as at least to maintain it ; in other words, the maximum
yield was fixed at that quantity of marketable timber, which
reached maturity every year, thus maintaining the mature
growing stock in the forest and utilising the actual increment.
With the view of utilising an excess of mature material it was
laid down, that, if the proportion of first class trees appeared
excessive as compared with the younger classes, extra cuttings
might temporarily be made, and i-ice versa ; hence, the method
is one based on increment and growing stock. Various safe-
guards were added, such as an allowance for trees, which it did
not pay to extract ; where few second and third class trees
existed, some first class trees were left standing to provide
seed for regeneration ; immediately along the banks of streams
cuttings were made very sparingly, etc.

826 DETERMINATION AND REGULATION OF THE YIELD.

For the rest, the method leaves a free hand to the forester,
who arranges the cuttings with due regard to sylvicultural
requirements and a proper succession of the different coupes.

The numher of trees of the several size classes were
originally ascertained by counting, or measuring, them along
narrow strips, generally 100 feet broad, laid through the
forest along the line of march (called " linear valuation
surveys"). From the contents of these sample strips (or
plots), the contents of the blocks, or forest, were calculated.
The rate of increment was determined by counting the con-
centric rings on a sufficient number of stumps, thus ascer-
taining the average number of years, which a teak tree takes
to reach the limits of the several size classes.

The original method was subsequently further elaborated,
so that the sample plots are now systematically arranged over
the area, with the view of obtaining correct data for the
number of trees in the several blocks of the forest. The
cuttings, based on these data, were also localised : in other
words, an area check was added to the calculated yield, so as
to guard against over or under cutting.

The method does not claim to be theoretically quite correct,
but it is correct enough, wherever large areas have to be dealt
with in a short time. It works expeditiously, and, if judiciously
applied, prevents a deterioration of the forest. Had it not
been for this method, the valuable teak forests of Lower
Burma might have been exhausted, before their sustained yield
capacity had been ascertained. It is a method to be strongly
recommended for adoption in countries, where systematic forest
administration is in its earlier stages, and where only a limited
number of species are as yet of commercial value.

D. Regiilation of the Yield according to Increment and
Growing Stock, combined with the Allotment of
Areas to the several Periods of a Rotation.

This method was originally elaborated by Carl Heyer, and
classed under C, as it rested on the xlustrian method.

HEYER S METHOD. 327

Subsequently it was further developed, especially by Gustav
Heyer, until it became the combination indicated in the above
heading: it is generally known as " Heyer's method."

1. Theory of the Method.

The theory of Heyer's method is as follows : —

{(I.) To arrange all woods into a general working plan
according to periods, so that each period contains the
same, or approximately the same, area. The object of
this arrangement is, to equalise the increment during
the second and subsequent rotations.

(h.) To equalise the real and normal growing stock, if any
difference should exist, in such manner and within such
time, as may be indicated in each case and approved by
the owner.

(c.) To utilise the real increment, calculating the mean for
a series of years, plus or minus the quota of growing
stock determined under (^).

It is obvious, that these objects can be realised only by a
complicated procedure, and even then only approximately,
because changes in one direction disturb the balance in
another.

2. Practical Application of the MetJiod.

{a.) The first step is to allot, by means of the table of age
classes, all woods to the several periods, and to equalise
the areas by suitable shittings, us indicated under the
method of periods by area ; care being taken to allot
the woods, as far as this is practicable, with due con-
sideration to sylvicultural requirements, and a proper
distribution of age classes.

(&.) The real increment is placed equal to the real final
mean increment, for which purpose it is necessary to
determine the final age of each wood (which may differ
from the normal final age) and its probable volume at

328 DETERMINATION AND REGULATION OF THE YIELD.

that age ; the latter divided by the former gives the
mean annual increment. In order to avoid having to
calculate the increment year by year, it is generally
calculated for a number of years, which may be called
a'. If an abnormal wood is cut over during the a' years
at an age differing from the normal, and a normal
wood grows up in its place, the increment must be
calculated separately for each part of a' years.
{(-.) The normal and real growing stocks are calculated as
for the Austrian method ; the former is placed

= — - , where / represents the normal final mean
'A

increment ; the latter is obtained by multiplying the

real final mean increment of each wood by its age.

The difference between the real and normal growing

stock is removed, as may be approved by the owner,

say, in equal amounts in the course of a years.

{(1.) The theoretical yield is then fixed by the formula —

y _ Real Increment of a' years , G,,,a — Cr„„,,„

a a

If d' is placed equal to a, that is to say, if the real

increment is calculated for the number of years, during

which any difference between the real and normal

growing stock is to be removed, the above formula

goes over into —

{e.) The next step is to ascertain, whether the woods
preliminarily placed into the several periods are suf-
ficient to meet the yield during each period, as cal-
culated by the formula under id), or whether they
contain too much or too little volume ; in the latter
case, suitable shif tings must be made, which neces-
sitate, of course, fresh calculations of the increment
and real growing stock, as the final ages of some of

HEYER S METHOD. 329

the woods are thereby altered. This process is con-
tinued until the requirements of the method are
realised, that is to say, until each period contains the
same area, and, at the same time, the volume neces-
sary to meet the yield as calculated under (d). As
already indicated, the forester must, in this respect, be
satisfied with approximate results.
(/.) The regulation of the yield is restricted to final returns.
The intermediate returns are estimated only for the
first period, or part of it, by means of yield tables, or
past experience, and added to the final yield.

3. Merits of the Method.

The method is one of great precision. On the other hand,
it is very complicated, and it calculates the increment, as well
as the normal and real growing stock, incorrectly, as in the case
of the Austrian method. The latter objection could be removed
by using suitable yield tables, instead of the final mean
annual increment, for the calculation of the increment and
normal growing stock, and by measuring the growing stock
actually standing in the forest. Nevertheless, the method
involves great labour, and the necessary calculations are of
an uncertain nature.

830

CHAPTER V.

CONTROL or EXECUTION AND RENEWAL OF
WORKING PLANS.

It is not sufficient to prepare a working plan ; it is also
necessar}' to see, that its provisions are carried out ; and when
the period, for which it lays down the management of a forest,
has come to an end, a new, or rather a revised, plan must be
prepared.

As the preparation of a iirst working plan is to some extent
based upon incomjilete data, it is of importance to keep a
careful record during its execution, so as to eliminate in the
course of time all doubtful elements. Apart from this, changes
in areas or in other respects may occur, which must be noted.
The work of control and renewal comprises, therefore, three
distinct operations : —

(1.) The record of changes as they occur.

(2.) The record of works.

(3.) The preparation of revised working plans from time to
time, or renewals.

1. Record of Lliaiitjea.

{((.} All changes in the areas must be recorded. Part of the
area may be sold or exchanged, or additional areas
bought ; areas, hitherto used for the production of wood,
may be set aside for other purposes, or rirr versa. The
progress of the cuttings may cause alterations in the
allotment of areas ; natural phenomena may produce
changes, such as floods, landslips, etc. All such changes
should be noted at the close of each year, in the maps
as well as in the tables of areas.

RENEWAL OF WORKING PLANS. 331

(b.) All final cuttings should be entered on the record and
the maps.

2. Record of Works.

The record of works has for its object —

(a.) To give a general view of all cuttings in the forest and

their distribution over the several woods or compart-
ments.
(/>.) To give the means of comparing the provisions of the

working plan with the execution or actual results.
The special shape to be adopted depends on local circum-
stances, but information on the following points is required : —
(1.) Result of each cutting according to quantity and amount

realised by its sale.
(2.) A comparison of the estimate with the actual results.
(3.) The harvest of minor produce according to receipts and,

if possible, quantity.
(4.) The data showing the net results of management. For

a sample see the table on pages 332 and 333.
(5.) The means of following up the history of each wood

or compartment, as illustrated in Appendix V., page

396.

3. Iieneiral of Working Plans.

The renewal may, in some cases, amount to an entirely new-
plan ; but in the majority of cases much of the work done on
the first occasion can be used again, only subsequent changes
being noted.

The most important part, of what remains from the pro-
visions of the first working plan, is the allotment of areas, or
the order of cuttings then initiated ; but even this frequently
requires modification.

The task at a renewal is, strictly speaking, the same as on
the first occasion, except that a good portion of the work need
not be done over again, and that the experience gained during

332 EXECUTION AND RENEWAL OF WORKING PLANS.

Table of Yield, Receipts

Wood Sold, in Solid Cvbjc
Feet.

Receipts, Shillings.

Ex-

Year.

Aiea,
Acres.

Timber.

Fire-
wood.

Bark.

Total

From
Wood.

From
Minor
Pro-
duce.

Total.

Har-
vesting

of
Wood.

Har-
vesting
Minor
Produce.

1891
1892

1900

Total...
Annual i
Average i

253

12,300

7,000

100

19,400

7,600

400

8,000

1,200

100

253

130,000
13,000

70,000
7,000

1,000
100

201,000
20,100

75,000
7,500

4,000
400

79,000
7,900

14,000
1,400

900
90

the past perioil makes tliat task a much easier one than on the

first occasion. Hence it may l)e indicated as follows : —

{(I.) Investigation of the manner in which the provisions of

the former working plan have been carried out, whether

there were reasons for departing from them, and, if so,

what they were.

(h.) Investigation of the extent to which the provisions of

the former working plan were judicious and appropriate.

RENEWAL OF WORK rya PLANS.

333

AND Expenses

PEN8E8. SHILLIKOB. ; SruKo's.

Forest Capital,
Shillikgs.

Per-
centage
given by
Forest
Capital
during

Year.

Re-
marks.

Form-
ation
& Im-
prove-
ment.

Ad-
miuis-

tra-
tion&

Pro-
tection.

Taxes,
&c.

Mis-
cella-
neous.

Total.

Total.

Per
Acre.

Soil.

Growing
Stock.

Total.

200

400

i200

100

2,200

5,800

22-92

31,100

128,700

159,800

3-63

2,100
210

4,000
400

2,000
200

1,000
100

24,000
2,400

.55,000
5,500

21-74

31,100

128,700

159,800

3-44

(c.) Preparation of a new working plan, based upon —
(1.) The old working plan.
(2.) The corrected records and maps.
(3.) The results of past yields in money and material.
(4.) The account of past works of formation, tending,
and improvement.

335

APPENDICES.

APPENDIX I.

A. Area of circles for diameters ranging from 1 inch to

60 inches.

B. Sum of the areas of circles for diameters ranging from

1 inch to 48 inches,
or,

Volume of cylinders for diameters ranging from 1 inch
to 48 inches and any length.

Example :

Find the area of 24 circles of 15 inches diameter.

Square Feet.
Area of 20 circles = 10 x 2-4544 = 24-544
Area of 4 circles = 4-9088

Total = 29-4528

Find the volume of a log 24 feet long with a mean
diameter of 15 inches.

Cubic Feet.
Volume of a log 20 feet long = 10 x 2-4544 = 24-544
Volume of a log 4 feet long = 4-9088

Total = 29-4528

336

APPENDIX I.

A.

lliEA (It

OlKC

LES FUK

Diameters

Diam.
in

inches

Area of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

Diam.

in
inches

^U-ea of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

10

0-005r,

20

0-0218

30

00491

40

0-0873

50

0-1364

1

•0067

1

•0240

1

•0524

1

-0:il7

1

-1418

2

■0079

2

•02G4

2

•0559

2

•ni)(;;5

■2 -1474

3

•0092

3

•0289

3

•0594

3

•1009

H -1532

-t

•0107

4

•0314

4

•0631

4

-l(i5(;

4 j -1590

5

•nl2:5

,-,

•0341

•0669

5

•1105

5 -1650

6

•(•140

G

•03(;9

6

-0707

G

-1154

r,

-1710

7

•0158

7

-0398

7

-0747

7

-1205

7

•1772

8

•0177

8

•0428

8

-0788

8

•1257

8

-1835

9

•0197

9

•0459

9

•0830

it

•1310

9

•1899

110

o-6r)00

120

0-78.-.4

130

0-9218

140

l-OC'.IO

15-0

1-2272

1

•(5721

1

•7986

1

•93G0

1

1-OS43

1

1 -2437

2

•0842

2

•8118

2

•9504

2

1-0997

2

1-2602

3

•(;9G5

3

•8252

3

-9648

3

1-1153

3

1 -2768

4

•7089

4

•8387

4

-9794

4

1-1309

4

1 -2936

5

•7214

5

-8.523

5

-9941

5

1-1467

5

1-3104

G

•7340

i;

•8GG0

G

1-008T

G

1-1G2G

6

r3274

7

•7467

7

•8798

7

1-0237

7

1-1785

7

r3444

8

•7595

8

•8937

8

1-0387

8

1-1946

8

r36l6

9

•7724

9

-9077

9

1-0538

9

1-2108

9

1^3789

210

2^4053

220

2-G398

230

2-88.52

240

3-1416

25-0

3^4088

1

2^4283

1

2-6G38

1

2-9103

1

3-1G79

1

3-43(;i

2

£•4514

2

2-G880

2

2-9356

2

3-1942

2

3^4636

3

2^4745

3

2-7122

3

2-9610

3

3^2207

3

3-4911

4

2-4978

4

2^7366

4

2-9864

4

3-2471

4

3-5188

5

2-5212

5

2^7611

5

3-0120

5

3-2748

5

3-5465

6

2-5447

6

2-7857

6

30377

6

3-3006

G

35744

. 7

2-5684

7

2-8104

7

3-0635

7

3-3275

7

3 -6024

8

2-5921

8

2-8352

8

30894

8

33545

8

3-G305

9

2-6159

9

2-8602

9

3-1154

'

3-3816

9

3-G587

40

8-7266

41

9-1684

42

9-6211

43

10-0847

44

10-5592

50

13-6354

51

14-1863

52

14-7480

53

15-3207

54

15-9043

60

19-6350

The circles of full inches were calculated with logarithms

APPENDIX I.

337

OF 1

Inch to 60 Ikches.

Diam.

in
inches

Area of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

Diam.

in
inches

Area of
circle in
square ft.

60

0-19G3

70

0-2673

8 0

0-3491

90

0^4418

100

0-5454

1

•2029

1

•2750

1

•3579

1

•4517

1

•5564

2

•2096

2

•2828

2

•3668

2

•4617

2

•5675

3

•2164

3

•2907

3

•3758

3

•4718

3

•5787

•2234

4

•2987

4

•3849

4

•4820

4

-5900

•2304

5

•3068

5

-3941

5

•4923

5

•6014

•2376

6

•3151

6

•4034

6

■5027

6

-6129

■2448

7

•3234

7

-4129

7

•5132

7

•6245 :

•2522

8

•3319

8

-4224

8

•5238

8

•6362

9

•2597

9

•3404

9

•4321

9

•5345

9

6481

160

1-3963

170

1-5763

180

1-7671

190

1 •968:i

200

2-1817

1

1'4138

1

1-5949

1

1-7868

1

1-9897

1

2-2036

2

1-4314

2

1-6136

2

1-8066

2

2-0106

2

2-2256

3

1-4492

3

1-6324

3

P8265

3

2-0316

3

2-2477

4

1-4670

4

1-6513

4

1-8465

4

2-0527

4

2-2699

5

1-4S49

5

1-6703

5

1-8666

5

2-0739

5

2-2922

(1

1-5030

6

1-6894

(j

1-8869

6

2-0952

(i

2-3146

7

1-5212

7

1-7087

7

1-9072

7

2-1167

7

2-3371

s

1-5394

8

1-7280

8

1-9277

8

2'1382

8

2-3597

•J

15578

9

1-7475

9

1-9482

9

2 •1.599

•'

2-3825

260

3-6870

270

3-9761

280

42761

290

4-5869

300

i-JObl

1

3-7154

1

4-0056

1

4-3067

1

4-6186

31

5-2414

2

3-7439

2

4-0353

2

4-3374

2

4-6504

32

5-5851

3

3-7725

3

4-0650

3

4-3682

3

4 -6823

33

5-9396

4

3-8013

4

4-0948

4

4-3991

4

4-7143

34

6-3050

5

3-8301

5

4-1248

4-4301

5

4-7464

35

6-6813

6

3-8591

6

4-1548

G

4-4612

6

4-7787

36

7-0686

7

3-8882

7

4-1850

7

4-4925

7

4-8110

37

7-4667

8

3-9174

8

4-2152

8

4-5238

8

4 -8435

38

7-8758

9

3-9467

9

4-2456

t)

4-5553

9

4-8760

39

8-29.-8

45

11-0447

46

11-5410

47

120482

48

12-5664

49

13-0954

55

16-4988

56

171042

57

17-7206

58

18-3478

59

18-9859

of 7 places ; the iutermediate values were t'ouud by Interpolation.
F.M. Z

338 APPENDIX I.

B. Table of the Sum of Circles for Diameters of

Number of
Circles, or
Length of
Cylinder.

Diameter in Inches.

1

2

3

4

5

6

7

8

1

0-005.5

0-0218

0-0491

0-0873

0-1364

0-1963

0-2673

0-3491

2

0-0110

0-0436

0-0982

0-1746

0-2728

0-3920

0-5346

0-6982

3

0016.-)

0-0654

0-1473

0-2619

0-4092

0-5889

0-8019

1-0473

4

00220

0-0872

0-1964

0-3492

0-5456

0-7852

1-0092

1-3964

5

0-0275

0-1090

0-2455

0-4365

0-6820

0-9815

1-3365

1-7455

6

0-0330

0-1308

0-2946

0-5238

0-8184

1-1778

1-0038

2-0946

7

0-0385

0-1.526

0-3437

0-6111

0-9548

1-3741

1-8711

2-4437

8

0-0440

0-1744

0-3928

0-6984

10912

1-5704

2-1384

2-7928

9

0-0495

0-1962

0-4419

0-7857

1-2276

1-7067

2-4057

.3-1419

17

18

19

20

21

22

23

24

1

1-5763

1-7671

1-9689

2-1817

2-4053

2-6398

2-8852

3-1410

2

3-1526

3-5342

3-9378

4-3634

4-8106

5-2796

5-7704

0-2832

■s

4-7289

5-3013

5-9067

6-5451

7-21.59

7-9194

8-6556

9-4248

i

6-3052

7-0684

7-87.56

8-7268

9-6212

10-5592

11-5408

12-5664

o

7-8815

8-8355

9-8445

10-9085

12-0205

13-1990

14-4260

15-7080

(•>

9-4578

10-6026

11-8134

13-0902

111318

15-8388

17-3112

18-8496

7

11-0341

12-3697

13-7823

15-2719

16-8371

18-4786

20-1964

21-9912

8

12-6104

14-1368

15-7512

17-4536

19-2424

21-1184

23-0816

2,5-1328

9

14-1867

15-9039

17-7201

190353

21-6477

23-7582

25-9068

28-2744

33

34

35

36

37

38

39

40

1

5-9396

6-3050

0-6813

7-0686

7-4667

7-8758

8-2958

8-7266

2

11-8792

12-6100

13-3626

14-1372

14-9334

15-7516

16-5916

17-4532

3

17-8188

18-9150

20-0439

21-2058

22-4001

23-6274

24-8874

20-1798

4

23-7584

25-2200

26-7252

28-2744

29-8668

31-5032

33-1832

34-9064

5

29-6980

31-5250

33-4065

35-3430

37-3335

39-3790

41-4790

43-0330

6

35-0376

37-8300

40-0878

42-4116

44-8002

47-2548

49-7748

.52-3590

7

41-5772

44-13.50

46-7691

49-4802

52-2669

.55-1306

58-0706

61-0862

8

47-5168

50-4400

53-4504

56-5488

59-7336

63-0064

66-3664

69-8128

9

53-4564

56-7450

60-1317

63-6174

67-2003

70-8822

74-6622

78-5394

APPENDIX I. 339

1 Inch to 48 iNCHESrAND OP THE VOLUMES OF CYLINDERS.

Number of
Circles, or
Length of
Cylinder.

Diameter in Inches.

9

10

11

12

13

14

15

16

1

0-4418

0-5454

0-6600

0-7854

0-9218

1-0690

1-2272

1-3963

2

0-8836

1-0908

1-3200

1-5708

1-8436

2-1380

2-4544

2-7926

3

l-32o4

1-6362

1-9800

2-3562

2-7654

3-2070

3-6816

4-1889

-t

1-7672

2-1816

2-6400

3-1416

3-6872

4-2760

4-9088

5-5852

r.

2-2090

2-7270

3-3000

3-9270

4-6090

5-3450

6-1360

6-9815

C)

2-6508

3-2724

3-9600

4-7124

5-5308

6-4140

7-3632

8-3778

7

3-0926

3-8178

4-6200

5-4978

6-4526

7-4830

8-5904

9-7741

S

3-5344

4-3632

5-2800

6-2832

7-3744

8-5520

9-8176

11-1704

1)

3-9762

4-9086

5-9400

7-0686

8-2962

9-6210

11-0448

12-5667

25

26

27

28

29

30

31

32

1

3-4088

3-6870

3-9761

4-2761

4-5869

4-9087

5-2414

5-5851

2

6-8176

7-3740

7-9522

8-5522

9-1738

9-8174

10-4828

11-1702

H

10-2264

11-0610

11-9283

12-8283

13-7607

14-7261

15-7242

16-7553

4

13-6352

14-7480

15-9044

17-1044

18-3476

19-6348

20-9656

22-3404

.-,

17-0440

18-4350

19-8805

21-3805

22-9345

24-5435

26-2070

27-9255

(1

20-4528

22-1220

23-8566

25-6566

27-5214

29-4522

31-4484

33-5106

7

23-8616

25-8090

27-8327

29-9327

32-1083

34-3609

36-6898

39-0957

8

27-2704

29-4960

31-8088

34-2088

36-6952

39-2696

41-9312

44-6808

9

30-6792

33-1830

35-7849

38-4849

41-2821

44-1783

47-1726

50-2659

41

42

43

44

45

46

47

48

1

9-1684

9-6211

10-0847

10-5592

11-0447

11-5410

12-0482

12-5664

2

18-3368

19-2422

20-1694

21-1184

22-0894

23-0820

24-0964

25-1328

3

27-5052

28-8633

30-2541

31-6776

33-1341

34-6230

361446

37-6992

4

36-6736

38-4844

40-3388

42-2368

44-1788

46-1640

48-1928

50-2656

5

45-8420

48-1055

50-4235

52-7960

55-2235

57-7050

60-2410

62-8320 1

fi

55-0] 04

57-7266

60-5082

63-3552

66-2682

69-2460

72-2892

75-3984 '

7

64-1788

67-3477

70-5929

73-9144

77-3129

80-7870

84-3374

87-9648

8

73-3472

76-9688

80-6776

84-4736

88-3576

92-3280

96-3856

100-5312

9

82-5156

86-5899

90-7623

95-0328

99-4023

103-8690

108-4338

113-0976

z 2

340

APPENDIX II

TABLES OF COMPOUND INTEEEST.

A. Amount to which a capital accumulates with compound

interest in n years : —

C„ = C„ X 1-0//'.
Let d',, = £50 ; n = 30 years ; 2^ = 2h per cent. ; then T..,, =

50 X 2-0976 = £104-88.
If )i = 32 years, then C',.- = C„x 1-025-'" x 1-025- = 104-88 x

1-0506 = £110-19.

B. Present value of a capital to Ije realised after n years : —

Let C'„ = £80 ; n — M) j'ears ; ^j = 2| per cent. ; then C„ =
80 x -3724 = £29-79.

C. Present value of a perpetual rental, B, due every n years : — -

" l-0i;"-r
Let B = £100 ; n = 50 years ; j^ = 2i per cent. ; then C'„ =
100 x -4103 = £41-03."

D. Present value of a rental, /•, due at the end of every year,

altogether n times : —

^ r(l-Oj/'-l)
" l-0;j" x -Op •

Let r = £10 ; a = 30 years ; j; = 2i per cent. ; then C,^ =

10 X 20-9303 = £209-303.
If the rentals refer to the past ii years, the amounts in this
Table must be multiplied by the corres^Jonding values
of l'02y\ to be taken from Table A, so as to comply with
the formula — •

r(l-Oj/'-l)
-O^j
In the above example —

C„ = 209-303 X 1-025"" = £439 ;
or —

., 10 {l-025«'^ - 1) 10 X 1-0976 p , on

APPENDIX II.

341

A. Amount to which a Capital op 1 accumulates with
Compound Interest in n Years: C'„, = Co x 1 "O^;".

No. of
Years

Per Cent.

2.

■2-5.

3.

3-5.

4.

4-!5.

5.

1

1-0200

1-0250

1-0300

1-0350

1-0400

1-04,50

1-0.500

2

1-0404

1-0.506

1-0609

1-0712

1-0816

1-0920

1-1025

3

1-0G12

1-0769

1-0927

1-1087

1-1249

1-1412

1-1576

4

1-0824

1-1038

1-1255

1-1475

1-1699

1-1925

1-2155

•'

1-1041

1-1314

1-1.593

1-1877

1-2167

1-2462

1-2763

a

1-1262

1-1597

1-1941

1-2293

1-2653

1-.3023

1-.3401

7

1-1487

1-1887

1-2299

1-2723

1-3159

1-3609

1-4071

8

1-1717

1-2184

1-2668

1-3168

1-3686

1-4221

1-4775

•1

1-1951

1-2489

1-3048

1-3629

1-4233

1-4861.

1-5513

10

1-2190

1-2801

r.3439

1-4106

1-4802

1-5530

1-6289

1.-)

1-3459

1-4483

1-5580

1-6753

1-8009

1-9353

2-0789

20

1-4859

1-6386

1-8061

1-9898

2-1911

2-4117

2-6533

2.-)

1-6406

1-8539

2-0938

2-3632

2-6658

3-0054

3-3864

30

1-8114

2-0976

2-4273

2-8068

3-2434

3-7453

4-3219

8.-)

1-9999

2-3732

2-8139

3-3336

3-9461

4-6673

5-5160

40

2-2080

2-6851

3-2620

3-9593

4-8010

5-8164

7-0400

4r,

2-4379

3-0379

3-7816

4-7024

5-8412

7-2482

8-9850

no

2-6916

3-4371

4-3839

5-5849

7-1067

9-0326

11-4674

55 .

2-9717

3-8888

5-0821

6-6331

8-6464

11-2563

14-6356

fiO

3-2810

4-.3998

5-8916

7-8781

10-5196

14-0274

18-6792

65

3-6225

4-9780

6-8300

9-3567

12-7987

17-4807

23-8399

70

3-9996

5-6321

7-9178

11-1128

15-5716

21-7841

30-4264

75

4-4158

6-3722

9-1789

13-1985

18-9452

27-1470

38-8327

80

4-8754

7-2096

10-6409

15-6757

23-0498

33-8301

49-5614

85

5-3829

8-1570

12-3357

18-6179

28-0436

42-15,S5

63-2544

90

.5-9431

9-2289

14-3005

22-1122

.34-1193

52-.5371

80-7304

95

65617

10-4416

16-5782

26-2623

41-5114

65-4708

103-0347

100

7-2446

11-8137

19-2186

31-1914

50-5049

81-5885

131-5013

110

8-8312

15-1226

25-8282

43-9986

74-7597

126-7045

214-2017

120

10-7652

19-3581

34-7110

620643

110-6626

196-7682

348-9120

130

13-1227

24-7801

46-6486

87-5478

163-8076

305-5750

568-3409

140

15-9965

31-7206

62-6919

123-4949

242-4753

474-5486

925-7674

1.50

19-4996

40-6050

84-2.527

174-2017

3.58-9227

736-9594

1507-9775

200

52-4849

139-5639

369-3558

972-9039

2550-7498

6656-6863

L7292-5808

342

APPENDIX IT.

B, Present Value of a Capital of 1, to be Realised after

n Years : Co =

l-Oyj"

Xo. of
Years

= 71.

Per Cent.

2.

2-5.

3.

3 •5.

4.

4-5.

5.

1

2

4
5

0

9804
9612
9423
9238
9057

0-9756
•9518
•9286
•9060
•8839

0

9707
9426
9151

8885
8626

0

9662
9335
9019
8714
8420

0-9615
•9246
•8890
•8548
•8219

09569
•9157
•8763
•8386
•8025

0^9524

■M070
•8638
-8227
•7835

6
7
8
9
10

8880
8706
8535
8368
8203

•8623

•8413
•8207
•8007
•7812

8375
8131
7894
7604
7441

8135
7860
7594
7337
7089

•7903
•7599
•7307
•7020
•6756

•7679
•7348
•7032
•6729
•6439

•7462
•7107
■6768
■6446
•6139

15
20
25
30
35

7430

6730
6095
5521
5000

•6905
•6103
•5394
•4767
•4214

6419
5537
4776
4120
3554

5969
5026
4231
3503
3000

•5553
-4564
•3751
•3083
-2534

•5167
•4146
•3327
•2670
•2143

•4810
•3769
•2953
•2314
•1813

40
45
50
55
60

4529
4102
3715
3365
3048

•3724
•3292
•2909
•2572
•2273

3066
2644
2281
1968
1697

2526
2127
1791

1508
1269

•2083
•1712
•1407
•1157
•0951

•1719
•1380
-1107

■0888
•0713

•1420
•1113
•0872
•0683 .
•0535

65
70
75
80
85

2760
2500
2265
2051
1858

•2009
•1776
•1569
•1387
•1226

1464
1263
1089
0940
0811

1069
0900
0758
0038
0537

•0781
•0642
•0528
•0434
•0357

■0572
•0459
•0368
■0296
•0237

•0419
•0329
•0257
•0202
•0158

90

95

100

110

120

1683
1524
1380
1132
09289

•1084

•0958

•08465

•06613

•05166

0699

0603

05203

03872

02881

0452

0381

03206

02273

01611

■0293

•0241

■01980

-01338

•00904

-0190
•0153
•01220

■00789
•00508

•0124

■0097

•00761

•00467

•00287

130
140
150
200

07620
06251
05128
01905

•04036
•03153
•02463
•007165

02144
01595
01187
002707

01142
00810
00574
001028

•00611
•00412
•00279
•000392

•00327
•00211
•00136
•000150

•00176
•00101
•00066

•0000578

1

APPENDIX IT.

348

C. Present Value of a Pebpetual Rental of 1. due eveky « Years

ft «

' lOpn.

I

Numbei
of Years

Per Cent.

2.

2-,x

3.

3-5.

4.

4-5.

5.

1

50-0000

40^0000

33-3333

28-5714

25-0000

22-2222

20^0000

2

24-7525

19^7531

16-4204

14-0400

12-2549

10-8066

9^7561

3

16-3377

13^0054

10-7843

9-1981

8-0087

7-0839

0-3442

4

12-1312

9-6327

7-9676

6-7786

5-8873

5-1943

4-0402

5

9-6079

7-6099

6-2785

5-3280

4-6157

4-0620

3-0195

6

7-9263

6-2620

5-1532

4-3620

3-7690

3-3084

2-9403

7

6-7256

5-2998

4-3502

3-6727

3-1052

2-7711

2-4504

8

5-8255

4-5787

3-7485

3-1565

2-7132

2-3691

2-0944

9

5-1258

4-0183

3-2811

2-7550

2-3623

2-0572

1-8138

10

4-5663

3-5703

2-9077

2-4355

2-0823

1-8084

1-5901

IT)

2-8913

2-2307

1-7922

1-4807

1-2485

1-0092

0-9268

20

2-0578

1-5659

1-2405

10103

0-8395

0-70.S4

•0049

25

1-5610

1-1710

0-9143

0-7335

-6003

-4980

-4190

30

1-2325

0-9111

•7006

-5535

•4458

-3043

-3010

35

1-0001

-7282

-5513

-4285

•3394

•2727

■2214

40

0-8278

-5934

-4421

•3379

•2631

•2070

-1056

45

-6955

-4907

-3595

•2701

•2066

•1000

-12.52

50

-5912

-4103

■2955

•2181

•1638

•1245

-0955

-5072

•3462

-2450

•1775

•1308

•0975

-0733

(JO

•4384

-2941

•2044

•1454

•1050

•0708

-0560

05

•3813

-2514

•1715

•1197

•0848

•0007

-0438

70

•3334

•2159

•1446

•0989

•0686

•0481

-0340

75

•2928

•1861

•1223

•0820

•0557

•0382

•0264

80

•2580

•1610

•1037

•0681

•0453

•0305

-0206

85

•2282

•1397

•0882

•0568

•0370

•0243

•0101

!)0

•2023

•1215

•0752

•0474

-03O2

-0194

•0125

95

•1798

•1059

-0642

•0390

-0247

•0155

-0098

100

•IGOl

-0925

-0549

-0331

•0202

•0124

•0077

110

•1277

•07081

•04028

-02326

-01356

•00796

•00409

120

•1024

•05447

-02966

■01038

•00912

-00511

•002874

130

-08249

•04205

•02191

-01155

•006142

•003284

•001703

140

•06668

•03255

•01621

•008164

•004141

•002112

•001081

150

•05406

•02525

•01201

-005774

-002794

•001357

•0006036

200

•01942

-007217

•002707

-001029

•0003920

•0001502

•00005783

344

APPENDIX II.

D. — i'RESEXT VaLUK OF A EkKTAL OF 1, DUE AT THE ElsT) OF EVERT

Year, altogether )> times: Co=:!li — "" " ^ •
1-U/." X -0/'

Number
of Years

Per Ci.kt.

2.

2-5.

3.

3-.3.

4.

4-5.

5.

1

0-9804

0-9756

09709

0-9662

U-9615

0-9569

0-9524

2

1-9416

1-9274

1-9135

1-8997

1-8861

1-8727

1-8.594

3

2-8839

2-85G0

2-8286

2-8016

2-7751

2-7490

2-7232

i

3-8077

3-7620

3-7171

3-6731

3-6299

3-5875

3-5459

-^

4-7135

4-6458

45797

4-5150

4-4518

4-3900

4-3295

6

5-6014

5-5081

5-4172

5-3285

5-2421

5-1579

5-0757

7

6-472n

6-3494

6-2303

61145

6-0020

5-8927

5-7864

8

7-3255

7-1701

7-0197

6-8740

6-7327

6-5959

6-4632

9

8-1622

7-9709

7-7861

7-6077

7-4353

7-2688

7-1078

10

8-9826

8-7521

8-5302

8-3166

8-1109

7-9127

7-7217

15

12-8493

12-3814

11-9379

11-5174

11-1184

10-7395

b.-3797

20

16-3514

15-5892

14-8775

14-2124

13-5903

13-0079

12-4622

25

19-5235

18-4244

17-4131

16-4815

15-6221

14-8282

14-0939

30

22-3965

20-9303

19-6004

18-3920

17-2920

16-2889

15-3725

35

24-9986

23-1452

21-4872

20-0007

18-6646

17-4610

16-3742

40

■27-355.>

2.-1028

23-1148

21-3551

19-7928

18-4016

17-1591

45

29-4902

26-8330

24-5187

22-4955

20-7200

19-1563

17-7741

5(J

:U-4236

28-3623

25-7298

23-4556

21-4822

19-7620

18-2559

55

!31748

29 7140

26-7744

24-2641

22-1086

20-2480

18-6335

()0

:^4-760t

30-9087

27-6756

24-9447

22-6235

20-6380

18-9293

a.)

6-1975

31 9646

28-4529

25 5178

23-0467

20-9510

19-1611

70

:!7-4986

32-8979

29-1234

26-0004

23-3945

21-2021

19-3427

75

38-6771

33-7227

29-7018

26-4067

23-6804

21-4036

19-4850

SO

39-7445

34-4518

30-2008

26-7488

23-9154

21-5653

19-5965

85

10-7113

35-0962

30 6312

27-0368

21-1085

21-6951

19-6838

l)U

H 5869

35-6658

310024

27-2793

24-2673

21-7992

19-7523

05

12-3800

36-1692

31-3227

27-4835

24-3978

21-8828

19-8059

100

43-0984

36-6141

31-5989

27-6554

24-5050

21-9499

19-8479

110

44-3382

37-3549

32-0428

27-9221

24-6656

220468

19-9066

120

45-3554

37-9337

32-3730

281111

24-7741

.22-1093

19-9427

1 30

46 1898

38 3858

32-6188

28-2451

24-8474

22-1495

19-9648

140

46-8743

38-7390

32-8016

28-3401

24-8969

22-1754

19-9784

150

47-4358

39-0149

32-9377

28-4074

24-9303

22-1921

19-9867

2C0

49-0173

39-7134

32-2431

28-5421

24-9902

22-2189

19-9988

345

APPENDIX III

YIELD TABLES

FOR

1. High forest of Oak, compiled by Wimmenaner, chiefly for low

lands, with 6 diagrams.

2. High forest of Beech, compiled by Schwappach, for Prussia.

3. High forest of Scotch Fine, compiled by Schwappach, for North

Germany.

4. High forest of Spruce, compiled by Schwappach, for Germany.

5. High forest of Silver Fir, compiled by von Lorey, for

Wilrttemberg.

6. High forest of Larch, preliminary table used in Saxony.

7. High forest of Alder, preliminary table used in Saxony.

8. High forest of Birch, preliminary table used in Saxony.

9. Coppice forest of Alder, Poplar and Willow, table used in

Saxony.
10. Coppice forest of Oak, Beech, Ash and Birch, table used in
Saxony.

Yield tables 1, 2, 3, 4 and 5 have been prepared as explained on
pages 97 to 104. All the yield tables are for one acre of normal, or
fully stocked, wood in solid cubic feet. The data in tables 6, 7, 8,
9 and 10 refer to all wood above ground, that is to say, exclusive
of roots and stools.

To convert solid cubic feet into cubic feet according to quarter
girth measurement, take three-fourths of the volume given as
" Timber over three inches diameter at small end," or two-thirds
of the volume given under " Timber and fuel." These reductions
are sufficiently accurate for all practical purposes.

I. Quality means the best which can reasonably be expected

on good, fertile land.
II. Quality means an average quality.
III. Quality naeans the lowest quality of locality, on which the
species can reasonably be grown. It differs very con-
siderably accoi'ding to species.

346

APPENDIX III.

Yield Table foe High Forest of OAX,

.\

ajor Tart of Wood.

Minor Part of Wood, or Intermediate
Yields.

Age.
Years.

Solid Oubic Feet.

Stems.

Mean

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yield.s.

XuiiiLcr.

Basal
Area.

Sq. Ft.

V

Diam.

Inches.

y

Height
Feet. /

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber
over
.3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber
over
3 in.
diam. at
small
end.

Summary

of

col. h.

Timb.T
and
Fuel.

Summary

of
col. f.

It

a

h

c

d

c

/

[1

//

/

3

10

40

1-

12

400

20

1 . 920

70

2-4

30

560

1,430

80

870

89

4-3

46

1,700

2,430

100

430

100

480

40

.-.10

103

6-1

60

2,930

3,570

290

490

390

920

r.o

820

115

8-2

71

4,000

4,640

390

510

780

1,430

(;o

28r.

125

9-9

79

4,960

5,570

440

540

1,220

1,970

70

1S7

133

11-4

86

5,790

6,430

470

540

1,690

2,510

80

1.^7

140

12-8

92

6,530

7,220

490

570

2,180

3,080

90

188

145

14-2

97

7,220

7,890

500

570

2,680

3,650

100

114

149

15-5

101

7,800

8,540

500

540

3,180

4,190

110

98

153

16 -9

105

8,820

9,150

490

540

3,670

4,780

120

s,-,

157

18-4

108

8,790

9,660

490

530

4,160

.5,260

130

7(;

KiO

i9-(;

111

9,220

10,180

460

510

4,620

5,770

140

()8

1G3

21-

113

9,620

10,580

460

500

.5,080

6,270

150

fil

lOH

22-3

115

10,010

11,000

440

490

5.520

6, 760

160

5(!

168

23-5

117

10,390

11,420

430

470

5,950

7,230

Note on the Z'se of Form Faetora. — Calculate the volume, according to quarter-
Form Factor = 149 x 101 x -89 = 5,869 cubic feet. (See pages 60—61.)

APPENDIX III.

847

I., OK Best, Quality or Locality.

Final Yield
Solid Cubic Feet.

Form Factoi

S.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Sum of

columns

(J and

Timber
in the
round
down to
Sin.
diam.

at
small
end.

Timber
according
to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum of

columns

/ and

h.

\'olunie.
Sum of
columns
/vindj.

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of
columns

fj and /,-.

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

]

'"

"

"

P

'1

f

«

t

H

(•

400

•83

400

40

40

560

1,430

•27

•20

•68

560

56

28

1,4.30

103

71

1,800

2,860

•41

•31

•59

1,800

124

60

2,860

143

95

3,220

4,060

•48

•36

•5S

3,320

152

S3

4,490

163

112

4,390

5,1.50

•49

•37

4,780

146

90

6,070

158

121

.5,400

6,110

•50

■37

•56

6,1S0

140

103

7,540

147

126

(3,200

6,970

•51

•38

•56

7,480

130

107

8,940

140

128

7,020

7,790

■51

•38

•56

8,710

123

109

10,300

1.36

129

7,720

8,460

•51

•38

•56

9,900

119

110

11, .540

124

128

8,300

9,080

•52

•39

•57

10,980

108

110

12,730

119

127

S,810

9,690

•52

•39

•57

11.990

101

109

13,880

115

126

9,280

10,190

•52

•39

•57

12,950

96

108

14,920

104

124

9,680

10,640

•52

•39

•57

13,840

89

10(?

15,900

9^

122

10,080

11,080

•52

•39

■57

14,700

86

105

16,850

95

120

10,450

11,490

•52

•39

■58

15,530

83

104

17,760

91

IIS

10,820

11,890

•53

•40

■58

16,340

81

102

18,650

89

u;

ith measurement, of a wood 100 years old : — T'^ Basal Area x Mean Height x

348

APPENDIX III.

i

Yield Table for High Fobest of OAK,

Age.
Voars.

Major Part nf Wood.

Minor Part of Wood, or Intermediati'
Yields.

Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

1
Periodic Yields.

Summarv of
Yields.

Nuinbpr.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Heiglit.
Feot.

Timber '

over

3 in.
diam. at

small

end.

Timber
and
Fuel.

Tiiiibei-

•i in.
diam. at
small

Timber
and
Fuel.

Timber

over

Sin.
diam. at

small

end.

Summarv

of

col. h.

Timber
and
Inel.

Summarv
of ■
col. J.

fl

h

('

(I

e

/

(1

h

/

J

//

10

30

•7

10

330

20

3,r/J0

57

1-7

21

100

960

•M)

i,48r,

75

3-

32

760

1,,590

300

3( M 1

40

820

91

4-5

43

1,630

2,340

90

330

90

630

50

.-.10

103

6-1

52

2,520

3,160

200

360

290

990

60

370

112

7-4

60

3,260

3,890

270

390

560

1,380

70

280

120

8-9

67

3,940

4,570

310

400

870

1,7S((

80

230

127

10-1

72

4,600

5,230

320

410

1,190

2,190

90

190

134

11-4

77

5,200

5,840

340

410

1,530

2,600

100

IGO

139

12-5

81

5,770

6,430

350

410

1,880

3,010

110

140

144

13-7

85

6,290

6,960

360

410

2,240

3,420

120

120

148

15-0

89

6, 750

7,450

3<-i0

410

2,600

3,830

130

105

151

16-2

92

7,170

7,9UO

360

400

2,!t6o

4,230

140

93

154

17-4

95

7,570

8,330

350

390

3,310

4,620

150

85

156

18-4

98

7,960

8,750

330

370

3,640

4,990

IfiO

^'

158

19-4

100

8,320

9,150

310

360

3,950

5,350

APPENDIX III.

349

II., OR Average, Quality of Locality.

Final Yield.
Solid Cubic Feet.

F

jrm Factor

Total YieM.
Solid Cubic Feet.

Timby.-.

Timber
and
Fuel.

Tim bei
in the
round

lown to

diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum of

columns

/ and

h.

Sum of
columns
, and

Volume. ,
Sum of 1

columns
/ and

Current
Annual
Incre-
ment.

Mean
Annual
Inere-
ment.

Volume.

Sum of
columns

g and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

1

711

n

"

J>

'/

/■

.«

t

"

r

.380

MO

330

33

33

KK)

<)<;o

•08

•0(i

■80

loo

10

"

900

03

48

7(!il

1,890

•32

■24

■t((5

7(')0

0(5

1,S90

93

03

1J2()

2,r)7o

•42

■31

'()()

1.720

9(5

43

2,970

108

74

2,72U

3,520

•47

■35

■59

2,S1()

109

5(5

4.1.50

118

83

^^,rm

4,280

•49

■37

•5S

;i.s2o

101

04

5,270

112

88

1,25U

4,970

•49

•37

■57

4..S10

99

(59

(5,350

108

91

4,020

5,(540

•50

■3S

■57

5,790

99

72

7,420

107

93

5,540

(5,250

•50

■38

■57

(1,730

94

75

8,440

102

94

6,120

0,840

•51

•38

•57

7,(550

92

77

9,4 10

100

94

(;,r,,-.o

7,370

•51

•38

■57

8,530

88

78

10,380

> '-^^

94

7,110

7,8(50

•51

•38

•57

9,350

82

78 1I,2S0

90

94

7,5.30

8,300

•52

•39

■57

10,130

78

78

12,1.30

85

93

7, '.120

8,720

•52

•39

■57

10,880

75

78

12,950

82

92

8,290

9,120

■52

•39

■57

11,000

72

77

13,740

79

92

8,G30

9,510

•53

•40

1

■58

12,270

07

77

14,500

7(5

91

850

APPENDIX III.

Yield Table for High Forest of OAK,

Age.
Years.

Major Part of Wood.

Minor Part of Wood, or Intermediate
Yield.s.

Solid Cubic Feet.

Stems.

Mean.

Volume.

(ri

Solid Cubic Feet.

Period!

3 Yields.

Summai-y of
Yields.

Number.

Basal
Area.

Sq. Ft.

Diam.
Inches

Height.

Feet.

Timber

over

Sin.
diam. at

.small

end.

Timber
and
Fuel.

Timber
over
3 in.
diam. at
small
end.

Timber
and
Fuel.

Timber

over

3 in.
diam. at

small

end.

Summarj
of
col. A.

Timber
and
Fuel.

Summary

of

col. i.

a

I

e

d

P

/

fl

h

'•

J

li

10

20

•4

5

250

20

6,900

39

1-

12

630

31)

3,300

59

1-8

19

970

170

170

40

1,640

74

2-9

26

470

1,340

200

370

.'0

1,010

85

3-9

33

990

1,770

30

230

30

600

00

670

96

5-1

39

1,540

2,270

100

230

130

830

70

480

104

6-3

45

2,120

2,790

130

260

260

1,090

SO

380

112

7-4

51

2,670

3,300

160

260

420

1,3.50

m

310

118

8-4

56

3,200

3,800

190

260

610

1,610

100

2.55

124

9-4

60

3,690

4,290

210

260

820

1,870

lln

220

129

10-4

64

4,140

4,740

230

290

1,0.50

2,160

120

1%

134

11-4

68

4,570

.5,170

230

270

1,280

2,430

i:{o

1G.5

139

12-4

71

4,990

.5, .590

230

260

1,510

2,690

1 10

14.-,

142

13-4

74

5,370

5,990

2.30

260

1,740

2,950

].jO

130

145

14-3

77

.5,730

6,370

200

260

1,940

3,2)0

160

115

148

15-4

80

6,070

6,7.50

200

230

2,140

3,440

APPENDIX III.

351

III., OR Lowest, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factors.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
down to
3 in.
diani.

at
.small
end.

Timber
according

to
quarter-
girth
mea.sure-
ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum of

<'olumii«

/ and

Sum of

columns

g and

Volume.

Sum of
columns

/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

(jf and

Cun-ent
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

1

m

n

0

P

'1

;•

s

t

U

V

250

£•50

250

25

25

.130

r36

630

38

31

1,140

•86

1,140

51

38

470

1,540

•24

•IS

•70

470

47

12

1,710

57

43

1,020

2,000

•35

•26

•63

1,020

55

20

2,370

66

47

1,640

2,500

■41

•31

•61

1,670

65

28

3,100

73

52

2,250

3,050

•45

•34

■(JO

2,380

71

34

3,880

78

55

2,830

3,560

•47

•35

•58

3,090

71

39

4,650

77

58

8,390

4,060

•48

•36

•58

3,810

72

42

5,410

7(;

60

3,900

4,550

•50

■37

•58

4,510

70

45

6, 1 60

75

62

4,370

5,030

•50

•37

•57

5,190

08

47

6,900

74

63

4,800

5,440

•50

■37

•57

5,8.50

66

49

7,600

70

63

r,,220

5,850

•51

■38

•57

6,500

65

50

8,280

68

64

5,000

6,250

•51

•38

•57

7,110

61

51

8,940

66

64

5,930

6,630

■51

•38

•57

7,670

56

51

9,580

(54

64

6,270

6,980

1
•51

•38

•57

8,210

54

51

10,190

61

64

352

APPENDIX III.

3,50U
3,000

2,500

H 1
B 2,00(1

a 1,500'

n i

'^-

^ !

'A
1,00C

1
60C

1
1

II

Ill

1 \

\

I.

\^

V

\

v

\

v^

\^

V;

^Vj

^

.

.i'

1

Fio-. 53.

-Diagram showing the Xiimher of Trees per Acre in Oak
Woods of I., II., aud III. Qualities.

175

150

1 125

1 100

i 75

<

^ 50

^

-^^

^

^

-^

^

X
X

^

//

y

1^

/

V

#

/

0

/

Fig. .54. — Diagram shoAviug the Baml Area of Trees per Acre in Oak
"Woods of r., II., aud III. Qualities.

APPENDIX III.

863

au

1^;

y^

^

^

S in

/

^

1

55
Eel

/

^

^

f)

^

^

AG El

ig. o5. — Diagram sliowiug the Mean Diameter of Trees in Oak "Woods
of I., II., and III. Qualities.

120

-^

■

t
H
=^ 80

g

a CO

a

55 40

<!

20
0

y

^

^

^

"^

/

^

^

^

-^

/

/

y^

^

y^

y

y

Fig. .of). — Diagram showing the Mean Height of Oak "Woods of I., II.,
and III. Qualities.

854

APPENDIX III.

/

16,000
g 14,000
p 12,(J00

/

/

A

/

/

/

/

^

O
Q

3 10.000

/

/

/

VOLUME, m SO

/

/

/

y

y

/

/

/

X

y

y

//

/

/'

/^

^z

/

^

>^

[^

I. Quality.

11. Quality.

in. Quality.

CO 80 100 120 140 160

AGE.

Fig. 57.— Diagram showing the Total Volume per acre of Oak Woods of I., II.,
and III, Qualities.

APPENDIX III.

355

y. ^ _^

Total Volume.

Timber in the
round above 3 in.
iliameter.

Timber
according to
quarter-girth
measurement.

SO
AGE.

Fig. 58. — Diagram showidg the Total Volume, the Volume of Timber over 3 in.
diameter at the small end, and the Volume according' to Quarter-Girth Measurement,
per acre of an Oak Wood of the I. Quality.

356

APPENDIX III.

Yield Table fou High Forest of BEECIJ,

Jlinor Part of Wood, or Intermediate

Age.
Years.

Major Part of Wood.

Yields.
Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yields.

Number.

Basal

Area.

Sq. Ft.

Diam.
Inches.

Height.
Feet.

Timber

over

3 in.
diam. at

.small

end.

Timber
and
Fuel.

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber

over

3 in
diam. at

small

end.

Summary

of

col. ft.

Timber
and
Fuel.

Snmmai \
of

col. ;.

a

ft

C

d

e

/

(1

h

i

J

u

10

15

•7

6

1.50

20

2,550

40

1-7

18

540

30

1,5.50

74

3-

31

690

1,600

200

200

40

«tl0

105

4-5

45

1,940

3,000

130

510

130

710

50

<;oo

131

6-3

56

3,330

4,620

400

660

530

1,370

60

123

148

8-

67

4,570

5,840

590

740

1,120

2,110

70

316

156

9-5

76

5,640

6,970

740

860

1,860

2,970

80

249

161

10-9

85

6,560

7,890

830

960

2,690

3,930

90

201

165

12-2

92

7,360

8,690

830

960

3,520

4,890

100

166

166

13-5

98

8,05(1

9,400

860

940

4,380

5,83(1

110

142

167

14-6

104

8,630

10,000

840

940

.5,220

(5,770

120

126

166

15-C

107

9,120

10,. 520

830

910

6,0.50

7,680

130

112

165

16-5

110

9,. 520

10,950

830

910

6,880

8,590

140

100

165

17-3

113

9,S5()

11,3(1(1

S20

900

7,7(K>

9,190

APPENDIX III.

357

I., OR Best, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factors.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in tlie
round
down to
3 in.
diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

Timber only.

1

Timber and Fuel.

Sum of

columns

/and

h.

Sum of
columns
g and

i.

Volume.

Sum of
columns

/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

(/ and

Current
Annual
Incre-
ment.

Mean

.\nnual
Incre-
ment.

I

m

)l

P

a

r

s

t

M

V

150

1-67

150

15

15

540

•75

540

89

27

G90

1,800

•30

•22

•70

690

69

23

1.800

126

60

2,070

3,.-.10

•41

•31

•(!3

2,070

138

52

3,710

191

93

8.730

5,280

•45

•84

•63

3,860

179

77

5,990

228

120 i

:,Am

(',,580

•4(;

•85

-.59

5,690

183

95

7.9.50

196

183

('..880

7,830

•48

•86

-.59

7,500

181

107

9.940

199

142

7,890

8,8.50

•48

•36

•58

9,2.50

175

116

11,820

188

148

8,190

9,650

•48

•36

•57

10,880

168

121

13.580

176

151

8,910

10,340

•49

•37

•58

12,480

1.55

124

15.230

1(15

152

9,470

10,940

•50

•37

•58

13,8.50

142

126

16.770

154

152

9,950

11,430

•51

•38

•59

15.170

132

126

18.200

148

152

10,350

11,860

•52

•39

•60

16.400

123

126

19.540

134

150

10,670

12,20 J

•53

•40

•61

17,. 5.50

115

125

20,790

125

148

85S

APPENDIX III.

Yield Table for High Foeest of BEECH,

:Major Part of AVood

Mmor Part of Wood, or Intermediate
Yields.

Tears.

Solid Cubic Feet.

Stem-s.

Mean.

1

Volume.

Solid Cubic Feet.

Periodic Yields.

' Summary of
Yields.

Timber

Number.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Height.

Feet.

Timber

over

Sin.
diam. at

small

end.

Timber
and
Fuel.

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

over
Sin.
diam. at
small
end.

Summarj-

of

col. A.

3

Timber
and
Fuel.

Summary

of

col. i.

a

in

h

c

d

e

/

9

h

i

Ic

10

•5

5

130

20

28

1-3

13

400

30

2,070

53

2-2

23

90

890

40

1,:U)0

81

3-3

33

940

1,790

230

230

:..

'.170

104

4-4

43

2,000

2,830

90

330

90

560

(iu

730

121

.0-5

r,2

2,920

3,800

270

370

360

930

70

.".SO

131

6-4

60

3,720

4,660

330

410

690

1,340

SO

4(;u

137

7-4

67

4,430

5,400

360

440

1,050

1,7S0

90

370

138

8-3

73

4,960

.5,930

460

.540

1,510

2,320

100

300

138

9-2

79

.5,340

6,320

560

640

2,070

2,960

110

•l-,()

\m

10-

84

.■.,620

6,590

600

690

2,67(1

3,650

120

210

1 •?,:,

10-9

88

r.,8G0

6,840

570

660

3,240

1,310

i:io

17.>

134

11-S

91

6,070

7,090

530

610

3,770

4,920

110

loO

132

12-7

93

6,260

7,300

490

570

4,260

5,490

APPENDIX III.

.359

II., OR Average, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factors.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
down to
Sin.
diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum uf

columns

/ and

h.

columns
g and

Volunu^

Sum of

columns

/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

g and

k.

Current
Annual
Incre-
ment.

Jlean
Annual
Incre-
ment.

I

Hi

n

0

P

1

r

s

t

U

V

130

2^6

130

13

13

400

11

400

27

20

90

890

•07

•05

•73

90

9

3

890

49

30

9-10

2,020

•35

•26

•67

940

85

24

2,020

113

51

2,090

3,160

•45

•34

•63

2,090

115

42

3,390

137

68

3,190

4,170

•46

•35

■60

3,280

119

55

4,730

134

79

4,050

.5,070

•47

•35

•59

4,410

113

63

6,000

127

86

4,790

5,840

•48

•36

•59

5,480

107

68

7,180

118

90

5,420

6,470

•49

•37

•59

6,470

99

72

8,250

107

92

5,900

6,9G0

•49

•37

•58

7,410

94

74

9,280

103

93

(5,220

7,280

•49

•37

■58

8,290

88

75

10,240

9(1

93

C,430

7,.500

•49

•37

•58

9,100

81

76

11,1.50

91

93

(!,600

7,700

•49

•37

■58

9.840

74

76

12,010

86

92

6,750

7,870

■51

•38

•59

10,520

68

75

12,790

78

91

yeo

APPENDIX III.

Yield Table for High Forest of BEECH,

Age.
Years.

51

ajor Part of Wood

Elinor Part of Wood, or Intermediate

Yields.

Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yields.

Number.

Basal

Area.

Sq. Ft.

Diaiii.

Incbe.s.

Height.
Feet.

Timber

over

3 in.
diam. at

small

end.

Timber
and

Fuel.

Timber
over
Sin.

diam. at
small
end.

Timber
and
Fuel.

Timber

over

3 in.
diam. at

small

end.

Summary

of

col. A.

Timber
and

Fuel.

Summary

of

col. i.

a

I

C

d

'

/

(1

h

i

J

k

10

8

4

3

90

20

18

9

7

210

30

34

1

()

13

450

40

2,000

57

2

3

20

400

840

40

40

50

1,510

80

3

1

28

930

1,510

130

170

m

1,200

98

3

7

34

1,530

2.i(;o

170

340

70

1,000

108

4

4

39

2,040

2,()90

190

530

SO

830

115

5

0

44

2,410

3.090

70

200

70

730

90

700

117

5

5

47

2,G70

3.370

130

200

200

930

100

nio

118

()

50

2,860

3,570

150

200

350

1,130

110

530

117

6

4

52

2,990

3,720

IfiO

210

510

1,340

120

470

IIG

6

7

54

3,030

3,820

170

230

f.80

1.570

130

430

115

7

5(;

3,100

3,900

1,50

190

830

1.760

140

390

114

'

3

57

3.220

3,970

140

170

970

1.930

APPENDIX III.

361

III., OR LOWEST, QUALITY OF LOCALITY.

Final Yield.

Solid Cubic Feet.

Form Factors.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round

town to
3 in.
diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber only.

Timber and Fuel.

Sum of
columns
/ and

Sum of

columns

g and

Timber
and

Fuel.

Volume.

Sum of
columns

/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.
Sum of
columns
g and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

m

n

0

JJ

a

r

•^

t

u

V

400

930

1,530

2,0i0

2,480
2,S()0
3,010

3,ir.o

3,2.:;0
3,310
3,360

yo

210
450
880
1,«40
2,330
2,880
3,2<.»0
3,570
3,770
3,930
4,050
4,090
4,140

•35
•42
•4(1

•48
•48
•49
•49
•49
•49
•49
•50

•26
•31
•34
•36
•36
•37
•37
•37
•37
■37
•37

4-17
1^59
1-02
•74
•07
•65
•64
•61
•61
•61
■61
•61
•61
■61

400
930
1,530
2,040
2.480
2,870
3,210
3,500
3,760
3,990
4,190

40
53
60

51
44
39
34
29
26
23
20

10
19
25
29
31
32
32
32
31
31
80

90

210

450

880

1,680

2,. 500

3,220

3,820

4,300

4,700

5,060

5,390

5,660

5.900

9

12
24
43

80
82

72
60
48
40
36
33
27
24

11
15
22
34
42
46
48
48
47
46
45
44
42

862

APPENDIX III.

Yield Table foe the SCOICH PINE,

Major Part of Wood.

Sq. Ft.

Diam.
Inches,

Height.

Feet.

Volume.
Solid Cubic Feet.

Timber

over

Sin.
diam. at

small

end.

Jlinor Part of Wood, or Intermediate
Yields.

Solid Cubic Feet.

Periodic Yields. I ^"^S °^

Timber

^'^nr 3in^

end.

Timber
and
Fuel.

Timber

over

3 in.
diam. at

small

end.

Summary

of

col. h.

Timber
and
Fuel.

Sumiuav

of

col. I.

10
20
30
40
50
60
70
80
90
100
110
120
130
140

1,420
1,010
720
510
370
290
230
200
170
150
140
1 130
125

45
98
127
145
157
165
172
175
178
181
182
182
183
183

1-5
3-6
4-8
6-1
7-5
9-

10-4
11-8
12-8
14-
14-9
15-4
16-1
16-4

12
29
44
55

65
73

80
86
91
95
99
103
106
108

1,000
2,260
3,520
4,560
5,430
6, 1 70
6,800
7,320
7,730
8, 100
8,430
8,700
8,950

800
2,200
3,440
4,500
5,420
6,220
6,930
7,550
8,060
8,460
8,830
9,150
9,420
9,660

20
210
510
660
610
510
440
410
400
360
310
290
260

110
560
800
860
740
550
500
460
430
390
340
310
290

20
230
740
1,400
2,010
2,520
2,960
3,370
3,770
4,130
4,440
4,730

110
670
1,470
2,330
3,070
3,620
4,120
4,580
5,010
5,100
5,740
6,050

4,990 6,340

APPENDIX in.

363

I., OR Best, Quality op Locality.

Final Yield.
Solid Cubic Feet.

Form Factor

Total Yield.
SoUd Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
lown to
Sin.
diam.

at
.small
end.

Timber
according

to
([uarter-

girth
measure-
ment.

Timber
ami
Fuel.

Timber only.

Timber and Fuel.

Sum of

i-olumns

/and

h.

.Sum of

columns

g and

Volume.

Sum of
columns

/and

J-

CuiTent
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

g and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

III

n

0

P

?

r

n

;;

U

r

800

r48

800

80

80

1 ,U20

2,310

•3.-.

•2(i

•77

1,020

102

51

2,310

151

115

2,470

4.0(10

•40

•30

•(J2

2,490

147

83

4,110

180

137

4,030

.-).300

•44

•33

•.".(i

4,2t;o

177

106

5,970

186

149

.■i,220

(),280

■ir,

•34

■53

5,9()0

170

119

7,750

178

155

(J ,040

G,960

•4."j

•34

•52

7,440

148

124

9,290

154

155

i;,680

7,480

•45

•34

•50

8,(i90

125

124

10,550

126

151

7,240

8,0.50

■45

•34

•50

9,700

107

122

11,670

112

146

7,730

8..520

•45

•34

■50

10,690

93

118

12,640

97

140

S,130

8,890

•45

•34

•49

11,500

81

115

13,470

83

135

.s,4(J0

9,220

•45

•34

■49

12,230

73

111

14,230

76

129

S,740

9,490

■45

•34

•49

12,870

04

107

14,890

60

124

s,y9o

9,730

•45

•34

•49

13,430

50

103

1.5,470

5S

119

y,2io

9,9r.o

•45

•34

■49

13,940

51

100

16,000

53

114

364

APPENDIX III.

Yield Table for the SCOTCH PINE,

Minor Part of Wood, or Intermediate

Age.
Years.

Major Part of Wood.

Yields.
Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yields.

Xumber.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Height.
Feet.

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber
over
3 in.
diam. at
small
end.

Timber
and
Fuel.

Timber

over

3 in.
diam. at

small

end.

Summary

of

col. h.

Timber
and
Fuel.

Summarx

of

col. i.

a

b

c

d

e

/

9

h

/

J

J/

10

30

1-

8

500

20

71

2-

17

400

1,370

30

1,(500

103

3-4

29

1,140

2,220

20

60

20

60

40

1,100

121

4-5

38

2,000

3,030

130

290

150

350

50

7(;o

132

5-(i

46

2,820

3,(;(;o

330

490

480

840

r,o

5(50

140

(;-8

52

3,460

4,190

370

470

850

1,310

70

440

M5

7-8

58

3,970

4,(;60

340

410

1,190

1,720

80

360

149

8-7

63

4,390

5,070

330

390

1,520

2,110

90

300

1.52

!)-f>

(58

4,740

5,430

300

360

1,820

2,470

100

2:.o

152

10-()

72

5,060

5, 730

270

300

2,090

2,770

110

220

1.53

11-3

76

5,340

6,020

240

2 70

2,330

3,040

120

200

153

11-8

79

5,620

6,290

200

230

2,530

3,270

130

180

154

12-5

82

5,860

6,530

170

200

2,700

3,470

APPENDIX III.

365

II., OR Average, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factors.

Total Yield,
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round

do^vn to
3 in.
diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

•Sum of

columns

f and

li.

Sum of

columns

ij and

Volume.
Sum of
columns
/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.
Sum of
columns
cj and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

n,

n

0

P

<I

r

s

t

u

V

500

2-08

500

50

50

400

1,370

•33

25

M4

400

40

20

1,370

87

68

1,160

2,280

•38

29

•74

1,160

76

38

2,280

91

76

2,130

3,320

•43

32

•66

2,1.50

99

54

3,380

110

84

3,1.50

4,1.50

•46

35

•60

3,300

116

66

4,500

112

90

3,8.30

4,6(i0

•48

36

•58

4,310

101

72

5,500

100

92

4,310

5,070

•47

35

•55

5,160

85

74

6,380

88

91

4,720

5,460

•47

35

•54

.5,910

75

74

7,180

80

90

5,040

.5,790

•46

35

•54

6, .560

65

73

7,900

72

88

5,330

6,030

•46

35

•52

7,1.50

59

72

8,500

60

85

r.,580

6,290

•46

35

•52

7,670

52

70

9,060

56

82

5,820

6,520

•46

35

•52

8,150

48

Hi

9,560

50

80

6,030

6,730

•46

35

•52

8,560

41

66

10,000

44

77

366

APPENDIX III.

Yield Tabli: for thi: SCOTCH PINE,

:\Iinor Part of Wood, or Intermediate

Major Part of Wood.

Yields.

Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yields.

Age.
Years.

Xumber.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Height.
Feet.

Timber
over
Sin.

diam. at
small
end.

Timber
and
Fuel.

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber

over

3 in.
diam. at

small

end.

Summary

of

c-ol. h.

Timbfi-
and
Fuel.

Summary

of

col. i.

"

h

c

d

e

/

9

7i

^

J

Ti

10

18

•6

4

200

20

40

1-4

8

450

30

76

2-2

14

200

860

40

2,000

98

3-

21

610

1,330

50

1,470

105

3-6

26

1,060

1,760

30

110

30

110

60

1,040

107

4-3

30

1,430

2,060

40

110

70

220

70

780

108

5-

34

1,730

2,360

50

100

120

320

80

620

109

5-7

38

1,970

2,570

60

100

180

420

90

510

110

6-3

41

2,170

2,760

70

90

250

510

100

420

110

6-9

44

2,340

2,920

80

90

330

600

110

350

110

7-6

47

2, .500

3,060

80

90

410

690

APPENDIX III.

367

III., OR Lowest. Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factors.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
down to
Sin.
diam.

at
small
end.

Timber
according
to Ti
quarter
girth F
measure-
ment.

Tiber

md

uol.

Timber only.

Timber and Fuel.

Sum of
columns
/and

Sum of
columns
g and

i.

Volume.
Sum of
columns
/and
J-

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

g and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

m

n

0

P

3

7"

S

t

U

^

200

2

78

200

20

20

450

1

41

450

25

23

200

860

•19

14

81

200

20

7

860

41

29

610

1,330

•30

22

65

610

41

15

1,330

47

34

1,090

L870

•39

29

64

1,090

48

22

1,870

54

37

1,470

2,170

•45

84

64

1,500

41

25

2,280

41

38

1,780

2,460

•47

35

64

1,8.50

35

26

2,680

37

38

2,030

2,670

•48

36

62

2,150

30

27

2,990

31

37

2,240

2,850

•48

36

61

2,420

27

27

.3,270

28

36

2,420

3,010

•48

36

60

2,670

25

27

3,520

25

35

2,580

3,150

•48

36

59

2,910

24

26

3,750

23

368

APPENDIX III.

Yield Table for the SPBUCE,

Age.
Years.

Major Part of Wood.

Minor Part of Wood, or Intermediatf
Yields.

Solid Cubic Feet.

Stems.

1
Mean.

Volume.
Solid Cubic Feet.

Periodic \Melds.

Summary of
Yields.

Number.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Height.

Feet.

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber
over
8 in.

diam. at
small
end.

Timber
and
Fuel.

Timber

over

3 in.
diam. at

small

end.

Summary

of

col. h.

Timbci
and
Fufl.

Sumniar\

of

col. i.

a

h

c

d

e

/

g

h

^

3

li

10
20

m

40
50
CO
70
SO
90
100
110
120

2,970
1,800
1,130
720
510
380
310
260
220
200
190

87

97
170
207
229
244
254
263
271
279
285
291

1-
2-4
4-2
5-8
7-6
9-4
11-1
12-5
13-8
15-2
16-2
16-8

8
20
35
51
65
76
85
93
99
104
109
112

700
2,920
5,540
7,750
9, .5.50
11,020
12,250
13,. 300
14,250
1.5,120
15,900

500
1,800
4,790
7,370
9,430
11,120
12,520
1.3,710
14,760
15,720
10,590
17,360

60
340
690
890
890
840
740
640
570
500

410
690
910
1,040
1,010
910
800
690
600
530

60
400
1,090
1,980
2,870
3,710
4,4.50
.5,090
.5,660
6,160

410
1,100
2,010
3,050
4,060
4,970

6,460

7,0(;o

7,590

APPENDIX III.

369

I., OR Best, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factors.

Total Yield.
Solid Cubic Feet.

Timber.

1 Timber
and
Fuel.

Timber
in the
round
down tc
3 in.
diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and

Fuel.

Timber only.

1

Timber and Fuel.

Volume.
Sum of
columns
/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.
Sum of
columns
g and

Current
Annual
Incre-
ment.

Mean
.\unual
Incre-
ment.

.Sum of

columns

/and

h.

Sum of

columns

y and

i.

I

VI

71

0

P

Q

r

s

t

%

c

500

P69

500

50

50

700

1,800

•36

27

•93

700

70

35

1,800

130

90

2,980

5,200

•49

37

•81

2,980

228

99

5,200

370

173

5,880

8,060

•52

39

•70

5,940

296

148

8,470

327

212

9,440

10,340

•52

39

•63

8,840

290

177

11,440

297

229

10,440

12,160

•51

38

•60

11,539

269

192

14,170

273

236

11,910

13,530

•51

38

•58

13,890

236

198

16,580

241

237

13,090

14,620

•50

37

•56

15,960

207

200

18,680

210

234

14,040

15,560

•50

37

•55

17,750

179

197

20,530

185

228

14,890

16,410

•49

37

•54

19,340

159

193

22,180

165

222

15,690

17,190

•49

37

•53

20,780

144

189

23,650

147

215

16,400

17,890

•49

37

•53

22,060

128

184

24,950

130

208

370

APPENDIX III.

YiKLD Table fok the SPIWCE,

Aye.
Years.

Major Part of Wood.

Minor Part of Wood, or Intennediate
Yields.

Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yields.

Xuiiiber.

Basal

Area.

Sq. Ft.

Diam.
Inches.

Height.

Feet.

Timber

over

3 in.
diam. at

small

end.

Timber
and
Fuel.

Timber
over
3 in.

diam. at
small
end.

Timber
and
Fuel.

Timber

over

Sin.
diam. at

small

end.

Summai-y

of

col. %.

Tinibrr
and
Fuel.

Summary

of

col. i.

"

h

C

d

e

f

U

//

'•

J

h

10

23

•6

4

400

20

G2

1-2

10

1,430

30

3,340

10.5

2-4

19

C70

2,020

40

l,y.50

142

3-7

30

2,110

3,900

30

390

30

3.0

:>()

1,280

Ki4

4-9

42

3,070

5,220

210

540

240

930

CO

s:)()

180

G-2

.-)2

5,000

0,400

410

()40

050

1,570

70

(;4o

191

7-4

CI

0,270

7,(i20

490

040

1,140

2,210

80

510

201

8 -.5

08

7,320

8,630

470

580

i,t;io

2,790

90

430

211

9 -.5

74

8,220

9,520

420

500

2,030

3,290

100

380

219

10-3

79

8,960

10,290

380

440

2,410

3,730

110

sno

220

10-9

82

9,030

10,980

340

380

2,750

4,110

120

320

232

11 -.5

84

10,200

11,590

300

330

3,050

4,440

APPENDIX III.

371

II., OR Average, Quality of Locality.

Final Yield.
Solid Cubic Feet.

F

orm Factoi

-

Total Yield.
Solid Cubic Feet.

Timber.

Timber
Fuel.

Timber
in the
round
down to
3 in.
diam.

at
small
end.

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

T

mber only.

Tim

x-r and Fuel.

Sum of

coluiims

/ ami

h.

Sum of
columns
i/and

Volume.

Slim of
column.s

/and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

colunuis

g and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

>.

"

"

J}

'1

r

•^•

t

«

)•

400

4^35

400

40

40

1,-130

2-31

1,430

103

71

07U

2,(;2o

•;i4

•25

1^31

070

(;7

22

2,020

119

87

2,140

4,290

CO

•37

•92

2,140

147

54

4,290

107

107

:i,,s,so

.">,7(50

■:>?,

•10

•7(;

3,910

177

78

(i.1.50

180

123

.-..iTU

7,100

■:a

•41

•(!!!

.5,710

180

95

8,030

188

134

(>,7()0

8,260

•54

•41

•(;5

7,410

170

io(;

9.830

180

140

7.71)0

!).210

•54

•41

•()3

8,930

152

112

11,420

159

143

S,li4(»

10,020

•53

•40

•CI

10,2.50

132

114

12.810

139

142

'.t,;5io

10,730

•52

•3'.l

•59

11,370

112

114

14,020

121

110

'.»,'■•'■"

11,3(;0

•52

•;','.»

•59

12,3SO

101

113

15,090

107

137

10,500

11,920

•52

•39

■59

13,250

87

110

16,030

94

134

ii li 2

372

APPENDIX III.

Yield Table for the SPRUCK

Aye.
Years,

7U
80
<J0
100

Major Part of Wood.

3,!)7()

2,ir.o

1,870

1,UOO

810

700

(150

Sq. Ft.

ir>

8S
Gl

s7
108

12:5

1H4
141

\:,2
ir,u

Diam.
Indies

Height.
Feet.

Solid Cubic Feet.

Timber

over

3 in.
diam. at

small

end.

1,870

2,7(;o
a,. -,30

1,140
4, (".80

Timber
and
Fuel.

I'oo

5.50
1,100

i,(;',>o

2,:5CiO

a,ioo

H,870
4,(;oo
5,230
.■>, 720

Minor Part of Wood, or Intermediate
Yields.

Solid Cubic Feet.

Periodic Yields

Timber

over

3 in.
diam. at

«mall

end.

ICO
170
100

Timber
and
Fuel.

270
2110
300
21 io
210

diam. at
small
end.

Summary

of

col. n.

230

400

Summary

of

col. i.

s(;o

1.120
1.330
1 ,.500

APPENDIX III.

373

III., on I;OWEST, Quality op Locality.

Final Yield.
Solid Cubic Feet.

Form Factoi

s.

Total Yield.
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
down to
Sin.
diam.

at
small
end.

Timber
according

to
quarter-
girth

ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum of

columns

/and

h.

Sum of
columns
sand

Volume.

Sum of

columns

/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

g and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

m

"

0

P

a

r

.«

t

U

V

200

6^67

200

20

20

O.'lO

2^90

550

35

27

1,100

2-

1,100

55

37

340

1,090

•20

•20

V30

340

34

9

1,690

59

42

960

2.(530

•40

•30

•99

960

62

19

2,630

94

53

1,040

3,390

TA

•38

•84

1,940

98

32

3,660

103

61

2,920

4,170

•56

•42

•78

2,990

105

43

4,730

107

Vy%

3,700

4,8f;0

•57

•43

•74

3,930

94

49

5,720

99

71

4,300

.5,440

•57

•43

■72

4,700

11

52

6,560

84

73

4,770

.5,890

•57

•43

•71

5,330

63

53

7,220

66

72

374

APPENDIX III.

Y:ei,d TAiiLE i-oii THK STLVEH Fin,

Age.
Years.

Major Part of Wood.

Minor Part of Wood, or Intennediate
Yields.

.Solid Cubic Feet.

Stems.

Mean.

Volnnie.
Solid Cubic Feet.

Periodic

Yields.

Summary of
Yields.

XninlHT.

Basal

Area.

.Sq. Ft.

Piam.
Inches.

■Height.
Feet.

Timber
over
3 in.
<liam. at
small
end.

Timboi
and
Fuel.

Timber
over
?. in.

diam. at
small
end.

Timber

and
Fuel.

Timber

over

3 in.
diam. at

small

end

.Summary

of

col. 7i.

Timb,v
an<l
Furl.

8ummar.\

of

col. 1.

«

h

c

d

e

/

fJ

h

'■

,/

1i

10

10

•o

3

300

20

B5

1-3

9

880

.30

71

2-5

18

500

1,760

iO

1,400

126

4-

30

1,700

.3,1.30

60

290

60

29n

.')0

990

171

5-6

4.5

3,670

4,940

360

640

420

930

(!()

OCO

20.-,

7 '5

r»8

5,700

7,070

570

790

990

1,720

70

400

2.S3

9-r,

71

7,960

9,450

1,000

1,260

1,990

2,9S(i

80

.S40

2.0-)

11-7

82

10,350

11,9.50

1,290

1,570

3,280

4,5.50

1)0

2.50

273

14-2

91

12,5,50

14,2.30

1,430

1,710

4,710

6,260

]()()

200

288

10-2

98

14,290

16,060

1,.360

1,570

6,070

7,830

110

1 SO

300

17-.-,

104

15,780

17,610

8C0

1,000

6,9,30

8,830

120

170

310

18-3

109

16,990

18,880

710

830

7,640

9,660

130

100

320

19-1

112

17,850

19,760

600

690

8,240

10,3.50

HO

150

330

20-1

115

18,840

20,840

310

360

8,550

10,710

APPENDIX III.

375

I., OR I^EST, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Foi-m Factoi

s.

Total Yield.
Soli.l Cubic Feet.

Timbor.

Sum of

columns

/and

Timber
and
Fuel.

Sum of

columns

g and

Timber
in the
round
down to
3 in.
diam.

at
small

Timber
according

to
quarter-
girth
measure-
ment.

Timber
and
Fuel.

T

mber onl

••

Timber and Fuel.

Volume.
Sum of
columns
/ and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of

columns

f/ ami

);.

Current
Annual
Incre-
ment.

1

Mean
Annual
Incre-
ment.

I

in

n

0

P

'1

/'

■^

t

w

V

300

10 •

300

30

30

880

£•79

880

58

44

r,(jo

1,760

•39

•29

1-38

500

50

17

1,760

88

58

L760

3,420

•4.5

•31

•83

1,760

126

44

3,420

166

85

4,030

5,580

•48

•3,-,

•64

4,090

210

82

5,870

245

117

r>,270

7,860

•48

•36

•.59

6,690

260

111

8,790

292

146

S,9<iU

10,710

•48

•36

-.57

9,950

326

142

12,430

364

178

11. (UO

18,.520

•49

•37

•57

13,630

368

170

16,500

407

206

13,980

1.5,040

-.51

•38

•57

17,260

363

192

20,490

399

228

ir,.r,.50

17,6.30

-.51

■38

. ••^7

20,360

310

204

23,890

340

239

ir,.(;40

18,61(1

•.51

•38

•56

22.710

235

206

26,440

255

240

17,700

10,710

•.50

■37

•56

24.630

192

205

28,540

210

238

lS.4.-,0

2().4.5(»

-.50

•37

•55

26,090

146

201

30,110

157

232

19,1.50

21,200

-.50

■37

"55

27,390

130

196

31,550

144

225

376

APPENDIX III.

Yield Table for the SILVER FIB,

Major Part of Wood.

Minor Part of Wood, or IntermfMliat.-

Yields.

Solid Cubic Feet.

Stem.s.

Mean.

Vohime.
Solid Cubic Feet.

Periodic Yields.

Summary of
Yields.

Age.
Years.

Xumber.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Height.
Feet.

Timber

over

3 in.
diam. at

small

end.

Tim bel-
aud
Fuel.

Timber
over
3 in.

iliam. at
small
end.

Timber
and
Fuel.

Timber

over

Sin.

diam. at

small

end.

Summary
col. h.

Timber
Fuel.

Summary
of

col. ;.

a

b

c

d

e

/

ff

h

i

J

k

10

7

•3

2

200

20

18

•7

6

500

30

36

1-3

13

1,000

40

2,700

75

2-3

22

650

1,900

.50

2,000

127

3-4

33

1,880

3,180

140

320

140

320

GO

1.330

159

4-7

44

3,530

4,690

330

530

470

850

70

880

182

6-2

55

5,070

6,3.50

510

730

980

1,580

80

590

203

7-9

65

6,750

8,130

740

970

1,720

2,551)

90

420

220

9-8

73

8,540

10,000

900

1,140

2,620

3,690

10<)

310

235

11-8

81

10,140

11,650

940

1,180

3,560

4,S7<.

110

250

24(;

13-4

87

11,470

13,020

950

1,140

4,510

6,010

120

230

255

14-3

92

12,500

14,080

750

870

5,260

6,880

130

210

2G2

15-1

96

13,180

14,790

570

650

5,830

7,530

HO

200

268

15-7

99

13,830

15,480

230

250

6,060

7,780

APPENDIX III.

377

n., OR Average, Quality of Locality.

Final Yield.
Solid Cubic Feet.

Form Factor

.

Total Yield,
Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
down to
3 in.
diam.

at
small
end.

Timber

according
to

f|\iarter-
girth

measure-
ment.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum of

columns

/ and

h.

Sum of

columns

g and

Volume.

Sum of

columns

/and

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.

Sum of
colunin.s

g and

Current
Annual
Incre-
ment.

Mean
Annual
incre-
ment.

I

m

n

0

I>

1

r

S

t

u

V

200

14-29

200

20

20

500

4-63

500

30

25

1,000

2-14

1,000

50

33

650

1,900

39

29

1-15

650

65

16

1,900

90

47

2,020

3,500

45

34

•76

2,020

137

40

3,500

160

70

3,860

5,220

50

37

■67

4,000

175

67

5,540

204

92

r,,.580

7,080

51

38

•63

6,050

205

86

7,930

239

113

7,490

9,100

51

38

•62

8,470

242

106

10,680

275

133

9,440

11,140

52

39

•62

11,160

269

124

13,690

301

152

11,080

12,880

53

40

•61

13,700

254

1.37

16,520

283

165

12,420

14,160

54

41

•(51

1.5,980

228

145

19,0.30

251

173

13,2.^0

14,950

53

40

•60

17,760

178

148

20,960

193

175

13,750

15,440

52

39

•59

19,010

125

146

22,320

1.36

172

14,060

15,730

52

39

•58

19,890

88

142

23,260

94

166

878

APPENDIX III.

YiEM) TAniii: for the Slf^Vhli Fill,

Age.
Years.

Major Part of Wood.

Minor Part of Wood, or Intermediate

Yields.

Solid Cubic Feet.

Stems.

Mean.

Volume.
Solid Cubic Feet.

Periodic Yields.

Summary ol'
Yields.

Number.

Basal
Area.

Sq. Ft.

Diam.
Inches.

Height.

Feet.

Timber

over

Sin.
diam. at

small

end.

Timber
and
Fuel.

Timber

over

3 ins.
diam. at

small

end.

Timber
and
Fuel.

Timbei'

over

Sin.
diam. at

small
end.

Summarv

of

col. h.

Timb.T
and

Furl.

Sumniaiy

of

col. /.

"

//

(■

(f

r

f

f/

h

i

J

/.■

10

2

■2

2

100

20

4

•6

5

220

30

10

1-

9

440

40

23

1-5

16

150

990

.-0

86

2-4

24

1,000

1,860

(JO

2,100

124

3-3

33

1,990

2,930

70

230

70

2.S0

70

1,180

14.5

4-2

42

3,060

4,090

210

410

280

)M(i

SO

1,060

162

5-3

51

4,190

5,300

400

600

680

1,210

•to

780

I7r,

6-4

59

5,370

6,570

630

840

1,310

2,os(i

11)0

.-.70

1S8

7-8

66

6,430

7,700

790

930

2,100

3,01(1

110

130

198

9-2

71

7,270

8,6(10

8()0

970

2,960

3,98(1

120

3.-)0

205

10-4

76

7,890

9,280

570

640

3,530

4,620

130

310

209

11-1

79

8,360

9,780

500

570

4,030

5,190

HO

2'JO

215

11-7

82

8,800

10,280

280

320

4,310

5,510

APPENDIX III.

379

III.. f'K TiOWEPT QtTATJTY OF LOCALITY.

Final Yield.
Solid Cubic Feet.

Form Factors.

1
Total Yield.

Solid Cubic Feet.

Timber.

Timber
and
Fuel.

Timber
in the
round
I own to
3 in.
diam.

at
small
end.

Timber
according

to
quarter-
girth ,
uieasnrf-
mi-nt.

Timber
and
Fuel.

Timber only.

Timber and Fuel.

Sum of
columns
/and

Sum of

columns

and

Yoluran.

Sum of
columns

/ and

J-

Current
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

Volume.
vSum of
columns

CuiTent
Annual
Incre-
ment.

Mean
Annual
Incre-
ment.

I

m

n

" I>

i

r

*•

t

U

V

100

25-

100

10

10

220

11

220

12

11

440

4

89

440

22

15

1.50

990

•41

•31

2

69

150

15

4

990

55

25

1,000

1,860

•48

•36

90

1,000

77

20

1,860

87

37

2,060

3,160

•49

•37

72

2,060

106

34

3,160

1.30

53

3,270

4,500

-.50

■37

67

3,340

128

48

4,730

157

68

4,.590

.5,900

•51

•38

64

4,870

1.53

61

6,54(1

181

82

6,000

7,410

•52

•39

64

6,680

181

74

8,6.50

211

96

7,220

8,630

■52

•39

62

8,530

185

85

10,710

206

107

8,130

9,.570

•52

•39

61

10,2.30

170

93

12,580

187

114

8,460

9,920

•51

•38

1

60

11,420

119

95

13,900

142

116

8,860

10,3.50

•51

•38

59

12,390

97

95

14,970

107

115

9,080

10,600

•50

•37

1

58

13,110

72

94

15,790

82

113

880

APPENDIX III.

J'UHI.l.MlNARY YiEI.I) Ta1U.ES

Larch.

Alder.

Birch. J

Age.
Years.

Quality classes,
cubic feet

in soli.l

Age.
Years.

Quality classes, in solid
euhic feet.

Age.
\ ears.

Quality classes, in solid
cubic feet.

I.

II.

III.

I.

II.

Til.

I.

II.

III.

10

760

470

170

10

860

510

160

10

670

400

110

20

1,890

1,140

360

20

1 ,800

1.01(0

340

20

1,410

820

230

30

3,290

1,940

570

30

2,800

1,700 r,i()

30

2,360

1,.360

390

40

1,840

2,790

790

40

3,820

2,330

760

40

3,370

1,940

540

50

6,400

3,640

990

50

4,790

2,930

950

50

4,300

2,470

690

60

7,800

4,400

1,170

60

5,730

3,520

1,130

60

5,120

2,920

790

70

9,060

5,100

1,340

70

6,640

4,050

1,300

70

5,740

3,230

840

80

10,190

5,730

1,500

80

7,530

4,560

1,460

80

6,230

3,460

870

90

11,200

6,290

1,040

90

8,360

5,040

1,600

100

12,120

6,800

1,760

100

9,100

5,470

1,710

110

12,950

7,260

1,870

120

13,680

7,650

1,960

130

14,310

7,960

2,020

HO

14,860

8,260

2,060

Coppice of Alder, Poplar,
Willow.

Coppice of -"Oak, Beech, Ash,
Birch.

Age.
Years.

Quality classes, in solid
cubic feet.

Age
Years.

Quality classes, in solid
cubic feet.

I.

II.

III.

I.

II.

III.

5

490

260

30

r,

310

160

15

10

1,000

510

90

10

640

330

45

15

1,540

860

160

15

980

510

85

20

2,100

1,190

240

20

1,330

700

130

25

2,730

1,510

300

25

1,730

930

175

30

3,360

1,840

350

30

2,120

1,140

220

35

3,940

2,140

400

3.-.

2,460

1,330

260

40

4,520

2,420

430

40

2,800

1,510

290

381

APPENDIX IV

General Working Plans for the Method of Allotment of Woods
to the several Periods of one Eotation.

A. Allotment according to Area.

B. Allotment according to Volume, and Area and Volume

combined.

382

APPENDIX IV. A.

Gknekal Wouking Plax of a High Forest Working Section of

A.— Allotment according

Coiniiart-
nieut.

Area.

Acres.

A};e in
ISSS.

Allotment of WooDy to

I. Period.
1888—1907.

II. Period.

iyOS-1927.

III. Period
19-2S— 47.

Area.
Acres.

Mean
Ape

when
Cut

Over.

Aiea.
Acres.

Mean
Age

when
Cut

Over.

Area.
Acres.

Mean
Age

when
Cut

Over.

1

18-78

80

-4+0-

is-rs

130

2

7-98

fiO

7-98

110

3

5-7<)

00

-B'^

100

4

io-(;8

40

5

9-l-t

15

6

3-21

130

3-21

140

7

.u

10

8

8-9o

50

^«yo-

lOO"

y

3-6(;

75

*^

4^5

10

lO-os

75

10-68

105

11

8-70

75

8-70

105

12

12(i.-.

75

12-6,j

,S'J

' n.L--

t05-

lo t}.")

i:{

3-43

8(1

3-43

00

4^t^

Hth

.;-99

(;-s2

IC.

ii;

.h;7

(;5

/^.L'-

-^©-

a-07

ll.j

■u'Oi

17

3-81

70

."i-S] j 1(10

18

■ .V29

70

5-29

KM)

19

-y-ji

75

5-54

105

20

10-58

82

1(I-5S

92

21

3-19

13

"'idO-lf)

1

»n.oi

.

2y-ii7

IV 111

.J4-0:J

■jfij'oy

33-43

lleinarhs. — The aroas, wliioh have been shifted from

APPENDIX IV. A.

y83

Beech Woods with a Moderate Admixture of Oak, Ash and Conifers.
TO Area. Rotation, lUU Years.

THE Several Periods.

V. Period. 1968-87.

IV. Period.
1948-U7.

Blanks.

Kemarks.

With
Overwood.

Without
Overwood.

Mean

Mean

Mean

Aiea.
Acres.

Age
when

Cut
Over.

Aiea.
Acres.

Age
when

Cut
Over.

Area.
Acre.s.

Age
when

Cut
Over.

Area.
Acres.

576
10-68

S-95
3-(J6

130
110

120
145

6-18
7-3i

105
100

3-26

6-99
(J-82

105

lOG
106

Shifted, because the wood is of
vigorous growth and the second
period is overstocked.

Shifted to fill up the IV. period.

Of good growth ; shifted to fill up
the IV. period.

Shifted to provitle fur the I. period.
Shifted to relieve the 11. period.

3-19

S3

-s*w-

40*

Shifted to provide for IV. period.

Mean area of period - ^^^''^^ - 32-03
5

13.52

Oil .TC

^2-24

17-07

30-39

their proper age class, are printed in ifalict>

384

APPENDIX IV. A.

1 . List of Woods alkeadv under Kegenekation in 18S8 and Quan-
2. List of Woods Selected for Utilisation and

'■^"^^ I Compart- j^
Number. "^-t. , ^^

Tkeks to be

Left as
Stakdards

At the
(luean). '

L IWiods (dread ij it ltd c

5

5r44

■

7;^4

Total

16-78

Beech

104

107

Oak.

IG

otch pine

104

107

Beech

lie.

1111

Total

2, Woods to be Cut and Itef/enemtcd

3-21
12-G;i

Beech

130

140

Oak

3

Beech

75

,S."i

Oak

71

81

Oak

1.5(1

Conifers

70

80

Beech

80

".HI

Oak

11

Beech

•JO

lou

Oak

.VI

Scotch i)iue

80

HO

APPENDIX IV. A.

3«5

tity of overwood remaining in them in the beginning of 1888,
Regeneration during the 1'eriod of 1888—1907.

Yield in Solid Ci'bic Feet.

Regeneration.

Remarks.

Estimate.

Actual

Result.

Natu-
ral,
Acres.

Artificial.

Present
Volume.

Incre-
ment.

Mean

Totul. 1 per

Acre.

Mannei of
Formation.

Species.

Area.
Acres.

Begeneration in 1888.

5,238

151

5,389

- 596

5-00

Planting

t Oak

Spruce
Oak

I:

Increment
5238 .^
Iu4

232

'

239

1 ■

'

)

[ 2-84

= 151 cub.
ft.

8,091

209

8,300

1,131

4-50

Planting

- Ash

8091
TT6

Spruce

I

= 209 c"b.
ft.

13,.561

367

13,928

9.50

7-28

during the Period of 1888—1907.

19,827

33,237

4,444

1,525
4,442

626

21,352
37,669

5,070

6,659
■3,442

2-00
7*50

Sowing
Sowing

Oak

Scotch
pine

1 Larch

1-21

■ 5-15

130
= 1525
cub. feet.

706

101

807

^ Spruce

14,575

1,822

16,397

4,780

200

Sowing
Planting

Oak

Ash

1-00
•43

36,279

4,031

40,310

•3,957

6-00

Planting

Larch
Spruce

l4-5e

1,384

173

1,557

17-50

1 Scotch
\ pine

110,452

12,710

1
123,162! 4,123

12-.37

386

APPENDIX lY. A.

Calculation of Yield for tiii^ I. I'hkioi), isss— ii

Sources of Yield.

Solid Cubic Feet.

Yiel.l.

Grand
Total.

Mean
Annual
Yield.

Detailed.

Total.

a. Thinuingsf .....
I. Other intermetliate yields

e. Balance in woods already under
regeueratiou

il. Final yield ol: woods to be re-
generated

* To be deducted as remaining at end
of period

r. r.alance of d to be cut

/. Total of c and e . . . .

Total of all yields

.50,402
13,'J2«

50,402

50,402
115,298

2,520
5,7()5

13,928
101,370

12:^,162
21,71)2

165,700

8.285

j- See next page.

* The calculation is made as follows : — Uegeneration ])erinil = jo years.
I\Ican volume per acre of woods in first period = 4,123 cubic feet. Kcmain,
when seeding cutting has been made = 4,123 X •<> = 2,474 cubic feet. It is
assumed that the 2,474 cubic feet are cut away in annually equal shares of J^th,

that is to say = ■ ' = 217-4 cubic feet annually ; hence the ten coupes,

160ir
of 100
c(iual lo
C'oiipe X.
2,474

' acres of area each, will have per acre at the end of ihe period volumes

Coupe IX.

2,474 -2:il:^
10

Coiipe VIII.

2 474
2 474_nil:lX2-...2,474-^',,/ x 8
10

Coupe II.
!,47-
10

Coupe I.

2,474-2dIix9

10
= 247-4

Total = l|j:!l5 X ""^ (2,474 + 217-1) = 21,792 cubic feet.

APPENDIX IV. A.

387

Local Yield Table for Thinnings.

Age Class.

Mean height of dominant part of Wood
at end of age class, in feet.

Yield of Tliinnings
c' solid per acre.

21— 30

16

170

81— i<i

28

200

-11— 50

88

230

51— 60

U

245

61— 70

49

260

71— SO

52

230

81— 1)0

54

200

!) 1 — 100

-

155

Total

1,690

This table has been used to calculate the expected yield of
thinnings during the next 20 years. The details have been
omitted ; the total volume amounts to 50,402 cubic feet.

{;c 2

388

APPENDIX IV. B.

B.— tJ^ENERAL Working Plan for the Method of Periods by Volume,

Data of the Woods in the
Eotation, 100 Years.

Age of

Woor.s.

Allotment of Woods

Compart-
ment.

Area in
Acres.

'

Final
Yield per

Acre,
in Cubic

Feet.

Present,
Years.'

Final.

I.

Over 80

Years.

188S-1907.

II.

61-80.
190S-I927

III.

41-60.
I92S-I947.

Volnme in Cubic

1

18-78

80

.W

6,045

94,745

2

7-98

60

110

6,045

48,239

3

5-76

60

130

G,S17

4

10-68

40

110

6,045

5

9-44

15

105

.5,809

6

3-21

130

140

7,117

22,846

7

7-31

10

100

5,573

8

8-;to

50

120

6,460

9

3-(i6

75

145

7,267

10

10-08

75

105

5,809

62,040

11

8-70

75

105

5,809

50,538

12

12-65

75

125

6,63S

83,971

13

3-43

80

90

5,045

17,304

14

0-99

16

106

5,856

15

6-82

16

106

5,856

1(5

6-07

65

115

6,252

41.701

17

3-81

70

100

5,573

21,233

18

5-29

70

100

5,573

29,481

19

5-54

75

105

5,809

32,182

20

10-58

82

92

5,151

54,498

21

3-19

13

103

5,715

195,474

160-15

189,393

173,919

Remark. — The compartments, which have been shifted

APPENDIX IV. n.

389

and for the method by area and yolujie combined.
Tables at Pages 882—388.
Regenerative Period, 10 Years.

TO Periods.

Remarks.

Akeas Placed into
Periods

THE Se\

ERAL

Remarks.

V.

1-20.

1968-1987.

IV.

21-40.
1948-1967.

I.

ir.

HI.

IV.

V.

Feet.

18-78

7-98

39,266

5-76

(i4,o60

54,887
40,90G

3.21

10-68

9-44
7-34

57,817

8-95

26,597

40,f(38
89,!I38

18,231

3-43
10-58

10-68
8-70

3-81
5-29
ry54

1-2-65
6-67

3-66

6-99
6-82

3-79

188,240

194,845

36-00

34-02

27-30

29-05

33-78

from their proper age classes, are printed in italics.

390

APPENDIX Y.
General WowKiNf; I'f.an iihawn

ACCORDTXO

Itotatidii.

Cr>MPAKTMENTS.

Distribution of Aok

1 — iO years old.

4l-r,o.

fil-80.

81—100.

Number.

1
Cubic feet. Acres.

Cubic feet. | Acres.

Cubic feet.

Acres.

Cubic feet.

Acres.

1
2
3
4
5
6

8
9

48:030

200.945

19,072

21,189

109,479
26,487
28,605
13,420

41
117
34

38

87
24
51

48

70,630
1(;9.514

201,299
46,617

20

-10

37

n

192.117

423,787
25,074
35,316

40
67

1.5.892

353,15()

494,418

42,379

49
49

105

Total

Normal state under a
rotation of 12<i years

Comparison of real "j +
and normal state/ -

467,227

440

488.060

108

676.291

117

905, S15

Calculation of the Yield.
This is clone according to the formula given on page 318 :

Annual yield = !,,,,, + ''"'^ ~ ^""'■"""
a

The real increment, J,,.„,,
The real growing stock, &..,„,
The normal growing stock, G„

The surplus of growing stock

= 102,696 cubic feet.
=: 8,939,771 „
= 7,456,200 „

= 1,483,571 cubic feet.

Assuming, that this surplus is to l)e removed in the course of 50
years, the yield would he —

1,483,571

Annual yield = 102,690 +

or during the first 10 years

50

102,096 + 29,671

= 132,367,
1,323,670 cubic feet.

APPENDIX V.

391

TO THE Austrian Assessment Method.
] 2( » Years.

Classes.

I^fCREMENT.

Volume

■

Over ]00 j

ears.

Total

acre,

Annual, per acre.

Total in

.0 years.

cubic
feet.

Cubic feet.

Acres.

Cubic feet.

Acres.

Normal.

Real.

Normal.

Keal.

34.250

4

152,910

(•.5

2.352

85

70

55,250

45,500

iis,(i(;2

12

(;.I7.13(>

211

3.304

S5

75

179,350

158,250

;^si.4(»s

37

4(i(i.4s(i

71

5.(141

70

(U

49,700

43.310

1. (Km;. SCI

14S

l.(i2S.()5()

l.S(i

S.753

85

71

158,100

132,060

1.. -.22, 1(14

13:!

I.:i22.1(t4

133

11.444

100

71

133.000

94,430

.■.4(l.:52!t

43

l.(i2S.u.-)()

2S3

5,7.53

KKI

78

283,000

220,740

:-5(;.-).s7(>

41)

:c.s.4(;(;

13S

(•..945

85

,S5

117,300

117,300

459,103

34

5(55,403

95

.5.952

100

71

95,000

67,450

1,373,758

124

1,387,178

172

S.3(]5

100

8(J
7(j

172.00U

147,920

(i,402,345

584

8,939,771

1,354

(i,(J03

1,020,9(J0

7,45(;,20O

5,507

92

1,242,700

1.4S3.571

1 .09(i

16

15,740

The yield for the next ten years having been fixed, the forester
decides where it is to be cut. He selects in the first place all
sylvicultural necessities, such as severance cuttings, the removal
of shelter trees over young regeneration ; next he adds all woods
which are poor in increment, especially those which have suffered
from natural phenomena ; finally he makes up the total yield by
adding the oldest woods, with due consideration of a proper distri-
bution of the age classes over the area. In this way, the Special
Working Plan on the next two pages has been obtained.

A detailed record of the w^ork done in each compartment is kept
(see page 396) ; from these data, and those on pages 392 — 393,
the Summary on pages 394 — 395 is prepared, w^hich compares the
provisions of the working plan with the actual results.

392

APPENDIX V.

Special Working Plan.

Coniiiart-
ments.

Description of Cuttings,
Cultivation, &c.

CrTTINOS.

Cultiva
tion.
Acres.

Draining,

ditches.

Feet.

Road con-
struction.
Feet.

Final.
Cubic
feet.

Inter-
mediate.
Cubic
feet.

1.

2.

3.

4.

Final cutting in regene-
rated part

Filling up blanks with
spruce ....

Thinning, and cutting can-
cerous silver firs

Total

*a. Thinning of shelter-wood
and partial final cutting.
Filling up blanks with
spruce and Scotch pine .

a & h. Thinning and re-
moval of cancerous trees

Total

a. Seeding cutting, and

partly final cutting
hk.c. Rest.

Total

a. Thinning of shelter-
wood, seeding cutting in
the fully stockecf parts
by the removal of can-
cerous and large trees

h. Rest

Total

a. Thinning and removal
of cancerous trees .

hk-Q,. Rest.

Construction of an export
road to meet the main
road ....

Total

34,000

10,000

3

34,000

10,000

3

35,000

53,000

10

35,000

53,000

10

.53,000

53,000
311,000

341,000

l!t,000

19,000

4,900

19,000

19,000

4,900

* u, b, c refer to sub-compartments.

APPENDIX V.

393

Special Working Plan — continued.

Compart-
ments.

Description of Cuttings,
Cultivation, &c.

Cuttings.

Cultiva-
tion.
Acres.

Draining,

ditches.
Feet.

Road con-
struction.
Feet.

Final.
Cubic
feet.

Inter-

mediate.

Cubic

feet.

(').

a. Cutting of all old stan-

dards and cancerous trees

4.5,000

Thinning ....

3.000

b. Thinning of shelter- wood

and partially final cutting.

li»8,000

Filling up blanks with

spruce ....

12

e. Cutting out of old defec-

tive trees where young

growth exists

14,000

Construction of an export

road to meet the main

7.

road ....
Total

a. Thinning and removal

9,500

257,000

3,000

12

9,500

of cancerous trees .

47,000

47,000

b. Rest.

c. Removal of standards

and cancerous trees

2.5,000

Thinning

15,000

Construction of an export

s.

road ....
Total

In the regeneration area :

5,000

72,000

62,000

5,000

thinning of shelter-wood

and partially final clear-

ing ; in the rest seeding

cutting ....

163,000

Filling up blanks with

spruce ....

3

Construction of an export

<).

road ....
Total

Continuation of regenera-

3,500

1(53,000

3

3,500

tion cuttings and re-

moval of cancerous trees

195,000

Thinning in fully stocked

parts ....

7,000

Filling up blanks with

spruce and Scotch pine .

8

Construction of an export

road ....
Total

3,000

195.000

7,000

8

3,000

394

APl'KNItlX V.

^UM.MAin' ui Tin; I'kovi^sion.-

Compartment.

Total

Provisions of Working Plan.

CuKe..t.L"^

34,000 10,000

So, 000 53,0(10

53.000

341,000

19,000 : 1!),000

257,000

72,1100
l(;:{,ooo
195,000

Total.
Cubic Feet.

44,000

ss.ooo

53,000

311,000

38.000

2<>0,000

(;2,ooo 134,000
h;:!, 01 III
7,(J00 202,000

154.0!)0

Cultiva-
tion.
Acres.

1.323.00(1

12

Dialnin};.
Fi-ft.

Road
Construc-
tion.
Feet.

4,900

!l,.500

5.000
3..500
3.000

25.ilO0

Xotr. — The i-xccs.s was due to heavy windfalls; it will not derange future

APPENDIX V

395

WoKKiXG Plan axd oi- the Execution.

Final.
Cubic Feet

Results of Actual Work Done.

Comparison of
Proposed and Ex-
ecuted Cuttings.

Cuttings.

Inter-
mediate.
Cubic
Feet.

33,034 12,549
r)4,517 75,000

132,900

177,169

86,606 68,301

95,852
111,049
197.660

Total.
Cubic
Feet.

Culti-
atioii
Acres

45,
129,517

132,900

177,169

154.90;

364,079

95,852
111,049
197,660

.408.716

Road
Con-
.struc-
tion.
Feet.

5,003

Cut too
much.
Cubic
Feet.

1,583
41,517

Cut too
little.
Cubic
Feet.

5,299
3,691
2.953

104,079

163,831

38,148

51,951

4.340

Exces.s due to
windfalls and
snow break.

Excess due to
windfalls and
snow-break.

Held back, on
account of ex-
tra fellings in
other compts.

Excess due to
windfalls.

Excess : wind-
falls and con-
struction of
road. !

Thinning held
over.

Held back on
account of ex- I
cess in other !
c 0 m p a r t-
ments.

arrangements, as there is yet a consideiable excess of growing stock in the forest.

396

APPENDIX V.

Sample Page of the Dktailed Coxtroi. Book.

C mil jiK lime lit 1.

Year.

Dpscription of Cuttings, Culti-
vation, ell-.

Cuttings.

Cultiva-
tion.
Acre.s.

Draining

Ditche.s.

Feet.

Road
Con-
.struc-
tion.
Feet.

Final.
Cubic

Feet.

Inter-
mediate.
Cubic
Feet.

Prov'moH of Worlilng Plan.

Final cutting in regenerated p^rt

31,000

Filling up blanks with spruce .

3

Thinning and cutting of can-
cerous silver firs

Total .

10,000

31,000

10,000

3

-

-

Execution.

1884

Final cutting ....
Dry and windfall wood .

14,297
813

1885

Windfalls

()65

1886

Final cutting, thinning . . .
Windfalls

6,166
547

832

1887

Windfalls

1,363

1888

Final cutting, thinning
Planting .....
Windfall

7,759
82

11,717

1-7

1889

Dry wood, windfalls . . .
Planting .....

649

2-2

1890

Windfalls

Planting

(593

1891

Planting ... . .

1892

Planting

1893

Planting

Total .

1

33,034

12,549

4-4

397

APPENDIX VI.

Notes on the Formulae for Compound Interest (see page 116).

Summation of Geometrical Series.

Let a be the first position in a geometrical series, q the factor
with which the first position is multiplied in order to obtain the
second position, and so on, and 11 the number of positions. Then
the sum

S = a + aq + aq" + aq^ + . . . + aq"~K

By multiplying both sides with q, the equation becomes
Sq = aq + ags -|- aq^ + aq''' . . . + aq''\

Deduct the first from the second equation :
Sq - S = aq" - a, or
S{q -l) = a ir - 1).
S = _i£ — Z — I (for a rising series).

This is the formula for the sum of a rising series. In the case of a
falling series (g < 1), a more convenient form is obtained, by
multiplying the formula above and below by - 1, which gives the
formula —

S = — ^ — Z_^' (for a falling series).

If now n = CO , then q'^ = 0, and
S = (for a falling infinite series).

Formula III.—C„,,, = ^ O-'^P""' - ^) is thus obtained :
C',„„ = E + B X 1-Op'" + B X 1-Op^"' + . . . + B X VOf^-''"\

398 APPENDIX VI.

Here a = B and q = l-0;y"; hence,

C = ^ (I-QF'"- 1) or = ^ (1 - l-Oj^""-)
l-OiJ'"-! ' 1 - l-Ojy- •

Formula IV.-C = '' i^-^P"-^)

This formula is obtained by introducing iit = 1 into Formula III.

Formula F.-CV = ^ (l-QiJ'""-!)
l-0iJ'""(l-0p'«-l)

1-0^/" ^ l-O/-'- ^ • • • ^ i-o^.-
7? 1

*^o — 1 , which, alter reduction, leads to

1 - ^

Formula V.

Formula VI.~C, = 'lM^!:zi) is obtained by introducing
vi = 1 into Formula V.

Formula VII.— C, = 1^.

^<j = 1-7.- +T-r>-> + . • . + -,-,s— Si- Here « — ^ ^, and ^7 = --:- •

r

hence 6' = ^^ = Jl

1 - _L -^p

Formula VIII.— C,, = ^

l-Oj)"-!

c =^-+^- + ... + JL

Here a = ^ J' ; </ = —p.— and u = 00 ; hence ,

APPENDIX VI. 399

C = I'Qj^" ^ -R

" -,_ J_ l-Op"-l*

C.= ^^+ ^' + ^^ + ... -^

Here a = ,-^; ; g = —7-— ; and ;i = 00 ; hence,
1-O^y" -^ 1-0^;" '

B
" 1 _ 1 l-0»" - 1 '

Funnuld X. — C'„ — ',7^-- — y- is obtained l)y multiplying
Fonnula VIII. by l-O^;"; or in the following way : —
c: = 11 + -IL- + JL, + . . . + A_

P

Fonuida XI. — /• = _ ^ — - x -Op
l-0/j"-l

11 . B, . r . r

+ 4-. ..00= + +...00'

l-Qp" ^ 1-0/" ^ 1-Qp ^ l-Qp- ^

or, according to Formulas VIII. and VII.,

Formula XII.— r = -^ x l-Qjj"-'" ^ .^
1-Op" — 1

or, according to Formulas IX. and VII.,

B X l-Oj)"-'" r T B X 1-Op"-'" ^,

400 APPENDIX VI.

Formula XIII.— r = ^ ^ ^'^^'" x -O;;
l-Op"-l

E) 1 -^ I -R , '■,'■(

1-029" 1-Op-" l-Oj) 1-Oy-

or, according to Formulas X. and VII.

B X l-0»" }■ , B X 1-Op" ^ ,,

INDEX.

A.

Accui'acy of metliods fordetermiu-

ing volume, 63
Age classes, distribution of, over
forest, 220
normal, 206

,, ,, size of, 209

,, ,, table of, 271
Age of trees and woods, 72
Alder, yield table of, 380
Allotment of woods to periods,

metbod of, 311
Analysis of Scotch pine tree, 83
Annual coupe, 207
Appendices, 335
Area increment, 82

,, of circles, 336, 338
Areas, survey of, 248

„ table of, 268
Austrian method, 317

,, ,, working plan for,

390

B.

Bark, volume of, 34
Beecb, yield tables of, 356
Birch, yield table of, 380
Boundaries, register of, 268
Branch and root wood, volume of,

32
Brandis' hypsometer, 24
,, method, 324

Callipers, 7

Change of sylvicultural system, 305

Choice of rotation, 204

,, ,, species, 291
Christen's hypsometei', 23

F.M.

Circles, area of, 326
sum of, 338

Collection of statistics, 248

Compartment, the, 277

Compartments, description of, 250,
269

Compass, tree, 11

Compound interest, formuLo of, 116
,, ,, notes on for-

mulae for, 397
tables of, 340

Conditions in and around the forest,
266

Control of working plans, 330

Conversion of system, 305

Coi^i^ice woods, yield tables of, 380

Cost value, definition of, 112
,, ,, of forests, 147
,, ,, of forest soil, 131
,, ,, of growing stock, 137

Coupe, annual, 207

Cutting series, the, 281

Cylinders, volume of, 338

D.

Demarcation of the divisions of a

forest, 288
Dendrometer, 11

Description of compartments, 250
Determination of quality, 256

,, yield, 295
Diameter gauge, 7

,, increment, 80
,, increment, measurement
of, 7, 12
Division of forest area, 276
Divisions of a forest,' demarcation

of, 288
Draudt's method, 54

D D

402

INDEX.

E.

Estimate, determiuation of volume
by, r.9
,, ocular (of Aolume), 35
,, of receipts and expense.-^,

lis.

Expectatioia value, definition of,
112
,, value of forest soil,

122
value of forests, 144
,, value of growing

stock, 133
Expenses, estimate of, 118

,, receipts and yields, 264

Felled trees, measurement of, 28
Financial results of forestry, 151
,, rotation, 194
,, test applied to methods
of treatment, 163
Fixed annual coupes, method of,

311
Forest mensuration, 3
,, per cent., 190
,, percent, determination of,

157
,, valuation, 109
Forestry, determiuation of the
profit of, 152
,, financial results of, 151

Forests, cost value of, 14-7

, , determination of the rental

of, 149
,, expectation value of, 144
,, rental value of, 148
, , sale value of, 148
,, valuation of, 144
Formation, method of, 293
Form factors, 36

,, „ determinations of

volume by means

of, 60—61

Formukv of compound interest, 116

,, of compound interest,

notes on, 397

Foundations, the, of forest manage-
ment, 169

General method of measuring the
volume of woods,
45
,, ,, modifications of, 52

Girth, measurement of, 6
Growing stock, 251

,, ,, cost value of, 137
,, ,, expectation value

of, 133
,, ,, increment and yield,
relation between,
238
,, ,, normal, 225
,, ,, normal, value of, 141
,, ., sale, or utilisation

value of, 139
., ., valuation of, 133

H.

Hartig's, Robert, method, 59
Height increment, 79

,, of trees, measurement of,
14
Heyer's method, 326
Highest income, rotation of, 200
Hundeshagen's method, 320
Hypsometer, Brandis', 24

,, Ohristen's, 23

,, Weise's, 21

Increment, the, 174

,, borer, Pressler's, 12

,, determination of, 78

,. growing stock and

yield, relation be-
tween, 238
,, in height, 79

of area, 82
,, of diameter, 80

,, of single trees, deter,

mination of, 79

INDEX.

403

Increment of whole woods, 92

of woods, determined
by increment of the
past, 93
, , of woods by yield tables,

93, 104
,, of volume, 82, 174

,, per cent., volume, 183

,, price, 189

quality, 18G
Instriiments used in mensuration, 6
Interest, choice of rate of, 113

formulre of comi)ound, 1 1 (>
,, notes on the formulse for

compound, 397
, , rate of, yielded by forestry ,

157
,, tables of compound, 340

Judeich's method, 296

Larch, yield table of, 380
Length of logs or trees, measure-
ment of, 14
Locality, 250

M.

Management, objects of, 1
Mantel's, von, method, 323
Maps, 273
Measurement of diameter, 7

,, of diameter incre-

ment, 12
of felled trees, 28
of girth, 6
,, of height of trees, 14

,, of length of logs or

trees, 14
,, of standing trees, 35

Mensuration, forest, 3
Method, Brandis', 324
Heyer's, 32G
Hundeshagen's, 320
Judeich's, 296

Method of allotment of woods to
periods, 311
of areas, working plan for,
382
, , of fixed annual coupes, 311
,, of periods by area, 312
,, of periods by area and

volume, 316
,, of periods by volume, 314
of treatment, 290
of volume, working plan
for, 388
,, the Austrian, 317
,. von Mantel's, 323
Money vield tables, 120

N.

Normal age classes, 206

,, forest compared with real

forest, 240
,, growing stock, 225
,, growing stock, value of, 141
,, yield, 233
Notes of future treatment, 263
,, on formulse for compound
interest, 397
Numbering the divisions of a forest,
288

0.

Oak, yield tables of, 346
Objects of management, 1
Ocular estimate (of volume), 35

Per cent., forest, 190

,, ,, determination of,
157
Physical rotation, 203
Preparation of working plans, 244
Pressler's increment borer, 12
Price increment, 189
Profit of forestry, determination of,

152
Property, value of. 112

404

INDEX.

Q.

Qualities of locality, table of, 269
Quality classes of yield tables, 95

,, determination of, 256

,, increment, 186

E.

Eate of interest, choice of, 113
. , , , , . of forestry, deter-

mination of, 157
Eeal forest compared with normal

forest, 240
Eeceipts and expenses, estimate of,

lis

,. expenses and yields, 264
Eegulation of yield, 295
Eenewal of working plans, 330
Eental of forest, determination of,
149
value, definition of, 113
,, value of forests, 148
Eeport, statistical, 268
Eides, the system of roads and, 284
Eoads and rides, the system of, 284
Eoot wood, volume of, 32
Eotation, 194, 294

choice of, 204
financial, 194
of greatest production of

volume, 202
of highest income, 200
physical, 203
technical, 203

Sale value, definition of, 113
„ value of forests, 148
„ value of forest soil, 131
,, value of growing stock, 139
Sample plots, determination of

volume by means of, 66
,. trees, determination of

volume by means of, 43
,, trees, general method of,

45

Scotch pine tree, analysis of, 83
„ yield tables of, 362
Severance cuttings, 282
Silver fir, yield tables of. 374
Soil, cost value of, 131
., expectation value of. 122
,, sale value of, 131
,, valuation of forest, 122
Species, choice of, 291
Spruce, yield tables of, 368
Standing trees, measurement of, 35
Statistical report, 268
Statistics, collection of, 248
Stem, volume of, 28
Sub-comiDartment, the, 278
Sum of circles, 338
Survey of areas, 248
System, change of sylvicultural, 305
conversion of, 305
,, sylvicultural, 291

Tables of compound interest, 340
Technical rotation, 203
Tending, method of, 294
Treatment, method of, 290

,, notes regarding future,

263
Tree compass, 11
Trees, age of, 72

Type trees, determination of volume
by means of, 43

U.

Urich's method, 57
Utilisation vahie of growing stock,
139

Valuation of forests, 109

of forest soil, 122

,, of the growing stock, 133

,, of whole woods or

forests, 144

Value of growing stock of a single

wood, 133

INDEX.

405

Value of normal growinfr stock, 141

,, of property, 112
^"olume determination, comparative

accuracy of methods of,

63
. , deteiinination of by sample

plots, 66
. , determination of by samjjle

trees, 43
, , determined by estimate, 69
, , determined by form factors,

61
,, determined by volume

tables, 61
,, estimated by j-ield tables,

70
.. increment, 82, 174
.. increment per cent., 183
,. of bark, 34

„ of branch and root wood, 32
„ of cylinders, 338
,, of stem, 28
., of whole woods, 43
,. rotation of greatest pro-
duction of, 202
,, tables. 39

W.

Weise's hypsometer, 21
Woods, age of, 72

,, increment of, 92
,, volume of, 43
,, whole, valuation of, 144
"Working cii'cle, the, 276

,, plans, control and renewal

of, 330
,, plan for Austrian method,
390
plan for the method of
areas, 382

Working plan for the method of
volume, 388
,, plan report, 245
,, plans, preparation of. 244
section, the. 278

Xylometer, 26

Y.

Yield, determination and regula-
tion of the, 295
,, increment and growing
stock, relation between,
238
normal, 233

receipts and expenses, 264
.. table of alder, 380
.. table of birch, 380
.. table of larch, 380
.. table of past, 272
.. tables,' 345

tables, construction of, 97
., tables, determination of in-
crement by means of, 93
, , tables, estimating volume by
means of, 70
tables, local and general, 95
.. tables, objects and contents
of, 94
tables of beech, 356
tables of coppice woods, 380
tables of, generally. 93
,. tables of money, 1 20
.. tables of oak, 346
,. tables of Scotch pine, 362

tables of silver fir, 374
., tables of spruce, 368
,, tables, quality classes, 95

END OF VOLUME III.

BPADBURY, AGNEW, & CO. LD., PRINTERS, LONDON AND TONBBIDOE.

Library
N. C. State College