m

LIB Y

FACULTY OF FORESTRY
UNIVERSITY OF TORONTO

* '

DE. SCHLICH'S MANUAL OF FOKESTKY,

VOL. III.

EKEATA.

Page 49, line 14 from top, for = ^—, — — , read V1= -V—
„ 50, „ 7 „ foot, /or (v + i/ + v" + ...), read

V

64, „ 12 „ foot, for F J-^, read F= SxH-

97, between lines 14 and 15 add (2 a) The mean dia-
meter of trees.

120, for lines 5 & 6 from top, substitute " A rental R is
due after n years, and again every n years, for
ever ; it is equal to an annual rental of — ."

140, line 4 from foot, for Under, read By.
145, ,, 3 ,, foot, for (1'ojp — 1), read (l*opr — 1).
163, ,,2 „ foot, for curr- p, read curr- pf.
181, lines 14 and 15 from foot, strike out the words
" the increment of."

n 'i 10 I

186, line 3 from foot, for /, read I .

192, „ 3 „ foot, /or /, read, V.

194, „ 4 „ top, /or 4-37-, read 4'37 = .

n t 10 /

194, ,, 5 ,, top, for / read I -
V v

196, „ 2 „ top, for i^"1^ read l°8 S-\og ^

10 n

198, ,,3 ,, top, for current, read correct.

203, last column of table, for Indicatin, read Indicating.

220, line 3 from top, for r = 20 „ read r = 20 years.

Page 221, line 8 from foot, for mxr, read t x r.
,, 224, ,, 3 ,, top, for Coupe No. , read Coupe No. 20.
,, 224, ,, 10 ,, top, /or Coupe No. 20, readCoupeNo. 1
,, 227, „ 12 „ foot, for Under, read By.
„ 240, „ " 8 „* top, /or Under, read By.

,, 245, ,, 14 ,, \ top, for annual yield, read final annual
yield.

,, 249, „ 3 „ top, for (m-l) x I, read (m-1) I

" 2

„ 267, „ 17 „ foot, for Under, read By.
,, 280, ,, 7 ,, foot, add the word "soil" after geology.
,, 342, ,, 13 ,, foot, read 6. Determination of the

yield.

,, 349, line 2 from foot, for a lotment, read allotment.
,, 374, first column, for Holier Oclisen, read Holier

Ochsenkopf.

,, 370, line 7 from foot, after single, add the word " trees."
,, 392, in heading, fill in figures 7 and 8.
,, 394, „ ,; ,, „ figure 4.

Note. — Some of the above mistakes do not occur in all copies of the book.

With the Author's Compliments.

A

MANUAL OF FORESTRY,

MANUAL OF FOBESTBY

BY

WILLIAM SCHLICH, C.I.E., PH.D.,

PRINCIPAL PEOFESSOR OF FORESTRY AT THE ROYAL INDIAN ENGINEERING COLLEGE,
COOPERS HILL ',

LATE INSPECTOR GENERAL OF FORESTS TO THE GOVERNMENT OF INDIA.

VOLUME III.

FOREST MANAGEMENT.

WITH 53 ILLUSTRATIONS.

LONDON :

BRADBURY, AGNEW, & CO. LD., 8, 9, 10, BOUVERIE STREET.

1895.

LONDON :
BRADBURY, A6NEW, «fe SO. LD., PRINTERS, WHITEFR1ARS.

U.

PEEFACE.

IN the Preface to the first volume of this Manual I intimated
that the work would comprise the following parts : —

I. THE UTILITY OF FORESTS.
II. PRINCIPLES OF SYLVICULTURE.

III. FORMATION, KEGENERATION, AND TENDING OF WOODS.

IV. FOREST FINANCE:

V. FOREST WORKING PLANS.
VI. FOREST PROTECTION.
VII. FOREST UTILIZATION.

Parts I. to V. have been dealt with in this and the two
previous volumes. My colleague, Mr. W. E. Fisher, has
translated Dr. Hess' excellent work on " Forest Protection."
That work will appear almost simultaneously with this volume,
and take its place as Volume IV. of this series. Mr. Fisher
has also commenced the translation of Dr. Gayer's classical
work on " Forest Utilization," which will be published
towards the end of the present year, and make the fifth and
final volume of this Manual.

Under these circumstances I have now completed the task
which I set myself at starting. That task consisted in
providing, in the first place, text books on the various branches
of forestry for the students at Coopers Hill College. At
the same time I have endeavoured so to prepare the books

vi PREFACE.

that they might also be useful to others who desired to become
acquainted with forest science in Central and Western Europe.

As I have stated elsewhere the principles of forest manage-
ment hold good all the world over. In endeavouring to
explain these principles it seemed to me right and proper
to be guided by the experience gained in those countries
which have taken the lead in forestry, namely, Germany and
France. In these countries systematic forest management
became a necessity almost a hundred years ago, so that their
methods are now. based upon long experience and a rich
crop of investigations.

Economic forestry has not been developed in the same
degree in Britain, because it was of subordinate importance.
Of late, however, many voices have been heard urging the
subject upon the attention of the public and the government
of the country. It has more particularly been suggested
that the depression in agriculture, the continuous flow of
population into the towns, and the ever increasing number of
the unemployed, are matters which might raise more extended
forest operations into the position of an economic necessity.
Ten years ago I showed, and so have many others since,
that timber worth at least £12,000,000, which could be pro-
duced locally, is annually imported into this country ; also that
more waste land is available in these Islands than is necessary
to produce that timber. On the other hand it has been said
that the home grown timber cannot compete with the imported
material. This is not the place to enter into the details of
the question, but I desire to draw attention to two points :— -

In the first place, British timber cannot compete with the
imported timber because, as at present grown, it is of inferior
quality, being generally shorter and less clean of branches and

PREFACE. Vll

knots. Moreover, conifers generally grow too quickly in
Britain, because the woods are too heavily thinned while
young; hence the individual trees increase too rapidly, and
produce timber inferior to that of the same species imported
from the Baltic, and grown in crowded woods.

Secondly, the home-grown timber is brought into the market
in fluctuating quantities, so that neither a regular timber trade,
nor superior methods of working up the material, nor forest
industries, have a chance of developing and thriving. In
short, the whole business is far too haphazard.

Economic forestry, to be successful, must be conducted
on true sylvicultural principles, arid the yield must be so
regulated, that, approximately, the same quantity of material
may be brought into the market every year ; in other words,
the principle of a sustained and well-regulated yield must be
recognized. Then, and then only, can adequate financial
results be expected from forestry.

These are the principles which I have endeavoured to
explain in this and the previous two volumes. Whether the
student proposes to follow the profession of a forester in this
country, in India, the Colonies, or in America, makes no
difference ; the principles are the same everywhere. Once
they have been thoroughly assimilated, the student will without
difficulty apply them to the special conditions with which he
may have to deal in any part of the world.

While I was Inspector General of Forests to the Govern-
ment of India, I was fortunate enough to obtain sanction to
the establishment of that branch of the Indian Forest
Department, which is known as " The Working Plan Branch."
This, no doubt, was a very important step, because the
measure provided that gradually working plans should be

viii PREFACE.

prepared for all Government forests, and that the Inspector
General of Forests should control the execution of the working
plans. The results have been very satisfactory, as the
management of the Indian forests has been placed on a
safer basis, and the principle of continuity of action been
more fully recognized. Absolute security, however, has not
as yet been established in this respect. From time to time
re-action is liable to set in. Hence I was anxious to set
forth in the present volume the principle and paramount
importance of a " sustained yield " of forests.

It is not for me to say in how far I have succeeded in my
task; it is, however, a matter of satisfaction to me that a
second edition of the first two volumes will have to be issued
shortly. This gives me hope that the cause of systematic
forestry is gaining ground, and that it will impress itself more
and more upon the minds of those who leave this country tp
govern India and the Colonies. Should this happy anticipa-
tion be realized, then the progress of forest administration in
India will be definitely assured. When forestry in Britain has
once become an essential part of the industry based upon the
soil, those who leave these shores will be duly impressed
\>y its importance, and they will bring to their spheres of
action a sympathetic understanding of the business, which
will go a long way to prevent any oscillating policy that other-
wise might threaten to interfere with the progress of forest
management in India and the Colonies. Continuity of action
will then become the order of the day, without which no
industry can flourish, whatever its name or nature may be,
and least of all forestry, the produce of which frequently
requires a century and more to mature.

In writing the present volume, I have, apart from my

PREFACE. IX

own experience, extending over many years, utilized chiefly
the following works : —

For Forest Mensuration :

(1) Schwappach, " Leitfaden der Holzmesskunde."

(2) Baur, " Holzmesskunde."

For Forest Valuation :

(1) G. Heyer, " Waldwerthrechnung."

(2) Wimmenauer, " Grundriss der Waldwerthrechnung."

In compiling the tables at pages 394 to 397, I have used
those appended to the above-mentioned two works, and I
desire to express herewith my best thanks to the family of
the late Professor G. Heyer (under whom I studied forestry),
and to Professor Wimmenauer, for the permission which they
kindly gave me to do this.

For Forest Working Plans :

(1) Heyer, " Die Waldertrags-Regelung."

(2) Judeich, " Die Forsteinrichtung."

As Judeich's " Bestandswirthschaft " is the method of regu-
lating the yield of forests which commends itself to me more
than any other, I have naturally largely drawn upon Judeich.
At the same time I have introduced certain modifications into
the method where it seemed too rigid.

I have also made occasional use of,

(1) Puton, " Traite d'Economie Forestiere."

(2) Hess, " Encyklopadie " und " Methodologie der

Forstwissenschaft," Part III.

I am indebted to my colleague, Mr. A. Lodge, Professor

X PREFACE.

of Mathematics at this College, for his kind assistance in
looking over the proof sheets of Parts I. and II. of this
volume.

Herr Forstassessor Alwin Schenck has been good enough
to obtain for me the working plan for the Krumbach Communal
Forest, contained in Appendix A, and I herewith tender to
him my best thanks.

The extract from the working plan for the Herrenwies
Range, Appendix C, was prepared by me while I was on
tour with the students of this College during the summer
of 1893, the records having been kindly placed at niy disposal
by Herr Oberforster Ziegler of Herrenwies.

W. SCHLICH.

COOPERS HILL,

28th February. 1895.

TABLE OF CONTENTS.

PAGE

PREFACE . v

FOREST MANAGEMENT.

INTRODUCTION 1

PART I.

FOREST MENSURATION .... 3

CHAPTER I.

INSTRUMENTS USED IN FOREST MENSURATION . . 6

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

2. Instruments for the Measurement of the Diameter . . . .7

3. Instruments for the Measurement 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 . . .27

CHAPTER II.

MEASUREMENT OF FELLED TREES . . . 29

1. Volume of the Stem 29

2. Volume of the Branch and Root Wood . . . . . . 33

3. Volume of the Bark . . 34

Xll CONTENTS.

CHAPTER III.

PAGE

MEASUREMENT OF STANDING TREES . . . 35

1. Ocular Estimate 35

2. Estimate of Volume by Means of Form Factors 36

Table of Form Factors 30

3. Estimate of Volume by Means of Volume Tables 39

4. Measurement of Standing Trees by Sections 40

5. Pressler's Method of ascertaining the Volume of Standing Trees . . 41

CHAPTER IV.

DETERMINATION OF THE VOLUME OF WHOLE WOODS. 43

SECTION I. — MEASUREMENTS EXTENDING OVER THE WHOLE WOOD . 43

I. Measurement of all Trees 43

II. Determination of Volume by Means of Sample Trees . . . . 43

A. The Height is a Function of the Diameter . . .44

,1. Description of the General Method 44

2. Modifications of the Method 51

a. Draudt's Method 52

b. Urich's Method :>:>

c. Robert Hartig's Method . . . .• . . . . :>.s

3. Comparative Accuracy of the Several Methods . . . tnt

4. Determination of the Volume by Means of Form Factors

and Volume Tables . . . . . \ . . . til

B. The Height is not a Function of the Diameter . . . <'•">

SECTION II.— DETERMINATION OF VOLUME BY MEANS OP SAMPLE

PLOTS 6<>

SECTION III.— DETERMINATION OF VOLUME BY ESTIMATE . . •,!>

CHAPTER V.
THE AGE OF TREES AND WOODS . . . . 72

1. Determination of the Age of Single Trees 72

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

CONTENTS. Xlll

CHAPTER VI.

PAGE

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 95

A. Determination of the Future Increment according to the

Mean Annual Increment of the Past . . . . . 96

B. Determination of the Increment by Means of Yield Tables . 90

I. Of Yield Tables generally . . 96

II. Determination of the Increment by Means of Yield Tables . 105

PAET II.

FOREST VALUATION . . . . .111
CHAPTER I.

PRELIMINARY MATTERS . . . . . 114

SECTION I. — VALUE OF PROPERTY GENERALLY 114

SECTION II.— CHOICE OF RATE OF INTEREST 114

SECTION III.— FORMULAE OF COMPOUND INTEREST . . . .118

SECTION IV. — ESTIMATE OF RECEIPTS AND EXPENSES . . . . 120

Money Yield Tables for Scotch Pine and Beech 122

CHAPTER II.

VALUATION OF FOREST SOIL .... 124
SECTION I.— THE EXPECTATION VALUE OF FOREST SOIL . . .124
SECTION II. — THE COST VALUE OF FOREST SOIL . . . 132

SECTION III. — THE SALE VALUE OF FOREST SOIL . 133

XIV CONTENTS.

CHAPTER III.

PAGE

VALUATION OF THE GROWING STOCK . . . 134

SECTION I. — VALUE OF THE GROWING STOCK OF A WHOLE WOOD . 134

1. Expectation Value of a Whole Wood . . . • . . . . 134

2. Cost Value of a Whole Wood 138

3. Sale or Utilization Value of a Whole Wood 140

4. Relation between Expectation and Cost Values of a Normal Wood . 141

5. Relation between Expectation and Cost Values on the one hand

and Utilization Value on the other 142

SECTION IT. — VALUE OF PAET OF A WOOD 143

SECTION III. — VALUE OF THE GROWING STOCK OF A NORMAL SERIES

OF AGE GRADATIONS * . .144

CHAPTER IV.

VALUATION OF WHOLE FORESTS . . . . 149

1. Expectation Value of a Forest 141)

2. Cost Value of a Forest 152

8. Sale Value of a Forest . .153

4. Rental Value of a Forest 153

*

CHAPTER V.

DETERMINATION OF THE RENTAL OF FORESTS . 154

CHAPTER VI.

THE FINANCIAL RESULTS OF FORESTRY . . . ir><>

SECTION I.— THE METHODS OF CALCULATING THE FINANCIAL RESULTS

OF FORESTRY 156

1. Determination of the Profit of Forestry 157

2. Determination of the Rate of Interest yielded by Capital invested

in Forestry lf>2

SECTION II.— THE FINANCIAL TEST APPLIED TO THE METHOD OF

TREATMENT 167

1. Choice between Forestry and Agriculture . . . . • . . 167

2. Choice of species and Sylvicultural System 168

8. Choice of Method of Formation 168

4. Choice of Method of Tending 168

5. Determination of the Financial Rotation 168

fi. Determination of the Financial Ripeness of a Wood . . .169

CONTENTS. XV

PART III.

PAGE

PRINCIPLES OF FOREST WORKING PLANS . . . 171
INTRODUCTORY 173

CHAPTER I.

THE INCREMENT . . . . . . 178

SECTION I.— QUANTITY INCREMENT 178

1. Progress of Volume Increment . . . . . . . 178

2. Quantity Increment per cent 184

3. Yield Tables for the Scotch Pine 188

SECTION II.— QUALITY INCREMENT 192

SECTION III. — PRICE INCREMENT 19»

SECTION IV.— ADDITION OF THE SEVERAL INCREMENT PER CENTS.

LEADING TO THE FOREST PER CENT 196

CHAPTER II.

THE ROTATION 200

1. The Financial Rotation 200

Financial Yield Table for Scotch Pine . 202

2. Rotation of the Highest Income 207

3. Rotation of the Greatest Production of Volume .... 208

4. The Technical Rotation 209

5. The Physical Rotation 210

6. Choice of Rotation 211

CHAPTER III.

THE NORMAL AGE CLASSES . . . .212

1. The Annual Coups or the Area to be cut annually . . . . 213

2. Size of the Age Classes 215-

3. Distribution of the Age Classes over the Forest 227

CHAPTER IV.

THE NORMAL GROWING STOCK . . .231

1. Calculation of the Normal Growing Stock as regards its Volume . 232

2. Calculation of the Financial Value of the Growing Stock . . . 239-

XVI CONTENTS.

CHAPTER Y.

PAGE

THE NORMAL YIELD 240

1 . The Yield determined by Area or Volume 240

2. The Financial Value of the Normal Yield . . 244

CHAPTER VI.

RELATION BETWEEN INCREMENT, GROWING STOCK AND

YIELD 245

1. Allotment of Increment during a Rotation 245

2. Allotment of Increment during the Regeneration Period' . . .248

3. Relation between Yield and Normal Increment .... 250

4. Relation between Normal Yield and Normal Growing Stock . . 251

CHAPTER VII.

THE REAL FOREST COMPARED WITH THE NORMAL FOREST 253

,

PART IV.

PREPARATION OF FOREST WORKING PLANS
INTRODUCTION

CHAPTER I.

COLLECTION OF STATISTICS .... -'•">'.)

SECTION I.— SURVEY AND DETERMINATION OF AREAS .... -'">'•>

SECTION II. — DESCRIPTION OF EACH WOOD OR COMPARTMENT . . 261
1. The Locality ........ -261

•2. The Growing Stock -)(>>-'S

3. Determination of the Quality of each Wood 267

4. Notes regarding Future Treatment 267

SECTION III. — PAST RECEIPTS AND EXPENSES 278

SECTION IV.— GENERAL CONDITIONS IN AND AROUND THE FOREST . 280

CONTENTS. XV11

PAGE

SECTION V.— THE STATISTICAL REPORT . . • ; ;.• ~. ., .281

1. Register of Boundaries . ., ;....,.. ..,">. i .. . . . 282

2. Table of Areas v *••..• ...- .283

3. Description of Compartments . . . .... . . 284

4. Table of Qualities of Locality . . .•..•- . . .284

5. Table of Age Classes . . . . . .:'-,. . .' • -,- . '•'-. '. 285

6. Table of Past Yields .'..'. .*."/'.' .287

7. Maps •'.- '....' . •• * •'. :. '••• .' ' •.--.• : - . 287

CHAPTER II.

DIVISION AND ALLOTMENT OF FOREST AREA . 292

1. The Working Circle .' .' .' . . . . '. . .292

2. The Compartment . . .'.-•". . . ' . . . . 293

3. The Sub-Compartment .'../'. . '. . . .294

4. The Working Section . . . . ' . - ' . - '. , . . . 295

5. The Cutting Series ". .. . ' . ' .'. . . . . .297

6. Severance Cuttings . • . . • . • . ... . . . . . 298

7. The System of Roads and Rides 300

8. Demarcation of the Divisions of a Forest 303

9. Naming and Numbering of the Divisions of a Forest . . . 304

CHAPTER III.

DETERMINATION OF THE METHOD OF TREATMENT . 305

1. Species . . . . . . ... ... . . 306

2. Sylvicultural System ' ' r :. -: . •. 306

3. Method of Formation . . . .' . '. . " . . . 308

4. Method of Tending : .• ; • • . . . '. . . . 309

5. Rotation . . . . . ; . . . . . 309

CHAPTER IV.

DETERMINATION AND REGULATION OF THE YIELD . 310
SECTION I.— DIVISION OF FOREST INTO FIXED ANNUAL COUPES . .311

SECTION II.— ALLOTMENT OP WOODS TO THE SEVERAL PERIODS or A

ROTATION 312

1. The Method of Periods by Area . .313

2. The Method of Periods by Volume 314

3. The Method of Periods by Area and Volume combined . . . 316
VOL. in. • b

XVU1 CONTENTS.

PAGE

SECTION III.— REGULATION OF THE YIELD ACCORDING TO INCREMENT

AND GROWING STOCK . . 317

1. The Austrian Method 317

2. Hundeshagen's Method . . . . 320

3. Von Mantel's Method 323

3. Brandis' Method 325

SECTION IV.— KEGULATION OP THE YIELD ACCORDING TO INCREMENT
AND GROWING STOCK, COMBINED WITH THE ALLOTMENT
OF AREAS TO THE SEVERAL PERIODS OF A ROTATION . 327

SECTION V.— SELECTION OF WOODS FOR CUTTING IN ACCORDANCE
WITH SYLVICULTURAL REQUIREMENTS AND THE OBJECTS
OF MANAGEMENT .330

1. Application of the Method to Clear Cutting in High Forest and the

Shelter-wood Compartment system , . 331

2. Application of the Method to other Sylvicultural Systems . . 335

3. Change from one Sylvicultural System to Another ; called a Con-

version 338

CHAPTER Y.

THE WORKING PLAN REPORT . . . .341

CHAPTER VI.

CONTROL OF EXECUTION AND RENEWAL OF WORKING PLANS 344

1. Record of Changes 345

2. Record of Works • . . 345

3. Renewal of Working Plans . . . .... . .346

APPENDIX A.

Working Plan for the Communal Forest of Krumbach (Yield regulated

according to Method of Periods by Area) 349

APPENDIX B.

General Working Plan for the Method of Periods by Volume . . .362

APPENDIX C.

Working Plan for a Portion of the State Forests of the Herrenwies Range

(Yield regulated according to the Austrian Method) .... 364

CONTENTS. XIX

APPENDIX D.— TABLES . . Y.

I. Yield Tables used in Saxony for the Determination of the Quality of
Locality . . . . . . . * ...... 386

II. Area of Circles for Diameters of 1 inch to 60 inches .... 390

III. Volume of Cylinders and Sum of Circles, for diameters of 1 inch to

48 inches . . .... ...... 392

IV. Tables of Compound Interest

A. Amount to which a Capital accumulates in the Course of n Years . 394

B. Present Value of a Capital to be realized after n Years . . . 395

C. Present Value of a Perpetual Eental due every n Years . . . 396

D. Present Value of a Rental due at the End of every Year altogether n

Times . . ...•»'. . . .397

FOKEST MANAGEMENT.

INTRODUCTION.

THE management of forests depends, apart from local con-
ditions, 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, land-
slips, avalanches, 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 duty of the forester to see that these objects
are realised to the fullest extent.

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 latter.

The economic working, whether it aims at the production of
a special class, or the greatest quantity of produce, or the best

VOL. III. B

2 INTRODUCTION.

financial results, must be based on the yield of the forest.
In order to determine this, 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 deter-
mination of the dimensions of trees, the volume
of trees and whole woods, their age and
increment.

PART II. — FOREST VALUATION, dealing with the determina-
tion of the capital employed in forestry, and
the financial results produced by it.

PART III. — PRINCIPLES OF FOREST WORKING PLANS.
PART IV. — PREPARATION OF FOREST WORKING PLANS.

PAET I.

FOREST MENSURATION.

B 2

FOREST MENSURATION.

FOREST Mensuration deals with the determination of the
dimensions, volume, 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 basis 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 cubic foot.

The subject has been divided into the following chapters : —

I. OF THE INSTRUMENTS USED IN FOREST MENSURATION.
II. OF -THE MEASUREMENT OF FELLED TREES.
III. ,, ,, „ ,, STANDING TREES.

IV. „ ,, ,, ,, WHOLE WOODS.

V. DETERMINATION OF THE AGE OF SINGLE TREES AND
WHOLE WOODS.

VI. DETERMINATION OF THE INCREMENT OF SINGLE TREES
AND WHOLE WOODS.

CHAPTER I.

INSTRUMENTS USED IN FOREST MENSURATION.

INSTRUMENTS 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 object, either to ascertain the various dimensions, or to
calculate from them the volume ; in the latter case the measure-
ment of the girth or diameter is used to calculate the sectional
area, on the assumption that it forms a circle.

The instruments may be classified as follows : —

t
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, of 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 the tape are subject to various sources

MEASUREMENT OF THE DIAMETER. 7

of inaccuracy, amongst which the following deserve to be
mentioned : —

(a) The sections of most trees are not circles.
(6) 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 be obtained, but the procedure takes
more time, and is therefore not employed where large numbers
of trees have to be measured.

2. Instruments for the Measurement 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 compasSr

a. The Calliper 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
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 on next page).

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

8 INSTRUMENTS USED IN MENSURATION.

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.

Where large numbers of trees are to be measured, it is
desirable to round off the limits of each unit ; for instance, if

Vertical Section of Movable
Arm.

Fig. 1.— Friedrich's Calliper.

the rule is divided into intervals of inches, the first division
line is placed at J inch from zero, the second at 1 J, the third
at 2|, and so on (Fig. 2). In this way all trees measuring
from J to 1J inches are recorded as having a diameter of
1 inch, those from 1J to 2J inches as 2 inches, and so on.
A good calliper 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 which it is likely to be subjected to.

(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.

MEASUREMENT OF THE DIAMETER,

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

Callipers of iron would be too heavy and too cold in winter,
hence they are made of wood. As wood alters with the
degree of humidity, the movable arm is liable to jam at one

o e

CD

© 0

Fig. 2.

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 : —

Gustav Heyers 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, b the wedge, and c the section of the mov-
able arm. The wedge is fastened to a screw, which can be
moved by a key at d. On moving the wedge from left to right,
it presses the rule upwards and thus tightens it ; on moving the

10

INSTRUMENTS USED IN MENSURATION.

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.

Friedrich's Calliper. — In this
instrument the section of the
rule has the shape of a rectangle,
while the opening of the mov-
able 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 b
(above). As these points are
liable to wear awa}r, thus causing
Fig. 3.— Heyer's Calliper. the arm to assume a position
which is no longer at right

angles to the rule, Bohmerle has added a spring at b, which

can be moved by a screw, until the true position of the arm is

established.

b. Accuracy of Measurements icith the Calliper.

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.

MEASUREMENT OF THE DIAMETER.

11

(3) In the case of excentric 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 trees which

are divided into two or
more limbs below the
fixed height of measure-
ment, each limb must be
measured and recorded
as a separate tree.

(6) The calliper must be placed

at right angles to the axis
of the tree, and the rule
must touch the tree.

(7) The reading must be

taken while the calliper
rests on the tree, and not
after it has been with-
drawn. Fig. 4.— The Tree Compass.

c. 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 c and d, while it can be read off at li on the arc/, 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 continued use.

d. Dendrometers.

In some cases certain dendrometers 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

12 INSTRUMENTS USED IN MENSURATION.

of the observer from the tree. From these data the diameter
is calculated. Instead of the angle, the distance a b between
the two lines of sight can be measured, in which case the
diameter is obtained in the following way (Fig. 5) :—

and

A B = G- -4 x a 6.
Oa

If, therefore, the instrument gives a b and Ca, and the dis
tance C A has been measured, the diameter can be calculated.

Fig. 5.

So far, instruments of this class have not obtained a footing
in practice, because those at present available do not work with
sufficient accuracy and C A is difficult to ascertain.

3. Instruments for the Measurement of the Diameter Increment.

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

MEASUREMENT OF THE DIAMETER INCREMENT. 13

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 is hollow and serves to receive the

Fig. 6. — Pressler's Increment Borer.

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
rings, and 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 C}7lindrical
column of wood enters the hollow borer, which is severed from
the tree except at its base ; then the wedge is inserted between

14 INSTRUMENTS USED IN MENSURATION.

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, which 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 accord-
ing to the length of the borer. The breadth of the con-
centric rings is then measured. If the rings are not distinct,
a smooth surface may be prepared with a sharp knife.

4. Instruments for the Measurement of the Length of Felled

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 well
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).

HEIGHT MEASURING.

15

a. Geometrical Height Measuring.

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 below the horizontal plane ; or above 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

o ,'

Fig. 7.

similar triangles are formed, which are used for the determina-
tion of the height of the tree.

Let A B (Fig. 7) be the height of the tree.

D B SL ray from the eye of the observer to the top of the

tree.

D A, ditto to the foot of the tree.
D C a horizontal line.

a, b, and c the points where the three rays hit the plumb-
line. Then the height is determined as follows :

The horizontal line hits the tree between the top and
foot. Here the following equation holds good : —
B C :bc = D C : D c

(1)

16
and

Again,
and

Hence,

INSTRUMENTS USED IN MENSURATION.
be x D G

A G :ac = D C : DC

A r _ ac x D G
~D~e

BC+AC=AB= height of tree = ft <* + _a c) x 7? 0

Fig. 8.

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

DC

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

H = AC-BC = ia

In each of the above three cases two measurements are

HEIGHT MEASURING.

17

required, unless the foot of the tree happens to be at the same
level with the eye of the observer. The horizontal distance
D C must be measured, and a c, b c and D c are read off upon
the instrument in the same units in which D C has been
measured.

The measurement of D C can be avoided in the following
manner (Fig. 10 on next page) : —

A staff M N, of a known 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 n, and the similar
triangles D C M and D c m, as well as D C N and D c n, so
that the following equations hold good : —

D G :Dc = A B :ab
and

D G :D c = MN : mn ;
hence,

and

A B :a I = M N :mn

= H = a - x M~N = ab x l
m n mn

18

INSTRUMENTS USED IN MENSURATION.

This equation can easily be modified for the cases when the
horizontal plane lies above the top or below the foot of the
tree.

The indirect determination of the distance by means of a
staff is less accurate than measuring it on the ground, as it is
difficult to read off in n with sufficient accuracy, owing to its
smallness and the necessarily primitive arrangement of the
height measuring instruments.

•"*-- -
c. .

**

Fig. 10.

If the length of a b = h can be 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 tying between the said rays are
proportionate to the lengths of the rays.

Let D A = L (Fig. 11) be the length of ray from the eye of
the observer to the foot of the tree, Da — I that from the eye to
the plumb line, A B = H the height of the tree, and a b = h 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,

I :L = h :H
and

x h.

HEIGHT MEASURING.

19

In this case L may be measured along the surface of the soil,
whether it be level or slanting, while I and h are read off on
the instrument.

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

.1*

Fig. 11.

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.

(3) Slanting position of the tree.

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

c 2

20 INSTRUMENTS USED IN MENSURATION.

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

b. Trigonometrical Height Measuring.

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

4,

Fig. 12.

of the observer to the top and foot of the tree. In A B C D
(Fig. 12) :-

E G = D C x tan. b
and in A D C A,

hence,

A G = D G x tan. a
C = H = DC (tan. a + tan. b).

If the horizontal line of vision passes below the foot of the
tree, the above formula becomes : —

H = D 0 (tan. b - tan. a).
If it passes above the tree,

H = D G (tan. a - tan. b).

Ill each of these cases, the measuring of the horizontal line
D C can be avoided by placing a staff of known length along-
side the tree. In that case (Fig. 13) :

and
hence,

HEIGHT MEASURING. 21

M C = D C x tan. m ; N G = D C x tan. n
M N = I = D C (tan. m + tan. n}

DC =

tan. m + tan. n

By introducing this value into the former equation, the
height is obtained as : —

TT _ I x (tan. a + tan. 6)
tan. m + tan. n

N

Fig. 13.

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 useful Instruments.

Weises Instrument. — It consists of (1) a tube (T) with an
objective in the shape of a cross at one end (0) and an eye-

22 INSTRUMENTS USED IN MENSURATION.

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. (8) 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.

OP
Fig. 14. — Weise's Hypsometer.

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

In using the instrument, a position is chosen from which
both the top and foot of the tree can be seen ; then the hori-
zontal 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 the 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 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 off. This number gives the

WEISE S HYPSOMETER. 23

number of feet (or yards as the case may be) from the hori-
zontal 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 the observer and the foot of the tree, which
is obtained in the same way, by directing the tube towards the
foot of the tree, reading the height on the prolongation of the
scale towards 0.

The theory of the instrument rests upon the similarity of

Fig. 15.

the triangles with the sides R H D and r h d; that is to
say, the following equation holds good :—

d : h = D : H
and

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.

Christens Instrument. — [t consists of a piece of metal (see
Fig. 16) with protruding upper and lower edges (see a and I).
The instrument is based upon the theory explained on page
17, which avoids the measurement of a base line. A staff
of known length = I, say 4 yards, is placed alongside the foot
of the tree. The instrument is then held in a vertical position

INSTRUMENTS USED IN MENSURATION.

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 b ; then the point is marked

5 -

2O_;
25

Fig. 16. — Christen's Hypsometer.

on the instrument, where a ray from the eye to the top of the
staff hits the instrument at c. In this way similar triangles
are formed, in which the following equation holds good :—

or

A B

If now a
values for A

= 12 inches, and Z = 4 3rards, and successive
= height of tree, are introduced, corresponding

BRANDIS* HYPSOMETEK AND CLINOMETER. 25

values of b c are obtained and can be marked on the instru-
ment. 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 top of the staff 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.

Fig. 17. — Brandis' Hypsometer and Clinometer.
(The front lid removed, so as to show the wheel.)

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.s

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

Brandis' Instrument* (Fig. 17). — This instrument is based
on the trigonometrical method of height measuring. It con-
sists of a tube with an objective o at one end and an eye-piece,
e, in the shape of a horizontal slit, at the other. Attached
to this tube is a wheel, which is weighted on one side and
swings between two pivots, so that it always maintains the

* To be obtained from Herr Max Wolz, Mechaniker, Bonn, Germany.

26 INSTRUMENTS USED IN MENSURATION.

same position when at rest. Oscillations can be arrested by a
stop (see at * 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 alongside 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.

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
eye of the observer to the foot of the tree measured. The
height is then found by the formula (see Fig. 18) :—

jj- _ DA x sin (u + I)
cos. u

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

DIRECT MEASUREMENT OF VOLUME. 27

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 the same time an admirable clinometer,
with which the angles of slopes can be measured and roads
laid out.

The author has used the instrument extensively both for

Fig. 20. Fig. 19.

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 construction
renders it admirably adapted for forest work.

6. Instruments for the Direct Measurement of the Volume.

For this purpose the xylometer, either alone or in combina-
tion with a scale, is used. The method is based upon the
fact that a submerged body displaces a volume 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

INSTRUMENTS USED IN MENSURATION.

which the wood is submerged. Before and after immersion
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 submerging large quantities of wood,
the whole is first weighed, and only a fraction immersed. Let
the weight of the whole be = W, that of the immersed portion = w,
the volume of the former = F, of the latter v, then : —

W : w = V : v
and

V = v- x W.
w

Instead of having a graduated vessel, the latter ma}T be filled
up to an opening, then the wood is immersed, the outflowing
water caught in a separate vessel and measured (Fig. 20).

CHAPTER II.

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. Fig. 21.

Thus the uppermost part, a, of an
undivided stem has generally the shape of a cone, the lowest
part, c, that of a truncated semicubical paraboloid, while the

30 MEASUREMENT OF FELLED TREES.

bulk between these extremes approaches in shape a truncated
Apollonian paraboloid or a cylinder.
If h = the height, or length,

S = the lower section,

s = the upper section, and

*,„= the middle section (Fig. 22),

the volume of each of the above-mentioned truncated solids is,
according to Simpson's rule : —

6
This formula reduces : —

For the cylinder to V = S x h

For the cone to V = S-^JL

3

And for the Ap. paraboloid to V = 'S + s x A or =Sm x h.

By means of these formulas 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 sections of
moderate length, each can, without com-
mitting any appreciable error, be considered as a truncated
paraboloid, the volume of which is —

Or,

V=smxh.

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

VOLUME OF THE STEM.

31

According to this method the volume of the whole stem is
obtained by means of the following formula (see Fig. 23) : —

Volume of stem = sl l^+s^h^+Ss h.3+. . .,

where slt s2, ss . . . are the sectional areas taken in the middle
of successive paraboloids, and hl9 h2) hs . . . the corresponding
heights or lengths. If the pieces are made of equal length,
the above formula changes into the following : —

Volume of stem = (s14-S2+s3 + « • •) '&•
This formula is used in all scientific investigations, and the

I*,, jfc^..- *»*.:. *2 -->;.,-

Fig. 23.

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

V=SmxH,

where Sm represents the 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 g = girth, and d = diameter, the section
is : —

32 MEASUREMENT OF FELLED TREES.
01'

' 4 "

and

V='Q79QxcfxH,
or

V='7S5xd*xH.

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 App. D. pp. 390 to 393.)

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) Part of the stem ; the lowest and uppermost parts

differ most.

(2) Age of tree ; }roung trees are more regularly shaped than

old trees.

(3) Species.

(4) 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 great axis of which lies, in the same locality, as a
rule in a constant direction. Where trees are much exposed
to wind, the great axis lies generally in the direction of the
prevailing wind ; in Western Europe, therefore, from west to
east or from south-west to north-east.

The inaccuracy caused by measuring the girth and calcu-
lating therefrom the sectional area has been found to amount
to about 7 per cent, on an average ; where only one diameter is
measured the error may be the same or even more ; where two
diameters at right angles are measured and the mean taken, the
error generally does not exceed 2 per cent, of the true value.

VOLUME OF BRANCH AND ROOT WOOD. 33

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

In comparing this with the real sectional area = '0796 X<f,
it is found that the quarter girth method gives only 78J% of
the true volume, omitting 21 J 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 corresponding
to the other, by deducting 21 J per cent, of the volume.

2. Volume of Branch and Root Wood.

In some cases special pieces of branch and root wood are of
a sufficiently regular shape to measure and calculate their
volume separately in the manner given above. As a general
rule, however, such wood requires a different treatment. Its
volume is ascertained by shaping it according to custom, and
stacking 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,
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 xylometer and ascer-
tain the volume by measuring the quantity of the displaced
water. From the data thus obtained, average coefficients are
calculated.

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 : —

VOL. III. D

84 MEASUREMENT OF FELLED TREES.

(1) Shape and nature of the pieces ; thick, smooth, and

straight pieces give more solid contents than thin, hent,
uneven pieces.

(2) Length of pieces; short pieces pack better than long

ones, hence they give a higher percentage of solid
contents.

(8) Method of stacking; careful stacking causes the per-
centage of solid wood to be considerably increased.

It is evident from the above remarks that no absolutely
average data can be given. By way of illustration, it may
be mentioned that the coefficients which are officially re-
cognized in Hesse-Darmstadt as representing averages, are
the following : —

Split firewood . . . ' . , . = •?
Round firewood billets under 5" diameter = '6
Root 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 stolid wood and 30 cubic feet of air, etc.

3. Volume of the Bark.

In many cases it is desirable to ascertain the volume of the
bark, especially when it is sold separately, as in the case of
tanning bark. This can be done stereometrically or xylo-
metrically. In the former case the pieces of wood are
measured before and after barking, the difference giving the
volume of the bark. 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 20 per cent, of the total volume. Schwappach found
on a limited number of trees the following results :—

Oak . . . = 15— 20J

Ash . . . = 12—14
Elm . . . - 9—11

Birch . . . = 13—17

Alder . . = 16—19

Lime . . . = 16—19

Aspen . . = 9—13

Scotch Pine . . = 10—16

35

CHAPTER III.

MEASUREMENT OF STANDING TREES.

1. Ocular Estimate.

ORIGINALLY, the volume of standing trees was estimated,
either merely by observation, or after having measured such
dimensions as could easily be ascertained, namely the diameter
and height. 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 opportunities
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 con-
stantly. 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 absolutely ocular estimates led to the
measuring 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 form of the tree. By degrees it was considered
desirable to collect data regarding the form of various trees,

D 2

86 MEASUREMENT OF STANDING TREES.

which might be utilized in subsequent estimates, and thus
foresters arrived at the following method.

2. Estimate of Volume by means of Form factors,
a. Definition and Classification of Form factors.

Under "form factor" is understood the proportion which
exists between the volume of a tree and that of a regularly-
shaped body which has 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 only the latter is
used. Let s be the area of the basal section of the tree, h its
height, /the form factor, and v the volume, then —

Volume of^ cylinder = sxh,
Volume of tree =v = sxh xf,

and

Form factor =/=•-•

J sxh.

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 early youth.

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.

(9) Timber form factors, which refer only to those parts of
the tree which are classed as timber, whether they are

FORM FACTORS.

87

taken from the stem or branches, omitting all other

material.

Form factors for branch wood, fagots, or root wood only are,
as a rule, not used ; their volume is ascertained by utilizing
the results of actual fellings and determining their proportion
to the volume of timber.
As it would be highty
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
variable, the following
kinds of form factors
may be distinguished : —
(1) Absolute Form
factors. — The diameter
(or girth) is measured at
any convenient height
above the ground, and

Fig. 24.

Fig. 25.

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 b}7 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 TVth, aVth, 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

88 MEASUREMENT OF STANDING TREES.

same proportion to the total height. There are, however,
various drawbacks to the employment of these form factors.
In the first place the height of the tree must be determined
before the point of measurement can be fixed ; secondly, the
latter may be 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 Measurements made at Height 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
now generally fixed at 1/8 metres = to about 4' 3".) 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.

h. Determination of Form factors.

Formerly form factors were estimated, taking into con-
sideration 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 recognized that the variations due to age can be omitted,
except in scientific investigations.

FORM FACTORS.

39

The following table shows the form factors for a number of
species : —

FORM FACTORS FOR THE SCOTCH PINE ACCORDING TO KTJNZE,
SPKUCE AND BEECH ACCORDING TO BAUR, AND SILVER FIB

ACCORDING TO LOREY.

Height
(or Length).
Feet.

TIMBER ONLY DOWN TO 3 INCHES
DIAMETER. .

TIMBER AND FIRKWOOD (EXCLUSIVE OF
ROOT WOOD).

Scotch
Pine.

Spruce.

Silver
Fir.

Beech.

Scotch
Pine.

Spruce.

Silver
Fir.

Beech.

20

•14

•18

•27

•13

•83

•88

•83

•73

30

•32

•31

•38

•21

•68

•77

•77

•67

40

•45

•41

•51

•30

•62

•69

•68

•62

50

•48

•47

•53

•40

•57

•64

•65

•59

60

•47

•48

•53

•45

•53

•61

•63

•57

70

•46

•49

•52

•47

•51

•59

•60

•56

80

•46

•49

•52

•48

•50

•57

•59

•56

90

•45

•48

•50

•50

•50

•55

•56

•57

100

•45

•47

•49

•51

•49

•53

•55

•58

110

•44

•46

•48

•52

•49

•51

•52

•59

120

•43

•44

•47

•52

•48

•49

•51

•60

130

•43

...

...

•48

140

•42

•48

150

...

•41

•47

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.

3. Estimate of Volume ~by means of Volume 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 can be denned 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 conse-
quently 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 4' 3" above the
ground.

Volume tables are now-a-days less used than form factors, as
the latter are more handy.

4. Measurement of Standing Trees by Sections.

Analogous to the measurement of felled trees by 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. (p. 12), is subject to great inaccuracies ; hence the
method is without practical value.

PRESSLER S METHOD.

41

5. Pressler' s Method of ascertaining the Volume of Standing

Trees.

In order to avoid the determination and application of
average figures, Pressler devised the following method of
determining the volume by direct measurement on the tree :
He determines on the stem of the tree the point where the
diameter is one-half of that at chest-height ; let the distance
between the two points be h (Fig. 26). He
found that the volume of the stem above
height of chest is equal to f of the basal
area multiplied by h.

If s = basal area at height of chest and
v. = volume, then

v = _ x s x h.
o

The above formula agrees very well with
the results of actual measurements. To
the volume thus ascertained has to be added
that of the piece below height of chest,
which Pressler assumes to have also a
cross section = s. If its length is equal

to I, the volume of the whole stem conies

_ -}

to:

O O / Q \

v = -xsxh + sxl= ~s[h + -l]
3 3 \ 2 /

If now h + Z is put = H, the formula becomes

...I..

Fig. 26.

This formula gives the volume near enough for all practical
purposes ; to its amount has to be added the volume of
branches, whenever required. The drawback of the method
lies in the difficulty of ascertaining the point of the stem where
the diameter is equal to J of the diameter at chest-height.
Pressler ascertains it with an instrument specially constructed

42 MEASUREMENT OF STANDING TREES.

for the purpose ; but neither this nor any other instrument
works with sufficient accuracy. Moreover, the stems of many
trees are irregularly shaped, so that two or more places may
have the desired diameter, apart from the fact that in many
cases trees divide into two or more branches before the
diameter has fallen to J of the diameter at chest-height.

CHAPTEE IV.

DETERMINATION OF THE VOLUME OF WHOLE WOODS.

THIS chapter may 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.

SECTION 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, or that of selected trees, called sample
trees.

I. 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.

II. DETERMINATION OF VOLUME BY MEANS OF SAMPLE 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

v = sxh xf,

where s represents the basal area at a certain height, h the
total height, and / 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. In the case of
regularly-grown woods, however, there are always a number of

44 VOLUME OF WHOLE WOODS.

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 an 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
volume 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 once 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.

A. The Height is a Function of the Diameter.
1. Description of the General Method.

a. Formation of Diameter Classes.

The number of classes depends on the difference between
the largest and smallest trees of a wood, and the desired degree

GENERAL METHOD OF SAMPLE TREES, 45

of accuracy. As a rule all classes are given the same extent,
that is to say, either one inch, two inches, three inches, etc.,
or part of an inch. For the purpose of forest working plans
in Europe each class comprises one or two 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 If inch ; the second that from 1 J to 2J
inches, etc.

For scientific investigations the classes may be further
reduced to a part of an inch.

b. 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 be
measured at right angles, that is to say, 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.

46

VOLUME OF WHOLE WOODS.

c. TJw Booking of the 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 hook-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.

Oak.

Ash.

Beech.

Oak.

Ash.

Total

8

HMJflll

n

Ill

18

9

3

8

30
44

9

npiia

11 III

ill HI

23

13

10

13 E3 E3
3

pi;-

ts

37

13

9

59

11

27

14

7

48

• •

• • * • •
• •

Grand Total

105

49

27

181

The first method of booking is least liable to errors.

d. Selection 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

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

GENERAL METHOD OF SAMPLE TREES. 47

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 for the calcu-
lation 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 only in exceptional cases found, 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 false sample trees. Let v be = volume
of true sample tree, vf that of the false sample tree, s and s'
the corresponding basal areas, then v is found by the formula :

and

e. Determination 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
sections of moderate length, from 3 to 10 feet, according to
the desired degree of accuracy, and the volume of each section
is ascertained separately according to the formula : —

Volume = section in the middle x by the length.

48 VOLUME OF WHOLE WOODS.

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. Experience 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 Volumes of the Classes and of the whole Wood.

Here several cases may occur :

(1) One sample tree has been measured, 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

V= volume of whole wood,

FI» VZf Vz . . . = volumes of classes 1, 2, 3 ...

vlt vz, Vz . . . = volumes of mean sample trees of successive

classes,
nlt n2, ns . . . = numbers of trees in successive classes,

then

V1 = v1xnlf F2
and

F=F1+F2+F3+. . . = vlx

GENERAL METHOD OF SAMPLE TREES. 49

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

If the volumes of the approximate sample trees are v/ ; t?a' ;
vs' . . . and the corresponding basal areas = »/ ; s/ ; s3' ;
. . . . then

v _v1'xsl v _ ra' X s2 . v _<Xg3

K ! — - — X %! , K 2 — - ', - X 7?2 ) ' 3 -- 7 - X W3 . . .
Si S2 %

As

sx x wx = Si = basal area of the first class,

s2 x ?i2 = $2 = basal area of the second class, etc.

the volume of the wood is :

Si S2 S3

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

_ « + < + V" + . • •) X Sl . _ « + V" + V*" + . . .) X St

l . y _ *

/ 7/ //x

etc., and
F_«+V+V// + - - .) x S, «+ V+V+ . . .) x £2

' " ' " //X

g. Clubbing together several Classes, leading to the Method of the
Arithmetical mean Sample Tree.

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

WL w2, ^3 ... be the numbers of trees in the several classes
«u s.>, s3 . . . ,, basal area ,, ,, „ ,,

Jin h.2, h3 . . . ,, heights „ „ ,, ,,

•/i,/2>/3 ... » form factors „

and

s, h, f the basal area, height and form factor of the mean
tree of all classes thrown together.

VOL. III. E

50 VOLUME OF WHOLE WOODS.

then the following equation holds good : —

V= Wj x »j x 7^ x/!+ w2 x s, x 7i2 x/2+ . . .

= (7*1 + ^2+ • • •) X 8 X /I X/.

If it is now assumed that li± X /i = 7i-2 X /a = 7ts X /3
= h X /then the above equation becomes :

and

. ~N

where S = basal area of all trees of the group, and

N = total number of trees ,, ,,
In other 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 :
V=vxN,

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 :

since s X N = 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 + vf V" + -.)xS

The above method rests on the assumption that hlfl =
fci/i -&«/«=...= hf.

This, however, is not absolutely correct, though it holds
good approximately in 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 one group, the least

MODIFICATIONS OF GENERAL METHOD. 51

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-three sample trees of various
diameters felled and measured. Only timber down to 3"
diameter at the small end has been included in the account.
The wood is situated in the Cooper's Hill School forest at
Caesar's Camp, on gravelly sand, with a fair layer of humus,
showing a quality between III. and IV. according to Weise's
yield tables. The statement on pp. 52 and 53 illustrates the
procedure which has just been described.

2. Modifications of the Method.

It has been shown above that the volume of a wood is repre-
sented by the formula : —

F=F1+F8+F,+ . . . = v1x

rr o o

It is obvious that, as long as the fractions — ^ -, — ,

differ, the volumes of the sample trees in the several classes
must be measured separately. In order to avoid this incon-
venience, it has been proposed to fix the number of sample
trees in each class so, that

>Si Of> OQ

- = —=-- = . . . = a constant = c,
sl s.2 ss

when the above formula reduces to : —

V=(v1 + v2 + v3 + . . .)xc.

By following this method it is not necessary to keep the
sample trees separate ; they can be thrown together and
measured in one lot. This is a great convenience, which saves
also much time. The volume 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.

E 2

52 VOLUME OF WHOLE WOODS.

a. DraudVs Method.

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

Sl S2 S8

Let be

If p per cent, of the trees in each class are taken as sample

CALCULATION OF VOLUME BY INCH CLASSES, FOUR GROUPS, AN!

FOR ONE ACRE OF SCOTCH

Mameter
in
Inches.

Number
of
Trees.

Basal
Area in
Square
Feet.

METHOD OF INCH CLASSES.

METHOD o

Diameter
of real
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
Area.

Diamete

4

4

•349

4-0

•087

1-80

'7

5
6

12
26

1-637
5-105

5-25
6-4

•150
•223

3-27
4-41

36
101

1

83

18-048

•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

22-532

9-25

•467

12-13

585

II.

144

65-010

•451

9-1

10

51

27-817

9-6

•503

11-63

643

11

34

22-439

11-0

•660

16-19

550

\

12

16

12-566

12-1

•799

20-41

321

r

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

15
lf>

5
8

6-136
4-189

15-0
16-4

1-227
1-467

28-40
38-53

142
110

. IV.

16

19-892

1-243

15-1

17

2

3-153

17-tf

1-576

39-50

79

Total..

302

146-261

3460

DEAUDT S METHOD.

53

trees, the proportion of these to the total number of trees is

79

= ~- = -op. By multiplying each term in the above
equation by this coefficient, the following equation is ob-

tained : —

Vx 'op = vl X H! X '

'op+vs xn3X'op + .

Here, vlxnlX'op represents the volume of the sample trees
in the first class, v2Xn2X 'op that of second class, &c. If the

THE ARITHMETICAL MEAN SAMPLE TREE OP THE WHOLE WOOD
IINE WOOD, 70 YEARS OLD.

FOUR GROUPS.

METHOD OF ARITHMETICAL MEAN SAMPLE-TREE.

TIEAL SAMPLE TREES.

Volume
of
Group.

Number
of

Trees.

Basal
Area
of all
Trees.

Mean Sample Tree
of Wood.

HEAL SAMPLE TREES.

Volume
of
Wood.

Diameter

Basal
Area.

Volume.

Basal
Area.

Diameter

Diameter

Basal
Area.

Volume.

6-4
6-5

Total

9-25
9-40

Total

11-5
11-6

Total

15-0
15-0

Total

•223
•230

4-41
4-52

356

1571
1089

455

\

' 302

146-251

•484

9-4

9-25
9-40
9-60

Total

•467

•482
•503

12-13
10-81
11-63

3482

•453

8-93

•467

•482

12-13
10-81

•949

22-94

•721
•734

17-43
19-17

36-60

1-452

34-57

1-455

1-227
1-227

27-79
28-40

2-454

56-19

Total...

3471

/

V

34-57x146-251 Q1

32 cubic feet.

1-452

54 VOLUME OF WHOLE WOODS.

volume of all the sample trees, v x X n l x 'op + r 2 x n ., x 'op +
. = vt then

V X *op = v
and

x

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 neglecting '50
and under, taking 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 main-
tained ; in other words, the volume of the actual sample trees

does no longer represent the true value -=75^* To avoid this

1U(J

inaccuracy, Draudt introduces the basal area of the whole
wood =$, and of the sample trees =s, by saying: —

s : S = v : V,
and

V=vxS.
s

This formula is used to calculate not only the whole volume,
but also that of timber and firewood separately.
The advantages of Draudt's method are : —

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

and

(2) That it yields a high degree of accuracy.

Its drawbacks are : —

(1) That in rounding off the number of sample trees in each

class, inaccuracies are likely to be 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 following example will further explain the

URICH S METHOD.

55

method. The data are the same as those used in the previous
example, but they have been multiplied by ten all round, in
order to obtain a larger number of trees.

CALCULATION OF VOLUME ACCOEDING TO DEAUDT'S METHOD.
Area = 10 Acres.

Diameter

No.
of
Trees.

Basal
Area.

Percentage
-1%
Multiplied
by Number
of Trees.

SAMPLE TREES.

Volume
of
Wood.

Number
Bounded
Off.

Basal
Area
should be

Basal
Area
really is

Volume.

4
5

40
120

3-49
16-37

•40
1-20

1

•136

•150

6

260

51-05

2-60

3

•588

•669

7

410

109-57

4-10

4

1-068

1-228

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

It

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

1-009

15

50

61-36

•50

1

1-227

1-227

16

30

41-89

•30

17

20

31-53

.•20

3020

1462-51

30-20

30

14-891

15-223

357-60

34357

,, 357-60

V — —

]

x 1462-51 0,Q-r
— o4o;/

Per Acre = 3436

L5-223

I. UricVs Method.

In order to avoid the slight 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 arranges the trees in
groups, so that each contains the same number of trees ; he
then calculates the arithmetical mean sample tree for each
group. For the rest he proceeds on the same lines as Draudt,
so that he obtains the volume of the whole wood by the same
formula, namely :• —

56

VOLUME OF WHOLE WOODS.

Urick'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.

CALCULATION OF VOLUME,

GROUPS.

Diameter.

Number
of

Number of Trees.

Basal Area.

Trees.

No.

Diameter.

i

Detailed.

Total.

Detailed. Total.

4

40

4

40

3-49

5

120

5

120

16-37

I. -

6

260

1

6

260

51-05

7

410

(

7

335

755

89-53

160-44

/

7

75

20-04

8

420

II. 1

8

420

146-61

9

510

I

9

260

755

114-87

281-52

9

250

110-45

10

510

III.

10

505

755

275-44

385-89

/

10

5

2-73

11

340

11

340

224-39

12

160

12

160

125-66

13

90

13

90

82-96

IV. |

14

60

14

60

64-14

15

50

15

50

61-36

16

30

16

30

41-89

17

20

17

20

I.".

31-53

634-66

3020

3020

1462-51

URICH S METHOD.

57

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. —

ACCORDING TO URICH'S METHOD.

MEAN SAMPLE TREE.

HEAL SAMPLE TREES.

Volume
of
Wood,
Cubic feet.

Basal
Area.

Diameter.

Number.

Diameter.

Basal Area.

Volume.
Cubic feet.

Detailed.

Total.

1

6-4

•223

t

•213

6-25

2

6-5

•230

•453

3

7-5

•307

•373

8-25

4

8-5

•394

•701

5

9-4

•482

•511

9-7

6

9-6

•503

•985

7

12-1

•799

•841

12-4

8

12-1

•799

1-598

Total...

3-737

88-36

34581

Per Acre

= 3458

v_ 88-36 x 1462-51 „ , _fi1
-- -34581'

58

VOLUME OF WHOLE WOODS.

c. Robert Hartufs Method.

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 Eobert Hartig argues that the number of

MEASUREMENT OF VOLUME ACCORDING

GROUPS.

Diameter

Number
of
Trees.

Basal
Area.

Vrk

DicUii6tcr

Number of Trees.

Basal Area.

JMO.

Detailed.

Total.

Detailed.

Total.

4

40

3-49

/

4

40

3-49

5

120

16-37

5

120

16-37

6

260

51-05

6

260

51-05

L

1337

365-53

7

410

109-57

7

410

109-57

8

420

146-61

8

420

146-61

9

510

225-32

9

87

38-44

'

(

9

423

186-88

10

510

278-17

II.}

751

M.V7K

1

10

328

178-90

/

10

182

99-27

11

340

224-39

III.J

11

340

575

224-39

365-29

12

160

125-66

)

I

12

53

41-63

12

107

84-03

13

00

82-96

13

90

82-96

14

60

64-14

14

60

64-14

IV. ,

357

') 365-91

15

50

61-36

15

50

61-36

I

16

30

41-89

16

30

41-89

17

20

31-63

1

17

20

/

31-53

Total..

3020

1462-51

3020

1462-51

EGBERT HARTIG S METHOD.

59

sample trees in each class or group should be proportionate to
the volume which it contains, and not to the number of trees.
As the volume is fairly proportionate to the basal area, Eobert
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 number of trees to give that basal area, he calculates

TO ROBERT HARTIG'S METHOD.

»

MEAN SAMPLE
TREES.

REAL SAMPLE TREES.

Volume
of
Groups
and of
Whole
Wood.

Remarks.

Basal
Area.

Diameter

No.

Diameter

Basal Area.

Volume.

Detailed.

Total.

•273

7-1

2

7'5
7-5

•307
•307

•614

13-54

8061

8334

8638

8992

13-54 x 365-53

•614

8061 cubic feet.

Per Acre = 3402
cubic feet.

•487

9-4

4

9-4
9-6

•482
•503

•985

22-44

•635

10-8

5
6

10-7
10-7

•624
•624

1-248

29-51

1-025

13-7

7
8

13-1
13-6

•936
1-009

1-945

47-80

Total... 34025

60 VOLUME OF WHOLE WOODS.

the mean sample tree for each group, and selects an equal
number of these for each.

The formula for K. Hartig's method is as follows : —

Sf Sf S'
As — , -?, — ?, . . . are not equal the one to the other,

Oi Ss> So

it follows that the sample trees must be measured and the
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.
For example, see pp. 58 and 59.

3. Comparative Accuracy of the 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 : —

•\r 4.1. i r • i. T Volume Difference

Method of inch classes : in c\ in %.

Each inch class being calculated separately . = 3460 ... 0

All sample trees being thrown together . . = 3554 ... +27
Method of four groups :

Each group being calculated separately . . = 3471 . . . + '3

All sample trees being thrown together . . = 3433 ... - -8

Method of arithmetical mean sample tree . . . = 3482 . . . + '6

Draudt's method = 3436 ... - 7

Urich's method = 3458 ... - -06

Hartig's method :

Each group being calculated separately . . = 3402 ... - 17

All sample trees being thrown together . . = 3457 ... - -09

METHOD OF FORM FACTORS. 61

It will be seen that for the methods as described above the
greatest difference amounts to 1/7 per cent. Even if, in the
case of ordinary inch classes, all sample trees are thrown
together, the difference amounts only to 2*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 than
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.
This conclusion appears justified by the facts that in regularly-
grown woods the basal area is a most powerful factor, and
that the height is to a sufficient extent a function of the
diameter or girth.

4. Determination of Volume by 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=SxHxF.

How the basal areas of the trees of a class or a wood are
obtained has already been explained. The mean height of a

62 VOLUME OF WHOLE WOODS.

number of trees, or of a whole wood, is ascertained in the
following way : —

hence

ISXF.

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

CALCULATION OF VOLUME BY

ACCORDING

Diameter

Number
of
Trees.

Basal
Area.

ascer-
tained
from 23
Sample
Trees.

Area
Multiplied
by

Height
cxri.

By Inch-Classes.

By Four

Form
Factors.

Volume.

Basal
Area.

Basal Area
Multiplied
by Height

a

b

C

d

K

•f

g

h

i

4

4

•349

38

13-26

•43

6

5

12

1-637

40

65-48

•45

29

18-048

77.V2I5

6

2G

5-105

42

214-41

•45

96

7

41

10-957

44.

482-11

•46

222

8

42

14-661

46

674-41

•47

317

9

51

22-532

48

1081-56

•47

508

> 65-010

3146-82

10

51

27-817

50

1390-85

•48

668

/

11

34

22-439

52

1166-83

•48

560

12

16

12-566

54

678-56

•48

326

43-301

2309-97

13

9

8-296

56

464-58

•47

218

14

6

6-414

58

372-01

•47

175

1"

15

5

6-136

60

368-16

•47

173

19-892

1201-68

16

3

4-189

62

259-72

•47

122

17

2

3-153

64

201-79

•47

95

.

Total...

3515

METHOD OF FORM FACTORS.

63

yy_

S

in words : "the mean height is equal to the total volume of
cylinders erected over the spot where the measurement of the
diameters is taken, 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.

MEANS OF FORM FACTORS.

TO KUNZE'S FORM FACTORS.

Groups.

By One Group.

»

Mean _ 1
Height-^

fl

Form
Factors.

Volume
JiXkxl.

Basal
Area.

Basal Area
Multiplied
by Height.

Mean

Height °
n

Form
Factor.

Volume
yxpxq.

li

I

mi

n

0

2

£

)'

42-95

•45 =

349

48-45

•47 =

1479

^46-25

7433-73

50-83

•48 =

3568

53-35

•48 =

1109

60-42

•47 =

565

Total

3502

64 VOLUME OF WHOLE WOODS.

If a somewhat smaller accuracy suffices, the following method
may be followed : — A number of trees are selected which show
about an average diameter and height, their heights accurately
measured and the mean taken, which represents the mean
height of the class, or wood. In some cases the height of the
arithmetical mean sample tree is taken as the mean height of
the wood. Good results are obtained by ascertaining the
mean height by graphic interpolation. In that case the
diameters are plotted as abscissa and the heights as ordinates ;
an average line is then drawn between the various points which
gives the mean heights for successive diameters.

It remains to be noted, that the heights obtained by means
of these simplified methods are generally a foot or two smaller
than that obtained according to the formula : —

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 : —

V=SxHxF,
i iS x H

If volume tables are used, the calculation is made according
to the formula : —

V=nxsxhxf.

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

Difference
in % com-
pared with

The example on pp. 62 and 63 shows :— Volume- or(,*h«ry

Volume calculated with Kunze's form factors according ' method?8

to inch classes ........ = 3515 + 1-6

Volume calculated with mean height of trees arranged

in four groups ........ = 3502 + 1-2

Volume calculated with mean height of whole wood . = 3568 + 31

METHOD OP SEVERAL HEIGHT CLASSES. 65

These data show that form factors for Scotch pine obtained
from measurements in Germany are well applicable to woods
in England.

B. 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.

In some cases it happens that the different height classes
are separated according to area, for instance where a marked
change in the quality 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,
a case which is comparatively rare, 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 described
under A.

Cases where more than two height classes, in addition to
diameter classes, are called for, are very rare. Generally, the
distinction of height classes is a matter of considerable diffi-
culty, unless the heights are measured. They are only neces-
sary where a very high degree of accuracy is aimed at.

The following example will show the manner of booking in
the case of two height classes : —

VOL. III.

66

VOLUME OF WHOLE WOODS.
BEECH.

Diameter
in
Inches.

I. Height-
Class.

II. Height-
Class.

TOTALS.

I. Height-
Class.

II. Height-
Class.

Total.

8

tiMW

Mini |i
TnT II

18

12

30

9

mil || in i Mil
TnT TTiTTTtt

JILL Jill Mil
TnT TTTT MM

mm m\\\

34

18

52

10

MM Mil MM INI
TrTT TTTT TTTTTltT

tMM!
HHII

MM MM MM Mil

TnTTnT Tttt tttt

mm\\\

47

33

80

11

INI MI; fin MM
TnT TnT TnTTnT

tittW-Httllll

mmmm

39

20

59

12

WIMII

nil MM i

TnT Tttt 1

17

11

28

Grand Total

155

94

249

SECTION II. — DETERMINATION OF VOLUME BY MEANS OF
SAMPLE PLOTS.

1. Definition.

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 plot. It may be denned 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 wood.

Let

A = area of wood,
a = area of sample plot,
V— volume of wood,
v = volume of sample plot,

METHOD OF SAMPLE PLOTS. 67

then the following proportion is assumed to exist : —

v : V=a: A
and

Again, if

v_vxA

N= number of trees in the wood,
n = number of trees on the sample plot,
then

v: V=n:N,
and

n

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 counting of all trees gives hardly less trouble
than measuring them, it yields only a small saving of labour,
and it can only come into consideration 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-
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 aver-
age. In very large woods it may become desirable to
take several sample plots and calculate the mean.

(b) Several qualities occur, which are clearly separated

according to area. Here each quality is treated sepa-
rately, and one or more sample plot taken in each
part (Fig. 27).

F 2

68 VOLUME OF WHOLE WOODS.

(c) Several qualities exist, which change gradually from one
to the other. In this case the sample plot may take
the shape of a strip, which runs through the whole
wood, so as to include a due proportion of each
quality (Fig. 28). As this is difficult to accomplish,
it is generally better to follow the method given
under (b), to divide the wood into several parts, and
to take a sample plot in each.

Fig. 27. Fig. 28.

(d) 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 stock-
ing ; the more uniform this is, the smaller may be the sample
plot. It follows that they may be made smaller in young fully-
stocked woods, than in old irregularly stocked areas.

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 % of the whole area, but in young woods it may be
much less, down to a quarter of an acre in very young woods.

ESTIMATING THE VOLUME. 69

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. Measurement of Volume 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 desir-
able 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 measure-
ment 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 very extensive areas have to
be assessed, or where the value of 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 pur-
pose of sale, in fact where a high degree of accuracy is wanted,
the whole wood should be measured.

SECTION III. — DETERMINATION OF 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 : —

70 VOLUME OF WHOLE WOODS.

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

This method, being the oldest and roughest of all, consists
in 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. It stands to reason that the method requires great ex-
perience and practice on the part of the estimator, and even
then considerable mistakes may be made.

2. Estimating by Trees.

Under this method each tree is estimated separately, the
volume of the wood being obtained by 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 according 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 clearing strips for roads or rides

METHOD OF YIELD TABLES. 71

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
in cut woods, which show the volume of woods according to
species, age, quality of locality, etc.

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 best 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 very 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.

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
heen 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. The 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 dis-
tinguished : —

i. DETERMINATION FROM EXISTING RECORDS.

Reliable records yield the best results, if they refer to in-
dividual trees. In the case of trees which form part of the
wood they are not always accurate, as many woods are not
altogether even-aged.

ii. DETERMINATION BY ESTIMATE.

As a general rule, it may be assumed that the larger the
tree the older it is. Taking, therefore, into consideration the

AGE OF TREES. 73

conditions under which a tree has grown up, its age can be
estimated within 10 or 20 years, at any rate 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. DETERMINATION BY THE NUMBER OP ANNUAL 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. DETERMINATION 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
excentric.

I. Felled Trees.

It is by far the best method to fell a tree and count the
concentric rings on the stump. 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

74 AGE OF TREES AND WOODS.

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.

The business may be facilitated by smoothing the surface,
by making a slanting cut, or by 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 it is desirable to
avoid mistakes in this respect, the stool must be split open
along the centre and the rings counted to the starting point.

In this way the physical 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. By the latter is
understood the actual growing age, leaving out of consideration
any years during which the tree may have been at a stand-still,
owing for instance to heavy shade from above.

2. Determination of the Age of 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

AGE OF WOODS. 75

to avoid exceptionally thick trees, as such trees may represent
former advance growth.

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
to the complete stocking of the area, it is generally desirable
to examine several trees and take the mean.

1). 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 wood is understood
that period which an even- aged wood requires to produce the
same volume as the uneven-aged wood.

Let

alt a>2, %, . . . be the ages of the several age classes ;
vi> vz> vs> ... be the volumes of the several age classes ;
7, 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 : —

vl+v2+vs + . . . = IxA,
and

m

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 : —

a+aj...

0? d,,

76 AGE OF TREES AND WOODS.

By substituting this expression for I in the above equation,
the latter becomes : —

(1) l

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 approxi-
mately proportionate 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
ml; mz; ms; . . . . and the average annual increment
per acre by i1; i2; i^; . . . . then formula (1) can be
written in this way (after Gustav Heyer) : —

x % x a1 _, ??i2 x 2 X a2 _, m3 x % X as

or

A _ m! x ij x E! + m2 x i2 x a2 + m3 x i3 x a3 + . . .
m.! x ^ + m2 x i2 + m3 x i3 + . . .

If it is now assumed that :

i1 = iz = ?,3 = . . .

the above formula reduces to the following :

m.! + m2 + 10.3 + . . .

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 the increment culminates, as it then
changes but slowly.

Andre follows yet a different method. He bases the calcu-
lation upon the number of trees in the several age classes. If
they are n1; nz; ns; . . . . his formula would be :

AGE OF WOODS. 77

nx + n2 + n3 + . . .

All these formulae are somewhat troublesome. 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 :

where n represents the number of sample trees or age classes.

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

Example : —

Let

— E\C\ fWi — - O QPY»PQ />?

i — t)\J //t/i — *-i clCl t/o /c-i

% = 70 m;} = 2 „ HS= 800

^ = 80 Wl4 = 1 fj TO4= 300

Mean age according to formula :

, 4000 + 9000 + 7000 + 4000 _ 24000 = 63-2

4000 9000 , 7000 4000 380
"50" 60 " 70 " 80

A _2 x 80 x 50 + 3 x 150 x 60 + 2 x 100x70 + 1x50x80 = 61.6
2x80 + 3x150 + 2x100+1x50

_ 2 x 50 + 3 x 60 + 2 x 70 + 1 x 80 = 62>5

— 2 + 3 + 2 + 1

/4\ J - 150° x 50 + 160° x 60 + 80° x 70 + 300 x 80 = 5g.g
1500 + 1600 + 800 + 300

50 + 60 + 70 + 80 = 65

\°) •"• — A

78

CHAPTER VI.

DETERMINATION OF THE INCREMENT.

DURING every 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 increase 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.

(8) 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 the 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

HEIGHT INCREMENT. 79

removals must be taken into account, in determining the total
increment laid on.

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. — DETERMINATION 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 series of sections, the length of
which depends on the desired degree of accuracy. The con-

80 DETERMINATION OF THE INCREMENT.

centric rings are then counted at the end of each section, and
from the data thus obtained, the height of the tree at successive
periods of life can be ascertained, either by calculation, or
interpolation.

Generally, graphic interpolation gives the better results, as it
equalizes accidental irregularities. In this case the abscissae
represent the ages and the ordinates the corresponding
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.

b. Height Increment 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 falling
already, 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 (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 Past.

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

DIAMETER INCREMENT. 81

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
with Pressler's increment borer. The number of years for
which it can be ascertained depends on the length of the
cylinder 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 in 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 off, 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,
equally arranged 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, say for every five, 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 be easily determined.

By repeating the above operation at successive heights from
the ground, the increment can be ascertained in the several
parts of the stem.

82 DETERMINATION OF THE INCREMENT.

I. 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 treat-
ment, me /e especially the proposed degree of thinning.

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 n years ago, then

Basal increment ) _DzX7t_d2 x TT
during n years j ~ ~~4. ~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 the Past.

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. DETERMINATION OF THE INCREMENT BY SECTIONS.

If the increment of only a limited number of years, n, is
desired, it can be ascertained by means of the increment borer.

VOLUME I!s7CREMENT OF SINGLE TREES.

83

The breadth of n rings is ascertained at regular intervals, and
the difference 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.

The tree having been divided into a suitable number of
sections, each is cut through in the middle, the number of
concentric rings counted on the basal area, and the size of
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 each cross section are
marked on horizontal lines, and the points thus obtained con-
nected by a series of lines, which represent the stem curves of
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 investiga-
tions can only refer 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 cross sections : —

Section I. taken at foot of tree

showing 97 concentric rings.

II.

5 feet above ground „

95

n

III.

15 „ „

89

IV.

25 „ „

85

5)

V.

35 „ „ „ „

80

VI.

45 „ „

72

VII.

55 „ „

64

VIII.

"'* 55 53 55 55

34

IX.

fift
wo 55 55 55 5)

26

Top = 9 feet long.

Total height = 77 feet.

G 2

DETERMINATION OF THE INCREMENT.

Height of
Section.

Number of
Rings.

Number of Years
which the Tree
took to reach
that Height.

0

97

0

5

95

2

15

89

8

25

85

12

35

80

17

45

72

25

55

64

33

64

34

63

68

26

71

77

0

97

Radius of Section I.
at 0* from the ground
in inches.

Radius of Section II.
at 5' from the ground
in inches.

Radius of Section III.
at 15' from the ground
in inches.

Radius of Section IV.
at 25' from the ground
in inches.

Total = 11-50

Total = 8-82

Total = 6-92

Total = 6-38

97 = 10-56

95 = 8-32

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 = 5-74

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

5 = 1-30

Radius of Section V.
at 36' from the ground
in inches.

Radius of Section VI.
at 45' from the ground
in inches.

Radius of Section VII.
at 55' from the ground
in inches.

Radius of Section VIII.
at 64' from the ground
in inches.

Total = 6-03

Total = 5-81

Total = 3-54

Total = 2-12

80 = 5-96

72 = 5-75

64 = 3-46

34 = 2-07

70 = 5-71

62 = 5-40

54 = 2-98

24 = 1-66

60 = 5-28

52 = 4-87

44 = 2-40

14 = -88

50 = 4-80

42 = 4-31

34 = 1-85

4 = -24

40 = 4-37
30 = 3-85
20 = 2-95
10 = 1-35

32 = 3-74
22 = 3-05
12 = 1-90
2 = -35

24 = 1-40
14 = 1-03
4 = -41

Radius of Section IX.
at 68' from the ground
in inches.

Total = 1-43

26 = 1-39

16 = 1-02

6 = -50

ANALYSIS OF A SCOTCH PINE TREE.

85

Fig. 29. — Graphic representation of the Height Increment.

Note. — The tree grew in a very favourable locality, but it was overtopped
by other trees at the age of about 40 years ; hence the abnormal height growth.

86

DETERMINATION OF THE INCREMENT.

no TO ^o <vo so «o TO so 90 too

Fig. 30. — Graphic representation of the Diameter Increment.

CALCULATION OF THE VOLUME OF THE TREE AT
DIFFERENT AGES.

Number
of
Section.

Diameter
in
Inches.

Basal
Area in
Square
Feet.

Length
in
Feet.

Volume
in
Cubic
Feet.

Number
of
Section.

Diameter
in
Inches.

Basal
Area in
Square
Feet.

Length
in
Feet.

Volume
in
Cubic
Feet.

Whole Tree, including Bark ; age -
97 Years.

Whole Tree, without Bark ; age =
97 Tears.

1

17-6

1-69

10

16-9

1

16-6

1-50

10

15-0

2

13'8

1-04

10

10-4

2

13-6

1-01

10

10-1

3

12-8

•89

10

8-9

3

12-4

•84

10

8-4

4

12-1

•80

10

8-0

4

11-9

•77

10

7-7

5

11-6

•73

10

7-3

5

11-5

•72

10

7-2

6

7-1

•27

10

2-7

6

6-9

•26

10

2-6

7

4-2

•10
Total Ti

8
mber =

•8

7

4-1

•09
Total Ti

8
mber=

•7

55-0

51'7

8 | 2-9 | -05
Total Timber and

r

Fuel =

•15

8
5

2-8
Potal Tin

•04 | §
iber and Fuel =

•12

55-15

51-82

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

ANALYSIS OF A SCOTCH PINE TREE.

87

Fig. 31. — Graphic representation of a Tree Analysis.

r

88

DETERMINATION OF THE INCREMENT.

Number
of
Section.

Diameter
in
Inches.

Basal
Area in
Square
Feet.

Length
in
Feet.

Volume
in
Cubic
Feet.

Number
of
Section.

Diameter
in
Inches.

Basal
Area in
Square
Feet.

Length
in
Feet.

Volume
in
Cubic
Feet.

1
2
3
4
5
6
7

8
To

1
2
3
4
5
6

7
8

T

1
2
3
4
5
6

7
1

1
2
3
4
5

6

7

!I

TreeS

15-7
12-9
11-9
11-4
10-8
6-0
3-3

1
2-0

tal Timl

Tree T

14-7
12-3
11-2
10-6
9-7
4-8

1-8
1-0

otal Tim

Tree 6

13-5
12-1
10-6
9-6
8-6
3-7

2-0
otal Tin

Tree 6

12-5
10-9

10-0

8-7
7-5

2-8
1-0

'otal Tin

7 Yean

1-34
•91

•77
•71
•64
•20
•06

Cotal Tir
•02

>er and ]

1 Tears

1-18
•83
•68
•61
•51
•13

Total Ti
•02
•01

ber and

7 Years
•99
•80
•61
•50
•40
•07

Total Ti
•02

iber and

7 Years
•85
•65
•55
•41
•31

Total Ti
•04
•01

iber and

Old.

10
10
10
10
10
10
8

aber =
I 1

?uel =

Old.

10
10
10
10
10
10

13-4
9-1
7-7
7-1
6-4
2-0
•5

1
2
3
4
5

6

7

T

1
2
3
4
5

6
T

1
2
3

4
5

I
1

Tree 4
11-5
9-9

8-8
7-7
6-1

2-1
•6

otal Tim

Tree 3

10-1
8'5
7-6
5-9
3-8

2-4
otal Tin:

Tree 2

8-7
7-0
6-6

2-7
1-6

otal Tin

Tree 1

6-8
4-5

2-6
1-2

'otal Tin
Tree '

2-6
1-2

'otal Tin

7 Years
•72
•53
•42
•32
•20

Total Ti
•02
•002

ber and

7 Years

•56
•39
•32

•19

•08

Total Ti
•03

iber and

7 Years

•41

•27
•17

Total Ti
•04

•01

iber and

7 Years

•25
•11

Total Ti
•04
•01

iber and

r Years
Total Ti
•04
•01

iber anc

Old.
10
10
10
10
10

mber =
10
i

TTnpl

7'2
5-3
4-2
3-2
2-0

21-9
•20

22-10

5-6
3-9
3-2

1-9

•8

15-4
•07

46-2
•03

46-23

11-8
8-3
6-8
6-1
5-1
1-3

39-4
•16

39-56

9-9
8-0
6-1
5-0
4-0
•7

33-7
•04

Old.

10
10
10
10
10

mber =
I

Fuel =

Old.

10
10
10

mber =
10
1

Fuel =

Old.

10
10

mber =
10
I

Fuel =

Old.
mber =
10
1

Fuel =

8
^

Fuel =

Old.

10
10
10
10
10
10

mber =
i

Fuel =

Old.

10
10
10
10
10

mber =
10
1

Fuel =

15-47

4-1
2-7
1-7

8-5
•40
•02

8-92

2-5
1-1

33-74

8-5
6-6
5-5
4-1
3-1

2

3

4

1

3-6
•40

•02

4-02

o-o

•40
•01

• 0-41

: 27-7
•4

•01

28-11

1
2

1

ANALYSIS OF A SCOTCH PINE TREE.

89

Recapitulation.

The stem of the tree had, at the age of 97 years :
A total volume of =55*15 cubic feet.

Of this was

= 55-15-51-82 = 3-33 cubic feet

,
Bark

Leaving

= 6 per cent, of total volume.

Timber =
Firewood =

51*7 cubic feet.
•12

Total Timber and Firewood = 51*82 cubic feet.

By graphically representing the volume of wood at the several
ages, figure 32 is obtained, which, with the previous diagrams,
gives the following data : —

50

P

O 10

..

I

/

WJ •EO SO 10 56 GO TO 80 OO 1DO

AGE

Fig. 32. — Graphic representation of the Volume Increment.

90

DETERMINATION OF THE INCREMENT.

Age of Tree.

Height in Feet.

Diameter without
Bark, at 5' above
Ground, Inches.

Volume without
Bark in
Cubic Feet.

Periodic Incre-
ment for every
Ten Years.

0

_

10

20

4-0

1-8

1 w

i 4-2

20

38

7-4

6-0

j

6-0

30

51

9-1

12-0

1

i 6-0

40

58

10-6

18-0

j «

\

1 6-0

50

62

11-9

24-0

j

i 5-9

60

64

12-8

29-9

j

I

5-4

70

67

13-9

35-3

J

|

6-7

80

70

15-0

42-0

J

6-0

90

74

16-0

48-0

|
I

3-8

97

77

16-6

51-8

1

Total

51-8

ii. DETERMINATION OF 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 V be the volume of the tree at the present time,

v that n years ago, H and h the corresponding heights, figure 33,

and S and s the corresponding basal areas at ~- and -^-, then
I=V-v = SxH-sxh.

TT

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

Fig. 33.

BY FORM FACTORS. 91

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 n concentric rings.

Then the basal area s at ~ is ascertained, either by making a

JL

cross section at the spot, or by 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
the diameter increment must be measured in several places of
the circumference, so as to obtain the mean.

-H

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

•g. He obtains the increment according to the formula :

I=Sxh-sxh=(S-s) h.
The error due to omitting the top is said to be compensated

TT

for by S having been taken somewhat below ^-.

a

iii. DETERMINATION OF INCREMENT BY FORM FACTORS.
Let S be the basal area of a tree, taken at chest height ; s the
basal area of the tree n years ago taken at the same height ;
H and h the corresponding heights, and F and /the corres-
ponding form factors, then the increment : —

I=SxHxF-sxhxf.
In the case of a standing tree, H is measured with a height

92 DETERMINATION OF THE INCREMENT.

measurer, h is estimated, S is obtained by measuring the
X - - - diameter with a calliper, 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 = /, the
formula becomes :

H

Fig. 35.

The method can only give approxi-
mately correct results, because h has to
be estimated. It must also not be over-
looked, 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 trees.

I. Volume Increment of the Future.

The increment which a tree may be expected to lay on in
the future can be estimated either from its own past incre-
ment, especially that of the immediate past, or by comparing
it with other older trees.

i. ESTIMATE ACCORDING TO PAST INCREMENT.
The increment is represented by the formula :
In = S X Hx F-s X h xft

where s x h x/is the value of the present volume, 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, H 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 /.

OF THE FUTURE. 93

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 :

I* = (S-8) h,

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

ii. ESTIMATE BY COMPARISON WITH OTHER OLDER TREES.

The increment I which a tree A now a years old, and con-
taining a volume va is likely to lay on during the next n years,
can be ascertained by examining another tree B grown under
the same conditions but now a + n years old, which with a
present volume = va + n had, when a years old, a volume
equal va. The increment which the second tree has laid on
during the last n years, may be assumed as equal to that which
the first tree is likely to lay on during the next n }rears. The
assumption holds good only if the weather and treatment are
the same during both periods.

It is, however, not always easy to find exactly the tree
wanted, and as a rule a tree differing somewhat in volume and
age must be taken, which involves the following corrections : —

Supposing the age of the second tree is a + t instead of
a + n, and its volume =va + t> then, if the increment has
been steadily laid on, the following equation holds good : —

t : n = It : In = va+t-va : In
and

In=(va+i-Va}X~.
t

94 DETERMINATION OF THE INCREMENT.

If, on the other hand, t = w, but the second tree had only
a volume va' in the year «, then the increments of the two
trees may be assumed to bear the same proportion as the
volumes, or:

,,. . „ '_ T • T ' Qr,;i 7" — T ' V Va — (vf _ ti' \ V ^a
va • la — ln • *-n ana *» = *» x — /— \v a+n v a) X — •

Va V a

Now:

*W = »a + T X Va - Va = Va+n X

Va va

or —

^a+» • va = V a+n '• ^a >

in words : the proportion which exists between the volumes of
the second tree n years ago and now, holds good also as regards
the volumes of the first tree now and n years hence.

If both, the ages and volumes, differ, it may again be
assumed that the increments of the two trees show the same
proportion as the volumes. In that case :—

Va - va = In Of Va : In of Va'

And—

All these calculations assume that the increment of n years
has been laid on in annually equal quantities, which is only
approximately correct. The degree of accuracy depends on
the length of the time n, and the differences between n and t
and between va and v' a.

This method of calculating the volume of a single tree is
so complicated, that it is not used in practice ; it has been

OF WHOLE WOODS. 95

explained here, as it forms the basis of calculating the incre-
ment of whole woods, to be explained further on.

Example : —

Find the increment which a tree now 50 years old with a
volume of 30 c' is likely to lay on during the next 10 years.

A tree has been found, now 58 years old, with a volume of
40 c', and which had 33 cubic feet when it was 50 years old.

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 of the factors which
lead up to it, height, diameter, or basal area increment, can
be followed backwards with a considerable degree of accu-
racy. 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 successive
development of the individuals existing at the time of examina-
tion, but they throw no light on that of those trees which have
disappeared in course of 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, which may be taken as the upper
height of the wood at those periods. 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 per cent, 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

96 DETERMINATION OF THE INCREMENT.

the former amounts of these out of the present quantity is more
or less speculative.

Under these circumstances one of the following two methods
may he 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
calculated on the growing stock present at the time of measure-
ment. According to the age of the wood, it may he 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, during which no thinnings are made, say 10 years.

B. Determination of Increment by means of Yield Tables.

I. OF YIELD TABLES GENERALLY.

1. Definition of Yield Table.

It has already been explained that the progress of height,
diameter, basal area, and volume increment can be repre-
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 fixed 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, which
are called Yield or Increment Tables.

OF YIELD TABLES GENERALLY. 97

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 fixed age, either from year to year, or for
intervals of a certain number of years.

2. Object and Contents of Yield Tables.
Yield tables are used for a great variety of purposes, as :

(a) Determination of the volume of woods.
(&) „ „ „ increment of woods.

(c) ,, ,, ,, quality of localities or of woods.

(d) ,, ,, ,, most profitable 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 progressive volume which may be found in a fully-

stocked wood.

(2) The number of trees.

(3) The basal area of trees.

(4) The height of the wood.

(5) The form factors.

(6) The current annual and mean annual increment.

Separate yield tables must be prepared for

(a) Each species.

(b) Each method of treatment, as high forest, coppice wood,

and combination forest.

(c) Each quality of locality.

The volume is given divided into the different classes of
wood, as timber, firewood, fagots, etc. The volume of thinnings
is entered separately from that of final yields.

Yield tables are only prepared for " normal " woods, that is
to say for woods which are fully stocked, taking into considera-

VOL. III. H

98 DETERMINATION OF THE INCREMENT.

tion the species, quality of locality, and the adopted method oi
treatment. Such woods are produced if no extraordinary in-
fluences 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 " general " yield table.

The question, what limits should be assigned to the applic-
ability 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.

4. Quality 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 a yield table should therefore
be based on data obtained from localities of precisely the same
quality. Practically, however, an immense number of different
qualities exist, hence in practical forestry some concession
must be made, by being satisfied with a limited number, which
rarely exceeds five, and frequently three are quite sufficient.
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

QUALITY CLASSES OF YIELD TABLES. 99

accuracy, and that the 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 indi-
cation 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=sxkxf.

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
preferable to the basal area. While two woods which have the
same basal area may have very different heights, experience
has shown that two normal woods of the same height have
approximately the same basal area. It follows that the height
is, next to the volume itself, the best indicator of the qualit^y 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 multi-
plied by the mean diameter be used.

H 2

100 DETERMINATION OF THE INCREMENT.

5. Metlwds of Constructing Yield Tables.
The following methods have been proposed : —

a. Annual or Periodical Measurement of the Growing Stock of one and

the same Wood ; in the second case the Intermediate Values are
found by Interpolation.

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.

b. Annual or Periodical Measurement of the Growing Stock of a limited

number 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
years old, the same volume as the present 20-years-old wood
has ; again, the 60-y ears-old wood the same volume when it
was 40 years 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 exactly of the same quality, or woods which will de-
velop in the same manner, there can be no doubt that
ultimately satisfactory yield tables can only be obtained 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

PREPARATION OF YIELD TABLES. 101

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. Measurement of a large number of Woods of different ages once, so
that Yield Tables are obtained immediately.

Until yield tables, prepared as indicated under b, 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 are 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 ; it will be dealt with
in detail further on.

i. SELECTION OF WOODS FOR EACH QUALITY CLASS BY MEANS OF AN
INDICATING 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 its forming factors, as basal area,
height and form factor, which the trees of a mature wood
had at the several periods of its life. Guided by the data thus
obtained, woods are selected, the dominant trees of which show
the same dimensions as those of the mature trees at the same
age. Such woods are assumed to give a true representation
of what the now mature wood was at the same age. When a

* Professor of Forestry at the University of Munich.

102 DETERMINATION OF THE INCREMENT.

sufficient number of woods of various ages have been selected,
normal sample plots 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 tree of which possesses the same dimensions
as the mean tree of the mature wood at the same time. 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 Robert Hartig, analysed only
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 age. Such woods are considered as
having been produced on localities of the same quality, so that
the}r can be united into one yield table.

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

ii. BAUR'S METHOD OF PREPARING YIELD TABLES.

After a sufficient number of normal sample plots on all sorts
of qualities have been carefully measured (at least 30 for each
desired quality class), the volumes are marked as ordinates
over the corresponding ages as abscissa (see figure 36).

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 falling into each strip are considered as belonging to

BAURS METHOD.

103

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 tahle 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 application, and it yields good results.

Instead of limiting the quality classes in the manner described
above, the average quantity of final yield which corresponds
to each quality class can be once for all determined. Thus
in Germany it has been decided to consider that normal Scotch
pine woods, which contain (in round numbers) at an age of
100 years : —

10,000 cubic feet per acre, shall be considered as I. quality

7 ,yuu ,, ,, ,, ,, j-i. 5,

6,000 „ „ „ „ III. „

4,300 „ „ „ „ IV. „

2,900 ,, ,, ,, ,, V. ,,

EXAMPLE OF PREPARING YIELD TABLES ACCORDING TO BAUR'S METHOD.

Scotch Pine : 3 Quality Classes to be distinguished.
Woods Measured as follows : —

No.

£•];£.

Basal

Area,
sq. ft.

Mean
Height,
feet.

Volume
in solid
cub. ft.

Xo.

Age.
Years.

No.
of
Trees.

Basal
Area,
sq. ft.

Mean
Height,
feet.

Volume
in solid
cub. ft.

1

15

62

16

1800

21

76

295

173

70

5500

2

17

60

14

1400

22

79

265

177

72

6300

3

18

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

2:,

94

190

196

93

9000

6

29

2400

' 99

25

2050

26

94

240

150

67

6000

7

34

1480

133

35

3250

27

94

218

177

80

7300

8

35

1670

113

32

2800

28

96

248

150

69

5300

9

35

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

51

104

160

192

94

9200

12

48

860

132

40

2900

32

106

169

177

86

7150

13

49

680

154

52

4700

33

106

220

160

69

5700

14

50

750

132

44

3500

34

108

173

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

369

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

104

DETERMINATION OF THE INCREMENT.

WOODS SEPARATED INTO QUALITIES. (See figure 36.)

No.

Age.

No.
of
Trees.

Basal
Area.

Mean
Height.

Volume

No.

Age.

No.
of
Trees.

Basal
Area.

n'ssa.v-™

/. Quality.

13
16

49
62

680
450

154
169

52

65

4700
4700

1
5

15
27

1400

62
130

16
33

1800
3300

21
22

76
79

295
265

173

177

70

72

5500
6300

9

35

910

156

46

4450

27

94

218

177

80

7300

10
15
17

46
54
62

620
450
369

165

182
184

55
69
73

4800
6400
6200

29
32
34

97
106
108

200
169
173

176
177
179

82
86
86

6950
7150

8100

19

74

270

192

83

7800

38

115

150

176

88

7500

23

81

245

192

86

7200

25
30

94
99

190
170

196
194

93
93

9000
8200

III. Quality.

31

104

160

192

94

9200

3

18

...

61

13

1100

36

109

151

196

96

8500

6

29

2400

99

25

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. Quality.

20
24

74

85

350
290

146

156

61
62

4000
5030

2

17

...

60

14

1400

26

94

240

150

67

6000

4

21

84

20

1700

28

96

248

150

69

5300

7

34

1480

133

35

3250

38

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

75

6000

YIELD TABLE FOR THE SCOTCH PINE, I. QUALITY.
Derived from the Curves in figures 36, 37, 38 and 39.

INCREMENT.

Age.

Number
of
Trees.

Basal Area.
Square Feet.

Mean
Height
Feet.

Volume.
Cubic Feet,
solid.

Current

Mean

i Annual.

Annual.

10

HO

10

900 90

90

20

2000

92

23

2100 120

105

30

1200

133

40

3300

120

110

40

770

160

54

4500

120

112

50

520

175

64

5400

90

108

60

380

186

73

6250

85

104

70

300

190

80

6950

70

99

80

250

192

86

7600

66

96

90

200

193

90

8200

60

91

100

160

194

94

8660

45

86

110

150

194

97

9100

45

83

120

140

194

100

9500

40

79

WITH THE HELP OF YIELD TABLES.

105

«}000

1

,'T!

*'

•IS

V

/

s

TfT QTJAUTT

10° i»o X1O-

Fig. 36. — Graphic representation of the Volume per acre of 40 different Woods and
their allotment to Three Quality Classes, according to Baur's method.

II. 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 necessary to
decide in the first place which of the quality classes of the
tables corresponds with the given wood ; in other 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

106

DETERMINATION OF THE INCREMENT.

\

\

\

1.0 to -50 HQ 50 Co lo go So 100 ixo 120

Fig. 37. — Graphic representation of the Number of Trees per Acre.

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 agree 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
proportion to the two volumes. Let va be the present volume
of the wood, Va the nearest volume given in the table ; Va + n
the volume given in the same table for the year a + n ; and
va+n the desired volume of the wood in the year a + w, then

WITH THE HELP OF YIELD TABLES.

107

O lo -io to <to to 60 To go do loo uo 1

AGE.

Fig. 38. — Graphic representation of the Basal Areas per Acre.

lo Zo 'so

Fig. 39. — Graphic representation of the Height Growth.

the following equation may be assumed to hold good (see figure
40):—

rr . „ _ v . »-,
' a • ua — v a+n • va+n

and

108
and

DETERMINATION OF THE INCREMENT.

Increment in n years = va+n

V V ii
— Tl 7, — / a+n * c« 7. _

^/vJ-ti. V n T^ I'/Y

This method rests upon the assumption that the selected
yield table represents correctly the progressive increment of
the wood, of which the increment is to he ascertained. As

-AGE

Fig. 40.

this is only approximately the case, the degree of accuracy of
the method depends —

(a) On the degree to which va approaches V a, and

(b) 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 following the above method, it is essential to measure the
volume on a "normal" sample plot, because only then can
the true quality 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. 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.

WITH THE HELP OF YIELD TABLES. 109

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 altogether
useless to measure the volume for the purpose of selecting
the proper yield table. For such woods the quality class
must be selected 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 as
number of trees, diameter, form factors, basal area and height,
the last is the most suitable. Indeed, actual investigation
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, are 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 incre-
ment of the table modified in proportion to the difference be-
tween the actual height and that given in the table. If, more-
over, the wood is not fully stocked, the increment given in the
table must be further modified in the manner indicated above.

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

110

DETERMINATION OF THE INCREMENT.

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 incre-
ment for the next ten years ?

YIELD TABLES.

Quality.

Height.

Volume in the
Year 60.

Volume in the
Year 70.

I.

72

6750

—

II.

60

5420

—

III.

51

4060

4530

IV.

42

3360

—

V.

35

2670

—

The wood belongs to the III. Quality.
According to the formula —

1*0-70= (4530-4060) x |? x^ = 457 cubic feet.

Ill

PART II.

FOREST VALUATION.

118

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, growing stock, or forest.

These values must be determined in all cases of sale, or for
the purpose of assessing forest property, or where it is pro-
posed to divide a property. Soil and growing stock also form
the capital invested in forestry, and their value must be as-
certained for the purpose of gauging the financial success of
the forest industry. The latter subject is generally dealt with
in a separate part called, by continental foresters, " 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
formulEe 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. ,, „ THE GROWING-STOCK.

,, IV. ,, „ WHOLE WOODS OR FORESTS.

,, V. „ ,, THE RENTAL.

,, VI. METHODS OF CALCULATING THE FINANCIAL
RESULTS OF THE FOREST INDUSTRY AND OF
DETERMINING THE MOST PROFITABLE TREAT-
MENT OF FORESTS.

114

CHAPTER I.

PRELIMINARY MATTERS.

SECTION I. — VALUE OF PROPERTY GENERALLY.

PROPERTY means an object which serves for the satisfaction
of a requirement. The degree of utility of a property indicates
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 production
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 expectation value, by which is understood the

present net value of all yields which a property may
be able to give ; it is determined by discounting all
net incomes derivable from the property to the
present time.

(2) The cost value,- or the total outlay on the acquisition or

production of a property.

CHOICE OF RATE OF INTEREST. 115

(3) The sale value, or the price which can be realized by

the sale of a property ; if the sale is open to com-
petition, the sale value becomes the market price,
which depends on supply and demand.

(4) The rental value, by which is understood the capital

which corresponds to the rental which the property
is capable of yielding. This value is ascertained by
capitalizing the rental according to the formula —

,. , KentalxlOO 72x100

Capital = — — = - .

rate per cent. p

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

SECTION II. — CHOICE OF KATE OF INTEREST.

By rate of interest is understood the proportion between the
yearly interest (I) and the capital (Cy which has yielded it, as
represented by the formula —

Bate of interest = -.

G t *

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

p=IxlOO.

c

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

(a) The degree of security of the investment and the safety
with which it }ields a return. In a general way it
may be said that the rate of interest is inversely
proportional to the safety of the investment.

(6) The supply and demand of capital, which changes from
time to time, and with the locality.

(c) The general credit of the country in which the industry

I 2

116 PRELIMINARY MATTERS.

is carried on, in other words the interest yielded by
Government securities (called Consols in England).
It follows that the general rate of interest applicable to the
forest industry is not 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 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 conve-

nience 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, while those of fields differ much accord-
ing to the seasons.

(b) Forests require much less labour, and the

management is comparatively simple.

(c) Temporary high prices can be fully utilized by

cutting more than the normal yield for a
time, or vice versa.

CHOICE OF RATE OF INTEREST. 117

(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
soil.

It has been shown above that —

By substituting the value S of the soil for C, and the
rental R of the soil for. I, the above equation becomes —

The drawback of this method lies in the difficulty of ascer-
taining correctly the value of the soil and of the rental without
having previously determined the rate of interest; in other
words such a determination would turn in a circle.

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

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

The conditions for the applicability of the method are : —

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

(b) That the forest is, at any rate approximately, in such a

condition that it can yield a steady annual return.

(c) That the price realized for the forest was the result of

genuine competition.

There is great difficulty in complying with all these con-
ditions, so that, on the whole, neither this nor the first
methods are of much practical value.

118 PRELIMINARY MATTERS.

(8) Determination based upon the rate of interest obtainable
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 in many cases the agricultural rate
of interest can be applied to the forest industry.

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

The rate of interest of Consols may be too high in some
cases, and too low in others, according to the general credit
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, 2J per cent.

SECTION III. — FORMULAE OF COMPOUND INTEREST.

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

1. Amount or the Future Value to ivhicli a Capital
accumulates.

A capital C0 put out at p per cent, compound interest
accumulates in the course of n years to the value : —

Cn = C0xl'opn .... (I.)
or log. Cn = log. C0 + ?ixlog. I'op.

where Iv*-- and

2. Discount, or Determination of Present Value.
The present value C0 of a capital Cn to be realized n years
hence, is : —

log. C0 = log. Cn-nxlog. I'op.

FORMULA OF COMPOUND INTEREST. 119

3. Summation of Rentals.

a. Future Value.

A rental R becomes due for the first time after m years, and
is repeated altogether n times at intervals of m years ; its
value after m X n years is : —

- _B(l-op""-l)

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

b. Present Value.

A rental R becomes due for the first time after m years, and
is repeated n times after intervals of m years ; its present

value is : —

r = R(l'opmn-l) ,y }

I-opmn(l'opm-l)

A rental r is due at the end of each year, altogether n times ;
its present value is : —

r l-»-l

°~ 1-pp-x-op-

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

O= — . . . . (VII.)

'op

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

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

120 PRELIMINARY MATTERS.

A rental R is due now, and then after every n years, for
ever ; its present value is : —

r _Rxl'opn /Y ,

°°~ l-op'-l

4. Conversion of an Intermittent into an Annual Rental.

A rental R is due every n years, commencing from the
present time ; it is equal to an annual rental of —

-F^Ti*'*' ;. - - (XI.)

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

A rental R 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 which give future or present values for various
rates of interest. The Tables at page 394, which give the
values for Formula? I., II., VIII., and VI., suffice for all
ordinary forest calculations.

SECTION IV. — ESTIMATE OF RECEIPTS AND EXPENSES.

1. Receipts.

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

a. Major Produce.

This comprises all yields of wood, that is to say, timber and
firewood. Bark is generally included ; if it is severed from

ESTIMATE OF RECEIPTS AND EXPENSES. 121

the timber before disposal, it is sometimes classed as minor
produce.

Major produce is subdivided into that obtained from final
cuttings (final yield), and that from thinnings, etc. (intermediate
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.

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 rises with the rotation.

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.

&. Minor Produce.

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

2. Expenses.

The expenses comprise the cost of administration, protec-
tion, formation, harvesting, construction of roads, slides,
houses, taxes, etc. The amounts must be locally ascertained.

122

PRELIMINARY MATTERS.

3. Examples of Money Yield Tables.

Subjoined follow two money yield tables, the first being
based upon Weise's yield table for Scotch pine, III. quality,
and the second upon Schwappach's yield table for the beech,
III. quality.

MONEY YIELD TABLE FOE ONE ACRE OF SCOTCH PINE WOOD.

According to Weise. III. or middling quality ; calculated with English
prices ; brushwood under 3 inches diameter omitted.

YIELD IN CUBIC
FEET.

NET VALUE OF RETURNS.

Per Cubic Foot,
Pence.

Total, Shillings.

AGE.

Inter-

Total

REMARKS.

mediate

Final.

Inter-
mediate

Final.

Inter-
mediate

Final
and
Inter-

mediate

a

b

C

(I

e f 9

n

20

30

30

830

48

2'

1-

138

4

142

For simplicity's
sake, it has been as-
sumed that the thin-

40

1970

289

2'5

1-5

406

36

442

nings are made at
the end of every 10

50

2700

403

3-

2*

675

67

742

years ; hence column
h gives Ihe values of

60

3300

413

4-

2-5

1100

86

1186

the wood before the

thinnings are made.

and column f the

70

3820

303

5*

3-

1592

91

1683

values which remain

after the thinnings.

80

4260

327

B-

3-5

2130

95

2225

Example.— In the

year 60 the volume

90

4620

282

7-

4-

2695

94

2789

amounts to 3300 +
41 3 =37 13^, of which

100

4910

248

8-

5-

3273

103

3376

413 fall in the thin-
ning, while 3300

remain. The corre-

110

5150

213

9-

6-

3862

106

3968

sponding values are
1100 + 8(3 = 1186 shil-

120

5340

104

10-

7-

4450

96

4540

lings.

4

(/<»/</€

MONEY YIELD TABLES.

123

MONEY YIELD TABLE FOR ONE ACKE OF BEECH WOOD.

According to Schwappach, III. or middling quality, calculated with English
prices ; brushwood under 3 inches diameter omitted.

AGE.

YIELD IN CUBIC
FEET.

NET VALUE OF RETURNS.

REMARKS.

TJV_OI Inter-
Fmal- mediate

Per Cubic Foot,
Pence.

Total, Shillings.

Final.

Inter-
mediate

Final.

Inter-
mediate

Total
Final
and
Inter-
mediate

a

I c

(I

e f g

h

30
40
50

8G
943
2001

86

2-
3-

4-5

3-

14
236

750

21

14

236
771

See remarks on
money yield table
for a Scotch pine
wood.

60

29J5*

272

6-

4-

1457

91

1548

70

3716

329

7-

4-5

2167

123

2290

80

4430

357

8-

5.

2953

149

3102

90

5045

400

9-

6'

3784

200

3984

100

5573

414

10-

7-

4644

241

4885

110

6045

400

ir

8-

5541

267

5808

120

6460

400

12-

9-

6460

300

6760

130

6817

386

13-

10-

7385

322

7707

140

7117 ; 372

14-

11-

8303

341

8644

124

CHAPTER IT.

VALUATION OF FOREST SOIL.

THE soil can be utilized in two ways : —

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

Or by letting it produce 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
supposition that it is used for the production of forest
crops; for this purpose it determines the expectation, cost,
and sale value.

SECTION I. — THE EXPECTATION VALUE OF FOREST SOIL.

1. Method of Calculation.

In conformity with the definition given at page 114, 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. Present Value of Returns.

(1) Final Yields. — Let the rotation contain r years, and let
the value of each final yield, less cost of harvesting, = Yr, to be
realized every r years, then the present value of all final yields
for ever amounts, according to formula VIII. (page 119),
to:—

y

Present value of all final yields = - r _ .

To//— 1

EXPECTATION VALUE. 125

(2) Intermediate Cuttings, or Thinnings. — Let Ta, Tb, Tc
. . . Tq, represent the value of thinnings, less cost of
harvesting, occurring in the years a, b, c, . . . q. Each
of these thinnings occurs during every rotation, that is to say,
every r years. Thus the first thinning occurs after a years,
again after a + r years, again after a + 2 x r years, and so
on ; hence the present value of all these thinnings, according
to formula. IX. : —

= Taxl'opr~a Tbxl'ojf~b
l-opr-l ' l'opr-l

^Tax l'opr~a+ Tb x l'ojf-b
l'opr-l

(3) Minor Produce. — These are dealt with in the same way
as thinnings, if they occur at regular intervals. Let Ms, Mh

. Mst be the values of minor produce occurring in the
years s, t . . . z, and again every r years, then their
present value is —

Msxl'opr-8+Mtxl'opr-t

l'opr-l

If items of minor produce 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**.

'op

I. 'Present Value of Expenses.

(1) Cost of Formation. — Assuming that c represents the
cost 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 :—

C ^ 1 V}71^*

Total present value of cost of formation = - J .

1'oj/— 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—

126 VALUATION OF FOREST SOIL.

(2) Annually Recurring Expenses. — Let e represent the annual
value of all annually recurring expenses, as cost of administra-
tion, taxes, etc., then the total present value of all such expenses
comes to —

^ = E,
'op

or the capitalised value of the annual expenses.

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

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

c. Formula for the Expectation Value of Forest Soil
I
This formula would he represented by an addition of all

the items enumerated under a less those under b. In order
to shorten the formula, without destroying its accuracy, it may
be assumed —

(1) That Ta, Tb, . . . Tq, 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 ; and

(3) That the cost of formation at the commencement of each

rotation comes to the same amount.

The expectation value Se of the soil is then represented by
the formula —

Q Vr + Ta x ropr~a + . . . + TQ x l-opr q -ex ropr

-T^i-

or, as

cxl'or)r c

c +

l'opr-l I'opr-l

g =Yr + T>xl'pp^ + ... + Tqxl-qp'-^-o_( E)
l-op*-l

Example : — An acre of land is to be cultivated at once with
Scotch pine, and to be worked under a rotation of 80 years.
It is expected to yield the returns given in the mpney yield

EXPECTATION VALUE. 127

table at page 122. The expenses are expected to be as
follows :—

Cost of formation every 80 years = 60 shillings.

Annual expenses for administration, taxes, etc. = 3 shillings.

Interest = 2J per cent.

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

2225 + 4 x l-02530 + 36 x l'02540 + 67 x 1-02530
<? = _ + 86xl-02520+91 x 1-02510- 60 x 1-025* _ 3
"l ;025*

Calculating with the tables at page 394, the above becomes

Se= (2225 + 4 x 3-4371 + 36 x 2-6851 + 67 x 2'0976 +
86 x 1-6386 + 91 x 1-2801-60 x 7'2096) x '1610-120.

Se = (2225 + 13-7484 + 96-6636 + 140-5392 + 140-9196
+ 116-4891 - 432-5760) x '1610 - 120.

Se = 2300-7839 x '1610 -120 = 250 shillings = £12 10 0.

This shows that, under the above conditions, and calculating
with 2J per cent, compound interest, it pays to plant Scotch
pine on land of the III. quality, if it can be purchased for
^£12 10s. an acre or under.

Assuming now that an acre of land is planted with beech,
that it yields the returns given in the money yield table at
page 123, and that all other conditions remain the same, the
expectation value of the soil will be —

Se =

3002 +jtt x 1-02530+91 x 1-Q2520+123 x 1-Q2510-60 x 1-Q2580

l-p25<w-l
-120.

£e = 366 shillings = £18 6 0.

It follows that under the above conditions it pays to plant
beech on lands of the III. quality, if it can be purchased for
£18 6s. an acre or under.

Note. — It must not be overlooked that a beech soil of the
III. or middling quality, would at least represent a soil of the
II. quality, if planted with Scotch pine.

128 VALUATION OF FOREST SOIL.

2. Matters ivhich affect the Expectation Value of the Soil.

As indicated by the formula, the expectation value of the
soil depends on —

(a) The absolute amount of receipts and expenses.

(b) The length of the rotation.

(c) The time when the intermediate returns are realized.

(d) The time when the costs of production have to be

incurred ; and

(e) The rate of interest with which the calculation is made.
Each of these matters must be further considered.

a. The absolute amount 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 ex-
pectation values thus obtained are likely to differ considerably ;
hence the importance of selecting the most suitable species for
each piece of land.

b. 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 period it falls 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 expec-
tation 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, Jhe
following values are obtained for the expectation value : —

EXPECTATION VALUE. 129

Se for a rotation of 30 years . = — 105 shillings.

Se ,, ,, jj 40 „ . = + 50

Se „ „ „ 50 „ . = + 121 „

Se „ „ j, 60 „ . = + 196 „

Sg „ „ „ 70 „ . = + 236 „

Se „ „ „ 80 „ . = + 250 „ fn^n

Se „ „ „ 90 „ . = + 245

Se „ „ „ 100 „ . = + 229

Se j, „ „ 110 „ . = + 207

Se „ „ „ 120 „ . = + 180

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.

c. The Time when the Intermediate Returns are Realized.

The earlier the intermediate returns occur, other matters
being the same, the higher will be the expectation value.

Example. — The presentvalue of a thinningj.worth 86 shil-
lings, made in the year 60, and again every lOO^years, is =

86xl'02540 01 ..„.

5MZT = 21 Billings.

If the same thinning were made in the year 30, and again
every 100 years, its present value would be =

It follows that strong thinnings made at an early age can
considerably increase the expectation value. At the same time
it must not be overlooked that the small material obtained from
early thinnings is not always saleable 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.

VOL. III. K

130 VALUATION OF FOREST SOIL.

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
affect later returns.

d. The Time when the Costs of Production have to 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 =

c * /•«/»'' 60xl'02510°

t >•/>*- 1 1-025100-1

65 '5 shillings.

If the cost amounted to 120 shillings each time, the present
value would be =

120xl'02510°

— r = 1B1 shlllmgs-

Thus it may happen that the expectation value is higher
under the system of natural regeneration, than under the clear
cutting system with planting.

e. The Rate of Interest with which the Calculation is made.

A, high_rate_of interest^ gives alowexpectatign value of_tlie^.
soil, and vice versa. The value is, however, not in inverse pro-
portion 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 of interest.

Example. — Taking the same data as above, and calculating

EXPECTATION VALUE.

131

the expectation value of the soil with 2J and again with 3 and
4 %, the following values are obtained : —

ROTATION.
Years.

CALCULATION MADE WITH

2i%

3%.

4%.

60

+ 196

+ 104

s.
- 15

70

+ 236

+ 123

+ 5

80

+ 250

+ 124

- 3

90

+ 245

+ 113

- 15

This example shows :—

(1) By raising the per cent, from 2J to 3, the expectation
value for a rotation of 80 years falls from 250 to 124 shillings,
and calculated with 4% to - 3 shillings.

(2) By making the calculation with 4 °/o the expectation value
becomes practically nil, and under a higher per cent, it becomes
negative.

(3) The expectation value of the soil culminates : —

Calculated with 2J% at about 82 years.
)> )> 3 ,, ,, 78 ,,

4 72

J) J> •t J) J> »~ J5

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 production 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 : —

(a) That all items of expected incomes and expenses are accu-
rately known. In order to comply with this condition,
accurate and suitable yield tables are required. More-
over, future prices of produce and expenses must be
estimated on the basis of those at present prevailing

132 VALUATION OF FOREST SOIL.

a matter which introduces much uncertainty into the
calculation.

(b) That the calculation is made with a suitable rate of in-

terest. It has been shown above that this is a matter
beset by considerable difficulty.

(c) That the rotation corresponding to the maximum expec-

tation 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 produce
consequent on changes in the areas set aside for the produc-
tion 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.

(2) The sum expended in rendering it fit for cultivation,
such as drainage or irrigation, levelling, fixation, etc.

(8) 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
2J%, to

S. = (10+5)xl-0255 + 2xl-0252 = £19 1 5

COST VALUE AND SALE VALUE. 133

The cost value of the land may be accepted as the true
value : —

(1) If the owner agrees to let the land go at the price which

represents his own outla}^ on it :

(2) If the expectation value of the soil cannot be ascertained

with any degree of accuracy :

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 value of forest soil is understood the value
which it realizes 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 con-
siderably from the value which the land has if used for the
production of forest crops, the sale value being generally
higher in the case of good lands, and lower in the case of in-
ferior lands, because the former yield a higher rental under
field crops, and the latter under forest crops.

The sale value of forest soil may be taken as expressing the
true value : —

(1) If forest soil is to be disposed of voluntarily for other

uses.

(2) In the case of forced sales, when the local value has to

be ascertained, rather than the forest value.

134

CHAPTEE III.

VALUATION OF 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) A whole wood or a series of woods.

(2) A part of a wood, such as one or more trees, one or

more units of measurement, or one or several }rears
increment.

SECTION I. — VALUE OF THE GROWING STOCK OF A WHOLE

WOOD.

1. Expectation Value of a Whole Wood.

The expectation value of the growing stock of a wood now
m years old is equal to the present value 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 finally cut over.

a. Method of Calculation.

Starting from the same data as those given in the case of the
valuation of forest soil, the receipts consist of : —

(1) Final yield in the year r = Yr ; present value =

r,

(2) Intermediate yields, as thinnings, to be realized in the
years n, o, p, and q ; their present value amounts to : —

EXPECTATION VALUE. 135

Thinning in the year n = --- - -*j

_ T0xl'opr

~

_ T
~

~~

Expenses :

(1) Annual expenses to be incurred from the year m to the
year r ; their present Value amounts to : —

00 />

- + - ~ + . . . + - — - = (according to Formula VI.)
I'op I'op- l'opr~'

e d'm/~TO— "h
= e (l'opr-m-l) = 'op V _ = E (l'opr-m-l)

l-opr~mx'op l'opr~m l'opr~m

(2) Eent of soil to be paid from the year m to the year r ;
its annual amount may be denoted by S X 'op ; the total
present value of the rent of the soil during r - m years amounts
to:—

Sx'op tS_x^op_ , _, Sx-op _ S X'op (I opr~m — 1)

l- op Top7" i-opr~m ^^

= S (l'opr-m-l)

The formula for the expectation value of a wood stands
therefore as follows: —

r. _ Yr + Tn x l-opr-n + . . . + Tq x l-opr-« - (S + E) (l-

--

Example. — A fully-stocked Scotch pine wood, worked under
a rotation of 80 years, is feloniously burned when 45 }^ears
old ; what compensation per acre should be paid to the owner,
if the expected returns are those indicated in the table at
page 122.

/t,-H

.*. c , I ,, A *

^ ^

-- 3 0.

*$</•£ i '->TAN^ J ~ " (' ' ^'; -;X?^P^

136 VALUATION OF THE GROWING STOCK.

Rate of interest = 2£ per cent.
Value of soil = 250 shillings.

Annual expenses =3 „ to be incurred at the end of
each year : —

2225 + 67 x r02530 + 86 x r02520+91 x T02510

45r _ -(250 + 120) (1-02535-!)

1-02535
*°Ge = 891 shillings = £44 11 0

~b. Notes on the Expectation Value of the Growing Stock.

The expectation value of the growing stock depends on the
following matters : —

i. THE ABSOLUTE AMOUNT 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 if the soil is again to be used for forest
purposes ; if the soil can be more profitably used for agricul-
ture 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. If a larger value of soil is intro-
duced, 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 : —

1683 + 67 x l-02520 + 86 x T02510

shillings.

EXPECTATION VALUE. 137

For a rotation of 80 years : —

45Ge = 891 shillings.

For a rotation of 90 years : —

2789 + 67 x l'02540+86 x 1'02530+91 x 1-02520
45r +95 xl-02510- (250 + 120) (1'02545-1)

1-02545

= 878 shillings.

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 129).

Assuming 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 realize —

At an age of 70 years . . = 1200 shillings.

„ 80 „ . . . . = 2000 „
„ 90 „ "• • • =2789 „

then the expectation value of the wood under these rotations
would be as follows : —

For a rotation of 70 years : —

For a rotation of 80 years : —

tSGf = 2000-870^26^1)
1 025

For a rotation of 90 years : —

For a rotation of 100 years : —

It will be observed that the maximum expectation value of
the growing stock is, in this case, obtained under a rotation
of 90 years.

138 VALUATION OF THE GROWING STOCK.

iii. THE AGE OF THE WOOD.

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
expectation value of the growing stock for the year 59 will
probably be higher than for the year 61.

Immediately after the area has been stocked in 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 the Growing Stock of a Whole 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 ha3 yielded
before the year m.

a. Method of Calculation.

Costs of Production. — (1) The present value of the rent of
the soil during m years comes to :—

Sxl'opm-S = S (l'opm-l).

(2) The present value of the annual expenses during m
years (see Formula IV.) :—

= e x 1 -opm~l + ex l'opm~* + . . . + e,

COST VALUE. 139>

(3) Present value of cost of formation : —
= cxl-opm.

Receipts. — These consist of all previous thinnings and items
of other incomes ; they may be represented hy Ta, Tb, . . . T^
Their present value is —

= Ta x l-opm~a+ Tb x l-opm~b + . . . + T\ x l'opm~l.

Should any items of income have occurred in annually equal
amounts, such as shooting, grazing, etc., they can be summed
up according to the Formula IV.

The general formula for the cost value is therefore : —

mGc = (S + E) (l-opm - 1) + c x l-opm - (Ta x l-opm-a
+ Tb x ropm~b + . . . + Tj x Top™-1).

Here mGc still includes the thinning of the year m. If the
calculation is made for what remains as final yield to go on
with, then the thinning in the year m = Tm must also be
deducted.

Example. — Taking the same data as before, the cost value
comes to : —

45GC=(250 + 120) (l'02545-l) + 60xl-02545-(4xl-02515

+ 36xl-0255).
45(2C = 891 shillings, as in the case of the expectation value.

b. Notes on the Cost Value.

The cost value of the growing stock depends on : —

(1) The absolute amount of the receipts and expenses up to

the year m.

(2) The Age of 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 : —

140 VALUATION OF THE GROWING STOCK.

(a) the calculation has been made with the expectation

value of the soil ;

(b) the receipts and expenses were of the normal amounts,

and

(c) the wood is fully stocked, or normal, at the end of the

rotation.

Proof. — Let in = r, then,
rGe=(S+E) (l-op>'-

By introducing the expectation value of the soil, the above
equation becomes : —

which, after reduction, leads to : —

'Gc = Yr.

(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 vice versa.

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.

3. Sale Value, or Utilization Value, of the Growing Stock of a
Whole Wood.

Under the sale value of the growing stock of a wood is
understood that price which it would realize in the open
market.

A wood may be sold under one of two conditions : —

SALE VALUE. 141

(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 he would have to meet
certain other expenses. Hence the sale value should
be equal to the expectation value.

(b) The wood is to be cut down at once. In this case the

sale value would be the price which the cut material
realizes 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.

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 be-
comes positive, rising at first slowly, then more rapidly, reach-
ing its maximum value far beyond the period at which the mean
annual increment culminates, in fact not until the annual in-
crease in the value per unit of measurement is no longer suf-
ficient 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 existing between the Expectation and Cost Values of

the Growing Stock of a Normal Wood.

Looking at the formula? for the expectation and cost values,
it will be observed that the soil rental and annual expenses
appear in the negative form in the one, and in the positive
form in the other ; again, the thinnings appear positive 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.

142 VALUATION OF THE GROWING STOCK.

Proof. — Let mGe = mGc, immediately after the thinning in
the year m has been made, then,

Yr+TnxI'opr-n + . . . + rgxl-ojf-g

= (S+E) (I'opm-l) + cxl'opm-(Taxl'opm-a+. . .

After making the necessary reduction, it will be seen that
this equation can only hold good, if —

„ Yr+Taxl'opr-a+. . . + T,xl'opr^-cxl'opr
l'opr-l

in other words, if the expectation value of the soil is introduced
for 8.

It must, however, not be overlooked that the above holds
good only in the case of normally stocked woods. If a wood
has been too thinly stocked from early youth, 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 Valu.es of
the Growing Stock of a Normal Wood on the one hand,
and the Utilization Value on the other hand.

The utilization 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 utilization value of young woods is
smaller than the expectation, or cost value. On approaching
the end of the rotation the difference is small, and it is then
the safest plan to value the woods according to their utilization
value, as the calculation of the expectation and cost values is
based upon more or less uncertain data.

VALUATION OF PART OF A WOOD. 143

SECTION II. — VALUE OF A PART OF A WOOD.

1. Value of Single Trees.

The average value of a single tree is obtained by dividing
the value of the whole wood, whether it be the expectation,
cost, or utilization value by the number of trees.

The special value of a certain tree can be ascertained by
estimating its utilization value, or according to the formula of
the expectation or cost value, by introducing the data referring
to the special tree in question, an operation which is beset by
considerable difficulties.

2. Value per Unit of Volume.

This is obtained by dividing the value of a wood (or tree)
by the number of units of volume contained in the wood (or
tree).

3. Value of the Increment of One or More Years.

The value of x years increment is equal to the value of the
wood x years hence less the present value of the wood. The
calculation can be made for x years forward or backward.
In either case the expectation, or cost value may be calculated.

a. The, Expectation Value.
(1) Calculated for the year m + x : —

l'0pr-(m+x)
_Yr+Tnxl'opr-n+. . .-(S+E) (l'opr-m-l)

l-opr-m

v , _ (Yr+THxl'ojT*+. . . + S+E}(l'op*-l)
\-of~™

(2) Calculated for the year m : —

Valne = (Yr+Tnxl'opr-n+. . . + S+E) (l-ops-l)

144 VALUATION OF THE GROWING STOCK.

I. The Cost Value.

(1) Calculated for the year m + x :

Value = (S+E) (l'opm+x- 1) + c x l'opm+x-(Ta x l-opm+*-»
+ ...)- [(S + E) (l'opm- 1) + c x l'opm
-(Taxl'opm-" + ...)].

Value = l'opw fs+jE+c -(—«- + . . .Yl (l'opx-l).

(2) Calculated for the year m :—

Value = l-opw-a! [s+JS+c-y^M-. . .Yj (l-op*-l.)

The cost value becomes equal to the expectation value, if the
expectation value of the soil is substituted for S, a matter
which is easy to show. In either case it becomes, calculated
for the year m + x :—
Value

For the year m this value has to be divided by l'opx.

SECTION III. — 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 = Yr, and every year there will be thinnings in the
gradations which have reached the ages of a, b . . . q
years ; at the same time every year formation would cost
c shillings, while supervision would 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."

NORMAL GROWING STOCK. 145

1. Time of Year for which the Calculation should be made.

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 within
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 year 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.

2. Expectation Value of the Normal Growing Stock.

For simplicity's sake, it shall, in the first place, be assumed,
that only one intermediate return is obtained, in the year q ;
then the values of the various age gradations will be as
follows : —

r.lr _Yr-(S+E)(l'op*-l)

etc.

-

q.lr _Yr+Tqx 1-ojf-g -(S+E) (l'
l-opr*-*

etc.

or _Yr+Tqxl-opr-«-(S+E) (1-op-^l)
~ToF~

By adding up all these quantities the following sum is
obtained : —

VOL. III. L

146 VALUATION OF THE GROWING STOCK.

.r

-op l-opz VojfJ \l-op

1 * opr X 'op l'oprx'op

^
l'oprx 'op

Introducing now the other intermediate returns which occur
in the age gradations aged a, b, . . . their values will
appear in the same manner as the return which occurred in the
age gradation q, namely as : —

Taxl'opr-a(l'opa-l) t Tbxl'opr-b(l'opb-l)
l'opr x 'op l'opr x 'op

Hence, the general formula for the expectation value of the
normal growing stock runs thus : —

(Yr+S+E) (I'opr-l}+Tax l'opr~a (l'opa-l)

Norm. Gr. ) = _ +. . - + Tqx l'opr~q (l'opq-l)
Stock Ge j l'oprx'op

-r (S+E).

Assuming that in the above formula Yr) Ta . . . Tq,
S and E are given for the unit of area, say 1 acre, then the
formula represents the value of the normal growing stock for
r acres. Consequently the normal growing stock for the unit
of area is : —

«- ___ ( ^
rxl'oprx'op

By introducing the soil expectation value into the formulas
given above, and substituting its value

S' -Yr+TqXl-opr-a+. . . + Tqxl'opr-q-cxl'opr _ «

NORMAL GROWING STOCK. 147

in the first part of the formula, it reduces to :
Yr+Ta+. . .
'op

f)

or, as£ = — ,

Yr+Ta + . .

'op

In words : The expectation value of the growing stock of
a normal working section is equal to the capitalized annual net
income minus the value of the soil.

For the unit of area the formula is :

Yr+Ta + .

rx 'op

8. Cost Value of the Normal Groiving Stock.

Assuming the same conditions as before, and also that only
the a year old gradation has given an intermediate yield, the
values of the successive age gradations come to : —

°GC=(S+E) (l'op°

1GC=(S+E) (l'opl

etc.
aGc=(S+E)(l'opa-

a+lGc = (S+E) (l'opa+l-l) + c x l'opa+l-Ta x I'op

etc.
r~lGc=(S+E) (l'opr~l- 1) + c x l'opr'l-Ta x l'opr-a~l.

The sum of these expressions comes to : —

(S+E)(l'op° + l'opl + . .

-op 'op 'op

By introducing now the further intermediate returns

'op 'op

L 2

148 VALUATION OF THE GROWING STOCK.

the general formula for the cost value becomes : —

(S+E + c)(l'opr-l)-[Ta(l'opr-a-l) + . . .
Norm. Gr. 1 + Tq (1-opT*-!)]

Stock Gc J -op

- r(S+E).

For the unit of area : —

(S+E + c) (l-opr-l)-[Ta(l'opr-a-l) + . . .

Norm. Gr. \_ _ + r<r(l'qpr-g--l)]
Stock Gc j rx'op

-(S+E).

If again the calculation is made with the soil expectation
value, as before —

Norm. Gr. Stock of } _ Yr+ Ta+. . . + Tq- (c + r x e)
Work. Section Gc ] ~ ~~^~ ' "

Norm. Gr. Stock ) _Yr+Ta+. . . + Tq-(c + rxe) _ «
of Unit of Area j rX'op

or the same as was obtained for the expectation value.

4. Capitalized Rental of Normal Growing Stock.

The value of the normal growing stock may also be obtained
by capitalizing the annual net rental and deducting therefrom
the value of the soil.

The annual net income is represented by the expression :—

Yr+Ta + . . . + Tq-(c + rxe)',
hence the value of the growing stock is equal to :—

- _ „

'op •

or for the unit of area

Yr+Ta+. .. + Tq-(c+rxe) « .

- ~~ *Je t

rx 'op

that is to say, the same as the expectation and cost values
calculated with the soil expectation value.

149

CHAPTER IV.

VALUATION OF WHOLE WOODS OR FORESTS.

THE value of a whole 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
the 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. Calculation under the supposition that the same Species and System
of Management are retained, after the present Crop has teen
Harvested.

(1) The value of the forest is equal to the value of the soil
and 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 the age of the existing growing stock = m, then the
expectation value of the forest is : —

Yr+Tnxl'opr~n+. . . + Tqxl'opr~q

m-l] _ q

be

. . . + Tqxl'opr-(l-E(l'opr-m-l)+rSe

- 4; -X

150 VALUATION OF FORESTS.

By introducing the value of rSe —

ro = Yr+Taxl'opr-a+. . .+ Tqxl'opr-q
l'opr-l

the above formula becomes

^ ^

l'opr-l

-E.

If m 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 formulae become respectively :

l'opr~m
and
m l'opm (Yr+Taxl'opr-a + . . .

l'opr-l
If ?7i = 0, and cultivation has not yet taken place —

Yr+Taxl-opr-a+. . . + TqxI'opr-'*-cxl-opr
op . _ -E (l'opr-m-l)+rSe _

l'opr

tion value.

(2) The forest expectation value can also be calculated
direct out of the expected receipts and expenses, in which
case —

V V 71 rP

mTf> _ •*• r i •*• r _j_ _i_ •*• n i -*• n

" l'opr~m l'opzr~m l'opn~m l'opr+n~m

T T

-f _ •*•» 4. _|_ ^a _1_

'tr+n-m 1 ^ .r-tm-a) .

c c + V--EJ-

'op*r-m * ')

l'opr-m

EXPECTATION VALUE. 151

, TaXl'0P

l'opr-l l'opr-l l'opr-l

cxl'op™ w

+ • • • — l - Ft ~~ ^ >

l'opr — 1

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 122 ; if rotation
= 80 years; cost of formation = 60 shillings; per cent. = 2J;
and annual costs per acre = 3 shillings.

l-02545(2225 + 67 x l'02530+86 x 1'02520

-^o

1-02580-!
^Fe = 1141 shillings = £57 I 0.

It was found before : —

At page 127 . 80Se = 250 shillings.

136 . *Ge = 891

Total . . 1141 „ = £57 1 0
as above.

In the case of the present growing stock being abnormal,
the corresponding values must be introduced into the account
(see page 137).

b. Calculation under the supposition that, after the cutting over of the
present crop, another species or another method 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 / must be determined, under which the

152 VALUATION OF FORESTS.

expectation value of the present growing stock reaches its
maximum.

The value of the forest is then represented by the formula —

> Y+ Txl'o>'-n+. . .-E l-o'-n

If the present growing stock is abnormal, a further modifi-
cation is required, by substituting the abnormal for the normal
returns.

2. Cost Value of a Forest.

a. The Cost Value of a Forest is equal to the Cost Value of the Soil,
plus that of the Grotving Stock.

(1) For any soil value : —

c)l-opm-[Taxl'opm-a+. . .

(2) By introducing the expectation value of the soil, the
above becomes, for normal woods : —

-[Taxl'opm-a+. . ,

l'op>-n+. . .+ j|^+. . .-c)

l'opr-l~

This, it will be observed, is equal to the expectation value
of the forest.

b. The Cost Value can be 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 —

mFe=Sxl'opm+E (l'opm-l)+cxl'opm-(Taxl'o2}m-a+. . .)
= (S+E+c) l'opm-[Taxl'opm-a+. . .

as before.

COST, SALE AND RENTAL VALUES. 153

3. Sale Value of a Forest.

By the sale value of a forest is understood the value
estimated according to prices realized 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. Rental Value of a Forest.

Under the rental value of a forest is understood the
capitalized rental which it is capable of yielding. If the
annually equal rental is = R, the rental value would be : —

Rental value = ; — - •

This method is only applicable in the case of a forest which
can be so managed that it yields an annually (or periodic)
equal rental. The rental is represented by —

Yr+Ta+Tb + . . . + Tq-(c + rxe),
and the rental value of the forest is —

_Yr+Ta+Tb + . . . + Tq-(c+rxe) .
•op

Or, if — — is denoted by = E,
'op

Rental value of a whole series = Yr+T*+- ' - + T^C -rXE.

'op

The mean value of one age gradation would amount to —

+ ' ' '
r x 'op

Rental value per unit of &rea,= Yr+ Ta + ' ' ' + T<*~~C-E.

'

154

CHAPTER V.

DETERMINATION OF 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 'op. 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 cost of cultivation,
is expressed by —

ex Top'

1. Rental of the Soil.

Under 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 R8

\~Yr+Taxl-

This rental, it will be observed, is the rental of the soil
expectation value = rSe X 'op.

RENTAL OP FORESTS. 155

2. Rental of the Growing Stock.

This is calculated from the value of the growing stock in the
same way as in the case of the soil rental.

3. Rental of the Forest.

The rental of the forest is equal to the net return yielded hy
the forest (soil plus growing stock). In the case of the
annual working, the forest rental is equal to : —

Rf=Yr+Ta+. . . + Tq-(c + rxe).

If Yr, Ta . . . c and e refer to the unit of area, the
rental for the unit of area is : —

Unit of area Rf = Yr+T<* + - •

156

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 which exists between the yield
and the capital which produces it. Hence, when several
methods of treatment lead to the realization 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 OF 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 ;

(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.

DETERMINATION OF THE PROFIT. 157

1. Determination of the Profit of Forestry.

a. Calculation for the Intermittent Working.
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 they must he calculated
for one and the same time. In the first place, that time shall
be the commencement of the rotation when the area is about
to be planted or sown for the production of a forest crop.

i. CALCULATION FOR A BLANK AREA.
Let as before : —

Yr be the final yield occurring in the year r and again in
2 x r, 3 x r, and so on for ever ;

Ta, Tb . . . Tq, the thinnings occurring in the years
a . . . q, and again in a + r . . . q + r years,
again in & + 2 x r . . . # + 2 X r years and so on ;

Sc the cost value of soil ;

E the capitalized annual expenses = - :

'op

c the cost of formation expended now, and again every
r years ;

C the capitalized cost of formation = c- ---- ^ ;

l'opr — 1

p the per cent, at which money 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 represented by

_Yr+Txl'opr-a+. . .

l'opr-l
while the present value of all costs comes to ? —

SC+E+C.

Hence the profit of forestry is expressed by the formula : —

Profit=P= r,+ Ta x i-«s^+._. •+ r. x i-°^-- (

158 THE FINANCIAL RESULTS OF FORESTRY.

This formula can also be written as follows : —

p _ (Yr+Taxl'opr-a+. . . + TqxI-opr-«-cxl'opr
\ l'opr-l

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-Sc.

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 realized 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 realized if, although Se = Sc at the

outset, the soil expectation value is afterwards in-
creased, either by higher returns or by smaller costs,
or by both ; in other words, by improved and more
economic management.

(8) 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 the per cent. p. 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 security.

ii. CALCULATION OF THE PROFIT FOR A WOOD NOW m YEARS OLD.

It is assumed that the returns and costs are of the normal
amount.

DETERMINATION OF THE PROFIT. 159

The receipts consist of: —

(a) All items of income realized between the formation of

the wood and the year m, with accumulated interest
to the year m : —

Taxl'opm~a+...Tm.

(b) All items of income to he realized between the year m

and the end of the present rotation r, discounted to
the year m : —

Tnxl'opr-n+. . .

(c) All items of income to be realized during subsequent
rotations, amounting to : —

Taxl'opr~a+. . .

(l'opr-l)xl'opr-<
The costs are : —

(a) Past costs with compound interest to the year m : —

Scxl'opm+E (l'opm — l) + cxl'opm.

(b) Costs to be incurred from the year m to the end of the

rotation : —

E(l'opr-m-l)

(c) Costs to be incurred during future rotations : —

E cxl'opr

l'opr~m (l'opr-l) X l'opr-m'

By deducting all costs from the receipts, the profit is
obtained and represented by the following formula : —

Profit P =

Yr+ Ta x l'opr~n + . . . + Tqxl'opr-q-E (l«opr-m-l] T

+ ."r-m V1')

Yr+Taxl'of -« + ... -cxl'of

~

\

E) - (IL)

160 THE FINANCIAL RESULTS OF FORESTRY.

-Sc . . . . . . . . . (HI.)

In this formula expression (II.) represents the expectation
value of the soil discounted for r — m years, and the bracketed
part of expression (III.) represents the cost value of the m
years old growing stock ; hence the above formula can be
written as follows :—

Profit P =

Yr+Taxl'opr-n+. . . + Tqx

Here again the positive part represents the expectation
value of the forest (see page 149), and the negative part the
cost value of the forest ; hence :—

Profit P = mFe-mFe.

It will be seen that this formula agrees with that given for
a blank because for the year o 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 158, headings (1) to (4),
with regard to the formula P = Se — Sc also hold good with
regard to the formula P = Fe — Fc.

b. Calculation for the Annual Working.

In this case the returns and costs occur regularly every
year. If they are of annually equal amounts, the returns
are = Yr + Ta + . . . . + Tq.

The costs consist every year of —

(1) Interest on the value of the soil . . = rxS0X'op;

(2) „ „ „ „ normal grow-

ing stock . . . . . =rxnG0X'op;
(8) The annually recurring cost of a4minis-

tration, protection, taxes, etc. . . =rxEx 'op ;
(4) The cost of formation . . . . = c ;

DETERMINATION OF THE PROFIT. 161

hence total annual costs =

and the annual profit : —

Annual P =
Yr+Ta + . . . + Tq-[(rxS0+rxnGc+rxE)x'op + c].

This formula can be written thus : —

Annual P —

Yr+Ta+. . . + Tq-c-rxe-[rxSc + rxnGc~]x'op;

or,

Annu,OP= Yr+T.+. . . + Tt-c-rx< x j x nQ
'op 'op

Now : —
Annual P

= capitalized value of annual profit = total profit ;
expectation value of the

'op

Yr+Ta+. . . + Tq-c-rxe_
'op

forest under the annual working = Fe ;

r x Sc + r x nGc = cost value of forest = F0 ;

hence total, or capital, value of profit of the whole forest : —
Total P = Fe-Fc.

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.

162 THE FINANCIAL RESULTS OF FORESTRY.

2. Determination of the Rate of Interest yielded by the Capital
invested in Forestry, called the Forest Per cent.

a. Calculation for the Intermittent Working.

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.

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 question. The current
annual per cent, is equal to that quotient multiplied by 100.

Let:—

Ym be the utilization value of a wood at the end of the year m,

•* m+l » >j j» » >j j> 7/1+1,

then —

-^m+l ~~ *j»

represents the increase in value which has been laid on during
the year m + l. Deducting from this e, the annual costs, the
net increase is equal to —

V —V — P

•*• m+l *« °«

The cost value of the wood at the end of the year m (or
beginning of the year m + 1) is represented by : —

(a) the value of the soil with compound interest to the

year m =

Scxl'opm.

(b) the cost of formation with compound interest to the

year m —

c x l'opm.

(c) The value of the annual costs during m years with

CURRENT RATE OF INTEREST. 163

compound interest calculated for the end of the
year m =

'op

(d) From these amounts must be deducted all returns
realized between the formation of the wood and the
end of the year m —

Taxl'opm-a+TbxI'opm-b + . . . + TlxI'opm-l+Tm.

The forest per cent. = °pf with which the invested capital
is working during the year ra + 1 is, therefore, expressed by

the formula : —

•

(Ym+l-Ym-e)lW

The denominator in the above formula can also be written
thus : —

(SC+E) (l'opm

On reference to page 139, 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. = (Ym+l-Ym-e)xWO*_ (Ym+1-Ym-e}xlW
Sc+mGe mFc

By substituting the utilization value of the growing stock
for its cost value, the formula becomes —

* This formula differs from that usually given in continental works, which is
as follows :

It is easy to show that this formula is only correct for the year in which
= general per cent.^?.

M 2

164

THE FINANCIAL RESULTS OF FORESTRY.

Similar to the progress of the current annual increment of
a wood, the current annual forest per cent, is at first small,
then rises, reaches a maximum, and then falls again. The
maximum is greater than that attained by the mean annual
increment, and also it occurs earlier (see fig. 41).

Fig. 41.

Of special interest to the forester is the relation which exists
between the current annual forest per cent. «= °pf and the

Culmination oj mean p/.

Year when Se culminates.

Fig. 42.

general per cent. p. At first cpf is < p, then comes a time
when the two are equal ; after that °pf > p, and after a further
lapse of time epf becomes =p a second time (fig. 42), but
beyond that period the forest per cent, is permanently smaller

MEAN EATE OF INTEREST. 165

than p, unless exceptional conditions produce once more a
sudden rise in the current annual forest per cent.

The second occasion occurs in the year when the expecta-
tion value of the soil reaches its maximum. Hence the formula
for the current annual forest per cent, can he used to gauge
the financial ripeness of a wood, as will be shown 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 : —

__x .

-

\ l'opr-l -op

The producing capital at the commencement of the rotation
is equal to the cost value of the soil = Sc. Hence the mean
annual forest per cent, under the intermittent working is : —

/r,+r.x i-gp^+. . .+Taxi-oP'-«-cx i-ofr^ x

V i'of-1 L _xlOO

meane

anPf=-exp.

Sc

If 8>8m then «™pf>p.

If the expectation value of the soil is equal to the cost value,
then the mean annual forest per cent, is equal to the general
per cent, p, which proves the correctness of the above formula.

The highest mean annual forest per cent, is obtained under
that rotation for which the expectation value of the soil
culminates ; it is then equal to the current annual forest per
cent, (see fig. 41).

166 THE FINANCIAL RESULTS OF FORESTRY.

b. Cakulation for the Annual Working.

Under the annual working, with equal annual increment
yield and costs, the current annual forest per cent, is equal to
the mean annual forest per cent. In this case the annual net
return amounts to : —

Yr+Ta + . . . + Tq-c-rxe,
and the producing capital to —

rxSe+rx*Ge;

hence

mean _ •*r+-*a+* • • + -Lg — C —

v

rxSe+rxnGc

~-> _ -*r"i -*• a\~ • • • H~ •*- q C TX6 ~lf)f)
Fc

By multiplying and dividing the enumerator in this formula
by 'op, the following is obtained : —

r,+r.+...+r,-c-rxA x 100

or, as the part in brackets is equal to the expectation value of
the

This formula is identical with that obtained above for the
profit = Fe-Fc:

IfFe>Fc,then
IfFe=Fc, then

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.

CHOICE BETWEEN FORESTRY AND AGRICULTURE. 167

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 this 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, 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) The 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 amounts of profit for each case
and to compare them.

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 =

l'opr-l

168 THE FINANCIAL RESULTS OF FORESTRY.

Kental 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 : —

r+ Ta X 1

=r-

where Yf 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 Sylvicultural System.

In both cases the choice is determined by the expectation
value of the soil. It depends on :—

(a) the value of the returns and the time when they occur.

(b) the cost of formation, and the amount of the annual

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 differences in the expectation
value of the soil under the various methods of formation, such
as planting, sowing, or natural regeneration.

4. Choice of Method of Tending, especially in respect of the

Time and Strength of Thinnings.

This is best effected by calculating the expectation value of
the growing stock for the different methods of thinning, and
comparing them.

5. Determination of the Financial Rotation.

The financial rotation, or that which gives the best financial
results, may be determined in various ways, as : —

FINANCIAL RIPENESS OF WOODS. 169

(a) The rotation which yields the highest expectation value

of the soil, or the highest soil rental.
(6) The rotation which gives the highest net return for the

forest.
(c) The rotation which, taking a certain value of the soil,

gives the largest profit or the highest mean annual

forest per cent.

6. 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
the forest per cent. : —

curr. (Ym+l-Ym-e}xWO

is greater than the general per cent, p, the wood is not
ripe. If current pf = p, then the wood is just ripe. If
current pf < p, then the wood is past ripeness and, if left
standing, a financial loss is incurred.

The above short notes will suffice for the present. The
application of these principles will be found in the next part
of this volume.

PAET III.

PRINCIPLES OF FOREST WORKING PLANS,

OR,

DESCRIPTION OF THE NORMAL FOREST.

173

PRINCIPLES OF FOREST WORKING PLANS.

INTRODUCTORY.

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 realized. As
the latter differ widely, it follows that working plans cannot be
drawn up according to any special 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 will 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. Under the former, timber, fire-
wood and bark are understood. It is in the nature of things
that forests should chiefly yield 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 realization of
major produce.

Major produce is again divided into the final and interme-
diate yields. The latter comprise the thinnings 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.

The major produce of forests, wood, is one of the indispen-

174 PRINCIPLES OF WORKING PLANS.

sable articles of life, but it is bulky, and not adapted for a long
transport by land. To this must be added that long periods
of time elapse between the planting and harvesting of trees.
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 man-
agement based upon the principle of a sustained yield.

Generally speaking, a " sustained yield " is secured, if all
areas which have been cleared are restocked within a reason-
able 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 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 " strict or equalized
annual working."

The regulation of the yield of forests worked intermittently
is very simple. It is only necessary to ascertain the most
profitable rotation, taking into consideration the objects of
management, and to make the thinnings whenever they become
necessary.

Although the method of annual working, and especially of
the equalized 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 favours the development of a regular and steady

market, 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.

INTRODUCTORY. 175

(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 : —

(a) It cannot as a rule be introduced without cutting certain

woods at an age differing from that which is most
profitable.

(b) Owing to the necessity of bringing annually the same

quantity into the market, it interferes with the com-
plete utilization of special demands for forest produce,
or the omission of cuttings when the demand is slack.

These remarks show that the intermittent as well as the
annual working possess peculiar advantages, and that the
choice depends on circumstances. In the majority of cases
the annual working will be found more suitable, without,
however, strictly adhering to it when it would involve sacri-
fices 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 or
thinnings, 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

yield equal intermediate returns.

(2) Thinnings depend much more than final cuttings on

the method of formation and tending.

(3) The yield of thinnings depends frequently on events

which do not occur regularly, or which cannot be fore-
seen, so that it is almost impossible to estimate it
correctly beforehand.

Hence, it is desirable to confine the regulation of the annual
yield to the final cuttings, and to be satisfied with an approxi-
mate equalization of the intermediate returns, such as will
naturally happen, if the final cuttings are systematically
equalized; provided always that the thinnings are not made
so heavy as to affect the subsequent final returns.

176 PRINCIPLES OF WORKING PLANS.

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 in a simple form, which is
uninfluenced by external interfering circumstances. Such an
ideal state differs, of course, for every different method of
treatment, in accordance with the objects at which the manage-
ment 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.
(8) A normal growing stock.

By normal 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 by a preponderance of
certain age classes.

By a normal distribution of age classes is understood a
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 arranged normally, 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, so that each year a wood of the normal age

INTRODUCTORY. 177

can be cut, and 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
forest per cent, of which has sunk below the general per cent.
p (see p. 169).

In accordance with these definitions, the following matters
demand special attention : —

1. The increment.

2. The rotation, or the normal 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.

VOL. III.

178

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.

3. Price increment.

SECTION I. — QUANTITY INCREMENT.

By quantity increment is understood the increase in the
volume caused by the growth of a tree or a wood. It is
measured by the cubic foot solid, or the cubic foot stacked.
The different kinds of quantity increment and the modes of
measuring them have been explained 'in Forest Mensuration,
p. 82. 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 at pages 188 to 191, the various classes of in-
crement have been calculated separately for final, intermediate,
and both yields together.

1. Progress of Volume Increment.

a. Of Single Trees.

The volume increment is produced by an annual elongation
of the crown and roots, and by the laying on of a new layer

QUANTITY INCREMENT.

179

between wood and bark all over the stem, branches and roots.
As a general rule the stem or trunk is the most important part
of the tree ; hence the forester is specially interested in the
height and diameter growth.

It has been explained in Volume I. of this Manual, p. 161,
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 locality and method of treatment ; besides,
there is in this respect a great difference between seedlings
and coppice shoots.

Generally speaking, in the case of seedlings 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 to
the forester, but the data at present available give wide limits
for those periods. Taking the various quality class es together
the following table gives the limits of the periods and the mean
year of the maximum height growth : —

SPECIES.

CURRENT ANNUAL HEIGHT
INCREMENT.

MEAN ANNUAL HEIGHT
INCREMENT.

Limits of
Period when
the Maximum
occurs.

Average Year
when Maximum
occurs.

Limits of
Period when
Maximum
occurs.

Average Year
when Maximum
occurs.

Scotch pine

15—40

20—55
25—55
20—90

28
38
40
55

30— 55
38— 80
41— 92
50—140

43

59
67
95

Spruce

Beech

Silver Fir

On the whole, the culmination occurs earlier : —

(1) In the case of light- demanding species, and

(2) In the better localities.

In the case of teak, the current annual height increment

N 2

180 THE 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, though some-
what quicker during early life. S&1 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 off early, nor do such shoots, rare
cases excepted, reach the same ultimate height as seedling
trees.

The comparative height growth of different species has been
dealt with at p. 163 of Volume I. of this Manual.

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
are comparatively more tapering, while those with the crown
reduced 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 coefficient 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 4£ feet above the ground, are used, and at p. 39 the form
factors for the following trees were given : —

QUANTITY INCREMENT. 181

Scotch pine, according to T. Kunze.

Spruce, ,, „ Baur.

Silver Fir, ,, ,, Lorey.

Beech ,, ,, Baur.

These factors refer to trees grown in fairly crowded woods.

Similar figures for oak, based on the measurements of a
sufficiently large number of woods, are not yet available, but
until they have been obtained the form factors for beech may,
within reasonable limits, be used for oak grown in fully stocked
woods. In the case of oak' trees grown in coppice with
standards, form factors are out of the question.

b. Increment of tuJiole 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
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 lowei
branches, thus producing more valuable trunks.

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 con-
sisted, must be removed by degrees, because they are gradually

182 THE INCREMENT.

overtopped and suppressed ; 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 considerable
portion of the former, will be removed in the thinnings, in the
same degree as, with the advancing age of the wood, the.y lose
their dominant character and join the secondary part of the
growing stock.

The progress of the increment in whole woods has, by no-
means been determined for all important species, though much
material bearing on this question has been collected of late
years on the continent of Europe. In India matters are still
more backward. So much, however, has been determined,
that both the current and mean annual increment culminate
much earlier than had been supposed.

The yield tables for some of the more important European
species justify the following conclusions : —

(1) The current annual increment rises rapidly after the

first youth is passed, and reaches its maximum about
the time when the height growth culminates ; it then
falls, and reaches zero at the death of the wood.

(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. Gustav Heyer has proved this in
the following manner : —

Let cit cz, c3, . . . cn, cn+1, be the current annual increments
of successive years ; mlt m2, ra3, . . . mn,' mn+1, the mean annual
increments for the same years ; then the current annual incre-
ment of the year (n + 1) is represented by—

QUANTITY INCREMENT.

183

or
and

CH+I = (n + 1) mn+l -nx mn,

ca+1 = nx mn+l + mn+l -nx mn,

CH+I ~ w»+i = n (mn+1 - mn) .

It follows that if mn+l^,mn, then also cn+1^.wn+1; and if
mn+l = mn, then also en+1 = wn+1, as it was proposed to prove.

(4) When the mean annual increment culminates, the
current annual increment must, naturally, already be
past 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
current annual increment is already falling.

Example : —

Year.

Current
Annual
Increment.
Cubic feet.

Total
Increment.
Cubic feet.

Mean Annual
Increment.
Cubic feet.

Year.

Current
Annual
Increment.
Cubic feet.

Total Mean Annual
Increment. Increment.
Cubic feet. Cubic feet.

1

30

30

30

7

120

716 102

2

65

95

47

8

108

824 103

3

105

200

67

9

94

918 102

4

126

326

81

10

80

998 100

5

138

464

93

11

68 1 1066 96

6

132 596

99

12

62 1128 94

Or graphically represented : —

1-00

8c

€.0
40

4

Fig. 43.

184 THE INCREMENT.

(5) Whenever the object of management consists in the
realization of the greatest return of volume, the rota-
tion must coincide with the year in which the mean
annual increment culminates. The time when the
maximum for final yield only occurs, differs from that
for final plus intermediate yields ; the difference may
amount to 10 and, even 20 years, especially if heavy
thinnings are made at an early period.

2. Quantity Increment Per cent.

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 indepen-
dently of the actual volume, it is usual to give it in per cents.,
and to call the proportion the " increment per cent." ; by this
is, therefore, understood the current annual increment which is
laid on by every 100 units of volume.

; The increment per cent, is used, sometimes to calculate from
the present volume the increment which is likely to be laid on
in the immediate future, but is chiefly employed for the purpose
of testing the activity of the capital invested in forestry.

Let the volume of a tree or wood at a certain age = v,

„ ,, the same tree or wood one year later = F;

then the increment of one year i = V — v.

Let further the increment per cent, of the volume = pv,
then

and

pc = Zn?xlOO = -xlOO.

v v

The same expression is obtained by considering V as the
accumulated value of v, produced by v working with interest
for one year, in other words :

QUNTITY INCREMENT PER CENT. 185

This gives :—

as before.

The increment per cent, p is naturally very large during the
early youth of a tree or wood ; but as the volume increases
year by year, that is to s&y the denominator in the above
equation, while the annual increment does not increase in any-
thing 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 tempo-
rarily produce an exception to the above rule, as they may
retard the sinking of the increment per cent.

Instead of comparing i with v, it can be brought into re-
lation with F; in that case the increment per cent, becomes : —

=x 100=x100.

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 V as the value produced by placing v for n years at
compound interest, working with pv per cent., as : —

From this

and

or-

186 THE INCREMENT.

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 incre-
ment during the n years is laid on in annually equal quantities,
and by 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 : pv

and

V-v 200
n *

This formula gives pv somewhat too small ; but the difference
is so slight, that it can be neglected for all practical purposes.

Example : —

Let v (in the year 70) = 3820 cubic feet ;

„ V (in the year 80) = 4260
then —

or

V-v 200 4260-3820 200 w
*•- V+v X T = 4260 + 3820 X lo =

If any thinnings have been made during the n years, their
amount must be added to F, 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 —

or

4260 + 327-3820. 200

-

-

QUANTITY INCREMENT PER CENT. 187

A law of considerable importance in the preparation of work-
ing plans, which was discovered by Pressler, runs thus : —

" The increment per cent., in its gradual fall, is expressed for
the year r, in which the mean annual increment culminates, by
the formula —

100
For final yield only: .... pv= .

For final and intermediate yields : p'v =

where t represents the sum of all thinnings expressed in per
cent, of the final yield.
The proof is eas}T : —

The increment per cent, is,

pv = -xlQQ.

v

In the year r, when the mean annual increment culminates,
the current annual increment is equal to the mean annual in-
crement, that is to say, i = - ; introducing this value in the

T

above formula, it becomes

r v r
For final and intermediate yields let : —

T = total of intermediate yields to the year r',
v = final yield in the year r',

then the maximum mean annual increment —

_v'+T
r'

If pvf be the corresponding increment per cent., then
, v'+T 100 100

r v r \ v

If now t represents the per centage of T in v't then —

T

t~^7x

188
and

THE INCREMENT.

— —
100'

Introducing this value into the above formula of pv, the
latter becomes : —

,_100/., , txv' \_100 + £
~V~\ +100x7/~ ~7~

The formula? pv = — ~ and pv' = -— ^ are used to gauge the

ripeness of growing woods which are worked for volume of
production only. If it is found that the increment per cent.

YIELD TABLE FOB ONE ACRE OF A SCOTCH PINE WOOD,

Timber down to

FINAL YIELD.

INTERMEDIATE

Age
of

Mean
Height
of
Domi-

Volume

Increment in Cubic Feet solid.

Volume

Incre-

Wood.

nant
Trees.

Cubic
Feet
solid.

Periodic.

Current
Annual.
d

Mean
Annual.

Per
Cent.

Cubic
Feet
solid.

Periodic

Current
Annual

_ i

To

~io

a

1)

C-

d

e

/

9 '

h

i

ft

10

5

—

20

15

30

1-5

800

80

39-88

48

5

30

26

830

28-

48

1140

114

9-03

289

29

40

35

1970

49-

289

730

73

3-20

403

40

50

43

2700

54-

403

600

60

2-03

413

41

60

51

3300

55

413

520

52

1-47

363

36

70

57

3820

55-

868

440

44

1-10

327

88

80

63

4260

53-

327

360

36

•81

282

28

90

67

4620

51-

282

290

29

•61

248

25

100

71

4910

49-

248

240

24

•48

213

21

110

73

5150

47'

213

190

19

•86

164

16

120

75

5840

44-

164

QUANTITY INCREMENT PER CENT.

189-

100
in a certain year r is still greater than , it shows that the

T

moment when the mean annual increment culminates has not

100
yet been reached — the wood is not yet ripe. If pv < —

100

then ripeness is past ; and if pv = — , the wood is just ripe.

r

It remains to add, that the formula for the increment per
cent, can be applied to height, diameter, or basal area incre-
ment, as well as to volume increment.

Example. — The accompanying two tables are yield tables for
the Scotch pine III. quality, according to Weise, the first for

III. OK MIDDLING QUALITY, ACCOKDING- TO WEISE.
3 inches diameter only.

YIELDS.

TOTAL YIELD.

merit.

Volume in Cubic
Feet solid.

Increment.

Age

of

Wood.

Mean
Annual
_ m
a

Total to
present
Age.

Columns
c + h.

Columns
c + TO.

Periodic
d + i.

Current
Annual
e + k.

Mean
Annual

0

a

Per
Cent.

I

in

n

0

P

1

r

s

10

30

30

1-5

20

843

85

40-16

1-6

48

873

878

29-

30

1429 143

10-53

8-0

337

2259

2307

58-

40

1133

113

4-65

15-

740

3103

3440

69-

50

1013

101

3-24

19-

1153

3713

4453

74-

60

883

88

2-40

21-

1516

4183

5336

76-

70

767

77

1-85

23-

1843

4587

6103

76-

80

642

64

1-41

24-

2125

4902

6745

75-

90

538

54

1-11

24-

2373

5158

7283

73-

100

453

45

•89

23-

2586

5363

7736

70-

110

354

35

•67

23-

2750

5504

8090

67-

120

190

THE INCREMENT.

YIELD TABLE FOR ONE ACRE OF A SCOTCH PINE WOOD,

Timber and

FINAL YIELD.

INTERMEDIATE

Age
of
Wood.

Mean
Height
of
Domi-
nant
Trees.
Feet.

Volume,
Cubic
Feet
solid.

Increment, in cubic feet solid.

Volume
in
Cubic
Feet
solid.

Incre-

Periodic.

Current
Annual.
d

Mean
Annual.

Per
Cent

Periodic.

Current
Annual,
t

10

10

a

I

c

d

e

/

0

h

i

ft

510

51

10

5

510

51

780

78

9-72

20

15

1290

64

850

85

5-19

343

43

30

26

2140

71

343

760

76

3-10

614

61

40

35

2900

72

614

630

63

1-98

572

57

50

43

3530

71

572

530

53

1-41

529

53

60

51

4060

68

529

470

47

1-10

443

44

70

57

4530

64

443

420

42

•89

386

39

80

68

4950

<>2

386

350

35

•68

328

33

90

67

5300

59

328

280

28

•51

286

29

100

71

5580

56

286

240

24

•42

243

24

110

73

5820

53

243

190

19

•32

186

19

120

75

6010

•

50

186

timber down to 3 inches diameter, and the second for timber
and firewood, in each case for one acre ; the data refer to the
volumes above ground only.
The second table shows that —

(1) The current annual increment, for final returns only,

culminates about the year 25.

(2) The mean annual increment, for final returns only,

culminates about the year 40, that is to say, when
it is equal to the current annual increment.

(3) The current annual increment, for final and inter-

mediate returns, culminates about the year 35.

QUANTITY INCREMENT PER CENT.

191

III. OR MIDDLING QUALITY, ACCORDING TO WEISE.
Fagots.

YIELD.

TOTAL YIELD.

ment.

Volume in
Cubic Feet solid.

Increment.

Age
of

Wood.

Mean

Mean

Annual.
m
a

Total to
present
Age.

Columns

c + h.

Columns
c + m.

Periodic

d + i.

Current
Annual.
e + k.

Annual.

0

a

Per Cent.

I

m

n

0

P

1

r

s

510

51

510

510

51

10

780

78

9-72

1290

1290

64

20

1193

119

6-77

12

343

2483

2483

83

30

1374

137

5-08

24

957

3514

3857

96

40

1202

120

3-53

30

1529

4102

5059

101

50

1059

106

2-66

34

2058

4589

6118

102

60

913

91

2-05

36

2501

4973

7031

100

70

806

81

1-65

36

2887

5336

7837

98

80

678

68

1-29

36

3215

5628

8515

95

90

566

57

1-02

35

3501

5866

9081

91

100

483

48

•83

34

3744

6063

9564

87

110

376

38

•63

33

3930

6196

9940

83

120

(4) The mean annual increment, for final and intermediate

returns, culminates about the year 60, when it is
equal to the current annual increment.

(5) Both the current and mean annual increment of final

and intermediate returns culminate later than in the
case of final returns only.

(6) The increment per cent, forms a falling series in each

case.

(7) The increment per cent, of final yield for the year 40, when

the mean annual increment culminates, should be —

192 THE INCKEMENT.

This agrees with the table, as it shows —

For the period 30-40 : p = 3'10
„ 40-50: p = l-98
or about 2'5 for the year 40.

For final and intermediate returns :—

jj;_100+SXl00^100+51_2.52

The table shows —

For the period 50-60 : / = 2'66
„ 60-70 : / = 2-05
between which 2*52 lies.

(8) The maximum quantity return will be obtained under a
rotation of 60 years.

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 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.

If in the course of n years the net value of the unit of
volume rises from q to Q, then the quality increment is
-= Q — q, and the corresponding per cent, is obtained by the
formula : —

and

or

QUALITY INCREMENT. 193

An approximately correct value for pq is obtained by the
formula : —

The quality increment may be rising, falling, or its move-
ments may be more or less irregular ; hence it is impossible
to indicate these movements in a mathematical form.

Woods grown for firewood only show little or no quality
increment after middle age ; except, perhaps, in so far as the
per-centage of stem- to branch wood increases. The latest
investigations seem even to indicate that wood taken from
middle-aged trees has a higher heating power than wood taken
from older trees although they 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
dimensions.

(2) The per centage 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 quantity increment is still above nil.

Example. — A Scotch pine wood 60 years old contains : —

Timber = 3,300 cubic feet, worth 4d. per cubic foot.
Firewood = 760 „ „ „ Id. „ „

Hence, mean quality :

3300x4 + 760x1
«" -406CT -=3'44P*nce-

The same wood in the year 70 has : —

Timber = 3,820 cubic feet, worth 5d. a cubic foot.
Firewood = 710 „ „ „ Id. „

VOL. III. O

194 THE INCREMENT.

Hence :

3820x5 + 710x1 Q7
Q= "4530- -4-37 pence.

And:

-- ',

4-37^3-44 xl'op,10

And

p, = 2-42 per cent.

Approximate value :

4-37-3-44 200 0 QQ

X TO =238percent-

Calculating the quality increment per cent, for timber only
with the data given in the table at page 122, the following
values are obtained for pq according to the formula :—

Period 30— 40 years . . . pq = 2'26

40— 50 „ . . . „ = 1-84

50— 60 „ . . . „ = 2-92

60— 70 „ . . . „ = 2-26

70— 80 „ . .; . „ = 1-84

80— 90 „ .. ;v. . „ = 1*55

90—100 „ . v ' . „ = 1-34

„ 100—110 „ . . . „ = 1-18

„ 110—120 „ . . „ = 1-06

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

PRICE INCREMENT. 195

major part of the wood, hence extremes in this respect must
be avoided.

SECTION III. — PRICE INCREMENT.

Under price increment is understood the increment caused
by a change in the price of forest produce generally, inde-
pendent of the accompanying quality increment. It can be
positive, nil, or negative.

Example. — A hitherto inaccessible forest is brought into
communication with a large town by the construction of a
railway; the increase in the prices of the produce of the
forest represents the price increment, which in this case is
positive.

Or, Owing to an increased import of forest produce the
price of the home production falls generally ; this represents a
fall of prices, in other words a negative price increment.

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 affect 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 = S — s, and

S = sxl'op8n

196 THE INCREMENT.

10-

Again, the approximate value : —

SECTION IV. — ADDITION OF THE SEVERAL INCREMENT

PER CENTS. LEADING TO THE FOREST PER CENT.

On reference to page 163 it will be seen that the current
annual per cent, with which the capital invested in a wood
works, is expressed by the formula :—

_(Ym+l-Ym-e) 100_(Ym+l-Ym-e) 100.
Sc+mG0 Fc

or, if mGc is taken as = Ym,

_(Ym+l-Ym-e)xlW
Pf S0+Ym

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-, quantity-, and price increment.

The determination of the combined increment per cent,
is done in the following manner : A property which has
at present a value = w increases during the next n years

in volume by pv per cent, annually.
„ quality „ pq „ „

,, price ,, ps ,, ,,

Its value W at the end of the n years may be expressed by
the formula : —

THE FOREST PER CENT. 197

W— W X l'0pv* X I'op* X l'op,n;

or

or

-l .*g* .»g«g« ,

100 1002 1003

or

1002

In this equation the right side expresses nothing else than
the current per cent, with which the forest capital w works
during the period of n years, in other words what has been
called at page 163 the current annual forest per cent. The
proof is easy : If n = 1, the original formula becomes : —

W=w (l'opv) (l'opq} (l'ops)
and also :

W=w (1-op,).
Hence

l-opf=(l-opv) (l'opq) (rop8)

and

, -LV +*, + « qv sy s,

100

Hence the above formula can be written thus : —

This formula was introduced by Pressler, who called
the curpf thus obtained the indicating per cent. (Weiserpro-

198 THE INCREMENT.

cent.). Pressler went out of his way to call the above expres-
sion the approximate value of cpf, whereas it represents the
absolutely current value of it, as has just been proved.

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. (See page 169.) 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 w and W.
The capital value w of the forest at the present time is
represented by the value of the soil and growing stock,
correctly = S + mGc- As the formula is only used in the case
of woods which are at or near maturity, the utilization value
may be substituted for the cost value of the growing stock,
so that

This is the capital which it is proposed to let work for
another n years. During that period it increases to the value
of the forest in the year ra + n, from which amount must be
deducted the annual costs during n years with compound
interest, so that : —

W=Ym+n+S-E (l-op»-l)
and

If between the years ra and ra + n a thinning has been

* This formula differs from that given by Pressler and Judeich for the reasons
indicated in the footnote at page 163.

THE FOREST PER CENT. 199

made, say in the year xt its value with compound interest to
the year m + n must be added to W, so that the formula
becomes : —

cur. pr _ 1(?0 / ° 7 Ym+n + Tx X l-0p°+ ' + S - E (l'OPn - 1) _ A*

In either case the value 8 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 : —

our. n _ (Ym+l-Ym-e)xWQ

Pf— - -

agreeing with that given at page 163 for the current annual
forest per cent.

Example. — Taking the data in the table at page 122, and
putting p = 2J per cent., S = 250 shillings, e = 3 shillings,
the following values of pj> are obtained : —

For the period 70 — 80 years : —

log (100 +ft) - 2 + lQg (218Q + 95 + 25° ~ B4) " lQg (1592 + 250>
7°->/=2'86.

For the period 80 — 90 years : —
log (lQO+ry)-2+log (2695 + 94 + 250-34) -log (2130 + 250)

The current annual forest per cents, given in the table
at page 202 have been calculated in this way, and they show
that the financial ripeness occurred during the period 80 to 90,
or more precisely in the year 82.

* This formula differs from that given by Pressler and Judeich for the reasons
indicated in the footnote at page 163.

200

CHAPTER II.

THE ROTATION.

BY rotation is understood that period of years which elapses
between the formation of a wood 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 different
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 differs 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.

Each of these may be indicated by the objects of manage-
ment, and it is necessary to explain them in some detail.

1. The Financial Rotation,
a. Calculation of the Financial Rotation.

By the financial rotation is understood that under which
a forest yields, if calculated with a given per cent, and

THE FINANCIAL ROTATION. 201

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 = Se X 'op

Yr+Taxl'opr-a+. . . + T(/xl'opr-y-cxl'opr
l'opr-1-

'op
(See page 154.)

(6) Or yields the highest profit : —

P = Se-Se.
(See page 158.)

(c) Or yields the maximum mean annual forest per cent. :

(See page 165.)

Of these, the first formula is the most convenient, and the
procedure is as follows : — In the forest for which the financial
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 122. 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 is = 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
during the period of 40 — 50 are assumed to have been made
in the year 50.

202

THE ROTATION.

FINANCIAL YIELD TABLE FOR
Value of St

(According to Weise's Volume Yield Table for the III. Quality, calculated

(See Table

a

, I ;

d

e

Year.

NET VALUE OF YIET.DS,
IN SHILLINGS.

Sum of
Intermediate
Yields with
Compound
Interest
to Date,
Shillings
p = 2-5.

Total Yield
to Date
(b + d)
Shillings.

Final.

Intermediate.

30

138 4

4

142

40

406

36

41

447

50

675

67

120

795

60

1100

86

239

1339

70

1592

91

397

1989

80

2130

95

603

2733

90

2695

94

866

3561

100

3273

103

1212

4485

110

3862

106

1657

5519

120

4450

96

2218

6668

This table shows that the financial rotation falls between the
years 75 and 85. In order to ascertain the exact year, the
rentals given in column k of the table have been plotted (see
figure 44). It will be seen that the financial rotation falls
into the year 82, when the rental reaches its maximum.

In column I the current annual forest per cent, is given,
calculated according to the formula on page 199. These
data show that the forest- or indicating per cent, passes
from above 2J per cent, to below 2J per cent, between the
years 75 and 85. By plotting the per cents, (see figure 45),
it is found that the exact time falls into the year 82, that is to
say, the same year when the annual soil rental culminates.
Hence the wood was financially ripe in the year 82.

THE FINANCIAL ROTATION.

203

ONE ACRE OF SCOTCH PINE WOOD.

= 250 shilling*.

with English prices ; brushwood, under 3 inches diameter, omitted.)

at page 122.)

/

ff h

i

li

I

Cost of
Formation
= 60s., with
Compound
Interest
to Date,

Total Yield
less cost of
Formation

Shillings.

Value of
Wd7~

Soil

jrross Rental

g

h
Shillings.

Soil
Net Rental
i —Annual
Expenses,
Shillings.

Current
Forest =
or Indicatin
Per Cent,
during even
10 Years.

Shillings.

126

16

43-903

0-36

-2-64 ,

5-42

161

286

67-403

4-24

+ 1-24

3-86

206

589

97-484

6-04

3-04 *

L

4-25

264

1075

135-992

7-90

4-90 {

I

3-47

338

1651

185-284

8-91

5-91 {

I

2-86

433

2300

248-383

926

6-26 {

t

2-36

554

3007

329-154

9-14

6-14 \

2-01

709

3776

432-549

8-73

5-73 ,'

L

1-73

907

4612

564-902

8-16

5-16 \

1-48

1161

5507

734-326

7-50

4-50 J

b. Notes on the Financial Rotation.

Owing to the uncertainty of the data upon which the calcu-
lation is based, the financial rotation can only be 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. An altera-
tion of 1 per cent, in the general per cent, p may cause the
financial rotation to rise or fall by 10 to 20 years.

As has been explained on a previous occasion (page 118),
the general per cent, applicable to forest finance may for

20*

THE ROTATION.

Britain at present be placed at 2| per cent. As the rate
of interest has, for a series of years, steadily declined, it is
desirable to make calculations for the future rather with a
lower, than a higher rate of interest.

Of the receipts, the final yield is by far the most important
item. Its present value can be easily ascertained, but fore-
casts for the future are of a risky nature. If, in the future,
the proportion between the prices 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

t :

5 «

2o 30

YE^*-R « .

Fig. 44.

produced in the reverse case; that is to say, if for instance
timber of small dimensions rises in price while that of large
dimensions falls, or vice versa. Such changes are difficult to
foresee ; the experience of the last decades shows, no doubt,
that timber of large dimensions is not unlikely to rise in
price ; hence the selected rotation should be rather above than
below the financial rotation.

The intermediate returns exercise a considerable influence
upon the actual amount of the rental, but a comparatively
small effect upon its culminating point ; in other words, early
thinnings reduce the financial rotation only to a limited

THE FINANCIAL ROTATION.

205

extent, and if they are made so heavy, that they reduce the
value of the final return, they may even have the opposite
effect.

Of the costs, the 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.

Taking all effects together, it may be said that the financial
rotation is low : —

(1) in the case of forests \vhere only firewood is saleable,
that is to say, where an increase in quality per unit
of volume ceases at a comparatively early age ;

2-5

83

AGE

Fig. 45.

(2) if trees of small dimensions can be sold as timber, for
instance in mining districts, in hop-growing coun-
tries, etc.

The financial rotation is high: —

(1) in localities with an unfavourable soil or climate, such

as high exposed situations, where the trees take a
longer time to reach marketable dimensions ;

(2) in thinly populated districts, where prices generally

rule low for small dimensions, while large timber
can be exported to other better paying markets.

c. Correction of the calculated Financial Rotation.

The length of the financial rotation, as obtained by a first
calculation, is subject to correction, because it is based

206 THE ROTATION.

upon certain rates obtainable for the various classes of pro-
duce, 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 intro-
duced, more small and less large timber will be produced;
also the proportion between timber and firewood will be
altered. This may produce a fall in the average price of
produce, and consequently a rise in the financial rotation.
The reverse effect would be produced, if the 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 brought
into the market, which may be accompanied by a change in
prices.

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.

d. Introduction of the Financial Rotation.

Although every deviation from the financial rotation is
accompanied by a financial loss, yet it is very desirable that
it should be introduced, if not already followed, 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 experi-
ence indicate a higher rotation than that originally calculated.
Hence, it is desirable to keep always somewhat above the
theoretical financial rotation.

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 sufficiently large to absorb the extra
supply of produce thrown upon the market, without causing
any appreciable change in prices. If the forest is, however,

ROTATION OF HIGHEST INCOME. 207

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 number of
years in the rotation, represents the annual income.

Hence, the rotation in this sense is that under which the
expression —

Yr+Ta+Tb + . . + T9-c-rxe
Annual income = -J/—- — —

r

becomes a maximum.

As the annual expenses and the cost of formation are
generally the same for differing rotations, the above expression
can be reduced to the following : —

Gross annual income = jrr+r«+r» + ' ' + T<*.

r

This rotation falls, as a rule, a number of years beyond the
financial rotation.

Example. — Taking the data contained in the table at page
202, the net annual income amounts to : —

For a rotation of : —

Shillings.

2130 + 4 + 36 + 67 + 86 + 91 + 95-60-

orv *^^ X O Of7.£M

80years = — — - =27'61

208 THE ROTATION.

For a rotation of—

Shillings.

2695+4 + 36 + 67 + 86 + 91 + 95 + 94-

60-90x3 _ qi.-Q

90 years = — =3153

yu

8273 + 4 + 36 + 67+86 + 91 + 95 + 94+

103-60-100x3
100}Tears = — - 100~ =34'89

3862 + 4+36 + 67 + 86 + 91 + 95 + 94+

103 + 106-60-110x3 o7.7ft

110 years = -- — =3776

120yearS =

4450+4 + 36 + 67 + 86 + 91 + 95 + 94 +
_ 103 + 106 + %- 60 -120x3

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 no longer cover the increase in the expenses. 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
column k of the financial yield table at page 203. The net
soil rental under a rotation of 120 years comes to 4'50 shillings,
and under one of 80 years to 6*26 shillings.

3. Rotation 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,
that is to say, the year when the volume increment per cent.

100
is equal to - in the case of final yield only, or equal to

— , in the case of final and intermediate returns (see
page 187).

ROTATION OP GREATEST VOLUME PRODUCTION. 209

Let volume of final yield be = Fr
Volume of thinning in the year a = va

,» >» » b = vb

etc.,

„ „ „ <1 = Vq

then the rotation of the greatest production is that in which

the value r ' — £ becomes a maximum.

f

The calculation can be made for timber and firewood, or for
timber only.

Example. — Taking the data for total yield in the table
at page 189, for timber only, the rotation of the greatest pro-
duction would fall about into the year 80, which is approxi-
mately the financial rotation.

For timber and firewood (page 191) 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 Technical 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, telegraph 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 difference between the technical and financial
rotations.

5. The Physical Rotation.

By the physical rotation is 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

VOL. III. ' P

210 THE ROTATION.

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 towards the end of the principal height growth.

In the case of coppice woods the age must be below 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 Rotation.

The choice of rotation, or the age at which a wood is to
be cut over, is one of the most important questions in forest
management. Many and varied are the arguments which
have been brought forward 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 with 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 necessary ; where hop-
poles are wanted, a very low rotation would be called for ; 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,

CHOICE OF ROTATION. 211

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 realiza-
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 deter-
mined, 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 ha is called
upon to make in order to realize his special object.

It need hardly be pointed out that the above procedure suits
all possible cases which may come under consideration.

p 2

212

CHAPTER III.

THE NORMAL AGE CLASSES.

IT has been stated at page 176, that by a normal dis-
tribution of age classes is 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

B0i t 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 an-
nual yield, 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 must be one
year old, with a difference
of one year in the age of
every succeeding two gra-
dations.

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.

H
t "

H

H
SJ «

a

Fig. 46.

THE ANNUAL COUPE. 213

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
will be again dealt with further on. For the present it is
assumed that the quality of locality is the same throughout.
The questions then are : —

(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?

1. The Annual Coupe, or the Area to be cut annually.

This differs according to the method of treatment. (For a
description of the latter, see page 203 of Volume I.)

a. Coppice and Coppice ivith 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 : —

Let total area = A
Eotation of the coppice = r,

then the annual cutting area c = . This holds good for the

coppice with standards system, because the annual cutting
area is governed by the coppice only.

#. Clear Cutting in High Forest.
Here is again:

if each clearing is at once restocked. Frequently it happens,

£14 THE NORMAL AGE CLASSES.

however, that the cleared coupes lie fallow for one or more,
say s years ; in that case :

c- A

~~

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.

c. The ShelUr-ivood Compartment System.

Under this system the regeneration of each coupe extends
over a number of years, say m ; hence it is necessary to throw
m annual coupes together into a periodic coupe, the crop on
which is, by gradual cuttings, led over, in the course of m
years, into a young wood. The size of the periodic coupe is,

therefore =— X m.
r

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 r + m years old, and the

M|

mean age r + — years ; in other words the procedure would

lead to a raising of the rotation from r to r + — years ;

2

Or, the first cutting may be made in the year r — - and

2

the last in the year r + — , so that the mean final age comes

to r years.

In the present chapter the latter is assumed.

d. The Selection System.

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 I, then —

SIZE OF THE AGE CLASSES. 215

A

Annual cutting area = - .

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

would he equal to - .

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 thrown together. If a class contains n gradations^ its

*•

area would be = n x c. The number of age classes = - is

variable.

Another way 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 n 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 II., and so on; for instance, if n = 20 —

First age class I., contains all woods 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
its age. 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. An effort should be made to alter

216 THE NORMAL AGE CLASSES.

this. The area of the age classes under the several methods
of treatment is now as follows : —

a. Ckar Cutting in High Forest.
The area of each age class, in a normal state, is : —

A A

C = n x c = n X -, or C = n x -

r 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 = 1050 acres
Rotation r = 100 years
s = 5 „
n = 20 „
then:

, ,. A 1050 1A
Annual age gradation = = -\?\ — = 10 acres ;

and the age-classes :

Blanks c x s 10x5 =50 acres.

d ( 1— 20 years old woods) = cx n = 10x20= 200 „

Cu (21— 40 „ „)=„=„= 200 „

C/77(41— 60 „ „)=„=„= 200 „

C/F (61— 80 „ „)=„=„= 200 „

Cv (81—100 „ „)=„=„= 200 „

.4 = 1050 acres.

b. /Shelter-wood Compartment System.

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 = Cv ; it wanders gradually through the
whole forest, until, at the beginning of the second rotation, it
is found in the original position. As regeneration sometimes

THE SHELTER-WOOD SYSTEM. 217

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 r + ™ years old. Assuming that s years pass, after the first

2

regeneration cutting, until the new crop is fully started, then

A

the annual cutting area, as before, = — - - , and the area of the

T -\- 8
£

regeneration class = - X m. The latter contains the areas
r + s

as yet blank, young trees from 1 to m — s years old, and the
remaining old trees ranging in age from r— ^ + lto

years. Now, it may happen that m — s = n ; in that case the
youngest age class does not exist by itself, but forms part
of Cv. Again, it may occur, that m — s > 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 — s<^n : —

Cv = --
r+s

218 THE NORMAL AGE CLASSES.

C, = — xro.

r+s

Total number of annual coupes = n — (in — s) + 4 X n + m ••
5xn + s = r + s.

(2) m — s = n: —

r+s

-A-
r+s

Cv =-A-xn

r+s
Total number of coupes = 4xw+??t=5

(3) 77i — s>n, but m —
C7 =0

r+s

r+s

-t Cw =— -xm
r+s

Total number of coupes = 2 X n — (m — s) + 3 X n + m = 5 X n
+ 8 = r+s; and so on.

It is obvious that for the shelter-wood system 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

COPPICE WOODS. 219

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 : —

T-\-S

Or again —

CV = - x n

IV

Example.— As above, A = 1050 ; r=100; s = 5; ?i

=~ X 20 = 200

CF+C,+(7/+C/7-^(xl05-40) = 650

Total . . . 1050

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
five gradations are thrown together, so that C/ comprises the
1 to 5-years-old gradations, Cn those from 6 to 10 }rears, etc.

220 THE NORMAL AGE CLASSES.

Example : —

Area = 200 acres
r = 20 „
n = 5 „

The arrangement of age classes would be normal, if —

GI — — — x 5 = 50 acres.
20

r 200 - -n

//=W "

r _200 -_ -0

c~

5= 50 "

Total 200 acres.

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

= -x «.

r

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 cutting 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

COPPICE WITH STANDARDS.

221

left standing to form the youngest age gradation of the over-

A

wood. That portion would occupy an area = -, assuming

H

that each age gradation of the overwood occupies the same
extent of ground. The area of the youngest age class of

A

overwood comes to = —- x n.
2i

Assuming now that the youngest overwood class 1 to r 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.

Immediately before cutting, the arrangement would be as
follows : —

Underwood, Age in Years.

1

2

3

r-1

r

Overwood Age Class Ci age

1

2

3

r-1

r

, On „

r+1

r+2

r+3

2 r-1

2xr

» ,, ,, Cm „

2 r+1

2r+2

2r+3

...

••

3 r-1

3xr

Cr ..

(<-l) r+1

(<-l) r+2

(<-l)r+3

...

txr-1

txr

It will be seen, that a normal coppice with standards forest
must have an overwood which consists of ra x r = R age
gradations ranging from 1 year up to R years old.

Example. — A forest of 200 acres worked under a rotation of
20 years for the underwood, and 100 years for the overwood,
100

has

20

= 5 overwood classes. On the 10 acres which are

about to be cut, will be found : —

Underwood = 20 years old

Overwood = 100, 80, 60, 40 and 20 years old.

222

THE NORMAL AGE CLASSES.

The next oldest coupe contains —

Underwood = 19 years old

Overwood = 99, 79, 59, 39 and 19 years old.

The youngest coupe contains —
Underwood = 1 year old
Overwood = 81, 61, 41, 21 and 1 years old.

60TEET —

IrOFEEST —

ctovi-H a

Fig. 47.

The appended figure 47 illustrates the distribution of the
several age gradations over the area.

COPPICE WITH STANDARDS. 223

The area occupied by each overwood class can only be
determined by assuming that each gradation occupies an equal
area 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
class were brought together on separate areas, then the over-
wood, apart from the coppice, would form an open high forest
resembling a selection forest. The areas to be allotted to the
several classes may, therefore, be considered as equal. The
youngest would contain the standards from 1 to r years, the
next those from r + 1 to 2 r years, and so on. By degrees,
the youngest class passes through all the intermediate stages,
until it becomes 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.

j[

The annual coupe is c = — and ^4 = c x r.

T)

The number of overwood classes is = — = t , hence —

r

A A c,

Area of each age class on each annual coupe = — = = — .

R txr t

As the whole forest consists of r coupes, each overwood
class, consisting of r gradations, contains, in a normal forest,

c A

- X r = — units of area. This shows that, theoretically,

v L>

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; r = 20, number of overwood classes

* = 5.

A 200
Normal annual cutting area c — — = = 10 acres.

On each coupe each age gradation ) c 10
of overwood occupies . . j 1 ~ 5

THE NORMAL AGE CLASSES.

The area and distribution of the several age classes is as
follows : —

Coupe No. 1, oldest:

Underwood = 10 acres = 20 years old.

Overwood 2

,i = 20 „ „

2

,, = 40 „ „

2

„ = 60 „ „

2

,, = 80 „ „

2

,, =100 „ „

Co?/pe No. 20, youngest :

Underwood = 10

acres = 1 year old.

Overwood 2

» = •*• » »

2

,, =21 „ „

2

,, =41 „ „

2

,, =61 ,, „

2

» =81 ,, ,,

If now the underwood is arranged into four classes of 5 years
each, and the overwood into five classes of 20 years each, the
following areas are obtained for each class : —

Undenvood :

G! = 1 — 5 years old = 5x10= 50 acres.
Cn= 6—10 „ „ = „ = 50 „
(77/7=11—15 „ „ = „ = 50 „
CIV = 16-20 „ „ = „ = 50 „

Total A = 200 acres.
Overwood :

Cf = 1 — 20 years old = 20 x 2 = 40 acres.

C//=21— 40 „ „ = „ = 40 „

C777=41— 60 „ „ = „ = 40 „

0/r = 61— 80 „ „ = „ = 40 „

Cv =81—100 „ , = „ = 40 „

Total A = 200 acres.

COPPICE WITH STANDARDS. 225

It will be seen that the total area has been distributed
amongst the underwood, and a second time amongst the
overwood.

By allotting the overwood to the four underwood classes,
the following four combination classes, called "coppice with
standard classes," are obtained : —

Class I., the youngest.

Underwood, 1 — 5 years old = 10 x 5 = 50 acres

Overwood, 1—5 „ „ - 5x2-10 „

21—25 „ „ = „ =10 „

41—45 „ „ - „ =10 „

61 — 65 ,, „ = ,, =10 ,,
81 — 85 ,, ,, = , = 10

Total C Underwood = 50 acres

I Overwood =50 ,,

Class II.

Underwood, 6 — 10 years old = 50 acres

Overwood, 6 — 10 „ „ =10 „

26-30 „ „ =10 „

46—50 „ „ =10 „

66—70 „ „ =10 „

86—90 „ „ =10 „

m . i ( Underwood = 50 acres

lotal

(. Overwood =50 „

Class III.

Underwood, 11 — 15 years old = 50 acres

Overwood, 11 — 15 ,, ,, =10 ,,

31—35 „ „ =10 „

51—55 „ „ =10 „

71—75 „ „ =10 „

91—95 , =10

rp . i i Underwood = 50 acres

Overwood =50 ,,

VOL. III. Q

226 THE NORMAL AGE CLASSES.

Class IV.

Underwood, 16 — 20 }rears old = 50 acres

Overwood, 16 — 20 ,, ,, =10 „

36— 40 „ „ =10 „

56— 60 „ „ =10 „

76— 80 „ „ =10 „

96—100 , =10 „

rp , i j" Underwood = 50 acres

I Overwood = 50

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.
More especially, it gives some idea of the relative number of
trees which should be found in each class or gradation. As
each should occupy about the same area, 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.

e. The Selection Forest.

Here the age classes are intermixed, as in the case of the
overwood in coppice with standards, or even more so. The

number of age classes will, theoretically, be equal to '! .

t

Let A = 1,000 acres ; r = 100 ; / = 20; then each annual
cutting area = - - = — '—- = 50 acres, and the distribution
would be as follows : —

DISTRIBUTION OVER THE FOREST.

22?

Coupe No. 1 (youngest).
1 year old trees = 10 acres

21
41

61

81

= 10
= 10
= 10
= 10

Coupe No. 2.
2 year old trees = 10 acres

22

42
62

82

= 10

= 10
= 10
= 10

Total = 50 acres

Coupe No. 19.

Total = 50 acres

Coupe No. 20 (oldest).
19 years old trees = 10 acres 20 years old trees = 10 acres
39 „ „ „ =10 „ ! 40 „ „ „ =10 „
59 „ „ „ =10 „ j 60 „ „ „ =10 „
79 =10 I 80 =10

99

„ =10 „
Total = 50 acres

100

= 10

Total =50 acres

Each year the 100 years old trees in the oldest coupe would
be cut, which cover an area equal to one-fifth of the coupe, or
equal to 10 acres, thus cutting once the whole area of the forest
in 100 years. It is needless to add, that such regularit}T is
never reached in practical forest management.

3. Distribution of the Age Classes over the Forest.

Under a normal distribution of the age classes is under-
stood that which admits of a proper succession of cuttings, so
that each wood is cut at the proper age, and that external
dangers can be successfully resisted.

It has already been explained that every deviation from the
normal age interferes with the full realization of the objects of
management; hence the age classes should be so distributed
that no such deviations are called for. The latter are generally
caused by threatening dangers, such as strong winds, dry air
currents, danger from frost, fire, insects, &c., sometimes by
considerations for a successful regeneration.

Strong ivinds or gales are a most important consideration.

228

THE NORMAL AGE CLASSES.

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
on the east, so that the cuttings proceed gradually from east
to west. (See diagram, fig. 48.)

_r

o 6 xo 16 3.0

Fig. 48.

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 wind, so that
the cleared areas, which are to be naturally regenerated, must
be situated to the leeward of the seed-bearing trees.

Large clearings in one place are generally objectionable
because the soil is liable to dry up, and damage by frost is

DISTRIBUTION OVER THE FOREST.

229

more likely to occur : hence in extensive forests cuttings must
be made in several localities in each year so as to clear only a
small area in one and the same locality.

Insects and fire are most injurious when several annual
cuttings adjoin each other, because the former wander from
one coupe to the next, while fire spreads more rapidly in
young woods than if the area is 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 lo-
cality 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 neces-
sary not to cut in the
same locality more fre- Fig> 49.

quently than once in

every 4 years, the series of age gradations would be divided
into 4 cutting series, of which each would comprise 5 coupes.
(Figure 49.)

Cutting
Series

A would comprise the coupes now old 20, 16, 12, 8, 4 years.

C „ „ „ „ „ „ 18,14,10,6,2 „

D „ „ „ „ „ „ 17,13, 9,5,1

As a general rule, a careful distribution of the age classes

230 THE NORMAL 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 which are
difficult to regenerate naturally. In all these cases a distribu-
tion 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 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.

Reasons for adjoining the annual coupes are : —

(1) Best security against damage by storms.

(2) Reduction to a minimum of damage by overhanging trees.

(3) Reduction of the cost of transport of forest produce.

Reasons against adjoining the annual coupes are :—

(1) Increase of danger through fire, insects, and dry winds.

(2) Defective protection of young growth against raw winds.

The subject will again be referred to in Part IV. when
dealing with the division and allotment of areas.

231

CHAPTER IV.

THE NORMAL GROWING STOCK.

IT has been stated at page 176 that under 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 wood 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 increment added to that growing stock
during the rotation.

232 THE NORMAL GROWING STOCK.

(2) Because several methods base the calculation of the
yield upon the difference between the normal and
real growing stock.

The amount of the normal growing stock is proportional to
the length of the rotation ; the higher the latter, the greater
the former.

In calculating the normal growing stock only the principal
part of the woods which give the final yield are taken into
account, because, as previously explained, the determination of
a sustained yield is, in the first place, based upon the final
.yield.

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 Volume.

The calculation can be made either by means of yield tables
or the mean annual increment. The former is the only correct
method, but the latter must be explained, as it is used by
several methods of calculating the yield. The calculation
differs for the several methods of treatment.

a. Clear Cutting in High Forest.

(1) Calculation from Yield Tables. — If a yield table is
available for a forest, which gives the final yields from year to
year, the normal growing stock is equal to the sum of all
yields in that table from the year 1 to the year r (the rotation) ;
that sum would represent the normal growing stock of r units
of area, and for the season when the annual growth has been
completed, but before the annual cuttings are made; in Europe
this would be autumn.

If the yield table, and this is generally the c«se, 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

CLEAR CUTTING IN HIGH FOREST. 233

volumes rise within each period of n years according to an
arithmetical series, that is to say, by adding the same amount
of volume each year.

Let be volume in the year 0 =0 cubic feet,

JJ 5> >> '" " » »>

j> » ?i « X fl — - 0 n ,,

3 x n = <• „

» M » 4 X 7i = r? ,, „

then : —

Total volume from yearo to year n minus a = (0 + a) x — — — a

«

,, ,, n ,, 2 X« minus b = (a + b) X — — — b

a

n \ 1
,, ,, 2xw ,, 3 x n minus c = (b + c) x -— — — c1

„ 3x?^ „ 4X7Z
Total volume from o to 4 x ?i years =

Normal Gr. Stock, Grn =

This is the calculation for autumn.

If the oldest age gradation is cut away during winter the
normal growing stock in spring must be d cubic feet less than
that in autumn, that is to say :• —

Gn in spring = n (

\

111 spring the growing stock consists only 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

234 THE NORMAL GROWING STOCK.

assumed that one half of the annual increment has been laid
on ; in other words that the growing stock is then equal to the
arithmetical mean of those in spring and autumn : —

Example.-~A. forest of 100 acres, to which the data given in
the Table at page 190 apply, worked under a rotation of
100 years, has the following normal growing stock : —

In autumn mGn= 10 (510 + 1290 + 2140 + 2900 + 3530 + 4060

+ 4530 + 4950 + 5300 + 2790) + 2790 =
10x32000+2790 = 322,790 cubic feet.
Tn spring mGn= 10 x 32000-2790 = 317,210 „ „
In summer mGa = 10 X 32000 = 320,000 „ „

The same forest, if worked under a rotation of 80 years,
would, for. summer, have the following growing stock : —

"0>

10 (510+1290 + 2140 + 2900 + 3530+4060 + 4530 + 2475) —

80

100

= 214,350 X ~ = 267,937 cubic feet, which is considerably less
80

than if the area is worked under a rotation of 100 years.

(2) Calculation with the Mean Annual Increment. — Assuming
that the current annual increment is the same throughout
the rotation and equal to the final mean annual increment,
then the volumes of all normally stocked gradations, from the
youngest to that r years old, would form an ascending
arithmetical series, the sum total of which would represent
the normal growing stock.

Let i = volume of the 1 year old gradation, then

„ 2 x i — „ „ 2 years „

*

,, I* X 1 = ,, ,, T ,, ,, ,, ,,

and the sum of all gradation is : —

CLEAR CUTTING IN HIGH FOREST.

Now r x i = volume of oldest age gradation and also
= to increment of all gradation in one year, which may be
placed = J, then : —

r@n = Lx r + 7. This is for autumn.

2 2

For spring there would be :—

r rxri ri Ixr I

a2 a 3 -

For summer, the arithmetical mean of the two : —

•G.-1"

The normal growing stock is, therefore, equal to the volume
of the oldest age gradation multiplied by half the number of
years in the rotation, or equal to the total increment of one
year multiplied by half the number of years in the rotation.

Example. — Data as above ; rotation = 100 years, then : —

For autumn O. = - -+ = 281, 790 cubic feet.

4 A

„ 5580x100-5580 Or7/. 0-m
„ spring Gn = -- - -- -__ = 276,210 „ „

n 5580 x 100 Or70 nAr1

,, summer Gn = -- — =279,000 „ „

The forest treated under a rotation of 80 years would
have : —

For summer *>Gn = 495°0X 8Q x ^ = 247,500 cubic feet,
& oO

or less than above.

It will be seen that the normal growing stock calculated by
the mean annual increment is smaller than that calculated
from a yield table. This is, however, by no means always the
case. Taking, for instance, the data in the table at page 190,
and calculating the normal growing stock for various rotations,
and a number of acres equal to the number of years in the

236

THE NORMAL GROWING STOCK.

rotation in each case, the following results are obtained for
spring :—

Rotation
in Years.

NORMAL GROWING STOCK.

Calculation from Calculation from
Yield Table. tcretn?

Excess of Calcula-
tion from Mean
Annual Increment.

30

27,630

31,030 + 3,400

40

52,450

56,550 + 4,100

50

84,285

86,485 + 2,200

60

121,950

119,770 2,180

70

164,285

156,285 8,000

80

211,875

195,525 - 16,350

90

262,950

235,850

- 27,100

100

317,210

276,210

- 41,000

The above example shows that the normal growing stock,
calculated with the mean annual increment, is larger than that
calculated from a yield table up to the age of 50 years ;
between 50 and 60 years the two are equal, and after that the
latter is greater than the former. Under these circumstances
it is evident that, except for a rotation from 50 to 60 years, a
considerable error is committed in the above case by calcu-
lating the normal growing stock with the mean annual increment
of the final crop.

I. Shelter-wood Compartment System.

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 not occur, but the deviations
compensate each other in the long run ; anyhow a more
accurate determination is practically impossible.

COPPICE WITH STANDARDS. 237

c. Coppice and Coppice with 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 in each age class, and the average volume per tree
in each, somewhat in the following manner : —

If the normal number of trees in each of the r, 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, within each class, in volume
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 —

where Fr + 1 represents the volume of all trees r + 1 years old,
and F2r that of all trees 2 r years old. In the same way
the next age class would be represented by —

and so on. Adding all positions together the normal growing
stock of overwood comes to : —

This amount does not comprise the youngest age class of
all, which still forms part of the underwood.

238

THE NORMAL GROWING STOCK.

Example : —

Area of a coppice with standards forests = 100 acres.
Rotation of underwood = 20 years.
„ ,, overwood = 100 ,,

100
Number of overwood classes = t - = 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

200

•9

40-

40

200

2-0

400-

41

130

2-65

344-5

60

130

15-

1950-

61

80

15-75

1260-

80

80

30-

2400-

81 .

40 31- 1240-

100

40 50-

2000-

Gn = 10x9634-5 -96,345 cubic feet, or per acre = 963 cubic
feet.

d. The Selection Forest.

The growing stock of a normal selection forest ma}' 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.

FINANCIAL VALUE. 239

2. Calculation of the Financial Value of the Normal
Growing Stock.

The various methods of calculating the financial value of the
normal growing stock have been explained at pages 144 to 148.
It has there been shown 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 those cases the value is expressed, for r units of
area worked under a rotation of r years, by the formula : —

Y^+T^

•op

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. p. Every deviation from this leads to
loss. As it is impossible to keep a forest always in that
condition, 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.

240

CHAPTER V.

THE NORMAL YIELD.

UNDER the normal yield is understood that which 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 p. 175.

The yield of major produce is further sub-divided according
to the different classes of wood, such as timber, fagots, root-
wood, &c. 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. The Yield determinedly Area or Volume,
a. Clear Cutting in High Forest.

(1) The Normal Final Yield is equal to the volume which
stands on the oldest age gradation.

A 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 p. 213). 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 = — Xn,or = — — x u.

r r+s

THE NORMAL YIELD. 24-1

Example :—

Area of forest . = 1000 acres
Rotation . . = 100 years

1000

Annual cutting area = — — - = 10 acres,
luu

if the area is at once re-stocked.

The annual yield of final returns, according to the table at
p. 190, amounts to 5580 + 286 per acre = 5866; for ten
acres = 5866 x 10 = 58,660 solid cubic feet. Final yield
during every period of 20 years = 58,660 x 20 = 1,173,200 cubic
feet.

(2) Intermediate Yield. — This consists 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 343 c = 3430
„ 40 „ „ =10 „ „ „ 614 c' = 6140
„ 50 „ „ =10 „ „ „ 572c' = 5720
„ 60 „ „ =10 „ „ „ 529c' = 5290
„ 70 „ „ =10 „ „ „ 443 c' = 4430
„ 80 „ „ =10 „ „ „ 386c' = 3860
„ 90 „. „ =10 „ „ „ 828 c' = 3280

Total = 32,150

(3) Total Normal Annual Yield = 58,660+ 32,150 =90,810
cubic feet.

b. Shelter-ivood 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

2

rotation is increased, and the calculation must be made
accordingly. Supposing the first cutting is made in the year

r, and the last in the year r+m, then the rotation =?*+ —

2

A
and the mean annual cutting area = —

, m

242 THE NORMAL YIELD.

Example : —

Let bew = 20; then rotation = 110 years. Annual cutting

1000
area = -^ = 9-09 acres. Volume standing on an acre at the

age of 110 years = 5820 + 243 = 6063 ; hence annual yield
= 6063x9-09 = 55,113 solid cubic feet.

The intermediate yields would amount to = 35, 010 cubic feet,
or: —

Total annual yield = 90,123.

The raising of the rotation has led to a reduction of the
yield.

c. Selection Forest.
If all trees which are cut in one year were brought together

A

on a portion of the area, the latter would be = — : hence the

T

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 which cuttings are made in each year ; this has been

^
placed above (p. 226), = . Everything which has to be cut

(j

on this area forms the normal annual yield.
Example : —

Area of a selection forest = 1000 acres
Kotation . . . = 100 years
I . = 20 years.

Then :

f =-00 = 50 acre,

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 number which
should reach maturity at the age of 100 years.

Taking the data in the table at p. 190, the material men-
tioned under (1) should give = 58,660 cubic feet, that is to say,

THE NORMAL YIELD. 243

the yield under the system of clear cutting. The material
under (2) represents the intermediate yields, which should
amount to 32,150 c'. Total yield = 90,810 cubic feet, as
before.

d. Coppice and Coppice with Standards.

The normal yield of coppice woods is calculated in the same
way as for clear cutting in high forest. In this case, the

A

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 is
composed 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, R years old, age gradation of
the overwood.

(3) The thinnings amongst the younger age gradations
of overwood standing on the annual coupe, and occasionally
in the younger underwood gradations.

Example : —

Taking the data given at p. 238, the yield in overwood is
as follows : —

40 trees (mature) 100 years old, each = 50 c' = 2000

40 „ „ 80 „ „ „ = 30 c' = 1200

50 „ „ 60 „ „ „ = 15 e' = 750

70 40 = 2 c' - 140

Total ... - 4090 c'
to which the volume of the underwood has to be added.

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,

1= 4090 cubic feet.

R 2

244 THE NORMAL YIELD.

2. The Financial Value of the Nnrmal 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, p, at which money can be obtained for
forestry, or at which money taken out of the forest can be
invested 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 sa}r, 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 p. 202, and a rotation of 80
years :—

Soil expectation value for 80 units of area = shlgs.

80x250 . . . . = 20,000

Financial value of normal growing stock . = 68,360

Total . . . = 88,360

Financial Normal Y= 88,360 X '025 = 2209 shillings ;
or 27*61 shillings for each acre of forest.

24.5

CHAPTER VL

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 bring them out clearly, the
system of clear cutting in high forest will be used as an illus-
tration; it will, in the majority of cases, also be assumed that
the current annual increment is equal to the final mean annual
increment.

1. Allotment of Increment during a Rotation.

Every normal series of age gradations contains, at the com-
mencement of the rotation, the normal growing stock. Every
year the oldest age gradation is cut over, which gives the normal
annual yield, and this yield is replaced during the following
growing season by the laying on of the normal increment.
The latter is laid on partly on 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 much of the total increment of one rotation is added
to the old growing stock, and how much to the new.

Making the calculation for spring, the youngest age gradation
is 0 years old, and the oldest r— 1 years. The former grows
for r 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 r — 1 years during the first rotation, when it is
cut over. All the increment laid on during these years goes

246 INCREMENT, GROWING STOCK AND YIELD.

to the old growing stock ; but that laid on during the last year
is not cut, but goes over to the second rotation, and so on.
This gives the following allotment, if the increment of one age
gradation during a year is called = i :—

Allotment of Increment to —

Old New

Growing Stock. Growing Stock.

Gradation now 0 years old — r x i . . 0

1 „ „ = (r-l)t . . i

2 „ „ = (r-2)t ., .• 2 -i

3 „ „ = (r-3)i . . 3 • t

„ (r-2) „ „ =[r-(r-2)]i . . (r-2) . t
„ (r-1) „ „ =[r-(r-l)]i . . (r-1) • i

The terms under each growing stock form arithmetical series,
and if added up, they come to the following : —

Placing now rxi = I, the above become :
Spring, £oM = /r+

If the calculation is made for autumn, then the positions of
the old and new growing stocks are reversed. Of the youngest
age gradation, now 1 year old, only (r — l)xi goes to the old,
and i to the new stock ; of the second age gradation, now 2 years
old ; (r — 2) x i goes to the old, and 2 x i to the new stock, and
so on. This gives —

Autumn, Gold

ALLOTMENT DURING A ROTATION. 247

Making the calculation for the middle of the growing season,
summer : —

Summer, Gold = — ^,

( &

r _Ixr

• » '"''new Q •

The quantity I is equal to the total increment of all grada-
tions laid on in one year, or the increment laid on \>y one age
gradation in course of a whole rotation. Hence the following
conclusions may be drawn : —

(1) The annual increment of a series of age gradations is

equal to the volume of the oldest age gradation.

(2) The total increment laid on during a rotation is equal to

twice the normal growing stock, calculated for the
middle of summer.

(3) Calculated for the middle of summer, the total increment

laid on during one rotation is equalty divided between
the old and new growing stock.

(4) The growing stock must increase, if less than the normal

increment is removed, and vice versa.

Example : —

Area of forest = 100 acres.

Rotation =100 years.

Data those contained in the table at page 190.

Calculation made with Mean Annual Increment : —

Annual increment of one age gradation = 55*8 cubic feet.

,, ,, ,, all gradations = 55'8xlOO = 5580
Total increment of all gradations during one rotation

-5580x100 = 558,000

Increment laid on by old growing stock = - - -- = 279,000

new

lew

What has been said above holds also good, if the current

INCREMENT, GROWING STOCK AND YIELD.

annual increment is substituted for the mean annual increment,
provided the calculation is made for the rotation, when the
normal growing stock calculated from a yield table is equal to
that calculated by the mean annual increment. For all other
rotations deviations occur, as the following example will
show : —

For a rotation of 100 years — Cubic feet.

Annual increment of all age gradations . . = 5,580
Total „ „ „ in 100 years = 558,000

Total yield in 100 years = 558,000

Normal growing stock in middle of summer, taken

from yield table =320,000

Increment laid on by old growing stock

- 558,000 - 320,000 = 238,000
new „ =558,000-238,000 = 320,000

2. Allotment of Increment during the Regeneration Period.

It is of interest to know, in the case of the shelter-wood
compartment system, how much of the increment laid on
during the regeneration period on the area under regeneration
goes to the old growing stock, and how much to the new. For
this purpose it may be assumed that the old wood is removed
in the course of m years by annuall}7 equal instalments, and
that the cuttings are made in the commencement of the
year. Total annual increment = I; the allotment is then as
follows : —

Allotment of Increment to —

Old Stock. New Stock.

During the first year (^zl) x 7. - x 7.

m m

„ second (^Z2)XJ. 2x7.

m m

m

x/=0.

ALLOTMENT DURING THE REGENERATION PERIOD. £49

Hence —

Increment on old stock =

f m-1
l^TX

m_(m-l)xl_mx I __ I
2~ ~~2~ 2"

Increment on new stock =

1 j j \m_ _mx I , I

m J 2 ~" 22'

If the first cutting is made at the end of the first year, then
the position is reversed, and —

Increment on old stock = — - — +—

mx I I
„ ,, new ,, = — - — — — .

For the middle of the growing season —

Increment on old stock = — — —

2

I . - „ ,,new „ =^.

For all practical purposes the same result is obtained, pro-
vided m is not too long, by adding to the existing old growing
stock half the increment which it would have laid on in the
course of m years if no cuttings were made, in other words
placing the expected yield equal to the volume of a wood, the

final age of which is increased by -^ years.

What has been said above, enables the forester to calculate
the annual yield which a wood under regeneration gives during
the period of m years, namely : —

mxl

Annual yield = ^ = ^f + 3-

Again, if the yield = Y has been fixed, the number of years
during which the wood under regeneration will give that yield,
can be calculated : —

250 INCREMENT, GROWING STOCK AND YIELD.

m 2
and out of this —

~"2"~~wT

and

a „
m =

Y- I

2

Example : — Table at page 190.

A wood of 10 acres, now 80 }rears old, is to be regenerated
during the next 20 years ; what will be its annual yield during
that period ?

.20 -5

2650 x 20 = 53,000, or per acre = 5300,

which is the same as the wood should have had when 90 years
old, if no cuttings had been made.

Again, supposing the yield has been fixed at 2,650 cubic
feet a year, the 10 acres in question will furnish that yield
for—

=20years

2650 -

3. Relation between Normal Yield and Normal Increment.
The normal final yield is equal to —

(a.) The volume of the oldest age gradation ;

(6) The mean annual final increment of all gradations ;

(c) The total current annual increment of all gradations.

Example : — Table at page 190.

Area of a normal forest = 100 acres
Rotation = 100 years.

NORMAL YIELD AND GROWING STOCK. 251

Cubic feet-
Every year a wood 100 years old is cut over, giving = 5580

Normal annual yield = 5580

Total mean annual increment = 55'8 x 100 . . = 5580
„ current „ „ -10(51 + 78 + 85 + 76

+ 63 + 53 + 47 + 42
+ 35 + 28) =
558x10 . . = 5580-

4. Relation between Normal Yield and Normal Groiving Stock.

If the normal yield (FJ is divided by the normal growing
stock (6rn) and the quotient multiplied by 100, the result ia

called the " utilization per cent."

Y
Utilization per cent. = -2. x 100.

(jrn

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 —

Utilization per cent. = increment per cent, of the whole

series of age gradations.
Placing the current annual increment equal to the mean

r X /
annual increment, and calculating Gn for summer = — -- — ,.

the utilization per cent, for the rotation of the maximum
volume production is always equal to twice the increment
per cent, of the oldest age gradation. It has been shown
above (page 187) that for the year in which the mean annual
increment culminates (rotation of maximum volume produc-
tion), the —

100
Increment per cent. = .

For the same rotation —

Utilization per cent. = £* x 100 = ~X 10°
G rxl

-252

The utilization per cent, must fall with the increase of r,
just as the increment per cent, has been shown to fall.

Example : — Table at page 190.

The greatest volume production occurs under a rotation of
40 years, hence : —

n rxl 40 x 2900 KQ nrkrk , . -
Gn=— — = 58,000 cubic feet.

2t _

Utilization per cent. =

72 x 100

Increment per cent, of oldest age -gradation = — - = 2'5%.

2900

A somewhat different result is obtained if Gn is calculated
from the positions of a yield table. For summer —

Gn=10 (510 + 1290 + 2140.+ 1450) = 58,900 cubic feet.
and —

Utilization per cent. = — o^0 = 5-38°/0, or more than 20°.

Calculating the per cent, for various rotations the following
data are obtained : —

UTILIZATION PER CENT.

ROTATION. By Mean Annual From Yield

Increment. Tables.

30 ..... G'67 7'46

40 . . . . . 5* 5'38

50 ..... 4- 4-10

60 . . . . . 3-34 3-27

In this case the two are equal some time between 50 and 60
y-ears, after which the per cent, calculated from yield tables is
.smaller than that calculated by the mean annual increment.

253

CHAPTER VII.

THE REAL FOREST 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 reality. A
forest which is absolutely, and in every respect, in a normal
condition does not exist, especially in the case of extensive
areas treated under high rotations ; and if an area 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. p.

Either one, more, 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

254 REAL AND NORMAL FOREST.

a suitable manner, followed by efficient regeneration and
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 cut over 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 endangering thereby
other adjoining woods. Only in this way is it possible to
avoid loss of increment in the future, due to the premature
cutting over of vigorous woods, or to the retarded cutting over
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 ex-
pediency to begin by establishing the numerically normal
state of the growing stock, because it can be reached while the
forest is in other respects highly abnormal.

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 lequirements 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 IV. of this volume.

PAET IV.

PREPARATION OF FOREST WORKING PLANS.

257

PREPARATION OF FOREST WORKING PLANS.

INTRODUCTORY.

A FOREST working plan has for its object 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 leading principles of management must
be indicated, and the yield calculated. The whole material is
then brought together in a working plan report. Finally,
arrangement must be made to control the execution of the
plans, and to collect additional information, so that every
succeeding working plan may be more accurate, and the
management ma}?- become more and more exact.

The subject may, therefore, be divided into the following
chapters : —

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.

IV. DETERMINATION OF THE YIELD.
Y. THE WORKING PLAN REPORT.

VI. CONTROL OF EXECUTION AND RENEWAL OF WORKING
PLANS.

The subjects coming under I., II., and III. are not easy to

VOL. III. S

£58 INTRODUCTORY.

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
forest into a number of divisions ; 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 manage-
ment have been pro vision all}r 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.

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
only be laid down 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 defective. It is desirable, 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.

259

CHAPTER I.

COLLECTION OF 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 condition 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 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

s 2

260 COLLECTION OF STATISTICS.

done by professional surveyors ; the following remarks refer
only to those points in which the forester must participate.

Before the survey is commenced, various preliminary
matters must be attended to, such as : —

(1) Regulation 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, pas-
tures, 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 con-

sisting of different species, or -different ages, or
different quality classes. The latter is only neces-
sary in very valuable forests.

The method of survey depends on the value of the forest, as
represented by its returns ; the higher the latter, the more
accurate 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 staff.
The details, such as the limits of woods and of sub-com-
partments, 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

DESCRIPTION OF COMPARTMENTS. 261

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
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. — DESCRIPTION OF EACH WOOD OR COMPARTMENT.

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, 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 Locality.

By locality is understood the soil (and subsoil) and the
climate, which depends 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 Volume I. of this Manual, pages 104 — 157.

262 COLLECTION OF STATISTICS.

From what has been said there it will be easily understood
that a description of the soil and climate must form part of the
basis upon which a working plan rests.

In describing the climate and soil the following points
deserve attention : —

a. Climate.

(1) The geographical position of the locality, as indicated

by latitude and in many cases also the longitude,
especially 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, &c.

(3) The surroundings of the locality, in so far as they are

likely to affect the local climate.

b. 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 at page 150 of Volume I. and in Forest
Mensuration. Some further remarks on the subject will be
found in the last part of this section.

THE GROWING STOCK. 26S

2. The Growing Stock.

The growing wood, or the crop produced on an area, repre-
sents the results of the activity of the locality under a certain
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. Method of Treatment, or Sylvicultural System.

The different methods of treatment have been described at
p. 203 of Vol. I.

In this place the forester must ascertain the system under
which the wood has actually been managed in the past.

b.

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 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 J 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 oak, 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 perma-
nent or temporary, whether it is of special sylvicultural or

264 COLLECTION OF STATISTICS.

financial importance, such as a shelterwood (or nurses) over
another tender species, or a soil protection wood, standards
of valuable species, &c.

The undergrowth, shrubs, herbs, &c., should also be
described.

c. Density of the Growing Stock.

To every method of treatment, as determined by the objects
of management, corresponds a normal densit}^ of the growing
stock. Deviations from that density are expressed by such
terms as over-crowded, under-crowded, open, very open,
interrupted, irregular, &c. 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 1. 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.

Under 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, &c., or are altogether unfit for the
production of trees, such as bare rocks, boulder drifts, swampy
ground which cannot be drained, &c. As regards the latter, it
is not always easy to draw the line between actual blanks and
woodland, as they frequently have a thin stocking, which may
give a small return from time to time.

d. Age.

The methods of determining the age of trees and woods
have been given at pp. 72 to 77.

THE GROWING STOCK. '265

An absolutely accurate determination of the age is only
necessary when the data are required for the preparation of
yield tables or other scientific purposes. Fairly approximate
data suffice for the purpose 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 classed 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.

A minute calculation of the mean age is rarely called for.

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 30 years old.

In the regeneration class the age of the overwood and
underwood must be given separate!}7.

In selection forests it suffices to give the limits of the age
gradations, which 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.

e. Origin and Past Treatment.

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

266 COLLECTION OF STATISTICS.

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
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 different
species, if their value per unit of measurement differs con-
siderably. It is useful to give all volumes in solid measure, as
solid cubic feet. The proportion between the different classes
of produce need only be given for each working section ; bestr
according to local proportionate figures, if such are available.

The different methods, according to which the volume can
be measured, have been described at pages 43 to 71. The
choice of the method of measurement depends on the circum-
stances of each case.

g. Increment, 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,

QUALITY OF WOODS. 267

if the yield is fixed for a whole rotation, or when the increment
forms the principal basis for the determination of the yield.
In the latter case both normal and real increment must be
ascertained. AVhen the yield is fixed for only one, or at the
outside two periods, 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 quantity-, 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 woods, the financial
ripeness of which is doubtful, that is to say, for woods which
are approaching the normal final age, and woods which have
suffered by injurious agencies, such as wind, snow, fire, insects,
damage by game, etc.

3. Determination of the Quality of each Wood.

a. General.

Under 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 with 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 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

'268 COLLECTION OF STATISTICS.

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 pro-
duced by faulty treatment, by injurious external agencies, such
as drought, frost, wind, fire, insects, diseases of the trees, 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 effected. 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 give.

On page 150 of Volume I. 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) B.y 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 and 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
growing 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-

QUALITY OF WOODS. 269>

sents the quality, the best way is to ascertain the volume of
the growing stock and the number of years in which it has
been produced. In dividing the volume by the age of the
wood, the mean annual increment is obtained. Both volume
and mean annual increment depend on the locality and the
past treatment of the wood.

It is evident that in reality 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 V. Of these I. should represent the lowest
and V. the best quality, but unfortunately the reverse num-
bering has been largely introduced. A still more convenient
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 diifers with the species and
method of treatment.

The quality can be determined with the help of yield tables,,
or the final mean annual increment.

I. Determination of the Quality with the help of Yield Talks.

The preparation of yield tables has been explained in Forest
Mensuration (page 96). Such tables represent the progress
of increment, or volume, 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, however, 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

270 COLLECTION OF STATISTICS.

for the Scotch pine prepared for Germany may safely be used
in the south of England. The fact is, that the sources of
inaccuracy inherent to 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.

The general yield tables given at page 386, Appendix D,
are used in Saxoii}r for the determination of the quality class.

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 the volume ; here the quality must
be estimated by the general condition of the crop, and especi-
ally its height growth. Indeed, the latter may be used even
in older woods, as long as height growth 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 inves-
tigation of the quality of the locality combined with the con-
dition 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.

c. Determination of the Quality by the Final Mean Annual Increment.

This method has sometimes advantages, especially if the
areas are to be reduced to one common quality ; but it has the
great disadvantage that the final age of each wood must be
fixed, since the mean annual increment changes with the age at
which the wood is cut over. Moreover it is almost impossible
to fix the final mean annual increment without the help of
yield tables.

QUALITY OF WOODS. 271

d. Reduction to One Quality.

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 have to calculate only with 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 calculation becomes most simple ; either if yield tables
are used, in which the yields of the several classes are indicated
the best by 1 and the others in decimals of 1 ; or, if the
reduction is made with the final mean annual increment or
yield.

Again, the reduction can be made under one of the two
following conditions : — Either 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
of the area ; or, the above equality is not required, in which
case any quality can be used as the standard, frequently
that being chosen which exists over the greater part of the
area,

i. REDUCTION BASED UPON THE FINAL MEAN ANNUAL INCREMENT.

(a) Calculation with the Mean Quality. — Under mean quality
is understood that 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 aly a2, as ... be the several areas,
•>, y\> 2/2? 2/3 • • • the corresponding annual yields per unit

of area,
,, Y the mean yield per unit of area, then

272 COLLECTION OF STATISTICS.

and

. . . = total annual yield
• • • total area

Example : —

A working section of 1000 acres contains :—

Block (1) 200 acres with 60 c' average increment

„ (2) 100 „ „ 50 „ „

„ (3) 200 „ „ 40 „ „

„ (4) 500 „ „ 30 „ „ „ then-

Mean quality

200x60+100x50+200x40 + 500x30,,, ,
1000

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 :

In the above example :

Block (1) The proportion is 60 : 40 ; hence the reduced area
x is obtained by means of the equation —

A s\ f* r\ r\r\f\ 1 £\J\J s\ \)\) orv/"v

„ (2) 40 :
„ (3) 40 :
„ (4) 40 :

KH i of) . 7.

40
100 x 50

125 „
200 „
375 „

AC\ onn • T

40
40 x 200

30 = 500 ix „

40
80 x 500

40

Total . . . = 1000 acres.
If now the forest is to be divided into annual coupes of equal

QUALITY OF WOODS. 273

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

comes to = — ^ — = 100 acres. The real area of a coupe in
each block is calculated as follows : —

Block (1) 60 : 40 = 100 ; x and x = 4° *10Q = 66'67 acres

60

„ (2)50:40 = 100:* „ a; = 40*1QO = 80'00 „

50

„ (3)40:40 = 100:* „ x = 4° * ™° = lOO'OO „

40

„ (4)30:40 = 100:* „ * = 40*100 = 133*33 „

oO

or :

Coupe No. 1 = 66-67= 66'67 acres ^ n

9 fifi-fi7 fifi-AT 1 Taken from block

„ „ 2= bbb7 = bb b7 „ j- „ 1

,,3= 66-66= 66-66 „ J

„ 4= 80-00= 80-00 From block No. 2.

„ 5=20+75= 95-00 „

( and partly No. 3.

„ 6= 100 = 100 „ From block No. 3.
7-25-4-100- 125 i Partly fr°m N°' 3

,, <— ZO-hlUU— 140 ,, <

(. and partly No. 4.
„ 8= 133-33= 133-33 „ ^
,,9= 133-33= 133-33 „ I From block No. 4.
,,10= 133-34= 133-34 J

Total . . 1000-00 acres.

(&) Calculation with any Suitable Quality. — 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. The total reduced area may

274 COLLECTION OF STATISTICS.

be greater, equal or smaller than the actual area, according to
the size of the standard quality : —

Reduced A =

The reduced areas of the several parts are obtained b}r the
inverse proportion of their qualities to the standard quality;
thus : —

Reduced al —
Reduced a =

etc.

Example, as above : Let the standard quality = 50 c, then
Total reduced area =

200 x 60 + 100 x 50+200 x 40+500 x 30_ ftnn

- — — — — — — ouu acies,

ou

and for the several blocks : —

50

= acres

(3)

200x40

Total . . 800 acres.

800
Reduced area of annual coupe = — — - = 80 acres,

and the size of coupes in the several blocks : —

(1) 60 : 50 = 80 :# and a? = — ^~= 66'67

ou

(2) 50: 50 = 80 ix „ « = — — = SO'OO

50

QUALITY OF WOODS.

275

(3) 40 : 50-80: x and x = ~ = 100-

KA v Of)

(4)30:50 = 80:* „ % = ~~ = 133'33 ;

oU

as before.

It is obvious, tbat the last mentioned method is the more
convenient of the two.

ii. REDUCTION BASED UPON YIELD TABLES.

The reduction is based upon yield tables, of which the best
is indicated by 1 and the others by decimals of 1.

(a) Calculation with the Mean Quality. — The mean quality is
obtained by multiplying the several areas by their quality
figures, and dividing the product by the total area.

The reduced area of each part is obtained by calculating it
with the inverse proportion which exists between its own and
the mean quality.

Example : as above, but let —

Quality of Block No. 1 = '6

» » » 5> 2 = '5

3— '4-

, .

== **•

200 X -6 + 100 X '

'4 + 50° X

Mean quality

Beduced areas of the several blocks : —

(1) -4 : '6 = 200 :a?anda; = 2-0'6= 300 acres

-4.

(2) -4: -5 = 100:^ „ x = = 125

*

(3) '4 : "4 = 200 : x „ x = = 200

'

(4) -4: -3 = 500:* „ x = ^^= 375 „
Total = 1000 acres

276 COLLECTION OF STATISTICS.

1000
The reduced annual coupe would be = -— — =100 acres.

Area of a coupe in each block : —

(1) '6 ; '4 = 100 ; #anda; = '4 = 66'67 acres.

*O

(2) '5: -4 = 100:* „ * = - = 80

"5

(3) '4: '4 = 100: x „ x

(4) '3: -4 = 100:# „ o^ = 133'33 „

*3

as before.

(b) Calculation with any Standard Quality. — In this case
the several areas are multiplied by their respective quality
figures, and the sum of these products represents the reduced
area; in other words the standard quality is placed equal
tol.

Example : as above :—

(1) 200 X '6 = 120 acres

(2) 100 X '5= 50 „

(3) 200 x '4= 80 „

(4) 500 x -3 = 150 „

Total reduced area = 400 acres.

A r\c\
Eeduced area of annual coupe = — - = 40 acres.

Size of coupe in each block : —

(1) '6 : '1=40 : xandx==^ = 66'67 acres

*D

(2) -5: '1 = 40:* „ * = ^j= 80

(3) '4: '1=40:* „ * = ^=100

(4) -3: '1 = 40:* „ a; = 45 = 133-33 „

o

as before.

NOTES REGARDING FUTURE TREATMENT. 277

Under this method the size of the annual coupes in the
several clocks is obtained by dividing the reduced area of the
annual coupe, by the real quality figure of the wood, a method
which is the simplest of all.

4. Notes regarding Future Treatment.

While drawing up a description of each wood it is very
desirable to note down any 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.

(6) Cleanings, thinnings, or primings during the period for
which the working plan is prepared ; the volume to
be removed should be estimated.

(c) Degree of ripeness of the principal or final crop, taking

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 and an estimate of the volume to be removed.

(d) 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.

(e) Measures to be taken for the protection of the wood

against threatening dangers, especially fire.

278 COLLECTION OF STATISTICS.

(/) Other works to be undertaken, such as construction of

roads, draining, irrigation.
(g) Utilization of enclosures and improvement of boundaries

where practicable.
(/O Proposals regarding the formation of sub-compartments,

or the abolishment of those which exist, with reasons

for such proposals.

SECTION III. — PAST 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 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 as
yet small.

The following notes indicate the class of information which
may be required :—

1. Yield of Wood or Major Produce.

The yields should be given separately : —

(a) For the principal species.

(b) For the different classes of timber and firewood,

according to size or value.

(c) For final and intermediate yields.

(d) Of cash receipts should be given the total, and the mean

price of the several classes of material, separated
according to species.

(e) The areas over which cuttings extended should, if

PAST RECEIPTS AND EXPENSES. 279

possible, also be given separately for final and inter-
mediate cuttings.

2. Minor Produce.

Under this heading should be given the quantity of each
article of minor produce which has been removed and the
cash receipts obtained for it.

Receipts derived from areas not used for the production of
wood, such as fields, meadows, &c., should be separately
recorded.

3. Expenses.

These should be recorded separately for : —

(a) Cost of administration and protection.

(b) Taxes, rates, &c.

(c) Formation of woods.

(d) Tending and amelioration.

(e) Maintenance of boundaries.

(/) Construction of roads, drainage, irrigation, and other

works.
(g) Cost of harvesting, separated according to major and

minor produce.

4. Generally.

For forests worked on financial lines the receipts and ex-
penses should be so arranged that it is possible to ascertain: —

(a) The current forest per cent, of each wood whenever

desirable.

(b) The forest rental, being the difference between all

receipts and expenses. It is used to determine the
per centage which the forest capital has yielded.

(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

280 COLLECTION OF STATISTICS.

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 determined
as the cost value calculated with the value of the soil
as determined above, or as the utilization 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 enquiry 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. »

2. Description of boundaries and names of the adjoining

properties and their owners.
8. Topographical features of the locality.

4. General description of the geology and climate.

5. Former and present proprietors, financial position of

present proprietor, whether the funds for formation,
tending, administration, amelioration, &c., 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

THE STATISTICAL EEPORT. 281

property, or whether servitudes and privileges rest on
it ; in the latter case their extent should be recorded.

7. Bights enjoyed by the proprietor of the forest elsewhere,

such as rights of way or floating, or rights over other
lands, &c.

8. Kequirements 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, &c.

13. Conditions of game and its 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,
&c., into forest, or the reverse.

16. The staff of the forest, its organization and efficiency.

SECTION V. — THE STATISTICAL EEPOET.

The data which have been collected in the manner indicated
in the previous four sections, must be brought together in a
statistical report, accompanied by maps to illustrate it. The
form of this report depends entirely on the circumstances of
each case. In one instance it will be necessary to go into
minute details, in another a more summary treatment is indi-
cated. The following documents will ordinarily form part of
the report.

282

COLLECTION OF STATISTICS.

1. Register of Boundaries.
This should give : —

(a) The boundary marks in consecutive numbers.

(b) The angles backwards and forwards at each point.

(c) 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.

(e) 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.

DESCRIPTION OF

LOCALITY.

AREA, IN ACRES.

Boundaries.

Locality.

Working
Section or
Block.

Com-
part-
ment.

Sub-
com-
part-
ment.

Stocked

Blank.

Total

Caesar's

Camp

1

a

24

2

26

North % East :

Elevation: 420 feet'

SirJ.Hayter's
land.

above sea-level, slop-
ing towards the east,

South : Com-
partments 13
and 12.

with moderate gra-
dient, down to 380
feet.

West : Koman
road.

Geological Forma-
tion: Middle Bagshot
sands.

Soil : Loamy sand,

fairly good in upper
part and good in

lower part ; no pan

to 4 feet depth.

TABLE OF AREAS.

283

2. Table of Areas.

The following form of this table is given as an illustration ;
it serves as a summary of all areas, and shows how each part
is utilized : —

AREA NOT USED FOR THE PRODUCTION

LOCALITY.

Area used

OF WOOD, IN ACRES.

for the

Grand

Produc-

Total,

"Working
Section or
Block.

Com-
part-
ment.

Sub-
coin -
part-
ment.

tion of
Wood, in
Acres.

Roads
and
Rides.

Fields.

Meadows

Water,
etc.

Total.

in
Acres.

Cassar's

Camp . .

1

a

26

•4

2-2

—

•6

3-2

29-2

Etc.

REMAEKS. — The use of the fields forms part of the forester's emoluments.

COMPAETMENTS. (See next page.)

GROWING STOCK.

QUALITY OF

Sylvicul-r
tural Species.
System. |

Age,
in
Years.

Mean
Height
in
Feet.

Volume in
solid Cubic
Feet.

Lo-
cality.

Grow-
ing
Stock.

Remarks, and Notes
regarding Future
Treatment.

High

Forest

Oak = -4

70

Oak,

Chest-

Broad-
leaved

3

•8

The mixture of species
is uneven ; the Scotch

Chest-

nut &

= 34,000

pine is chiefly found

nut ='2

Beech

Scotch

in the Northern part.

= 54

pine

and the broad-leaved

Beech

= 28,800

trees in the South ;

= •1

Scotch

Northern p&rt is well

pine

62,800

stocked, Southern part

Scotch

= 60

open ; most of the

pine = -3

oaks and chestnuts are

frost-cracked.

Future Treatment :

Southern part is so

increment-poor, that

it should be cut over

during the next ten

years, leaving the best

oaks and chestnuts,

and underplanted or

sown, with beech (or

spruce). In the North-

ern part only dead or

dying trees should be

removed during the

next ten years.

284

COLLECTION OF STATISTICS.

3. Description of Compartments.

This description may be drawn up in a tabular form, or
otherwise ; the former is preferable, as it presents a more in-
telligible picture of the forest, and gives greater security that
nothing has been overlooked. It is quite impossible to recom-
mend any particular form for this table, but by way of illustra-
tion a form based upon those recommended by Judeich and
Heyer is given. (See form on previous pages.)

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. Table of Qualities of Locality.

LOCALITY.

QUALITY CLASSES OF LOCALITY.
Area in Acres.

Working
Section.

Com-
part-
ment.

Sub-
com-
part-
ment.

Sylvicultural
System.

I.

Lowest.

II.

III.

IV.

V.

Best.

Total
Area.

Remarks.

Caesar's

Camp

1

a

Scotch pine

26

26

with some

»

1

b

broad-leaved

14

14

trees here

»

2

and there.

32

6

38

»

3

High forest

17

17

H

4

16

15

31

»

5

12

17

4

33

n

6

25

6

31

»

7

20

7

27

Etc.

Total

29

49

67

50

22

217

TABLE OF AGE CLASSES. 285

It is always 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,
as the yield capacity depends on the species, sylvicultural
system and rotation.

The Saxon Tables (p. 388, App. D) give the following
mean production per acre for Scotch pine woods, under a
rotation of 80 years : —

For the V. Class (lowest) = 19 cubic feet.
IV. „ = 44 „

HI. „ = 70 „

II. „ = 96 „

I. „ (best) =122

The mean annual increment, or the yield capacity, of the
area shown in the above table, would therefore be : —

Yield capacity = 29 x 19 + 49 X 44 + 67 X 70 + 50 X 96 + 22 X 122

= 14,881 cubic feet,
or average yield capacity per acre = = 69 cubic feet.

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 age classes are
represented in normal proportion, and that the mean quality
of all woods was equal to '7, the actual yield would be equal to

14,881 x -7 = 10,417 cubic feet,
or 48 cubic feet per acre and year.

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
determination of the yield in the immediate future. It maybe
prepared in the following form : —

286

COLLECTION OF STATISTICS.
TABLE OF AGE CLASSES.

LOCALITY.

Present
Mean
Age.

AGE CLASSES, IN ACRES.

Working
Section.

Com-
part-
ment.

Sub-
com-
part-
ment.

I.
1—20.

II.

21—40

III.

41—60

IV.

61—80

V.

Over 80.

Blanks.

Regene-
ration
Class.

Caesar's
Camp

1

a

70

24

2

1

b

35

14

2

95

32

6

3

54

17

4

16

31

5

46

33

6

24

31

7

86
Total...

27

31

45

60

24

59

8

—

TABLE OP
Material Cut in Past Years,

YEAR.

CONIFERS.

BROAD-

Final. Intermediate.

Total.

Final.

TimberwFood.

Total.

Timber

Fire-
wood.

Total.

Timber.

Fire-
wood.

Total.

Tim-
ber.

Fire-
wo'd

To-

Si

1881
1882

7,200 1 1J50

i

8.950

4,700

1,300

6,000

11,900

3,050

14,950

i

•

i

1890

Total in 10
Years ..
Annual
Average . .

77,600 16,400
7,760; 1,640

94,000
9,400

36,400
3,640

12,200
1,220

48,600
4,860

114,000
11,400

28,600 142,600
2,860 14,260

2750
275

2600
260

5350
536

REMARKS.— The area set aside for the production of wood
amounted, in the beginning of 1881, to 217 acres.

PAST YIELDS AND MAPS.

287

6. Table of Past Yields.

This table should give the past yields in produce for as
many years as possible, and the mean annual yield calcu-
lated from these data.

The data should be separated, where practicable, according
to final and intermediate returns, and according to the prin-
cipal 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

PAST YIELDS.

in solid Cubic Feet.

LEAVED SPECIES.

TOTAL.

Intermediate.

Tim-
ber.

750

4100
410

Total

Final. Intermediate. Total.

Tim
ber.

750

1350
135

Fire-
wo'd

1650

2100
210

To-
tal.

2400

3450
345

Fire- To-
wo'di tal.

Timber

Fire-
wood.

Total.

T""»» ££

Total.

Timber.

wFood. Tota1'

1650

2400

7,200

1,750

8,950

5,450

2,950

8,400

12,650

4,700 17,350

4700
470

8800
880

80,350
8,035

19,000
1,900

99,350
9,935

37,750
3,775

14,300 52,050
1,430 5,205

118,100
11,810

33,300 151,400
3,330 15,140

The annual yield was fixed at 15,000 solid cubic fept : or
150,000 for the period of 10 years; hence the average cuttings
exceeded the fixed yield by 140 cubic feet annually.

288 COLLECTION OF STATISTICS.

impresses itself more readily on the mind of the forester than
a lengthy description. As it is not possible to represent every-
thing on one map, it is usual to prepare different sets, such as
the—

(a) Topographical map.

(b) Detailed map on a large scale.

(c) Map showing the nature and age of the growing woods,

called the stock map.

(d) Geological map.

(e) Soil map.

(/) Map showing the working sections and cutting series.
(g) Detailed road map.

There is, however, no need for so many separate maps, as
several of them can he combined into one.
Ordinarily three maps suffice, namely : —

a. The Geological 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.

I. The Detailed Map.

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.

THE STOCK MAP. 289

<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.

c. The Stock 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 necessary details, a representa-
tion of the existing species, sylvicultural systems and distribu-
tion 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 3roungest being given the lightest, and the oldest the
darkest shade ; the regeneration class receives some distin-
guishing mark.

Mixed woods may receive a separate wash, or they may be
distinguished by the addition of small trees or marks of various
•colours.

Coppice woods may receive a separate wash, if shown on the
same sheet.

Coppice with standards may be distinguished from coppice by
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.

The two following illustrations will further explain what has
been stated above : —

VOL. Ill, U

290

COLLECTION OF STATI

REPRESENTATION OF TWO CUTTING SERIES (THE UPPER CONSISTING OF
10 COMPARTMENTS, THE LOWER OP 6), AS PRESCRIBED IN SAXONY.

JL_.

STOCK MAP.

291

DIAGRAM SHOWING THE PROPORTIONS OF THE AGE CLASSES IN THE
ANTONSTHAL RANGE, SAXONY, FROM THE YEAR 3827 TO THE YEAR 1893,
WITH THE NORMAL PROPORTION INDICATED AT FOOT "OF DIAGRAM.

1827

u 2

292

CHAPTEE II.

DIVISION AND ALLOTMENT OP THE FOREST AREA.

1. The Working Circle.

BY a working circle is understood that 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 be the area of a property belonging
to the same owner ; the maximum will ordinarily be the area
forming one executive charge or range.

The division of an extensive property 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 officer may manage several working
circles ; for instance, if the owners of several small properties
join in employing one officer 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. 295

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 latter form the working circle, or a
part of it called a working section. The whole of this division
is effected by utilizing, 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 indicat-
ing how it should be laid out, to explain more fully what is
understood by compartment, sub -compartment, cutting series
and working section.

2. The Compartment.

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 unit of working should never be twisted
out of shape for the sake of including only one kind of growing
stock in each compartment.

The formation of compartments is necessary —

(1) For general orientation, so as to enable the forester to

define any particular part of the area accurately.

(2) To render all parts of the forest easily accessible, since

one or more sides of the compartment are always
formed by roads or rides.

DIVISION OF AREA.

(8) To assist in the prevention of fires, and to enable the
forester to stop any which may have broken out.

(4) For the location of the annual or periodic coupes.

(5) To facilitate the transport of forest produce.

(6) To obviate the necessity for repeated surveys of the

coupes.

(7) In some cases, to facilitate hunting and shooting.

The boundaries of compartments are formed by 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 rarely 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 intensity of management.

(2) The extent of danger from fire, and

(3) The size of the working circle.

3. The Sub-compartment.

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 ma}' be divided into two or
more sub-compartments ; the latter may be temporary, if the
differences will disappear after some time, or permanent. Sub-
compartments may be 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 by 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 there by.

THE WORKING SECTION. 295

4. The Working Section.

All parts of a working circle, which form one separate series
of age classes, are called a working section. If a working
•circle 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 prin-
cipal causes, which demand the formation of working sections,
are the following : —

a. Species.

If several species appear as pure woods in a working circle,
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. If, on the
other hand, the several species appear in mixed woods, such a
separation is neither practicable or necessary.

b. Sylvicultural 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 ap-
proximately even annual yield is expected. Unless this is
attended to, 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.

296 DIVISION OF AREA.

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 protect the interests of the owner.

e. Differences in the Quality of the 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 treat-
ment or rotations.

/. Distribution of Cuttings.

If cuttings must be made annually in different parts of the
working circle, it is often advisable to form different working
sections, though this is not absolutely necessary.

(j. Generally.

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 m
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 conditions, 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 be drawn up for each working section, thus making
the latter always identical with a working circle. Such a pro-
cedure is not desirable, because it involves extra labour and
repetitions in the working plan report. It is preferable, when-
ever 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

THE CUTTING SERIES. 297

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.

5. The 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 oil
page 229, that such a simple arrangement is, in the case
of high forest, rarely 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 229) ; 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 cutting
series depends on local circumstances. On the whole, small
cutting series are preferable, 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 suitable change of coupes can be arranged, so as to-

298 DIVISION OF AREA.

protect the forest against the dangers which may
make themselves felt, if two or more coupes adjoin
each other.

(3) The establishment of small cutting series assists the
forester in distributing the yield to meet local
demands.

In order to realize 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 adjoining
series. Where these conditions do not exist, they must be
specially provided by the clearance of broad rides between the
cutting series called severance cuttings.

6. Severance Cuttings.

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, wherever an existing
cutting series is too long, and where 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
withstand the effects of strong winds, when the wood on the

SEVERANCE CUTTINGS. 299

windward side has been cut. An example will explain
this. A wood comprising a and b is to be divided into two
cutting series I. and II. To prevent the trees in II. being
thrown by wind, when I. is cut over, a strip c is cleared some
time before cuttings in I. are commenced, so that the edge-
trees along the line d — e may become storm-firm.

Severance cuttings need not be straight ; they may, if neces-
sary, be curved, or run along two or three sides of a wood.
The latter is necessary, where the prevailing wind direction is
not constant, but oscillates, say, from north-west to south-
west. The breadth of severance cuttings differs according to
species, their height growth and the strength of threatening
winds ; it will ordinarily range between 30 and 60 feet.

Severance cuttings must be made while the wood to be pro-
tected is still young and capable of developing firm edge trees ;
such a development is generally no longer possible 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 windfalls is great, it is
desirable first to clear a narrow strip, and widen it a few years
afterwards in one or more instalments, so as to gradually
accustom the edge trees to the effects 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 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 dan-
gerous 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 windward
wood are commenced. Whether this measure will have the
desired effect is doubtful, but it is better than to risk a regular
severance cutting.

300 DIVISION OF AREA.

7. The System of Roads and Rides.

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 water partings, watercourses, precipices, fields,
meadows, &c., 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 decided on and marked
on the ground. Roads 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, and in hilly or
swampy ground they often assume a shape and direction,
which makes 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 dis-
tinction is made between major and minor rides.

a. Major Rides.

In so far as roads or natural lines are not available, cutting
series, and in many cases working sections, should be bounded
by major rides. These should run in the direction 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 6 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 form
wind -firm trees, and to become accustomed to other climatic
influences. In the case of woods consisting of species which
are easily thrown by wind, they should not be less than 30 feet

SYSTEM OF ROADS AND RIDES. 301

broad, and if the major ride is also used as a fire line, it may
be still broader.

The edges of the woods bordering on major rides should be
strongly thinned from an early age onward, so as to produce
strongly developed trees.

Major rides may be utilized 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 instance, 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 compartments.
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.

c. The Network of Rides.

Major and minor rides together form the net- work or system
of rides. The laying out of it is, especially in the case of
shallow-rooted species, chiefly dependent on the prevailing
wind direction. In the plains, the latter can generally be
determined without much trouble. In mountainous districts,
the matter is frequently beset by difficulties, because the con-
figuration of the ground may produce a local direction, which
differs from the general direction. No 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 stem, and above
all, by the direction in which trees have been thrown. As
regards the latter, it must not be overlooked that local storms

302

DIVISION OF AREA.

sometimes throw trees in a direction which differs from the
ordinary direction of gales. In many cases reliable informa-
tion can be obtained from local people who have lived for
some time in the locality.

The laying-out of the system of rides is of great importance,
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 only practicable in the plains ; on hilly ground
they must accommodate themselves to the configuration of the
ground. The following example (taken from Judeich) will
illustrate this : —

The forest occupies a ridge, the slope of which is indicated

by dotted contour lines . The top of the ridge, being

much exposed, must be treated as a separate working section

DIKKCTIOK.

Fig. 51.

DEMARCATION OF DIVISIONS. 303

under the selection system ; it is separated from the rest by a
major ride (B\ The slopes are treated under the compart-
ment system, and they are divided into two parts by the major
rides (A) (JB) and (c\ The numbers ^JM (jT) . . .

indicate the minor rides, and 1, 2, 3 . . . . the compart-
ments. The prevailing wind blows from the" west.

The division would probably be somewhat on the following
lines : —

Working Section I. = Compartment System.
Cutting Series A comprises compartments 1 & 2

» )) ^ » » 4

,, ., D ,, ,, 5 & 6

Working II. = Selection System.
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.

The coupes in compartments 1 to 6 run at right angles to
the major rides NLj and fC\ or up and down the hill side, as.
it is generally objectionable to let the coupes run horizontally,
even from the top gradually downwards.

8. Demarcation of the Divisions of a Forest.

It is generally desirable that all interior boundary lines.
should be demarcated by boundary marks so that they can
be recognized, if they should have become obliterated in con-
sequence 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

304 DIVISION OF AREA.

choose always the same side, say the north side of the major
rides, and the east side of the minor rides.

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

The methods of naming and numbering the divisions differ
much. Judeich recommends the following : —

(a) Working sections receive Eoman numbers = I, II, ...

(b) Cutting series receive names and slanting capital letters

= A,B . . .

(c) Compartments receive Arabic numbers = 1, 2 . . .

(d) Sub-compartments receive small Eoman letters = la, lb . .

(e) Major rides receive upright capital letters surrounded

by a circle = ^A \ MEM . . .
</) Minor rides receive small Arabic figures surrounded by

(See illustration on page 302.)

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 num-
bering the divisions is prescribed : —

Working sections are numbered = I, II, III, . . .
Periodic blocks ,, ,, = 1, 2, 3 ...
Compartments ,, „ = A, B, C . . . with

the addition of the number of the periodic block ;

thus IV (72 means Working Section IV, compart-

ment C in the 2nd periodic block.

305

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 dis-
cussed in this and the previous volumes, and the following
references will be useful : —

(1) For choice of species, see Volume II., pages 4 to 11.

(2) For choice of sylvicultural system, see Volume I., pages

226 to 232.

(3) For choice of method of formation, see Volume II.,

pages 169 to 180.

(4) For choice of method of tending, see Volume II.,

pages 189 to 228.

(5) For choice of rotation, see present volume, pages 200

to 211.

(6) The financial aspect of forestry has been explained at

pages 167 to 169 of this volume.

The determination of the method of treatment depends
chiefly on :

(a) The objects of management.

(b) The locality.

(c) The growing stock actually existing in the forest.

(d) The dangers to which the growing stock and the soil

are exposed.

(e) The conditions of demand and supply of forest produce.
(/) The legal position of the forest, existence of rights,

privileges, etc.

The nature of these determining factors shows that no
general rule can be laid down, but that the method of treat-

306 METHOD OF TREATMENT.

ment and the general lines of management must be determined
locally on the merits of each case. In the following lines 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, only justified 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 179 to 202 of Volume I.

2. Sylvicultural System.

This depends, of course, on the species which exist on the
area, or which have been selected for introduction.

High 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 the best system for the preserva-
tion 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, as a rule, by
a lower mean annual forest per cent. The growing stock is
also exposed to many dangers, such as snow, ice, wind, insects
and fire. High forest must be adopted in the case of all
species which cannot be regenerated b}r stool shoots or root
suckers.

SYLVICULTURAL SYSTEM. 307

As to the different kinds of high forest, clear cutting, shelter-
wood system, group system, selection forest, or their modi-
fied 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 intermediate forms stand between these two ex-
tremes. 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 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.

Coppice woods make smaller demands on the chemical and
physical properties of the soil ; they have a much smaller
capital, and generally give a higher mean annual forest per
cent. ; owing to the shortness of the rotation, the danger of
damage from outside (excepting frost and deer) 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. Coppice is only possible in the

x 2

308 METHOD OF TREATMENT.

case of those species which reproduce well from the stool. It
requires a fairly mild climate and protected position.

Pollarding gives frequently high returns, and it can be carried
on in conjunction with agriculture.

Coppice iviih standards holds an intermediate position
between 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 sylviculturai system, the species,
and the nature of the locality.

Natural regeneration is cheaper in itself, 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
seriously disturbed, and the loss of time, and other accom-
panying disadvantages, may more than outweigh the smaller
original outlay. Nor must it be forgotten that, as a rule,
natural regeneration must be augmented by a certain amount
of planting. 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 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
chiefly on the species and local conditions, a subject which
has been dealt with on pages 170 to 175 of Volume II.

As regards the preservation of the quality of locality, see
Sylvicultural System.

THE ROTATION. 309

4. Method of Tending.

This must be laid down in detail, but as the subject has
been fully treated in Volume II. it would only lead to
repetition to refer to it further in this place.

5. The Rotation.

The rotation is chiefly governed by the species, sylvicultural
system and the objects of management. Though the financial
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 preservation 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.

310

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 and yet 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 being made when the
condition of the wood demands such cuttings. This state of
affairs 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 from consideration for the
adjoining woods.

The task of the forester is, in such cases, to secure a
sustained annual yield, and yet to lead the forest gradually over
into the normal state as defined in Part III. of this Volume,
with the smallest possible loss to the owner. Many different
methods have been elaborated with the view of achieving that
task, which approach the subject from various points of view ;
the degree of success differs however considerably. It is not
proposed to describe here all methods, but only those which

THE ANNUAL COUPE. 311

deserve to be specially mentioned. These may, according to
their principal characteristics, be grouped in the following
manner : —

I. Division of the forest into fixed annual coupes.
II. Allotment of woods to the periods of a rotation.

1. According to area.

2. ,, ,, volume.

3. ,, ,, area and volume combined.

III. Regulation of the yield according to increment and

growing stock.

1. The Austrian method.

2. Hundeshagen's „

3. Von Mantel's

4. Brandis' „

IV. 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.)
V. Annual or periodic selection of woods for cutting in
accordance with sylvicultural requirements and the
objects of management (Judeich's method.)

SECT CON I. — 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.

A
The size of each annual coupe is = — , if the area is at once

A
re-stocked, or = - — , if each coupe lies fallow for s years.

T -f- S

In this 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

312 DETERMINATION OF THE YIELD.

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 the fundamental
principle, that the mdst 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 quite unsuited, except,
perhaps, for clear cutting with a very low rotation.

SECTION II. — ALLOTMENT OF WOODS TO THE DIFFEKENT
PERIODS OF A ROTATION.

In order to remove the great rigidity of the fixed annual
coupes, and to obtain a method which is suitable for the
treatment of high forests, especially those managed under the
shelter-wood systems, the several woods comprising a forest
are 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 woods are divided into as
many lots as there are periods in the rotation ; during
each period one of these lots is dealt with. Thus opera-
tions extend over the whole area once in each rotation.
Deviations from this arrangement occur occasionally, for
instance, if a sub-compartment is not cut over, or twice cut
over during the first rotation, in order to make the compart-
ment 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

METHOD OF PERIODS BY AREA. 313

first rotation; it may be smaller, equal, or larger than the
normal yield.

An essential part of 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 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 considered separately.

1. The Method of Periods by Area.

a. Description 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 little or no difference exists in the quality of the
in the different parts of the forest, the size of each

A

periodic coupe will be = — , where n 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

of the periodic coupe becomes = - — . Unless this is

done the periodic yields in the second and following 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 approximately the same area. .

The woods placed into the first period are measured, their

314 DETERMINATION OF THE YIELD.

volume calculated, and the increment for half the number of

years in the period, ^, added. The total of the volume thus
2

obtained is divided by the number of years in the period, so as
to obtain the average annual yield during the first period.

For an example see Appendix A, at page 349, where the
working plan for the communal forest of Kruuibach, a village
in Hesse-Darmstadt, has been given. This working plan is
being actually followed.

b. Merits 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; more especially, too large cutting-
series are likely to be established.

Another disadvantage is that a surplus of growing stock may
be dragged over a whole rotation, whereas it should be removed
as quickly 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 Method of Periods by Volume.

a. Description of the Method.

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

METHOD OF PERIODS BY VOLUME. 315

regulated ; in others the intermediate returns are utilized to
equalize the yields 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 equalize 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 B, page 362, only the final re-
turns have, for simplicity's sake, been equalized. The data
are those of the Krumbach communal forest given in
Appendix 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 p. 123. After making the
shiftings indicated in the general working plan, the volumes
allotted to the several periods stand as follows : —

Periodic Yield. Annual Yield.

I. period -189,393 cubic feet. 9,470 cubic feet.

II. „ -195,474 „ „ 9,774 „ „

III. „ -173,919 „ „ 8,696 „ „

IV. „ -188,240 „ „ 9,412 „ „
V. -194,845 „ 9,742 „

Total- 941,871 „ „ 9,419 „ „

An attempt to equalize the returns further would necessitate
the cutting up of compartments, which is not desirable.
The areas placed into the several periods are : —

316 DETERMINATION OF THE YIELD.

I. period = 36*00 acres.

II. „ - 34-02 „

III. „ = 27-30 „

IV. „ = 29-05 „
V. „ = 33-78 „

Total = 160-15
Mean periodic area= 32*03

b. Merits of the Method.

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-
zation 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 generally
beset by difficulties. Again, it drags a surplus of growing
stock over a whole rotation.

Whereas the method by area establishes the normal state of
the forest within one rotation, the method by volume takes
several rotations to accomplish this.

As regards its financial aspect, it stands on the same footing
as the method by area.

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

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 approximately the same, volume.

The equalization of the periodic areas and returns is effected
either by adding columns for the volume to the general
working plan used for the method by area, or by adding
columns showing the reduced areas to the general working
plan used for the method by volume. Shiftings are made until
both area and yield are the same, or approximately the same,
in each period.

THE AUSTRIAN METHOD. 317

It will easily be understood that such an equalization is a
difficult operation, especially in a very abnormal forest ; hence
more than approximate results cannot be attempted.

The method enjoys 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 the two previous
methods.

In practice various modifications of the above three methods
have been evolved, which sometimes partake more of the one,
and sometimes more of the other method.

SECTION III. — REGULATION OF THE YIELD ACCORDING
INCREMENT AND GROWING STOCK.

The methods belonging to this section calculate the yield
by means of a formula which is based on the increment laid
on, and any difference which may exist between the real and
normal growing stock. Having thus determined the yield, the
woods for cutting are selected from time to time in accor-
dance with sylvicultural considerations. There is no necessity
for drawing up a general working plan for a longer period
than suits the special requirements of each case.

A number of different methods come under this section, of
which, however, only the following need be mentioned here, as
the others are of little practical importance.

1. The Austrian Method.

(Die Oesterreicli 'scJte Cameral Taxation.}
a. Description of the Method.

In the year 1788 (during the reign of the Emperor Joseph II.,
one of the most enlightened sovereigns known in history) the
Austrian Government issued instructions regarding the as-
sessment of forests for the purpose of taxation. In these
instructions reference was made to the difference which may
exist between the real and normal growing stock of a forest.
This led to the knowledge that a forest, which is expected

318 DETERMINATION OF THE YIELD.

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 utilized; if the real
growing stock is greater than the normal, more than the real
increment must be removed ; if the real growing stock is
smaller than the normal, less than the real increment must be
xitilized, until the deficiency has been made good."

In carrying this excellent idea into effect, however, errors
were introduced, which are still upheld by 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 final

mean annual increment corresponding to the normal
rotation multiplied successively by the ages of all age-
gradations; the sum of all these products gives the

value Gn = Ix ^ (see p. 235). Here /represents the
A

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

THE AUSTRIAN METHOD. 319

to determine the real final age and the volume at that
age for each wood.

(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 : —

, v TJ IT , real Gr. Stk.— norm. Gr. Stk.

Annual Yield = real lncrement+ —

a

Y=Ir+G*~G*.

b. Merits of the Method.

The method was the first which based 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 utilization 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

320 DETERMINATION OF THE YIELD.

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
the real growing stock is equal to the numerical normal
growing stock, and yet there may not be a single mature
wood in the forest fit 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 ;

then the method is one of considerable merit. It enables the
forester to arrange the grouping of the age classes in the most
desirable way, and to do justice to all other sylvicultural
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 C, p. 364, has
been based upon the formula of this method.

2. Hundeshageri's Method,
a. Description of the Method.

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

HUNDESHAGEN'S METHOD. 821

F. /7 _ Y • Cr

real • ^* real •*• norm. • ^ norm.

Y

Y r1 v »

^-CrrX^-.

In words, the real yield is equal to the real growing stock
multiplied by the normal yield and divided by the normal grow-

" Y
ing stock. Hundeshagen calls the quotient — *, by which the

^*»

real growing stock is multiplied, the " utilization per cent."
(More correctly this indicates only the rate of utilization,

Y

whereas the utilization per cent, is — - x 100.)

G»

The normal yield is placed equal to the normal increment,
or equal to the contents of the oldest age gradation in a
normal series of age classes. The normal growing stock is
obtained by adding up the volumes given in a suitable yield
table ; under 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.

VOL. III. T

322 DETERMINATION OF THE YIELD.

b. Merits of the Method.

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 quan-
tity of growing stock which stands in a forest. On the con-
trary, 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 ;
it prescribes a definite annual yield, while not a single mature
wood may be present ; or it prescribes too small a yield,
whenever a considerable portion of the area is stocked with
decrepid 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 ac-
cording 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.

VON MANTEL'S METHOD. 323

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 uncer-
tainty. 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.

3. Von Mantel's Method.

Von Mantel, in arranging for the determination of the yield
of certain forests in Bavaria, laid it down that this should be
done according to the formula —

A 1Y* Id — ^ea^ G'rowm£ stock of the forest _ realG
Half the number 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 cal-
culated with the final mean annual increment. Hundeshagen's
formula —

V
V— f7* »

•* — ^ * ~~

G:

goes in that case over into —

j r r

n o o

The cutting of the yield according to Yon 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 (under which Yon Mantel

Y 2

324 DETERMINATION OF THE YIELD.

understands that actually present in the forest) is equal to the
normal growing stock, then his formula goes over into —

rxl

2

The formula gives, therefore, the correct yield, provided the
increment is normal.

If the actual growing stock is smaller than the normal, say

x>_?'Xl fhpTi flip

yPttl ^-^ — r\~~ 9 vllt/Xl L11C

rxl_

O 2^7' 7*

Yield = = 1— — — = I — ,

r r r

"2 2

which means, that less than the increment is cut.

Supposing that the real growing stock is greater than the
rxl
"2"

rxl

T T £ ~r i &

normal: realG=- --+x; 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 i&
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

growing stock and normal yield need not be determined ; in
other words, the method can do without yield tables. It is only

BRANDTS' METHOD. 825

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. Ijranctis' Method.

The method to he described under this Jiead will be better
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 con-
tained 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 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
remunerative. 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 at any rate ex-
posing 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 years ascertained under (2), he
ascertained the maximum number of trees which it was per-
missible to cut annually.

326 DETERMINATION OF THE YIELD.

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 at least maintaining the
mature growing stock in the forest, and utilizing the actual
increment. With the view of utilizing 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 vice 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, &c.

For the rest, the method leaves a free hand to the forester,
who arranges the cutting with due regard to sylvicultural
requirements and a proper succession of the different coupes.

The [number of trees of the several size classes were
originally ascertained by measuring or counting them along
narrow strips, generally 100 feet broad, laid through the
forest along the line of march (so called "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 concentric rings on
a sufficient number of stumps, thus ascertaining 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 localized : in other
words, an area check was added to the calculated yield, so
as to guard against overcutting.

HEYER'S METHOD. 327

The method does not claim to be theoretically quite correct,
because it does not accurately define the extent to which the
growing stock of marketable material may be reduced, or ought
to be increased, but it is correct enough wherever large areas
have to be dealt with in a short time. It works expeditiously,
and prevents a deterioration of the forest, if judiciously applied.
Had it not been for this method, the valuable teak forests of
Lower Burma might have been exhausted, before their sus-
tained }deld 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.

SECTION IV. — REGULATION OF THE YIELD ACCORDING TO IN-
CREMENT 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 Section III., as it rested on the Austrian
method. 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. Principle of the Method.

The principle of Heyer's method is as follows :—

(a) 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 prevent loss of increment
during the second and subsequent rotations.

(fe) To equalize 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 utilize the real increment, calculating the mean for a

328 DETERMINATION OF THE YIELD.

series of years, plus or minus the quota of growing

stock determined under (b).

It is obvious that these objects can only be realized by a
complicated procedure, and even then only approximately,
because changes in one direction disturb the balance in
another.

2. Practical Application of the Method.

(a) The first step is to allot, by means of the table of age
classes, all woods to the several periods and to equalize
the areas by suitable shiftings, as indicated under the
method of periods by area ; care being taken to allot
the woods with due consideration to sylvicultural
requirements, and a proper distribution of age classes,
as far as this is practicable.

(&) The real increment is placed equal to the real final mean
increment, for which purpose it is necessar}^ to deter-
mine the final age of each wood (which may differ from
the normal final age), and its probable volume at that
age ; the latter divided by the former gives the mean
annual increment. In order to avoid having to cal-
culate 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.

(c) The normal and real growing stocks are calculated as
for the Austrian method ; the former is placed

Ixr

— , where I 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.

HEYER'S METHOD. 329

(d) The theoretical yield is then fixed by the formula —
y_Real Increment of a' yea,YS.reaiG

If a 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 expression
goes over into : —

Y — real™ ~^~ real -^a — norm.®

a

(e) The next step is to ascertain whether the woods pre-
liminarily placed into the several periods are sufficient
to meet the yield during each period, as calculated by
the formula under (d), or whether they contain too
much or too little volume ; in the latter case, suitable
shiftings must be made, which necessitate, of course,
fresh calculations of the increment and real growing-
stock, as the final ages of some of the woods are thereby
altered. This process is continued until the require-
ments of the method are realized, that is to say, until
each period contains the same area, and at the same
time the volume necessary to meet the yield as cal-
culated 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, and
normal and real growing stock incorrectly, as in the case of

330 DETERMINATION OF THE YIELD.

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.

As regards the purely financial principle, the method stands
above the methods described under Section III., though it
does not do full justice to it.

SECTION IV. — SELECTION OF WOODS FOR CUTTING IN ACCORD-
ANCE WITH SYLVICULTURAL EEQUIREMENTS AND THE
OBJECTS OF MANAGEMENT.

The method now to be described has been gradually de-
veloped 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
Bestandswirthschaft" 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 method ap-
proaches the business, therefore, from a point which differs
from that of all the previously-described methods, as the latter
bring the forest as a whole into play, in order to determine
and regulate the yield.

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 ; the cuttings

JUDEICH'S METHOD. 331

I

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 centre of the method lies in the
establishment of a full increment and a proper arrangement of
the age classes. Not a word is said about the normal growing
stock, because this must come of itself, if the other two condi-
tions of the normal state are 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 requirements
of each wood are reconsidered, with due regard to the intro-
duction 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, or not, be one.

1. Application of Judeich' s Method to Clear Cutting in High
Forest and the Shelter -wood 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, a&
described in Chapter II. This plan enables the forester to
determine, in a general way, the order and direction in which

DETERMINATION OF THE YIELD.

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 sub-
sequent revisions, be gradually led over into more permanent
groupings.

b. Determination of the Final Yield.

The first step is to determine the rotation in accordance
with the objects to be aimed at, as laid down by the owner of
the forest. How this is done has already 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 step is to select, with due consideration of the
desired cutting direction and the establishment of suitable
•cutting series, the woods where final cuttings are called for
during the period, for which the working plan is to be 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 difficulties
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 woods ; the ripeness to

be determined by the objects of management. In the

JUDEICH'S METHOD. 33$

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
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 outturn. 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, the yield as calcu-
lated by the Austrian method, Hundeshagen's, or Heyer's
methods. 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 100 years, the mean annual coupe would be equal

2000

to ^rf^r = 20 acres. During a working plan period of 10
100

years the normal cutting area for it would amount to 20 X 10
= 200 acres. In other words, during a period of 10 years
200 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 age classes is fairly normal. In
all cases where considerable deviations from it 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

-334 DETERMINATION OF THE YIELD.

instance too large a proportion of old or defective woods exist,
and in others 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 area
to be dealt with. In the above case the area might be given
as 150 to 250 acres.

As long as the total area as determined above under (1) to
(3) falls between these limits, it may be accepted as the area
to be dealt with during the first ten years. If it is larger than
the maximum, then some of the most suitable areas enumerated
under (3) should be held over until the next period ; 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.

c. The Intermediate Yields.

The[limit between final and intermediate yields is not always
very 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.

(I)} 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 over is done during the working plan period
or later on.

2. Intermediate yields comprise all other returns derived
from —

(a) Cleanings.

(b) 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 first period.

JUDEICH'S METHOD. 335

The quantity of intermediate yields is best estimated accord-
ing to past local experience, with due consideration to the
condition of the several woods. Where the necessary local
data are not available, the most suitable average data obtained
elsewhere must be used. The woods to be cleaned and thinned
are put down according to their areas.

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 first
place, be regulated by the final cuttings. At the same time
the intermediate }delds may be utilized to equalize any un-
avoidable inequalities of the final yield. Under any circum-
stances both 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.

d. Separation of Yield into Classes of Produce.

The yield should be separated according to classes of pro-
duce, 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 the yield of the important species
separately, 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. Application of the Method to other Sylvicultural Systems,
a. Coppice.

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 influencing

336 DETERMINATION OF THE YIELD.

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
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 these 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 entirely 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 calculations. 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 local average figures.

1). Coppice with Standards.

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 243, can
only serve 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

JUDEICH'S METHOD. 337

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.

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, however,
not be forced to abide absolutely by that estimate, but be per-
mitted 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
summary way on the basis of local experience.

c. 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 desir-
able 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 avoid-
ing having to cut too much at one time.

The area to be taken in hand annually is obtained by divid-
ing the total area by the number of years, I, fixed as above.
By multiplying 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
cr the shelter-wood compartment system.

Example : —

Area of a selection forest = 600 acres,
Botation = 120 years,
I = 20 years,

600
Annual cutting area = — — =30 acres.

338 DETERMINATION OF THE YIELD.

Area to be dealt with during the first ten years = 300 acres.
On this area all 120-years-old trees are cut, as well as the
necessary number of younger trees, so as to reduce them to a
suitable number of mature trees. As it is a laborious matter
to ascertain the age of the trees, it is desirable to substitute
the diameter (or girth) at maturity 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.

The areas to be dealt with in each period of, say, 10 years,
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
trees 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 von Mantel's or Brandis'
methods described above.

3. Change from one Sylvicultural System into another, called
a Conversion.

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 one specific case will bring out the
essential points to be considered in each conversion : —

An irregularly-stocked forest of broad-leaved species, partly
coppice, or partly coppice with standards, shall be converted

CHANGE OF SYSTEM. 339

into a coniferous forest, a conversion which is indicated by 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.

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 has been completed. Supposing 60 years
were chosen for the period of conversion, then at its close the
oldest coniferous wood should have an age of 60 years.

By dividing the total area by 60, the area is ascertained
which should be converted annually.

In selecting the areas to be taken in hand year by }rear, 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, but more especially of the first,
decides the allotment of the annual coupes to the several
cutting series.

Example. — A coppice with standard forest of 1,200 acres
shall in the course of 60 vears be converted into coniferous

1200

forest. Every 10 years — — = 200 acres must be taken in

Of)

hand for conversion. In that case the yield during the first
10 years would consist of : —

340 DETERMINATION OF THE YIELD.

(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 with standards.

During the third 10 years : —

(1) The clearing of 200 acres ;

(2) The treatment of 600 acres as coppice with standards ;

(3) Thinnings in the oldest coniferous woods, £c.

It is evident, therefore, that the returns fall off 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 an^y cuttings in the
200 acres of coppice with standards which will come under
conversion during the next period of 10 years ; 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
oe sparingly done, so as to equalize the cuttings as much as
possible.

341

CHAPTER V.

THE WORKING PLAN REPORT.

UNDER the working plan report is understood the document
which gives, in a systematic manner, all the information
which has been indicated in the previous chapters, 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, very detailed plans should be drawn
up; for forests which give as yet only small returns simple
plans would be indicated.

By way of illustration the following arrangement is given,
but it must be understood that in one case many of the
headings may be omitted, while in another additional informa-
tion may be required : —

Working Plcm Report.

INTRODUCTION.
CHAPTER I. — GENERAL DESCRIPTION.

1. Name and situation of forest; name of proprietor.

2. Boundaries.

3. Area.

4. Configuration of the ground.

5. Kock 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.

342 THE WORKING PLAN REPORT.

11. Cost of extraction and of transport to markets ; supply

of labour.

12. General description of forest growth.

13. Injuries to which the crop is exposed.

14. Kate of growth.

15. Yield tables, volume tables, form factors, reducing co-

efficients, &c., used in the calculation of the volume
and increment of the woods.

16. Organization 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. „ sylvicultural system.

4. Determination of the rotation.

5. General lines of treatment.

6. „ „ yield.

CHAPTER V. — SPECIAL WORKING PLANS.

1. Plans of utilization.

a. Final cuttings.

b. Intermediate cuttings.

c. Minor produce.

2. Plan of formation.

3. ,, ,, other works.

4. Maps illustrating the condition of the forest and the

proposed treatment.

CHAPTER VI. — MISCELLANEOUS,

1. Reorganization of the forest staff.

2. Financial forecast.

THE WORKING PLAN REPORT. 343

3. Proposals for the control of the execution of the working

plan.

4. Miscellaneous observations.

The shape of the special working plans enumerated in
Chapter V. of the report depends entirely on local circum-
stances. Some forms will he found in the appendices of this
volume, such as were considered suitable for the forests in
question. On the whole it is desirable that the forms should
at once provide for a suitable control of the execution of the
working plan, a subject to be dealt with in the next chapter.

CHAPTER VI.

CONTROL OF EXECUTION AND RENEWAL OF WORKING PLANS.

IT is not sufficient to prepare a working plan ; it is also
necessary 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 plan, or rather a revised plan,
must be prepared.

As the preparation of a first working plan is to some extent
based upon doubtful data, it is of importance to keep a careful
record during its execution, so as to eliminate in the course
of time all such 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.

TABLE OF RECEIPTS

Year.

Area,
Acres

WOOD Sou), IN CUBIC FEET
SOLID.

RECEIPTS, SHILLINGS.

Ex-

Timber.

Fire-
wood.

Bark.

Total.

From
Wood.

From
Minor
Produce

Total.

Har-
vesting
of
Wood.

Har-
vesting
Minor
Produce

1891

253

12,300

7,000

100

19,400

7,600

400

8,000

1.200

100

1892

1900

Total
Annual
Average

253

130,000
13,000

70,000
7,000

1000
100

201,000
20,100

75,000
7500

4000
400

79,000
7,900

14,000
1,400

900
90

RECORD OF CHANGES AND OF WORKS.

345

2. The record of works.

3. The preparation of revised working plans from time to

time, or renewals.

1. Record of Changes.

(a) All changes in the areas must be recorded. Part of the

area may he sold or exchanged, or additional areas
bought ; areas hitherto used for the production of
wood may be set aside for other purposes, or vice versa.
The progress of the cuttings may cause alterations in
the allotment of areas ; natural phenomena may pro-
duce changes, such as floods, landslips, &c. All such
changes should be noted at the close of each year, in
the maps as well as in the table of areas.

(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

compartments.

«
AND EXPENSES.

PENSES, SHILLINGS.

NET RESULT, IN
SHILLINGS.

FORBST CAPITAL,
SHILLINGS.

Per-

Form-
ation
& Im-
prove-

Ad-
minis-
tra-
tion &
Pro-

Taxes,
&c.

Mis-
cella-
neous.

Total.

Total.

Per
Acre.

Soil.

Growing

Stock.

Total.

jiven by
Forest
Capital
during
Yearf

Re-
marks.

ment.

tection

200

400

200

100

2,200

5,800

22-92

31,100

128,700

159,800

3-63

2,100
210

4,000
400

2,000
200

1000
100

24,000
2,400

55,000
5,500

21-74

31,100

128,700

159,800

3-44

CONTROL OF WORKING PLANS.

(b) 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) Kesult of each cutting according to quantity and amount

realized 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 table on previous page.

(5) The means of following up the history of each wood

or compartment, as illustrated on page 384,
Appendix C.

3. Renewal of Working Plans.

When the period for which a working plan has been prepared
comes to an end, it must be renewed. Such a 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
the past period makes that task a much easier one than on the
first occasion. Hence it may be indicated as follows : —

(a) 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.

RENEWAL OF WORKING PLANS. 347

(b) Investigation of the extent to which the provisions of the

former working plan were judicious and appropriate.

(c) Preparation of a new working plan, hased 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.

APPENDIX A.

WORKING PLAN FOR THE COMMUNAL FOREST
OF KRUMBACH

IN THE

OBERFORSTEREI LINDENFELS, FORST WALD-MICHELBACH, IN

THE PROVINCE OF STARKENBURG OF HESSE-DARMSTADT.*

(PERIOD 1888—1907.)

PRELIMINARY REPORT.

THE preparation of a working plan for the communal forest of
Krumbach having been ordered by a resolution dated the 2nd May,
1887, the Grand-duoal Forstmeister in Wald-Michelbach and the
Oberforster in Lindenfels have agreed that the following main points
shall be attended to : —

(a) The forest in question shall form one working circle.

(b) The prevailing species is the beech, with which oak and

Scotch pine are associated in single trees here and there.
The method of treatment shall be that of high forest with
natural regeneration under a shelter- wood. In order to
increase the proportion of valuable timber, it is desirable
that, during regeneration, an increased number of useful
timber trees should be introduced, especially oak, then ash,
maple, silver fir, larch and spruce. The mixture shall,
especially in the case of oak, be in small groups suitably
distributed over the area, the best soil being selected lor
the oak. On stony, shallow soil spruce, larch, and Scotch
pine should be chiefly mixed into beech.

(c) The rotation should be fixed at 100 years.

(d) As the several species are not separated according to area,

only one working section is required to be called " mixed

* The method of determining the yield prescribed in Hesse-Darmstadt is that
of allotment of woods to the several periods of a rotation according to area.
The annual yield during the first period is ascertained and fixed by volume.

350 APPENDIX A.

broad-leaved high forest, with coniferous trees here and

there."
(e) As the difference in the quality of the locality ranges within

very narrow limits, only one quality class need be recog-
nized.
(/) The road system is complete. Though many of the roads

are steep and not very well laid out, it will not be necessary

to alter them at present.
(g) The mensuration of the woods, which will be regenerated

during the next 20 years (first period) is to be done

according to the method of Draudt-Urich.

THE FORSTMEISTER.— THE OBERFORSTER.
' 15th June, 1887.

DESCRIPTION OF COMPARTMENTS.
PKELIMINARY — GENERAL CHARACTER OF THE LOCALITY.

THE Krumbacher communal forest, comprising an area of
164" 6 2 acres, occupies the western and southern slopes of a mountain
which rises from the valley of the river Weschnitz, and forms a range
of some height. The highest part of the mountain (called Die
Stotz) and of the communal forest has an elevation above the sea
of 1,437 feet. The forest, commencing at the highest point, stretches
down to an elevation of 853 feet, being bounded at the lower edge
by other communal forests.

Geologically, the Stotzberg belongs to the granulite-syenite group
of the Odenwald ; more especially syenite rich in quartz with narrow
strips of granulite is here the forming rock. It disintegrates easily
into grit and forms a clayey or loamy soil, mixed with pieces of
stones, which is generally fresh and deep. Only on exposed ridges
and peaks is the soil shallow, dry and hard ; in these places the
broad-leaved species show only moderately good growth, whereas they
exhibit great vigour in all other parts.

As laid down in the Preliminary Report, only one quality class of
the locality has been recognized, which, assuming three classes, is the
II. or middle class.

APPENDIX A.

351

[ g. = good ; m. = middling ; b. =bad.]

BLOCK.

Com-
part-
ment.

Area.

Acres.

Quality
of
locality

Work-
ing
section

DESCRIPTION OF COMPARTMENT.

GROWING STOCK.

Age in

1888.

Growth

Den-

sity.

Quality

Farrenfeld 1

18-78

II.

I.

Situation : Western slope,

80

g-

g.

g-

moderately steep, with

shallow depressions.

Soil : Sandy loam, fairly

deep, fresh, stony, and

covered with boulders.

Wood: Beech (-9) with oat

(•1), latter mostly affected

with cancer ; thinned in

1878 ; in south-east a

group = 1'73 acres 30—40

years old of not yet

thinned beech.

»»

2

7-98

79

Situation : Western steep 60

m.

g-

m.

slope.

Soil : As in Compt. 1.

Wood: 50—70 years old

beech ('9) with oak ('I),

older and younger groups

changing ; requires thin-

ning.

3 ,

3

576

J j

||

Situation: Ridge with ad- I 60 ; m.

g-

m.

joining western slope.

| Soil : Very stony, covered

with boulders.

Wood : Beech with single

oaks ; requires thinning.

Heimaths

4

10-68

j j

Situation : Southern to

40

g-

g-

g-

south-eastern steep slope.

Soil : Sandy loam, very

stony.

Wood: Beech ='8, ash and

sycamore = -1, spruce and

larch = "1 ; thinned for

first time in 1878—86,

yielding 1377 c' solid.

5

9-44

j ,

SitiiMtion : Southern steep

15

g.

g.

slope, partly trough- i

shaped.

Soil : Fresh, deep ; in the

upper part somewhat

stony.

Wood : Beech regeneration

coupe ; on about 6 '18

acres fairly complete

young growth of beech

9 years old, with oaks

and maples, and on the

52-64

I

352

APPENDIX A.

[ g. =good ; m. = middling ; b. =bad.j

BLOCK.

Com-
part-
ment.

Area.
Acres.

Quality
locality

Work-
ing DESCRIPTION OF COMPARTMENT.
section j

GROWING STOCK.

Age in

1888.

Growth

Den-
sity.

Quality

Br. forward

52-64

II.

I.

stony parts spruce here

and there ; on 3 "26 acres

20—35 years old beech ;

thinned in 1887.

Heiinaths

6

3-21

„

fj

Situation : A narrow deep

130

g-

g-

g-

trough, sloping towards

the west, traversed by a

*

small rivulet.

Soil ; Very fresh, deep hu-

mus ; rich.

Wood : Open beechwood,

120 — 140 years old, with

long boles, under which a

good quantity of beech

advance-growth up to 10

years old.

M

7

7-34

II

>f

Situation : South - western

10

g-

g-

slope, pretty steep.
Soil : Sandy loam, fairly
deep and fresh.
Wood : Beech regeneration,

with oak, ash and maple

here and there ; requires

filling up in parts. Over
the young growth stands

an open beechwood in the

final stage, 116 years old.

8

8-95

M

.,,

Situation : Western steep

50

g-

g-

g-

slope.

Soil : Stony, fairly fresh

and deep.

Wood : On 7 -12 acres, beecli

= •8, oak ='2, age 50— 60
years ; thinned in 1875.

•69 acres and 1'14 acres

are two groups on western

edge containing beech =

•8, sycamore = '1, spruce

and larch ='1, aged 27

years ; thinned in 1881

for first time.

9

3-66

Situation and Soil : As in

75

g-

g-

g-

Compt. 8.

Wood : Beech ; thinned in

1875.

Kohlwald

10

10-68

II

„

Situation: Western fairly

75

m.

g-

m.

86-48

APPENDIX A.

353

[g. =good; m. = middling ; b. =bad.]

BLOCK.

Com-
part-
ment.

Area.
Acres.

Quality
of
locality

Work-
ing

section

DESCRIPTION OF COMPARTMENT.

GROWING STOCK.

Age in

J868.

Growth

Den-
sity.

Quality

Br. forward

86-48

II.

I.

steep slope, partly a

ridge.

Soil : Very stony, a good
part shallow and dry.

Wood: Beech =-9, oak =

•1, of moderate- growth,

especially on the ridge ;

last thinned in 1884—85.

Kohlwald

11

870

3 )

Situation : Western and

75

g

g-

g-

north-western steep slope.

Soil : Stony and covered

with debris of rock, but

mostly deep.
Wood: Beech =-9, oak='l;

last thinned in 1884—85.

12

12-65

J J

Situation : Western anil

75

m.

m.

m.

south - western slope,

steep.

Soil : Stony, on the ridge -

shaped south - western

parts shallow and dry.

Wood: 70—80 years old

beech, with some oaks

and a few conifers. The

covering of the soil pierced

by much grass.

|f

13

3-43

Situation : Western slope,

80

g.

g.

g.

moderately steep, some

depressions.

Soil : Fresh, humus-rich,

deep.

Wood : Beech, last thinned

in 1880 ; a few oaks.

Sausudel

14

6-99

))

Situation : South - western

10

g.

g.

g.

and southern steep slope.

Soil : Stony, fairly fresh.

Wood: Beech =7, oak =

= '2, Scotch pine, larch

and spruce ='1. In de-

pressions also some small

groups of ash.

15

6-82

>5

Situation and Soil : As in

16

g.

g.

g-

Compt. 14.

Wood: Thicket, the result

of natural regeneration,

containing beech ='6,

125-07

854

APPENDIX A.

[ g. =good ; m. = middling ; b. =bad.]

BLOCK.

Com-
part-
ment.

Area.

Acres.

Juality
ocality

Work-
ection

DESCRIPTION OF COMPARTMENT.

GROWING STOCK.

&s

Srowth

Den-
sity.

Quality

Jr. forward

125-07

II.

I.

oak = -2, Scotch pine,

larch, ',and a few ash =

•2. Some small stony

patches have been filled

up with spruce.

jaubhecke

16

6-67

Situation : Western and

65

m.

m.

m.

south-western slope, here

and there ridges.

Soil : Stony, here and there

shallow.

Wood: Beech with single

oaks, 60 — 70 years old.

In the south-eastern part

of the compartment about

1£ acres 22 years old

(beech = '5, spruce = '2,

larch ='3), once thinned.

17

3-81

„ Situation : Gentle western

70

m.

m.

m.

slope, with depressions.
Soil : Sandy loam, rather

stony, mostly deep.

Wood: Beech ='9, oak =

•1, with single birches ;

thinned in 1876.

18

5-29

Situation : Western slope,

70

g.

g.

g-

moderately steep with de-

pressions.

Soil: Fairly fresh, with a

good covering of leaves.
Wood: Beech =-8, oak =

•2 ; thinned last in 1880.

19

5-54

Situation : Western slope,

75

m.

m.

m.

moderately steep partly

in ridges.

Soil : Stony, here and there

covered with bilberry.

Wood: Beech =-9, oak='l,

with single Scotch pines ;

thinned in 1876—78.

Grosses

Kopfchen

20

10-58

j.

Situation : Ridge sloping

82

m.

m.

m.

gently towards the west,

with its northern to west-

ern steep slopes.
Soil: Sandy loam, stony,

on the top of the ridge

shallow.

156-96

APPENDIX A.

355

[g.=good; m. = middling ; b. =bad.]

BLOCK.

Com-
part-
ment.

Area.

Acres.

Quality
of
locality

Work-
section

DESCRIPTION OF COMPARTMENT.

GROWING STOCK.

Age in
1888.

Growth

Den-

sity.

Quality

Br. forward

156-96

II.

I.

Wood : Beech = -9, oak and

Scotch pine="l. In the

southern part on about l£

acres regeneration cuttings
have been commenced,

with incomplete 6 years
old growth of beech ; the

rest fully stocked, requir-

ing thinning.

Kleines

Kopfchen

21

3-19

ii

5>

Situation : Western slope,

13

g-

g-

g-

moderately steep.

Soil : Loamy sand, fairly
fresh and deep, with few

stones.

Wood : Beech, the result of

natural regeneration, with
an admixture of oak='l,

and Scotch pine =-2. The

mother trees were removed

in 1883,

Total area un-

der Wood .

160-15

Roads & Rides

4-47

Total area of

Forest . .

164-62

A A 2

356 APPENDIX A.

GENERAL WORKING PLAN OP THE HIGH FOREST WORKING

Block.

1

Com-
part-
ment

Area,
Re-
duced
Acres.

Age
in

1888.

3UALITY OF

LOCALITY

ALLOTMENT OF WOODS TO

I. Period.
1888—1907.

II. Period.
1908—1927.

III. Period.
1928—47.

No.

Pro-
por-
tional
Figure

Re-
duced
Area.
Acres.

Mean
Age
when
Cut
Over.

Re-
duced
Area.
Acres.

Age
when
Cut
Over.

Re-
duced
Area.
Acres.

Age
when
Cut
Over.

Tarrenfeld
leimaths

lohlwald

Sausudel
Laubhecke

Grosses
Kopfchen

Kleines
Kopfchen

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

21

18-78
7-98
5-76
10-68
9-44
3-21
7-34
8-95
3-66
10-68
8-70
12-65
3-43
6-99
6-82
6-67
3-81
5-29
5-54
10-58

3-19
160-15

s

80
60
60
40
15
30
10
50
75
75
75
75
80
16
16
65
70
70
75
82

13

ole H
II.

forkin
1-0

g Section : Mixed Broad-It

aved j
8-78

7-98

tfigh
130

110

...

...

3-21

140

10-68

8-70

105
105

...

...

12-65
3-43

85

90

6-67

115

3-81
5-29
5-54

100
100
105

10-58

92

29-87

34-02

33-42

Remarks. — The areas which have been shifted from

APPENDIX A.

857

SECTION OF THE COMMUNAL FOREST OP KRUMBACH.

THB SEVEKAL PERIODS.

REMARKS.

IV. Period.
1948— 67.

V. Period. 1968—87.

Blanks.

With
Overwood.

Without
Overwood.

Re-
duced
Area.
Acres.

Age
when
Cut
Over.

Re-

duced
Area.
Acres.

Age
when
Cut
Over.

Re-
duced
Area.
Acres.

Age
when
Cut
Over.

Re-
duced
Area.
Acres.

Forest, with Conifers here and there.

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.

» » 5>

Shifted to provide for the I. period.

» >j »

Shifted to relieve the II. period.

Shifted to provide for IV. period.
Mean area of period = — °^ = 32-03

5-76'
10-68

8-95
3-66

130
110

120
146

6-18
7-34

105
100

3-26

105

6-99
6-82

106
106

...

...

3-19

83

32-24

13-52

•^

~30-5<

17-07
)

their proper age class are printed in italics.

358

APPENDIX A.

I. LIST OF WOODS ALREADY UNDER REGENERATION IN 1888 AND QUAN-
II. LIST OF WOODS SELECTED FOR UTILIZATION AND

Serial
Number

Block.

Com-
part-
ment

AREA, ACRES.

Species.

AGE.

Work-
ing

Section.

TREES TO BE
LEFT AS
STANDARDS.

Actual.

Re-
duced.

In

1888.

At the
Time of
Cutting
(mean).

Species.

No.

I. Woods already under

1

Heimaths

5

9-44

9-44

Beech

104

107

I.

Oak

16

Scotch
pine

104

107

...

...

2

Heimaths
Total

7

7-34

7-34

Beech

116

119

...

...

16-78

16-78

II. Woods to be Cut and Regenerated

1

Heimaths

6

3-21

3-21

Beech

130

140

I.

Oak

3

2

Kohlwald

12

12-65

12-65

Beech

75

85

...

...

...

Oak

71

81

...

Oak

150

Conifers

70

80

...

...

...

3

Kohlwald

13

3-43

3-43

Beech

80

90

...

Oak

11

4

Grosses
Kopfchen

20

10-58

10-58

Beech

90

100

I.

Oak

54

Total .

Scotch
pine

80

90

L

...

...

29-87

29-87

APPENDIX A.

359

TITY OF OVERWOOD REMAINING IN THEM IN THE BEGINNING OF 1888.
REGENERATION DURING THE PERIOD OF 1888—1907.

YIELD IN SOLID CUBIC FEET.

BEGENERATIOK.

Remarks.

Estimate.

Ac-
tual
Re-
sult.

Natu-
ral.
Acres.

ARTIFICIAL.

Present
Volume.

Incre-
ment.

Total.

Mean
per
Acre.

Manner of
Formation

Species.

Area.
Acres.

Regeneration in 1888.

5238
232

151

7

5389
239

1 596

...

5-00

Planting

f Oak

(. Spruce

}~

Increment
5238 X3
"104
= 151

8091

209

8300

1131

...

4-50

Planting

f Oak
J Ash

^Spruce

1 2-84

8091 o

mx3

= 209

13,561

367

13,928

9-50

7-28

during the Period o/ 1888— 1907.

19,827
33,237
4444

1525
4432
626

21,352
37,669

5070

6659

[3442

2-00
7-50

Sowing
Sowing

Oak

. Scotch
I pine

j Larch

1-21

}5-15

19827 vlft

130 "
= 1525

706

101

807

J

Spruce

14,575

1822

16,397

4780

2-00

Sowing

Oak

1-00

Planting

Ash

•43

, Larch

36,279

4031

40,310

I 3957

6-00

Planting

J Spruce

4-58

1384

173

1557

J

Scotch
V pine

110,452

12,710

123,162

4123

17-50

12-37

300

APPENDIX A.

YIELD TABLE

OF

INTEEMEDIATE RETURNS FOR BEECH IN THE
KRUMBACHER COMMUNAL FOREST.

IN the absence of sufficient data for a local yield table, the normal
yield tables of Dankelmann have been used, after determining the
quality by means of the average height of the woods. Based upon
the latter, it has been ascertained that the Krumbacher Communal
Forest belongs to the IVth Quality of Dankelmann's yield tables for
the beech.

Small modifications were introduced, especially because it is
desired to increase the proportion of oak, ash, and conifers, a circum-
stance which necessitates a moderate increase in the yield of the
thinnings as compared with pure beech woods.

YIELD-TABLE.

Age Class.

Mean height of dominant part
of Wood at end of age class,
in feet.

Yield of Thinnings
c' solid per acre.

21— 30

16

170

31— 40

28

200

41— 50

38

230

51— 60

44

245

61— 70

49

260

71— 80

52

230

81— 90

54

200

91—100

—

155

Total . . .

1690

This table has been used to calculate the expected yield of thinnings

APPENDIX A.

361

during the next 20 years. The details have been omitted ; the total
volume amounts to 50,402 cubic feet.

CALCULATION or YIELD FOR THE I. PERIOD, 1888-1907.

Sources of Yield.

SOLID CUBIC FEET.

Yield.

Grand
Total.

Mean
Annual
Yield.

Detailed.

Total.

a. Thinnings .....
Z>. Other intermediate yields . .

c. Balance in woods already under
regeneration ....

d. Final yield of woods to be re-
generated

* To be deducted as remaining at end
of period

e. Balance of d to be cut . . .
/. Total of c and e .
Total of all yields . . .

50,402

50,402

50,402
115,298

2,520

5,765

13,928

13,928
101,370

123,162

21,792

...

...

165,700

8,285

* The calculation is made as follows : — Regeneration period = 10 years. Mean
volume per acre of woods in first period = 4123 cubic feet. Remains, when seeding
cutting has been made = 4123 x '6 = 2474 cubic feet. It is assumed that the 2474
cubic feet are cut away in annually equal shares of y^th, that is to say = =

1 f?A*1 ^

247 '4 cubic feet annually ; hence the ten coupes, of — — — acres of area each, will

100

have per acre at the end of the period volumes equal to

X. Coupe.
2474

IX. Coupe.

VIII.

"To"

ii.

24,74
10

= 247-4

Total = 160'15 x — (2474 + 247 -4) = 21, 792 cubic feet.

362

APPENDIX

GENERAL WORKING PLAN FOB THE METHOD OF PERIODS BY VOLUME, AND

DATA OF THE KRUMBACHER

Block.

Com-
part-
ment.

Area,
in
Acres.

AGE OF WOODS.

Final
Yield
per Acre,
in Cubic
Feet.

ALLOTMENT OF WOODS

Present,
in 1888,
Years.

Final.

I.
Over 80
Years.
1888-1907

II.

61-80.

1908-1927

III.

41-60
1928-1947

Volume in Cubic

Farrenfeld .

1

18-78

80

90

5045

94,745

...

...

2

7-98

60

110

6045

...

...

48,239

Heimaths .

3

4

5-76
10-68

60
40

130
110

6817
6045

...

5

9-44

15

105

5809

...

...

6

3-21

130

140

7117

22,846

...

...

7

7-34

10

100

5573

...

...

8

8-95

50

ISO

6460

...

...

...

9

3-66

75

145

7267

...

...

Kohlwald .

10

10-68

75

105

5809

...

62,040

...

11

8-70

75

105

5809

...

50,538

...

12

12-65

75

125

6638

...

...

83,971

13

3-43

80

90

5045

17,304

...

Sausudel .

14

6-99

16

106

5856

...

...

15

6-82

16

106

5856

...

...

Laubhecke .

16

6-67

65

115

6252

...

...

41,701

17

3-81

70

100

5573

...

21,233

18

5-29

70

100

5573

...

29,481

...

Grrosses
Kopfchen .

19

20

5-54
10-58

75

82

105
92

5809
5151

54,498

32,182

...

Kleines
Kopfchen .

Total . .

21

3-19

13

103

5715

...

...

...

160-15

189,393

195,474

173,919

SemarJt.—The compartments which have been shifted

863

B.

FOR THE METHOD BY AKEA AND VOLUME COMBINED, APPLIED TO THE
COMMUNAL FOREST. (See page 315.)

TO PERIODS.

Kemarks.

AREAS PLACED INTO THE SBVEBAC PERIODS.

Remarks.

IV.

21-40.
1948-1967.

V.

1-20.

1968-1987.

I.

II.

III.

IV.

V.

Feet.

...

...

18-78

...

...

...

...

...

7-98

39,266

...

...

5-76

64,560

57,817

54,837
40,906

...

...

...

10-68

9-44
7-34

3-21

...

...

...

8-95

26,597

...

...

3-66

...

...

10-68

...

...

...

8-70

...

40,933
39,938

...

3-43

12-65

6-99
6-82

6'67

...

...

3-81

...

5-29

...

...

5-54

...

18,231

...

10-58

3-79

188,240

194,845

36W

84-02

27-30

29-05

33-78

from their proper age classes are printed in italics.

364

APPENDIX C.

WORKING PLAN FOR A PORTION OF THE STATE
FORESTS OF THE HERRENWIES RANGE

IN THE BLACK FOREST, GRAND DUCHY OF BADEN.

(PEEIOD 1884—1893.)
WITH THE RESULTS OF THE ACTUAL WORKING.

GENERAL DESCRIPTION.

1. Area and Boundaries.
The areas are recorded as follows : —

(a} Productive area . . . . . 1,747 acres

(&) Unproductive area . . . • • * •• n^- »
(c) Other areas, including fields, meadows, etc. . 2 „

Total area . . = 1,749 acres

Alterations in the above figures will probably become necessary
when a fresh survey is made.

The outer boundaries are in order, but the internal boundaries
require rectification.

2. Locality.

The forest here in question occupies on the whole the slopes lying
between a hill range on the south and the river Schwarzenbach
on the north. The highest point of the hill range, the Hoher
Ochsenkopf, has an elevation of 3,465 feet above the sea, while the
lowest part, near the Schwarzenbach, is only 2,000 feet above the
sea, the mean elevation being placed at 2,600 feet.

The slopes, on which the forest is found, are mostly steep, level
spots being only found on the summits of the hills, and towards the
lower end, where granite and Bunter Sandstein meet.

The area is drained by the Schwarzenbach (a feeder of the
Raumiinzach) with its two feeders, the Gartenbach and Dobelbach.

APPENDIX C. 365

The first mentioned runs from west to east, and the two latter, more
or less, from south-west towards north-east. It follows that the
forest in the valley of the Schwarzenbach has generally a north
aspect, and in the valleys of the Gartenbach and Dobelbach a north-
west aspect on one side, and a south-east aspect on the other side of
the streams. All the forest areas (except those situated at the highest
elevations and which are of no importance) are protected by inter-
vening ranges against the prevailing winds.

Up to a mean elevation of 2,500 feet, .granite is the principal
rock, which is sometimes (though rarely) pierced by porphyry.
Above the afore-mentioned elevation the granite underlies upper
Bunter Sandstein (Yogesen Sandstein), and the latter accordingly
prevails in the larger part of the forest area.

The granite is generally rich in orthoclase and oligoclase, and
therefore decomposes readily, and furnishes mostly a deep soil rich
in mineral elements. The decomposition is facilitated, and the
quality of the soil improved,, by the remarkably numerous springs
which appear between the granite and the Bunter Sandstein. Hard
slow decomposing quartzite is of rare occurrence.

The Bunter Sandstein is characterized by rapidly and greatly
changing mineral composition, consisting sometimes of readily
decomposing - rock yielding a deep clay soil, in other cases of hard
quartz-gravel, frequently found on the surface in the numerous
boulder-drifts. The Bunter Sandstein has numerous rents and
fissures in all directions, so that it is rapidly drained, and the dis-
integration and decomposition are only rarely assisted by springs,
which at the best are scanty and intermittent. It follows that the
Bunter Sandstein soils, even when formed by the easily decomposed
and minerally rich clay sandstone, never equal the best quality of
the granite soil ; moreover, they change frequently and very sud-
denly, and without any visible cause, into almost unproductive areas.
On the flat hill tops, layers of fine white sand (produced by the
disintegration of the gravelly sandstone) frequently produces an
impermeable stratum, preventing the water from percolating, thus
causing bogs (or "Grinde") which often extend over considerable
areas and are almost unproductive.

The quality of the soil, therefore, ranges between good and
unproductive, in the following proportion : —

Good and fairly good to medium = 78 per cent.
Medium to indifferent = 12 „

Indifferent to unproductive = 10 „

366 APPENDIX C.

The climate is rough, and is characterized by long winters with an
abundant snowfall, and by rapid changes of temperature ; at the
same time it is throughout favourable for forest vegetation, especially
for conifers.

The details will be found in the description of compartments.
Generally speaking, the spruce and silver fir are the prevailing trees, the
former being more abundant in the middle and upper parts, the latter
at the lower elevations. The beech is associated with them locally
and in varying proportions. Scotch pine is found in the granite region
chiefly upon dry, steep, rocky slopes with a southerly aspect, and in
the sandstone region, especially on dry ridges and the top of the
mountains, as well as here and there in other localities. The three
conifers attain a maximum height of 140 feet, with regular shaped
and little tapering stems. Towards the upper limit of the area the
height growth diminishes rapidly, dwindling down to 20 or even 15
feet on the high plateaux. Here the mountain pine and the birch
are also found. Reproduction is generally good, except at the higher
elevations. A marked difference is found between northern and
southern slopes, the growth and reproduction being far more
vigorous on the former than on the latter.

The silver fir is much exposed to cancer. Windfalls and snow
breakage are fairly moderate, while the damage from insect attacks
is very small. During the years 1874-83, the following proportion
existed between the different classes of fellings : —

Cuttings caused by insect attacks = 1 per cent, of total fellings

„ „ snow breaks = 12 „ „ „

„ „ windfalls =16 „ „ „

Cancer and other diseases and injury = 19 „ „ „

Other cuttings = 52 „ „ „

Total = 100

4. Method of Treatment and Rotation.

The situation and the species necessitate the area being treated
under the high forest system. The quality gradations, as indicated
under 2, are so conspicuous locally that it is possible (as well as
desirable in order to secure a proper idea of the condition of the
forest), to group the growing stock according to its characteristics
as produced by the quality of the locality, and according to the

APPENDIX C. 3fi7

method of treatment thereby indicated. The actual basis of this
grouping is the yield, and based upon it, the net income or financial
result of the management. In this sense the forest may be divided
into the following three groups : —

a. Areas subjected to an intensive Management. — To this group
belong all areas which, in virtue of their quality (as indicated mainly
by the height growth of the trees on fully stocked areas) are capable
of producing large timber ; areas on which carefully conducted
regeneration fellings will produce natural regeneration within a
reasonable period of time, and where the cost of any artificial
assistance in regeneration is. commensurate with the anticipated
returns. As lowest limit of this group a normal increment of
43 cubic feet per year and acre, calculated for a rotation of 120
years, has been fixed. The area thus included in the group amounts
to 78 per cent, of the whole. It is with this area, and the growing
stock standing on it, that the management must more especially
reckon, and from which the largest possible sustained yield must be
secured. With a suitable composition of the growing stock and a
careful application of sylvicultural principles, that object may be
obtained under an average rotation of 120 years.

As regards the sylvicultural treatment, and especially the regenera-
tion of the woods, two different classes of forest or growing stock
(corresponding with two qualities of locality) stand out prominently.
First: Forest of spruce with a strong admixture of silver fir (the
latter occasionally predominating) more or less frequently
interspersed with beech and more rarely with Scotch pine.
Secondly: Forest in which spruce predominates with a slight
admixture of silver fir and here and there of Scotch pine, but
devoid of beech.

The first class of forest occurs in the granite area and on those
parts of the Bunter Sandstein (clay sandstone), which have deep
easily decomposed soils fit to be classed as good. The characteristic
features of this class of forest are the occurrence of beech and deep
soils, rarely covered with boulders or debris, lying mostly at the lower
elevations ; natural regeneration can here be successfully effected in
a comparatively short period of time.

The second class of forest occupies the stony slopes of the Bunter
Sandstein area, and in exceptional cases the quartzite parts of the
granite area. Here the soil is generally covered with loose boulders
and rock debris of varying size. These areas are nearly all found at
the middle to upper elevations. The conditions described demand

APPENDIX C

the maintenance of an uninterrupted canopy up to the age of
maturity, and a careful execution of the regeneration cuttings spread
over a prolonged period of time, or else weeds will spring up, which
make regeneration very difficult, and at any rate expensive.

On the whole, however, careful management is sure to be successful
in securing natural regeneration in all the areas pertaining to this
group ; for this purpose, as well as for the production of valuable
timber, a rotation of 120 years on an average is considered of
sufficient length. The length of the regeneration period differs
considerably in the different parts, varying on the whole from 30
to 50 years.

~b. The, second group consists of woods growing on soils, which, even
under the most careful management, cannot be expected to produce
trees of first or even second quality. The trees here produced are
of such limited height growth, that the production of valuable timber
is out of the question. The woods are found in the upper, and here
and there in the lower part of the Bunter Sandstein area, where the
soil is covered with large masses of the debris of gravelly sandstone,
which is not easily decomposed, and where the slightest interruption
of the canopy overhead is followed by the appearance of a dense
growth of bilberry and heather.

Nevertheless, these areas are capable of yielding timber of the
inferior classes, as well as firewood, and the returns which may
reasonably be expected from them, justify the application of a method
of treatment which, while avoiding any interruption in the canopy
and all expensive cultural operations, facilitates natural regeneration ;
in other words the treatment under the selection system by removing
all trees which are deteriorating or incapable of increasing in value.
It is difficult to fix any definite rotation, but it is estimated that the
trees will take about 150 years to reach maturity.

The lowest quality limit for this group has been fixed at 7 cubic
feet increment per acre and year, while the upper limit is, as already
indicated, 43 cubic feet. The area comprised in this group amounts
to 12 per cent, of the total area.

c. The third group comprises the so-called " Grinden," that is to
say the highest parts of the ridges, which are mostly level and have
a tendency to bogginess. They are covered by a dense growth of
bilberry and heather, and are incapable of producing more than a
stunted tree growth, which yields only a scanty quantity of firewood,
frequently not covering the price of preparing it ; hence financial
considerations are entirely out of the question, the areas being pro-

APPENDIX C. 369

tected merely for the sake of preserving some cover on the hill tops.
The group comprises all parts which produce an annual increment
per acre of 7 cubic feet and under ; they amount to 10 per cent, of
the total area.

In so far as the management aims at the production of valuable
material, and at favourable financial results as regards outlay for
artificial regeneration (where natural regeneration has failed), for
improvement, tending, etc., only the areas in the _first group can be
considered. But in the treatment of those forests which pertain to
the principal mountain region of the Black Forest, representing a
certain drainage area, the task of forestry goes beyond mere financial
considerations. It has in fact been recognized that it is necessary
to keep areas of this class well wooded for the sake of a proper
husbanding of the water supply in the streams. Accepting this
further task, the forest administration has endeavoured, during the
last 50 years, to afforest the poorly stocked and frequently entirely
bare areas at the higher elevations of the Bunter Sandstein region.
In so far as the cultural operations were confined to the boulder
drifts of the Bunter Sandstein, they were moderately successful, but
the cultural attempts made in the " Grinden " prior to 1870 turned
out failures. Since 1873 the cultural operations in the Grinden
present a more hopeful aspect, owing to the experience gained by
former failures, and it seems desirable to continue them in the
future.

The working plan deals in detail only with the forest area subjected
to intensive management, but the group worked under the selection
system has also been adequately noticed in the general provisions.

The working plan lays special stress upon the execution of
improvement fellings, more particularly the removal of cancerous
silver firs. For this purpose the ordinary thinnings are utilized ;
but over and above these, cancerous trees must also be removed
from the old woods, where otherwise no further thinnings would be
required. In regeneration fellings the trees to fall first under the
axe must be those attacked by cancer. Even then not nearly all
cancerous trees can be removed during the next ten years. This
fact teaches the management that in future a sharp attack must be
made on all cancerous trees at the time of the first and second
thinnings, even if a temporary interruption of the canopy should
thereby be caused. On the rich deep soils of the granite area, which
are almost exclusively concerned in these remarks, even an interrup-
tion of the canopy extending over a somewhat lengthy period would

VOL. III. B B

370

APPENDIX C.

not be a misfortune, and preferable to the maintenance of a full
canopy consisting to a considerable extent of cancerous trees. The
existence of enormous quantities of such trees on the granite
area was one of the reasons which led to the yield being fixed at its
present rate.

5. Utilization.

a. Yield of Major Produce.

The actual yield during the last 40 years has been as follows : —

Compartment.

YIELD, IN SOLID CUBIC FEET.

1844-53.

1854-63.

1864-73.

1874-83.

Total.

Area in
Acres.

1. Schwarzenbronn .

213,836

122,369

149,843

79,141

565,189

65

2. Schwarzenberg .

311,518

158,778

200,733

158,955

829,984

211

3. Riesenkopf . .

12,502

47,288

206,242

65,617

331,649

76

4. Mehliskopf .

—

—

—

—

—

34

5. Griinwinkel . .

19,742

124,629

57,423

202,252

404,046

202

6. Dobelbach .

26,875

42,697

30,195

69,925

169,692

178

7. Hoher Ochsenkopf

—

—

—

—

—

101

8. Kleingartenkopf .

34,256

2,331

1,448

1,024

39,059

76

9. Kleingarten

375,687

138,825

256,603

195,578

966,693

362

10. Grossgarten . .

62,544

46,688

26,417

59,118

194,767

175

11. Sachsenbronn

34,927

47,783

111,351

106,194

300,255

96

12. Gartenbach . .

86,311

83,345

494,665

156,412

820,733

172

1,178,198

814,733

1.534,920

1,094,216

4,622,067

1747

Average per year
Average per year and
acre . . . .

117,820
67-44

81,473
46-64

153,492
87-86

109,422
62-63

115,552
66-14

From the appended statistical table it will be seen that the
estimated increment of the next ten years amounts to 1,086,130
cubic feet.

The actual growing stock amounts to 9,488,731 cubic feet
The normal „ 7,892,160 „

The surplus of

1,596,571

APPENDIX C. 371

The surplus of growing stock is due to a surplus of woods over
100 years old. With favourable prices for timber, the removal of
this surplus in the shortest possible time would be advisable, so as
to prevent loss of increment, and take unnecessary capital out of the
forest, but as prices run low at present, it appears judicious to keep
the greater part of it over for a while.

A consideration of the several compartments showed that the
removal of the following material during the. next ten years is
advisable on sylvicultural grounds : —

Final cuttings . . . 1,146,000 cubic feet
Intermediate cuttings . 154,000 „

Total . . 1,300,000

As this amount exceeds the expected increment by 213,870 cubic
feet, equal to about -fth of the surplus of growing stock, the yield has
been fixed at 1,300,000 cubic feet, or annually :—

Final cuttings . . . 114,600 cubic feet
Intermediate cuttings . 15,400 „

Total . . 130,000 cubic feet.

If in the course of the 10 years prices should rise, there would
be no objection to reduce the surplus of growing stock further by
additional cuttings.

The disposal of the yield is effected as follows : —

(1) Free grant to the Roman Catholic Priest

at Herrenwies . . ... . 1,500 cubic feet

Free grant to the Eoman Catholic School

at Herrenwies . . . . . = 1,000 „

(2) Sale by public auction and occasionally

by private sale . . . ' . . = 127,500 „

Total annual disposals . -. 130,000 „

&. Minor Produce.

The principal items are forest pasture and the removal of litter,
the utilization of which is permitted to the Herrenwies settlers, as a
privilege.

According to Government orders the privilege of forest pasture
may be exercised only to such extent as the condition of the forest
and the requirements of regeneration may permit. The district

B B 2

372

APPENDIX C.

forest officer indicates from time to time the localities in which the
privilege may be exercised. The privilege of removing litter free of
charge is exercised under the same conditions. The exercise of these
privileges is nowhere injurious, and may be continued during the
next ten years.

The grass growing in blanks, on roads and in plantations has
hitherto been sold for the benefit of the State, and, under suitable
supervision, the practice may be continued.

The removal of building stones, the sale of plants, etc., is
insignificant.

6. Division into Compartments.

The contemplated new division into compartments must be post-
poned until the projected road system has been completed.

DESCRIPTION OF COMPAETMENTS.

Block and
Compartment.

Area in

Acres.

Description of Wood.

Name.

No.

I. Ochsenkopfe.

Schwarzenbronn

1

65

Spruce with silver fir, some beech,

Scotch pine, larch.

About -6 of area 30 — 50 years old, some

trees older.

About -4 of area 10 — 30 years old.

Above the road fairly complete stocking ;
in youngest parts still suffering from frost ;

below road still some blanks caused by

late cutting out of old trees ; in the latter

part still 120 — 150 years old spruce and

silver fir in the final stage ; these show a

decreasing increment. Growth on the whole

fairly good.

Schwarzenberg .

2

211

a = 130 acres ; 15 — 40 years old spruce

and silver fir with some Scotch pine and

beech ; some lately planted, younger, a few

up to 60 years old. About 25 acres planted.
Where the shelter wood has been removed,

stocking generally complete, in the rest
still patchy with patches of bilberry

intervening. Growth generally between

good and fairly good ; along Herrenwies

meadows partly only fair, the spruce

still suffering from frost. In the north-

western part, below the road, on the

Riesenkopf road, and in the south-east

along Dobelbach, on about 37 acres

110 — 140 years old spruce and silver firs

of decreasing increment are standing in

the final stage.

APPENDIX C. 373

DESCRIPTION OF COMPARTMENTS— continued.

Block and

Compartment.

Area in

Acres.

Description of Wood.

Name.

No.

b = 81 acres (in three parts), spruce

and silver fir with a few beech and

Scotch pine, generally 50 — 70 years old,

but some small groups only 30 — 50 years
old ; generally well stocked, here and

there somewhat thin and patchy. Growth

between good and fairly good. On 3 acres

on the Dobelbach, 80 — 90 years old spruce,

cover complete and growth good.

Riesenkopf

3

76

a = 47 acres ; 100 — 130 years old

spruce and silver fir, some older ; on the

whole cover fairly complete ; towards com-

partment Schwarzenberg somewhat thin,

but on about 10 acres with a fair young crop

of silver fir and spruce up to 15 years old.

Growth fairly good, on the higher part

inferior. About 5 acres along the road is

a windfall area, now stocked with some

silver fir and spruce growth.

b = 24 acres ; 9 — 20 years old spruce

(a few older), with some Scotch pine and

larch, mostly well stocked, showing good

to fairly good growth.

c = 5 acres ; Grinde, in upper part

heather covered, with 100 and more years

old short and stunted Scotch pine, some

spruce and mountain pine. On the whole

poorly stocked. Part underplanted with

20 — 40 years old spruce, which show very

poor growth.

Mehliskopf

4 ! 34

50 — 90 years old (and more), mountain

pine with some spruce, Scotch pine, birch

and mountain ash ; towards compartments

3 and 5 cover fairly complete, in the

southern and south-western parts inter-

rupted by larger and smaller areas of

heather. Growth inferior.

Grunwinkel

5 - 202

a = 186 acres ; 110 — 150 years old, some

older, spruce and silver fir, some beech

with a few Scotch pine. In irregular final
and seeding stage, in the southern part cover

still fairly complete in strips. On '4

of the area stocked with up to 30 years old

silver fir and spruce and a few beech.

Growth of old trees still fairly good ; on

some stony ridges (about 7 acres) middling

and inferior ; young growth mostly only

middling.

b = 16 acres on the highest part in the

south and west, Grinde ; heather-ground

374

APPENDIX C.

DESCRIPTION OP COMPARTMENTS— continued.

Block ami
Compartment.

Name.

Dobelbach

Hoher Ochsen-

Kleingartenkopf

No.

Area in
Acres.

178

101

Description of Wood.

with 100 and more years old crippled
Scotch pine, spruce, some mountain pine
and birch ; in some parts up to 60 years old
advance growth thinly stocked. Here and
there traces of plantings, 24 years old
spruce.

a = 133 acres ; 100—130 years old, some
up to 200 years, spruce and silver fir,
some Scotch pine ; on the whole cover
fairly complete ; only in the western
third along Grunwinkel through wind-
falls and dry wood cuttings somewhat
thin and patchy : in the thin parts as
yet little, up to 15 years old, advance
growth in single trees. Growth good to
fairly good. (Ilex found).

b = 27 acres (consisting of the upper
south-eastern portion and a ridge running
from it in a north-western direction to the
centre of the compartment), 100 — 130 years
old (some older), short-stemmed spruce
with some Scotch pine and silver fir
forming a thin, often very thin, wood ; in
parts younger up to 60 years old spruce,
or an incomplete miserable undergrowth
of 25 years old spruce and Scotch pine
(experimental planting). Growth middling
to inferior.

c = 18 acres (uppermost part on the
south) Grinde; heather-land with 100 years
and more old crippled Scotch pine, some
spruce, birch, thinly stocked ; here and
there remnants of 25 years old planted
spruce and Scotch pine.

70 and up to over 100 years old Scotch
pine and mountain pine with spruce,
some birch, sometimes forming a very
thin wood of single trees, sometimes in
smaller or larger groups ; everywhere
intersected by heather places and blanks.
Growth inferior, even crippled.

100 — 120 years old, in some parts younger,
some over 300 years old, spruce with
Scotch pine, few silver fir, some moun-
tain pine. In the western third and
on the eastern point still fairly well
stocked, some groups even well stocked ;
otherwise the wood is very thin and open.
Growth middling to inferior ; here and
there an incomplete miserable under-

APPENDIX C.

DESCRIPTION OF COMPARTMENTS — continued.

375

Block and
Compartment.

Area in
Acres.

Description of Wood.

Name.

No.

growth of 30 — 50 and more years old

spruce and Scotch pine (planted).

Kleingarten

9

362

a = 161 acres. Spruce and silver fir,

C

some beech. Mostly 50 — 80 years old, in

strips and single trees up to 100 years old,

others only 30 — 50 years old. In the

eastern part are about 50 acres 80—100

years old. Everywhere spruce and silver

fir standards up to 150 years old, mostly

showing good growth. Almost throughout

rather thinly stocked, here and there

patchy, in consequence of late final

cuttings and removal of cancerous silver

firs. Growth mostly good, only towards

the southern higher part decreasing.

& = 122 acres (in 3 places). Spruce and

15—40

silver fir with some beech, average _ 30

years old, some groups up to 50 years ;

mostly fully stocked. 120—150 years old

(some older) mostly pruned spruce and

silver firs in the final stage are standing

almost everywhere over the above younger

growth. The strip along Dobelbach is
finally cleared. Growth good ; of the old

trees fairly good.

c = 79 acres (upper part towards the

south), 120 — 300 years old pruned Scotch

pine and spruce, few silver fir and birch,
thinly stocked, often open ; on the whole

poorly undergrown with 20 — 50 years old

spruce (mostly planted), a few silver

fir ; the latter in some places form, with

up to 100 years old spruce, the picture of a
selection forest. Soil much covered with

heather. Growth middling to bad ; rarely

fairly good.

On 6 acres near compartment Dobelbach

on the main path, 100 and more years old

spruce, with a few Scotch pine and silver

fir, form a thin canopy and show

middling growth.

Grossgarten

10

175

a = 108 acres ; spruce and silver fir

80 — 110 years old, some up to 150, some

beech and a few Scotch pine. Partly

fully stocked, but the greater part some-

what thin, in the lower part very thin ;

and here spruce and silver fir advance

growth up to 50 years old in single trees

and groups. Growth good to fairly good ;

376 APPENDIX C.

DESCRIPTION OF COMPARTMENTS — continued.

Block and
Compartment.

Area in
Acres.

Description of Wood.

Name.

No

x

in the upper parts with stones (Halde),
partly middling only.

J = 37 acres. (Ridge through middle of

compartment and strip on south, south-

west, and north-west.) 90 — 110, some

up to 200 years old, spruce and Scotch

pine, some silver firs, in the uppermost

part some mountain pine in a thin, patchy,

and often very thin wood ; most of in-

ferior growth ; here and there traces of

30—40 years old spruce plantings.

c = 30 acres (adjoining compartment

Kleingarten). A wood resembling a selec-

tion forest, of spruce and silver fir with

beech, the trees 30 — 50 years old pre-

vailing ; little quite young. The 100 —120

years old and older trees appear single and
in groups. Growth good ; above the cattle

track inferior.

Sachsenbronn

11

95

100—120 years old (some up to 200

(and

years), spruce and silver fir, also some

2 acres

beech, namely : —

other

On 42 acres, final stage, partly pruned,

areas.)

throughout with years old (in the

20

western part up to 40 years old), silver

fir and spruce young growth ; about

25 acres in the position of the seeding

stage brought about by windfalls and

dry wood cuttings ; on 5 acres, 80—100

years old, generally complete cover ; in
the thinner stocked parts is found up to

15 years old silver fir and spruce young

growth ; on 12 acres (south-eastern corner,

near compartment Gartenbach) generally

canopy complete, here and there with a

little advance growth.

On 10 acres (in the west), 70—90 years

old, some older spruce with silver fir,

fairly complete canopy.

On 7 acres (western point), 12—40 years

old (in groups and single up to 60 years

old), mostly irregular young growth of

spruce with some silver fir, forming a

fairly complete stocking.
Growth of old trees good to fairly good,

in the pruned portions partly less good ;
growth of young wood fairly good.

APPENDIX C.

DESCRIPTION OF COMPARTMENTS — continued.

877

Block and
Compartment.

Area in
Acres.

Description of Wood.

Name.

No.

Gartenbach

12

172

110—140 years old spruce, silver fir,

some older, some Scotch pine, the latter

prevailing in places in the upper part, few

beech ; in the northern two-thirds in the

final stage, partly in seeding stage. In

these two-thirds about 85 acres are stocked

with young growth of spruce and silver

fir pretty completely, in the eastern part
very fully ; in the southern third still

fairly complete cover, but on the western
slope, already somewhat thin, as yet little

young growth. Growth in northern two-

thirds good, in the southern third good to

fairly good ; in the upper part, in the

south-east, only middling.

In the middle of the compartment are

3 windfall and 1 beetle clearing, together

12 acres ; of these, 7 acres fairly well

stocked with up to 25 years old spruce and

silver fir.

378

APPENDIX C.
TABULAE STATISTICAL EEPOET OF THE

COMPARTMENTS.

Name.

Number

DISTRIBUTION OF AGE'

1 — 40 years old.

Cubic feet.

sold. I 41-60. I 61—80.
AcreslCubic feetJAcresiCubic feet. Acres

_j _|

I. Working-Section = Yield-capacity over

Schwarzenbronn . 1 48,030 41 70,630 20

Schwarzenberg . . 2 200,945 117 169,514 40 192,117 40

Riesenkopf . . 3 19,072 34

Griinwinkel . . 5 21,189 38

Dobelbach . . 6

Kleingarten . . 9 109,479 87 201,299 37 423,787 67

Grossgarten . . 10 26,487 24 46,617 11 25,074 5

Sachsenbronn . . 11 28,605 51 35,316 5

Gartenbach . . 12 13,420 48

Total . - 467,227 440 488,060 108 676,294 117

Normal state under a
rotation of 120 years .

Comparison of real! +
and normal state . / -

II. Working-Section = Yield-capacity from

Dobelbach. . . . 6 1,770

Kleingartenkopf . . 8 10,595 25

Kleingarten . . . 9 10,948 25

Grossgarten . '. .10

Total 23,313 50

Normal state under
rotation of 120 years .

Comparison of real \ +
and normal state . / -

III. Working Section = Yield-capacity 7 cubic feet

Riesenkopf . . 3

Mehliskopf . . 4 18,900 34

Griinwinkel . . 5

Dobelbach . . 6

Hoher Ochsenkopf . 7

Total 18,900 34

Normal state under a
rotation of 120 years .

Comparison of real \ +
and normal state . j" -

Summary of the Three

Real state of forest . .
Normal state of forest .

Comparison of real \ +
and normal state . J -

APPENDIX C.

379

HEEEENWIES EANGE.

3

CLASSES.

Volume
per
acre,
cubic
feet.

INCREMENT.

81—100. | Over 100 years. | Total.

Annual, per acre.

Total in 10 years.

Cubic feet.

Acreslcubic feet.

AcresICubic feet.

Acres

Normal.

Real.

Normal.

Real.

45,500
158,250
43,310
132,060
94,430
220,740
117,300
67,450
147,920

15,892

353,'l56
494,418
42,379

1

4
2

49
49
5

3 cubic fe

34,250
118,662
381,408
1,606,861
1,522,104
540,329
365,870
459,103
1,373,758

1

et pe

4
12
37
148
133
43
49
34
124

r Acre an

152,910
697,130
400,480
1,628,050
1,522,104
1,628,050
958,466
565,403
1,387,178

auail

65
211
71
186
133
283
138
95
172

y.

2,352
3,304
5,641
8,753
11.444
5^53
6,945
5,952
8J065

85 .
' 85
70
85
100
100
85
100
100

70
75
61
71
71
78
85
71
86

55,250
179,350
49,700
158,100
133,000
283,000
117,300
95,000
172,000

905,845

105

6.402,345

584

8,939,771
7,456,200

1354

6,603
5,507

92

76

1,242,700

1,026.960

1,483,571

1,096

...

16

21
14
29
21

21

8,100
10,640
33,970
7,770

'5,740

5,670

10,640
22,910

7,770

7 tc

43 cubic

38,850
203,418
108,419
79,460

feet

27
51
54
37

per Acre

40,620
214,013
119,367
79,460

annu

27
76
79
37

ally.

1,504
2,816
1,511
2,148

30
14
43
21

430,147

169

453,460
362,880

219

2,071
1,657

28

60,480

46,990

90,580

414

7
7
7
7
7

'V

7
7
7
7
7

350
2,380
1,120
1,260
7,070

13,490

350

2,380
1,120
1,26C

7,070

12,180

1

md u

nder per

4,500

Acre
5

annually

4,500
18,900
11,300
7,400
53,400

95,500
73.080

5
34
16
18
101

900

556
706
411
529

...

...

11300
7^400
53,400

16
18
101

76,600

140

174

549
420

7

7

12,180

22,420

129

1,086,130

V

rorki

ng Sectioi

is.

9,488,731
7,892,160

1,315,360

1,596,571

229',230

1

380

APPENDIX C.
SPECIAL WOEKING PLAN.

COMPARTMENTS.

DESCRIPTION OF CUTTINGS,
CULTIVATION, &c.

CUTTINGS.

Cultiva-
tion.
Acres.

Draining,
ditches.
Feet.

Road con-
struction.
Feet.

Final.
Cubic
feet.

Inter-
mediate
Cubic
feet

1. Schwarzenbronn
2. Schwarzenberg .

3. Riesenkopf . .

4. Mehliskopf . .
5. Griinwinkel. .

f». Dobclbach . .

7. Hoher
Ochsenkopf .

8. Kleingartenkopf

Final cutting in regene-
rated part ...
Filling up blanks with
spruce
Thinning and cutting of
cancerous silver firs

Total .

a. Thinning of shelter. wood
and partial final cutting
Filling up blanks with
spruce and Scotch pine .
a & b. Thinning and re-
moval of cancerous trees

Total .

a. Seeding cutting, and
partly final cutting . .
b & o. Best.

Total ,
Rest.

a. Thinningof shelter-wood,
seeding cutting in the
fully stocked parts by the
removal of cancerous
and large trees
b. Rest.

Total . .

a. Thinning and removal
of cancerous trees .
b & c. Rest.
Construction of an export
road to meet the main
road . . . . .

Total .

Rest.
Rest.

34,000

10,000

3

34.000

10,000

8

35,000

53,000

10

35,000

53,000

10

53,000

53,000

318,000

318,000

4,900
4,900

19,000

19,000

19,000

19,000

...

APPENDIX C.

381

SPECIAL WORKING PLAN— continued.

COMPARTMENTS.

DESCRIPTION OF CUTTINGS,
CULTIVATION, &c.

CtTTTINGS.

Cultiva-
tion.
Acres.

Draining,
ditches.
Feet.

Road con-
struction.
Feet.

Final.
Cubic
feet.

Inter-
mediate
Cubic
feet.

9. Kleingarten . .

10. Grossgarten . .
11. Sachsenbronn .

12. Gartenbach

a. Cutting of all old stan-
dards and cancerous trees
Thinning . . . .

45,000

3,000

12

9,500

T). Thinning of shelter- wood
and partially final cutting
Filling up 'blanks with
spruce .
c. Cutting out of old de-
fective trees where young
growth exists . . .
Construction of an export
road to meet the main
road .

Total . .

a. Thinning and removal
of cancerous trees .
b. Rest.
c. Removal of standards
and cancerous trees . .
Thinning .
Construction of an export
road ....

Total . .

In the regeneration area :
thinning of shelter- wood
and partially final clear-
ing ; in the rest seeding
cutting .
Filling up blanks with
spruce . . . .
Construction of an export
road .

Total . .

Continuation of regenera-
tion cuttings and re-
moval of cancerous trees
Thinning in fully stocked
parts .
Filling up blanks with
spruce and Scotch pine.
Construction of an export
road

Total .

198,000
14,000

257,000

3,000 12

1

9.500

47,000
25,000

47,000
15,000

5,000

72,000

62,000

...

5,000

163.000

3

3,500

163,000

3

3,500
3 000

195,000

7,000

8

195,000

7,000

8

...

3,000

382

APPENDIX C.

SUMMARY OF THE PROVISIONS OF THE

Compartment.

PROVISIONS OF WORKING PLAN.

Cuttings.

Cultiva
tion.
Acres.

Drain-
ing.

Feet.

Road
Con-
struction

Final.
Cubic Feet.

Inter-
mediate.
Cubic
Feet.

Total.
Cubic Feet.

1. Schwarzenbronn . .

34,000

10,000

44,000 3

—

—

2. Schwarzenberg

35,000

53,000

88,000

10

—

—

3. Biesenkopf . . .

53,000

—

53,000

—

—

—

4. Mehliskopf

—

—

—

—

—

—

5. Grunwinkel . . .

318,000

—

318,000

—

—

—

6. Dobelbach

19,000

19,000

38,000

—

—

4,900

7. Holier Ochsenkopf .

—

—

—

—

—

—

8. Kleingartenkopf

—

—

—

—

—

—

9. Kleingarten . . .

257,000

3,000

260,000

12

—

9,500

10. Grossgarten

72,000

62,000

134,000

—

5,000

11. Sachsenbronn . .

163,000

—

163,000

8

—

3,500

12. Gartenbach
Total

195,000

7,000

202,000

8

—

3,000

1,146,000

54,000

1,300,000

«|..

25,900

Note. — The excess was due to heavy windfalls ; it will not derange future

APPENDIX C.

383

WOKKING PLAN AND OF THE EXECUTION.

COMPARISON OF

RESULTS OF ACTUAL WORK DONE.

PROPOSED AND Ex-<

ECUTED CUTTINGS.

i

Cuttings.

T> ,._ J

Remarks.

Culti-
vation
Acres.

Drain-
ing.
Feet.

xio&cL
Con-
struc-
tion.
Feet.

Cut too
much.
Cubic
Feet.

Cut too
little.
Cubic
- Feet.

Final.
Cubic Feet

Inter-
mediate.
Cubic

Total.
Cubic Feet

Feet.

33,034

12,549

45,583

4-4

—

—

1,583

—

54,517

75,000

129,517

5-0

—

—

41,517

—

Excess due to
windfalls and

snow break.

132.900

132,900

•1

: —

79,900

Excess due to

windfalls and;

snow-break.

177,169

177,169

•1

_

140,831

Held back, on

account of ex-

tra fellings in

other compts.

86,606

68,301

154,907

—

v _

5,003

116,907

—

Excess due to

—

—

—

—

—

—

—

—

windfalls.

342,444

21,635

364,079

8-4

:

9,679

104,079

:

Excess: wind-j

falls and con-

struction of

road.

95,852

—

95,852

—

—

5,299

—

38,148

Thinning held

over.

111,049

—

111,049: '9

—

3,691

—

51,951

Held back on '

account of ex-|

197,660

—

197,660 —

—

2,953

—

4,340

cess in other

1,231,231

177,485

1,408,716 18-9

—

26,625

108,716

—

c o m p el r T-
ments.

arrangements, as there is yet a considerable excess of growing stock in the forest.

384

APPENDIX C.

SAMPLE PAGE OF THE DETAILED CONTEOL BOOK.

1. Schirarzenbronn.

Year.

Description of Cuttings, Cultivation, etc.

CUTTINGS.

Culti-
vation.
Acres.

Drain-
ing
Ditches
Feet.

Road
Con-
struc-
tion.
Feet.

Final.
Cubic
Feet.

Inter-
mediate
Cubic
Feet.

Provision of Working Plan.

Final cutting in regenerated part

34,000

Filling up blanks with spruce

...

...

3

Thinning and cutting of cancerous
silver firs

10,000

Total ..

34,000

10,000

3

—

—

Execution.

1884

Final cutting

14,297

H

Dry and windfall wood

813

1885

Windfalls

665

1886

Final cutting, thinning

6,166

832

„

Windfalls . , . • .

547

1887

Windfalls . .

1,363

1888

Final cutting, thinning . . .

7,759

11,717

»

55

1889

Planting
Windfall

82
649

1-7

Dry wood, windfalls .

»

Planting . . . ...

...

...

2-2

1890

Windfalls . . . .

693

»»

Planting

...

•1

1891

Planting •...

•2

1892

Planting

•1

1893

Planting . . . . .
Total

...

...

•1

33,034

12,549

4'4

385

APPENDIX D.— TABLES.

THIS Appendix contains the following Tables : —

TABLE I. — Yield Tables used in the Kingdom of Saxony for the

determination of the Quality of Locality.
TABLE II. — Area of Circles for Diameters ranging from 1 inch to

60 inches.

TABLE III. — Volumes of Cylinders and the Sum of the Area of Circles
for Diameters ranging from 1 inch to 48 inches.

Example. — Find the volume of a log which has a
diameter in the middle of 15 inches and a length of
24 feet :—
Volume of 20 feet length

= 10 x 2-4544 . . = 24-544 cubic feet.
Volume of 4 feet length .= 4'9088 „ „

Total . . = 29-4528 „ „

In the same way : Area of
24 circles of 15 inches
diameter . . , = 2 9 '452 8 sq. feet.

TABLE IV. — Tables of Compound Interest : —

A. Amount to which a capital accumulates with com-

pound interest in n years : — Cn = C0 X l'opn.

B. Present value of a capital to be realized after

n
C. Present value of a perpetual rental due every

D. Present value of a rental due at the end of every
year, altogether n times, C0 = ^'n

If the rentals refer to the past n years, the positions in this
Table must be multiplied by the corresponding values of I' op*,
to be taken from Table IV., A., so as to comply with the formula :

r _r(l-opn-l}
i_/0 — - .
•op

VOL. III. C 0

386

APPENDIX D.

I. YIELD TABLES USED IN SAXONY FOB THE DETERMINATION
For One Acre of a normal, or fully stocked, wood in solid cubic feet, including

Oak.

Beech.

Age,
Years.

Quality classes, in solid cubic feet.

Age,

Years.

Quality classes, in solid cubic feet. »

I.

II.

III. IV.

V.

I. II. III.

IV.

v.

10

290

240

200

140

70

10

330

290

240

190

100

20

740

610

490

360

200

20

800

660

510

390

200

30

1,270

1,060

840

630

330

30

1,310

1,160

900

640

330

40

1,870

1,560

1,210

930

470

40

2,160

1,760

1,360

960

470

50

2,560

2,120

1,670

1,250

640

50

3,020

2,440

1,870

1,300

630

60

3,320

2,750

2,170

1,600

810

60

3,990

3,220

2,440

1,670

800

70

4,160

3,430

2,700

1,970

1,000

70

5,070

4,070

3,070

2,070

980

80

5,060

4,160

3,250

2,340

1,190

80

6,260

5,000

3,740

2,490

1,160

90

5,990

4,990

3,800

2,720

1,360

90

7,460

5,930

4,400

2,880

1,330

100

6,960

5,660

4,360

3,070

1,520

100

8,570

6,800

5,030

3,260

1,480

110

7,950

6,430

4,920

3,420

1,670

110

9,620

7,650

5,590

3,570

1,600

120

8,950

7,220

5,480

3,740

1,800

120

10,580

8,330

6,090

3,840

1,700

130

9,900

7,950

6,000

4,060

1,930

130

11,450

8,990

6,530

4,070

1,770

140

10,830

8,670

6,520

4,340

2,040

140

12,250

9,570

6,920

4,260

1,830

150

11,700

9,350

6,990

4,620

2,140

150

12,960

10,100

7,250

4,400

1,860

160
170
180
190
200

12,560
13,350
14,090
14,780
15,330

10,000
10,600
11,160
11,680
12,100

7,450
7,860
8,250
8,590
8,870

4,890
5,120
5,330
5,500
5,660

2,240
2,330
2,410
2,470
2,530

Example. — A fully stocked beech-
wood has a volume, when 60 years
old, of 3,220 cubic feet ; hence it
grows on a locality of the II. Quality.
Again, a fully stocked oakwood, 140
years old, shows a volume of 7,600
cubic feet ; hence it grows on a
locality between II. and III. Quality.

APPENDIX D.

387

OP THE QUALITY OF LOCALITY.
all wood above ground, but exclusive of roots and stumps.

Alder.

Birch.

Age,

Quality classes, in solid cubic feet.

Age,

Quality classes, in solid cubic feet.

Years.

Years.

I.

II.

III.

IV.

V.

I.

II.

III.

IV.

V.

10

860

690

510

340

160

10

670

530

400

260

110

20

1,800

1,440

1,090

730

340

20

1,410

1,110

820

540

230

30

2,800

2,260

1,700

1,160

540

30

2,360

1,860

1,360

860

390

40

3,820

3,070

2,330

1,580

760

40

3,370

2,660

1,940

1,230

540

50

4,790

3,860

2,930

1,990

950

50

4,300

3,390

2,470

1,560

690

60

5,730

4,630

3,520

2,390

1,130

60

5,120

4,020

2,920

1,810

790

70

6,640

5,350

4,050

2,730

1,300

70

5,740

4,490

3,230

1,970

840

80

7,530

6,050

4,560

3,060

1,460

80

6,230

4,840

3,460

2,070

870

90

8,360

6,720

5,040

3,370

1,600

100

9,100

7,300

5,470

3,640

1,710

Coppice of Alder, Poplar, Willow.

Coppice of Oak, Beech, Ash, Birch.

Age,

Quality classes, in solid cubic feet.

Age,

Quality classes, in solid cubic feet.

Years.

Years.

I.

II.

III.

IV.

V.

I.

II.

III.

IV.

V.

5

490

370

260

140

30

5

310

240

160

95

15

10

1,000

740

510

290

90

10

640

490

330

170

45

15

1,540

1,190

860

440

160

15

980

760

510

280

85

20

2,100

1,640

1,190

710

240

20

1,330

1,040

700

480

130

25

2,730

2,120

1,510

900

300

25

1,730

1,330

930

530

175

30

3,360

2,600

1,840

1,090

350

30 2,120

1,630

'

1,140

660

220

35

3,940

3,040

2,140

1,240

400

35

1,900

1,330

770

260

40

4,520

3,470

2,420

1,390

430

40

2,800

2,160

1,510

870

290

c c2

888

APPENDIX D.

I. YIELD TABLES USED IN SAXONY FOR THE
For One Acre of normal, or fully stocked, wood in solid cubic

Scotch Pine.

Larch.

Age,

Quality classes, in solid cubic feet.

Age,

Quality classes, in solid cubic feet.

Years.

:

Years.

I.

II.

III. IV.

V.

I.

II.

III.

IV.

V.

10

560

460

360

260

140

10

760

610

470

330

170

20

1,500

1,210

930

640

310

20

1,890

1,510

1,140

770

360

30

2,830

2,270

1,690

1,110

500

30

3,290

2,620

1,940

1,260

570

40

4,320

3,410

2,520

1,610

740

40

4,840

3,820

2,790

1,760

.790

50

5,800

4,590

3,370

2,140

960

50

6,400

5,030

3,640

2,260

990

60

7,220

5,690

4,160

2,630

1,170

60

7,800

6,120

4,400

2,700

1,170

70

8,550

6,730

4,920

3,100

1,370

70

9,060

7,070

5,100

3,130

1,340

80

9,750

7,670

5,600

3,520

1,550

80

10,190

7,960

5,730

3,500

1,500

90

10,830

8,520

6,200

3,890

1,710

90

11,200

8,750

6,290

3,840

1,640

100

11,760

9,250

6,730

4,220

1,860

100

12,120

9,460

6,800

4,140

1,760

110

12,520

9,850

7,170

4,490

1,980

110

12,950

10,100

7,260

4,420

1,870

120

13,100

10,300

7,500

4,700

2,060

120

13,680

10,660

7,650

4,630

1,960

130

13,490

10,600

7,730

4,830

2,120

130

14,310

11,130

7,960

4,800

2,020

140

13,690

10,760

7,830

4,900

2,160

140

14,860

11,560

8,260

4,950

2,060

APPENDIX D.

389

DETERMINATION OF THE QUALITY OF LOCALITY.
feet, including all wood above ground, but exclusive of roots and stumps.

Spruce.

Silver Fir.

Age,
Years.

Quality classes, in solid cubic feet.

Age,
Years.

Quality classes, in solid cubic feet.

I.

II.

III.

IV.

V.

I,

II.

III.

IV.

V.

10

460

400

330

260

140

10

430

360

290

210

110

20

1,430

1,170

930

660

330

20

1,190

970

760

540

270

30

2,790

2,260

1,700

1,160

540

30

2,920

2,000

1,500

990

460

40

4,420

3,500

2,600

1,690

770

40

4,130

3,260

2,390

1,500

670

50

6,190

4,870

3,560

2,240

990

50

5,920

4,630

3,350

2,060

890

60

8,050

6,290

4,530

2,790

1,190

60

7,800

6,090

4,370

2,640

1,120

70

9,890

7,700

5,520

3,320

1,390

70

9,730

7,580

5,410

3,230

1,360

80

11,690

9,080

6,460

3,830

1,570

80

11,690

9,090

6,450

3,820

1,570

90

13,360

10,350

7,330

4,300

1,740

90

13,550

10,480

7,400

4,340

1,760

103

14,910

11,520

8,130

4,730

1,900

100

15,350

11,850

8,320

4,840

1,930

• 1

110

16,270

12,550

8,830

5,100

2,030

110

17,030

13,120

9.200

5,300

2.090

120

17,420

13,420

9,420

5,420

2,140

120

18,610

14,310

10,000

5,690

2,220

130

18,320

14,120

9,890

5,560

2,220

130

20,010

15,350

10,690

6,030

2,320

140

18,920

14,550

10,180

5,820

2,270

140

21,240

16,250

11,290

6,300

2,390

150

22,280

17,020

11,760

6,500

2,430

1

390

APPENDIX D.

II. AEEA OF CIRCLES FOB DIAMETERS

Diam.
in

inch's.

Area of
circle in
square ft.

Diam. Area, of
in circle in

icli's. square ft.

Oiam. Area of
in circle in
nch's. square ft.

Diam.
in
nch's.

Area of
circle in
square ft.

Diam.
in
nch's.

Area of
circle in

square It.

1-0

eHX)55

24

0-0218

3-0 0-0491

40

0-0873

50

0-1364

1

•0<M?7

1 -0240

1 -0524

1

•0917

1

•1418

2

•0079

2

•0264

2 -0559

2 -0963

2

•1474

3

•0092

3

•0289

3 -0594

3 -1009

3

•1532

4

•iM(>7

4

•0314

4 -0631

1

•1056

4

•1590

5

•0123

6

•0341

5 -06(59

:» -1105

5

•1650,

6

•0140

6

•0369

6 -0707

c» -H54

6

•1710

7

•0158

7

•0398

7 -0747

7 1 -1205

7

•1772

8

•0177

8

•0428

8 -0788

S -1257

8

•is;;:,

9

•0197

9

•0459

1) -0830

'.» -1310

9

•1899

11-0

0-GCOO

120

0-7854

13-0 i 0-9218

14-0

1-0690

150

1-2272

1

•6721

1

•7986

1

•9360

1

1-0843

1

1-2437

2

•6842

2

•8118

•2 -9504

2

1-0997

2

1-2602

3

•696$

3

•8252

'A '9648

8

1-1153

3

1-2768

4

•7089

4

•8387

4

•9794

4

1-1309

4

L-2986

5

•7214

5

•8523

5

•9941

5

L-1467

5

1-3104

6

•7340

6

•8660

6

1-0089

6

1-1626

6

1-3274

7

•7467

7

•8798

7

1-0237

7

1-1785

7

l-.'Mll

a

•7595

8

•8937

8

1-0387

8

1 -194(5

8

1-3616

9

•7724

9

•9077

'.) 1-0538

9

1-2108
3-1416

9
250

1-3789

210

2-4058

220

2-6398

23-0

2-8852

24-0

:HOSS

1

2-088

1

2-6638

1

2-9103

1

3-1679

1

8-4361

2

2-4514

2

2-6880

2

2-9356

2

3-1942

2

8-4686

3

LM715

:; 2-7122

3

2-9610

3

3-2207

3

8*4911

4

2-4978

1 2-7366

I 2-9864

4

3-2471

4

:',-:, iss

5

2-6212

:, 2-7(511

r> 3-0120

:>

3-2748

6

8-6466

6

lK.417

<; 2-7*57

<; 3-0377

6

3-3006

6

::-:.7il

7

2-5084

7

2-8104

7

3-0635

7

3-3275

7

3-6024

8

2-5921

8

2-8352

8

3-0894

8

3-3545

8

3-6305

9

&-6159

8

i 2-8602

9

8'11M

1'

3-3816

9

8-6687

40

8-7266

11

INI;*!

42

9-6211

43

10-OS47

II

10-5592

50

i:n;:r,4

51

1 i-isr,.'{

52

1 l-7lso

58

16*8207

54

16-9048

60

1 9-r,350

Footnote.— The circles of full inches were calculated with logarithms

APPENDIX D.
OP 1 INCH TO 60 INCHES.

391

Diam.
in
inch's.

Area of
circle in
square ft.

Diam. Area of
in circle in
nch's. square ft.

Diam.
in

nch's.

Area of
circle in
square ft.

Diam.
in
nch's.

Area of
circle in
square ft.

Diam.
in
nch's.

Area of
circle in
square ft.

60

0-1963

70

0-2673

80

0-3491

90

0-4418

1,0-0

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

4

•2234

4

•2987

4

•3849

4

•4820

4

•5900

5

, -2304

5

•3068

5

•3941

5

•4923

5

•6014

6

•2376

6

•3151

6

•4034

6

•5027

6

«'6129

7

•2448

7

•3234

7

•4129

7

•5132

7

•6245

8

•2522

8

•3319

8

•4224

8

•5238

8

•6362

9

•2597

9

•3404

9.

•4321

9

•5345

9

•6481

16-0

1-3963

17-0

1-5763

18-0

1-7671

190

1-9689

200

2-1817

i

1-4138

1

1-5949

1

1-7868

1

1-9897

1

2-2036

2

1-4314

2

1-6136

2

1-#066

2

2-0106

2

2-2256

3

1-4492

3

1-6324

3

1-8265

3

2-0316

3

2-2477

4

1-4670

4

1-6513

4

1-8465

4

2-0527

4

2-2699

5

1-4849

5

1-6703

5 .

1-8666

5

2-0739

5

2-2922

6

1-5030

6

1-6894

6

1-8869

6

2-0952

6i

2-3146

7

1-5212

7

1-7087

7

1-9072

7

2-1167

7

2-3371

8

1-5394

8

1-7280

8

1-9277

8

2-1382

8

2-3597

9

1-5578

9

1-7475

9

1-9482

9

2-1599

9

2-3825

26-0

3-6870

27-0

3-9761

28-0

4-2761

290

4-5869

30-0

4-9087

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

5

4-4301

5

4-7464

35

6-6813

6

3-8591

6 : 4-1548

6

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

9

4*5553

9

4-8760

39

8-2958

45

11-0447

46

11-5410

47

12-0482

48

12-5664

49

13-0954

55

16-4988

56

17-1042

57

17-7206

58

18-3478

59

18-9859

of 7 places ; the intermediate values were found ty interpolation.

392

APPENDIX D.

III. TABLE OP THE VOLUMES OF CYLINDEBS AND OF THE

Length of
Cylinder,
or Number
of Circles.

DIAMETER IN INCHES.

1

2

3 4

5

6

7

8

1

0-0055

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

0-3926

0-5346

0-6982

3

0-0165

0-0654

0-1473

0-2619

0-4092

0-5889

0-8019

1-0473

4

0-0220

0-0872

0-1964

0-3492

0-5456

0-7852

1-0692

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

1-6038

2-0946

7

0-0385

0-1526

0-3437

0-6111

0-9548

1-3741

1-8711 '

2-4437

8

0-0440

0-1744

0-3928

0-6984

1-0912

1-5704

2-1384

2-7928

9

0-0495

0-1962

0-4419

0-7857

1-2276

1-7667

2-4057

3-1419

17

18

19

20

21

22

23

24

1

1-5763

1-7671

1-9G89

2-1817

2-4053

2-0398

2-8852

3-1416

2

3-1526

3-5342

3-9378

4-3634

4-8106

5-2796

5-7704

6-2832

3

4-7289

5-3013

5-9067

6-5451

7-2159

7-9194

8-6556

9-4248

4

6-3052

7-0684

7-8756

8-7268

9-6212

10*5592

11-5408

12-5664

5

7-8815

8-8355

9-8445

10-9085

12-0265

13-1990

14-4260

15-7080

6

9-4578

10-6026

11-8134

13-0902

14-4318

15-8388

17-3112

18-8496

7

11-0341

12-3697

13-7823

15-2719

16-8371

18-4786

20-19(54

21-9912

8

12-6104

14-1368

15-7512

17-4536

19-2424

21-1184

23-0816

25-1328

9

14-1867

15-9039

17-7201

19-6353

21-0477

23-7582

25-9668

28-2744

33

34

35

36

37

38

39

40

1

5-9396

6-3050

6-6813

7-0686

7-4(5(57

7-8758

8-21)58

8-7266

2

11-8792

12-6100

13-3626

14-1372

14-9334

15*7516

16*5916

i7-ir,:5i>

3

17-8188

18-9150

21-2058

22-4001

23-6274

24-8874

26-1798

4

23-7584

25-2200

1

29-8668

31-5032

33-1832

34-90(54

5

29-6980

31-5250

>

37-3335

39-3790

41-4790

43-6330

6

35-6376

87-8300

;

44-8002

47-2548

49-7748

52-359(5

7

41-5772

1!

i

52-2669

55-1306

58-0706

61-0862

8

47-5168

50-4100

j

59-7336

63-0064

66-3664

69-8128

9

53-4564

'

!

67-2003

70-8822

74-6622

78-5394

APPENDIX D.

SUM OF CIRCLES, FOE DIAMETER OF 1 INCH TO 48 INCHES.

Length of
Cylinder,
or Number
of Circles.

DlAMETEE 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

1-3254

1-6362

1-9800

2-3562

2-7654

3-2070

3-6816

4-1889

4

1-7672

2-1816

2-6400

3-1416

3-6872

4-2760

4-9088

5-5852

5

2-2090

2-7270

3-3000

3-9270

4-6090

5-3450

6-1360

6-9815

6

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

8

3-5344

4-3632

5-2800

6-2832

7-3744

8-5520

9-8176

11-1704

9

3-9762

4-9086

5-9400
27

7-0686
28

8-2962
29

9-6210
30

11-0448
31

12-5667
32

25

26

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

3

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

5

17-0440

18-4350

19-8805

21-3805

22-9345

24-5435

26-2070

27-9255

6

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
44

41-2821

44-1783

47-1726

50-2659
48

41

42

43

45

46

47

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

36-1446

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

6

55-0104

57-7266

60-5082

63-3552

66-2682

69-2460

72-2892

75-3984

7

64-1788

67-3477

70-5929

73-91 44

77-3129

80-7870

84-3374

87-9648

8

73-3472

76-9688

80-6776

M:47M

88'867<5

92-3280

96-8856

100-5312

9

82-5156

86-5899

90-7623

95-0328

99-4023

103-8690

108-4338

113-0976

394

APPENDIX D.

. AMOUNT TO WHICH A CAPITAL OF 1 ACCUMULATES WITH
COMPOUND INTEREST IN n TEARS CH=. C0xl'opn.

No. of
Years,

= n.

PER CENT.

2.

2-5.

3.

3-5.

V--

4-5.

5.

1

1-0200 1-0250

1-0300

1-0350

1-0400

1-0450

1-0500

2

1-0404

1-0506

1-0609

1-0712

1-0816

1-0920

1-1025

3

1-0612

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

5

1-1041

1-1314

1-1593

1-1877

1-2167

1-2462

1-2763

6

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

1-177:.

9

1-1951

1-2489

1-3048

1-3629

1-4233

1-4861

1-5513

10

1-2190 1-2801

1-3439

1-4106

1-4802

1-5880

MIL'S!)

15

1-3459 ; 1-4483

1-5580

1-6753

1-8001)

1-9353

2-0789

20

1-4859

1-6386

1-8061

1-9898

2- 11)11

2-4117

2-6683

25

1-6406

1-8539

2-0938

2-3632

2-6658

3-0054

3-3S6I

30

1-8114

2-0976

2-4273

2-8068

3-2434

3-7453

4-8311

35

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

45

2-4379

3-0379

3-7816

4-7024

5-8412

7-2482

8-9850

50

2-6916

3-4371

4-383^

5-5849

7-1 or,:

9-0326

1M67I

55

2-9717

3-8888

5-0821

6-6331

8-6464

11-2563

14-6356

60

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
75

3-9996
4-4158

5-6321
6-3722

7-9178
9-1789

11-1128
13-1985

15-5716
18-9452

21-7841
27-1470

30-4264

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

42-1585

63-2544

90

5-9431

9-2289

14-3005

22-1122

34-1193

52-6371

80-7304

95

6-5617

10-4416

16-5782

26-2623

41-5114

85-4708

103-0347

lliu

7-2446

11-8137

19-21B6

31-11)14

50-5049

81-6886

131-5013

110

8-8312

15-1226

25-8282

43-9986

74-7597

126-7045

214-2017

120

10-7652

19-3581

34-7110

62-0643

110-6626

196-7682

348-9120

130

13-1227

24-7801

46-6486

87-5478

163-8076

3or>-:.7.-.n

568-8409

140

l.V'.nx;.-,

31-7206

(•2-6919

123-4949

242-4753

474-5486

ltLT.-7C.7l

150

19-49%

40-6050

84-2527

174-2017

358-9227

73G-959I

1507-9775

200

139-5630

:<o-:r,r,s

972-9039

2550-7498

(;r,.-,r,-6863

L7292-5808

APPENDIX D.

395

IVs. PRESENT VALUE OF A CAPITAL OF 1 TO BE EEALIZED AFTER

n YEARS : (7. =

'Opn'

No. of
Years,

= 7J.

PER CENT.

2.

2-5.

3

3-5.

4.

4-5.

5.

1

,0-9804

0-9756

0-9707

0-9662

0-9615

0-9569

•9524

2

•9612

•9518

•9426

•9335

•9246

•9157

•9070

3

•9423

•9286

•9151 '

•9019

•8890

•8763

•8638

4

•9238

•9060

•8885

•8714

•8548

•8386

•8227

5

•9057

•8839

•8626

•8420

•8219

•8025

•7835

6

•8880

•8623

•8375

•8135

•7903

•7679

•7462

7

•8706

•8413

•8131

•7860

•7599

•7348

•7107

8

•8535

•8207

•7894

•7594

•?307

•7032

•6768

9

•8368

•8007

•7664

•7337

•7026

•6729

•6446

10

•8203

•7812

•7441

•7089

•6756

•6439

•6139

15

•7430

•6905

•6419

•5969

•5553

•5167

•4810

20

•6730

•6103

•5537

•5026

•4564

•4146

•3 70 9

25

•6095

•5394

•4776

•4231

•3751

•3327

•2053

30

•5521

•4767

•4120

•3563

•3083

•2670

•2314

35

•5000

•4214

•3554

•3000

•2534

•2143

•1813

40

•4529

•3724

•3066

•2526

•2083

•1719

•1420

45

•4102

•3292

•2644

•2127

•1712

•1380

•1113

50

•3715

•2909

•2281

•1791

•1407

•1107

•0872

55

•3365

•2572

•1968

•1508

•1157

•0888

•0683

60

•3048

•2273

•1697

•1269

•0951

•0713

•0535

65

•2760

•2009

•1464

•1069

•0781

•0572

•0419

'

70

•2500

•1776

•1263

•0900

•0642

•0459

•0329

75

•2265

•1569

•1089

•0758

•0528

•0368

•0257

80

•2051

•1387

•0940

•0638

•0434

•0296

•0202

85

•1858

•1226

•0811

•053?

•0357

•0237

•0158

90

•1683

•1084

•0699

•0452

•0293

•0190

•0124

95

•1524

•0958

•0603

•0381

•0241

•0153

•0097

100

•1380

•08465

•05203

•03206

•01980

•01226

•00761

110

•1132

•06613

•03872

•02273

.•01338

•00789

•00467

120

•09289

•05166

•02881

•01611

•00904

•00287

130

•07620

•04036

•02144

•01142 -00611

•00176

140
150

•06251
•05128

•03153
•02463

•01595
•01187

•00810
•00574

•00412 -00211
•00279 ! -00136

•00101
-00066

200

•01905

•007165

•002707

•001028

: 10150

•0000578

396

APPENDIX D.

IVc.— PRESENT VALUE OF A PERPETUAL RENTAL OP 1, DUE EVERY n YEARS :

\-op* - 1

Dumber
jf Years

071.

PER CENT.

2

50-0000

2-5

3

3-5

4

4-5

5

1

40-0000

33-3333

28-5714

25-0000

22-2222

20-0000

2

24-7525

19-7531

16-4204

14-0400

12-2549

10-8666

9-7561

3

16-3377

13-0054

10-7843

9-1981

8-0087

7-0839

6-3442

4

12-1312

9-6327

7-9676

6-7786

5-8873

5-1943

4-6402

5

9-6079

7-6099

6-2785

5-3280

4-6157

4-0620

3-6195

6

7-9263

6-2620

5-1532

4-3620

3-7690

3-3084

2-9403

7

6-7256

5-2998

4-3502

3-6727

3-1652

2-7711

2-4564

8

5-8255

4-5787

3-7485

3-1565

2-7132

2-3691

2-0944

9

5-1258

4-0183

3-2811

2-7556

2-3623

2-0572

1-8138

10

4-5663

3-5703

2-9077

2-4855

2-0823

1-8084

1-5901

15

2-8913

2-2307

1-7922

1-4807

1-2485

1-0692

0-9268

20

2-0578

1-5659

1-2405

1-0103

0-8395

0-7084

•6049

25

1-5610

1-1710

0-9143

0-7335

•6003

•4986

•4190

30

1-2325

0-9111

•7006

•5535

•4458

•3643

•3010

35

1-0001

•7282

•5513

•4285

•3394

•2727

•2214

40

0-8278

•5934

•4421

•3379

•2631

•2076

•1656

45

•6955

•4907

•3595

•2701

•2066

•1600

•1252

50

•5912

•4103

. -2955

•2181

•1638

•1245

•0955

55

•5072

•3462

•2450

•1775

•1308

•0975

•0733

60

•4384

•2941

•2044

•1 -15-1

•1050

•0768

•0566

65

•3813

•2514

•1715

•1197

•0848

•0607

•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

•0161

90

•2023

•1215

•0752

•0474

•0302

•0194

•0125

95

•1798

•1059

•0642

•0396

•0247

•0155

•0098

190

•1601

•0925

•0549

•0331

•0202

•0124

•0077

! 110

•1277

•07081

•04028

•02326

•01356

•00796

•00469

120

•1024

•05447

•02966

•01638

•00912

•iii):,]l

•002874

130

•08249

•04205

•02191

•01155

•006142

•003284

•001763

I lu

•06668

•03255

•01621

•008164

•004141

•002112

•001081

160

•05406

•02525

•01201

•005774

•002794

•001357

•000<5636

200

•01942

•007217

•002707

•001029

•0003926

•0001502

•0000.17s::

APPENDIX D.

397

IVD. — PRESENT VALUE OF A RENTAL OF 1 DUE AT THE END OF EVERY
YEAR. ALTOGETHER n TIMES : C0 = 7 ' °P — - 2 .

Number
of Years
= ft.

PER CENT.

2

2-5

3

3-5

4

4-5

5

1

0-9804

0-9756

0-9709

0-9662

0-9615

0-9569

0-9524

2

1-9416

1-9274

1-9135

1-8997

1-8861

1-8727

1-8594

3

2-8839

2-8560

2-8286

2-8016

2-7751

2-7490

2-7232

4

3-8077

3-7620

3-7171

3-6731

3-6299

3-5875

3-5459

5

4-7135

4-6458

4-5797

4-5150

4-4518

4-3900

4-3295

6

5-6014

5-5081

5-4172

5-3285

5-2421

5-1579

5-0757

7

6-4720

6-3494

6-2303

6-1145

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

10-3797

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

27-3555

25-1028

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

50

31-4236

28-3623

25-7298

23-4556

21-4822

19-7620

18-2559

55

33-1748

29-7140

26-7744

24-2641

22-1086

20-2480

18-6335

60

34-7609

30-9087

27-6756

24-9447

22-6235

20-6380

18-9293

65

36-1975

31-9646

28-4529

25-5178

23-0467

20-9510

19-1611

70

37-4986

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

80

39-7445

34-4518

30-2008

26-7488

23-9154

21-5653

19-5965

85

40-7113

35-0962

30-6312

27-0368

24-1085

21-6951

19-6838

90

41-5869

35-6658

31-0024

27-2793

24-2673

21-7992

19-7523

95

42-3800

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

22-0468

19-9066

120

45-3554

37-9337

32-3730

28-1111

24-7741

22-1093

19-9427

130

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 22-1751

19-9784

150

47-4358

39-0149

32-9377

28-4074

24-9303

22-1921

19-9867

200

49-0473

39-7134

33-2431

28-5421

21-9902

19-9988

4 «/»/.

UP P A ^
D r\ A i\

FACULTY OF FORESTRY
UNIVERSITY OF TORONTO

V

SD Schlich, (Sir) William

371 A manual of forestry

S33

1906 *N

v.3

PLEASE DO NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET

UNIVERSITY OF TORONTO LIBRARY