Digitized by the Internet Archive in 2009 with funding from NCSU Libraries http://www.archive.org/details/schlichsmanualo03schl SCHLICH'S MANUAL OF FORESTRY. u ERRATA. Page 56, lines 4, 5 and 6 from the top. Eliminate the sentence beginning with " The correctness " and ending with " Forestry Commission." 59, line 4 from top. For " 462 " substitute " 47 " 61, line 5 from top. For " 8 " substitute " -8 " 98, line 10 from top. For " one " substitute " the same " 122, line 1 from top. For " — " substitute " = " (equal) 131, line 4 from bottom. For " I." substitute " III." X T 135, line 8 from bottom. For " . ^- a " substitute " U 1 Op 1 0p a 219, line 2 from top. *Vw " F r 4- 1 " substitute " V r +i " 261, line 15 from bottom. Add " a " a^ f/je end of the line 312, line 8 from top. For " 122 " substitute " 124 " 312, line 1 from bottom. For " 7,072,640 " substitute " 7,022,640 " 313, line 2 from top. For " 707,264 " substitute " 702,264 " 313, line 3 from top. 4/ifer " Appendix V." add ", page 368" 313, line 13 from bottom. Eliminate " natural " SCHLICH'S MANUAL OF FORESTRY. VOLUME III. FOREST MANAGEMENT, INCLUDING MENSURATION and VALUATION. Sir Wm. SCHLICH, K.C.I.E., F.R.S., F.L.S., Ph.D., M.A. Oxox. LATE INSPECTOR-GENERAL OF FORESTS TO THE GOVERNMENT OF INDIA AND LATE PROFESSOR OF FORESTRY AT OXFORD. FIFTH EDITION. Revised, and the greater part rewritten. WITH 68 ILLUSTRATIONS. LONDON : BRADBURY, AGNEW, & CO., Ld., 10, BOUVERIE STREET. 1925. In former editions of this volume, numerous references were given to matters dealt with in Volume II., Silvi- culture. This has been found to be somewhat incon- venient, and the practice has, as far as possible, been abandoned. It has been obviated by giving, in connec- tion with the Determination of the Yield, short accounts of the various silvicultural systems (with a few illustra- tions from Volume II.). The manuscript of the present edition has been read by Mr. C. E. C. Fischer, Conservator of Forests, Madras, on leave, and the proofs from the press have been examined by my daughter, Miss Schlich. I am greatly indebted to them for their help. W. SCHLICH. Oxford, January 20, 1925. TABLE OF CONTENTS. TAGE INTRODUCTION 1 PART I.— FOREST MENSURATION 5 Chapter I. — Instruments used in Forest Mensuration . . 8 For the Measurement of the Girth, 8 ; Diameter, 9 ; Diameter Increment, 14 ; Length of Felled Trees, 15 ; Height of Standing Trees, 16 ; Volume (Xylometer), 25 ; Specific Gravity, 25 ; Solid Volume (Hydrostatic Method), 27. Chapter II. — Measurement of the Volume of Felled Trees . 28 Volume of Stem, 28 ; Branch and Root Wood, 32 ; Bark, 33. Chapter III. — Measurement of Standing Trees ... 34 Ocular Estimate, 34 ; By Form Factors, 35 ; Volume Tables, 39 ; by Sections, 41. Chapter IV. — Determination of the Volume of Whole Woods 43 Section I. — -Measurements extending over the AVhole Wood Measurement of all Trees ..... Measurement by Sample or Type Trees . The General Diameter Class Method Modifications of the General Method Method of Draudt, 52 ; Urich, 53 ; Hartig, 53 ; Examples, 54, 55 ; Form Factors, 56 ; Volume Tables, 59 ; Yield Tables, 60 ; Volume Curve, 61 ; Block's, 63 ; British Forestry Commissioner's Method, 64 ; Form Quotient, 66 Accuracy and Choice of the several Methods The Method of Diameter and Height Classes combined Section II. — Determination of Volume by Sample Areas Section III. — Determination of Volume by Estimate Chapter V. — Determination of the Age of Trees and Woods Single Trees, 74 ; Whole Woods, 76. Chapter VI. — Determination of the Increment ... 79 Section I. — The Increment of Single Trees ..... 80 Of Height, 80 ; Diameter, 81 ; Basal Area, 82 ; Volume, 82 ; Example of a Stem Analysis of a Scots Pine Tree, 83. Section II. — The Increment of Whole Woods . Mean Annual Increment of the Past Determination by Yield Tables .... Yield Tables Generally, 93 ; Quality Classes, 95 ; Con struction of Yield Tables, 95 ; by an Indicating Wood, 98 Baur's Method, 99 ; Forestry Commission's Method, 104. Calculation of the Increment ...... 107 VI TABLE OF CONTENTS. PAGE PART II.— FOREST VALUATION Ill Chapter I. — Preliminary Matters 114 Section I. — The Value of Property Generally . . . .114 Section II. — The Rate of Interest Applicable to Forestry . .115 Section III. — Useful Formulas . . . . . . .117 Arithmetical and Geometrical Series, 117; the Amount, 118; Discount, 119; Summation of Rentals, 119; Conversion of Intermittent to Annual Rentals, 122. Section IV. — Estimate of Receipts and Expenses .... 123 Money Yield Tables for Larch, Spruce and Scots Pine, 124. Chapter II. — Methods of Forest Calculations .... 129 Section I. — Valuation of Forest Soil 129 Section II. — Valuation of the Growing Stock .... 132 Section III. — Valuation of a Whole Wood ..... 134 Chapter III. — The Financial Results of Forestry . . 136 Section I. — Calculation for the Intermittent Working . . • 136 The Profit, 136 ; Current Annual Forest per cent., 138 ; Mean Annual Forest per cent., 142. Section II. — Calculation for the Sustained Annual Working . . 146 Description of the Normal Forest, 146; the Profit, 150; Per Cent,, 150. Section III. — Notes on the Financial Aspect of Forestry. . . 153 Chapter IV. — Some Samples of Applications .... 157 Agriculture and Forestry, 158 ; Choice of Species, 160 ; System, 160 ; Method of Treatment, 161. PART III.— THE FOUNDATIONS OF FOREST MANAGE MENT Introduction ......... Chapter I.— The Increment Section I. — The Volume Increment ..... Of Single Trees, 172; Whole Woods, 176; Volume Increment per cent., 182. Section II. — The Quality Increment ...... Section III. — The Price Increment ...... Section IV. — Combination of the Three Increments Chapter II. — The Rotation The Financial Rotation, 188 ; Rotation of Highest Net Income, 191 ; Greatest Volume Production, 192 ; the Technical Rota- tion, 192 ; the Physical Rotation, 193 ; Choice of Rotation, 193. Chapter III. — The Normal Age Classes ..... The Normal Annual Coupe, 196 ; Size of the Age Classes, 198 ; Distribution of the Age Classes over the Forest, 208. 165 167 172 172 184 186 187 188 195 TABLE OF CONTENTS. Vll PAGE Chapter IV. — The Normal Growing Stock 213 Chapter V. — The Normal Yield ...... 221 Chapter VI. — Relation between Increment, Growing Stock and Yield 224 PART IV.— THE PREPARATION OF FOREST WORKING PLANS 227 Introduction ........... 229 Chapter I . — Collection of Statistics ...... 235 Section I. — Survey and Determination of Areas .... 235 Section II. — Description of each Wood or Compartment . . . 236 Locality, 237 ; Growing Stock, 238 ; Quality, 242 ; Future Treatment, 248. Section III. — Past Yields, Receipts and Expenses .... 249 Section IV. — Conditions in and around the Forest . . . . 251 Section V. — The Statistical Report and Maps .... 252 Chapter II. — Division and Allotment of the Forest Area . . 260 The Working Circle, 260 ; Compartment, 261 ; Sub-Compart- ment, 262 ; Working Section, 262 ; Cutting Series, 265 ; Severance Cuttings, 266 ; System of Roads and Rides, 267 ; Numbering of Divisions, 271 ; Two Coloured Sketches to Illus- strate the Above, between 264-265. Chapter III. — Determination of the Method of Treatment . 272 Choice of Species, 272 ; Method of Formation, 273 ; of Tending, 274 ; Choice of Rotation, 275 ; Silvicultural System, 275. Chapter IV. — Determination and Regulation of the Yield . 276 Section I. — The Principal Systems ...... 277 The Selection System, 277 ; Brandis' Modification, 285 ; Fixed Annual Coupes, 288 ; Allotment to Periods, by Area, 290 ; by Volume, 291 ; by Area and Volume, 293 ; the Austrian Method, 293 ; Heyer's Method, 296 ; Hunde- shagen's, 299 ; von Mantel's, 301 ; the Compartment or Uni- form System, 303. Example, 309 ; Notes, 312. Modifications of the Compartment System : — - Le Quartier Bleu, 313 ; Group System, 315 ; Strip System, 315 ; Strip and Group System, 317 ; Wagner's Blendersaum- schlag, 317 ; Eberhard's Wedge Fellings, 321. The Coppice System, 323 ; Coppice with Standards, 324. Section II. — Auxiliary Systems ....... 326 High Forest with Standards, 326 ; Two Storied High Forest, 326 ; High Forest with Underwood, 327 ; Forestry and Agriculture, 327 ; Forestry and Pasture, 330 ; Forestry and Game, 330. Section III. — Choice of System ....••• 331 Vlll TABLE OF CONTENTS. Chapter IV. — continued. page Section IV. — Conversion of One System into Another . . . 333 Selection into Uniform System, 333 ; Coppice into High Forest, 334 ; Coppice with Standards into High Forest, 335 ; Broad- leaved into Conifer Forest, 336. Chapter V. — Control of Execution and Renewal of Working Plans 338 APPENDICES 341 Appendix I. A. — Area of Circles for Diameters of 1 to 60 Inches . 342 Appendix I. B— Sum of Circles and of Volumes of Cylinders . . 344 Appendix II. — Table of Quarter Girths in Inches, Feet and Squared 346 Appendix III. — Tables of Compound Interest .... 348 Appendix IV. — Abstracts from British, German and Indian Yield Tables 354 Appendix V .—Abstracts from Working Plans by Allotment to Periods 363 (A) By Area, 364 ; (B) By Volume, 370. Appendix VI.— Abstract of Working Plan by the Austrian Method . 372 INDEX 379 FOKEST MANAGEMENT. INTKODUCTION. 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, landslips and avalanches, preservation of game, hygienic effects, etc. (2.) The management of forests on economic principles, such as the production of a definite class of produce, or the greatest possible quantity of it, 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 and in the most economic manner. In some cases the realisation of indirect effects requires a special and distinct management, but in the majority of cases they can be produced in combination with economic working. The present volume deals chiefly with the economic aspect of forest management. The economic working 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 2 INTKODTTCTION. the capital invested in the forest, to regulate the yield according to time and locality and to organise the systematic conduct of the business. Accordingly, forest management may be divided into the following parts : — Part I. — Forest Mensuration, dealing with the determina- tion of the dimensions of trees, the volume of trees and whole woods, their age and increment. „ II. — Forest Valuation, dealing with the determination of the capital employed in forestry and the financial results produced by it. „ III. — The Foundations of Forest Management. ,, IV. — Preparation of Forest Working Plans. This volume is chiefly destined for the use of students of forestry, and its contents are arranged accordingly. Part I., " Forest Mensuration," and Part II., " Forest Valuation," should be considered as auxiliaries to Forest Management. They contain all the matters required by the student, and they should not be compared with special works on the two subjects, such as Baur's, Graves' and Chapman's " Forest Mensurations," and Heyer's, Endres' and Chapman's " Forest Valuations." These books deal not only with the methods of measuring and calculating, but also with all kinds of applications, many of which are not connected with forest management. Students, who have assimilated what is given in this volume on the two subjects, will have no difficulty in dealing with any case which may come before them in dis- charging the duties of an expert forest officer. In Mensuration several methods for the measurement of standing crops have been added which were not considered necessary when the earlier editions were published, or which have been elaborated since then. Of " Forest Valuation " the greater part has been rewritten, and the chapter on the financial results of forestry has been treated from a new point of view inaugurated by the author. The Continental yield tables of spruce, Scots pine and larch have been replaced by British yield tables prepared by the Forestry Commission, and a yield table of the Indian tree " sal " (Shorea robusta) has been added. There are also new money yield tables of larch, spruce and Scots pine. INTRODUCTION. 3 A great part of Management [Parts III. and IV.] has been rewritten on the basis of further experience gained since the publication of the fourth edition. Several new methods of treat- ment have been added, specially elaborated with the object of improving the process of regeneration and the preservation of the yield capacity of the soil. During recent years it has, more and more, been recognised that each laying bare of an area under forest has a deteriorating effect upon the sustained fertility of the soil, in all cases where the rainfall is unfavourably distributed over the seasons of the year and especially over the growing season. In such cases, drought, frost and also insects do increased damage ; more particularly, the degree of moisture in the soil is liable to be reduced below the minimum required for a healthy development of the new crop. Foresters of experience have recog- nised the importance of returning to the former practice of regenerating the forests under one of the shelterwood systems, whenever the quality of the soil is not of a high order and the climatic conditions unfavourable, planting and direct sowing of the seed on bare land being restricted to new afforestations, to places where natural regeneration has failed and in some cases to the cultivation of highly light-demanding and quick-growing species. The rainfall over the greater part of the British Isles is favourably distributed, but by no means over all parts ; years like 1911 and 1921 have shown the amount of damage which can be done by a drought of some duration. Many parts of the British Colonies are less favourably situated ; in these, drought is the rule and not the exception. In such cases, the results of leaving the areas exposed to unfavourable climatic conditions are very serious ; they should, as soon as possible, be brought under efficient pro- tection and, at any rate to begin with, managed under a simple method such as the selection system. This can by degrees be led over into the regulated selection system, which has been dealt with in full detail in Part IV. Whether, and to what extent, a more elaborate or concentrated system should ultimately be substituted may safely be left to future consideration. In India, apart from small experiments, it took 50 years of strenuous work before substantial progress with the conversion of the selection system into the compartment or uniform system could be begun ; even now the area taken in hand for that purpose is as yet a small b2 4 INTRODUCTION. part of the total area of the forests under the management of the Forest Department. Besides, such conversions have yet to prove that they are the blessing for the country which their promoters expect them to be. In the Colonies, at any rate, the most impor- tant work in the immediate future is to bring the forests under efficient control, to constitute an area of permanent State forests sufficient to give a sustained yield of produce in the future, to protect them against fire and to open them out for traffic, especially by a well-considered system of roads. The next measure will be to prepare suitable working plans for the different forests, based on the principle of a sustained yield in the future, and to regulate, according to time and locality, the manner in which it is to be realised. Important as these measures are, care should be taken to see that the prescriptions of management do not override the applica- tion of sound silvicultural principles. Management should be the servant and not the master of silviculture. It is the business of the latter to provide the conditions for the most favourable develop- ment of forest growth, of which the maintenance, if not the increase, of the fertility of the soil is the most important. PART I. FOREST MENSURATION. FOREST MENSURATION. Forest Mensuration deals with the determination of the dimensions, volume, age and increment of single trees and whole woods. The data thus obtained are required for the calculation of the material standing on a given area, the yield which a wood can give, the value of single trees, woods and whole forests. They serve also as the basis for the determination of the comparative value of different species and methods of treatment of woods, as well as for the calculation of the financial results of forestry generally. The matter dealt with in Part I. has been divided into the following chapters : — Chapter I. — Instruments used in Forest Mensuration. ,. II. — The Measurement of Felled Trees. ,, III. — The Measurement of Standing Trees. „ IV. — The Measurement of Whole Woods. „ V. — Determination of the Age of Single Trees and Whole Woods. „ VI. — Determination of the Increment of Single Trees and Whole Woods. The units of measurement of dimensions and volume are the British foot, square foot and cubic foot. 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, for the purpose of ascertaining these dimen- sions and to calculate from them the volume of the measured object. In the latter case, the area of the cross-cut section is calculated on the assumption that it forms a circle. It is called the " sectional " or " basal " area. 1. Instruments for the Measurement of the Girth. The girth may be measured with a tape, or with a string and a tape. The latter consists of a band about half an inch broad, so constructed that it alters its length as little as possible when wet. It is divided, on one side, into feet, inches and, if necessary, parts of an inch ; on the other side the sectional area corresponding to the girth may be marked, or the quarter girth. It is useful to have a small hook at 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. Flexible steel tapes have come much into use. The advantages of the tape are that it is easy to handle and to carry. Measurements with it are, however, subject to various sources of inaccuracy, amongst which the following should be mentioned : — (a) As the cross-sections of trees generally differ in shape from that of a circle, the calculation of the basal area calculated from the girth is liable to be incorrect. (b) Owing to the presence of rough bark, the measured girth is too long. (c) The tape is frequently not applied at right angles to the axis of the tree. MEASUREMENT OF THE DIAMETER. 9 In order to avoid some of the disadvantages, the girth is some- times measured with a thin string, which is then held parallel to a graduated tape. In this way more accurate results may be obtained, but the operation takes more time, and it is, therefore, uneconomic to employ it where large numbers of trees are to be measured. 2. Instruments for the Measurement of the Diameter. The diameter of cross-sections of felled trees is measured with an ordinary rule or a tape ; in other cases, the calliper is used, or sometimes the tree compass. a. The Calliper, or Diameter Gauge. The number of differently constructed callipers, as well as of other forest instruments, is very large, and it would take much Vertical Section of Movable Arm. Fig. 1. — Friedrich's Calliper. space to describe them all ; nor is it necessary to do so, as only comparatively few are of real practical use. Some of the latter kinds have been chosen to illustrate the theory in each case ; the actual value of the various instruments must be estimated by using them in the forest. 10 INSTRUMENTS USED IN MENSURATION. The calliper consists of a graduated rule and two arms. Of the latter, one is fixed at right angles to one end of 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, so that 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 Fig. 2. tree on the other side. The diameter can then be read off on the rule. 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 rarely used. The rule is divided into units, the size of which depends on the desired degree of accuracy. Ordinarily, they will be half inches, inches, or two inches, and, for very accurate measurements, decimals of inches. When large numbers of trees are to be measured, it is desirable to round off the limits of each unit ; for instance, if the rule is divided into inches, the first division line is placed at | inch from zero, the second at 1| inches, the third at 2|, and so on (Fig. 2). In this way, all trees measuring from MEASUREMENT OF THE DIAMETER. 11 \ to H inches are recorded as having a diameter of 1 inch, those from 1| to 1\ 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 to which it is likely to be subjected. (2.) The two arms must be at right angles to the rule or at least parallel to each other when pressed on to the tree. (3.) The movable arm must move with sufficient ease along the rule and yet not be too loose. Callipers of iron would be too heavy and too cold in winter ; the former objection can be removed by making them of alu- minium. Hitherto, callipers have generally been made of wood, although, with changes in the degree of humidity, the movable arm is liable to jam at one time or to move too easily at others. To avoid this drawback, various constructions have been adopted, resulting in a number of cal- lipers of which the following deserve to be 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 mov- able 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, 6 the wedge, c the section of the movable 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 wedge from right to left, it releases the rule and enables the arm to move more freely. To force the rule to follow the movement of the wedge, a spring is fastened at e which pushes Fig. 3. — Heyer's Calliper. 12 INSTRUMENTS USED IN MENSURATION. it from right to left, so that it is always kept in touch with the wedge. Friedrich's Calliper. — In this instrument the section of the rule has the shape of a rectangle, and the opening of the movable arm is larger than the section of the rule and placed slantingly 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 (see Fig. 1). In this position the arm rests on the two points a below and b above. As these points are liable to wear away, thus causing the arm to assume a position which is no longer at right angles to the rule, Boemerle has added a spring at b by which the true position of the arm is secured. Callipers have been designed which enumerate the number and classes of trees, and others which give their basal area. The con- struction is, in several cases, very ingenious, but they are generally very heavy, so that the labourer rapidly tires ; nor are these instruments always free from inaccuracies. They cannot be recommended for use in practical forestry ; hence it is not pro- posed to deal with them in this place. b. Accuracy of Measurement with the Calliper. To secure the greatest possible accuracy, the following pre- cautions must be taken : — (1.) Moss, creepers, etc., found on the tree must be removed before measurement. (2.) In the case of an abnormal swelling or indenture, the measurement must be taken above or below it, or both and the average taken. (3.) In the case of eccentric or elliptic shape of the cross-section, two diameters at right angles to each other must be measured and the mean taken. (4.) The height fixed for the measurement must be strictly adhered to. (5.) In the case of a tree divided into two or more limbs below the fixed height of measurement, each limb should 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 it. MEASUREMENT OF THE DIAMETER. 13 (7.) The reading must be taken while the calliper rests on the tree and not after it has been withdrawn. c. The Tree Compass. The shape of this instrument will be seen on reference to Fig. 4. The diameter of the tree or log is taken by the two points c and d, and it can be read off at h on the arc fg. 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 work. There is a difference of opinion as to the comparative accuracy of measurement and subsequent calcu- lations of the basal area from diameter and girth measurements. There is no doubt that the former works quicker, and, in the author's opinion, it gives more accurate results if two diameters at right angles to each other are measured. d. Dendrometers. In some cases dendrometers are used to measure the diameter of trees at some height from the ground. The theory is as follows : The angle which is formed by two rays running to the two sides of the tree is measured, as well as the distance of the eye of the observer from the tree. From these data the diameter at a certain height from the ground is calculated. Instead of the angle, the distance a b between the two rays is measured and the diameter obtained in the following way (see Fig. 5 on next page) : — CA:Ca = AB: ab,andAB = -^— X a b. If the instrument gives a b and C a, and C A is ascertained, the diameter at a certain height can be calculated. CA is = CD X sin. AC D, oi= VC D 2 + A D 2 . So far, instruments of this class have not obtained a footing in Fig. 4. — The Tree Compass. u INSTRUMENTS USED IN MENSURATION. practical forestry, because those available either do not work with sufficient accuracy or take too much time. 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. If no sections are available, as in the case of standing trees, the measurements are made with Pressler's Increment Borer (Fig. 6). Fig. 5. The instrument extracts a cylinder of wood from the stem, and it consists of the following parts : — (1.) A hollow borer, A, which is slightly conical from the handle towards the point. (2.) A handle, B, which serves as a lever when the instrument is in use. It is hollow and receives the borer, wedge and cradle when the borer is not in use (see E in Fig. 6). (3.) A wedge, C, which has a scale marked on one side where- with to measure the breadth of the concentric rings ; it is roughly toothed on the other side to assist in extracting the cylinder of wood. (4.) A cradle, D, in which the cylinder of wood is placed after extraction, to prevent its breaking. MEASUREMENT OF THE DIAMETER INCREMENT. 15 The borer is used in the following way : It is screwed in a radial direction into the tree, at right angles to its axis, to the desired depth, whereby a cylindrical column of wood enters the hollow borer and is severed from the tree, except at its base ; then the wedge is inserted between 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 of wood from turning Fig. 6. — Pressler's Increment Borer. round inside the borer ; the latter is then screwed backward one or two turns, whereby the base of the cylinder of wood is severed from the tree ; the borer is then screwed further in, which causes the severed cylinder of wood to be pushed back until it can easily be withdrawn and placed in the cradle. In this way, a column of wood about 0-2 inch in diameter and up to 6 inches in length is obtained, on which the breadth of the desired number of con- centric rings can be measured. If the rings are not distinct, a smooth surface can be prepared with a sharp knife. 4. Instruments for the Measurement of the Length of Felled Trees and Logs. The usual instruments are a tape or a measuring staff. The latter may be of varving length, say, up to 15 feet. It should be made of hard, straight-grained, well-seasoned wood and varnished 16 INSTRUMENTS USED IN MENSURATION. to protect it against moisture ; the ends may usefully be capped with iron plates. 5. Instruments for the Measurement of the Height of Standing Trees. The instruments which have been designed for the measure- ment of the height of standing trees are very numerous ; they may be divided into two classes, geometrical and trigonometrical height measurers. 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, by /777f/rf> ^^^^^^^ Fig. 7. either between the top and foot 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 of the tree. In either of these cases similar triangles are formed which are used for the determination of the height of the tree (Fig. 7). Let A B be the height of the tree ; E B a ray from the eye of the observer to the top of the tree ; E A a ray from the eye of the observer to the foot of the tree ; E C a horizontal ray ; a, b, and c the points HEIGHT MEASURING. 17 where the three rays hit the plumb-line ; then the height of the tree is determined as follows : — (1.) The horizontal line hits the tree between the top and the foot, when the following equation holds good : — EC Again, B C :b c = E C : E c, and B C = b c X , Ei C E AC: ac = E C : E c, and A C = a c X ~w~ tj c Hence, The height A B = BC + AC = (be + ac) x ^ =abx ~. (2.) The horizontal line passes below the foot of the tree. Then C is situated below A and AB = BC-AC = (bc-ac)x^ = abx E ^- . v ' E c E c (3.) The horizontal line passes above the top of the tree. Then C is situated above B and AB = AC-BC = (ac-bc)x^ = abx^-. v ' E c E c In each of the above three cases, two observations are required, unless the foot of the tree happens to be at the same level as the eye of the observer ; the values oi ac, b c, and E c are read on the instrument, while E C has to be measured. The value of a 6 can, however, be obtained by one observation in the following manner : — If two parallel objects are cut by two diverging rays, then the portions of the two parallel objects lying between the two rays are proportionate to the length of the rays. Let E A be the length of a ray from the eye of the observer to the foot of the tree, E a that from the eye to the plumb-line, A B the height of the tree, and a b the length of the plumb-line between the two rays going from the eye of the observer to the top and the foot of the tree ; then : — ■ E A Ea:E A =ab: A B, and A 5 = a 6 X -p- • t) a The values of a b and E a are obtained from the instrument, and E A must be measured. The instruments of this class are difficult to manage without a stand and, therefore, not to be recom- mended for ordinary work in the forest. 18 INSTRUMENTS USED IN MENSURATION. The measurement of the distance from the eye of the observer to the tree can be avoided by placing a staff, M A, of known length, L, alongside the foot of the tree. In this way, two further points M and m are given, as well as two similar triangles, E M A and E m a. Thus we have (see Fig. 8) : — E A : E a = A B : ab and E A : E a •■ = A M : a m, hence, AB:ab = AM; am, and AB = H <*b A ,, ab T a m am Ab %y M m , -• Fig. 8. This method is very simple, but somewhat less accurate than that which includes the measurement of the distance of the observer from the tree, because a m is very small and difficult to read accurately. The longer the staff L is, the more accurate will be the result. Measurements made with hypsometers based on the geometrical principle, especially those used without a stand, are liable to yield inaccurate results owing to various causes, such as inaccurate reading due to the unsteadiness of the plumb-line in windy weather, inaccurate measurement of the base line, and slanting position of the tree. The most accurate results are obtained if the distance of the observer from the tree equals the height of the tree. The inaccuracy of measurement with the better hypso- meters should not exceed 2 per cent, of the height of the tree. HEIGHT MEASURING. 19 b. Trigonometrical Height Measuring. This is based upon the measurement of the angles of elevation and depression indicated by rays running from the eye of the observer to the top and foot of the tree. In the triangle, EC B (Fig. 9), we have BC = E C X tan. u, and in triangle EGA, AC = EC X tan. 1 ; the height of the tree, H = BC + AC = E C X (tan. u -f- tan. 1). If the horizontal line of vision passes below the foot of the tree, the above formula becomes H = E C X s E ,' Fig. 9. < (tan. u — tan. 1). If it passes above the top of the tree, H = EC X (tan. 1 — tan. u). In each of these three cases, the measuring of the distance, E C, can be avoided by placing a staff of known length alongside the foot of the tree. In that case (Fig. 10, next page), we have : — M C = E C X tan. m, and AC = EC X tan. 1 ; and M A = EC X (tan. m + tan. 1). MA Hence EC tan. m -\- tan. 1" By introducing this value into the former equation, the height is : — ,, . tan. u + tan. 1 H = M A x : \— 4 , . tan. m + tan. 1 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 ; it is a 02 20 INSTRUMENTS USED IN MENSURATION. further advantage if, besides the angles, the corresponding tangents are marked on it. c. Description of some of the more useful Hypsometcrs. Weises Hypsometer. — It consists of a tube, T, with an objective in the shape of a cross at one end, 0, and an eyepiece, E, at the other. A scale is fastened longitudinally to the tube (called the height scale, H, Fig. 11), which is toothed on one side. It has the E/ V B ' / X * ■■■ ¥ 1 r C -'----j \. Fig. 10. zero point some distance from the end, and it is graduated from it in both directions. A second scale, D (called the distance scale), is inserted at the zero point of the height scale and moves at right angles to it. From the upper or zero point of this scale depends a plumb-line P. When not in use, 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 horizontal distance from the point of observation to the tree is measured, and the distance scale drawn out until it indicates at the zero WEISE S HYPSOMETER. 21 point of the height scale the number of units in the distance ; then the tube is raised and directed to 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 Fig. 11. — Weise's Hypsometer. top of the tree, the tube is gently turned from left to right whereby the plumb-line is caught by the toothed edge of the height scale. The number of units at the point where the plumb- -&. 'V 7 »>*' E 'xyH %•• Fig. 12. line was arrested give the height of the tree above the horizontal line in feet or yards, as the case may be. The number of units of measurement between the horizontal line and the foot of the tree is ascertained in the same way by directing the tube to the foot of the tree. The sum of the two readings gives the total height of the tree. 22 INSTRUMENTS USED IN MENSURATION. The theory of the instrument rests upon the similarity of the triangle with the sides EH D and rhd (see Fig. 12). The follow- ing equation holds good : — h d:h = D:H,andH = Dx d' B 20^ 25 ! c ■ A A w< -\ 'JUS ***** iJ2> STAfF ' 4YAMi Fig. 13. — Christen's Hypsometer. If, therefore, the units of the scales, which give h and d, are of the same size, and d is so fixed that its units are the same number as the units of the measured distance D, it follows that the above formula gives the height in feet or yards respectively, according to whether the distance, D, is given in the one or the other of these units. Christen's Hypsometer. — This consists of a piece of metal with protruding upper and lower edges (see at a and b, Fig. 13). The christen's and brandis' hypsometers. 23 instrument is based upon the theory explained above, which avoids the measurement of a base-line. A staff of known length, L, say 4 yards, is placed alongside the foot of the tree. The instrument is then held in a vertical position at some distance from the observer's eye and moved forward and backward, until the top of the tree is seen along the upper edge, b, and the foot along the lower edge, a ; then the point where a ray from the eye of the observer to the top of the staff, at M, hits the instrument, at m, gives the height of the tree. The instrument is con- structed in the following way : Similar triangles are formed in which the following equation holds good : — A B : ab = A M : a m, and AB — X L ; also a m = -y-^ X L. am A B If now ab = 12 inches, L = 4 yards, and successive values of A B> the height, are introduced, the corresponding values of a m are obtained and marked on the instrument. Thus, the heights can be read off the instrument, as stated above. The marks on the instrument are cuts, as then the top of the staff is more easily seen. The instrument has the disadvantage that the cuts are very close to each other for heights over 30 yards. This has lately been obviated to some extent by lengthening the instrument and making it with a hinge in the middle, so that it can be folded up when out of use. It is a very practical instrument, say, up to a height of about 100 feet, but it cannot be recommended for trees above that height. Brandis' Hypsometer. — This is based upon the trigonometrical method of height measuring. It consists of a tube with an objective at one end and an eye-piece, E, in the shape of a horizontal slit, at the other. Attached to the tube is a wheel which is weighted on one side (see at a, Fig. 14) and swinging between two pivots, so that it always maintains the same position when in use. Oscillations of the wheel can be arrested by a stop at 8. That point of the wheel which corresponds with the hori- zontal line is marked as zero, and from this point the wheel is graduated up to 60 degrees up and down. A lens is fastened alongside the eye-piece to facilitate the reading of the angle when the tube is directed to any point. The wheel is placed in a firm metal case. 24 INSTRUMENTS USED IN MENSURATION. In using the instrument, a position is taken from which the top and foot of the tree can be seen, the angles to the top and foot are read, and the distance from the eye of the observer to the tree is measured. Then H = E C (tan. u -f tan. 1) (see Fig. 9, on p. 19). For convenience of calculation, Brandis changed this formula as follows : — EC = E A X cos. 1, and H = E A X cos. 1 X (tan, u -\- tan. 1), sin. u X cos. 1 + sin. 1 X cos. u and H = E A X cos. 1 X cos. u X cos. 1 r, A sin. (u + 1) E A X — ! — ■ . COS. u Brandis uses the last formula, which involves the measurement of Fig. 14. — Brandis' Hypsometer and Clinometer. (The front lid removed, so as to show the wheel.) E A, the distance from the eye of the observer to the foot of the tree. A table accompanies the instrument, in which the heights corresponding to various distances and upper + lower angles are given. This table gives the upper angles at intervals of 2 degrees, and the lower angles at intervals of 5 degrees ; it is therefore necessary to place a staff with marked feet alongside the tree, so as to read on it the distance between the point where the lower ray hits the tree and its foot ; this has to be added to the measure- ment of the height. Brandis' instrument is at the same time a clinometer, with which angles of slopes can be measured and roads laid out. It may, therefore, be considered the most useful of the instruments here described. measurement of volume with xylometer. 25 6. The Xylometer, used for the Direct Measurement of the Volume. The method is based upon the fact that a body submerged in water displaces a volume equal to its own. The instrument con- sists of a graduated vessel (Fig. 16) to which a graduated scale is fixed. Before and after submersion, the level of the water is read on the scale, and the difference gives the volume of the submerged body. The method is used for the measurement of irregular pieces, such as rootwood and faggots. To obviate the necessity of submerging large quantities of wood, the whole is first weighed Fig. 15. Fig. 16. and only a portion submerged. Let the weight of the whole be W , that of the submerged part w, the volume of the former V and of the latter v, then W : w = V : v, and V W v X — . w Instead of having a scale attached to the xylometer, the latter may be filled with water up to an opening, the wood submerged, and the outflowing water caught in a graduated vessel (Fig. 15). In scientific investigations the xylometer is used in the deter- mination of the specific gravity and the solid volume of amorphous pieces of wood by the hydrostatic method. Although these matters are rarely required in practical forestry, the following notes on them may here be recorded : — 7. Determination of the Specific Gravity of Wood. The specific gravity of a piece of wood is the ratio which its weight bears to the weight of an equal volume of water ; in other 26 INSTRUMENTS USED IN MENSURATION. words, water is the standard of measurement and its gravity is placed at 1. A cubic foot of water at a temperature of 4 C Celsius weighs 62-5 lbs., and the specific gravity of any wood is found by dividing its weight in pounds per cubic foot by 62-5 ; con- versely, the weight in pounds per cubic foot of any wood is obtained by multiplying 62-5 by its specific gravity. Wood will sink or float according as its weight per cubic foot is more or less than 62-5, or its specific gravity more or less than 1. Example. — A piece of wood weighs 58 lbs. per cubic foot ; its specific gravity is = ^~— = -928. Or, a piece of wood has a specific gravity of 1-124 ; its weight per cubic foot is = 62-5 X 1124 = 70-25 lbs. Methods of Determination. — (1.) A regular shaped piece of wood is found, by mensuration, to have a volume = V, and its weight W = W in pounds ; then its specific gravity = ^ ^r-~ and its W weight in pounds per cubic foot = =^. Example. — A rectangular piece of wood of the dimensions 12" x 9" x 8" has a volume = -5 cubic feet and weighs 30 lbs. Its specific gravity = g2 g = -96 30 Weight per cubic foot = — = 60 lbs. (2.) If the wood is of an irregular shape its specific gravity may be determined either by the xylometric or by the hydrostatic method. (a) Xylometric Method. — The weight of the wood is found on a balance and the volume by submersion in a xylometer. The specific gravity or the weight in pounds per cubic foot is then calculated as described above for the regular shaped pieces. (b) Hydrostatic Method. —Weight of the wood in the air, W ; its weight while submerged in water, W ' ; then, as the loss of weight in water is equal to the weight of the same volume of water, specific gravity = w _ w - Example. — A piece of wood, which sinks in water, weighs 10-875 lbs. in air and 1-1875 lbs. when suspended in water ; its ■ ~ ., 10-875 specific gravity = ^^ _ - 1-123. VOLUME BY THE HYDROSTATIC METHOD. 27 If the wood floats in water, a weight, or sinker, must be added ; let S be the weight of the sinker under water. The specific W gravity of the wood = w s __ ^, . Example. — Let W (in the air) be = 3-5 lbs., S (in water) = 6-25 lbs., and the combined weight of wood and sinker under water, W = 5-875 lbs. 3.5 Then, specific gravity of the wood = ^5^ = "903. o'O ~p O'^O — O'o7o 8. Determination of the Solid Volume by the Hydrostatic Method. It has been shown above that if a piece of wood sinks in water its specific gravity is w , , w and also ~V X 62-5 W-W" hence V X 62-5 = W - W and V = W ~J V ' . o2-5 If the wood does float : — W W Specific gravity = y x ^ and also = w ^ s _ w \ hence V X 62-5 = W + S-W, and V = ^ K 62-5 The volume of the sinker should be deducted from V. Examples. — A sinking wood weighs in air = 35-25 lbs. ; in water = 7-5 lbs. Volume = £3-^ = -444 cubic feet. bJ'O A piece of floating wood weighs in air = 90625 lbs. ; S = 6-25 lbs. in water ; wood + S in water = 4-1875 ; T7 9-0625 + 6-25 - 4-1875 ._. .. , . V = -- _ = -178 cubic feet. 62-5 From this the volume of the sinker is to be deducted. 28 CHAPTER II. MEASUREMENT OF THE VOLUME OF FELLED TREES. The methods of measuring the various dimensions of felled trees have been explained in Chapter I. In this place the determination 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 considerably ; hence, they must be considered separately. 1. Volume op the Stem. If the stem, or trunk, of a tree had a regular or distinct geometrical 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 shapes of trees differ widely accord- ing to species, age and the conditions under which they have grown up, whether in the open or in a fully stocked wood. At the same time, trees of the same species and age, grown under the same conditions, generally show shapes which are nearly identical. Moreover, experi- ence has shown that each part of the stem shows approximately a constant form. Thus, the uppermost part, a (Fig. 17), of an undivided stem has generally the shape of a cone, the lowest part, c, that of a neiloid (truncated semi-cubical paraboloid), while the greater part of the trunk, between the two extreme ends, has a shape between a cylinder and a cone, which differs somewhat from that of a parabo- Fig. 17. loid, but the difference is generally small. Hence, VOLUME OF THE STEM. 29 the calculation of the volume may be effected by the use of the following formula : — u s v . If k = the height, or length, S = the lower cross section, s = the upper cross section, and s m = the middle cross section (Fig. 18), the volume, V, of each of the above-mentioned truncated solids is, according to (Simpson's) •-.-- s ■•->; rule— Fig. 18. F = g + «x«-+JL x> . This formula reduces — For the cylinder to V = S X h For the cone to V = — ^ — S 4- s For the truncated paraboloid to V = — ^ — X h, or, = s m X h. The first of these two formulas is known as Smallian's formula, and the second as Huber's formula. 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. As by far the greater portion of the stem approaches in shape a truncated paraboloid, it has been found that, if the stem is divided into a number of pieces of moderate length, each can, without committing any appreciable error, be considered as a truncated paraboloid. Of the two formulas the latter ( V = h X s m ) is the more convenient, and experience has shown that it is even more accurate than the former. According to this method, the volume of the whole stem is obtained by means of the following formula (see Fig. 19) : — Volume of stem = s 1 h 1 -{- s 2 h 2 -{- s 3 h 3 -\- . . ., where s v s 2 , s 3 . . . are the areas of the cross sections taken in the middle of successive paraboloids, and h v h 2 , h 9 . . . the 30 MEASUREMENT OF VOLUME OF FELLED TREES. corresponding heights, or lengths. If the pieces are made of equal length, the above formula changes into the following : — Volume of stem = (s x -f- s 2 + s 3 -f- . . .) h. This formula is used in all scientific investigations, and the degree of accuracy with which it works depends on the length of the pieces. For the purposes of determining the yield of woods and for the sale of logs, the formula is further simplified by considering each log as one paraboloid ; in other words, the volume is calculated Fig. 19. from the middle section of the log multiplied by its length, accord- ing to the formula — V = S m x H, where S m represents the area of the circle, or sectional area, in the middle, and H the total length of the log. Experience has shown this formula to give sufficiently accurate results for all practical purposes. The area of the cross-section is obtained, either by measuring the girth, or the diameter. If g = girth, d = diameter, and r the radius, the section is — f or and S = f- = -0796 X g 2 , 477 S = ?-£- = -785 xd 2 = r 2 x 77, 4 V = -0796 xg 2 X H = -785 X d 2 x H = r 2 x tt X H. In practical work, the sectional areas are taken from specially prepared tables ; there are also tables which give directly the volume of logs according to their mean girth and length, or their mean diameter and length. (See Appendix I.) All these calculations are made on the assumption that the section represents a circle. This is, however, rarely the case. VOLUME OF THE STEM. 31 As a rule, the degree of divergence from the circular shape depends on : — (1.) The part of the stem ; generally the lowest and uppermost parts differ most. (2.) The age of the tree ; young trees are more regularly shaped than old ones. (3.) The species. (4.) The conditions under which the tree has grown up ; in fully stocked 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 ir- regular ellipse, the greater axis of which lies, in the same locality, as a rule in a constant direction. Where trees are much exposed to wind, the greater axis lies generally in the direction of the prevailing wind : in Western Europe, therefore, from west to east or from south-west to north-east. The inaccuracy caused by measuring the girth, and calculating therefrom the sectional area, has been found to amount, on an average, to about 7 per cent. ; 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 amount. It follows that the latter is more accurate than the method of basing the calculation of the volume on the girth. 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 — S = |) 2 = -0625 x g* In comparing this with the real sectional area = -0796 X g 2 , it is found that the quarter-girth method gives only 78-5 per cent, of the true basal area and volume, omitting 21-5 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 quanti- ties corresponding to the other by deducting 21-5 per cent, of the volume. If the bark has been omitted in the measurements in 32 MEASUREMENT OF VOLUME OF FELLED TREES. both cases, no further correction is required. In measurements according to the quarter-girth, it is usual to deduct for the bark one inch out of every twelve of the quarter-girth, before the latter is squared. Hence, the deduction on account of bark comes to 12x12 — 11x11 = 144 — 121=23 square inches out of every 144. In other words, a reduction of 16 per cent, is made on account of bark. This may be too much in some cases and too little in others. It is a much better plan, in the case of felled logs, to remove a ring of bark, and to measure the girth or diameter over the wood only. 2. Volume of Branch and Root Wood. In some cases, pieces of branch and root wood are of a suffi- ciently regular shape to measure and calculate their volume 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, say, 100 cubic feet. Such a space would con- tain a certain amount of wood and of air. In order to obtain the proportion of each, the volume of some stacks of the different classes of wood, such as split wood, round billets, branch wood, faggots, or root wood, is carefully ascertained. 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 :.n a xylometer (see page 25) and ascertain the volume by measuring the quantity of the displaced water. From the data thus obtained, average coefficients are calculated and used on subsequent occasions. It is evident that different descriptions of wood give different coefficients. The solid contents of stacked wood depend on many things, amongst which may be mentioned : — (1.) Shape and nature of the pieces : thick, smooth and straight pieces give more solid contents than thin, bent, uneven pieces. (2.) Length of pieces : short pieces pack better than long ones ; hence, they give a higher percentage of solid contents. (3.) Method of stacking : careful stacking causes the per- centage of solid wood to be considerably increased. Under these circumstances, the coefficients differ in accordance VOLUME OF THE BARK. 33 with local conditions. By way of illustration, the following may be given : — Split firewood . . . . . . = -7 Round firewood billets under 5" diameter . = -6 Root and stump wood . . . . = -5 Faggot wood stacked (not bound) . . = -2 That is to say, 100 cubic feet of stacked split firewood contain 70 cubic feet of solid wood and 30 cubic feet of air, etc. 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 xylometrically. 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 immersed before and after barking. According to species, age, and locality, the bark comprises from 4 to 20 per cent, of the total volume. Schwappach found on a number of trees the following psrcentage of bark : — Oak . . = 15—20 Alder . = 16—19 Ash . . = 12—14 Lime . = 16—19 Elm . . = 9—11 Aspen . = 9—13 Birch . . = 13—17 Scots Pine . = 10—16 The Forestry Commissioners have published in their Bulletin No. 3 figures obtained from numerous measurements made in regular woods, which gave the following results : — Percentage of Bark. Quality Class according Scots Pine, Scots Pine, to Height at 50 years Larch. Spruce. Scotland. England. of Age. Per cent. Per cent. Per cent. Per cent. 80 feet 18 10 70 „ . 19-5 10 60 „ . 21 10 13-5 12-5 50 „ . 22 11 15 13 40 „ . . 22-3 12 16-5 13-5 30 „ . . 17 16 34 MEASUREMENT OF STANDING TREES. Tanning bark is usually sold by weight ; other bark is sold according to measurement, like firewood. In Britain, figures are sometimes locally obtained which indicate the proportion between the quantity of timber and that of tanning bark. Such figures vary according to local conditions and custom. CHAPTER III. MEASUREMENT OF STANDING TREES. 1. Ocular Estimate. Originally, the volume of standing trees was estimated. Such an estimate takes into consideration the special shape or form of each tree, and fixes the volume accordingly. The accuracy of purely ocular estimates depends entirely on the person who makes them. To be only approximately correct, the estimator requires great practice and occasional 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 constantly. Mistakes of 25 per cent, are of common occurrence, and they may reach up to 100 per cent, in the case of an inexperienced estimator. The uncertainty of purely ocular estimates led to the measure- ment 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 near the base, a matter which he must decide according to the peculiar shape of the tree. By degrees, it was considered desirable to collect data regarding the form of various trees which might be utilized in subsequent estimates, and thus foresters arrived at the method next to be described. MEASUREMENT BY MEANS OF FORM FACTORS. 35 2. Measurement of Volume by means of Form Factors. a. Definition and Classification of Form Factors. By " form factor " is understood the proportion which exists between the volume of a tree and that of a regularly shaped body of the same base and height as the tree. The form factor means, therefore, a coefficient with which the volume of the regularly shaped (geometrical) body must be multiplied in order to obtain the volume of the tree. Any regularly shaped body, the volume of which can easily be calculated by means of a mathematical formula, is suited for the 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 = s X h, Volume of tree = v = sxhxf, and v Form factor = f = — 7 . J s X h Various kinds of form factors are used in forestry, of which the following may be mentioned : — (1.) Stem form factors, which refer only to the volume of the stem above ground. (2.) Tree form factors, which refer to stem and branches, omitting root wood. (3.) Timber form factors, which refer only to the parts of the tree classed as timber, whether they are taken from the stem or branches, omitting all other material. The volume of the stem of a tree by itself is always smaller than that of the corresponding cylinder ; hence, the form factor for the stem only is always smaller than 1. If the volume of the branches is added, the form factor is sometimes greater than 1, especially during the early youth of the tree. Form factors for branch wood, faggots, 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. D2 36 MEASUREMENT OF STANDING TREES. As it would be highly inconvenient to measure the diameter, or girth, of the tree close to the surface of the ground where it is usually cut, it has been agreed to take the measurement at a convenient height. According to whether that point is fixed or variable, the following kinds of form factors may be distin- guished : — (1.) Absolute Form Factors. — The diameter (or girth) is measured at any convenient height above the ground, and the form factors refer only to the part a of the tree above that point (Fig. 20), while the volume of the piece b below it is ascer- tained by separate measure- ment and added to the part above it. 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, T Lth, J th, etc. (Figs. 20 and 21). In this case, the height of the ideal cylinder is equal to the height of the tree. Such form factors, it was believed, would have the advantage that all trees of the same shape would have the same form factor, since they have been measured at a height which bears in all cases the same proportion to the total height. There are, however, various drawbacks to the employment of these form 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 as regular as had been supposed ; that is to say, Fig. 20. Fig. 21. DETERMINATION OF FORM FACTORS. 37 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 and France now generally fixed at 1-3 meters = about 4 feet 3 inches.) 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 from the foot of the tree, the form factors of two trees which show the same shape but differ in height are not 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 con- sideration. Nevertheless, in practice, these are the only form factors now used. b. Determination of Form Factors. At first, form factors were estimated, taking into consideration 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 it comes practically to the same thing as estimating the volume direct. To eliminate such uncertainty, tables have been prepared which give the form factors for different species, heights, and ages, such tables being based upon the results obtained by the measurement of numerous felled trees. Of late years, it has been recognised that, for ordinary purposes, the variations due to age can be omitted, except where great accuracy is required, as in scientific investigations. The following table shows the form factors, taken from Con- tinental yield tables (see next page) : — 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 : — 38 MEASUREMENT OF STANDING TREES. Table of Form Factors, taken from Continental Tables. Height of Tree Form Factors for Timber in the round and Faggots. Height of Tree or Wood. or Wood. Feet. Oak. Beech. Alder. Birch. Scots Pine. Spruce. Silver Fir. Larch. Feet. 20 •70 •76 •56 •86 1-02 110 •77 20 30 •63 •69 •51 •23 •72 •89 •82 •66 30 40 •60 •65 •52 •34 ■64 •78 •69 •62 40 50 •59 •61 •52 •45 •58 •71 •64 •58 50 60 •59 •60 •52 •53 •55 •66 •61 •55 60 70 •58 •59 •52 •56 •53 •62 •60 •52 70 80 •58 •58 •51 •56 •52 •59 •59 •50 80 90 •58 •58 •51 •57 •58 •48 90 100 •58 ■59 •50 •55 •57 •47 100 110 •58 •60 ■50 •53 •56 •46 110 120 •58 •61 •49 •52 •55 •45 120 130 •52 •55 •44 130 140 •52 •55 •43 140 150 •51 150 Form Factors for Timber in the round down to 3 inches Diameter. 20 •31 •19 •20 •32 •36 •40 •32 20 30 •37 •33 •30 •12 •38 •48 •45 •39 30 40 •45 •41 •40 •26 •44 ■52 •48 •44 40 50 •49 •45 •45 •37 •46 ■53 •49 •46 50 60 •51 ■47 •49 •43 •47 •53 •50 •45 60 70 •52 •48 ■49 •45 •47 •54 •50 •44 70 80 •52 •49 •48 •45 •47 •52 •51 •43 80 90 •52 ■49 •47 •47 •51 •52 •43 90 100 •53 •50 •46 •46 •50 •51 •43 100 110 •53 •52 •46 •49 •51 •42 110 120 ■53 •54 •46 •49 •50 •42 120 130 •48 •50 •41 130 140 •48 •50 •40 140 150 •47 150 Form Factors for Timber according to Quarter-Girth Measurement. 20 •23 •14 •15 •24 •27 •30 •24 20 30 •29 •25 •23 •09 •29 •36 •34 •29 30 40 •34 ■31 •30 •20 •33 •39 •36 •33 40 50 •37 •34 •34 •28 •34 •40 •37 •35 50 60 •38 •35 •37 •32 •35 40 38 •34 60 70 •39 •36 ■37 •34 •35 •40 ■38 •33 70 80 •39 •37 •36 •34 ■35 •39 •38 •32 80 90 •39 •37 •35 •35 •38 •39 •32 90 100 •40 •38 •34 •35 •38 •38 •32 100 110 •40 •39 •34 •37 •38 ■31 110 120 •40 •40 ■34 •37 ■38 •31 120 130 •36 •38 •31 130 140 •30 •38 •30 1 10 150 i •35 150 Form Factors for larch, spruce, and Scots pine so far obtained in Britain will be found in Appendix IV. MEASUREMENT BY MEANS OF VOLUME TABLES. 39 3. Measurement of Volume by means of Volume Tables. If, instead of giving the form factors only, they are multiplied by the corresponding heights and basal areas, the volumes of the trees are obtained, which can be arranged into so-called " volume tables." The latter may be defined as tables which give the volume of single trees arranged according to species, diameter, height and in some cases also according to age. These tables rest upon the assumption that trees of the same species, which have reached an equal height and diameter (basal area) in about the same time, show also an equal volume. As regards the age of the trees, experience has shown that it afreets the volume to some extent, even for the same height and basal area, because with advancing age the stems become somewhat more full-bodied or less tapering ; or the tapering commences at a greater height than in younger trees. Hence, volume tables are sometimes divided into two parts — say, for trees below half the rotation in age, and secondly for trees older than about half the rotation. In order to use such tables, it is necessary to ascertain the diameter at chest-height, the total height and the approximate age of the tree, when the volume corresponding to these data can be obtained from the tables. It must, however, not be forgotten that the tables give only averages, and, consequently, only true results if used for determining the volume of a number of trees, or of whole woods. Tables of this kind have been prepared in Germany and France for many years past ; of late also by the Forestry Com- mission for larch and Scots pine. The numerous measure- ments made by the German Forest Statistical Association, during more than 50 years, have yielded a rich crop of data which have been arranged in tables according to species and dimensions. They are, no doubt, of great use, but they cover many pages, and it takes time to look up the particular dimensions. In the author's opinion, the method of taking the volume of the cylinder (equal to the height multiplied by the basal area) from the table in Appendix I., and multiplying it by the form factor, works quicker and suffices for all practical purposes. 40 MEASUREMENT OF STANDING TREES. Example. — An oak has a height of 80 feet, and a diameter of 24 inches at 4 feet 3 inches from the ground. The table in Appendix I. gives — Volume of cylinder . . . = 251-3 The form factor for timber (page 38) = -52 Volume of tree in the round . . = 251-3 x -52 = 130-7. Or, according to quarter-girth measurement, Volume = 251-3 X -38 = 98 cubic feet. Extracts from the British tables are appended : — British Volume Tables for Larch and Scots Pine. Girth at 4 ft. 3 ins. Inches. Total Height in Feet. Girth at 4 ft. 3 ins. Inches. 30—40 40—50 50—60 60—70 70—80 80—90 90—100 Volur. ne per Tree (Cubic Feet under Bark). Larch. 8 •08 8 12 •64 •66 •74 12 16 1-40 1-58 1-80 210 16 20 2-40 2-78 3-25 3-7 4-2 20 24 3-66 4-20 4-90 5-8 6-6 7-6 24 28 5-8 6-8 8-2 9-6 10-8 12-2 28 32 7-7 91 110 130 14-5 16-0 32 36 100 11-8 141 16-5 18-6 20-4 36 40 151 17-8 20-5 230 25-2 40 44 22-0 251 28-1 30-8 44 48 26-2 300 33-5 36-8 48 52 35-2 39-2 44-0 52 56 45-6 52-4 56 60 53-3 630 60 Scots Pine. 12 •64 12 16 1- 29 1-85 16 20 2- 1 2-88 , , 20 24 3- 2 414 5-3 6-5 24 28 4- 5 5-48 71 8-6 28 32 70 9-2 111 130 32 36 8-8 11-5 13-9 16-3 36 40 13-9 16-8 19-8 40 44 16-4 19-8 23-6 28-0 44 48 190 230 27-4 320 48 52 21-8 26-3 31-3 36-4 52 56 24-9 29-8 35-6 41-2 56 60 33-5 40-2 46-4 60 64 37-8 45-3 52-8 64 68 51-2 1 61-0 68 measukement by sections. 41 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 determined indirectly. The latter, as has been explained in Chapter I. (page 13), is subject to great inaccuracies. Where the diameter at half height is wanted, it is often esti- mated from the diameter at height of chest. The method is a rough one, but much used in Britain, France, and Belgium. As far as the author is aware, no uniform method of estimating the girth or diameter at half height from the girth or diameter at, say, height of chest has been recognised in Britain. Consequently, the actual estimate depends on the individuality of the estimator. No wonder, then, that different estimators obtain different results. The calculation of the volume by means of form factors, which represent the average of numerous measurements of trees lying on the ground, leaves no latitude to the estimator. He measures the diameter of the tree at height of chest and the height ; he takes the basal area and form factor out of a little table which he carries in his pocket and obtains the volume by a simple multi- plication. Example. — An oak tree, grown in a fairly stocked wood, has a diameter of 12 inches at height of chest and a total height of 70 feet. On refer- ence to the table in Appendix I., it is found that the basal area, corre- sponding to a diameter of 12 inches, is s — -7854, and on reference to page 38 the form factor for a height of 70 feet will be found to amount to -52 for timber in the round, or -39 for quarter-girth measurement. Hence, the volume V = -7854 x 70 x -52 = 28-5 cubic feet in the round, or V = -7854 X 70 X -39 = 21-4 cubic feet quarter-girth measurement. The product of -7854 x 70 can be obtained from the table in Appendix I. without multiplication. On the other hand, according to British custom, the estimator has to do three things : (1.) to measure the girth at height of chest, say, = 38 inches ; (2.) the length of serviceable timber, say 50 feet ; and (3.) to estimate the girth at 25 feet from the ground. Supposing he estimates a decrease of 20 per cent., then the girth at 25 feet comes to about 30 inches, and the volume, according to the quarter-girth measurement, amounts to — V = (7 ' 5) ' x 50 = 19-5 cubic feet. 144 42 MEASUREMENT OF STANDING TREES. If he estimates the decrease of the girth at 15 per cent., the girth at 25 feet from the ground would be 32 inches, and V = {8) \ * 5 ° = 22-2 cubic feet. 144 If he estimates the decrease at 25 per cent., the girth at 25 feet comes to about 28 inches, and (7)*x50 V ~ 144 In fact, the volume thus estimated would range from 17 to 22-2 cubic feet, and the only chance of obtaining the exact amount depends on the skill of the estimator, thus introducing a factor of considerable uncertainty. The most urgent need for calculating the volume of trees grown in Britain in fairly well-stocked woods is the collection of data from which form factors and volume tables can be calculated, whether for determining the volume in the round or according to quarter-girth measurement. The Forestry Commission has made a beginning by publishing volume tables for larch and Scots pine. Similar tables for other species will, no doubt, follow. The method is, however, not applicable in the case of hedgerow trees, or others grown under similar conditions. In the latter case, each tree must be measured, or estimated, separately. 43 CHAPTER 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 only over 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 measurement of all trees and that of selected trees called sample, or type, trees. A. Determination of the Volume by the 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. In all other cases, the following system is chosen, as it works more rapidly. B. Determination of Volume by means of Sample, or Type, Trees. The volume of a wood consists of the sum of the volumes of the individual trees. The volume of each tree is calculated according to the formula — v = s X h X /, 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 44 MEASUREMENT OF WHOLE WOODS. to ascertain them separately for each tree as indicated under A. In the case of regularly grown woods, however, there are always a number of trees which show, at any rate approximately, the same basal area, height and form factor, so that they can be thrown together and dealt with in a uniform manner ; in other words, all trees of a wood which show the same base, height and form factor are joined into one class ; the volume of one tree (or of a few trees) is ascertained, and the volume of the whole class obtained by multiplying the former by the number of trees in the class. If every class is dealt with in the same way, the 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 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, well-stocked woods, the height and form factor are approximately functions of the diameter of the tree ; in other words, trees of the same diameter or girth 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, or girth, classes only. In open woods, however, the height and form factor vary within such wide limits that, besides diameter classes, at any rate height classes also must be formed. In the case of selection forests and irregularly stocked woods generally, the volume of each tree must be separately ascertained. 1. Description of the General Diameter Class 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 of GENERAL DIAMETER CLASS METHOD. 45 accuracy. As a rule, all classes are given the same extent, that is to say, either 1 inch, 2 inches, 3 inches, etc., or part of an inch. For the purpose of forest working plans in Europe, each class comprises 1 or 2 inches : in India frequently, as yet, 6 inches. The calliper, used in measuring the diameters, should have a rounded-ofl scale, as described in Chapter I. — that is to say, in the case of inch classes, the first should comprise the space from | to 1^ inch ; the second that from 1| to 2\ 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 accurately. When- ever practicable, the height should be the height of chest of an average man, say, equal to 4 feet 3 inches. 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 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. c. The Booking of the Measurements. In measuring the diameter, the gaugers call out each measure- ment and in mixed woods also the species ; the book-keeper enters each announcement, repeating it at the time, so as to prevent mistakes. A book-keeper may work with one or two gaugers, the party 46 MEASUREMENT OF WHOLE WOODS. taking a narrow strip of 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 following samples will show : — Diameter in Inches, measured at 4' 3" from the Ground. 10 11 Species. Beech. U II I H i mi mr TnT ttTT Oak. Ash. fnf n Grand Total Number of Trees. Beech 18 23 37 27 105 Oak. 13 13 14 49 Ash. 27 Total 30 44 59 4s 181 The first two methods of booking are 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 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. 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. GENERAL DIAMETER CLASS METHOD. 47 A further requirement is that the sample tree should show a basal area which corresponds to the mean section of the class. Such a tree is not always found, so that it is necessary to take a tree as near as possible of the true section, and to modify the volume in proportion to the basal areas of the true and approxi- mate sample trees. Let v = volume of true sample tree, v' that of the approximate sample tree, s and s' the corresponding basal areas, then v is found by the formula — v : v' = s : s' and / s v: = v X -. s 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 tree is felled, the stem and all straight pieces of branches, in fact all regularly shaped parts, are divided into pieces of moderate length, from 3 to 10 feet, according to the desired degree of accuracy, and the volume of each section is ascertained separately by the formula (see page 29) : — v = s m X h. The volume of all irregular pieces, including root and branch wood, is ascertained, either by the xylometric method, or by proportionate figures, or by measuring their volume stacked, and multiplying it by 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 firewood, that proportion can be applied to other woods of a similar descrip- tion. The determination of the volume of sample trees by means of form factors or volume tables can be highly recommended, when- ever suitable tables are available, because they give averages, and that is just what is wanted in this case. Experience has shown 48 MEASUREMENT OF WHOLE WOODS. that form factors and volume tables are applicable for a con- siderable 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 in each class, the dimensions of which are exactly the average of the class. In that case, the volume of the class is obtained by multiplying the volume of the sample tree by the number of trees in the class. If — V = volume of whole wood, "^i> ^2' ^3 • • • — volumes of classes 1, 2, 3 . . . v v v 2 , v 3 . . . = volumes of mean sample trees of successive classes. n v n 2> n 3 . . . = numbers of trees in successive classes, then — V= V x X V 2 + 7g + . . . =v x x % + v % x n z + v 3 x w 3 + . . . (2.) The sample trees in the several classes differ in basal area from the mean basal areas. If the volumes of the approximate sample trees are v/, v 2 , v 3 ' . . . and the corresponding basal areas = s/, s 2 , s 3 , .... then T/ v/ X s, _ , 7 Vo X So T7 vJ X So V 1 = ^—— 1 Xn 1 ; F 2 = A - 7 - 2 X» 2 ; 7 3 = -^- 3 X n 3 . . . t> 1 6 2 S 3 As s 2 X n x = S ± = total basal area of the first class, s 2 X n 2 = S 2 = total basal area of the second class, etc., the volume of the wood is : — v _ VxSi v 2 ' x S 2 . v 3 ' X S 3 . *-~^r- + —^r~ + —^— + • • • (3.) Several sample trees are measured in each class. In that case — 1 7_ K'+«r+<"+ • ■ Qx^ ( V 2 '+V 2 "+V 2 '"+ . . .)XS 2 , ' S 1 f +S 1 "+S 1 '" + ... T S 2 '+S 2 "+S 2 '" + ... +••• METHOD OF ARITHMETICAL MEAN SAMPLE TREE. 49 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 n i> w 25 w 3 . . . be the numbers of trees in the several classes ^ij ^2> S3 • • • ,, basal areas ,, ,, ,, ,, h v h 2 , h 3 . . . „ heights „ „ „ ,, fi>f&fz • • • » form factors „ „ and s, h, f the basal area, height and form factor of the mean tree of the classes thrown together, then the following equation holds good : — V = n x XSjX h x x/j + BjXSjXJjX/jl... = (% + n 2 + . . .) X s X h X /. If it is now assumed that h x X f x = h 2 X f 2 = h 3 X / 3 = . . . = h X /, then the above equation becomes — » 1 X* 1 + n a Xs 2 4-... = (»i + n 2 +...)«, and _ n x X s x + n 2 X s 2 + • • • S_ n x + n 2 + . . . "IP where S = basal area of all trees of the group, and N = total number of trees ,, „ In words, the basal area of the average or mean 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 — 7 = v X N, where v represents the volume of the arithmetical mean sample tree with a basal area = s. If no tree can be found with the basal area s, another as near as possible to it is chosen of a section s', and the volume of the group is obtained by the formula : — v = ZL4-5 x n = £££, s s since s X N = S = the basal area of all trees in the group. 50 MEASUREMENT OF WHOLE WOODS. If several approximately mean sample trees are taken, the formula changes into the following : — .) X S V - fv' + v" + v'" + 8' + S" + S'" . . . The above method rests on the assumption that h 1 f 1 = h 2 f 2 = h 3 f 3 = . . . = hf. This, however, is not absolutely correct, though it holds good approximately in regularly grown woods. It follows that the degree of accuracy decreases with the increase in the number of classes which are clubbed together into a group, the least accuracy being obtained by joining all classes into one group. In this latter case, the method is known as " the method of the arithmetical mean sample tree." Example. — In order to illustrate this and the methods to be described hereafter, one acre of Scots pine wood, 70 years old, was callipered, and eighteen sample trees of various diameters were felled and measured. Only timber down to 3 inches diameter at the small end was included in the account. The following list shows the dimensions and the volumes of the sample trees : — Number. Diameter. Height. Basal Area. Volume, Solid. Inches. Feet. Square Feet. Cubic Feet. 1 7-50 37 •307 6-62 2 8-50 44 •394 7-26 3 9-25 66 •467 1213 4 9-40 46 •482 10-81 5 9-60 50 •503 11-63 6 10-70 40 •624 12-37 7 10-70 64 •624 1714 8 11-00 57 •660 16-19 9 11-50 56 •721 17-43 10 11-60 58 •734 19-17 11 1210 48 •799 20-41 12 1210 62 •799 22-40 13 1310 63 •936 2593 14 1316 56 1-009 21-87 15 1500 48 1-227 27-79 16 15-00 59 1-227 28-40 17 16-10 63 1-467 38-53 18 1700 64 1-576 39-50 The appended example illustrates the procedure which has been described above. CALCULATING THE VOLUME OF A WHOLE WOOD. 51 General Method of Calculating the Volume of a Whole Wood for an Acre of Scots Pine, 70 Years Old. A. — Calculation by Inch Classes. Diameter. Inches. Number of Trees. Basal Area. Square Feet. Sample Trees. Volume of Inch Class. Diameter. Basal Area. Volume. Cubic Feet. 8 9 10 11 12 13 14 15 16 5 10 30 40 50 45 30 20 10 1-75 4-42 16-36 26-40 39-27 41-48 3207 24-54 13-96 8-50 9-25 10-70 11-00 1210 1310 1500 15-00 16-40 •394 •467 •624 •660 •799 •936 1-227 1-227 1-467 7-26 1213 1714 1619 22-40 25-93 27-79 28-40 38-53 37 115 449 648 1,101 1,076 726 568 367 Total 240 200-25 5,087 B. — By Three Groups. Groups and Inches. Num- ber of Trees. Basal Area. Mean Sample Trees. Real Sample Trees. Volume of Group. Basal Area. Diam. Diam. Basal Area. Volume. Sq. Ft, Cub. Ft. I. 8, 9, and 10 II. 11, 12, 13 . III. 14, 15, 16 . 45 135 60 22-53 107-15 70-57 •503 •799 1-176 9-6 121 14-7 9-6 121 150 •503 •799 1-227 11-63 22-40 28-40 521 3,004 1,633 Total . 240 200-25 .. | 5,158 1 C '.—By the Arithmetical Mean Tree. 121 121 13-6 •799 •799 1-009 20-41 22-40 21-87 All inch classes . 240 200-25 •834 12-4 " 2-607 64-68 4,968 E2 52 MEASUREMENT OF WHOLE WOODS. 2. Modifications of the General Method. It has been shown above that the volume of a wood is repre- sented by the formula : — F=F 1 +F 2 +F 8 + . . . ^ 1 xf 1 + V2 xf 2 +^x~ 3 + . . . *1 *2 *3 Q S As long as the fractions —,—, + ••• differ, the volumes of the s 1 s 2 sample trees in the several classes or groups should be measured separately and the volume of each class, or group, calculated. In order to shorten the procedure, it has been proposed to fix the number of sample trees so that S-, S 2 So , , — ■ = —=—=... c, a constant. S 1 S 2 5 3 In that case the above formula reduces to 7 = (t>! + v 2 + v 3 + • • .) X c. By following this method, the sample trees of the several classes, or groups, can be thrown together and measured in one lot, while the volume of the whole wood is obtained by one calculation. This is a great convenience and saves much time. Based on this principle, a number of modifications of the general method have been elaborated, of which the following may be mentioned : — a. Draudt's Method. Draudt took p per cent, of the trees in each class as sample trees, the proportion of these to the total number of trees in each class being = z~ = -Op. He thus obtained the equation 7 X ■Op = v 1 X % X -Op + v 2 Xn 2 X -Op + v 3 X w 3 X -Op + . . The right side of this equation represents the volume of all sample trees equal to, say, v, giving 7 X -Op = v and F _ _v_ _ v X 100 _ -Op ~ p It generally happens, however, that the number of sample trees to be taken in each class includes a fraction of one tree. Draudt eliminates these fractions by considering -51 as a full sample tree and by neglecting -50 and under. The result of this operation is draudt's, urich's and hartig's method. 53 that the original proposition is no longer fully maintained ; more- over, some of the classes obtained no sample tree at all, and these are not represented in the calculation. Any degree of inaccuracy thereby caused depends on the total number of trees in the wood. There is no necessity to illustrate the method by an example, as it has been superseded by a further modification, which will be explained in the next paragraph. b. Urich's Method. In order to avoid the inaccuracy involved in Draudt's method, Urich proposes to form a number of groups, to allot to each the same number of trees, and to select the same number of sample trees in each group. The diameter of each sample tree should be the arithmetical mean of the group to which it belongs. In this way, the proportion between S and s is the same in each group, and the volume of the wood is, as in Draudt's method, obtained S by the formula 7 = vX - . Urich's method is thus a combina- J s tion of Draudt's method with that of the arithmetical mean sample tree of each group. The degree of its accuracy depends on the number of groups and on the number of sample trees measured in each. The method has the disadvantage that the basal area of the group sample trees must be calculated before they can be selected. Urich proposes to avoid this by estimating the mean diameter of the trees in each group. Experience has shown that the inaccuracy involved in this way is very small. An example of the method will be found on page 54. c. Robert Hartig's Method. In the two methods just described, each sample tree represents the same number of trees. As the volume increases rapidly with the increase of the diameter, it follows that a sample tree in a group of small trees represents a much smaller volume than one in a group of large trees. Hartig argues that each sample tree should represent the same volume and not the same number of trees, and he proposes to allot to each group an equal part of the total volume. As the latter is, of course, not known, and as the basal area fairly represents the volume, he allots equal parts of it to each group. He then calculates the basal area and diameter of 54 MEASUREMENT OF WHOLE WOODS. Urich's Method of Calculating the Volume of a Whole Wood for an Acre of Scots PrNE, 70 Years Old. Groups. Diameters and Number of Trees. Basal Area. Mean Sample Tree. Real Sample Trees. Volume of Wood. B. Area. Diam. Diam. B. Area. Volume. I. 8=5 9 = 10 10 = 30 11 = 35 80 1-75 4-42 16-36 23-10 •57 •82 111 10-2 12-3 14-3 9-6 10-7 12 1 131 15*0 150 •503 •624 •799 •936 1,227 1-227 11-63 1714 22-40 25-93 27-79 28-40 45-63 II. 11 = 5 12 = 50 13 = 25 80 3-30 39-27 2304 65-61 III. 13 = 20 14 = 30 15 = 20 16 = 10 80 18-44 32-07 24-54 13-96 89-01 Total of Wood 240 200-25 5-316 133-29 5,021 There is only one calculation according to the formula : — *7 1 t + U w A 13329 X 200,25 * nor i - * * Volume of the Wood = — — , olg = 5,021 cubic feet. 5-316 the mean sample tree for each group and selects the same number of these for each. The formula for Hartig's method is : — V . , &, 0» , So , v lX ~+ v 2>< 7 + ^X — + • s s s As — , — , — . . . are not of equal value, it follows that, theo- S l S 2 S 3 retically speaking, the sample trees should be measured and the volume of each group calculated separately. The addition of these volumes represents the volume of the whole wood. So far Robert Hartig. As his method stands, it is inferior to Urich's EXAMPLES OF URICh's AND HARTIG's METHODS. 55 Robert Hartig'S Method of Calculating the Volume of a Whole Wood for an Acre of Scots Pine, 70 Years Old. A — By Three Groups. Groups. Diameters and Number of Trees. Basal Area. Mean Sample Tree. Real Sample Trees. Volume of Groups and Wood. B. Area. Diam. Diam. B. Area. Volume. I. 8=5 9 = 10 10 = 30 11 =40 12 = 23 108 1-75 4-42 16-36 26-40 1805 •62 10-7 10-7 10-7 •624 •624 12-37 17-14 1-584 1,866 1518 66-98 1-248 29-51 II. 12 = 27 13 = 45 14 = 4 76 21-22 41-48 4-27 •88 12-7 121 131 •799 •936 22-40 25-93 66-97 1-735 48-33 III. 14 = 26 15 = 20 16 = 10 56 27-80 24-54 13-96 • • 1-18 14-7 15-0 150 1-227 1-227 27-79 28-40 66-30 2-454 56- 19 Total 240 200-25 4968 B. — By One Group. By throwing the three groups together, also the six sample trees, and making one calculation for the whole wood, we obtain : — 240 I 200-25 5-437 13403 4936 Formula for calculation : — t W J 13403 X 200 ' 25 A QQR U- f <. ^ olume of W ood = g^ — = 4,936 cubic feet. method because it involves the separate measurement of the sample trees of each group, and requires a number of calculations where only one is required under Urich's method. The author of this book has found, by trial calculations, that, if the sample trees are selected according to Hartig's method, they 56 MEASUREMENT OF WHOLE WOODS. can be thrown together and the volume of the whole wood ob- tained by one calculation, as in Urich's method, without any appreciable difference in the result, as will be seen by the example on page 55. The correctness of this view is confirmed by the results of the further example on page 64, being a record of the measurement of a wood by the British Forestry Commission. d. Determination of Volume by 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 methods. In all these cases the deter- mination of the volume is effected according to the formula : — V = S x H x F. How the basal area of a tree, class, or wood is ascertained has been shown above. The mean height of a number of trees or of a whole wood is ascertained in various ways, which differ somewhat in their degree of accuracy. The theoretically most accurate way is to obtain it out of the formula : — V = S X H X F = s ± X h x X /j + s 2 X h 2 X f 2 + . . . and H = SlX A i x /i + 5 2X h 2 xf 2 + ... Sx F This formula necessitates a knowledge of the form factors of all age classes and of the average form factor of the whole wood, which makes the determination of the mean height somewhat complicated. On reference to page 38 it will be seen that, for instance, the form factors for Scots pine, timber only, after the age of 40 years, and up to the age of 120 years, move between •45 and -47— in other words, they move within very narrow limits. The British yield tables so far published show equally narrow limits of change. Hence, a comparatively small inaccuracy is involved by assuming that the form factors of the several classes and the average form factor are very nearly of the same amount. This reduces the formula to : — Mean height = H = SlX h i+s 2 xh 2 + ... _ in words : " the mean height is equal to the total volume of FORM FACTORS AND VOLUME TABLES. 57 cylinders erected over the basal area of the trees divided by the total basal area." The mean height of a wood can also be ascertained by multiply- ing the mean height of each class with the corresponding number of trees and dividing the sum total thus obtained by the total number of trees in the wood, the method being expressed by : — „ n 1 xA 1 +n 8 xA 2 +... ff== N If a somewhat smaller accuracy suffices, a number of trees are selected which show about an average diameter and height, their height measured and the mean calculated, which represents the mean height of the class, group or wood, as the case may be. Another way is to take the height of the arithmetically mean tree as the mean height of the wood. The best method is to construct a " height curve " out of the measurements of a number of trees representing the several diameter classes. Assuming that nine trees selected in that way show the following dimensions : — Diameter in Inches. Height in Feet. Diameter in Inches. Height in Feet. Diameter in Inches. Height in Feet. 8-5 9-3 10-7 47 50 52 110 11-6 121 55 58 55 13-6 150 160 61 59 63 By plotting the heights as ordinates over the diameters as abscissae, Fig. 22 is obtained. B0 §55 n 50 45 • ^ 00 , — i l— ^— • 1(1 11 12 Diameter. 1(3 Fig. 22. 58 MEASUREMENT OF WHOLE WOODS. From this curve the following values of the heights of the several inch classes are read off : — Diameter in Inches. 9 10 Height Diameter Height Diameter Height in Feet. in Inches. in Feet. in Inches. in Feet. 45 11 54 14 60 49 12 56 15 62 52 13 58 16 63 By utilizing these data the mean height of the wood can be calculated. According to the basal area formula : — l-75x 45+4-42x 49+16-36X 52+26-40X 54+39-27 X 56+41 -48 X 58+32-07 X 60 Mean height = # = 57. +24-54X 62+13-96x63 200-25 = 57 According to the number of trees formula : — Mean height # = 56. 5x45+10x49+30x52+40x54+ 50X 56+45X 58+30X 60+ 20x62+10x63 240 = 56 According to the average of the sample trees : — Mean height = «+50 ± 52 ± 55^58+55+6I ± 59+63 = 55 feet. According to the heights of the mean sample trees of the inch classes taken from the height curve : — Mean height = 45+49+52+54+56+58+60+62+63 = ^ 9 The form factors must be obtained from form factor tables, if such are available. They are determined by the formula 7 F = ^ yj by measuring large numbers of felled trees when- ever fellings are made, and arranging the results into tables according to species, height and age (see page 38). An example of determining the volume of a wood by form fac- tors is appended (see page 59). The utilization of the form factor THE VOLUME TABLE METHOD. 59 method depends on the existence of form factor tables applicable to a particular locality, as they differ according to the quality of the locality. The form factors for Scots pine (average quality) given on page 38 refer to German woods, and are given as 462 for the wood here under consideration, while the corresponding form factors for Scots pine grown in Scotland are given as •39 in the yield tables published by the Forestry Commission. The latter are liable to be altered as further data become available. Calculation of the Volume of One Acre of Scots Pine 70 Years Old By Form Factors. A. — By Inch Classes. Diameter. Number of Basal Area, Average Form Volume. Inches. Trees. Square Feet. Height. Feet. Factor. Cubic Feet. c x d x e. a b c d e f 8 5 1-75 45 •45 35 9 10 4-42 49 •46 100 10 30 16-36 52 •46 391 11 40 26-40 54 •46 656 12 50 39-27 56 •46 1,012 13 45 41-48 58 •47 1,131 14 30 3207 60 •47 904 15 20 24-54 62 •47 715 16 10 13-96 63 •47 413 Total Volume = 5,357 B.— All Inch C Classes thrown together into One Group. 8 to 16 240 200-25 56-31 1 -462 5,210 e. The Volume Table Method. The method of preparing volume tables for single trees has been explained on page 39. Here the method of utilizing such tables for the determination of the volume of whole woods is dealt with. Theoretically, volume tables are obtained by multiplying the basal area at height of chest by the average height of the tree and by the form factor. In practice, they are obtained by measuring large numbers of trees whenever f ellings offer the necessary oppor- tunities. To be really useful, separate tables should be con- structed for different qualities of the locality, the latter being 60 MEASUREMENT OF WHOLE WOODS. determined by the height of the trees. Where great accuracy is essential, a further differentiation according to age is required, but this is not necessary for ordinary administrative purposes, such as the preparation of working plans. These tables give average data for the volume of trees of the several diameter classes, and that is just what is wanted in practical forestry. The volume of the whole wood is expressed by the formula : — V = v x X n x + v 2 X n % + v 3 X n 3 . . . The accuracy of the method should be exactly the same as that obtained by the method of form factors, while it avoids the difficult task of ascertaining the form factors separately. /. The Yield Table Method. The method of constructing yield tables is described in Chap- ter VI. They are tables which give the development of woods from their formation to the time when they are finally cut over, separately according to quality of locality. The volumes given for the several ages are used in determining the volume of grow- ing woods. For that purpose, the forester determines : — ■ (1.) The quality class of the locality. (2.) The density of the crop. (3.) The age of the crop. (4.) The mean height. The quality class in this case is best judged by the height growth ; the density of the crop is ascertained either by the basal area of the trees on a sample plot, or it is estimated ; the age is obtained either by the counting of rings on stumps, or by cutting one or more trees for the purpose, or it may be known from records. Based upon these data the yield can be taken from the yield tables. If, for a given age, the basal area in the table differs from that of the wood, it must be modified accordingly ; a second correction may be necessary owing to a difference in height. Example. — A Scots pine wood 60 years old has a mean height of 53 feet and a density equal to -8 of full stocking. The appropriate yield tables give the following data : — Quality Mean Height Volume. Class. at 60 Years. Cubic Feet. 1 67 4,840 II 57 . 4,250 HI 46 3,240 THE VOLUME CURVE METHOD. 61 The quality of the wood is between II. and III. class, but nearer to II., which has a volume of 4,250 cubic feet ; that amount must be reduced in the proportion of 53 : 57, owing to difference of height. As the density of the wood is only = -8, the remainder must be further reduced in the 53 proportion of 8:1, and the volume of the wood = 4,250 X -~ X -8 V = 3,161 cubic feet, In various European countries, where the management of forests has been organised and reliable yield tables have been compiled, the estimation of the volume by such tables is extensively prac- tised, and in some countries (as, for instance, in Hesse-Darmstadt) practically no measurements are made for the preparation of working plans and other administrative purposes ; in fact, the volumes are estimated by means of yield tables with such accuracy that the volumes obtained by subsequent fellings agree to a remarkable degree with the previous estimates, in addition to a great saving of work. Hence, the preparation of yield tables cannot be too strongly recommended to all countries where systematic management of the forests is aimed at. g. The Volume Curve Method. When no volume table suitable for the locality is available, the forester can construct a curve which gives the volume for the different size classes. He measures a limited number of sample trees, and plots their volumes as ordinates against the correspond- ing diameters as abscissa?. Between the points thus obtained he draws a mean curve, from which he can read off the volumes of trees of successive diameters, classed according to inches, half inches, or any other unit. Such a curve is called a " volume curve," and its data are used for the calculation of the volumes of the different diameter classes and of the whole wood, according to the formula : — Volume of wood = n t X v x + n 2 X v 2 + n 3 X v 3 + where >« l5 n 2 , n 3 . . . . represent the numbers of trees in the several classes and v v v 2 , v 3 . . . the volumes of the mean trees of the successive size classes taken from the volume curve. The degree of accuracy of the method depends on the number of measured sample trees used in the construction of the curve and the care with which they are selected. For practical requirements 62 MEASUREMENT OF WHOLE WOODS. the number need not be large ; generally it is quite sufficient to utilize the number of sample trees which must ordinarily be used under any of the methods described above. The plotting should be done on a large scale, which can then be reduced by photo- graphy, so as to bring the points closer together. This facilitates the drawing of the mean curve. Example. — A Scots pine wood, 70 years old, is found to contain 240 trees per acre, ranging from 8 to 16 inches in diameter at breast height. The following nine trees were selected fairly distributed over the several diameter classes (with a slight excess in the middle classes) showing the following results : — Diameter. Inches. Volume. Cubic Feet. Diameter. Inches. Volume. Cubic Feet. Diameter. Inches. Volume. Cubic Feet. 8-5 9-3 10-7 7-5 120 14-5 110 11-6 121 17-5 18-0 20-5 13-6 150 160 27-0 28-0 330 These results, being plotted in the manner explained above, give the curve shown in Fig. 23 : — 30 /» ^^ t I • . 25 Eh 3 3 on a a 3 > 15 % y/m • S • 10 • yr 11 12 Diameter in Inche*. 13 14 Fig. 23.— Volume Curve, BLOCK S METHOD. 63 From this curve, the volumes are read off for successive diameter classes and the volume of the wood calculated, as shown in the following table : — Diameter. Inches. Number of Trees in the Class. Volume of Mean Tree. Cubic Feet. Volume of Class. Cubic Feet. 8 9 10 11 12 13 14 15 16 5 10 30 40 50 45 30 20 10 50 100 13-5 17-0 20-5 24-0 27-0 300 330 25 100 405 680 1,025 1,080 810 600 330 Total 240 5,055 h. Block's Method of forming Groups. Block proposes a new method of forming groups, based on the opinion that the volume of the larger trees should be specially considered, as the smaller trees disappear in the subsequent thinnings. Accordingly, he forms a number of small groups from the largest trees downwards, placing, say, 20 trees per acre in each of the top groups, and an increasing number in the groups con- taining the smaller trees, with the residue in the last group. He also selects a number of sample trees, decreasing in number from the top downwards ; from these the volume of each group is separately calculated. Block considers his method as specially suited for the periodic measurement of permanent sample plots. It will be observed that Block favours the larger trees in two ways, by placing a smaller number of trees in them and by allotting more sample trees to them. It appears to the author of this book that this is overdoing the matter unnecessarily. At any rate, owing to the large number of groups and the separate calcu- lation of their volumes, the method involves very much more work than is required in Urich's or Hartig's methods, while experi- mental measurements seem to show that the increased accuracy, if any, is too small to compensate for the additional work. More- over, there is nothing to prevent an increase of the number of groups under Urich's or Hartig's method, if it should be con- 64 MEASUKEMENT OF WHOLE WOODS. sidered desirable ; or of giving extra sample trees to the groups of large trees. In the latter case, Urich's method would, however, lose the advantage of measuring up the sample trees in one lot, and of obtaining the volume of the wood by one calculation. With certain modifications, Block's method has been adopted by the Austrian Forest Research Institute at Mariabrunn, by the Prussian Research Institute at Neustadt-Eberswalde, and also by the British Forestry Commission in the measurement of the volume of permanent sample plots. Of the latter, a short description is given below. i. The British Forestry Commissioners' Method. The Commissioners have lately issued a memorandum dealing with the " Permanent Sample Plot Work." The latter is destined to serve for a variety of objects such as :— (1.) The determination of the volume of the stock at periodic measurements. (2.) The study of the increment of the plot under a continuous and definite system of management, so as to obtain data for the preparation and improvement of yield tables. (3.) To compare the development of adjoining sample plots in the same wood under different systems of management, so as to determine the best method of treatment for a particular species under a given set of conditions. To realise these objects, a very minute method of investigation has been designed, but in this place only the part referring to the determination of the volume of the crop will be mentioned. The trees in the plot are arranged, according to their girth (alas, not their diameter !), into \ inch girth classes. They are then allotted to a series of groups in the following ratio : — Area of Plot. Number of Group. 1 2 3 4 5 6 7 8 9 10 Number of Trees in each (J roup. •75 acre and over . 50 50 50 50 100 100 100 200 200 200 •3 to -75 acre 20 20 20 20 40 40 40 1 80 80 80 Below -3 acre 10 10 10 10 20 20 20 40 40 40 BRITISH FORESTRY COMMISSIONERS' METHOD. 65 Group 1 contains the largest and Group 10 the smallest trees. The basal area contained in each group is then worked out, as well as that of the average tree. Then, if possible, eight or more sample trees are selected, preferably in pairs, of as near as possible the average girth, height and shape of the class from which they are taken. It is essential that the sample trees should be spread evenly over the range of girth, and that they should, whenever possible, be taken from the surround of, and not within, the plot. The surround should be treated in the same way as the plot. The calculation of the volume is done for each group separately according to the formula V = S X H X F. To obtain the data required for these values, the following measurements are taken on each sample tree : — (1.) Girth at 4 feet 3 inches to the nearest | inch. (2.) Total height to nearest 6 inches. (3.) Timber height down to 3 inches diameter over bark. (4.) Girth at half timber height over and under bark. (5.) Length to lowest living branch = L c = lower crown. (6.) Length to lowest living whorl = U c = upper crown. The crown per cent, is obtained by the formula : — T Uc+Lc 2 Crown per cent. = j X 100, where L = total height. The volumes over and under bark are obtained by multiplying the basal area at half timber height over and under bark respec- tively by the timber height. The percentage of bark is obtained by the formula : — Bark per cent. = — V 1 mi X ^ The form factor is obtained by the formula : — Volume of tree Form factor Total height X basal area at 4 feet 3 inches' By introducing the volume over bark, or the volume under bark, the value of the form factor over or under bark respectively is obtained. Calculation of the Group Volumes and the Total Volume. — With the data given above, form factor and height curves are con- 66 MEASUREMENT OF WHOLE WOODS. structed. For the former, the form factors of the sample trees are plotted against their respective girths at 4 feet 3 inches, and a curve drawn through the points which express the mean relation- ship between girth and form factor. Similarly, the total heights of the sample trees are plotted against their girths and a girth height curve drawn. Mean height and form factor for each group are then read off the curves at the point coinciding with the mean girth of each group. The volume is then obtained from the following formula : — Volume of group = basal area of group X mean height X mean form factor. The addition of the volumes of the several groups gives the volume of the whole wood. A useful check on the method (it is suggested in the memoran- dum) especially where the trend of the form factor graph is doubtful, is obtained by plotting the volumes of the sample trees against the girths at 4 feet 3 inches and drawing a mean curve. The volume of the mean of each group can then be read off the curve and multiplied by the number of trees in the group, giving the volume of the group. These volumes can be compared with those found by the form factor method, and the latter adjusted if necessary. Thus, the volume curve decides in the end and acts as a corrector of any mistakes which may have been made in employing the exceedingly laborious form factor method. After all, it is clear that, if no mistakes are made in employing the latter, the results must be exactly those given by the volume curve method. Would it not save a great amount of work to employ the latter straight away, at any rate for the determination of the volume ? j. The Form Quotient Method. Theoretically, the formula V = S X H X F gives an abso- lutely correct expression, but in practice it has drawbacks. The determination of H can be effected by measurements of standing trees, but the determination of F necessitates the felling of a con- siderable number of trees. If the sample plot has a surround of sufficient size (and this should be the rule) all is well, because the sample trees can be taken from it. If a surround is not available, the sample tree must be taken from the plot itself. This leads to THE FORM QUOTIENT METHOD. 67 incomplete stocking, which reduces the value of the statistical enquiry unless trees taken out in thinnings are fit to serve as sample trees. To avoid this drawback, it has been proposed to substitute the form quotient Q for the form factor F. By form quotient is understood the proportion between the diameter taken at half the total height and the diameter at chest height. The former it is proposed to ascertain, either by measur- ing the angle between two rays from the eye of the observer directed to the edges of the tree, as well as the distance from the observer to the half -height diameter, or to send a man up for the purpose. To the author's knowledge, there is, except a theodolite, no clinometer fit to give a sufficiently accurate angle, owing to its small size and the possible irregularity of the half -height diameter, while sending up a man in the case of high trees seems altogether outside practical work. Recognising these difficulties, it has been proposed to cut down, after all, one or a few trees, so as to reduce the number of sample trees considerably as compared with the form factor method. But even that appears a doubtful expedient, because, to obtain a reliable form quotient, the cutting down of as many trees as for the construction of a form factor curve would be necessary. In these circumstances, the form quotient method offers no advantages over the form factor method, while it may give less accurate results. Jc. Other Methods. There are quite a number of other methods, some of which involve a very minute procedure ; others are only of some theo- retical value, and others give only approximate results. It would be going beyond the object aimed at in this book to give detailed accounts of these methods. All those likely to be utilised in the immediate future have been described above. I. Accuracy and Choice of Method. In the author's opinion, accuracy in measuring a wood depends far more on the care with which the operation is carried out than on the particular method adopted. Still, there are differences between the various methods. F2 68 MEASUREMENT OF WHOLE WOODS. For the measurement of permanent sample plots, the method of volume tables with 1-inch diameter classes is certainly to be recommended, provided that carefully prepared tables, classified according to quality of locality, height and age are available. In the absence of such tables, the volume curve method is undoubtedly the best substitute. Both methods give averages, and that is exactly what is wanted in statistical records. The method of form factors is, theoretically, just as good, but its application is more complicated and uncertain, unless accurate form factor tables are available. The author cannot find any reason for the adoption of Block's system of forming groups. It is an effort to attain super-accuracy, the realisation of which is doubtful, while it considerably increases the work. If the oldest groups really require some special attention, that can be given to them by allotting extra sample trees to them, instead of disturb- ing the method of placing the same number of trees in each group. The determination of the volumes of woods to be used in the preparation of working plans had best be done with data taken from yield tables. The method is quite correct enough for the purpose, and it reduces the work to a minimum. All it requires is a forester sufficiently trained to modify the yield table data correctly, according to local conditions. In the case of sales of woods, it will generally be wise to work according to the 1-inch diameter class method, with a mean sample tree for each class, using volume tables or volume curves, as the case may be. For general use, Urich's method of arranging the groups is specially recommended, together with the use of volume tables, if available. The form quotient method looks attractive at first sight, but, on closer acquaintance, it will be seen that it cannot be brought into the circle of practical politics. On the whole, it may be said that foresters should aim at the preparation of volume tables and yield tables. This done, the question of forest mensuration will be greatly simplified. Volume tables should be based on numerous measurements of cut trees, not only of those cut as sample trees, but wherever cuttings are made. The results should be arranged into, say, three qualities — best, middling and lowest — according to height HEIGHT IS NOT A FUNCTION OF THE DIAMETER. 69 growth. The trees placed in each quality class should be worked into separate volume tables. Experience will show, whether three classes are sufficient, or whether two additional classes (second and fourth) are required which, in the author's opinion, will not be the case. 3. The Height is not a Function of the Diameter. If in the case of equal diameters the heights differ considerably, then height classes may have to 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 marked changes in the quality of the locality occur, due to a change in the soil or subsoil, aspect, etc. In such cases the wood is divided into as many parts as there are different height classes, and each part is treated as a separate wood. The booking is done in the same way as that shown on page 46 for different species. If the different height classes are scattered over the whole area, as in selection forests, the diameter and height must be measured in each case. Where only two height classes are adopted, the height of each tree may be estimated, the diameter measured, and the tree placed in the one or other class. The necessity of forming more than two height classes is rare, except in selection forests. The distinction of height classes generally is a matter of some difficulty ; it is necessary only where a very high degree of accu- racy is aimed at. section ii.— determination of volume by means of sample areas. 1. General. Instead of measuring all trees in a wood, a certain part of the area may be selected, the volume on it ascertained, and from it the volume of the whole wood calculated. Such a part is called a sample, or type, area. It may be defined as a part of a wood which contains average conditions and especially an average volume of material per unit of area. Having ascertained the volume of the sample area, that of the whole wood can be calculated in two ways : either according to 70 MEASUREMENT OF WHOLE WOODS. area, or according to the number of trees on the sample area and in the wood. Let A — area of wood, a = area of sample area, V = volume of wood, v = volume of sample area, then the following proportion is assumed to exist : — v : V = a : A and y = v x A a Again, if N = number of trees in the wood, n = number of trees on the sample area, then v : V = n : N, and v x N V = n In the former case it is necessary to ascertain the areas, and in the latter the number of trees in both sample area and wood. As, however, the counting of all trees gives hardly less trouble than measuring them, the second method yields only a small saving of labour ; it would be adopted only when the area of the wood is not known, or cannot readily be ascertained. 2. Selection of Sample Areas. The proportion given above will hold good only if the sample area represents a fair average of the whole wood, so that it can be considered as a model of it ; in other words, if a measurement of the trees on it yields an average basal area of stems per unit of area, an average height and the same form factors. The sample areas 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 area may be selected anywhere, as long as the density of stocking represents an average. In METHOD OF SAMPLE AREAS. 71 very large woods, it may become desirable to take several sample areas and calculate the mean. (6.) Several qualities occur which are clearly separated accord- ing to area. In that case, each quality is treated separately, and one or more sample areas taken in each part (Fig. 24). (c.) Several qualities exist which change gradually from one to the others. In this case, the sample area may take the shape of a strip which runs through the whole wood, so as Fig. 24. Fig. 25. to include a due proportion of each quality (Fig. 25). As this is difficult to accomplish, it is generally better to follow the method given under (&.), to divide the wood into several parts and to take a sample area in each. 3. Extent and Shape of Sample Area. The sample area must be of sufficient extent to contain the different classes of trees in the same proportion as the wood. Hence, its size depends on the degree of regularity of the stocking ; the more uniform this is, the smaller may be the sample area. It follows that it may be made smaller in young, fully stocked than in old, irregularly stocked woods. The absolute extent of the sample area depends on the desired degree of accuracy. In mature woods, it should not be less than 5 per cent, of the whole area, but in young woods it may be less. Very small sample areas have the disadvantage that propor- tionately too many trees fall into the boundary lines. The best shape would be that which includes the greatest area as compared with the length of the boundary — in other words, a circle. As this is impracticable, it is usual to give to the sample area the shape of a square, or of a rectangle approaching a square. 72 MEASUREMENT OF WHOLE WOODS. 4. Measurement of Volume on Sample Areas. This can be done according to any one of the methods described above. As here a conclusion is drawn from the volume of a small area to that of the whole wood, it is desirable to measure the volume on the sample area as accurately as possible. 5. Merits of the Method of Sample Areas. The method of sample areas 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 area represents an average of the whole wood. Hence, it only yields accurate results in regular- grown, young and middle-aged woods, less so in old, irregularly stocked areas, or where the quality changes frequently. The method is chiefly useful where extensive areas have to be assessed, or where the value of the produce is small ; in fact, where a high degree of accuracy is either impossible to attain or not required. Where only small areas have to be measured, or where the value of a forest has to be ascertained for the purpose of sale, when a high degree of accuracy is wanted, the whole wood should be measured. SECTION III.— DETERMINATION OF THE VOLUME BY ESTIMATE. Instead of measuring the trees on the whole or a part of the area, the volume can be estimated in various ways, of which the following deserve to be mentioned : — 1. Estimating the Volume of the Wood as a Whole. This method, being the oldest and roughest of all, consists of going through the wood and estimating the volume, either of the whole wood, or per unit of area if the total area is known. The estimator must consider differences in the density of stocking, the average volume per tree, the differences in the quality of the locality, and, if for the whole wood at once, its area or number of trees. It stands to reason that the method requires great experience and practice on the part of the estimator, and even then considerable mistakes may be made. DETERMINATION OF VOLUME BY ESTIMATE. 73 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 carefully, 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 area 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 strips cleared for roads or rides give useful data for estimating the crop of the adjoining woods. In all such cases, the estimate is based on the volume per unit of area. 74 CHAPTER V. DETERMINATION OF THE AGE OF TREES AND WOODS. It is of importance to know, not only the actual dimensions of the trees and their volume, but also the time which has been necessary to produce them. To solve this question, the age of single trees, as well as that of whole woods, must be ascertained. 1. Determination of the Age of Single Trees. a. Standing Trees. All trees increase annually in diameter and also by the elonga- tion 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 deter- mining the age may be distinguished : — i. Determination from Existing Records. Reliable records yield the best results, if they refer to individual trees. In the case of trees which form part of a wood, they are not always accurate, as many woods are not even-aged. ii. 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 con- ditions under which a tree has grown up, its age can be estimated within 10 or 20 years as long as height-growth continues. In the case of very old trees, the limit of accuracy is much wider. At all times, this method requires much practice and experience, and even then it yields only approximately correct results. AGE OF FELLED TREES. 75 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 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 cylin- der of wood can be extracted from the stem, on which the concen- tric rings may be counted. The instrument does not, however, 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 generally grow more or less eccentric. b. Felled Trees. By far the best method is to count the concentric rings on a stump, and, if necessary, to fell a tree for the purpose. At the same time this is not always an easy operation, and in some cases it is altogether impracticable. It is easiest in the case of the so- called ring-porey broad-leaved species and in conifers which produce a darker-coloured summer or autumn wood than that formed in spring. Frequently, false rings appear. These may be distinguished from true rings by finding that they do not run right round the tree (Hornbeam, Alder). In the case of suppressed trees, the true rings are frequently so narrow, either all round or in parts, that they are difficult to distinguish. The business may be facilitated by smoothing the surface, making a slanting cut, or applying colouring matters (as indigo, alizarine ink, Prussian blue, alcohol coloured with aniline, sulphuric acid, etc.). Such colouring does not always produce the desired effect. 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 76 AGE OF TREES AND WOODS. obtained, the number of years which the tree took to reach that height must be added. If absolute accuracy is required, the stool must be split open along the centre and the rings counted to the starting-point. In this way, the phijsical 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, as, 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 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 standstill, owing, for instance, to heavy shade from above or unfavourable weather. 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 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 for the complete stocking of the area, it is generally desirable to examine several trees and take the mean. b. 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. AGE OF WOODS. 77 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 V be the volume of the wood ; a v a. 2 , a 3 . . . the ages of the several age classes ; v v v 2> v 3> • • • the volumes of the several age classes ; /, the mean annual increment of an even-aged wood of the same volume as the imeven-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 : — v i + v 2 + v 3 + • • • = 1 X A, and A-— -j- - - p As the even-aged and imeven-aged woods are assumed to have the same volume, it follows that / must be equal to the sum of the mean increments of the several age classes of the uneven-aged wood, that is to say : — z _Si + a + a + ... «i a 2 a 3 By substituting this expression for I in the above equation, the latter becomes — A = Vl+V 2 +V3+.. ■ (1>) V1.V2.V3. ; ai a 2 a 3 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 incre- ments of the several age classes. The method may be simplified by assuming that the age is approximately proportionate to the diameter ; in that case, 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 age classes are found on different parts of the area, the 78 AGE OF TREES AND WOODS. following formula may be used, where m v m 2 , m 3 , . . . represent the areas of the several age classes : — A _ m t x a t + m 2 x a 2 + m 3 x a 3 + • • . ,y \ m, + m 2 + m 3 + . . . ' '' This formula was first given by Giimpel. It gives good results 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 bases the calculation upon the number of trees in the several age classes. If they are % ; n 2 ', n 3 ; . . . , his formula runs thus : — A = n! x a t + n 2 x a 2 + n 3 x a 3 + . . • ,^ m + n 2 + n 3 + . . . [ '> All these formulas are somewhat troublesome. Formula (1) demands a knowledge of the volume and increment ; (2) of the areas occupied by each age class ; formula (3) requires the number of trees in each age class. In practice, the mean age is frequently taken as equal to the average age of the sample trees, or of the age classes, according to the formula : — A = a * + a2 + a3 + ' • ' (4 ) n • \ •) where n represents the number of sample trees, or age classes, as the case may be. Finally, the age of the arithmetical mean sample tree can be taken as the mean age of the wood. Example : — Let v x = 4,000 Oj =50 m 1 = 2 acres » x = 1,500 v 2 = 9,000 a 2 = 60 m a = 3 „ n 2 = 1,600 v 3 = 7,000 a 3 = 70 m 3 = 2 „ n 3 = 800 v 4 = 4,000 a 4 = 80 m i = 1 „ » 4 = 300 Mean age according to formula : — 4,000 + 9,000 + 7,000 + 4,000 24,00 (1) A= . 4000 9>000 7000 4)000== 380 - . =63-2 Years. (2) 50 + 60 + 70 + 80 2x50 + 3x60 + 2x70+1x80 „ 2+3+2+1 ,„, A 1,500 x 50 + 1,600 x 60 + 800 x 70 + 300 X 80 ( ' 1,500 + 1,600 + 800 + 300 ~ (4M= . . . 50 + 60 + 70 + 80 ; = 65 79 CHAPTER VI. DETERMINATION OF THE INCREMENT. During every growing season, a tree increases by the elongation 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 incre- ment 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. (3.) The total increment, or that laid on from the origin of a tree or wood up to a certain age, frequently that when the tree, or wood, is cut. (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 removals must be taken into account in determining the total increment produced. The determination of the increment may refer to the past (backward) or to the future (forward). As the former deals with 80 DETERMINATION OF THE INCREMENT. 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 speculation, and, therefore, less reliable. SECTION I —DETERMINATION OF THE INCREMENT OF SINGLE TREES. 1. Height Increment. a. Of the Past. The height increment of a standing tree can, in some cases, be ascertained by measuring the length of the annual shoots between the w r horls formed in successive years. This refers especially to some species of Pin us. In all other cases it is necessary to cut a tree for the purpose of ascertaining the number of years during which a certain length of it has been produced. In all cases, where a complete knowledge of the height incre- ment during the several periods of life is required, the tree should be divided into a number of sections, the length of which depends on the desired degree of accuracy. The concentric 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. Generally, graphic interpolation gives the best results, as it equalises 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 Scots pine tree, at p. 83. 6. 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 DIAMETER INCREMENT. 81 been reached or not. If it is already falling, it will continue to do so, and in that case the rate at which it is likely to fall must be estimated. In this way, the probable increment for a limited number of years (say 10) can be estimated with satisfactory accuracy. This is best done by constructing a height curve of the past and elongating it for the required period, so as to form a continuous graph. 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 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 distinguish- able, and that each ring represents one year's growth. The increment can be ascertained with much greater accuracy by felling a tree and measuring the breadth of the desired number of rings on the section, the latter being laid at right angles to the axis of the stem. The measurements are made with a scale sub- divided 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, arranged at equal distances over the section, and then taking the mean of the several readings. In the case of standing trees, the increment can only be ascer- tained for a limited number of years. If a tree is felled, the increment can be ascertained for the several periods of its life — 82 DETERMINATION OF THE INCREMENT. say, for every five, ten, or more years. The result can be graphi- cally represented and a mean curve of increment constructed, from which the increment for any desired intervals can easily be determined. By repeating the above operation at successive heights from the ground, the increment can be ascertained in the several parts of the stem. (See example below.) b. Diameter Increment of the Future. This is estimated from the increment of the immediately preceding period, taking into consideration how far the future diameter increment may be affected by the method of treatment, more especially the proposed degree of thinning ; the stronger the latter, the greater is the increment likely to be. 3. Sectional 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 during n years = g^_£Xjr = (D , -^)Xir e=(0 ,_ ( p )xm 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 imme- diate past, taking into consideration the proposed treatment, 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 commence- ment 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. VOLUME INCEEMENT FOR SINGLE TREES. 83 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. The breadth of n rings is ascertained at regular intervals along the stem, 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, diameter and volume 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, and the diameter at the several ages measured. The measurements are best plotted, so that a representation of a longitudinal section through the tree is obtained. For this pur- pose, 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, or diameters, of the cross -sections are marked on horizontal lines, and the points thus obtained connected by a series of graphs, which represent the stem curves at the several stages during the life of the tree. From the data thus obtained, the increment throughout the several periods of the life of the tree can be calculated. As the thickness of the bark at former periods cannot be ascertained, these investigations can refer only to the increment in wood, exclusive of bark. Example : — Analysis of a Scots Pine Tree, Stem only. 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 III. 15 „ „ 89 IV. 25 „ „ 85 V. 35 „ „ 80 VI. 45 „ „ 72 VII. 55 „ „ 64 mi. 64 „ „ 34 IX. 68 „ „ „ 26 Top = 9 feet long. Total height = 77 feet, 02, 84 DETERMINATION OF THE INCREMENT. Height of Section. Feet. Number of Rings. Number of Years which the Tree took to reach that Height. 97 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 97 55 H | 45 Eh H or o w 25 15 *^f — ' — ! — ' — i — T" 10 20 30 40 50 60 70 80 90 100 AGE, IN YEARS. Fig. 26.— Graphic Representation of the Height Increment. ANALYSIS OF A SCOTS PINE TREE. 85 IS 16 '/.' 14 w w u 12 tz; M fc 10 M ed" 8 H W S 6 «S ft 4 > AGE. 1 10 20 30 40 50 60 70 80 90] 100 AGE. Fig. 27. — Graphic Representation of the Diameter Increment at 5 feet from the ground. ■77 AGE. VJ 17' 27 37' 47 57] 67 77 ;S7 97 RADIUS, IN INCHES (EXAGGERATED). 10 Fig. 28. — Graphic Representation of a Tree Analysis (Vertical section of one-half of the Tree). 86 DETERMINATION OF THE INCREMENT. Radius of Section I. at foot of tree, in Inches. Radius of Section II. at 5' from the ground, in Inches. Radius of Section III. it 15' from the ground, in Inches. Radius of Section IV. \t 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 = 616 65 = 5-62 67 = 8-50 65 = 6-77 59 = 604 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 = 506 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 35' 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 = 603 Total = 5-81 Total = 3-54 Total = 2-12 80 = 5-96 72 = 5-75 84 = 3-46 34 = 207 70 = 5-71 62 = 5-40 54 = 2-98 24 = 1-66 60 = 5-28 52 = 4-87 44 = 2-40 14 = -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 = 305 12 = 1-90 2 = -35 24 = 1-40 14 = 103 4 = -41 Radius of Section IX. at 68' from the ground, in Inches. Total = 1-43 26 = 1-39 16 = 1-02 6 = -50 Calculation of the Volume of the Tree at Different Ages. Number of Section Dia- meter, Basal Area, in in j Square Inches. Feet. Length, in Feet. Volume, in Cubic Feet. Number of . Section. Dia- meter, in Inches. Basal Area, in Square Feet. Length, in Feet. Volume, in Cubic Feet. Whole Tree, including Bark ; age = 97 years. 17-6 1-69 10 13-8 104 10 12-8 •89 10 121 •80 10 11-6 •73 10 71 •27 10 4-2 •10 8 16-9 10-4 8-9 8-0 7-3 2-7 Whole Tree, without Bark ; age — 97 Years. 15-0 101 8-4 7-7 7-2 2-6 •7 16-6 1-50 10 13-6 101 10 12-4 •84 10 11-9 •77 10 11-5 •72 10 6-9 •26 10 41 •09 8 2-9 Total Timber •05 | S* 550 •15 2-8 Total Timber = 51-7 I -04 | 8 1 -12 Total Timber and Fuel = 5515 Total Timber and Fuel = 51-82 * Tbe top is considered as representing a cone, the volume of which = basal area x one-third of the height. Minimum size of timber = 3 inches. ANALYSIS OF A SCOTS PINE TREE. 87 Calculation of the Volume of the Tree at Different Ages — cont. Number of Section. Dia- Basal meter, | Area, in in Square Inches. \ Feet. Length, in Feet. Volume, in Cubic Feet. Tree 87 Years Old. 15-7 1-34 10 12-9 •91 10 11-9 •77 10 11-4 •71 10 10-8 •64 10 60 •20 10 3-3 •06 8 13-4 91 7-7 71 6-4 2-0 •5 2-0 Total Timber •02 I 4 46-2 •03 Total Timber and Fuel = 46-23 Tree 77 Years Old. 14-7 118 10 12-3 •83 10 11-2 •68 10 10-6 •61 10 9-7 •51 10 4-8 •13 10 11-8 8-3 6-8 6-1 51 1-3 Total Timber 1-8 I -02 | 8 1-0 -01 I 39-4 •16 Total Timber and Fuel = 39-56 Tree 67 Years Old. 13-5 •99 10 121 •80 10 10-6 •61 10 9-6 •50 10 8-6 •40 10 3-7 •07 10 9-9 8-0 61 50 4-0 •7 Total Timber •02 | § 7 | 2-0 Total Timber and Fuel 33-7 •04 Tre e57 Years Old. 12-5 •85 10 10-9 •65 10 100 •55 10 8-7 •41 10 7-5 •31 10 33-74 8-5 6-5 5-5 4-1 31 2-8 10 Total Timber •04 I 10 •01 i 27-7 •4 •01 Total Timber and Fuel = 28-11 Number of Section. Dia- meter, Inches. Basal Area, in Square Feet. Length, in Feet. Volume, Cubic Feet. Tree 47 Years Old. 11-5 •72 10 9-9 •53 10 8-8 •42 10 7-7 •32 10 61 •20 10 7-2 5-3 4-2 3-2 2-0 21 •6 Total Timber = 21-9 •02 10 I -20 •002 i A — Total Timber and Fuel = 22-10 Tree 37 Years Old. 101 •56 10 8-5 •39 10 7-6 •32 10 5-9 •19 10 3-8 •08 10 5-6 3-9 3-2 1-9 2-4 Total Timber = 15-4 •03 •07 Total Timber and Fuel = 15-47 41 2-7 1-7 Tree 27 Years Old. 8-7 •41 10 70 •27 10 5-6 •17 10 Total Timber = 1 2-7 1 -04 | 10 1 1-6 1 -oi 1 5 ! 8-5 •40 •02 Total Timber and Fuel = 8-92 2-5 11 Tree 17 Years Old. 1 6-8 1 -25 10 | 4-5 •11 10 | Total Timber = ! 2-6 •04 10 1 1-2 •01 1 ! 3-6 •40 •02 Total Timber and Fuel = 402 Tree 7 Years Old. Total Timber = 00 I 2-6 I 04 I 10 ! -4 1-2 -01 | -01 Total Timber and Fuel = 0-41 DETERMINATION OF THE INCREMENT Recapitulation. The stem of the tree had, at the age of 97 years : A total volume of = 55-15 cubic feet. Of this was Bark = 55-15 - 51-82 = 3-33 cubic feet. 6 per cent, of total volume. Leaving Timber (over 3" diameter) under bark = 51-7 cubic feet. Firewood Total Timber and Firewood •12 = 51-82 cubic feet. By graphically representing the volume of wood at the several ages, Fig. 29 is obtained, which, with the previous diagrams, gives the follow- ing data : — Diameter under Volume under Periodic Incre- Age of Tree. Height, in Feet. Bark, at 5' above Bark, in ment, for every ground, Inches. Cubic Feet. Ten Years. Cubic Feet. — — — } " [■ 4-2 I 6-0 } 6-0 10 20 40 1-8 20 38 7-4 60 30 51 91 120 40 58 10-6 180 6-0 50 62 11-9 240 [ 5-9 60 64 12-8 29-9 J I 5-4 70 67 13-9 35-3 1 I 6-7 80 70 150 420 [ 6-0 90 74 16-0 480 [ 3-8 97 77 16-6 51-8 Total 51-8 ii. Determination of the Increment by the Middle Section. If somewhat less accurate results suffice, the volumes can be ascertained by multiplying the sectional area in the middle by the height. Let V be the volume of the tree at the present time, BY THE MIDDLE SECTION. 89 60 50 U 40 30 § P O 20 / 10 ;20 30 40 50 60 70 [80 90 100 AGE, IN YEARS. Fig. 29. — Graphic Representation of the Volume. v that n years ago, H and h the corresponding heights (Fig. 30) H 2 H h and S and s the corresponding sectional areas at -^ and -x, then IT The height and the sectional area at "'•.!/' *>y / "'28 y/% Tf>, E • l? / / • ^Zfi y » ''•? i^/ • h33— ] / /' 'ii Six 1 •£ 13-'' Jsy ..'-' * ' /• /' ' , yli ► 5 A V^ *8 ,-'• •12 ////a \L ! L'/?\/ % i L ( //A'/ ///Z'y d I. QUALITY. 39 II. QUALITY. 33 III. QUALITY. 40 10 20 30 40 50 60 70 80 90 100 110 120 AGE, IN YEARS. Fig. 33. — Graphic Representation of the Volume per Acre of 40 different Woods and their_allotment to Three Quality Classes, according to Baur's method. METHODS OF CONSTRUCTING YIELD TABLES. 101 Example of Preparing a Yield Table according to Baur's Method. Scots Pine : 3 Quality Classes to be distinguished. Woods Measured as follows :— Age. Years. No. Basal Mean Volume Age. Years. No. Basal Mean Volume No. of Area, Height, in solid No. of Area, Height, in solid Trees. sq. ft. feet. cub. ft. Trees. sq. ft. feet. 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 25 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 31 104 160 192 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 Woods Separated into Quality Classes. (Fig. 33.) 1 5 9 10 IS 17 1!) 215 25 30 31 36 37 39 Age. No. of Trees. Basal Area. Mean Height. I. Quality. 15 62 16 27 1400 130 33 35 910 156 46 46 620 165 55 54 450 182 69 62 369 184 73 74 270 192 83 81 245 192 86 94 190 196 93 99 170 194 93 104 160 192 94 109 151 196 96 112 148 194 98 118 145 194 98 II. Quality 2 17 60 14 4 21 84 20 7 34 1480 133 35 8 35 1670 113 32 11 47 740 150 47 1800 3300 4450 4800 6400 6200 7800 7200 9000 8200 9200 8500 9700 9000 1400 1700 3250 2800 4230 No. Age. No. of Trees. Basal Area. Mean Height. 13 49 680 154 52 16 62 450 169 65 21 76 295 173 70 22 79 265 177 72 27 94 218 177 80 29 97 200 176 82 32 106 169 177 86 34 108 173 179 86 38 115 150 170 88 Volume ///. Quality. 18 61 13 29 2400 99 25 48 860 132 40 50 750 132 44 68 420 148 56 74 350 146 61 85 290 156 62 94 240 150 67 96 248 150 69 106 220 160 69 109 210 152 72 120 186 157 75 4700 4700 5500 6300 7300 6950 7150 8100 7500 1100 2050 2900 3500 4450 4000 5030 6000 5300 5700 6700 6000 102 DETEKMINATION OF THE INCREMENT. 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 10 20 30 40 50 60 70 80 90 100 110 120 AGE, IN YEARS. Fig. 34. — Graphic Representation of the Number of Trees per Acre. r | | METHODS OF CONSTRUCTING YIELD TABLES. 103 200 180 160 140 120 100 80 60 40 20 . J •/ •J / - 10 20 30 40 ".0 60 "0 80 90 103 110 120 AGE, IN YEARS. Fig. 35. — Graphic Representation of the Basal Areas per Acre. 10 20 30 40 50 60 70 80 90 100 110 120 AGE, IN YEARS. Fig. 36. — Graphic Representation of the Height Groivtk. 104 DETERMINATION OF THE INCREMENT. Yield Table for the Scots Pese, I. Quality. Derived from the Curves in Figs. 33, 34, 35 and 36. Age. Number of Trees. Basal Area. Square Feet. Mean Height. Feet. Volume. Cubic Feet, Solid. Increment. Current. Annual Cubic Feet. Mean. Annual Cubic Feet. 10 20 30 40 50 60 70 80 90 100 110 120 2000 1200 770 520 380 300 250 200 160 150 140 30 92 133 160 175 186 190 192 193 194 194 194 10 23 40 54 64 73 80 86 90 94 97 100 900 2100 3300 4500 5400 6250 6950 7600 8200 8650 9100 9500 90 120 120 120 90 85 70 65 60 45 45 40 90 105 110 112 108 104 99 95 91 86 83 79 c. The British Forestry Commission's Method. Before the appointment of the Commission in 1919, Mr. R. L. Robinson, then of the Agricultural Department, had commenced the collection of statistics required for the preparation of British yield tables. This work was at once taken up by the Commission, of which Mr. Robinson had become the technical member. While in most of the Continental yield tables the determination of the quality class was based upon the volume per acre produced in a certain number of years, the Commission found that a different method was required in the case of British yield tables, because the available number of normally stocked sample plots was very limited. Most of the British woods had been inefficiently treated, and more particularly the thinnings had either been too heavy or been neglected, so that the quality class could not be deter- mined by the volume on the ground. In these circumstances, the Commission decided to effect the division into quality classes by means of the mean height growth of the woods, as that is closely connected with the volume production and comparatively little affected by the different methods of treatment. The sample plots were classified according to the height of the crop at a standard age, for which 50 years was selected in the case of coniferous woods, which were, to begin with, under considera- THE BRITISH FORESTRY COMMISSION'S REPORT. 105 tion. In this the Commission was guided by the following reasons : — (1.) By the time a coniferous wood has reached the age of 50 years, the producing factors of the locality should have found decisive expression in the crop, so that the height growth would be an indication of the productive power of the locality. Exceptions might occur, but their number would be small. (2.) As there were only a small number of suitable old woods available, it was not desirable to fix the age higher than 50 years, so as to secure a sufficient number of sample plots. (3.) It was decided that every 10 feet of height growth at the age of 50 years should represent one quality class, and that the mean height should be a multiple of 10 feet. The mean height thus gives the name to the class. For instance, the 70 feet class represents all woods between 65 and 75 feet. Example. — The best quality class of larch in Britain is the 80 feet class, which means that the mean wood of this class attains a height of 80 feet in 50 years, the upper and lower limits being 85 and 75 feet respectively. Similarly the 70 feet class runs from 75 to 65 feet, with a mean of 70 feet, and so on down to 35 feet. In this way, the following quality classes were formed : — or Larch and Norway Spruce : For Scots Pine : I. Quality class (80 feet) I. Quality class (60 feet) II. „ „ (70 „ ) II. „ „ (50 „ ) III. „ „ (60 „ ) III. „ „ (40 „ ) IV. „ „ (50 „ ) V. „ „ (40 „ ) The sample plots of 50 years of age and over are allotted to their respective classes by means of age-height curves, prepared for each sample plot from the sectional analysis of three sample trees. The next step is to construct a mean age-height curve for each class out of all woods assigned to the class. These mean quality curves are drawn to pass through the heights of 80, 70 and 60 feet at 50 years. The combined graphs are then completed by interpolating a limiting curve between each pair of mean curves. These limiting curves pass through the heights of 85, 75 and 65 feet at 50 years. 106 DETERMINATION OF THE INCREMENT. It may be asked, whether an equally satisfactory classification of qualities would not be obtained if the mean heights of the woods were plotted as ordinates over the ages as abscissae in the same way as volumes are plotted in Baur's method ? The adoption of such a plan would certainly save a considerable amount of labour. The younger plots below 50 years of age which, owing to the nature of the classification, cannot be used for constructing the quality classes, are assigned to the classes to which they belong. Example. — A Larch plot 30 years old and 46 feet high falls between the 65 and 75 feet limiting lines, and thus belongs to the 70 feet class. European Larch. 80 ft. Class. 10 20 30 40 50 60 AGE IN YEARS. Fig. 37. — Diagram showing Quality Classes of European Larch. BY YIELD TABLES. 107 The several plots are then measured, and the obtained data worked up into yield tables in a manner similar to that followed in the case of Baur's method described above. So far only yield tables for larch, Norway spruce and Scots pine have been published in the Forest Commission's Bulletin No. 3, together with some preliminary tables for Douglas fir, Corsican pine, Japanese larch and some notes on other species. Additional tables will, no doubt, follow in due time. The tables for larch and Norway spruce refer to Great Britain and Ireland, but separate tables have been considered necessary in the case of Scots pine for England and for Scotland for reasons which are not altogether convincing. 6. 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 that of 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 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 pro- portion to the two volumes. Let v a be the present volume of the wood, V a the nearest volume given in the table ; V a + tl the volume given in the same table for the year a + n j and v a + n the required volume of the wood in the year a + n, then the following equation may be assumed to hold good (see Fig. 38) : — Va : V a = V a + n '. V a + n and V a + n =V a + nX fT" " a 108 DETERMINATION OF THE INCREMENT. and T T , • A V a + nXV a 1 = Increment in n years = v a + n — v a = 79 — V a 1 = V a + n V a -1 . This method rests upon the assumption that the selected yield table correctly represents the progressive increment of the wood Curve of yield table. ! «. — ■ Curve of wood dealt with. r of which the increment is to be ascertained. As this is only approximately the case, the degree of accuracy of the method depends — (a.) On the degree to which v a approaches V a , (b.) On the difference of ages, that is to say, the difference between a and a -\- n ; the smaller this is, the more accu- rate 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 aug- mented in the same proportion, before it is used for the deter- mination of the quality class and the selection of the yield table. At the same time, this procedure is subject to errors, as it is not always easy to determine correctly the proportion between the actual and normal stocking. BY 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 determined by means of an older wood growing in the vicinity on a locality of similar quality ; the same procedure is followed in the case of blanks. If no such older wood is available, the soil and climate must be examined and the best possible estimate of the quality made accordingly. As the measurement of the volume takes much time, and as it is difficult to estimate the exact proportion between the actual and normal stocking, it has been proposed to select the proper yield table for a wood by means of one factor 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, is com- paratively easy to ascertain. In selecting the appropriate yield table, the mean height is used in the same way as has been described for the volume. If the height agrees with one of the heights given in the yield table for the same age, the increment can be read off directly. If it differs, the nearest is selected and the increment of the table modified in proportion to the difference between the actual height and that given in the table. Should, moreover, the wood not be fully stocked, then the increment given in the table must be further modified in the manner indicated above. The height by itself is no true indicator of the quality for very young woods ; for such, as well as for blanks, other woods growing in the vicinity must be utilized, or the soil and climate examined. Example. — A Scots pine wood has a height of 53 feet when 60 years old, and a volume of 3,800 cubic feet; find the probable increment for the next ten years. 110 DETERMINATION OF THE INCREMENT. Yield Tables. Quality. Height at 60 years. Volume in the Year 60. Volume in the Year 70. I. II. III. 73 52 30 6,960 4,660 2,170 5,070 The wood belongs to the II. Quality. According to the formula — In — (Va + n N h a v a Va) X -r- X — h a Va ho - 70 = (5,070 - 4,660) x|x |^ = 341 cubic feet. The British Forestry Commission, in accordance with its method of classifying the woods used in the construction of its yield tables, determines the quality class to which any wood belongs entirely by the mean height. If, for example, a larch wood 40 years old has a mean height of 58 feet, it falls within the 70 feet class. If there is a difference between the yield table height curve and that of the wood under consideration, a correc- tion must be made in a manner similar to that indicated above. As regards the use of yield tables generally for the purpose of determining the future increment, it must be remembered that the yield tables give data representing averages obtained from extensive investigations. Hence, they may give amounts, if used for a single wood, which differ somewhat from actuals ; their full usefulness is secured only when applied to a number of woods, when such differences compensate each other. In some Continental countries the accuracy of yield tables has reached such a high degree that, for the purpose of working plans, their data are at once accepted without further corrections as soon as the quality class has been determined in accordance with the height growth of each wood. Experience has shown that any possible difference between forecast and actuals is well below the percentage of error to which operations of this kind are always subject. Ill PAET II. FOREST VALUATION. 113 FOKEST VALUATION. Forest Valuation deals with a variety of subjects, such as : — (1.) The determination of the value of forest soil, the growing stock and the forest as a whole. (2.) The determination of the financial results of forestry and of all matters connected therewith. (3.) The determination of the most profitable method of treatment of forests. These matters must be determined in cases of sale, partition and assessment of forests for taxation. The soil and the growing stock also form the principal part of the capital invested in forestry, on which the financial results depend. In order to deal with the matters 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 formulas 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. The subject of forest valuation has been arranged under the following headings : — Chapter I. — Preliminary Matters. „ II. — The Methods of Calculation. „ III. — The Financial Results of Forestry. „ IV — Examples of Application. 114 CHAPTER I. PRELIMINARY MATTERS. SECTION I.— THE 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 latter may present itself in various ways. A piece of property may possess value, because it can be used for a certain purpose, such as an article of food, or for the production of another kind or class of property, such as a set of carpenter's tools, or raw materials consumed in various industries. 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, such as a piece of land situated in the middle of another estate ; or the value may be due to special conditions, such as an article of food 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 the following may be specially mentioned : — (1.) The Sale Value, or the price which can be realised by the sale of the property ; if the sale is open to general com- petition, the sale value becomes the Market Value, which depends on supply and demand. (2.) The Cost Value, or the total outlay on the acquisition or production of a property. (3.) The Rental Value, by which is understood the capital corresponding to the rental which the property is capable of yielding ; it is commonly expressed by a certain number of years' purchase. (4.) 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 to the present time RATE OF INTEREST APPLICABLE TO FORESTRY. 115 all incomes derivable from the property and deducting from them the present value of all expenses to be incurred for the realisation of the incomes. The expectation value represents the economically correct value of a piece of property ; the drawback, however, is that its determination depends on the estimate of future returns and expenses. SECTION II. -THE RATE OF INTEREST APPLICABLE TO FORESTRY. In determining the value of a property, all calculations must be made with compound interest, as all money, whether capital or interest, is capable of again yielding interest. Hence, the deter- mination of the rate of interest applicable to an industry is of the first importance. Compound interest is applied in the case of forestry, which, from a financial point of view, is an industry like any other commercial undertaking. The producing capital in forestry is, theoretically, the cost value of the forest. As this is in many cases difficult to ascertain, especially in State forests, the market value should be substituted for the cost value. Neither the application of simple interest or a special reduction of the per cent, is admissible, as it would lead to wrong conclusions, nor could the results of forestry be compared with those of other industries. By rate of interest is understood the proportion between the yearly interest (/) and the capital (C) which has yielded it, as represented by the formula : — Rate of interest = ~. By rate per cent., or shortly per cent., is understood the yearly interest yielded by a capital of 100 ; hence : — Per cent, p = -^ X 100. The rate of interest applicable to an industry depends chiefly on : — (1.) The degree of security of the investment and the safety with which it yields a return. In a general way it may be said 116 PKELIMINARY MATTERS. that the rate of interest should be inversely proportional to the safety of the investment. (2.) The supply of, and demand for, capital, which change from time to time and with the locality. (3.) The general credit of the country in which the industry is carried on — in other words, the interest yielded by Government securities (called Consols in Britain). It follows that the rate of interest applicable to an industry cannot be a fixed quantity. In the case of forestry, the following points must be considered : — (a.) The safety of capital invested in forests. The soil offers a high degree of security, but the growing stock is subject to damage by man, animals, especially insects, fungi, wind, snow, rime and, above all, by fire, drought and frost. The degree of danger differs much according to species, method of treatment, length of rotation, climate, etc., but the extent of damage can be kept within narrow limits by careful management. (6.) The price of forest produce is, on the whole, less subject to sudden fluctuations than the value of money. (c.) Compared with the cultivation of field crops, it should be noted that forests, once placed under systematic manage- ment, yield annually equal returns of produce, while those of agricultural lands differ much according to the season, and that forests require much less labour. (d.) Temporary high prices can be fully utilized in the case of forests by cutting more than the normal yield for a time, or vice versa. Bearing these matters in mind, attempts have been made to determine the rate of interest applicable to the forest industry in various ways, such as the following : — (1.) Determination based upon the rate of interest obtainable in agriculture. This is frequently justified, although differences exist between the two methods of using the soil, which frequently are difficult to estimate. (2.) Determination based on the rate of interest yielded by Government securities. This rate of interest may be too high in some States and too low in others. The method is justified in well-regulated States. USEFUL FORMULAS. 117 (3.) Determination based upon the relation between the rental and the capital value of the forest. This method is practic- able only if — (a.) The annual rental of the forest is accurately known ; (6.) The forest is, at any rate approximately, in such a condition that it can yield a steady annual return. In practice, these conditions are difficult to fulfil, except in the case of the strictly annual working. (4.) Determination of the mean annual forest per cent, by placing the market value of the soil equal to the expecta- tion value of the soil calculated from future returns and expenses. This method will be explained after the manner of determining the expectation value has been given. SECTION III.— USEFUL FORMULAS. 1. Arithmetical and Geometrical Series. These are useful auxiliaries in forest valuation. The arithmetical series is built up by starting with an initial term, a, and adding a fixed quantity, q, to every succeeding term. Let a = 6 and q = 3, the series would consist of 6 + 9 + 12 + 15 + 18 + 21 . . ., and the sum of the series n would be S = (6 + 21) X « = 81 ; in words : the sum of an a arithmetical series is = the sum of the first + the last term X by half the number of terms. The geometrical series consists of an initial term, which ia multiplied by a fixed quantity to form the successive terms, as : — S = a + aXq-{-aXq 2 + aXq 3 + . . . + a X q n ~ l . With a view to obtaining a formula for the sum, the above equation is multiplied on both sides by q, becoming : — Sxq = aXq + aXq 2 + aXq 3 + aXq*+ . . . + a X q n . Deducting the first equation from the second, the result is, after reduction : — S X q — S = aX q n — a, or S (q — 1) = a (q n — 1), 118 PRELIMINARY MATTERS, and g = g(g"-l) q-l Example : — S = 6 + 18 + 54 + 162 + 486 + 1458 = 2184, or 6(3«-l) 6X 728 S= 3 _ i = —2— = 2184 - The above formula is suitable for the summation of both rising and falling series, but a more convenient formula for falling series is obtained by multiplying the enumerator and denominator in a n «»\ the above formula by — 1, thus obtaining S = — ^ — . This becomes for an indefinite series, as o* = 0, : S = = . 1 — j 2. The Amount or Future Value. A capital C , put out at p per cent, compound interest accumu- lates in the course of n years to the value of — C„ = C x l-Of, or log. C« = log. C + n x log. l-0p . (I.) In this case the following equation holds good : — C :C 1 = 100 : 100 + p and C x = C X ^_+? = Co (l + j^o) = C X l-Op. Again, C x : C 2 = 100: 100+^ and C 2 = C 1 (^ti 9 )= Co X l-0p n and ultimately C n — C X l-0j9 n , as above. Example. — A sum of £5 has been expended in planting an acre of land with Scots pine, which is expected to be ready for pit timber at the age of 40 years. To what amount will the £5 have increased, if the money was taken out of an investment yielding 4 per cent, interest ? Log. C 40 = log. 5 + 40 X log. 1-04 Log. 5 = -6989700 ; 40 x log. 1-04 - 40 x -0170333 = -6813320. Log. C 40 = log. (-6989700 + -6813320) = log. 1-3803020 = £24 0s. Id. By using the table in Appendix I. the use of logarithms will be avoided, as C. a = 5 x 4-801 = £24 0s. Id. SUMMATION OF RENTALS. 119 3. Discount or Determination of the Present Value. The present value C of a capital C n to be realised n years hence Q is C = - ^ n , or log. C = log. C n -nx log. l-Op . . . (II.) Example. — The final crop of a Scots pine wood at the age of 40 years is expected to be worth £50. What is its value at the present time ? (p = 4 per cent.) log. C = log. 50 — 40 X log. 1-04 Log. Co = 1-6989700 - -6813320 = 10176380 ; and C = £10 8s. 2d. By using the table in Appendix I. we obtain G = 50 X -2083 = £10 8s. 2d. 4. Summation of Rentals. a. Future Values. A rental R becomes due for the first time after m years and is payable altogether n times at intervals of m years ; its value at the end of m X n years is : — C mn = R + Rx V0p m + R X l-0p 2m + . . . R x roy- 1 *'". Here the first term a is = R, and q = l-0p"' ; hence : — _ R(1-Qp™»-1) ^mn — i.Qtfti J K^ 1 ) Example. — A sum of £10 is due after 10 years and again every 10 years, altogether eight times ; its value at the end of 80 years, calculated with 3 per cent, interest, will be — 10(1-0380- 1 ) 10 x 9-6409 C *° ~ 10310 _ 1 - —^439^ - £28 ° bS - M - A rental R is due at the end of each year altogether n times . its value is obtained by placing m = 1 in Formula III. — c =i 'y-" (iv.) 120 PRELIMINARY MATTERS. Example. — A shooting rent of 4 shillings per acre is obtained during 80 years, payable at the end of each year ; calculating with 3 per cent., •2 x 9-6409 the accumulated value at the end of 80 years is C 80 = -^ = £64 5s. U. b. Present Values. A rental R becomes due for the first time after m years, and is payable altogether n times after intervals of m years ; its present value is — r R i R i | R ° ~~ l-0p m "*" l-0p 2m "T" • • • "I" 1-Opnm- 7? 1 Here a = f^ and? = L0^' R xj r, l-0» m L Vl-0j0" Hence C = — [} \l-0p m ) J 1- ' l-0p m which, after reduction, leads to R(h0p™-1) „ l-0p mw (l-0^ m — 1) v '' This formula can also be obtained by discounting Formula III. down for mn years. A rental R is due at the end of every year altogether n times ; its present value is — as m = 1 : _ fl (1-0^- 1) rvI , _ i-o^« x -Ojb K '' Example. — If the general expenses of management per acre of forest amount to 6 shillings annually, and if that amount is spent during 80 years, the present value, calculating with 3 per cent., and using the table in Appendix I., amounts to C = 6 X 30-2008 = 181-2 shillings = £9 Is. 2d. A rental R is due at the end of each year for ever ; its present value is — n — _A_" 4_ R 4_ R 4- 4- R ~ 1-Op "*" l-0p* "*" l-0p 3 T • • • T l-O^' PRESENT VALUES. 121 Here a = j-tt-, and q 10/ * l-0p R Hence C = -1^- = ^ .... (VII.) 1 ~Ydp Example. — If the annual costs of management, 6 shillings, have to be incurred for ever, their present value, calculated with 3 per cent., comes to C« = ^= 200 shillings, as compared with 181 shillings during the first 80 years. If the calculation is made with 5 per cent, interest, the respective numbers would be 120 and 117-6 shillings respectively, showing practically a negligible difference. A rental R is due after n years and again every n years for ever ; its present value is — C - -iL 4- R 4- 4- R » l-0j» M ^ l-Oja 2 " ^ ' ' ' ^ 10p° AS a = T^n' 10jo" Example. — A thinning worth £10 is made in the year 30 of the first rotation of 100 years, again in the year 130, and again every 100 years for ever ; its present value is, p being 3 per cent. : — 10 x 1-0** 70 Co = jT Q3ioo_ i = 10 X 7 ' 9178 X -° 549 = £ 4 6s - ud - A rental (or payment) is due now and again every n years for ever ; its present value is : — ■ r - 7? -J- ^ -L ^ o_ _i_ ^ ^ l-0p n "*" 1-Op 2 " + • • • + i-Ojo 06 c R _ R x 1-Op" °~ _J_ ~~ 10jo»-l l-0p n (X.) Example. — An acre of land is planted now at a cost of £5, and again every 80 years for ever ; the present value of all these payments, with p = 3 per cent., is — C = 5 x 10-6409 x -1037 = £5 10s. 4d. 5. Conversion of Intermittent into Annual Rentals. The conversion is effected by multiplying the capital value of the intermittent rental by Op. Examples. — Placing Formula VIII. equal to Formula VII., we obtain : — 7? r J? jr-, and the Annual Rental r = . n -. X -Op. l-Opn - 1 .Qp' ~ l-0p» - 1 Again, Formula IX. = Formula VII. : — _ R x l-0p n - m 1-Opn _ l x -Op. All the above-mentioned formulas can be solved by means of logarithms or with the assistance of tables, such as those given in Appendix I. The latter give the values for Formulas I., II., VI. and VIII. ; they suffice for all ordinary calculations. RECEIPTS AND EXPENSES. 123 SECTION IV.— ESTIMATES OF RECEIPTS AND EXPENSES. An estimate of the future receipts and expenses is required for the purpose of determining the probable financial returns of foresty. It should be made with great care on the basis of local investigation and the results in the past. 1. Receipts. Foresters divide the receipts into two classes — namely, (1) those from major or principal, and (2) from minor or accessory produce. The former include all yields of wood whether timber or firewood, while minor produce comprises all other items. Bark is generally included in timber, but if it is severed from the wood before disposal, it is sometimes classed as minor produce. Major produce is obtained partly from final cuttings (final yields) and partly from thinnings (intermediate yields). Major Produce. — The local investigations include the measure- ment of existing woods, if any, and the determination of their volume, age, height, current and mean annual increment. If a sufficient number of suitable woods of various ages are available, future returns can be estimated with fair accuracy. If the number of local woods is deficient, or if none are available, the character of the soil and climate must be ascertained and an estimate made of the yield capacity, or quality class. By means of such an estimate and with the help of suitable yield tables, a local yield table is prepared, with which the best possible selection of the appropriate quality class is effected. The data in the yield table, modified to suit local conditions, are then converted into money values based on the local prices of the several classes of timber and firewood, thus producing a so-called " Money Yield Table." Minor Produce. — The amounts and values of these items must be ascertained locally. 2. Expenses. The expenses comprise a variety of items, such as the cost of administration, protection, formation, tending of growing woods, harvesting of produce, construction of roads and other means of 124 PRELIMINARY MATTERS. Money Yield Table for Larch based on Measurements recorded in the Forestry Commissioners' Bulletin, No. 3. Age. Years. Mean Height. Feet. Mean Girth at 4' 3". Inches. Yield, c'. Final. Thin- ning. Net Value of Returns. Per c', Pence. Final. Thin- ning. Value per Acre, Shillings. ,. Age. Final. Thin- ning. Total. 10 20 30 40 50 60 70 80 First Quality. 10 18 7 300 3 75 75 10 20 40 16 1,560 80 6 4 780 27 807 20 30 58 24 2,900 265 7 5 1,692 110 1,802 30 40 71 30 3,880 465 8 6 2,587 232 2,819 40 60 80 36 4,570 560 9 7 3,427 326 3,753 50 60 87 41 5,130 645 10 8 4,275 430 4,705 60 70 94 46 5,630 615 11 9 5,161 461 5,622 70 80 100 49 6,070 460 12 10 6,070 383 6,453 80 3,090 1,969 Second Quality. 14 200 3 50 50 31 13 900 60 6 4 450 20 470 48 20 2,100 210 7 5 1,225 87 1,312 61 27 3,050 380 8 6 2,033 190 2,223 70 33 3,700 460 9 7 2,775 268 3,043 77 38 4,250 510 10 8 3,545 340 3,885 84 43 4,760 525 11 9 4,363 394 4,757 90 47 5,170 410 12 10 5,170 342 5,512 2,555 1,641 10 20 30 40 50 60 70 80 transport, the construction of houses, taxes, etc. All these must be ascertained locally. It is customary to deduct the cost of harvesting at once from the receipts and to enter only the net amount into the account. 3. Samples of British Money Yield Tables. Money yield tables play an important part in forest valuation. They must be based upon measurements in the forest, and an exact knowledge of local conditions, more especially of the prices of produce ruling in the localities to which the valuation refers. Until quite recently, only Continental yield tables were available, BRITISH MONEY YIELD TABLES. 125 Money Yield Table for Larch based on Measurements recorded in the Forestry Commissioners' Bulletix, No. 3. Age. Years. Mean Height Feet. Mean Girth at 4' 3". Inches. Yield, c' Filial. Thin- ning. Net Value of Returns. Per c', Pence. Final. Thin- ning. Value per Acre, Shillings Final. Thin- ning. Total. Age. Years. 10 20 30 40 50 60 70 80 Third Quality. 10 11 150 10 20 26 10 560 3 140 140 20 30 39 17 1,460 70 6 4 730 23 753 30 40 51 23 2,290 235 7 6 1,336 117 1,453 40 50 60 29 2,910 360 8 7 1,940 210 2,150 50 60 67 34 3,440 400 9 8 2,580 267 2,847 60 70 74 39 3,910 430 10-5 9 3,421 322 3,743 70 80 79 44 4,300 360 120 10 4,300 300 4,600 80 1,855 1,239 Fourth Quality. 9 100 20 450 31 13 900 100 3 2 225 17 242 41 20 1,570 200 6 4 785 67 852 50 25 2,160 240 7 5 1,260 100 1,360 57 30 2,660 260 8 6 1,773 130 1,903 64 36 3,100 350 9 7 2,325 204 2,529 69 40 3,470 325 1,475 10 8 2,892 217 3,109 735 10 20 30 40 50 60 70 80 most of them having been prepared for German, Austrian and Swiss conditions. The preparation of these tables was com- menced many years ago on a uniform plan, and many of them have now been brought to such a state of perfection that in the case of systematic management future returns can be estimated without any further detailed measurements in the forest. Copies of such tables were published in previous editions of this Volume, as samples. They have also been used by some British foresters with such modifications as differences in climate and other con- ditions demanded. Now we have for the first time reliable volume yield tables, 126 PRELIMINARY MATTERS. Money Yield Table for Scots Pine in Scotland, based on Measure- ments RECORDED LN THE FORESTRY COMMISSIONERS' BULLETIX, No. 3. Age. Years. Mean Height. Feet. Mean Girth at i' 3" Inches. Yield, c'. Final. Thin- ning. Net Value of Returns. Per c', Pence. Value per Acre, Shillings. Final. Thin- ning. Final. Thin- ning. h i Total. Age. Years. 10 20 30 40 50 60 70 80 90 100 First Quality. 13 4 200 26 10 800 100 2 1 133 8 141 40 18 1,940 150 3 2 485 25 510 51 25 3,120 280 4 3 1,040 70 1,110 60 31 4,100 370 5 4 1,729 123 1,852 67 36 4,840 455 6 5 2,420 190 2,610 72 41 5,440 510 7 6 3,173 255 3,428 77 46 5,920 500 8 7 3,937 292 4,229 81 50 6,350 400 9 8 4,762 267 5,029 84 53 6,720 210 10 9 5,600 158 5,758 2,975 1,388 10 20 30 40 50 60 70 80 90 100 Second Quality. 10 10 . , 20 20 30 31 15 1,300 ioo 3 2 325 17 342 40 41 21 2,480 150 4 3 827 37 864 50 50 27 3,450 220 5 4 1,437 73 1,510 60 57 32 4,250 270 6 5 2,125 112 2,237 70 62 38 4,880 350 7 6 2,847 175 3,022 80 67 42 5,400 400 8 7 3,600 233 3,833 90 71 46 5,880 385 9 8 4,410 257 4,667 100 74 49 6,200 330 10 9 5,167 247 5,414 2,205 1,151 10 20 30 40 50 60 70 80 90 100 prepared from numerous actual measurements of woods and sample plots in Great Britain and Ireland. The work was com- menced before the War by the forestry branch of the Board of Agriculture, under the direction of Mr. R. L. Robinson (now the technical Commissioner of Forestry) by the establishment and periodic measurement of sample plots. When the War caused extensive cuttings, steps were taken to measure the crops on as many areas as possible, and the results of all measurements were worked up into volume yield tables for larch, Scots pine and Norway spruce. The number of woods and sample plots measured BRITISH MONEY YIELD TABLES. 127 Money Yield Tables for Norway Spruce, based on Measurements RECORDED LN THE FORESTRY COMMISSIONERS' BULLETIX, No. 3. Age. Years. Mean Height Feet. Mean Girth at 4' 3* Inches. Yield, c'. Final. Thin- ning. Net Value of Returns. Per c' Pence. Final. Thin- ning. Value per Acre, Shillings FinaL ning: TotaL Age. Years. First Quality. 10 12 20 31 30 51 23 3,500 iio 2 1-5 583 51 634 40 66 33 5,250 925 3 2 1,312 154 1,466 50 80 42 6,760 960 4 3 2,253 240 2,493 60 91 50 8,020 860 5 4 3,342 287 3,629 70 100 55 8,960 665 6 5 4,480 277 4,757 3,820 1,009 Second Quality. 10 10 20 27 30 43 20 2,840 300 2 1-5 473 37 510 40 58 30 4,490 540 3 2 1,122 90 1,212 50 70 38 5,890 700 4 3 1,940 175 2,115 60 79 46 6,940 670 5 4 2,892 223 3,115 70 87 53 7,800 565 6 5 3,900 235 4,135 2,775 760 10 20 30 40 50 60 70 10 20 30 40 50 60 70 10 20 30 40 50 60 70 Third Quality. 9 22 36 16 2,140 200 2 1-5 357 25 382 49 25 3,680 400 3 2 920 67 987 60 33 4,930 550 4 3 1,643 137 1,780 68 41 5,910 430 5 4 2,462 143 2,605 75 47 6,730 300 6 5 3,363 125 4,390 1,880 497 10 20 30 40 50 60 70 were : for larch 481, for Scots pine 334, and for spruce 157, making a total of 972. In addition, 128 plots of Japanese larch, Douglas fir, Corsican pine, and other conifers were measured and pre- liminary tables prepared, but further statistics are required before final yield tables for these exotic species become available. The larch and spruce woods are arranged into five quality classes 128 PRELIMINARY MATTERS. each, and the Scots pine woods into three, according to their mean height at the age of 50 years, as follows : — Species. Mean Height. Quality Class. Larch and Spruce M »» ... >f »> ... Scots Pine ..... 9t ^ • . • • • 9* ft • • ' • 80 feet 70 „ 60 „ 50 „ 40 „ 60 „ 50 „ 40 „ I. II. III. IV. V. I. II. III. The results were published in the Forest Commissioners' Bulletin, No. 3, of June, 1920. Copies will be found in Appendix V. It is proposed to use some of these yield tables to illustrate the methods of determining the financial results of forestry in Britain. For that purpose, the volume yield tables have been converted by the author into money yield tables, as given on pages 124 — 127. For larch, Classes I. to IV. are given, while Class V. has been omitted, as the planting of that class of locality would lead to financial loss, even if the land were given free. For spruce, Classes L, II. and III. (average) are given, and for Scots pine Classes I. and II. (average) for Scotland. In each case, the columns b, c, dand e are taken from the volume yield tables, while columns / to j give the money values of the final cuttings and the thinnings. Columns b and c show the class of produce obtained under varying rotations. The prices per cubic foot of final cuttings and of thinnings are approximately the averages of those which prevailed before the War. Present prices are as yet affected by the results of the War, and it is diffi- cult to say what they will be a few years hence, 129 CHAPTER II. METHODS OF CALCULATING THE VALUE OF FORESTS. SECTION I.— VALUATION OF FOREST SOIL. The soil can be utilized in two ways : — Either by using it direct, as for mining, quarrying, construction of buildings, etc. Or by using it for the production of other goods, such as field or forest crops. In each of these cases, the soil may have a different value. Forest valuation ascertains the value which the soil has if used for the production of forest crops. For this purpose, it determines the market, cost and expectation values and also the rental of the soil. 1. The Market Value of Forest Soil. By this is understood the value which soil realises in the open market. In most localities a market value of soil has been estab - lished. In the majority of cases it represents the value which the soil has for certain purposes, such as agriculture. In the latter case, the market value of good land is generally higher than the forest value, and lower in the case of inferior land. 2. The Cost Value of Forest Soil. By this is understood the sum of all expenses incurred in acquir- ing the land and rendering it fit for forest culture. These expenses comprise : — (1.) The price paid for the land. (2.) The sum paid for the improvement of the land, such as drainage, irrigation works, levelling, fixation, etc. (3.) The interest accumulated on the outlay under (1) and (2) up to the time when the first forest crop is started, less any income derived from the land during that period. 130 CALCULATING THE VALUE OF FORESTS. Example. — A piece of land was bought for £5 per acre, a further sum of £2 per acre was spent on draining the land, and it became fit for planting after three years. At the end of that time a sum of £1 per acre was received as shooting rent and grazing fee. The cost value of the land per acre at the time of planting, allowing 4 per cent, interest, amounted to S c = (5 + 2) x 1-04 3 - 1 = £6 17s. U. 3. The Expectation Value of Forest Soil. By the expectation value of forest soil is understood the value of all returns expected from the soil in the course of time, less the value of all the expenses which must be incurred to obtain those returns, discounted, in both cases, with compound interest to the time when the first planting or sowing of the land was made ; in other words, the commencement of the first rotation. For the purpose of obtaining a formula for the soil expectation value, the best method is to take each of successive rotations by itself, and to assume that what happens during the first rotation is repeated during every succeeding rotation. It is convenient to calculate the values of all receipts and expenses, except annually recurring items, during the first rotation for the end of that rotation, such as — (1.) Cost of formation, c shillings, value in the year r = c X l-0p r . (2.) Thinnings in the years, a, b, . . . q, indicated by T a , T b , . . . T q = T a x i-oy-« + T b x \-0p- b + . . . + T q X 1 -Ojt/ ~ q . Other produce being realised periodically is dealt with in the same way as thinnings. The value of casual items of income or expenditure must be calculated separately and added to or subtracted from the value of S e as calculated above. (3.) Final cutting in the year r = Y r . The net amount of these items comes to : — y r + T a x i-op r - a + T b x i-oy- 6 + . . . + T q x vop-i-c X l-0p r . This amount, together with the same amount realised at the end of each succeeding rotation, must be discounted to EXPECTATION VALUE OF FOREST SOIL. 131 the commencement of the first rotation, which is done according to Formula VIII. , by dividing it by l-0p r — 1. (4.) From the amount so far obtained must be deducted the net amount of the annually occurring receipts and expenses, e, calculated for the commencement of the first rotation. As these expenses have to be met for ever, their present value, according to Formula VII., amounts to -^-. Amongst the expenses included in e are the cost of administration, protection, upkeep of roads, and other means of com- munication, taxes, etc. ; amongst the annual receipts appear shooting rents, grazing fees, etc. The general formula for the soil expectation value, in its simplest shape, runs, therefore, as follows : — Y r + T a x 1 0p ra + T b x 1 0p rb -+-...+ ~ T q x 1 Op r -q — cx 1 0p r _e_ e_ 10p r -l Op Another somewhat more complicated method of calculation is to discount directly with compound interest all items of receipts and costs to the beginning of the first rotation ; the difference between the two represents the soil expectation value. It leads to exactly the same formula as that given above. Example. — An acre of land is to be planted at once with larch. It has been found, after due investigation, that it is capable of yielding returns like those in the money yield table for III. quality of larch given on page 125, and that the desired class of timber can be obtained under a rotation of 60 years. The expenses are expected to be as follows : — Cost of planting every 60 years = 100 shillings. Annual expenses less annual income = 6 shillings. Money for expenses taken out of an investment giving 4 per cent, interest. The expectation value of the soil will be : — _ 2 847+23xl-04 30 +117xl-04 20 +2 1 0xl-04 10 -100xl-04 6l > _ 6 ' ~~ 1-04- 60 - 1 ~ -04' By using the Tables in Appendix I^the above value becomes : — S e = [2847 + 23 x 3-2434 + 117 X 2-1911 + 210 X 1-4802 - 100 X 10-5196] x -105- ~. S e = 105-8681 shillings. 132 CALCULATING THE VALUE OF FORESTS. SECTION II.— VALUATION OF THE GROWING STOCK (OR STAND). The value of the growing stock can be determined as the market, cost, or expectation value. The valuation may refer to a single wood, or to a whole series of age gradations, representing the normal growing stock of a working section or of a whole forest. 1. The Market Value of the Growing Stock of a Single Wood. By the market value of the growing stock of a wood is under- stood the price which it would realise if offered to public compe- tition. It may be sold under one of the following conditions : — (1.) The wood is to be cut down at once. In this case the value is ascertained by determining the volume of the growing stock and multiplying it by the average price of the unit of measurement. It represents the utilization value. (2.) The growing stock is sold, but allowed to grow on for a number of years. In this case, the purchaser would have to rent the soil for a number of years, and to meet certain other expenses ; in other words, the sale value would be equal to the expectation value to be dealt with below. The utilization value of very young woods is generally small, so that sales under condition (1.) are rare, until the growing stock has reached, or at any rate approached, ripeness for domestic or industrial purposes. Hence, young woods, if sold at all, are generally disposed of under condition (2.). 2. The Cost Value of the Growing Stock of a Single Wood. The cost value of the growing stock of a wood now m years old is equal to the value of all costs of production, less the value of all returns which the wood has yielded before the year m, both amounts being calculated for the year m. Costs of Production. — (a) The value of the rent of the soil during m years : S X 1-Op™ - S = 8 (l-Op'" - 1). (6) The value in the year m of the cost of formation = c X 1 0p m . EXPECTATION VALUE OF THE GROWING STOCK. 133 (c) The value of the annual expenses during m years (Formula IV.)^(l-0p--l) = ^(10p™-l). Receipts. — These consist of all previous thinnings and other items of income realised before the year m ; they may be represented by T rt , T b . . . T t . Their value in the year m is : — T a X l-Op* - « + T b x 10p m - b + . . . + T, x 1 -0p m ~ l . The general formula for the cost value G c is, therefore : — m G c =(S c + E) (10p m - l)+cx 10p m - [T a x 10p ma + . . . + T, 10p ml ~| . Example. — Taking the same data as in the case of the soil expectation value and S, the cost value of the soil =100 shillings, the cost value of the 45 years old growing stock comes to : — *>G C = (100 + 150) (1-04 45 - 1) + 100 x 1-04 45 - |~23 X 1-04 15 + 117 x 104 5 1 . ^Gc = 250 x 4-8412 + 100 X 5-8412 - |" 23 x 1-8009+117 x 1-2167 1 . i5 G c = 1611 shillings. 3. The Expectation Value of the Growing Stock of a Single Wood. The expectation value of the growing stock of a wood now m years old is equal to the value, in the year m, of all incomes which may be expected from the wood between the year m and the end of the rotation in the year r, less the value of all expenses which must be incurred during the same period of time. Using the same data as those given in the case of the valuation of the forest soil, the receipts consist of : — Thinnings to be realised in the years n, o . . . q, and the final yield in the year r. Their value in the year m amounts to : — T T T T v ■L n | J- o | ■*- v | -L q a « — m ' 1 .A/>iO — m i 1 .fi/nP — m I 1 .fin? — ra ' l-Op"-" ' l-0j9°- m l-0p p_m l-0p«- m ' 1-Oj/ 134 CALCULATING THE VALUE OF FORESTS. or, if brought under the same denomination — T n hOjf-» T q \-0f-« Y r *r—m t~ • • • I -l .fVnr — m l-Opr-m I ' ' ' I 1-Opr-m ' \.Q p r - m' The expenses consist of : — (1.) The rent of the soil to be paid from the year m to the year r, the annual amount being S e X -Op. The total amount (Formula VI.) comes to (S e X •0p)(l-0p f - M -l) = S e (l-0p r ->»-! ) l-Opr-m X .Q p l-0p r - m (2.) The annual expenses are (according to Formula VI.) : — e {I0p r ~ m — 1) = E (l-0p r ~ m — 1) l-Qpr-m x .Q^ " l-0p r ~ m The formula for the expectation value of the growing stock is : — G € Y r + T n x 10p r - n + . . . + T q x l-Op'-i -(S. + E) (l-0p r - m -l) l.Qpr-m Example. — Taking the same data as before, larch III. quality, the expectation value of a 45 years old growing stock is : — 2847 + 210 x 1-04 10 - (105-8681 + 150) x v n-04 15 — i^ i5 G e = HM» - = 1,639 shillings. The valuation of the growing stock of a whole forest, consisting of a series of woods, is dealt with further on. SECTION III.— VALUATION OF A WHOLE WOOD (SOIL AND GROWING STOCK). 1. The Cost Value of a Whole Wood. The cost value of a wood is equal to the cost value of the soil plus that of the growing stock. Let the age be m years : — •F t = S + (S + E) (l-0p m - 1) + c x l-0p m - (T a X l-0p m - a + . . . + Ti x l-0p m - % which becomes, after reduction : m F c =(S + E + c) X l-0p m - (T a X l-0p m " a + . . . + + T, X l-0p m - 1 +E). EXPECTATION VALUE OF A WHOLE WOOD. 135 Example.— Visaing m = 45 years, r = 60 years, p = 4 per cent,, and S c = 100 shillings. S E c *F t = (100 + 150 + 100) X 5-8412 - (23 X 1-8009 4- 117 X 1-2167 + 150) i°F c = 1,711 shillings. The results obtained before were — & + mQ e = 100 + 1611 = 1711. 2. The Expectation Value of a Whole Wood. The expectation value of a wood is equal to the expectation value of the soil plus that of the growing stock : — Y r + TaX 1-0/-"+ . ..+T q X 1-0;/-'- l-Opr-m and S 6 + Y r + T n x h0p r -« + . • • + T q X l-0p--« - £(l-0//-' n — 1) "J- = \.()pr-m This formula involves two calculations, one of S e and a second of .F e . They can be combined into one by introducing the expec- tation value S e as given on page 131, thus obtaining, after the necessary reductions, the following formula :— 10p m (Y r + T n x 10p rn + . . . + T q x 10p r -i + j£; - + - + iV g E . 1 0p r - 1 Example.— Let m = 45 years, r = 60 years, and p = 4 per cent. :— 1-04 45 (2847 + 210 X 1-4802 + 23 X -3083 + i5F 117 x -2083- 100) 150 *• = 1-04 60 - 1 v>F e = 1,745 shillings. The results obtained before were : F e = S e + G e = 106 + 1639 = 1745. The cost value, i5 F c = 100 + 1611 = 1711, is smaller than the expectation value, because the soil was obtained for less than its expectation value. 136 CHAPTER III. THE FINANCIAL RESULTS OF FORESTRY. The financial results of forestry can be determined in one of the following two ways : — (1.) Determination of the profit, that is to say, the surplus of receipts over costs of production, allowing compound interest at a certain rate on both. (2.) Determination of the rate of interest yielded by the capital invested in forestry, called the " forest per cent." SECTION I.— CALCULATION FOR THE INTERMITTENT WORKING. 1. Calculation of the Profit of Forestry. In the case of a single wood of approximately even age, the returns and costs do not occur at the same time, but at intervals of various length ; hence, they must be calculated for one and the same time. In the first place, that time shall be the com- mencement of the rotation, when the area is about to be planted or sown for the production of a new forest crop ; secondly, the profit in the case of a wood now m years old. a. Calculation for a Blank Area. In addition to the signs used above, let " p " be 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 ; or the minimum per cent, at which the proprietor is willing to invest money in forestry. The profit is then repre- sented by : — Profit = Receipts — Costs, calculated for the year 0. Profit = Y r+TaX l-Of — + ... + T, X Hy « _ 1-Op' - 1 \ ^ ^l-Op' — lJ CALCULATION OF THE PROFIT OF FORESTRY. 137 This formula may also be written as follows : — Profit = ( Y r + TgX l-0j/~" + • . . + y g X l-0j/-g-cx l-0j>' _ F \ \ l-0» r — 1. / -s e . As the part in brackets represents the expectation value of the soil, the formula is reduced to : — Profit = S e — S c . In words : the profit in the case of a blank area, after allowing p per cent, interest on all receipts and costs, is equal to the difference between the expectation and the cost values of the soil, hence : — (1.) The greater the difference the higher will be the profit over and above p per cent. ; in other words, the management must aim at the highest possible expectation value of the soil and the lowest cost of production admissible with due consideration for efficiency. (2.) If the cost value of the soil is equal to the expectation value, the profit is nil, and the capital invested in the forest gives exactly p per cent. If the cost value is greater than the expectation value, a financial loss is incurred, and it would be 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. b. Calculation for a Wood m years old. Analogous to that employed for a blank area, the profit of a whole wood now m years old is expressed by : — Profit = m F e - m F c . The formula for the expectation value will be found on page 135. The cost value may be the price paid on purchase, or it may be determined as given on page 134. If the returns and costs are the same in either case, the following equation should hold good : — The profit = m F e - m F c = (S e - S e ) X l-0p m . 138 THE FINANCIAL RESULTS OF FORESTRY. The conclusions drawn above as regards the profit of a blank area also hold good as regards that obtained from a forest m years old. Example. — It has been found above that S e — S c = 105-8681 — 100 = 5-8681 shillings per acre. Also : i5 F e - i5 F c = 1744 - 1711 = 34, and (S e - S c ) X 1-04 45 = 5-8681 x 5-8412 = 34 shillings per acre. 2. Determination of the Rate of Interest yielded by the Capital Invested in Forestry. The general aspect of the matter has been considered in Chapter I. (page 115), where it has been stated that the per cent, applicable to the forest industry may be ascertained in one of the following three ways : — (1.) To accept the per cent, used in the agricultural industry, or (2.) To accept the per cent, yielded by Government Consols, or (3.) To determine the forest per cent, from the net receipts and capital of forests. The first and second methods give results which are more or less estimates, even if modified according to local conditions ; hence, the scientific forester must aim at more satisfactory results under the third method. In dealing with the matter, a distinction must be made between the intermittent working and the strictly annual working of a forest. The determination of the per cent, under the latter method is comparatively easy, but much more complicated under the former. In that case the interest changes from year to year, because the capital and the increment change with advancing age of the wood. A further distinction is necessary between the current annual and the mean (or average) annual forest per cent. a. The Current Annual Forest Per Cent. As already indicated, the per cent, yielded by an ordinary capital is expressed by the formula — •p, Annual interest , nn I Per cent, p = ^— 3 — -. ^ X 100 = ^ X 100. Producing capital C CURRENT ANNUAL FOREST PER CENT. 139 This formula is used in the case of forestry by introducing the proper values for I and C. These are the net annual value incre- ment of a wood for I and the cost value of the forest for C at the commencement of the year in question. Let the utilization value of the growing stock be = m G v at the beginning of the year and = m + l G y at the end of the year, then m + x G y — m G y represents the increase in the value which has been produced during the year. Deducting from this amount the net annual costs e, the net increase in value is equal to m + 1 G V — m G v — e, and the formula for the current annual forest per cent, is : — Current p f = { b > „/> ' ) X 100 = (- % + ,„g- " ) X 100. Against the use of this formula is the difficulty of ascertaining the value increment of the growing stock during one year. The amount is small compared with the limit of error involved in the measurement of a growing wood ; moreover, annual increments vary from year to year. Hence, it is necessary to determine the increment during a number of years, say 5 or 10 or n years. During the n years the annual value increment of the growing stock, as well as the producing capital, change from year to year under the influence of growth, on the one hand, and the effect of expenses, on the other hand ; in other words, the value of the forest in the year m + n is produced by the value of the forest in the year m working with compound interest at a certain rate of interest which may be called p/, the forest per cent., according to the formula : — Out of this is obtained — m + ntf n /m + np n /m + n]? WPf = -nrp- > and h °Pf = V -^f~> and '°Pf = V ^F - 1 ' yrn + nj? -^ 100, or, in logarithms :— l gm + njT_l g mff log. (100 + #) = 2 + UO THE FINANCIAL RESULTS OF FORESTRY. This formula is known as Pressler's " Weiserprozent " formula, which the author translated, many years ago, as the " Indicating Per Cent." If calculated for successive periods, it indicates whether a wood is financially ripe or not. As long as the indicat- ing per cent, is larger than the per cent, p at which money can be otherwise invested 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 sunk and become equal to the general per cent, p, the wood is financially ripe. If the wood is kept growing after that age, the indicating per cent, is smaller than the general per cent, p, and the wood is passed financial ripeness, unless an unexpected rise in the price per unit of measurement occurs. The use of the above formula is complicated, as the value of F has to be calculated in the first place. Hence, in the case of forests under fairly regular treatment, foresters substitute the utilization value (G v ) for G, thus obtaining results sufficiently accurate for practical purposes. The formula then becomes : — Current p f = 100 X [ V '^^f' - l] , and ... (1) log. (100 + p f ) = 2 + l0g - { " 1 + 7 ' Gv + Sc) n ~ l0g - ^ + Se) . (1) In order to avoid the use of logarithms, various formulas have been evolved. Pressler obtained such a formula by assuming that the value increment during the n years is produced in annually equal quantities, and that the producing capital is equal to the arithmetical mean of the growing stocks present at m and m -f n years. He thus obtains the equation — Capital Annual increment I'* + nQ i mQ \ (m + rift mQ \ I <*!,+ t^ . ( W kg) = 1(X) . 1 n rj m + nQ. mQ onn and Current ft=;fT ^ p |xf . . . (2) The formula was obtained by experimental measurements. CURRENT ANNUAL FOREST PER CENT. 141 Examples. — Given the data in the yield table for larch III. quality, and n — 10, the following result is obtained for formula (1) above : — Period 40-50 : Log.(100 + i> / ) = 2 + log. (2150 + 100) - log. (1336 + 100) 10 Pj = 4-59. Period 50-60 : p f = 3-75. Period 60-70 : p f = 3-67 According to Formula (2) the results are : — Period 40-50 : Current p, 2150 - 1336 200 , -_ C -^r = 4-67 per cent. 2150+ 1336 10 Similarly for Period 50-60, p. = 3-79, and for 60-70, p. = 3-68 per cent. Comparison of the Results. Period. By Formula I. By Formula II. Difference. 40—50 50—60 60—70 4-59 3-75 3-67 4-67 3-79 3-68 Average + 0-08 + 004 + 0-01 .. +0-04 467 Formula (2) gives slightly higher values, but the difference is so small that it may well be neglected. Assuming in the above example that the general per cent, is equal to 4 per cent., it will be observed that the indi- cating per cent, during the period 40 — 50 is 379 greater than 4 per cent, and smaller during the period 50 — 60 ; hence, the two must be equal at some time between 40 and 60. To ascer- tain the exact year, the data may be plotted as in Fig. 39, which shows that, according to the data of Formula (2), the indicating per cent, is equal to 4 per cent, in the year 52—53. 1 1 1 1 45 50 AGE. 52-5 55 Fig. 39. — Showing Age of Financial Ripeness. 142 THE FINANCIAL RESULTS OF FORESTRY. b. The Mean Annual Forest Per Cent. The determination of the mean annual forest per cent, has, in the past, puzzled foresters very considerably. Various methods of determination have been evolved, but none were satisfactory. Only one of these will be mentioned here, because it was given in previous editions of this volume for want of a more satisfactory method at the time. It was based on utilizing the general formula p = — x 100, and introducing into it the values for / and C appertaining to forestry. The annual net income calculated for the commencement of the rotation is expressed by S e X -Op and the producing capital by S c , so that the formula becomes — S e X -Op , AA S e mean p f = ~ — — X 100 = ~- X p, p being the per cent, fixed by the proprietor, or the forester. It is clear that the equation holds good only when p happens to be = mean p/. For all other periods of the rotation, the formula gives only approximately correct results, the difference depending to a great extent on the accuracy with which p has been estimated, and on the difference between the year for which the calculation is made and the year when p = pj. The author kept the matter in mind, and when preparing his " Forestry in the United Kingdom," he evolved a new method, described at pages 41 to 51 of that pamphlet, published in 1904. He brought the market value of the soil into direct relation with the expectation value of the soil by placing the one equal to the other, thus obtaining the formula — „ _ Y r -\-T a xl-0p- a + . . . +y g xl-0jt/-g-cxl-0j/ _ _e_ c ~ 1-Qp r — 1 -Op* In this equation p represents the mean forest per cent, corre- sponding to a given cost value of the soil. The lower the latter is, the higher will be the mean forest per cent., and vice versa. The u difficulty was, however, that the equation is not directly soluble, f/and the author proceeded, therefore, to make trial calculations. ll He calculated the soil expectation values with various per cents., MEAN ANNUAL FOREST PER CENT. 143 and plotted the results opposite the soil cost values, both on the same scale. He thus obtained a graph from which the mean forest per cent, could be read off for any soil cost value. The point, where a line drawn horizontally from any soil cost value meets the graph of expectation values, gives the mean forest per cent, for that soil value. When writing the above-mentioned pamphlet, the object was to determine the mean forest per cent, for various species managed for the production of fair-sized saw timber, and the calculations were made for : — Larch managed under a rotation of 70 years. Ash „ „ „ 70 Scots pine ,, 35 35 5 • *» 80 Spruce ,, 55 90 Beech ,, 35 120 Oak 55 130 The calculations were based upon yield tables modified to meet English conditions. By way of illustration, the author gave the calculations for larch. The returns for that species were given as follows : — A thinning in the year 20, value = 10 shillings 55 55 55 30 ,, = 7b ,, „ „ 3, 40 „ =220 „ 55 55 55 50 ,, = 270 ,, 60 „ = 300 A final yield in the year 70, value = 3,900 shillings. The cost of planting was given as £4 10s. Ocl. per acre ; the net amount of the annual expenses for administration, etc., at 4 shillings per acre. The following soil expectation values were obtained : — £ s. d. dated with 2| per cent. = 910 shillings = 45 10 S5 55 3 = 576 = 28 16 S3 35 °2 = 364 = 18 4 35 55 4 = 221 = 11 1 S3 35 41 *2 = 123 = 63 >» 33 5 = 55 = 2 15 144 THE FINANCIAL RESULTS OF FORESTRY. These data were plotted with the per cents, as abscissae and the soil values as ordinates, giving the following graph for a rotation of 70 years. 45 40 ' \ \ w 35 2 30 o \ 25 P |Z! ■< o H P4 15 10 8 6 1 3-5 i PER CENT. Fig. 40. — Schlich's Graph, indicating the Mean Forest Per Cent. Schlich's " Forestry in the United Kingdom," 1904.) (From As a separate graph is required for each rotation, a second example was given for a rotation of 40 years, suitable for the production of pit timber or other material of a similar size. Thus, the author of this book initiated in 1904 the method of determining the mean annual forest per cent, by means of a graph, which was obtained by plotting a series of trial calculations made with MEAN ANNUAL FOREST PER CENT. Indicator Graph for Larch III. Quality. 145 350 300 / / / / 250 200 / f / t / 150 100 i 1 / / / 1 / / <1 <, **w + 50 z ^, L_ ^N X. j Y ^ ^ ^ 50 >. -100 q 0' O /0 3-5 % 1 o/ * /o 4-5% 30 40 50 60 70 80 ROTATION. Fig. 41. various per cents. It will be observed that Fig. 40 indicates the mean annual forest per cent, for a rotation of 70 years as equal to 4-7 per cent., if the cost value of the soil amounts to £5.* * By an oversight, due to the author's illness from July, 1904, to October, 1905, the new method was not incorporated in Volume ILT. f.m. l 146 THE FINANCIAL EESULTS OF FORESTRY. Subsequently, iu 1919, Mr. W. E. Hiley, Research Officer at the School of Forestry, Oxford, calculated the expectation values for larch for various rotations, and constructed with them a graph which gives the mean forest per cent, for any rotation and also the year in which the forest per cent, reaches its maximum (though this is already given by the expectation values). Hiley called it the " indicator graph " and published it in the July number, 1919, of the Quarterly Journal of Forestry. The appended Fig. 41, constructed with the data for larch III. quality, page 125, will explain the indicator graph. It will be observed that Hiley's graph is based on the same principle as Schlich's graph. * The former involves, however, much more work than the latter, which is a consideration, as every change of the quality class requires a separate graph. In cases where the object is to give a general idea of the financial aspect of forestry over a considerable stretch of country, Hiley's graph is in its place, but in the majority of practical cases the calcula- tion for one rotation according to Schlich's graph is quite sufficient especially when the proprietor, or forester, decides to grow a definite class of produce for which a definite rotation is indicated. The Sub-Committee on Forestry, 1915, when dealing with the financial aspect of forestry in Great Britain and Ireland, assumed a suitable rotation for each species to be cultivated, and deter- mined the mean forest per cent, for each species by Schlich's method of graphs (see pages 65 to 68 of the Report, or pages 103 to 108 of Volume I. of Schlich's " Manual of Forestry," 4th Edition). SECTION II.— THE FINANCIAL RESULTS OF A FOREST WORKED FOR A SUSTAINED ANNUAL YIELD. A distinction must be made between a forest which is in the " normal state," and one which consists of a number of woods of various ages and areas deviating from the normal state. 1. Description and Value of the Normal Forest. If a forest is so managed that it yields annually, or periodically, an equal return, it must contain a series of woods of equal yield capacity ranging in age from 1 to r years. If the difference in * Apparently Hiley had not seen my "Forestry in the United Kingdom " when he conceived the idea of constructing his graph, though he had seen it before he published his graph. DESCRIPTION AND VALUE OF THE NORMAL FOREST. 147 age between every two successive woods is 1 year, the whole is called a "normal series of age gradations"; if the difference amounts to several years — say, 5, 10 or more — it is called a "normal series of age classes." In the former case, the oldest age gradation will be cut year after year ; in the latter case, the oldest age class will be cut in the course of a number of years in such proportion that an annually equal return is obtained. Taking the case of a normal series of age gradations running from 1 to r years, there will remain after the annual cutting, say, in winter, a series of woods running from to r — 1 years, and this is called the " normal growing stock." It is brought up to the full series during the next growing season in spring and summer, and again reduced to the normal growing stock during the next winter ; it is the minimum growing stock present in the normal forest. Its value is obtained by adding up, either the expectation values, or the cost values of all the age gradations from to r — 1 years old. The expectation values of the several age gradations, according to the formula on page 135, are as follows : — '-i(? c = Y r -(S + E) (1-0^-1) 'G, 1-Op 1 Y r - (S + E) (1-Op* -1) l-0p 2 Y T -(S + E)(l-0f- -*-l) l-0p r Y r + T 9 x l-0p r -«-Qg + ff)(l-Qp r - ( «- 1) - 1) °G e Y r + T g x l-Of- ? - (S + E) (1-Oj/ - 1). l-0p r By introducing the other thinnings in the years a, b, . . . p and adding up all the items, the following formula is obtained : — (Y r + S + E)(l>0f -l) + T a X l-0p r - a X (l-0j9 a - 1)+ • • . + norraalQ _ ^ X l-Of * X (10j»« - 1) he ~ 1-0^ X -Op r(b + H). L2 148 THE FINANCIAL RESULTS OF FORESTRY. By introducing the soil expectation value for S into the formula, the latter reduces to : — ituiinn . ~~ Yr + Ta + T *+ ' • • + Tq ~ C -r(S e + E), nor >n al Ge = Y r + T a + . . . + T, - (c + f X e) _ f ^ ^ The cost values of the several age gradations, according to the formula on page 134, are as follows : — oG c = (S + E) (l-0p° - 1) + c X l-0p° iG c = {S + E) (l-0p l - 1) + c x l-Op 1 «G C = {S + E) (l-0p a - 1) + c X l-0p a - T a a + iG c = {S + E) (l-0p a + 1 - 1) + c x l-0p a + 1 — T a X l-0p r-iG e = {S + E) (V0p r - 1 - 1) + c x l-0p r - 1 - T a x l-Op'-"- 1 . . . — T q x 1-Oj/-'- 1 . The sum of these equations comes to : — (5 e + E + c) (l-Qp'-l) - NMV| = [^(i-Qp^- fl -i) + ... + ^(1(^-^-1)] _ f ^ + ^ By introducing the soil expectation value for S c , this expres- sion becomes the same as that for the expectation value of the growing stock, namely : — Y r + T a + . . . + T q - normalG = normalG = \C -\- T X e) r X S . -Op DESCRIPTION AND VALUE OF THE NORMAL FOREST. 149 By adding the value of the soil, r X S e , to the normal growing stock, the value of the normal forest is obtained : — nonnalV = Y r + T a + . . . + T q - (c + T X e) e -Op If, on the other hand, the soil cost value, S c , is introduced in the above formula, and it differs from S e , then the value of the normal F c differs from the normal F e . The value of the normal F e can also be obtained by capitalising the net annual return, Y r + T a + . . . + T q — (c + r X e). This is done either by multiplying it by a certain number of years' purchase or by dividing it by -0^?. If, in that case, p is equal to the mean annual forest per cent., the formula represents the expectation value of the normal forest ; if p is arbitrarily fixed by the proprietor at the rate which he paid for the money invested in the forest, the formula gives the cost value of the forest. Examples. — Taking the date a for larch III. quality, the mean annual forest per cent, (as calculated by the graphic method) at 4 per cent., S c as 100 shillings and S e as 105-8681 (as ascertained on page 131), the following results are obtained for a rotation of 60 years : — 2847+ 23+ 117+210- (100 +60 x 6) ao .„« .-.. normalFe = ! ! '-— 5 > _ 68,425 shillings norma! F c = G c + S e ." (Sc = 100 shillings). (100 + 150 + 100) (1-04 60 - 1) - [23 (l-04 30 -l)+ 117 (1-04 20 - 1) + normOQc = 21 ° ^ 1 ' ^ 4 °~ 1)] 60(100+ 150). 350 x 9-5196- (23 x 2-2434+ 117 x 1-1911 + in 210 x -4082) an _._ normalQc = — '- 60 X 250. •04 G e = 61,001 and normalFe = 61-001 + 6,000 = 67,001. The difference F e - F c = 1,424 shillings is due to S c 10 + 150)] x 7 = 20,230 shillings. Comp.2:F c = [350 X I0p i5 (23 x l-0^ 15 + 117 x l-0p 5 + 150)] x 13 = 22,238. Comp.z-.Fc = [450 x l-Op 25 - (20 x l-0p 5 + 150)] x 25 = 25,632 shillings. Comp.i: F e = [550 X l-O^ 10 - 150] x 15 = 9,962 shillings. Cost Value of the whole Forest = 78,062 shillings = £3,903 2s. Od, Calculation of the Net Income. — The forest will be cut over once in the course of 60 years, and the cuttings during that period will be : — Final Yields. Comp. Area. Quality. Present Age. Years. Age when Cut. Yeafs. Yield. Shillings. 1 2 2 3 3 3 4 4 Total .. 7 3 10 10 10 5 5 10 III. III. III. II. II. II. I. I. 60 45 45 25 25 25 10 10 60—66 52—54 55—64 45—54 55—64 65—69 55—59 60—70 22,071 6,636 28,470 30,430 38,850 17,920 22,335 60,375 60 227,087 NOTES ON THE FINANCIAL ASPECT. 153 Thinnings. — During one rotation of 60 years, thinnings, up to and includ- ing that to be made in the year 50, are obtained in each compartment. They may be estimated at the following amounts, according to the data given in the yield tables : — In the III. quality area of 20 acres x 350 per acre = 7,000 shillings. In the II. quality area of 25 acres x 565 per acre = 14,125 In the I. quality area of 15 acres x 695 per acre = 10,425 Total of Thinnings . . . . 31,550 Grand total of all cuttings . . 258,637 Average Annual Cutting . . . 4,311 From this amount must be deducted the annual costs, consisting of the cost of planting 1 acre, c = 100 shillings \ and the cost of administration, etc., V= 460 60x6= 360 shillings J Annual Net Return .... 3,851 shillings. By introducing the values of the capital and of the mean annual net return into the above formula the mean annual forest per cent, is obtained as : — mean Pf = ' x 100 = 4-9 per cent. The actual per cent, under the above given arrangement of cutting will be somewhat less than 4-9 per cent, during the first part of the rotation and more than 4-9 per cent, during the second part of the rotation, but, by slightly altering the annual coupes, the cuttings can be so regulated that wood to the value of 4,311 shillings is cut every year throughout the rota- tion, giving approximately 4-9 per cent, annually from the beginning of the rotation to its end. SECTION III.— NOTES ON THE FINANCIAL ASPECT OF FORESTRY. The forecast of financial results of forestry depends on an estimate of future returns and expenses based upon past experi- ence ; hence, they are to some extent problematic. The degree of uncertainty depends on the intensity of management. It is considerable in the case of irregularly stocked and unsyste- matically managed forests ; it is small in the case of forests which have been intelligently managed for some time, and for which accurate data have been kept setting forth past receipts and expenses. Such forests exist in several European countries, where future returns are estimated with marvellous accuracy, with the assistance of accurate yield tables for different species 154 THE FINANCIAL RESULTS OF FORESTRY. and qualities of locality. Fortunately, a beginning has now been made to supply such tables based upon measurements made in Great Britain and Ireland, and when sufficient progress has been made in that direction, the reproach that British forestry is com- parable to " gambling in futures " will be, to a considerable extent, a matter of the past. Of the two methods of determining the financial results of forestry, by the profit and the mean forest per cent., the former is perhaps less laborious than the latter. It is adopted in cases where the proprietor requires a fixed minimum per cent., without which he is not willing to embark on forestry. The method of the mean annual forest per cent., on the other hand, converts a profit into an addition to the fixed per cent., and a loss into a reduction of it ; in other words, it gives the full per cent, which may be expected under a given set of conditions, and it is applicable to all cases. The mean annual forest per cent, depends on a great variety of conditions, some of which have already been indicated, but it may be useful to refer to them again : — (1.) The rate per cent., being calculated from the soil expecta- tion values, has a most powerful effect upon the financial results. A high rate gives a low expectation value, and vice versa. The increase, or decrease, is, however, not exactly in inverse proportion to the rate of interest. Again, under a low rate of interest the expectation value cul- minates later than under a high rate. The expectation values for larch III. quality, are as follows : — Rotation. Soil Expectation Values. 3 per cent. 3i per cent. 4 per cent. 4J per cent. 30 157 90 41 5 40 312 197 115 55 50 365 216 122 52 60 374 214 106 31 70 385 209 92 + 10 80 364 183 66 —12 The expectation value for a rotation of 80 years, for instance, falls from 364 shillings, calculated with 3 per NOTES ON THE FINANCIAL ASPECT. 155 cent., to — 12 calculated with 4| per cent. It may be added that the values calculated with 5 per cent, are all negative, showing that larch grown on a locality of III. quality does not give 5 per cent., even if the soil is given free. The above data further show that the maximum soil expectation value is obtained at the following ages : — iilat< ?d with 3 per cent.. i at the age of 70 years. j> S 1 jj °2 jj jj jj 55 „ JJ „ 4 jj jj jj 50 „ JJ „ 4i jj jj jj 40 „ (2.) The culmination of the expectation values, and conse- quently of the mean forest per cent., occurs earlier in the case of the better quality classes than in that of the lower classes. The appended statement of mean forest per cents, illustrates this. Taking the mean per cents, of larch grown on land the market value of which is £5 per acre, the cul- minating ages are : I. quality at 30 years ; II. quality at 40 years ; III. quality at 50 years ; IV. quality at 70 years. In the case of Scots pine : I. quality at 60 years ; II. quality at 70 years. The per cents, for spruce show smaller differences : I. quality at 60 years ; II. quality at 60 years ; III. quality at 65 years. The tables at present available for spruce up to 70 years are based on a somewhat limited number of measurements, and they are liable to alteration on further investigation. (3.) The appended table shows that the mean per cent, of larch IV. quality is so small that it is more profitable to grow either spruce or Scots pine on such localities. Even larch III. quality give lower results than spruce I. quality for rotations above 40 years. The Forestry Commissioners, in their Bulletin No. 3, advise not to plant larch on locali- ties below III. quality, that is to say, on localities where it does not reach a mean height of 55 feet in 50 years. 156 THE FINANCIAL RESULTS OF FORESTRY. Table of Mean Annual Forest Per Cents., according to the Cost Value of the Soil and the Quality Class. Rotation. I. Quality. II. Quality. III. Quality. Average. IV. Qual- ity. Cost, or Market, Value of the Soil. £ : 5 10 15 20 5 10 15 20 5 10 15 5 Larch. 20 6-3 51 4-3 3-8 3-6 2-9 30 6-7 5-7 5-0 4-6 5-6 4-7 40 3-6 3-4 2-9 40 6-3 5-5 4-9 4-5 57 4-8 4-3 3-9 4-2 3-5 30 50 5-7 5-0 4-6 4-2 5-3 4-6 41 3-9 4'3 3-6 3-2 30 60 5-3 4-7 4-3 4-0 50 4-4 3-9 3-7 41 3-6 3-2 3-2 70 50 4-5 41 3-8 4-7 4-1 3-8 3-6 3-9 3-5 3-3 3 3 80 4-7 4-2 3-9 3-6 4-4 3-9 3-7 3-4 3-8 3-4 3-2 31 Spruce. 30 3-2 2-4 2-0 1-8 2-0 1-9 1-8 1-7 1-9 1-3 40 4-2 3-7 3-2 2-8 3-7 31 2-8 2-4 2-9 2-5 2-2 50 4-6 40 3-7 3-3 41 3-6 3-2 2-9 3-7 3-2 2-8 60 47 41 3-8 3-5 4-2 3-7 3-4 31 3 8 3-4 2-9 70 4-5 4-0 3-7 3-5 40 3-7 3-4 31 3*8 3-4 30 Scots Pine. 30 21 1-5 40 3-5 2-9 • • 2-7 2-2 60 3-8 3-3 2-9 • • 3-2 2-7 60 3 9 3-4 30 3-3 2-8 70 3-8 3-4 30 3*4 2-9 80 3-6 3-3 2-9 .. 3-3 2-8 90 3-5 3-2 2-8 • • 3-2 2-7 100 3-4 30 2-7 31 2-6 157 CHAPTER IV. EXAMPLES OF APPLICATIONS. The objects of the forest proprietor, or forester, may vary very considerably. His object may be to aim at the realisation of the most favourable economic results — that is to say, the production of the greatest possible quantity or quality of produce, or he may desire to produce indirect effects, such as the preservation of moisture, the stability of the soil, the effect of forests upon the climate, hygienic effects and similar matters. The realisation of the latter effects frequently, though not necessarily, reduces the financial results of forestry. Still, as forests represent capital, the forester must never lose sight of the economic aspect of the industry. For this purpose, he must study the laws of produc- tion, the most suitable method of treatment under a given set of conditions, so as to raise the receipts to the highest point, and practise economy in expenditure. Extravagance has no place in forestry, because the industry gives, in the nature of things, only a moderate interest on the invested capital. Forest valuation forms the basis upon which rest, to a great extent, the decisions which determine the management of forests, as well as many questions coming under the head of Silviculture. It is not intended to deal in this place with all such matters, but to offer some notes on a few cases which present themselves to the forester in all stages of his practical work. They may serve as guides in dealing with other ques- tions. If the financial merits of different methods of utilizing land are to be compared, it must be assumed that in each case those con- ditions exist which render the methods in themselves as profitable as possible. In that case, it may be said that the most profitable method is that which yields the highest profit or the highest mean annual per cent., provided, in the latter case, that the invested capital is of the same amount in each method. If the 158 EXAMPLES OF APPLICATIONS. capitals are of different amounts, the following cases must be distinguished : — (1.) The method employing the greater capital is the more profitable if it yields the higher per cent. (2.) The method 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 per cent., it cannot be decided off-hand whether it is the more profitable or not, because the total profit depends on two factors, namely, the rate of interest and the amount of the invested capital ; in that case, it is necessary to calculate the actual amount of profit for each method and to compare the one with the other. These tests may be applied to all questions connected with forest management. 1. Choice between Agriculture and Forestry. On pages 28 to 31 of Volume I. (4th edition) of the author's " Manual of Forestry," it has been pointed out that, as a rule, forestry must give way to other industries for which the land is required. As regards agriculture, its claims are paramount whenever the production of food is concerned. And yet, in certain cases land may give better financial results if placed under forest than if used for agriculture. The present object is to define the boundary between the two industries from a financial point of view. The case most frequently occurring is, whether an area of bare land will yield a higher return, say, per acre, if used for agriculture or for forestry ? To answer that question involves a complicated procedure, because there is a great difference between the two industries. In agriculture the returns and expenses occur regu- larly every year, while in forestry they are spread over a whole rotation, and, to be comparable with those of agriculture, they must be discounted to the commencement of the rotation with a certain rate of interest, which should be the mean annual forest per cent. The following procedure is suggested : — In the case of agriculture, to do full justice to the problem, it will be necessary to ascertain the local value of the land, say, per acre, and the average net receipts derived from the land. The CHOICE BETWEEN AGRICULTURE AND FORESTRY. 159 latter would involve a complicated investigation of the several items of incomes and outgoings, such as interest on capital outlay, cost of working and administration, taxes, rates, etc., so as to arrive at the true amount of the net income per year from the land. That amount is, however, represented by the letting value of the land, which can be accepted as the interest obtained from the bare land. Assuming, for instance, the local value of the land to be £5 per acre, the letting value to be six shillings, and the pro- prietor's annual outgoings in the way of taxes, etc., to be two shillings, the net annual interest on a capital of £5 would be four shillings, and the per cent. — net rent , _- 4 _ n nA . p = rr^r X 100 =-rn7r>< 10° — 4 per cent. 1 capital 100 As regards forestry, it is necessary to determine the quality of the locality, the most suitable method of treatment and species, and to use, or construct, a suitable money yield table, as well as to estimate the necessary expenses. The forester will then calculate the maximum soil expectation value with the agricul- tural per cent., and compare it with the soil cost value. The selection of agricultural or forestal use depends on whether > S c = S e . < Example. — For agriculture S c = 100 shillings and p a = 4 per cent., as above. For forestry it has been found that the land is best suited for larch, and that the receipts are likely to be those indicated in the money yield table on page 125, III. quality for larch. The cost of formation has been estimated at £5, and the annual net expenses at 6 shillings per acre. The soil values, calculated with 4 per cent., for various rotations have been found to be those given below. From them the 4 per cent, graph has been constructed from which the mean annual forest per cents, for rotations from 30 to 80 years have been obtained : — Rotation, Years. Soil Expection Value, shillings. Mean Forest Per cent. 30 41 3-4 40 115 4-2 50 122 4-3 60 106 41 70 92 3-9 80 66 3-8 160 EXAMPLES OF APPLICATIONS. As the soil expectation value under a rotation of 50 years is greater by 22 shillings than the cost value, forestry is more profit- able than agriculture, provided that the rotation falls between 40 and 60 years. If a rotation of less than 40 or more than 60 years were adopted, the mean forest per cent, would be less than 4 per cent. ; hence, agriculture would be the more profitable use of the land in that case. 2. Choice of Species. It is not proposed to deal here with the general suitability of a species for a definite piece of land, or the objects of the proprietor of the land ; that is done in silviculture and management. If, however, two or more species answer well on general grounds, the choice should, in economic forestry, fall on that which gives the best financial results, as indicated, for a certain cost value of the soil, by the highest soil expectation value or, which comes to the same result, by the highest mean forest per cent. Example. — Compare, for instance, larch III. quality with spruce III. quality. Given a piece of land, value £5 per acre, which suits larch and spruce equally well, and making the calculation with 4 per cent, (which happens to be near the mean forest per cent, of either species), the following results are obtained : — Maximum Rotation. S e , Pf. Per cent. Larch III. quality . . .50 122 4-3 Spruce III. quality . . .60 58 3-8 It is evident that it is more profitable to grow larch. If, on the other hand, the same locality would produce a spruce wood of I. quality, the maximum soil expectation value under a rotation of 60 years would amount to 211 shillings, representing a mean forest per cent, of 4-7, compared with 4-3 per cent, under larch III. quality. It would be more profitable to grow spruce. 3. Choice of Silvicultural System. Having selected the species to be grown, the forester will con- sider what silvicultural system is best adapted to realise the objects of the proprietor, taking local conditions into account. As regards the financial results, considerable differences may exist between the different systems. High forest generally yields the greatest quantities and also the highest qualities of METHOD OF TREATMENT. 161 timber ; it also protects, and even improves, the permanent yield capacity of the locality. On the other hand, it requires a con- siderable capital, especially if a high rotation is adopted. It is obligatory in the case of conifers. There are different kinds of high forest, such as in the clear cutting, the uniform, group and strip- systems of shelterwoods, the selection system and others. Coppice woods are possible only in the case of species which reproduce freely from the stool ; they require a much smaller capital than high forest. In some cases high forest is financially more profitable, in others coppice woods. The comparative merit in this respect is obtained by ascertaining the maximum soil expectation values or the mean forest per cents, of the competing systems. 4. The Method of Treatment. From a financial point of view it is essential that the expenses are kept as low as adequate efficiency permits, and that the receipts should be as high as possible, taking into consideration the demands of a sustained yield. In this respect, the following matters are of special importance : — a. Effect of the Cost of Production. The principal items of the cost of production are the interest on the cost of the soil, the cost of formation, and the annual expenses for administration, protection, road construction, etc. The economic value of the soil utilised in forestry is expressed by its maximum expectation value. If the market value of the soil is greater than that, there will be a financial loss, and if it is smaller, a financial gain, being expressed respectively by a lower- ing or raising of the mean forest per cent., or by a negative or positive profit. Hence, the forester's effort must be to make the expectation value of the soil at least equal to, or, if possible, greater than, the market value. This can be done by careful and judicious management, but only within certain limits. If the market value of the soil reaches, or exceeds, a certain amount, it may be beyond the forester's power to make its utilization in forestry remunerative as compared with its employment in other 162 EXAMPLES OF APPLICATIONS. industries, such as agriculture. Generally speaking, it may be said that high grade soils give a better return in agriculture, and low grade soils in forestry. The exact limit between the two classes of soil depends on local conditions. The cost of formation, whether by sowing, planting, or natural regeneration, having to be incurred at the commencement of the rotation, has a most powerful effect upon the financial results. It is essential that it should be kept as low as possible compatible with efficiency. In this respect, many questions must be con- sidered which cannot be dealt with in detail in this place, such as the employment of skilled labourers, the cost of nursery plants, the planting distance, the amount of weeding of young planta- tions, the employment of small plants, and various other items. The question of the planting distance requires special attention. Wide planting reduces the cost per acre very considerably, but in the case of many species it may result in the production of an inferior class of produce, so that the initial saving may be con- siderably more than balanced by subsequent loss. As it is generally of importance to cover the soil within a limited number of years, the actual planting distance depends on the rate of growth of the selected species, the quality of produce which it is desired to secure, and the price obtainable for thinned-out material. A considerable saving may be effected by producing a wood by natural regeneration, but, if it is accompanied by a loss of time, it may be cheaper to sow or plant. The annual expenses do not change much in a well-regulated forest. There may be some moderate difference between those of a high forest as compared with a coppice forest, though, in either case, competent administration is of paramount importance. b. Effect of the Intermediate Returns. The effect of the intermediate returns upon the financial results depends on the time when they are realised and on the strength and value of the thinnings. The earlier the intermediate returns occur, other matters being the same, the higher will be the expec- tation value and the lower the cost value. Example. — A thinning worth 210 shillings usually made in the year 50 in the case of a larch woo-i III. quality worked under a rotation of 60 years, EFFECT OF INTERMEDIATE RETURNS. 163 210 x 1-04 10 and again every 60 years is worth T&jgi ~ ^2-6 shillings. If the same thinning were made in the year 40 and again everj^ 60 years, its 210 X 1-04 20 present value would be 60 =— = 48-3 shillings. Again, the stronger the thinning is made the greater the effect upon the financial result. It would be doubled by cutting 420 shillings worth of wood instead of only 210, provided that the extra heavy cutting does not reduce the final cutting in the year 60. If that were the case, the advantage gained might be more than neutralised, a matter deserving the careful consideration of the forester, especially during the earlier part of the wood's fife. Receipts from minor produce, especially if they occur early, affect the expectation value in the same way as those from thin- nings. 5. The Financial Rotation. By the financial rotation is understood that which coincides with the occurrence of the maximum soil expectation value or, which is the same thing, with the occurrence of the maximum mean annual forest per cent. It changes with the quality, or yield capacity, of the locality. The rotation generally is dealt with in Part III. of this volume. m3 165 PART III. THE FOUNDATIONS OF FOREST MANAGEMENT. 167 THE FOUNDATIONS OF FOREST MANAGEMENT. Forest working plans regulate, according to time and locality, the management of forests in such a manner that the objects of the industry are as fully as possible realised. As the latter differ widely, it follows that working plans cannot be drawn up according to any uniform pattern. The working plan for a protection forest or a park-like forest is altogether different from that of a forest which is managed on economic principles. In this volume, only forests of the latter class will be considered, that is to say, it 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 for a specific purpose. The yield (or the return) of a forest consists of major or principal, and minor produce. By the former, timber, firewood and bark are understood. It is in the nature of things that forests should yield chiefly such articles ; at the same time, articles of minor produce (such as turpentine, fodder, grazing, fruits, caoutchouc, etc.) are frequently of considerable importance, demanding modifications of that management which would be indicated by considering only the realisation of major produce. Major produce is derived from the final and intermediate yields. The latter comprise the thinnings and other cuttings which are made from time to time during the course of the life of a wood, while the former is the return yielded by the final cutting of the wood to be followed by a new crop, whether the old crop is re- moved in one cutting or by a number of successive cuttings, as in the case of natural regeneration under a shelter wood. The major produce of forests, wood, is one of the indispensable articles of life, but it is bulky and not adapted for a long transport by land. Hence, it must in many cases be produced locally. To this must be added that long periods of time elapse between the planting and harvesting of woods. Both these matters make it desirable that the yield of forests should be continuous and brought 168 THE FOUNDATIONS OF FOREST MANAGEMENT. into the market in annually equal, or approximately equal, quantities, necessitating a management based upon the principle of a sustained yield. Generally speaking, a sustained yield is secured if all areas which have been cleared are re-stocked within a reasonable time, and the young woods which spring up properly tended, so that the soil continues to produce crops of wood. At the same time a distinction must be made between — (1.) The intermittent working, if the successive final returns are separated by a varying number of intermediate years. (2.) The annual working, if final cuttings occur in each year. If the latter are approximately equal in quantity year by year, the method is called the " equalised annual working." The regulation of the yield of forests worked intermittently is very simple. It is only necessary to ascertain the most suitable rotation, taking into consideration the objects of management, and to make the intermediate cuttings whenever they are neces- sary. The matter becomes more difficult when an equal annual yield is expected. Although the method of annual working, and especially of the equalised annual working, is not an absolute necessity, still it is in the majority of cases highly desirable, more especially where extensive areas are under treatment, or where a steady market has to be regularly supplied. It has considerable advantages, of which the following may be mentioned : — (1.) It is best adapted to meet the requirements of the market, and therefore favours the development of a regular and steady demand with a sustained competition of purchasers. (2.) It affords equal employment year after year, and enables the administration to maintain a regular number of work- men and to instruct them thoroughly in their work. (3.) It secures to the owner an equal, or approximately equal, annual income, and facilitates budget arrangements. On the other hand, the method has disadvantages, such as : — (1.) It cannot be introduced without cutting certain woods at an age differing from that which is most desirable, in all cases where a regular series of age gradations does not exist, or where the age gradations are unfavourably dis- tributed over the area. INTRODUCTORY. 169 (2.) Owing to the necessity of bringing annually the same quantity of produce into the market, it interferes with the complete utilization of special demands for forest produce, or the omission of cuttings when the demand is slack. These remarks show that each of the two methods of working possesses peculiar advantages, and that the choice depends on local conditions. In the majority of cases, the annual working will be found more suitable and profitable, without, however, strictly adhering to it when it would involve sacrifices out of proportion to the general advantages of the method. Correctly speaking, in order to have equal annual returns it would be necessary to regulate the intermediate cuttings as well as the final returns. Against such an arrangement the following reasons may be given : — (1.) Areas, which yield equal final returns, do not always give equal intermediate returns. (2.) Thinnings depend much more than final cuttings on the method of formation and tending ; they must be made when they are necessary, so that the time for their execu- tion can, in many cases, only be determined a short time before they become necessary. (3.) The yield of intermediate cuttings depends frequently on events which do not occur regularly, or which cannot be foreseen, so that it is almost impossible to estimate it correctly beforehand ; for instance, in the case of wind- break, snow-break, death caused by disease or insects, etc. Hence, it is desirable to confine the regulation of the annual yield, in the first place, to the final cuttings, and to be satisfied with an approximate equalisation of the intermediate returns, such as will naturally happen if the final cuttings are systemati- cally equalised ; provided always that the thinnings are not made so heavy that they affect the subsequent final returns to an extent which would neutralise the advantages of heavy thinnings. If a forest is to yield a return, either annually or periodically, it must be in a certain state. In order to determine what this state should be under a given set of conditions, it is useful to construct an ideal pattern, such as would be presented by a forest which has 170 THE FOUNDATIONS OF FOREST MANAGEMENT. grown up uninfluenced by external interfering circumstances. The 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, or, if established, not per- manently maintained. The normal state of a forest, under a given set of conditions, depends chiefly on the presence in it of — (1.) A normal increment. (2.) A normal distribution of the age classes. (3.) A normal growing stock. By 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, for the time being, by a prepon- derance of certain age classes and a deficiency of others. By a normal distribution of age classes is understood a series of age gradations or classes so arranged that at all times, when cut- tings are to be made, woods of the normal age are available of sufficient extent and in such a position that no obstacles to their cutting exist. The normal growing stock is that which is present in a forest, in which the age gradations are normally arranged and show the normal increment. It can, however, also be present (in quantity) in an abnormal forest, if the deficiency of some woods is made good by a surplus in others. For the strictly annual working and the clear cutting system, a forest is, therefore, normal if it consists of a series of fully stocked woods equal in number to the number of years in the rotation and of the same yield capacity, so that each year a wood of the normal age can be cut, and that the returns are equal, at any rate in quantity if not in value. From a financial point of view, the further condition must be added that there should be no woods in the forest the current increment per cent, of which has sunk below the mean annual forest per cent. m j)f. INTRODUCTORY. 171 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 gradations or classes. (4.) The normal growing stock. (5.) The normal yield. (6.) The relations which exist between growing stock, increment and yield. 172 CHAPTEK I. THE INCREMENT. Every tree or wood may lay on three different kinds of incre- ment : — (1.) Volume or quantity increment. (2.) Quality increment i . . „ , , . /0 , -r, . . • Also called the value increment. (6.) rnce increment ) SECTION I.— THE VOLUME INCREMENT. By volume increment is understood the increase in the quantity of wood produced annually, periodically, or during the whole lifetime of a tree or wood, called respectively the current annual increment (C.A.I.), and the mean annual increment (M.A.I.) ; the latter may refer to a limited number of years, a period, or to the total increment laid on by a tree or wood. The increment is measured by the solid cubic foot or by the stacked cubic foot. The manner of determining the increment is given in Forest Mensuration. For the purpose of forest management, it should be mentioned that for short periods, say 5 to 10 years, the periodic mean annual increment is frequently accepted as the current annual increment without introducing any appreciable error. The calculation of the increment may refer to the final yield only, or to the intermediate yields, or to both together. 1. The Volume Increment of Single Trees. This is produced by an annual extension of the crown and roots, and by the addition of a new layer between wood and bark all over the stem, branches and roots. As a general rule, the stem, or trunk, is the most important part of the tree, and the forester is specially interested in the height and diameter (or girth) growth. Height Growth. — It is explained in silvicultural works 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 VOLUME INCREMENT OF SINGLE TREES. 173 productive power of the locality, the age of the tree and the method of treatment ; there is, further, a considerable difference, in the case of most species, between seedlings and coppice shoots. The table and Fig. 42 (pp. 174-5) exhibit the height growth of some of the more important species grown in Britain and on the Continent, the data referring in each case to localities of the first quality class, and it is assumed that the trees have grown in fairly stocked woods raised from seedlings. The data for larch, Norway spruce and Scots pine have been taken from the yield tables published by the Forestry Commissioners in Bulletin No. 3. Unfortunately, British height growth tables for the other species are not yet available ; hence a comparison of one group with the other is only approximately correct. In the illustration some data of the height growth of Vancouver Douglas fir in Britain have been added, which show that this tree grows more rapidly than any other tree which can be grown in Britain. It should be stated, in the first place, that larch and spruce grow in the early part of their life more rapidly in Britain than on the Continent, and that Scots pine grows more slowly. All three grow quicker than beech, oak and silver fir during youth, and up to the age of 60 years. From that age onward, considerable changes take place. While larch is the fastest growing tree to begin with, it is caught up and passed by spruce at the age of about 50 years. At the age of about 65 Scots pine is passed by beech and oak, while silver fir passes oak a few years after- wards, and gradually also beech. At this time beech passes oak, and it is itself parsed by silver fir shortly afterwards. The latter species catches up, and passes, larch at the age of nearly 120 years. In consequence of these changes, the final order at the age of 120 years is as follows : — Vancouver Douglas, Norway spruce, silver fir, larch, beech, oak and Scots pine. A similar relative height growth occurs in the other quality classes. On the whole it is, however, somewhat modified by local conditions. It should be noted that the actual height growth is, in the case of many species, considerably influenced by the density of a forest crop. A fair degree of density accelerates it, while too dense stocking retards it, especially in the case of broad-leaved species, which have a tendency to become flat headed at a comparatively early age. 174 THE INCREMENT. Table showing the Comparative Height Growth of some European Species, in Feet. Age, Years. Data taken from British Yield Tables. Data taken from Continental Yield Tables. Age, Years. Larch. Norway Spruce. Scots Pine. Silver Fir. Beech. Oak. 10 20 30 40 50 60 70 80 90 100 110 120 18 40 58 71 80 87 94 100 104 107 108 109 12 31 51 66 80 91 100 108 114 118 122 126 13 26 40 51 60 67 72 77 81 84 86 87 3 9 18 30 45 58 71 82 91 98 104 109 6 18 31 45 56 67 76 85 92 98 104 107 10 25 37 48 58 67 73 79 83 87 91 94 10 20 30 40 50 60 70 80 90 100 110 120 The data printed in italics for Scots pine beyond the age of 100, for larch beyond the age of 80, and for spruce beyond the age of 70 years, are estimates based on the increment laid on immediately before those ages. The relative height growth is of paramount importance in silvi- culture, and especially in the formation and maintenance of mixed woods. It indicates the species which can be successfully mixed, as well as the measures to be taken to protect the slower growing species against suppression by their faster growing companions. As shown in Forest Mensuration, height growth is also used to distinguish between the different quality classes of the locality. The periods at which the current annual and mean annual height increments reach their maxima are also of great interest to the forester, but the available data give somewhat wide limits for these periods. In a general way, the maxima occur earlier in the case of light-demanding species than in that of shade bearers. They occur, according to the British yield tables, at the following ages : — Quality Classes. Current Annual Increment. Mean Annual Increment. I. II. III. IV. I. II. III. IV. Larch Norway spruce . . 20 25 20 25 25 30 30 30 30 30 30 35 35 40 35 45 THE HEIGHT GROWTH OF SINGLE TREES. 175 It will be noticed that the maxima occur earlier on good quality than on inferior soils. In the case of teak (Tectona grandis), the current annual height increment generally reaches its maximum during the first five Diagram showing the Comparative Height Growth. 140 120 100 H 80 60 40 Vancouver Douglas- <-»** *<*' * f2 v?y / f / /* Iff" 4 1 f 1 / / ' i / / f/// 4 Mr" f S Spruce. Silver Fir. Larch. Beech. Oak. Scots Piue. 40 60 80 AGE, YEARS. Fig. 42. years of the tree's life. Deodar (Cedrus Deodara) shows a height growth similar to that of spruce. Sal (Shorea robusta) has a remarkably even rate of growth up to the age of 80 to 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, few cases excepted, reach the same ultimate height as seedling trees. Diameter, or Girth, Increment. — This depends on the quality of 176 THE INCREMENT. the locality and the size and activity of the leaf -surf ace. As a consequence, free- growing trees increase more rapidly in diameter than those grown in fully stocked woods. At the same time, the position of the leaf-surface on the stem is of importance. Trees with the crown coming down to the ground are more tapering than those with the crown restricted to the upper part of the stem, which show a more cylindrical shape. Hence, the forester aims at killing Table showing the Diameter Growth in Inches of some European Species of Trees in Fairly Fully Stocked Woods. Age, Years. Data taken from British Yield Tables. Data taken from Continental Yield Tables. Age, Years. Larch. Norway Spruce. Scots Pine. Silver Fir. Beech. Oak. 10 20 30 40 50 60 70 80 90 100 110 120 51 7-6 9-6 11-1 13-4 14-7 15-9 170 180 190 200 7-3 10-5 13-4 15-9 17-8 19-7 21-5 22-5 240 25-0 5-V 8-0 9-9 11 5 131 14-7 15-9 16-9 180 190 0-5 1-3 2-5 40 5-6 7-5 9-6 11-7 14-2 16-2 17-5 18-3 0-7 1-7 30 4-5 6-3 8-0 9-5 10-9 12-2 13-5 14-6 15-6 10 2-4 4-3 61 8-2 9-9 11-4 12-8 14-2 15-5 16-9 18-4 10 20 30 40 50 60 70 80 90 100 110 120 The data for larch beyond the age of 80, for spruce beyond 70 years, and for Scots pine beyond 100 years are estimates based on the immediately preceding increment. They are printed in italics. A comparison of the British yield tables with the German tables shows that larch, spruce and Scots pine show a more rapid diameter increment in the former country. the lower branches naturally, which he achieves by maintaining an appropriate density of stocking until towards the latter part of the life of his woods. Whenever the object is to produce a high quality of timber, he sees that a young wood establishes a com- plete leaf canopy at an early age, and subsequently he regulates the thinnings so that at all times each tree has the most suitable growing space. A tendency has been perceptible of late years to introduce wide planting so as to reduce the initial cost, to be followed by very heavy thinnings. This may be justifiable where the production of volume only is aimed at, but, in the author's THE DIAMETER GROWTH OF SINGLE TREES. 177 view, it is a serious mistake where high-class timber is to be pro- duced. In the latter case, a high form factor of the stem should be the object of the forester. The appended table and Fig. 43 show the diameter growth of some species. Diagram showing the Relative Diameter Growth. Spruce. 60 80 AGE, IN YEARS. Fig. 43. 178 THE INCREMENT. 2. The Volume Increment of Whole Woods. The various methods of determining the volume and increment of woods are dealt with in Forest Mensuration. Here only those points will be considered which are of special interest to the manager of a forest. The increment of a wood consists, during the first part of its life, of the full increment of the individual trees. As soon as the trees close overhead, the extension of the Table showing the Volume production of some European Species. I. Quality, Timber only, in Cubic Feet. Woods fully Stocked. Data taken from British Data taken from German Yield Tables . Yield Tables . Age. Years. Age. Years. European Norway Scots Silver R h Oak. Larch. Spruce. Pine. Fir. 10 600 10 20 1,640 1,500 800 560 20 30 3,245 3,910 2,050 500 690 1,800 30 40 4,690 6,585 3,495 1,760 2,070 3,320 40 50 5,940 9,055 4,805 4,090 3,860 4,780 50 60 7,145 11,175 5,960 6,690 5,690 6,180 60 70 8,260 12,780 7,045 9,950 7,500 7,480 70 80 9,160 14,300 8,040 13,630 9,250 8,710 80 90 10,000 15,800 8,940 17,260 10,880 9,900 90 100 10,800 17,250 9,695 20,360 12,430 10,980 100 110 11,500 18,650 10,400 22,710 13,850 11,990 110 120 12,000 20,000 11,000 24,630 15,170 12,950 120 The data for larch beyond the age of 80, for spruce beyond 70, and for Scots pine beyond 100 years are estimates, based on the immediately preceding increment ; they are printed in italics. The volume production includes all thinnings. crown is impeded, and a struggle for existence sets in. As long as the degree of density is moderate, the height growth is not reduced ; a moderate degree of density of the leaf canopy actually encourages it. On the other hand, too dense a stocking may cause a reduction of the diameter growth. Although, during this period, the individual tree may lay on less increment than it would do in a free position, a fully stocked 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 per unit of area. What degree of density THE VOLUME INCREMENT OF WHOLE WOODS. 179 of a wood gives the maximum of production has been much studied, but in the case of many species final conclusions have not yet been reached. In the meantime, it should be remembered that a fairly full stocking encourages height growth, decreases the tapering of the stem and kills the lower branches, thus producing a high quality of timber. While the loss of material is very small in the case of trees Volume Production — Timber only. I. Quality Class. 20,000 E-i H 16,000 ft p 3 p "j 12,000 a S P g 8,000 > 7* / s / / / / / / / / / > / / / / 7 * s s s y y - ' y' y / r / / / yS. y y s ^y^ /^y^ ^y '<^y^ ^>^ l^^ 4,000 ^s^^yy C^'- <**' 7 Silver Fir 1 Spruce 2 Beech 3 Oak 4 Larch Scots Pine 3 2 40 So 60 AGE. 100 120 Fig. 44. grown in the open, it becomes very considerable in fully stocked woods. Not only do the lower branches die, but the greater number of the trees must be removed, because they are gradually overtopped, suppressed and finally killed by surrounding trees of stronger height growth ; such trees form, ordinarily, the material removed in thinnings. In fully stocked woods, a distinction is X 2 180 THE INCREMENT. made between the dominating trees and the rest of the stocking ; the former are called the major or primary part of the growing stock, and the latter the minor or secondary part. As the life of the wood advances, not only the latter, but also a con- siderable portion of the previously dominating trees will be removed in the thinnings, in the same degree as they lose their dominating character and join the secondary part of the growing stock. The appended table and Fig. 44 exhibit the volume produc- tion of some European species. They represent the volume of timber only produced on first class-localities. The Continental yield tables used are those for silver fir by Lorey, for beech by Schwappach and for oak by Wimmenauer. It will be observed that at the age of 40 years the comparative production is as follows : — Silver fir, 1,760 cubic feet ; beech, 2,070 ; oak, 3,220 ; Scots pine, 3,495 ; larch, 4,690 ; Norway spruce, 6,585. Then great changes take place in the relative position, so that at the age of 80 years the sequence is as follows : — Scots pine, 8,040 ; oak, 8,710 ; larch, 9,160 ; beech, 9,250 ; silver fir, 13,630 ; spruce, 14,300. This relative position is again altered and the differences in production are further increased, so that the position at the age of 120 years is as follows : Scots pine, 11,000 ; larch, 12,000; oak, 12,950; beech, 15,170; spruce, 20,000; silver fir, 24,630. It should, however, be noted that the volumes of larch beyond 80, of spruce beyond 70, and of Scots pine above 100 are estimates. Further experience may show that the volume production of spruce at an advanced age may be above that now estimated. The progressive increment per acre and year is shown in the table on next page. The given data justify the following conclusions : — (1.) The current annual increment of light-demanding species (larch, Scots pine and oak), and also of the moderate shade bearer, spruce, rises rapidly after the first few years and reaches its maximum generally about the time when the height growth culminates. In the case of shade bearers, the maximum volume increment occurs later than the maximum height growth, in beech by 20 years and in silver fir by 40 years. THE VOLUME INCREMENT OF WHOLE WOODS. 181 (2.) The mean annual increment keeps at first below the current annual increment ; the two become equal some time after Table showing the Current Annual Increment (C.I.) and the Mean Annual Increment (M.I.) per Acre and Year, including Thinning?. Timber down to 3 Inches at small end, in Cubic Feet. I. Quality. Data taken from British Yield Data taken from German Yield Age. Years. Tables. Measured under Bark. Tables. Measured over Bark. Age. Years. Larch. Norway Spruce. Scots Pine. Silver Fir. Beech. Oak. C.I. M.I. CI. M.I. CI. M.I. CI. M.I. CI. M.I. CI. M.I. 10 10 96 56 20 168 78 241 75 125 40 50 69 124 28 20 30 144 108 267 131 144 68 126 17 138 23 15?, 60 30 40 125 117 247 165 131 87 210 44 179 52 146 83 40 50 119 181 96 82 77 96 50 120 212 115 260 183 140 60 111 119 160 186 108 99 326 111 ! 181 95 130 103 60 70 90 118 152 183 99 101 368 142 175 107 123 107 70 80 84 115 150 179 90 100 363 170 163 116 119 109 80 90 80 HI 145 175 75 99 310 192 155 121 108 110 90 100 70 108 140 172 70 97 235 204 142 124 101 110 100 110 50 105 135 169 60 95 192 206 132 126 96 109 110 120 100 167 92 205 126 108 120 the current increment has passed its maximum, after which date the mean increment is larger than the current incre- ment. Naturally, the mean increment reaches its maxi- mum at the time when it is equal to the current increment. (3.) During the period between the two maxima the current increment is falling and the mean increment rising. 182 THE INCREMENT. The appended illustration for larch (Fig. 45) will show this : — 200 c 4^/. ***^/j ■^ ^A >.\ 10 30 40 50 AGE, IN YEARS. 7n Fig. 45.— Relation of C.A.I, and M.A.I, of Larch. (4.) Whenever the object of management is to obtain the greatest volume production, the rotation should coincide with the year in which the mean annual increment cul- minates. Taking the data for larch as an example, the current increment culminates in the year 29 and the mean increment in the year 58 ; hence, in the course of 58 years two crops 29 years old can be grown giving a total volume of 2 X (105 X 29) = 6,090 cubic feet, while one rotation of 58 years gives 119 X 58 = 6,902 cubic feet, or 812 cubic feet more. The data given above for the best quality class exhibit the differences in height, diameter, and volume production of the more important European species. It stands to reason that the data diminish according to the reduction of the quality. On this point a reference to the yield tables given in Appendix IV. is invited. 3. The Volume Increment per Cent. So far the increment has been expressed in actual volume or cubic feet. In addition, it is useful to ascertain the proportion which exists between the total volume of the tree or wood at a certain age and the increment laid on during one or several years before or after that age. In order to express that proportion independently of the actual volume, it is usual to give it in per THE VOLUME INCREMENT PER CENT. 183 cents, and to call it the " increment per cent." By this is under- stood the current annual or periodic increment which is laid on by every 100 units of volume. By analogy with what has been said in Part II., let m V be the volume of a wood in the year m, and m + n V the volume in the year m + n, then : — »> /m + ny m + ny _ my x J.^. ftn ^ Carrent^^ __ JQQ x y __ 100, Or log m + n V — loff m V log. (100 + Pv) = 2 + -^ l ^—L t an d n Pressler's approximate formula becomes m + ny_my £00 Currents y rv — m + ny _|_ my A w ' Example : — Let the volume at the age of 40 be = 2,290 cubic feet, and in the year 50 = 3,270 cubic feet, then .I** > « , log. 3,270 - log. 2,290 , Log. (100 + p v ) = 2 + -2 — ! s , and p v = 3-53 per cent. ; and according to Pressler's formula, m + nV-mV 200 _ 3,270 - 2,290 200 , _ „ m + ny + mv X IT ~ 3,270 + 2,290 X 10' and ^ ~ AbS ' If a thinning has been made during the n years, its volume must be added to that of m + n V. The increment per cent., p„, is very large during the early youth of a wood, or tree, but as the volume increases with advancing age, while the annual increment does not increase in anything like the same proportion, and in fact begins to decrease comparatively early, it follows that the increment per cent, becomes smaller year by year. Heavy thinnings may produce an exception to that rule, as they would temporarily reduce the producing capital- By calculating the volume increment per cent, with formula 2 for various periods, the following results are obtained : — Period 20—30 = 9-28 per cent. Period 50—60 = 2-76 per cent. n 30—40 = 5-35 „ „ 60—70 = 2-31 „ 40—50 = 3-53 „ „ 70—80 = 1-75 „ 184 THE INCREMENT. It remains to add that the above formulas can also be used to determine the height, diameter and basal area increment per cent. SECTION II.— THE QUALITY INCREMENT PER CENT. By quality increment is understood the increase in the value per unit of volume. It is produced, in the first place, by larger pieces of timber frequently fetching higher prices per unit of measurement, and secondly by a reduction of the cost of harvest- ing 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 m Q to m + n Q, then the quality increment per cent, is obtained by the formula — and Pa =100(^^-1); and log.(100 + ft ) = 2 + 1 °g-" + *«- 1 °^ . An approximately correct value for p q is obtained by the formula — m + nQ_mQ 200 P«l — m + nQ_j_mQ X "Jf • The quality increment may be rising, falling, or its movements may be more or less irregular ; hence, it must be ascertained in each case. Woods grown for firewood show only little or no quality incre- ment after middle age ; except, perhaps, in so far as the per- centage of stem-wood increases. The latest investigations seem to indicate even that wood taken from middle-aged trees has a higher heating power than wood taken from older trees, although the latter may be perfectly sound. Matters are different in the case of timber forests ; here the THE QUALITY INCREMENT PER CENT. 185 quality increment rises, in the majority of cases, at any rate, beyond middle age and frequently to an advanced age, because : (1.) Trees of large dimensions are, up to a certain limit, more valuable per unit of volume than those of small dimen- sions, though exceptions to this rule occur frequently. (2.) The percentage of timber to firewood increases, at any rate up to a certain age. The quality increment per cent, sinks, on the whole, with advancing age, though more or less irregularly ; it can become nil and even negative if the timber commences to decay. Example. — A Scots pine wood 60 years old contains — Timber = 3,300 cubic feet, worth 4rf. per cubic foot. Firewood = 760 „ „ „ Id, Hence, mean quality — — ■^ 3 - 300x ^o 76 ° Xl -^P— • The same wood in the year 70 has — Timber = 3,820 cubic feet, worth 5d. a cubic foot. Firewood = 710 „ „ „ id. Hence — - * » Q - 3,820 X 5 + 710 x 1 V j-ggQ, = 4-37 pence. And 4-37 = 3-44 x l-Opq™ log. (100 + p q ) = 2 + l°g- *37- log. 3-44 And 10 Pq = 2-42 per cent. Approximate value — 4-37 - 3-44 200 „ „„ Pq = 4-37 + 3-4 4 X To" = 2 ' 38 per cent - 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, especi- ally while the wood is still young. Here, a few years' extra growth may cause a great rise in the quality per unit of measure- ment. On the other hand, if thinnings are kept over too long, they interfere with the proper development of the major part of the wood ; hence, extremes in this respect must be avoided. 186 THE INCREMENT. SECTION III.— THE PRICE INCREMENT PER CENT. By price increment is understood the increment caused by a change in the price of forest produce generally, independent of the accompanying quality increment. It can be positive, nil, or negative. Example. — A hitherto inaccessible forest is brought into com- munication 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 negative price increment. The price increment depends partly on the forester, and partly on external causes over which he has little or no control. Of the former class of causes are, for instance, the construction of good roads, development of industries which consume forest produce, improvement in the general management leading to a higher net value per unit of measurement. It is out of the question to construct a law showing the changes in price. In some cases, such changes affect all classes of produce, in others only certain kinds. In any circumstances, it is almost impossible to foresee them, except in special definite cases. At the same time, the price increment is of considerable import- ance, as it affects the financial ripeness 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 m S represents the value of the unit of measurement at the present time, and m + ">S the corresponding value after n years, the price increment is = m + n S — m S, and m + »S = m Sx I0p, n log. (100+ p,) = 2 + Again. the approximate value — log. m + n S — log. m S + "S- m S 200 X n S + m S n COMBINATION OF THE INCREMENT PER CENTS. 187 SECTION IV.— COMBINATION OF THE THREE INCREMENT PER CENTS. A forest of the present value of m F, working with the three per cents. p v , p q , and p s , increases in one year to m + 1 F = m F x l-0p v X l-0p q X l-0p„ and, if l-0p v X l-0p q X l-0p s is placed = 1-Ojoy, then m + \p _ m F x i.Q pf} and m + np = mtf x l.Q p ^ Out of this is obtained the value of current p n f during n years : — current p/ = m x ^ _____ _ 100j and i /iao i x .-, , log. m + "F — log. M F log. (100 + p f ) = 2 + -M s— . This is the formula for the forest per cent, given at page 3 39. As there, so here, the value of m F is taken as the utilization value of the growing stock -f- the value of the soil. For an example, see Part II., page 141. 188 CHAPTER II. THE ROTATION. By rotation is understood the period of time which elapses between the formation of a wood and the time when it is finally cut over. The determination of the length of the rotation is one of the most important measures in forest management. It depends on the objects which the proprietor is aiming at, and these differ with every change of conditions. In some cases the proprietor desires to realise indirect effects, such as the protection of the soil, amenities, hygienic effects, etc., in which high rotations may be indicated. In other cases, the economic aspects of forestry are paramount, such as the production of the greatest quantity or highest quality of produce, the production of a definite class of timber, or high financial results. Accordingly, the forester arranges the rotations under various titles, such as : — (1.) The financial rotation, (2.) The rotation of the highest income, (3.) The rotation of the highest volume production, (4.) The technical rotation, (5.) The physical rotation, and various others of minor importance. As forests represent capital, they are, in economic forestry, expected to yield an adequate return. Hence, the financial rotation has been placed first ; by it the financial loss involved in the adoption of a different rotation is measured. 1. The Financial Rotation. By it is understood the rotation which, after allowing compound interest on all outgoings and receipts, gives the highest net profit over and above a fixed per cent., or the highest mean annual forest per cent. The methods of calculating either the one or the other have been explained in Forest Valuation. THE FINANCIAL ROTATION. 189 The profit is given by the formula — Profit = S e — S c , respectively = F e — F c , calculated with a fixed per cent, (see pages 136-7). The maximum mean annual forest per cent, is obtained by calculating the soil expectation values with various per cents, and constructing a graph, from which the per cents, corresponding to varying soil cost values can be read off (see pages 142-6). Owing to the uncertainty of the future returns and expenses, from which these calculations are made, the financial rotation can only approximately be ascertained. Moreover, it changes with every change of conditions. In these circumstances, it can serve only as a general guide. Its accuracy will increase with the perfection of the available yield tables. It should also be noted that it is impossible to forecast prices in the future ; they may rise or fall. Hence, all calculations should be made with present prices, or those which prevailed in the immediate past. All these matters make it desirable to fix the actual financial rotation somewhat higher than the calculated number of years. The growing stock of a wood has, in the majority of cases, little value during the first part of the rotation, so that the yield would not even cover the cost of harvesting, and the expectation value of the soil would be a negative amount. With advancing age it should become positive, and increase in value until it reaches its maximum amount, after which time it decreases. A second maximum is sometimes reached, owing to a sudden increase in the price per unit of measurement of the yield. In any case, under a high rotation the expectation value would, under ordinary conditions, again become negative. Example. — Calculating the expectation value for larch III. quality with 4 per cent., the following values are obtained if S c = £5 : — Rotation. Soil Expectation Value. Mean Forest Per Cent. 30 40 50 60 70 80 41 shillings. 115 „ 122 „ 106 „ 92 „ 66 „ 3-4 per cent. 4-2 „ 43 41 3-9 3-8 190 THE ROTATION. In this case, the maximum is reached under a rotation of 50 years, or perhaps a couple of years before that time. This rotation is the " financial rotation," being the most profitable from a financial point of view. The forester must then consider whether, and to what extent, a deviation from the financial rotation is required, so as to realise the objects of the proprietor. Deviations from the financial rotation may be due to various considerations, as indicated above. In all such cases the effect is a reduction of the forest per cent. If, for example, the rotation in the case of larch III. quality is raised from 50 to 80 years, the mean per cent, is reduced from 4-3 to 3-8 per cent. The actual length of the financial rotation differs very con- siderably. Generally speaking, it may be said that the financial rotation is low in localities of a high yield capacity ; where an increase in the price per unit of volume ceases at a comparatively early age, such as localities where only firewood is saleable ; where trees of small dimensions can be sold at timber prices, such as in mining and hop-growing districts. The financial rotation is high in localities with an unfavourable soil and climate, such as high and exposed situations where the trees take a longer time to reach marketable dimensions ; in thinly populated districts where prices generally rule low for small dimensions, while large timber can be exported to other better- paying markets. The length of the financial rotation as obtained by a first calculation is subject to correction, because it is based upon prices obtainable for the various classes of produce at the time. These may be changed if the financial rotation differs from that hitherto followed. If the calculated financial rotation is lower than that existing, and the former is introduced, more small and less large timber is produced, which may cause a fall in the average price of the produce. The reverse effect will be produced if the financial rotation is the higher of the two. In either case, a change in the rotation will be accompanied by a change in the permanent growing stock. The difference between the old and the new growing stock must be removed in the one case or saved up in the other ; in other words, either more or less timber than previously is thrown upon the market for a time, which may further disturb prices. THE ROTATION OF THE HIGHEST NET INCOME. 191 In these circumstances, any change in the rotation should be introduced cautiously, and, on the whole, it is desirable to keep somewhat above the theoretical financial rotation. If the change refers to a small area, it can be carried out at once, provided the demand for produce is sufficiently large to absorb the extra cut- tings without any appreciable change in prices. If the forest is of some extent and the demand for produce uncertain, it is pre- ferable to make the change gradually, so as to spread the extra supply of produce over a number of years, or to bring up a deficient growing stock to the proper amount by moderate annual savings.* 2. The Rotation of the Highest Net Income. By this is understood the rotation which yields the highest net income calculated without interest and irrespective of the time when the items of income and costs occur. The average net annual income is obtained by dividing the sum of all incomes, minus the sum of all costs of one rotation, by the number of years in the rotation according to the formula : — Mean annual net income = ■ — — — * The rotation for which this expression reaches the maximum amount is the rotation of the highest net annual income. It occurs, as a rule, a considerable number of years beyond the financial rotation. Example. — From the money yield table for larch III. quality the following amounts for the net annual income are obtained, to which the mean forest per cents, for the several rotations have been added : — ■ Rotation. Mean Annual Net Income. Mean Forest Per Cent. 30 40 50 60 70 80 25 shillings. 28 „ 38 „ 46 „ 55 „ 62 „ 3-4 per cent. 42 43 41 3-9 3-8 * In an article published by the Author in 1865, it was shown that a moderate reduction in the price of the produce placed on the market may be financially preferable to leaving surplus growing stock in the forest. (See Allgemeine Forst und Jagd Zeitung of 1865.) 192 THE ROTATION. It will be observed that the annual net income is still rising under a rotation of 80 years, and likely to do so for another 10 or 20 years — in fact, until the increase in the expenses overtakes that in the volume and quality of the increment. At the same time, it will be observed that the maximum mean annual forest per cent, occurred under a rotation of 50 years with 4-3 per cent., and that it had fallen to 3-8 per cent, under a rotation of 80 years, involving a considerable financial loss. This loss will further increase with a further rise of the rotation, and it represents the penalty which the proprietor has to meet for going beyond the financial rotation. At the same time, other considerations may, and in many cases will, justify the adoption of such a course. 3. The 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. Let the volume of the final yield be V r , and the volumes of the thinnings in the years a, b, . . . q be represented by V a , Vb, • • • Vq, then the rotation of the greatest volume production is that under which the value Y r + Va + V b . . . + V, - becomes a maximum. The calculation can be made for timber and firewood or for timber only. Example. — Taking the data for larch III. quality, the amounts are : — Rotation. Yield, c'. Rotation. Yield, c'. 30 40 50 51 65 71 60 70 80 75 77-2 76-9 The maximum occurs under a rotation of 70 years, which is 20 years above the financial rotation, involving a reduction of the mean forest per cent, from 4-3 to 3-9 per cent. 4. The Technical Rotation. By this is understood the rotation under which a forest yields the most suitable material for a special purpose, such as, for THE CHOICE OF ROTATION 193 instance, for general construction, 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 vary much, the technical rotation may occur at any age, before, at and after the age of the financial rotation. 5. The Physical Rotation. This term is applied to various conditions. It may be that rotation which coincides with the natural lease of life of the trees, as in protection forests, parks, etc. In other cases it indicates the age of woods which is most favourable for natural regeneration, taking into consideration the conditions of the locality and the silvicultural system under which the forest is managed. In the latter case it cannot be lower in high forest than the age when the trees commence to produce good seed in sufficient quantity, nor as high as the age when the production of good seed has ceased, the best period being that about the end of the principal height growth. In the case of coppice woods, the rotation must be below the age at which the trees cease to produce good healthy shoots when cut over. 6. The Choice of Rotation in Practical Forestry. The choice of rotation, or the age at which a wood is to be cut over, is, as already stated, one of the most important questions in practical forestry. Many and various are the arguments which have been advanced in favour of one or the other rotation. On one side, it is asserted that the financial aspect should decide the choice of rotation, since forests represent capital which should yield an adequate interest. On the other side, it is said that the general usefulness of the forests should be the deciding factor, since other considerations are of more importance to the com- munity than high interest, and more especially so in the case of State forests. The latter argument introduces a difference between private and public forests. In the author's view, the question should be governed by the objects which the proprietor desires to realise, whether the forests belong to private persons or to the State. The former will, in the majority of cases, be 194 THE ROTATION. guided by financial considerations, though not in all. The State, while not ignoring the financial aspect, must consider other demands in the interest of the community as a whole. For instance, protection forests must generally be managed under high rotations ; the same holds good in growing timber for ship construction ; where land is scarce the rotation of the highest volume production might be indicated ; in other cases, where small dimensions are wanted for important industries, low rotations may be adopted ; special rotations may be neces- sary where an adequate supply of forest produce is essential to safeguard the country against a timber famine or other emergency, etc. Whatever the desired rotation may be, the proprietor should know what financial sacrifice its adoption involves, in case it differs from the financial rotation. Hence, the general procedure in fixing the rotation may be described as follows : — (1.) The proprietor should define the objects at which he is aiming, and especially the class of timber which he desires to produce. The forester should then indicate the rotation under which these objects can be realised in the most economic manner. (2.) The forester should then calculate the financial results of that rotation, and also of the financial rotation. The difference in the financial results gives the financial loss involved in deviating from the financial rotation. (3.) In the case of the clear cutting system, and especially under short rotations, the forester should draw special attention to the injurious effects which may be produced by repeated exposure of the locality to atmospheric influences. With such information before him, the proprietor can give his final decision, whether he be a private person or the State. The third point given above is of paramount importance when the management aims at a sustained yield. However tempting the clear cutting with subsequent planting or sowing may be, it has more and more been recognised of late years that, except under specially favourable climatic conditions, frequent exposure of the locality leads in the long run to a reduction of the yield capacity of the locality, especially where light-demanding, thin- THE NORMAL AGE CLASSES. 195 crowned, or shallow-rooted species are cultivated in pure woods. In such cases the rotation should not be short, or, at any rate, an admixture of a soil-improving species should be given, either at once or by under-planting at an early age. The above method of determining the rotation refers to fairly even-aged woods. Its principal usefulness consists in bringing order into the management, and in indicating the time during which the forester should go round the whole area of a working section. In uneven-aged woods, such as the selection forest, the standards in coppice with standards, and irregular forests generally, it is almost impossible to fix an average rotation with any degree of accuracy. In such cases, the ripeness of the individual trees is determined by their reaching the size desired by the objects of management and by the proportion of trees in the several size classes. CHAPTER III. THE NORMAL AGE CLASSES. When, under the system of working for a sustained annual yield, the rotation has been fixed, it is necessary that, year after year, or period after period, the required mature woods are forth- coming, so that the calculated annual yield may be obtained. This involves the establishment of a normal series of age grada- tions. By that term is understood a series of age gradations or classes 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 the age classes or gradations must each be of the proper extent, and that they are properly grouped and distributed over the forest. If a forest is to be managed according to the system of a sus- tained annual yield and the clear cutting system, it must contain a series of age gradations equal to the number of years in the rotation ; the oldest age gradation must, immediately before cutting, have the age of the rotation, the youngest must be one year old, with a difference of one year in the age of every two gradations. 196 THE NORMAL AGE CLASSES. 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 again be dealt with further on. For the present it is assumed that the quality of locality is the same throughout. Frequently, a number of age gradations are thrown together into an age class. The following questions thus arise : — (1.) What is the area to be cut annually under the different methods of treatment ? (2.) What is the size of the age classes ? (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. a. Coppice and Coppice with Standards. The annual coupe is determined by dividing the total area of the forest, or working section, by the number of years in the rotation under which the coppice is worked. Let total area = A, and the rotation 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. b. Clear Cutting in High Forest. Here again : A c — — , r if each clearing is at once re-stocked. It frequently happens, however, that the cleared coupes lie fallow for one or more, say s years ; in that case : A C ~r + s> THE ANNUAL COUPE. 197 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 Shelter-wood Compartment or Uniform 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 regeneration coupe, the crop on which, by gradual cuttings, is led over in the course of m years into a young wood. The size of the regeneration coupe is, there- , A lore, = — X m. r In this case, the first of the successive cuttings towards regenera- tion may be made — Either in the year r, so that the trees removed at the end of the regeneration period would be r + w* years old, and the mean age vn r + ■H" years ; in other words, the procedure would lead to a raising a 771 of the rotation from r to r + « years ; Or, the first cutting may be made in the year r — ^- and the last in the year r -f- k-> so that the mean final age comes to r years. In this 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 num- ber of years to go round the forest, and before cuttings are again made on the same area. If that number is I, then — Annual cutting area = j . Example. — In the beech forests of Buckinghamshire, which are worked under the selection system, it is usual to go round once in 198 THE NORMAL AGE CLASSES. seven years ; in that case the annual cutting area would be equal A to -=- . In other cases, as in the Indian Sal and teak forests, I is longer, generally from 15 to 40 years. 2. Size of the Age Classes. . In forests of some extent which are worked under a high rota- tion, 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 AGE 10 20 30 40 50 60 70 80 90 100 Fig. 46. — A Normal Series of Age Classes, treated under the Uniform System. with larger groups, that is to say, to join a number of age grada- tions into an " age class." The normal size of such an age class depends on the area of the annual coupe and the number of such coupes thrown together. If a class contains n gradations, its area would be = n X c. T The number of age classes = - is variable. 6 n 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. SIZE OF THE AGE CLASSES. 199 111 this way, the number of the age class indicates directly the limit of ages of the woods contained in it. The reverse method, of calling the oldest age class I., the next oldest II., etc., is less desirable, but unfortunately it has been largely adopted. The number of years included in an age class is called a " period," and the area dealt with in the course of a period is called a " Periodic Coupe " (French : " Affectation "). The area of the age classes under the several methods of treat- ment will be as follows : — ■ a. Clear Cutting in High Forest. The area of each age class, C, in a normal state, is — C = n X c = n X — , or C = w 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 = 1,000 acres, rotation r = 100 years, s = years, n = 20 years. Then, Annual age gradation = — = ' » = 10 acres ; r 1UU and the age classes : — C x ( 1 — 20 years old woods C 2 (21— 40 * „ C 3 (41— 60 C 4 (61— 80 C fi (81—100 „ = c x n = 10 x 20 = 200 acres. = „ = „ = 200 „ = „ = „ = 200 „ = „ = „ = 200 „ = „ = „ = 200 „ A = 1,000 acres. b. Shelterwood 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 may be indicated by ?n. There is always an area under regeneration which contains a certain number of old and young trees, called the Regeneration Class = C v . It progresses gradually through the whole working section, and is found in its original position at the beginning of the second rotation. 200 THE NORMAL AGE CLASSES. The appended illustration 47 further explains this process in the case of m = n. 81—100 Period Pi C 2 c 3 c 4 Hb 02 C 3 ('4 c, c 3 c\ C'i C Y 2 G, o, c 2 ^ o, ^2 n, in which case C e contains not only the oldest age class, but also a portion, if not the whole, of the second oldest age class. Hence, the size of the several age classes may be expressed as follows : — (1.) m < n. C x = — X n ; C 2 = — X n ; C 3 = — X n; C' 4 = — x n ; A A C 5 = - x {n — m), and C v = — X m. Example : — Let m — 15 ; n = 20 ; r = 100 ; A — 1,000 acres ; Annual coupe = 10 acres. C x = 10 X 20 = 200 ; 0, = 10 x 20 = 200 ; C 3 = 10 X 20 = 200. n. Example. — Let m — 30. C\ = C 2 = C 3 = 200 each = 600 ; C' 4 = 10 x 10 = 100 ; C 5 = ; C B = 10 x 30 = 300. Total = 600 + 100 + 300 = 1,000 acres. It is obvious that in the case of the shelterwood system with natural regeneration the above allotment is only of an ideal character, because the actual duration of the regeneration is so uncertain. The regeneration class, the oldest and the youngest classes are subject to modifications between 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 allot- ment may then be represented as follows : — C 2 — C 3 = C 4 = 200 each together = 600 acres ; C 5 + C x = Cv= 1000 - 600 = 400 „ Total = 1,000 acres. 202 THE NORMAL AGE CLASSES. Or, if regeneration extends over a still longer period : — C' 3 = (7 4 = 200 each, together = 400 acres ; C 5 + G x + C 2 = C v = 1000 - 400 = 600 „ Total = 1,000 acres. This system has been practised for 100 years in parts of the Black Forest, as well as elsewhere, in Germany (Femelschlag- betrieb). A somewhat modified form of it has of recent years been developed in France, where it goes by the name of Quartier Bleu, owing to the areas under regeneration being painted blue on the French forest maps. All parts of the regeneration area which become fully stocked with young growth are taken out, and joined with the middle-aged areas, while corresponding areas of old woods are moved into the Quartier Bleu. 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 the formation of age classes is not necessary. If the latter should be desirable, generally not more than five gradations are thrown together to form an age class. Example : Area = 200 acres ; r = 20 years ; annual coupe = 10 acres ; each age class = 10 X 5 = 50 acres, and number of age classes = 4. d. Coppice with Standards. Here each coupe contains coppice (underwood) and standards (overwood). As far as the underwood is concerned, the arrange- ment is exactly the same as in the case of simple coppice ; the A A annual age gradation is = — , and the age class, if any, = — X n. The distribution of the overwood, in its normal condition, is somewhat peculiar, which may usefully be explained here, though it is only of theoretical value. In the first place, it should be remembered that cuttings in both the under- and overwood on the same area must be made at the same time, or rather those in the overwood must be made immediately after the underwood has been cut over, and before the new coppice shoots appear ; hence, the rotation R of the SIZE OF THE AGE CLASSES. 203 overwood must be a multiple of the rotation r of the underwood, say R = r X t. In each annual coupe, when cutting comes round to it, a certain portion of the underwood (chiefly seedling trees) is left standing to form the youngest age gradation of the overwood. That por- tion should occupy an area = ^> assuming that each age grada- tion of the overwood occupies the same extent of ground. The A A area occupied by each age class of overwood comes to = p X r = — . 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 overwood 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 Cj age „ „ c 2 „ 1 r+1 2r+l (<-l)r+l 2 r + 2 2r + 2 (<-l)r + 2 3 r+3 2r+3 (<-l)r+3 r-1 2r-l 3r-l txr-l r 2xr 3x r txr It will be seen that a normal coppice with standards forest must have an overwood which consists of t X r — R age grada- tions 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, has ^- = 5 overwood classes. On the 10 acres which are about to be cut will be found — Underwood = 20 years old. Overwood = 20, 40, 60, 80 and 100 years old. 204 Fig. 48. — Coppice with Standards. One_Coupe. Rotation of underwood = 20 years. Rotation of overwood Coppice just cut. 100 years. i i Fig. 49. — Coppice with Standards. One Coupe. Rotation of underwood = 20 years. Rotation of overwood = 100 years. Age of coppice, 10 years. Fig. 50. — Coppice with Standards. One Coupe. Rotation of underwood = 20 years. Rotation of overwood Age of coppice 20 years 100 yi SIZE OF THE AGE CLASSES. 205 The next oldest coupe contains — Underwood =19 years old Overwood = 19, 39, 59, 79 and 99 years old. The youngest coupe contains — Underwood = 1 year old Overwood = 1, 21, 41, 61 and 81 years old. DISTRIBUTION OF THE OVERWOOD IF COPPICE WITH STANDARDS. TWENTY COUPES. SO FEET- COUPES— 1 2 3 4 5 6 7 8 9 101112 13141516171819 20 Fig. 51. — (Conventional.) The figures 48, 49, 50, and 51 illustrate the distribution of the several age gradations over the area. 206 THE NORMAL AGE CLASSES. The area occupied by each overwood class can be determined only by assuming that each gradation occupies an equal extent of ground ; hence, the youngest gradation will have most trees and the oldest least. Imagining now that the age classes of the over- wood were not intermixed, but that the trees of each class were brought together on separate areas, then the overwood, apart from the coppice, would form an open high forest. Of these woods, the youngest would contain the standards from 1 to r years, the next those from r + 1 to 2 r years, and so on. 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. The annual coupe is c = — and A = c X r. n The number of overwood classes is = — = L hence — r R = tX r. Area of each age class on each annual coupe = ~ = = -, 1 R t x r t = 2 acres. or, 200 200 10 100 5 x 20 5 As the whole forest consists of r coupes, each overwood class, consisting of r gradations, contains, in a normal forest, c A 200 - X r = — units of area, or -=- = 40 acres. This shows that, t t o theoretically, the proportion of the age classes is the same as in high forest, although the distribution is different. Example. — Data as before. A — 200 ; R = 100 ; r = 20, number of ovenvood classes t — 5. A 200 Normal annual cutting area c = — = -^p- =10 acres. r 20 On each coupe each age gradation! c 10 , j . }-=-—— 2 acres, of overwood occupies . .it 5 SIZE OF THE AGE CLASSES. 207 The area and distribution of the several age classes are as follows : — Coupe Xo. 20, oldest : Underwood =10 acres = 20 years old. Overwood on 2 „ 2 „ 2 „ 2 2 = 20 = 40 = 60 = 80 = 100 Coupe No. 1, youngest : Underwood =10 acres = 1 year old. Overwood on 2 ,, = 1 „ „ „ „ 2 „ = 21 years „ „ 2 „ =41 „ „ „ 2 „ =61 „ „ „ 2 „ =81 „ „ The normal state of the age classes in the case of coppice with standards is of a still more ideal character than in the case of the shelterwood compartment system ; it can only serve as a mathematical guide for the treatment of such woods, as it gives some idea of the relative number of trees which should be found in each class or gradation. Each of these should occupy about the same area ; hence, the youngest class must contain a large number of trees, which is gradually reduced to a comparatively small number in the oldest age class. The actual proportion in these numbers depends on the species, the quality of the locality and the objects of the proprietor. e. The Selection Forest. If the annual cuttings extend over the whole area, then all age classes are, theoretically speaking, represented in all parts of the forest ; if, on the other hand, the cuttings pass over the forest in the course of a number of years, say I, then the age classes will, to some extent, gradually become located similarly to the distribution of the overwood in a coppice with standards forest. The number of age classes will, theoretically, be equal to -.. I 208 THE NORMAL AGE CLASSES. Example. — Let A — 1,000 acres ; r = 100 ; I = 20 ; then each annual A 1,000 ltting area =-j= -^f : approximately be as follows cutting area = -=- = ^— = 50 acres, and the distribution would Coupe No. 1 {youngest). 1 year old trees =10 acres ~* >> ?> >> == 1U >! 41 „ „ „ = 10 „ 61 „ „ „ = 10 „ 81 „ „ „ = 10 „ Coupe No. 2. 2 year old trees =10 acres 22 42 62 82 = 10 = 10 = 10 = 10 Total = 50 acres Coupe. No. 1! . 19 y ears old trees = 10 acres 39 ?> ?? ?j = 10 ,, 59 J9 ?> JJ = 10 ,, 79 ?5 >9 ?J = 10 ?> 99 M J? JJ = 10 ?» Total = 50 acres Total = 50 acres Coupe No. 20 (oldest). 20 years old trees = 10 acres 40 „ JJ ss = 10 „ 60 „ ?) 5? = 10 „ 80 „ ?5 S9 = 10 „ 100 „ ?j »^ = io „ Total = 50 acres Each year the 100 years old trees in the oldest coupe would be cut, and they should cover an area equal to one-fifth of the coupe, equal to 10 acres, thus cutting the whole area of the forest once in 100 years. It is needless to add that such regularity is never reached in practical forest management. Regeneration of the cut spots may occur in the following year, but, as a rule, it occurs gradually, extending over several years, unless planting or artificial sowing is done. Details of the management of selection forests will be found in Part IV. 3. Distribution of the Age Classes over the Forest. By a normal distribution of the age classes is understood that which admits of a proper succession of cuttings, so that each wood is cut at the proper age, and that the other woods are protected against external dangers, in so far as this can be done by careful management. It has already been explained that every deviation from the normal age interferes with the full realisation of the objects of management ; hence, the age classes should be so distributed that no such deviations are called for. Of special importance, in DISTRIBUTION OVER THE FOREST. 209 this respect are threatening dangers, such as damage by strong winds, dry air currents, drought, danger from frost, fire, insects, etc., and, in some cases, considerations for a successful regenera- tion. Strong winds or gales are a most important consideration. Their prevailing direction must be ascertained, and cuttings should generally proceed against it. Assuming that the strong winds 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 AGE AGE B. Arranged in five Cutting Series. Fig. 52. — A Normal Series of Age Gradations, treated under the Clear Cutting System. diagram, Fig. 52, upper part.) In this case, the younger age classes gradually break the force of the wind, while the youngest (in the diagram) will grow up exposed to the strong wind ; its edge trees will develop strong root systems, and the wood will then be able to resist the force of the wind when it grows up to become the oldest age gradation. Nevertheless, shelter belts may be required in addition. 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. In cases where clear cutting, followed by artificial regeneration, is practised, protection of the cleared areas against the sun is frequently essential. As a consequence, the direction of cutting 210 THE NORMAL AGE CLASSES. may have to be changed into north to south. The breadth of the cleared area should not exceed the height of the adjoining old wood, but it may be of any length. To increase the effect of the old wood, the edge is sometimes given a zig-zag shape, a subject dealt with in Part IV. Dry winds 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 deter- mine 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, as, for instance, under the strip system with regeneration by seed fallen from trees standing on the adjoining area. Drought is a formidable enemy to successful forest manage- ment in all cases where the amount or distribution of the rainfall over the seasons of the year is unfavourable. In some countries droughts occur practically every year, especially in spring and early summer. In such cases the forester must strive to reduce their effect by avoiding large clearances in one place, or, better still, by effecting regeneration under shelterwoods. This matter is of paramount importance in the choice of the system of manage- ment. Large clearings in one place are generally objectionable, because the soil is liable to dry up, and damage by frost is likely to occur ; hence, in extensive forests the area to be cut annually may have to be divided into a number of small coupes situated in different parts of the forest. Insects and fire are likely to be most injurious when several cuttings made in consecutive years adjoin each other, because the former wander from one coupe to the next, while fire spreads more rapidly in continuous young woods than if they are interrupted by older woods. These circumstances demand in many cases, and especially where clear cutting is practised in coniferous woods, that a second cutting should not be made in any locality until the former coupe has been successfully restocked. 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 DISTRIBUTION OVER THE FOREST. 211 worked under a rotation of 100 years, it was considered necessary not to cut in the locality adjoining a previous cutting except after a lapse of five years, the series of 100 age gradations would be divided into five cutting series, of which each would comprise 20 coupes. (See Fig. 52, lower part.) Cutting Series A would comprise the coupes now 100, 95 . . 10, 5, years old. „ B „ „ „ „ 99, 94 . . 9, 4, „ „ ,, ,, L/ ,, ,, ,, ,, Jo, Jo . . o, 6, ,, ,, „ D „ „ „ „ 97, 92 . . 7, 2, „ „ „ E „ „ „ „ 96, 91 . . 6, 1, „ „ As a general rule, a careful distribution of the age classes over the area of the forest is of special importance in the case of species which are easily thrown by wind, liable to attacks by insects, to danger from fire or frost, and also those which are difficult to regenerate naturally. In all these cases, a distribution must be aimed at which allows the cutting of each wood when mature, VIEW OF A FOREST DIVIDED INTO CUTTING SERIES WORKED UNDER THE STRIP SYSTEM. (ONE SERIES MARKED.) / / / "^'^tik 8m -y*!a 0jfk ■Fii m ; - ' : 'f ^H WsBbs \ ¥'■■-. '":. ■'• ';?, v ;.-'• ffi - " $& f^Tu- PREVAILING WIND DIRECTION. > Fig. 53. CUTTING DIRECTION. < without thereby endangering on the one hand the adjoining woods and on the other the successful regeneration of the cleared area. The above considerations must specially guide the forester in the case of forests worked under the systems of clear cutting, and also of the shelterwood compartment system. They are of less importance in coppice, coppice with standards, and selection 212 THE NOEMAL AGE CLASSES. 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.) Production of a larger percentage of high-class timber. (4.) Reduction of the cost of transport of forest produce. Reasons for the establishment of cutting series are :— (1.) Reduction of danger through fire and insects. (2.) Better protection of young woods against raw or dry winds, frost, and diseases. (3.) Greater freedom in selecting the areas to be cut over at any time. To illustrate this point, Fig. 53 is added, which shows a bird's-eye view of a large number of cutting series. 213 CHAPTER IV. THE NORMAL GROWING STOCK. It has been stated at page 170 that by the normal growing stock is understood that present in a forest which has a normal series of age gradations or classes and a normal increment. This being so, the forester need only see that the age classes and increment are normal, and the normal growing stock will be present as a natural consequence. It happens, however, that, as far as volume is concerned, the normal growing stock may be present if neither the normal age classes nor 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 prob- ably 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 final cuttings would have to be suspended for a considerable number of years. In these circumstances, the normal growing stock measured by a certain number of cubic feet 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. (2.) Because several methods of treatment base the calculation of the yield upon the difference between the normal and real growing stock. The amount of the normal growing stock depends on the length 214 THE NORMAL GROWING STOCK. of the rotation ; the higher the latter, the greater is the former for one and the same area and quality class. In calculating the normal growing stock, only the principal part of the woods, which gives the final yield, is taken into account, because, as previously explained, the determination of a sustained yield is, in the first place, based upon the final yield. The normal growing stock can be looked at from the volumetric or the financial point of view. SECTION I. —CALCULATION OF THE VOLUME OF THE NORMAL GROWING STOCK. 1. Clear Cutting in High Forest. It has already been explained on page 147 that, under the system of clear cutting and a sustained yield, the normal growing stock consists of a series of age gradations ranging from years to r — 1 years old, with a difference of one year between the ages of every two succeeding age gradations ; this occurs in a temperate climate in spring, before the annual increment has been laid on. a. Calculation from Yield Tables. If a yield table is available for a forest which gives the produce standing in it from year to year, the normal growing stock is equal to the sum of the major part of all the growing stocks given in that table from the year to the year r — 1 ; that sum would represent the normal growing stock in spring of r units of area. If the yield table, and this is generally the case, gives the volumes only from period to period, say for every n years, then the approximate amount of the normal growing stock can be calculated by assuming that the volumes rise within each period of n years according to an arithmetical series — that is to say, by adding the same number of cubic feet each year. Let the rotation be r, the interval between every two positions in the yield table n, and the volumes for these positions in the Years o n 2n 3n r — n r Volumes V V n V 2n V 3 „ . . V r - n V r , then : CLEAR CUTTING IN HIGH FOREST. 215 Volume of gradation to n = (V + V„) X ^J— w to 2n = (V n + 7 2M ) X ^i- Volume of gradation 2w to 3ra = ( F 2n + 7 3 „) x n ^ 1 f — w to r = (F r _„ + V r ) x — ^— . The sum of these amounts comes to : — -+-- (y + 2V n + 2F 2 „ + 2V 3n + . . . + 2F,_ „ + V r ) = (« + l) (F. + F 2/l + F 3B + •-.; + Y r -n + . It should be noted that V n , 7 2 „, F 3 „, ... F r _ » have been twice introduced in the above calculation ; these values must be deducted to make the calculation correct, leaving the true value at : — Normal growing stock = In + lj I V n + V 2>1 + V 3>1 -f . . . -f Yr-n + £) - (F. + 7 2>i + F 3n + . . . F r _ B ), which, after reduction, gives : — Normal growing stock = n X f F w + F 2n + T 7 3 „ + . . . + "r — n ~T~ 7T ) i" 2"- This is the value for autumn. To obtain the value for spring, the volume of the oldest age gradation V r must be deducted, giving— Normal growing stock for spring = n ( V n + V 2>1 -f F 3 „ + . . . + F,-. + J)-£ 216 THE NORMAL GROWING STOCK. The average of the two values gives the growing stock for the middle of the growing season, say midsummer : — Normal growing stock for summer = n ( V n + V 2 „ + V 3n — . . . + 7,-. + %). Example. — Given an area of 80 acres worked under a rotation of 80 years for larch to which the yield table for larch III. quality applies, the normal growing stock would amount to : — Spring 60 G nO rmal = 10 (150 + 560 + 1,460 + 2,290 4- 2,910 + 3,440 + 3,910+ 2,150)- 2,150 = 10 x 16,870 - 2,150 = 166,550 cubic feet, Autumn S0 G n ormal = 10 X 16,870 + 2,150 = 170,850 „ Summer 80 G n ormal = 10 x 16,870 = 168,700 „ As the differences between the three amounts are small, foresters are in the habit of using the somewhat shorter formula for summer. Assuming that the 80 acres were worked under a rotation of 60 years, 60 G n = 10 (150 + 560 + 1,460 -f- 2,290 + 2,910 + 1,720) - 1,720 = 89,180. This is the G n for 60 acres. As the total area is 80 acres, the 80 G n for 80 acres is obtained by multiplying 89, 190 by g- = 118,907 cubic feet. Hence, if the forest, hitherto worked under a rotation of 80 years, is in future to be worked under one of 60 years, the normal G n would have to be reduced by 166,550 — 118,907 = 47,643 cubic feet. That amount can be taken out of the forest in addition to the annual increm?nt ; in the reverse case 47,653 cubic feet would have to accumulate in the forest to bring up the 80 G n to its proper amount. b. Calculation with the Mean Annual Increment. A shorter, but less accurate, method of calculating the normal growing stock is based upon the assumption that the normal final yield is produced in annually equal instalments throughout the rotation ; in other words, that the growing stock of the several age gradations forms an arithmetical series. If one year's incre- ment is equal to i, the growing stock of succeeding age gradations would be : — Year . .=12 3 ... r— 1 r Growing stock . = i, i X 2, i X 3, . . . (r — 1) X i, r X i T T % T and G n = {i -f r i) X ^ = y + r i X -^. THE SHELTERWOOD COMPARTMENT SYSTEM. 217 As r X i represents the growing stock of the oldest age grada- tion, and is also equal to the total increment, /, laid on by all gradations during one year, the above formula may be written thus : — Ixr , /' Ixr I a Ixr G„, autumn = —^- -\-^) Spnng= — ^ g ; Summer= ~Y~ ■ The growing stock calculated by this formula (for spring) is larger than that calculated from yield tables for short, and smaller for long rotations, as the following table will show : — ■ Normal Crowing Stock (Spring) of Scots Pine I. Quality. Rotation. From Yield Tables. From Mean Increment. Excess from M.I. 30 40 50 60 70 80 90 100 18,780 43,440 79,050 123,380 174,480 231,040 28,130 60,790 100,450 142,780 187,680 233,840 + 9,350 + 17,350 + 21,400 + 19,400 + 13,200 + 2,800 292,175 357,340 282,575 332,640 - 9,600 — 24,700 2. The Shelterwood Compartment, or Uniform, System. The normal growing stock, is theoretically, the same as for the clear cutting system, provided that the regeneration cuttings are so arranged that one-half are made before the year r and the other half after it, that the timber in the regeneration class is removed in annually equal quantities, and that regeneration takes place in the middle of the regeneration period. In reality, this occurs only rarely, but the deviations compensate each other in the long run. Another point is that the forester has, in the majority of cases, to deal with two or more quality classes. In such cases, he must deal with each quality class separately, or proceed with a com- bined system somewhat on the lines of the following example :— Example. — Let there be 100 acres stocked with Scots pine, of which 40 acres are I. class quality and 60 acres II. class. The wood is divided into five age classes of 20 acres each, but parts of the two quality classes 218 THE NORMAL GROWING STOCK. are found in each age class. Utilizing the data for Scots pine I. and II. quality (page 126) the calculation would be as follows : — ■ Class. I. II. III. IV. V. Mean Age. 10 30 50 70 90 I. Quality Class. Volume Area. per , Acre. 40 200 40 1,940 40 4,100 40 5,440 40 6,350 Total. 8,000 77,600 164,000 217,600 254,600 II. Quality Class. 60 60 60 60 60 Volume per Acre. 100 1,300 3,450 4,880 5,880 Total. 6,000 78,000 207,000 292,800 352,800 Grand Total. 1 4,000 5 155,600 5 371,000 5 510, 400 5 607,400 = 2,800 = 31,120 = 74,200 = 102,080 = 121,480 331,680 Total normal growing stock = 331,680 cubic feet. Average per acre = 3,317 „ 3. Coppice and Coppice with Standards. The calculation for simple coppice is the same as that for clear cutting in high forest. For coppice with standards forest, the calculation must be made separately for underwood and standards, and the results added. The amount of the former depends chiefly on the number of standards per acre. If the latter are numerous, the normal grow- ing stock of the coppice is frequently so small that it can be neglected. The calculation of the normal growing stock of the overwood is a complicated and uncertain operation, and chiefly of theoretical value, as it gives an idea of the proportions which ought to exist between the several age classes. The method of calculation may proceed on the following lines : In accordance with the objects of the proprietor, the normal number of standards in each of the r, 2 r, 3 r . . . old age classes, and the volumes of the average standards in each of the classes are ascertained. Assuming that the trees increase in volume in each class according to an arithmetical series, it is possible to interpolate the volume of the trees r + 1, 2r T l, . . . years old. Omitting the future standards which THE SELECTION FOREST. 219 as yet form part of the coppice, the normal volume of the first age class above the age of r would be^ \V H 0l + V 2r J, the next class - (V 2r + 1 + V& ) and so on, and the normal growing stock Gn = \ (V f + i + V, f + V 2r + i + V«r + . • • + V nr ) . Example. — Area of a coppice with standards wood = 20 acres. Rotation of coppice = 20 years ; of overwood = 100 years. Number of overwood classes = — = 5. Area of each coupe = 1 acre. Number of Stan- Mean Volume per Total Volume of Age of Gradations. dards in Gradation. Tree, Cubic Feet. Gradation. 21 40 1 40 40 40 5 200 41 26 5-5 143 60 26 15 390 61 16 15-75 252 80 16 30 480 81 8 31 248 100 8 50 400 G„ = Uo + 200 + 143 + 390 4- 252 + 480 + 248 + 40o) X g- G n = 2153 X 10 = 21,530. Average per acre = 1,076 cubic feet. The above volume should be present immediately before the annual cutting is made. From it should be deducted the volume annually removed, which consists of the following quantities : — Annual Yield : 14 trees 40 years old, each 5 cubic feet = 70 cubic feet. 10 „ 60 " „ „ „ 15 „ „ = 150 „ „ 8 „ 80 „ „ „ 30 „ „ = 240 „ „ 8 „ 100 „ „ „ 50 „ „ = 400 „ „ Total annual yield = 860 cubic feet. Hence, normal annual growing stock before cutting = 20,670 cubic feet. It may be added that the annual increment in this case is : Annual increment I = 40 x 5 -f 26 X 10 + 16 X 15 + 8 X 20 = 860 cubic feet, which is equal to the annual yield. 4. The Selection Forest. As all age gradations are represented in all parts of the forest, it is difficult to give a precise expression of the normal growing stock. Theoretically speaking, in a normal selection forest all age 220 THE NORMAL GROWING STOCK. gradations should be represented in the same proportion as in the system of clear cutting in high forest ; hence the volume should be the same in both cases. In practice, however, this is rarely, if ever, the case. As a general rule, the older age classes occupy more area than the younger ones. In these circumstances, all that can be said is that the age gradations should be represented in such manner and proportion that the returns meet the objects of the proprietor, Avhether he aims at the production of trees of certain sizes or at other classes of produce. In Part IV., when dealing with the determination of the yield of selection forests, the subject will be further explained. SECTION II.— THE FINANCIAL ASPECT OF THE NORMAL GROWING STOCK. The method of calculating the financial value of the normal growing stock is dealt with in Forest Valuation. Here it suffices to state that it is equal to the capitalised annual net receipts, minus the value of the soil, as represented by the formula : — yonn„, Gn = Y r + T a + T b +... + T q -{ c + rxe) _ f x ^ where p represents the mean annual forest per cent. It depends on the value of S introduced whether the formula represents the cost or expectation value of the growing stock. 221 CHAPTER V. THE NORMAL YIELD. By the normal yield is understood that which a normal forest can permanently give. It can be determined for one year or for a number of years ; in the latter case it is called the " periodic yield." The normal yield consists of the final and intermediate (thin- nings) returns. The yield of wood is generally subdivided into various classes, such as timber, cord-wood, faggots, root-wood, etc. In order to bring them into the account, all the different classes are reduced to one common standard, that is " the solid cubic foot." The yield can be determined by area, by volume, or by its financial value. How this is done will be shown in Part IV. of this book. Here only a few remarks as regards the normal yield will be recorded. 1. Determination by Area and Volume. a. Clear Cutting in High Forest. The normal final yield is equal to the volume which stands on the oldest age gradation of a normal series of gradations. The A A normal annual cutting area is = — or = — . — , according as to ° r r -f- s whether the cleared area is at once restocked or allowed to lie fallow for s years. The volume standing on this area will give the normal final annual yield, provided the stocking is normal. The A A periodic normal coupe for n years is = — X n, or = —q_~ s x n - In either case, the thinnings have to be added. Example. — A Scots pine forest of first-class quality has an area of 100 acres, and is managed under a rotation of 100 years ; hence, the normal annual cutting area will be equal to 1 acre ; it will be restocked as soon as 222 THE NORMAL YIELD. cleared. According to the yield table on page 126, the annual yield will consist of : — (1.) The final yield, being the stand on the 100 years old gradation 6,930 cubic feet. (2.) The yield of thinnings from the years 20 to 90 = 2,765 Total normal yield = 9,695 cubic feet. Mean annual yield per acre = 97 cubic feet. The normal yield differs largely according to the quality of the locality and species, as the following data will show : for a rotation of 80 years in all cases, in cubic feet per acre : — Quality Classes. I. II. 96 146 86 III. IV. 61 92 v. 44 72 61 31 39 ( Larch in Britain Clear cutting - Spruce in Britain [Scots pine in Scotland . . ,-,. ., , f Silver fir in Germany Shelterwood J Beech in Germany system |^ ak in Germany 115 175 101 170 116 109 77 117 67 106 68 72 The normal annual yield must be equal to the total annual increment. To cut less than that amount leads to a higher rota- tion, and vice versa. It will also lead to a reduced yield, if the rotation is fixed at an age beyond that at which the mean annual increment culminates. b. The Shelterwood Compartment, or Uniform, System. The calculation of the normal yield is the same as in the case of the clear cutting system, provided that the rotation r is main- tained ; in other words, that cuttings are commenced in the year years and an equal volume is removed annually during the in regeneration period of m years. c. The Selection Forest. The determination of the yield of selection forests will be dealt with in Part IV. That of the normal yield is only of theoretical interest. If all trees which are cut in one year were brought together on a portion of the area, the latter would be equal to — , DETERMINATION BY AREA AND VOLUME. 223 so that the normal yield should be equal to that of the clear cutting or uniform systems. Such regularity is, however, never reached in the selection forest, nor in many cases desired. The case may be considered from a different point of view : As only a part of a selection forest is dealt with in each year, say = y , the normal cuttings may be described as the following :— (1.) All trees in that area which have reached the age of the rotation (or rather the size corresponding to that age), including trees removed for silvicultural or other reasons. (2.) Thinning in the other age classes of the cutting area. (3.) Thinnings, if necessary, in the part of the forest outside the area -j . The total of these cuttings might be called the normal yield. To carry out these operations correctly is one of the most arduous duties of the forester, whenever a sustained yield is the object of the proprietor. The only secure way of determining the incre- ment, and consequently the current yield, is to make periodic measurements of the growing stock, as explained in Part IV. d. Coppice and Coppice with Standards. The normal yield of simple coppice is calculated in the same way as that for high forest clear cutting. It consists of the cutting of the oldest age gradation and any thinnings which may be neces- sary in the younger age gradations. In coppice with standards the annual cutting area is the same as in simple coppice. The normal annual yield consists of : — (1.) The underwood on the oldest age gradation, less those stems 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 age gradations on the rest of the area. (4.) Necessary cleanings or thinnings in the underwood on the younger age gradations. 224 RELATION BETWEEN YIELD AND GROWING STOCK. 2. The Financial Value of the Normal Yield. Having calculated the value of the normal growing stock, as indicated on page 148, the financial normal yield is obtained by multiplying that amount by 0-0p, where p represents the mean annual forest per cent. CHAPTEE VI. RELATIONS BETWEEN GROWING STOCK, INCRE- MENT AND YIELD OF A NORMAL FOREST. Relations exist between these three quantities which are of great importance in determining the yield. In order to bring these out clearly, the system of clear cutting in high forest will be used as an illustration. a. Allotment of Increment during One Rotation. It is assumed that a normal series of age gradations contains at the commencement of the rotation the normal growing stock. Dealing, in the first place, with the final yield only, it is clear that every year the oldest age gradation gives the normal final yield, and this is replaced, during the following growing season, by the laying on of the normal increment. The latter is added partly to the old growing stock and removed with it in the course of the first rotation ; while the balance of the annual increment accumu- lates on the cleared areas, and forms a new growing stock which is carried over into the second rotation. The question then arises, how much of the total increment of one rotation is added to the old and new growing stocks respectively ? Making the calculation for spring, the youngest age gradation is at the commencement of the rotation years old, and the oldest r — 1 years. The oldest of these gradations will be cut over after one year, when one year's increment has been added to it, while the increment laid on by this gradation during the remaining r — 1 years will be carried over into the second rotation. The gradation r — 2 years old at the commencement of the rotation will add two years increment by the time it is cut over, and r — 2 years incre- ment is carried over into the second rotation, and so on down to ALLOTMENT OF INCREMENT. 225 the gradation years old at the commencement of the first rota- tion. Calling i the mean annual increment of one gradation in one year, and r X i = I the increment of r gradations in one year, the following division of the increment between the old and new growing stocks is obtained : — Age of Gradation at the Commencement of the First Rotation. Allotment of Increment to the Old Growing Stock. Allotment of Increment to the New Growing Stock. r — 1 r -2 r -3 i 1 X i 2 X i 3xt / -t / / -i I — 2 X * /-3xt i Totals Or (*' + /) x \ Making the division for the autumn, the values are as follows :- t I ■ T I Amount of increment / X ~ — ~ 9 I X ^ + 9 And for the middle of the growing season : — Amount of increment / X „ Ix I. Hence, the total final yield during the first rotation, calculated for the middle of the growing season, amounts to : — Total final yield = the original growing stock plus the accumu- lated increment = 2 X normal G n . To this amount, the yield from the thinnings has to be added. This comes to the same amount year after year, as will be seen from the following example : — Example. — Taking the yield table for larch I. quality, the yield of 80 acres under a rotation of 80 years would, for the middle of the growing season, be : — Final yield = 6,070 X 80 = 485,600 Thinnings = 3,090 X 80 = 247,200 Total yield in 80 years Average annual yield, 80 acres „ „ „ per acre 732,800 cubic feet, 9,160 „ „ 114 „ „ 226 RELATION BETWEEN YIELD AND GROWING STOCK. b. Relation between the Normal Yield and the Normal Growing Stock. If the normal yield, Y„, is divided by the normal growing stock G n , and the quotient multiplied by 100, the " Utilization per Cent." is obtained : — p v = ^- X 100. It gives the units of yield for every 100 units of growing stock, which, in a normal working section, is equal to the normal incre- ment per cent. The utilization per cent, decreases with the increase of the rotation, as the increment per cent, decreases. Example. — Taking the data for larch I. quality (page 124) we have : — G n = 10 (300 + 1,560 + 2,900 + 3,880 + 4,570 + 5,130 + 5,630 -f- 3,035) G n = 10 X 27,005 = 270,050. The yield is as follows :— Final yield = 6,070 + intermittent yield = 3,090 ; total yield = 9,160. (\ 070 Hence, utilization per cent, of final yield = '„ „_» X 100 = 2-25 per cent. Utilization per cent, of final + inter- q iao mediate yield = 2 -^^ x 100 = 3-39 „ „ The rate of utilization is used in Hundeshagen's method of determining the yield of forests, as explained in Part IV. 227 PART IV. THE PREPARATION OF FOREST WORKING PLANS. and v «i ^/i + «2 2/2 + a 3 ?/3 + • • • total annual yield a ± -\- a 2 -\- a 3 -\- . . . total area Example : — A working section of 100 acres contains — Block (1) 20 acres with 60 cubic feet average increment, „ (2)10 „ „ 50 „ „ (3)20 „ „ 40 „ „ (4) 50 „ „ 30 „ „ „ then- Mean quality „ 20 x 60 + 10 x 50 + 20 X 40 + 50 X 30 .. , . , , Y = — YTin " = cubic feet. By reduced or modified area is understood that which would produce, with a uniform quality = Y, the same yield as the actually existing areas with their own qualities. The reduced area of each block is obtained by applying, in each case, the inverse proportion of that which exists between the actual and the mean quality : — Y : y = a : a' and reduced area a' = — y^-. In the above example — Block (1) The proportion is 60 : 40 ; hence the reduced area is obtained by means of the equation — 20 x 60 = 30 acres. 10 X 50 ; 12 . 5 2 ~ 40 20 x 40 3 ~ 40 50 X 30 40 = 20 = 37-5 Total = 100 acres. These figures show the proportion in which each block participates in the production of the total yield. REDUCTION TO ONE QUALITY. 247 If now the forest is to be divided into annual coupes of equal yield capacity, the area to be placed in each is also obtained by calculating with the inverse proportion of the qualities. Example. — The above forest shall be divided into ten coupes of equal yield capacity ; then the reduced area of each coupe is 100 10 = 10 acres. The real area of a coupe in each block is calculated as follows : — 40 v 10 Block (1) 60 : 40 = 10 : x, and x x = u * iU = 6-667 acres. „ (2) 50 : 40 = 10 : x 2 „ x 2 = ^^^ = 8-000 „ „ (3)40:40=10:^ „ x 3 =^L™= 10-000 „ „ (4) 30 : 40 = 10 : * 4 „ * 4 = 40 * 10 x 13-333 or, 30 Coupe No >? 99 1 2 = 6-667 acres = 6-667 .. | Taken from block >> >> 3 = 6-666 ?j J No. 1. >» >» 4 = 8-000 5> From block No. 2. » » 5 = 2-0 + 7-5 = 9-500 >> /Partly from No. 2 ( and partly No. 3. »» »» 6 = 10000 5» From block No. 3. >» >> 7 = 2-5 + 10 = 12-5 9f (Partly from No. 3 ^ and partly No. 4. >> >» 8 = 13-333 if 1 J» » 9 = 13-333 M VFrom block No. 4. >> >» 10 = 13-334 >» / Total = 100 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. It may be greater, equal, or smaller than the actual area, according to the size of the standard quality : — Reduced A = '■ X ». + «.*». + «.** + •• - . 248 COLLECTION OF STATISTICS. The reduced areas of the several parts are obtained by the inverse proportion of their qualities to the standard quality ; thus : — Reduced a' x = 1 y, , Reduced a\ = 2 y, , etc. Example, as above. — Let the standard quality = 50 cubic feet, then total reduced area = 20 X 60 + 10 X 50 + 20 X 40 + 50 X 30 = g() acreg 50 and the reduced area of : — _,. . ... 20 x 60 „. Block (1) — =g — = 24 acres. f2 , 10X50 " (2 > ^50 " ._. 20x40 " ( ' — 50 — = " ... 50 X 30 " (4) -50- = 3 ° " Total = 80 acres. 80 Reduced area of annual coupe = ^ = 8 acres, and the size of coupes in the several blocks : — (l)*i=-ft J = 6-667 (2)* 2 =^- 8= 8 -° 00 50 ) X 40 ) X 30 (3)^3=^^=10-000 (4)^=^^=13-333; as before. It is obvious that the last-mentioned method is the more con- venient of the two. 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 NOTES REGARDING FUTURE TREATMENT. 249 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 manage- ment 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 circumstances ; 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 prunings during the working plan period ; 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 current forest per cent, should be calculated. If it appears advisable that final cuttings should be made, the method of cutting should be given, as well as an estimate of the volume to be removed. (d.) Method of regeneration to be followed and the species to be grown, if this should occur during the working-plan period. (e.) Measures to be taken for the protection of the wood against threatening dangers, especially fire. (/.) Other works to be undertaken, such as construction of roads, draining, irrigation, etc. (g.) Utilization of enclosures and improvement of boundaries where necessary and practicable. (h.) Proposals regarding the formation of sub-compartments, or the abolishment of those which exist, with reasons for such proposals. SECTION III.— PAST YIELDS, RECEIPTS, AND EXPENSES. There is no surer basis in estimating future returns than those of the past ; hence, it is of importance to ascertain and note down the yield in material, the cash receipts, and costs for as many years as the available data admit. These data will, however, only be forthcoming if records have been kept for some time past. 250 COLLECTION OF STATISTICS. As far as may be practicable, past yields, receipts and costs should be given for each unit of working — that is to say, each wood or compartment. If the records have not been kept in sufficient detail, the data for each working section should be given ; the latter may also be sufficient where the management is as yet in a backward condition, or where the receipts are small. The following notes indicate the class of information which may be required : — 1. Yield of Wood, or Major Produce. The yield should be given separately — (a.) For the principal species. (b.) For the different classes of timber and firewood, according to size or value, (c.) For final and intermediate returns separately. (d.) The total cash receipts and the average price of the several classes of material, separated according to species. The areas over which cuttings extended should, if possible, also be given, separately for final and intermediate cuttings. 2. Minor Produce. Under this heading, the quantity of each article of minor produce which has been removed, and the cash receipts obtained for it should be given. Receipts derived from areas not used for the production of wood, such as fields, meadows, etc., should be separately recorded. 3. Expenses. These should be recorded separately for — (a.) Cost of administration and protection. (6.) Taxes, rates, etc. (c.) Formation of woods. (d.) Tending and amelioration. (e.) Maintenance of boundaries. (/.) Construction of roads, other means of transport, drainage, irrigation, and other works. (g.) Cost of harvesting, separated according to major and minor produce. GENEEAL CONDITIONS. 251 4. Generally. For forests worked on financial lines, the receipts and expenses should be so arranged that it is possible to ascertain — (a.) The capital value of the forest, being the sum of the value of the soil plus value of the growing stock. (6.) The forest rental, being the difference between all receipts and expenses, (c.) The current forest per cent, of each wood whenever desirable. (d.) The mean annual forest per cent, (see Part II., Forest Valuation). 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 ascertained at this early stage, and they should be used for a general description of the forest to be incorporated into the working-plan report. The field of inquiry here indicated is of considerable extent ; the following matters may be mentioned : — (1.) Name and situation of forest, giving the latitude and longitude where necessary. (2.) Description of boundaries and names of the adjoining properties and their owners. (3.) Topographical features of the locality. (4.) General description of the geology, soil and climate. (5.) Former and present proprietors ; financial position of the latter, whether the funds for formation, tending, adminis- tration, amelioration, etc., are available ; whether specially heavy cuttings must be made to meet the demands of the proprietor. (6.) Nature of proprietorship ; whether full and unfettered property, or whether servitudes and privileges rest on it ; in the latter case their extent should be recorded. (7.) Eights enjoyed by the proprietor of the forest elsewhere, such as rights of way or floating, or rights over other lands, etc. (8.) Requirements of the surrounding population, and condition 252 COLLECTION OF STATISTICS. of the market for forest produce generally ; special indus- tries in the vicinity which require forest produce, such as mines, smelting works, saw mills ; imports which compete with the local supply ; substitutes 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, drought, fire, insects, fungi, etc. (13.) Conditions of game and cattle grazing ; their effect upon the forest. (14.) Past seed years of the more important species. (15.) Opportunities for consolidating the property, either by exchange or purchase ; conversion of fields, meadows, etc., into forest, or the reverse. (16.) The staff of the forest, its organisation and efficiency. SECTION V.— THE STATISTICAL REPORT. 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 some instances, it will be necessary to go into minute details ; in others, a more summary treatment is indicated. The following documents will ordinarily form part of the report : — 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. THE STATISTICAL REPORT. 253 (d.) The nature of the boundary line, whether a road, water- course, water-parting, 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. 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 : — Locality. Grand Total. In Acres. Area used for the Produc- tion of Wood. In Acres. Area not used for the Production of Wood. In Acres. Working Section or Block. Com- part- ment. Sub- com- part- ment. Roads and Rides. Fields. Meadows. Water, etc. Total. Caesar's Camp. 1 a Etc. 29-2 26 •4 2-2 •6 3-2 3. Description of Compartments. This description may be drawn up in a tabular form or other- wise ; the former is preferable, as it presents a more intelligible picture of the forest, and gives greater security that nothing has been overlooked. It is quite impossible to recommend any particular form for this table, but by way of illustration the appended form is given. (See pages 254-5.) In this table, the quality of locality indicates that which corre- sponds 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, where- with to calculate the forest per cent. 254 COLLECTION OF STATISTICS. Description of Locality. Working Section. Caesar's Camp Com- part- ment. Sub- com- part - ment. Area, in Acres. Stocked 24 Blank. 26 Boundaries. North & East : Sir A.Hayter's land. South : Com- partments 13 and 12. West : Roman road. Locality. Elevation : 420 feet above sea-level, slop- ing towards the east with moderate gra- dient, down to 380 feet. Geological Forma- tion: Middle Bagshot sands. Soil : Loamy sand, fairly good in upper part of compartment, and good in lower part ; no pan to 4 feet depth. 4. Table of Qualities of Locality. Locality. Quality Classes of Locality. Area in Acres. Total Area. Silvicultural System and Working Com- part- ment. com- Acres. Species. Section. part- I. II. III. ment. Best. Middling. Lowest. Caesar's High forest Camp 1 a 26 26 of Scots pine 1 b 14 ii with some 2 38 32 6 broad-leaved 3 17 17 trees here 4 31 16 15 and there. 5 33 i2 17 4 6 31 25 6 7 27 7 20 Etc. Total 217 36 116 65 DESCRIPTION OF COMPARTMENTS. 255 Compartments. Growing Stock. Sllvicul- tural System. High Forest Specie9. Oak = -4 Chest- nut =-2 Beech =•1 Scots pine =-3 Age, in Y ears. 70 Mean Height in Feet. Oak, Chest- nut & Beech =54 Scots pine = 60 Volume in solid Cubic Feet. Broad- leaved =34,000 Scots pine =28,800 62,800 Quality of Lo- cality. Grow- ing Stock II. (or mid- dling) Remarks, and Notes regarding Future Treatment. The mixture of species is uneven ; the Scots pine is chiefly found in the northern part and the broad-leaved trees in the south ; the nor- thern part is well- stocked, the southern part is open ; most of the oaks and chest- nuts are frost-cracked. Future Treatment. — The southern part is so increment poor that it should be cut over during the next ten years, leaving the best oaks and chest- nuts underplanted with beech. In the northern part only dead or dying trees should be removed during the next ten years. Whenever the management is of a certain intensity, it is useful to prepare this table, as it enables the forester to calculate the total yield capacity of the area. In the table, each working section must be recorded separately, as the yield capacity depends on the species, silvicultural system, and rotation. Assuming that the yield tables for Scots pine given in Appendix IV. apply to the woods in question, and that the latter are worked under a rotation of 80 years, the normal mean production per acre and year will be as follows : — For the I. Quality class = 100 cubic feet. II. „ „ = 86 „ III. „ „ = 67 M The mean annual increment, or the yield capacity, of the area shown in the above table would therefore be — Yield capacity = 36 X 100 + 116 X 86 + 65 X 67 = 17,931 cubic feet, or average yield capacity per acre = ' = 83 cubic feet. 256 COLLECTION OF STATISTICS. This figure represents the normal yield ; the real or actual yield depends on the quality of the growing stock and the ages of the several woods. Assuming that the mean quality (density of stocking) of all woods were equal to -7, the actual yield would, for the present, be equal to — 17,931 X -7 = 12,552 cubic feet, or 58 cubic feet per acre and year, while measures would have to be taken to increase the yield capacity in the future by growing more completely stocked woods. 5. Table of Age Classes. This table is of great importance, as it gives a correct idea of the proportion of the different age classes, a matter which affects the determination of the yield in the future. It may be prepared in the following form : — Table of Age Classes. Locality. Present Age Classes, Areas in Acres. Working Section. Com- part- ment. Sub- com- part- ment. Mean Age. I. 1-20. II. 21-40. III. 41-60. IV. 61-80. V. Over 80. Blanks. Total. Caesar's Camp 1 1 2 3 4 5 6 7 a b 70 35 95 54 16 46 24 86 Total.. 31 i4 3i n 33 24 32 27 2 6 26 14 38 17 31 33 31 27 31 45 50 24 59 8 217 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 calculated from these data, as in the example on the next page. Similar statements are prepared for the different species, or groups of species, and a summary of the whole drawn up. Where specially valuable timber has been cut, like oak standards, teak, etc., the results can be entered separately. MAPS. 257 Table of Past Yields. Material cut in Past Years, in solid Cubic Feet. Year. Conifers. Final. Intermediate. Total. Timber. Fire- wood. Total. Timber. Fire- wood. Total. Timber. Fire- wood. Total. 1881 1882 7,200 1,750 8,950 4,700 1,300 6,000 11,900 3,050 14,950 1890 Total in 10 years Annual 77,600 16,400 94,000 36,400 12,200 48,600 114,000 28,600 142,600 average 7,760 1,640 9,400 3,640 1,220 4,860 11,400 2,860 14,260 Remarks. — The area set aside for the production of wood amounted, in the beginning of 1881, to 217 acres. The annual yield was fixed at 15,000 solid cubic feet : or 150,000 for the period of 10 years ; hence, the average cuttings were below the fixed yield by 740 cubic feet annually. 7. Maps. It is most useful to represent on maps the data required for the preparation of a working plan, so far as this can be done. Such maps give at a glance a clear picture of the forest which impresses itself more readily on the mind than a lengthy description. As it is not possible to represent everything on one map, it is usual to represent different classes of information on different sets, such as the — (a.) Topographical map. (6.) Geological map. (c.) Soil map. (d.) Detailed map on a large scale. (e.) Map showing the nature and age of the growing woods, called the stock map. (/.) Map showing the working sections and cutting series. (g.) Detailed road map. (h.) Map showing the qualities of locality. 258 COLLECTION OF STATISTICS. There is, however, no need for so many separate maps, as several of them can be 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 limits of the various qualities of locality can be entered by lines of a dis- tinguishing colour, the quality being indicated by a number. b. 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. (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, compartments and sub-compartments, with their names and numbers. c. The Stock Map. This has for its principal object to show 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 con- tain, apart from the necessary details, a representation of the existing species, silvicultural systems, and distribution of the age classes. This can be done in a variety of ways, as, for instance, in the following : — In high forest the principal species are shown by different Fig. 54. REPRESENTATION OF TWO CUTTING SERIES (THE UPPER CONSISTING OF 10 COMPARTMENTS, THE LOWER OF 5). PREVAILING WIND DIRECTION. CUTTING DIRECTION. mmh y- <- Jl II II (I II IL Rotation = 80 years. The White Lines indicate the coupes to be cleared during the next 10 years. [To fare p. 258. MAPS. 259 washes ; the age classes by different shades of the same wash, the youngest being given the lightest, and the oldest the darkest shade ; the regeneration class receives some distinguishing 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. By way of illustration, Fig. 54 is added. It illustrates two cutting series, a number of these constituting a working section, or a complete series of age gradations. Further details and illustrations will be found in Chapter II. s2 260 CHAPTEE II. DIVISION AND ALLOTMENT OF THE FOREST AREA. 1. The Working Circle. By a working circle is understood the area which is managed under the provisions of one and the same working plan. The area of a working circle depends on local conditions. It is intimately connected with the general organisation of a forest property. Assuming that the unit of an executive charge is repre- sented by a range, a working circle may comprise all areas included in one range. Sometimes the conditions differ so much that different working plans are drawn up for parts of one range, but, as a rule, this should be avoided unless several small pro- perties are comprised in one range. This occurs frequently in many European states, where Government forest officers manage both State and communal forests. Hence, it may be said that the minimum size would be the area of a property belonging to the same owner ; the maximum should ordinarily be the area forming one executive charge, or range. In some cases two or more ranges are worked under one working plan, but, with the advance in the intensity of management, such cases would disappear. 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, such as motor cars, enable the range officer to move rapidly from one part of his charge to another. 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 THE COMPARTMENT. '261 small, so that an intense and detailed management may be possible. 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 a working section consisting of a complete series of age gradations or age classes. In some cases a working section is identical with a working circle, or the latter may contain several of the former. The whole of this division is effected by utilizing, in addition to the outer boundaries, interior natural lines, such as waterpartings, 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 indicating how they should be laid out, to explain more fully what is under- stood by compartment, sub-compartment, cutting series, and working section. 2. The Compartment. By compartment is understood the unit of working ; it forms the unit of the division of the forest. This definition should never be lost sight of. If the boun- daries of a compartment can be made to coincide with those of wood showing a certain composition or age, so much the better, but it is a mistake to insist upon such an arrangement ; the main point is that each compartment should be of a certain size, so as to realise its objects as the unit of working. If that area includes two or more different kinds of growing woods, they may be dis- tinguished as sub-compartments ; but the boundaries of the compartment should never be twisted out of shape for the sake of including only one kind of growing stock. The formation of compartments is necessary — (1.) For general orientation, so as to enable the forester to define accurately any particular part of the area. (2.) To render all parts of the forest easily accessible, since one or more sides of the compartment should abut on roads or rides. 262 DIVISION AND ALLOTMENT OF THE FOREST AREA. (3.) 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 shape of compartments depends on the configuration of the ground. In the plains, a rectangular shape (with sides 2 : 1, or 3 : 2) is most suitable. On hilly ground, such a shape is not always practicable ; but the actual shape should, as far as possible, approach that of a rectangle. The size of compartments cannot be laid down ; it depends chiefly on — (1.) The size of the working circle. (2.) The intensity of management. (3.) The extent of danger from fire. 3. The Sub-compartment. If, within the limits of a compartment, considerable differences exist in respect of species, silvicultural system, age of growing stock, quality of locality, etc., it may be divided into two or more sub-compartments ; the latter may be temporary if the differences will disappear after some time, or permanent. Sub -compartments may be marked by shallow ditches or other cheap boundary marks. They form the units of treatment. The forester should not go too far in the formation of sub-com- partments, 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 thereby. The formation of sub- compartments depends on the intensity of management. 4. The Working Section. A part of a working circle which forms a separate series of age gradations or classes is 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 THE WORKING SECTION. 263 more series of age classes — that is to say, a division of the working circle into two or more working sections. The principal causes which demand the formation of working sections are the following : — a. Species. When several species appear in a working circle as pure woods, they must be placed in different working sections if they require essentially different treatment, or if a certain quantity of material of each species has to be cut annually. When, on the other hand, the several species appear in mixed woods, such a separation is neither practicable nor necessary. b. Silvicultural System. Each silvicultural system may demand the formation of a separate working section. If, for instance, part of a high forest is treated under the uniform system, and another part as a selection forest, each part must be formed into a separate working section. Coppice woods and coppice with standards must always form separate working sections. c. Rotation. Even in the case of the same species and silvicultural system, areas worked under different rotations must be placed in different working sections whenever an even, or approximately even, annual yield is expected. Unless this is done, it will happen, either that the annual yield is uneven, or, if the same quantity is cut every year, that the different rotations merge into one. d. Servitudes. If part of a working circle is subject to servitudes, it should be placed in a separate working section ; this is necessary to pro- tect the interests of the owner, as well as of the right holder. 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 264 DIVISION AND ALLOTMENT OF THE FOREST AREA. of different species, or the adoption of different treatment or rotations. /. Distribution of Cuttings. If cuttings must be made annually in different parts of the work- ing circle, so as to supply local demands, it is often advisable to form different working sections, though this may not be absolutely necessary. g. Size of the Working Circle. When the area of a working circle exceeds a certain limit, it may be more convenient to divide it into several working sections, although no difference in the character of the growing stock and the management exists. In this way, better arrangements can be made for the execution of the work. h. 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 in this respect. A separate record must be kept for each working section, and they cause extra trouble and expense in other ways ; hence, moderate differences of 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 procedure is not desirable, because it involves extra labour and repetitions in the working plan report. It is preferable, whenever practicable, to have one working plan for each executive charge, because the management of the different working sections can be so arranged that they supplement each other, thus enabling the forester to provide for a proper allotment of work amongst the staff, and a proper distribution of the yield. Where the areas managed on different lines are mixed up with each other, the division of a working circle into two or more working sections becomes a necessity. The areas belonging to one working section need not form a consolidated block ; they may be scattered amongst areas forming another working section. Sketch of the Existing Division of a Working Circle into Working Sections, Compartments and Sub-Compartments, in 1925. © 4 a 8 © b 7 6 fe- ®b © a 12 b 10 9 16 15 14 13 20 19 18 17 w. y» > < «s PREVAILING WIND DIRECTION. Fig. 55a. CUTTING DIREC1 [ON. Explanation of Fig. 55, representing an Executivt Charge, or Range. The area represents one Working Circle, which, by a system of rides, has been divided into 20 compartments, stocked as follows : — Working Section I. = Oak high forest with an admixture of beech, comprising compartments .'5, 4, 56, 66, la, 8a, 9, 10a, 116, 126, 15a, 16a. Working Section II. = Conifer high forest, comprising compartments 1, 2 5a, 6a, 76, 86, 106, 11a, 12a, 13, 14, 17, 18. Working Section III. = Coppice woods, comprising compartments 156. 166, 19, 20. It has been decided that sub-compartments 56 and 66, being of III. quality class, shall be converted into conifer woods ; sub-compartments 76, 86, 106, 11a, and 12a, into oak with beech, being I. and II. quality class ; while 15a and 16a, being III. quality class, will be converted into coppice woods. Sketch of a Division of a Working Circle to be Established during the First Rotation. 4 F 3 8 F : 7 EH I 2 A 6 B 5 10 G 9 16 J 15 14 C 13 20 K 19 18 [) 17 )»■ PREVAILING WIND DIRECTION. > < «c CUTTING DIRECTION". Fig. 55 b. Division into ten Cutting Series, each consisting of two Compartments. [Conifers. Cutting Series A = Compartments 1 and 2 Working Section I. Working Section II. Oak. Working | Coppict . Section III. I B = , t , , C = , - 5 D = , E = , F = , > G = , H = , I ,, , K = 6 13 „ 14 17 „ 18 3 7 4 S 9 „ 10 11 „ 12 15 „ 16 19 „ 20 the cutting series. 265 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 circumstances of each case. It has, however, been pointed out above, that such a simple arrangement is, in the case of high forest, not always admissible, and that every working section in such a forest must be further divided into several parts, which are called " cutting series." Only such a further division gives the necessary order and elasticity to the arrangement of the coupes. Each cutting series should comprise a number of gradations, the ages of which differ by a certain number of years (see diagram on page 209) ; ordinarily, 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 in one cutting series depends on local circumstances. On the whole, small cutting series are desirable, as each gives a point of attack where cuttings can be made. (See Fig. 53, page 211.) Amongst the advantages of small cutting series, the following may be men- tioned : — (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 pro- tect the forest against the dangers which may make them- selves felt if two or more annual coupes adjoin each other. (3.) The establishment of small cutting series assists the forester in distributing the yields to meet local demands. In order to realise these advantages, it is necessary that each cutting series should receive a shape and be so situated that the coupes can be suitably arranged, and that cutting in one series does not interfere with the requirements of adjoining series ; in other words, each cutting series must be independent of its neigh- bour. Where these conditions do not exist, they must be specially 266 DIVISION AND ALLOTMENT OF THE FOREST AREA. 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 whenever an existing cutting series is too long, and when it is desirable to divide it into two or more series, or where an older wood is situated on the windward side of a younger wood. Their object is to accustom the edge PREVAILIHC Wr«D DIOCCTIOH > ► SEVERANCE CUTTING CDTTIDC omecTion •< < iliilliiiiili illfwtiftM ITH AUNUAL ENLARCCNEKT WITH PERIODIC E»LAIICE»E»T Fig. 56. — After Wagner. 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 windward side has been cut. The above illustration will explain this. Severance cuttings need not be straight ; they may, if necessary, be curved, or run along two or three sides of a wood. The latter is necessary 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 protected is still young and capable of developing firm edge trees ; such a THE SYSTEM OF ROADS AND RIDES. 267 development is generally no longer possible after the trees have passed middle age. They must be made, in the windward wood, some 15 to 20 years before the regular cuttings are commenced. Where danger from windfalls is great, it is desirable first to clear a narrow strip, and to widen it a few years afterwards in one or more instalments, so as gradually to accustom the edge trees to the 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 consists of a widening of the road on the windward side of it. If the proper time for making a severance cutting is past, and the wood to be protected is too old, it would be a dangerous procedure to make such a cutting. In that case, it is better to make a series of thinnings in the strip along the edge of the wood to be protected before cuttings in the windward wood are com- menced. Whether this measure will have the desired effect is doubtful, but it is better than to risk a regular severance cutting. 7. The System of Roads and Rides. As already indicated, working sections, cutting series and com- partments must be separated from each other by natural or artificial lines. Apart from suitable natural boundary lines — such as waterpartings, watercourses, precipices, fields, meadows, etc. — roads are the best boundaries of compartments and cutting series, because they facilitate the transport of the produce. It is, there- fore, desirable that, in the first instance, a suitable network of roads should be designed 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 consump- tion. Besides, on hilly or swampy ground they often follow a direction which renders them unfit to serve as boundaries. The missing division lines are provided by a system of rides, that is to say by cleared strips of various breadths. A distinction is made between major and minor rides. 268 DIVISION AND ALLOTMENT OF THE FOREST AREA. a. Major Rides. In so far as roads or natural lines are not available, working sections, and in many cases cutting series, should be bounded by major rides. These should, as far as possible, run parallel to the prevailing wind direction, so that the adjoining woods on both sides produce wind-firm edges. Deviations from this rule may be necessary in hilly country, and where young crops require shelter against the sun. In coppice and coppice with standards, the major rides need not be broad, unless they are used as roads for the transport of the material. In high forest, they must be broader, because they are used as severance cuttings. In the case of woods consisting of species which are easily thrown by wind, they should not be less than 30 feet broad, and if the major ride is also used as a fire line, it may be still broader. The edges of the woods consisting of species easily thrown by wind, if bordering on major rides, should be heavily 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 past 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. 6. Minor Rides. Minor rides should run, more or less, at right angles to major rides ; they complete the delimitation of the compartments. Minor rides need not be more than 6 to 8 feet broad, unless they are used as fire lines. The direction of the coupes must be deter- mined according to local conditions ; no general rule can be laid down. In the case of clear cutting and artificial regeneration the coupes should be so arranged that the young crop receives the best possible protection against drought. On sloping ground they should proceed from the top downwards, etc. THE SYSTEM OF ROADS AND RIDES. 269 c. The Network of Rides. Major and minor rides together form the network or system of rides. The laying out of it depends, especially in the case of shal- low-rooted species, chiefly 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 configuration of the ground may pro- duce 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 stems, and by the direction in which trees have been thrown. As regards the latter, it must not be overlooked that local storms sometimes throw trees in a direction which differs from the ordi- nary direction of gales. In many cases, reliable information 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. Regular networks of rides with right angles at the corners are practicable only in the plains ; on hilly ground they must accommodate themselves to the configuration of the area. The example given below will illustrate this. The forest occupies a ridge, the slope of which is indicated by dotted contour fines, . The top of the ridge, being much exposed, must be treated as a separate working section worked under the selection system ; it is separated from the rest by a major ride f B V The slopes are treated under the uniform system, and they are divided into two parts by the major rides ( A J I B J and ( C ). The numbers ( 1 j ( 2 J . . . indicate the minor rides, and 1, 2, 3 . . . the compartments. The prevailing wind blows from the west. 270 DIVISION AND ALLOTMENT OF THE FOREST AREA. N. PREVAILING WIND DIRECTION. s. Fig. 57. The division would probably be somewhat on the following lines : — Working Section I., Uniform System. Cutting Series A comprises compartments 1 & 2 ,, „ B „ compartment 3 G 4 55 55 ^ JJ 55 * „ „ D „ compartments 5 & 6 Working Section II., Selection System, comprises compartments 7, 8, and 9. The general cutting direction would be from east to west, a direction which is indicated by the numbering of the compart- ments. The coupes in compartments 1,2, and 3, being on a slope with a direction from N.E. to N.W., would probably run parallel to the minor rides. Those of compartments 4, 5, and 6, being a slope running from S.E. to S.W., would best be arranged running from the highest part gradually down to the lower edge, so as to protect the young growth against the drying effect of the sun. DEMARCATION AND NUMBERING. 271 8. Demarcation and Numbering 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 recognised if parts of them should have become obliterated in consequence of cuttings, windfalls, etc. For this purpose, boundary marks may be placed at all points where rides cross, or where they form an angle. If straight rides are very long, it is useful to have inter- mediate marks at suitable distances. Such marks are placed on one side of the rides, so that they may not interfere with the trans- port of the produce ; it is useful always to choose the same side, say the north side of the major rides and the east side of the minor rides. The methods of naming and numbering the divisions differ much. The author recommends the following : — (a.) Working sections receive Roman numbers = I., II. . . . (6.) Cutting series receive slanting capital letters = A, B. . . . (c.) Compartments receive Arabic numbers = 1, 2. . . . (d.) Sub-compartments receive the same with small Roman letters attached, l a , 1&. . . . (e.) Major rides are indicated by two parallel lines. (/.) Minor rides are indicated by single lines. (g.) Metalled roads should be indicated by heavy black lines. Sometimes a number of compartments are joined into a " block " ; if so, the latter should receive a name. The numbering of compartments should be consecutive throughout the working circle, unless the latter consists of two or more entirely separated blocks ; it leads to confusion to have a separate series for each working section. The numbering should be done so as to indicate the cutting direction. In the French State forests, the following system of numbering the divisions was prescribed until a short time ago : — Working sections are numbered = I., II., III. . . . Periodic blocks „ „ = 1, 2, 3. . . . Compartments „ „ = A, B, C, . . . with the addition of the number of the periodic block ; thus IV. C 2 means Working Section IV., compartment C in the 2nd periodic block. 272 CHAPTEE III. DETERMINATION OF THE METHOD OF TREATMENT. On the basis of the statistical report and the division and allot- ment of the area, the forester decides upon the method according to which the forest is to be treated. The selection of the method depends on a variety of matters, of which the more important may be mentioned : — (a.) The legal position of the forest, the existence of rights of third parties, or privileges enjoyed by them. (6.) The objects aimed at by the proprietor, whether he be a private person or the State. He should decide whether he aims at indirect or direct effects ; in the latter case, he should indicate the classes of produce which he desires to obtain, (c.) The character and quality of the locality. (d.) The existing growing stock according to species and the degree of their development ; also the dangers to which the existing species and the soil are exposed, (e.) The conditions of the market, the extent of the demand, and the supply of produce from other forests. (/.) The supply and cost of labour. These and other considerations influence the selection of the most suitable method. The following subjects deserve special attention. 1. Choice of Species. The subject is dealt with in Silviculture (see pages 122 — 128 of Vol. II., 4th edition). In the present case, the forester should carefully ascertain the degree to which the existing species have met the objects of the proprietor, and proved to be suitable for the locality. If they do not answer, the forester should not hesitate to change them for other more suitable species. At the same time, the introduction of new species should not be lightly THE METHOD OF FORMATION. 273 undertaken, as it generally involves some temporary loss, and it may lead to disappointment in the future. Species which have been tried within a reasonable distance of the locality and given satisfactory results should receive first consideration. The cultivation of untried, and especially exotic, species should, in the first place, be tried on a small scale. In such cases, the formation of mixed woods deserves consideration, as they give a choice between two species as to which is to be kept for the final crop. 2. The Method of Formation. The various methods of formation are dealt with in Silviculture (see pages 275 — 284, of Vol. II., 4th edition). The choice depends on the species, the nature of the locality, and the selected silvi- cultural system. Artificial regeneration generally forms part of the system of clear cutting in high forest, but it may also be done under shelterwoods ; it is necessary in the case of first afforesta- tions, and frequently also when a change in the species is contem- plated. The choice between direct sowing and planting depends on the species and local conditions. Natural regeneration is cheaper than sowing and planting and, if successful, leads to fully stocked woods. In the case of many species, however, seed years do not always come when they are wanted, in which case the operation of regeneration may be seriously disturbed ; the loss of time and other accompanying disadvantages may more than outweigh the saving in the original outlay. Moreover, natural regeneration must frequently be augmented by planting or sowing. The choice of the method of formation in high forest depends practically on the degree of moisture of the locality. Where the rainfall is scanty and irregularly distributed over the seasons of the year, and where long droughts are of annual occurrence, regenera- tion should be effected imder a shelterwood, either provided naturally or by planting and sowing. Where the opposite con- ditions prevail, planting and sowing on clear land is admissible. The latter is necessary in the case of highly fight-demanding species ; on the other hand, species which are tender while young should be raised under a shelterwood. The quality of the locality is also of great importance . Generally speaking, regeneration on cleared areas may be fully justified in 274 DETERMINATION OF THE METHOD OF TREATMENT. localities with a high, yield capacity, while regeneration under shelterwoods is indicated on areas of middling yield capacity and essential on those of poor quality, especially in hilly localities. 3. The Method of Tending. (See pages 287—323, of Vol. II., 4th edition.) To sow or plant an area is a comparatively simple business when once the most suitable species has been selected ; the process of natural regeneration requires considerable skill ; the most important work of the forester is the application of a suitable method of tending, and especially the method of thinning the wood from the completion of the process of regeneration to the time when the wood is ripe for final cutting. The tending must be so arranged that throughout life each tree receives just that growing space which produces the most profitable results accord- ing to the objects of the proprietor. Views on this subject differ much. Until some 30 years ago, the method of early and heavy thinnings prevailed in Britain, giving unsatisfactory results, while on the Continent the system of light and frequently repeated thinnings prevailed, leading to fully stocked woods of high value. Since then, a change has taken place in both cases, but in opposite directions. The system of lighter thinnings has found favour in Britain, while a number of Con- tinental foresters now advocate heavy thinnings. It has been proved that there is not much difference between the two systems as regards the total production, but there is a different division of it between thinnings and final returns. In some cases, as much as half the increment is taken out in the thinnings, reducing the final yield to the other half. The thinnings are no longer restricted to the removal of suppressed and dominated trees ; a part of the dominating trees is also taken out even at a comparatively early age, while the suppressed and dominated trees are left (Eclaircies par le haut). The justification for this is the belief that the system gives better financial results. But is this so ? No doubt, early and comparatively heavy thinnings act favourably in a financial respect, but they generally give too much growing space to the remaining dominating trees, which are liable to produce in the final cutting a less valuable class of timber, so that the previous THE SILVICULTURAL SYSTEMS. 275 advantage may be more than wiped out. This consideration limits the heaviness of the thinnings ; they should never be made so heavy that they interfere with the most favourable develop- ment of the trees that will constitute the final crop. The most favourable proportion between thinnings and final crop can be determined only by the collection of comparative statistics, when the heavily thinned woods reach maturity, and their value can be compared with that of woods produced under the system of light and frequently repeated thinnings. 4. Choice of Kotation. (See pages 188 — 195 of this volume.) The determination of the rotation depends chiefly on the species, the method of treatment and the objects of the proprietor. The financial aspect should never be lost sight of, but there are weighty reasons why departures from the financial rotation are desirable and even necessary. Amongst these, the preservation, or even improvement, of the yield capacity of the locality demands first consideration, and next the class of the desired produce. In the latter case, frequently, a special size of the trees in the final crop is substituted for a rotation fixed by a certain number of years. 5. The Silvicultural Systems. A description of these is given in Silviculture, where it is required to understand the various methods of the formation and regenera- tion of woods. Here it is wanted especially for the determination and regulation of the yield. The number of systems is very large, some 70 having been enumerated. There are a limited number of principal systems, while the rest are modifications of these. They may be classified in various ways, of which the following will serve as an illustration : — I. — Principal Systems. (A.) High or seedling forest. (1.) Clear cutting and subsequent regeneration. (2.) Regeneration under a shelterwood. (a.) By treating one or several compartments in a uniform manner (the compartment or uniform system, with various modifications). T 2 276 DETERMINATION AND REGULATION OF THE YIELD. (6.) By groups. (c.) By strips. (d.) By strips and groups combined. (e.) By single trees (the selection system). (B.) The coppice system. (C.) The combination of the seedling and coppice systems (coppice with standard system). II. — Auxiliary Systems. (1.) High forest with standards. (2.) Two-storied high forest. (3.) High forest with soil protection wood. (4.) Forestry combined with the growth of field crops. (5.) Forestry combined with pasture. (6.) Forestry combined with the rearing of game. Any of these systems may be utilised in the determination and regulation of the yield, as shown in the next chapter. CHAPTEK IV. DETERMINATION AND REGULATION OF THE YIELD. As long as the owner of a forest is satisfied with intermittent returns, the regulation of the yield is strictly governed by silvi- cultural considerations ; that is to say, thinnings are made when they are necessary, and every wood is cut over when it is just ripe, according to the objects of management. If the owner desires a sustained annual or periodic yield of equal or approximately equal quantity, although the forest is at the time 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 may have to be made at ages differing from the normal, as determined by the objects of management ; even thinnings may have to be postponed, instead of being made THE REGULATED SELECTION SYSTEM. 277 when the condition of the woods demands them. These deviations may be brought about by a surplus or deficiency of mature woods, or by their being so situated that they cannot be cut at the proper time, out of consideration for the safety of adjoining woods. The task of the forester in such cases is to secure a sustained annual yield, and yet to lead the forest, with the smallest possible loss to the owner, gradually over into the normal state. Many different methods have been elaborated with the view of achieving that task, which approach the subject from different points. As indicated in the introduction to this part, the older methods started by considering, in the first place, the forest as a whole, determining the yield, and then seeing in which parts of the forest it had best be cut. Moreover, working plans were prepared for long periods of time, usually a whole rotation. Gradually, a method was elaborated which considers, in the first place, the con- dition and requirements of each wood for a limited number of years, and adds up the operations thereby indicated. The sum of these cuttings represents the yield, but it is subject to a modifica- tion in so far as it would interfere with a sustained yield in the future. This method of determining the yield should be the basis upon which working plans should be prepared in all cases where a sustained yield is aimed at. It is not possible, nor necessary, to deal in this chapter with all the numerous methods elaborated in the course of time ; only those will be described which have been, or are likely to be, adopted. SECTION I.— THE PRINCIPAL SYSTEMS. 1. The Regulated Selection System. The selection system is the oldest of all systems. Originally, people selected the trees which suited their requirements and relied on Nature to replace what had been taken away. Probably the first attempt to control these operations was connected with the establishment of what are now called " protection forests," that is to say, areas which must be maintained under forest for the sake of their indirect effects. Apart from such areas, the bulk of the forest in the world is still selection forest, and much of it has been reduced in value owing to insufficient protection and 278 DETERMINATION AND REGULATION OF THE YIELD. control. As a consequence, many of the selection forests in Europe have been converted into the " uniform system " with a view to obtaining higher returns. It has, however, been recognised of late years that the returns from proparly treated selection forests are not necessarily smaller than those from areas treated under the uniform system. This has lead to a considerable improvement in the management of many of the remaining selection forests, which will now be described. a. Description of the System. Character of the Sijstem. — All size or age classes from one year old plants to the oldest trees are represented by single trees or Fig. 58. — Selection Forest. (Conventional Sketch.) small groups in all parts of the forest, and, theoretically, the work of selecting trees for cutting extends at all times over the whole forest. In practice, however, the forest is divided into a number of blocks, or compartments, which are taken in hand in turn for treatment^ so that the cuttings return to the same part after the lapse of several years, called a " period." The size of the com- partments and the length of the period depend on the intensity of management. The greater the intensity, the smaller will be the compartments and the shorter the period. The natural regenera- tion of the forest is effected under and between the shelter of the old crop, especially where single trees or small groups of trees have been removed. If natural regeneration fails, artificial sowing or planting is not excluded, though it is required only in exceptional cases. THE REGULATED SELECTION SYSTEM. 279 Preservation of Fertility. — The system secures at all times an equal degree of protection to the soil, more especially as regards the preservation of a suitable degree of moisture. Protection is given not only from above, but there is also side shelter, owing to the mixture of the several size classes in all parts of the forest. On sloping ground the rainfall is effectively retained ; avalanches, the carrying away of fine earth, landslips, etc., are prevented or at any rate moderated. As a consequence, protection forests situated in mountainous districts are usually managed under this system. All these matters act beneficially upon the producing factors of the locality, which is a substantial offset against any shortcomings of the system in other respects. External Dangers. — Views differ somewhat regarding the extent to which selection forests are exposed to external dangers, as compared with the more uniform shelterwood systems. In the author's opinion, the selection system is, on the whole, the more favourable of the two, because only very small areas are at one time exposed to the injurious effects of the sun and unfavourable air currents. Damage by frost and drought is less, and probably also that from wind- and snow-break. The Production of Wood. — Owing to the conversion during the last century of considerable areas of selection forests into the uniform systems, comparative observations are somewhat scarce. These conversions were due to the belief that selection forests produce smaller quantities of wood than the uniform systems. It has, however, been recognised of late that this opinion was due to the fact that many selection forests were not managed as efficiently as should have been the case. At any rate, there are now some selection forests which, owing to careful and rational treatment, are giving returns which are, as regards volume pro- duction, equal, if not superior, to the uniform shelterwood systems. Young growth, no doubt, develops slowly, as it is much kept back by the older trees, but this is made good by more active development when it has reached the full enjoyment of sunlight and the benefit of more favourable moisture conditions secured by the continuous protection of the soil. The Quality of the Timber. — There can be no doubt that in many cases the boles of the trees produced under the selection system are less clean of low branches than those grown under the uniform 280 DETERMINATION AND REGULATION OF THE YIELD. shelter wood systems. In the case of some species, the trees are also liable to suffer in height growth. These are, no doubt, short- comings. On the other hand, the system is well suited for the production of trees with a large diameter, or girth, as the trees can be left in the forest for any length of time. b. The Management of Selection Forests. There cannot be any doubt that the successful treatment of selection forests depends more on the individual efficiency and zeal of the forester than is the case in any other system. To obtain really good results, it is essential that the forester should have a detailed knowledge of all parts of the forest, as he has, so to say, to guide each promising tree throughout all stages of its life. All depends on his personal judgment in the selection of the trees to be left for further development, of those to be cut, and of the time of removal. It follows that the forester must be given great freedom of action, and yet his measures must fit into the frame- work of a general scheme of management whenever a sustained yield is aimed at. Given such a manager, all will be well, but, fail- ing this, mischief may be the consequence. There has been a protest of late against all kinds of control of the local managers, and a demand for full liberty. These are ideas which are not followed in other branches of human activity, and they are certainly out of place in forestry, where forethought for future requirements during long periods of time is essential. The details of a general working scheme depend on local con- ditions, but the following may serve as an illustration : — c. Determination and Regulation of the Yield. The first and important measure is to divide the forest into a suitable number of compartmerfts. The size of these depends on the total area of the forest and on the intensity of management. Where the latter is well advanced the compartments should be small, say not more than 50 acres. In the case of extensive areas it may be desirable to arrange the compartments into two or more working sections, and the compartments in each working section should be consecutively numbered — that is to say, one series of THE REGULATED SELECTION SYSTEM. 281 numbers for each working section, and still better for the whole forest, unless it is of very large extent. The second measure should be to treat each compartment on its own merits, with due reference to the yield of the whole section. If by careful treatment each compartment is gradually brought to its highest possible production, all must be well in the whole forest. The third measure should be to ascertain the exact condition of each compartment, and from that date to keep a separate account for each unit of division of all measures taken and acts done within its boundaries. The establishment of sub-compartments should be reduced to a minimum. If they are of a temporary nature, they will naturally disappear in course of time. If a permanent distinction of part of one compartment is necessary, it is much better to establish two compartments at once instead of sub- compartments. With a view to determining the yield capacity of each compart- ment and to lay down its further treatment, the growing stock, or stand, must be carefully measured and classified. The latter may differ in accordance with local conditions, but generally it would be somewhat on the following lines : All trees down to a minimum diameter (or girth) would be carefully measured, and their volume ascertained. These trees with their volume would be divided into several classes ; in some cases into large, medium, and small trees ; in other cases more distinct limits are adopted. For instance, let the minimum diameter at height of chest be 6 inches (or 20 inches girth) and each class comprise a range of 6 inches ; there would be the following size classes : First class = 6 to 12 inches ; second class = 12 to 18 inches ; third class = 18 to 24 inches ; fourth class = 24 to 30 inches, and so on. By numbering the classes in this way, the number of each class at once indicates its limits. Unfortunately, the reverse method of numbering from the largest class downwards has been much adopted. All young growth below 6 inches diameter is examined, so as to ascertain whether it is of sufficient quality to assure the required number of saplings to replace the larger trees which will be removed from time to time ; if not, suitable cultural measures must be adopted. Throughout all stages of treatment the yield must be intimately connected with the increment. The one must be equal to the other 282 DETERMINATION AND REGULATION OF THE YIELD. in all cases where the proportion between the classes is such that the objects of the proprietor can be indefinitely realised ; in other words, if the growing stock is normal. If there is either a defi- ciency or surplus of growing stock, in the one case less and in the other case more, then the actual increment should be cut, as a temporary measure, until the normal condition has been estab- lished. The difficulty is to ascertain the actual increment at starting. An effort may be made to determine it by examining the incre- ment of the immediate past and adopting that for the immediate future, until more reliable data become available. The latter can be obtained only by remeasurements after short intervals of, say, 5, 10, or n years. Let the volume in the beginning be V v that after n years V n , and the volume removed during the n years = Y P (p = periodic), then the increment during the n years amounts to Ip = V n + Y p — V x . In this way the increment for the whole compartment can be ascertained, as well as for each class of trees. With every succeeding periodic measurement, the determination of the increment becomes more and more accurate.* In cases where the degree of intensity of treatment is very high, the investigation of the increment may be extended to single trees. It is not possible to define the normal condition of the growing stock by a formula, as can be done in other systems. It can only be described as that which yields permanently the greatest return of the class of timber desired by the proprietor. The normal state can, as a rule, be reached only gradually in the course of several periods, during which the forester establishes the proper propor- tion between the several size classes, each consisting of vigorous promising trees. Their numbers should be such that each tree is given enough growing space required for full development and no more, according to the size class to which it belongs, and the light required for the proper development of young growth. With this reservation, a full stocking of the area should be aimed at, so as to obtain a full return, and to produce as clean and well-shaped boles as may be possible under the existing conditions. * Several methods have been developed in India by Messrs. S. H. Howard, E. A. Smythies and others, which are very ingenious, but complicated, nor are they free from uncertainties. In the author's opinion, the above method is the only way of determining the increment accurately. THE REGULATED SELECTION SYSTEM. 283 The procedure had better be further explained by a small example. Example. — Given a selection forest of 300 acres which has been divided into 10 compartments of an average size of 30 acres each. Taking one of these compartments, it was found to contain a young growth below 6 inches diameter fit to furnish the several classes above 6 inches with a sufficient number of recruits. These classes contained at starting the numbers of trees and their volumes given in columns b, c, and d of the appended table : — Number and Limit of Class. Diameter, Inches. At Starting, per Acre. After 10 Years (End of I. period) per Acre. Number of Trees. Average Volume per Tree. Cubic Feet Volume Total. Cubic Feet. Number of Trees. Volume Total Cubic Feet. Volume of Cut Trees. Cubic Feet. During 10 Years. Total Volume. Cubic Feet. f+g. Less Volume at Start- ing. Cubic Feet. Incre- ment during 10 Years. h-i. a b c d e / 9 h i i I. = 6—12 II. =12—18 III. = 18— 24 IV. =24—30 90 40 15 5 10 25 60 140 900 1,000 900 700 90 41 21 9 900 1,025 1,260 1,260 200 400 120 140 1,100 1,425 1,380 1,400 900 1,000 900 700 200 425 480 700 150 •• 3,500 161 4,445 860 5,305 3,500 1,805 This is the growing stock present at the commencement of the first period of, say, 10 years. It is proposed to remeasure the stock at the end of the 10 years, so as to obtain the data necessary for the determination of the periodic increment. As it is not desirable to suspend cuttings during the first period, nor to overcut the compartment, the forester must make the best estimate he can of the probable increment during the first 10 years. In some cases he may obtain sufficient information from adjoining forests to formulate his estimate. Failing this, he will probably attempt to ascertain the average increment laid on during the last 10 years by examining average-sized test trees of the several age classes. Assuming that he estimates it at 1,200 cubic feet per acre, and that a similar increment may be expected during the next 10 years, this quantity may be cut during the first period. But there is another consideration — namely, the present proportion of the volume in the several size classes. It will be observed that the two older classes contain only 1,600 cubic feet, against 1,900 in 284 DETEKMINATION AND REGULATION OF THE YIELD. the two younger classes. This is out of the proper proportion, as the former should contain at least half the total volume. In these circumstances, it is desirable to reduce the yield somewhat — say, to 800 cubic feet during the first 10 years — so as to provide, at any rate, some additional trees in the oldest age class. At the end of the first period it should be considered whether a further addi- tion to that class is desirable. If the proportion between the several size classes is not governed by the objects of the proprietor, the most desirable proportion would probably be that which exists if each size class occupies the same area ; in the above example, 75 acres, less the area which must be allowed to give to the young growth under 6 inches diameter the necessary light for proper development. The compartment, having been managed on these lines, is remeasured at the end of 10 years, when, it is assumed, it contains the stock shown in columns e to j of the above statement. The latter shows that the increment during the 10 years amounted to 1,805 cubic feet per acre. This is the maximum amount to be cut during the second period of 10 years. Whether the full amount is to be cut, or whether a further augmentation of the growing stock is desirable, depends on the experience gained during the 10 years. In this way, by repeated periodical measurements, the forest will gradually be brought into the condition of realising the objects of the proprietor to the fullest extent. There can be no doubt that some remarkable results have been obtained by the adoption of the regulated selection system. Keturns well over 100 and up to 150 cubic feet per acre and year have been shown in several cases, as, for instance, in the Oberwol- fach communal forest and in the Schifferschafts forests of For- bach, both in the Black Forest ; in Neuchatel in Switzerland and in other forests of the Jura. More comparative experience is, no doubt, required before a final judgment of the system is justified, but in the meantime foresters will be well advised to pay careful attention to it. Its great assets are the continuous protection of the soil and the preservation of a suitable degree of moisture. The drawback is the more branchy nature of the trees in the older classes, though this can be somewhat reduced by the pruning of the lower branches while they are still small. The pruning should be done in instalments, beginning at a comparatively early age BRANDIS' SYSTEM. 285 with, say, the lowest 10 to 15 feet of the bole and carrying it up the tree by similar stages as the tree increases in height. The operation is, no doubt, expensive, but very good results have been obtained by it in the Oberwolfach communal forest. The expense can be reduced by restricting the pruning to the trees which will remain to reach the largest class. It has been claimed that the system is applicable to all species, but that view cannot be accepted. It is suitable for shade-bearing and perhaps moderately shade-bearing species, while decided light-denianding species could not be naturally regenerated unless the older trees are placed so far apart that the principal advantage of the system, the protection of the soil and the preservation of a suitable degree of moisture, would be seriously reduced. 2. Brandis' System. (Sometimes called the Indian System.) A Modified Selection System. There are as yet many forests on the earth containing a mixture of many species of which only one or a few are of value. For such forests a modified selection system is required, and one of the kind was evolved by Sir Dietrich Brandis soon after his appointment as superintendent of the Pegu teak forests in Burma, in the year 1856. These forests contained teak in varying proportion, which has since been found to amount to about 10 per cent., while the other 90 per cent, of the growing stock consisted of species which, at that time, were of no value. The latter were allowed to be removed free of charge without let or hindrance. As to the teak trees, the minimum marketable size was fixed at 6 feet girth measured at 6 feet from the ground ; these were called I. class trees. Brandis was anxious to ascertain as quickly as possible the number of first-class trees which might be removed annually without endangering a sustained yield in the future. For this purpose, he ascertained : — (1.) The number of I. class teak trees in the forests, and (2.) The time which it takes to replace them. By dividing the number of I. class trees obtained under (1.) by the number of years obtained under (2), he ascertained the 286 DETERMINATION AND REGULATION OF THE YIELD. maximum number of trees permissible to be cut annually. Bran- dis fixed the annual yield accordingly, and thereby saved the valuable teak forests of Lower Burma from destruction. He allowed, however, a temporary increase if he found an excess of I. class trees. Various safeguards were added, such as an allowance for trees which it did not pay to extract ; where few second- and third-class trees existed, some first-class trees were left standing to provide seed for regeneration ; immediately along the banks of streams cuttings were made very sparingly, etc. For the rest, the method leaves a free hand to the forester, who arranges the cuttings with due regard to tilvicultural requirements and a proper succession of the different coupes. The numbers of trees of the several size classes were originally ascertained by counting, or measuring, them along narrow strips, generally 100 feet broad, laid through the forest along the line of march (called " linear valuation surveys "). From the contents of these sample strips (or plots) the contents of the blocks, or forest, were calculated. The rate of increment was determined by counting the 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 localised : in other words, an area check was added to the calculated yield, so as to guard against over- or under- cutting. The method does not claim to be theoretically quite correct, but it is correct enough wherever large areas have to be dealt with in a short time. It works expeditiously, and, if judiciously applied, prevents a deterioration of the forest. Had it not been for this method, the valuable teak forests of Lower Burma might have been exhausted before their sustained yield capacity had been ascertained. It is a method to be strongly recommended for adoption in countries where systematic forest administration is in its earlier stages, and where only a limited number of species are as yet of commercial value. BRANDIS SYSTEM. 287 Example : — This example is based upon data contained in the working plan for the East Yoma, Salsuwa, and Tindaw Reserves in the Thayetmyo Division of Burma, drawn up by Mr. A. Rodger, then Deputy Conservator of Forests. The productive area of the forests amounts to 84,022 acres, divided into 51 compartments. Of these, one was counted out altogether, while at least two sample plots in each of the other 50 compartments were marked, and the trees counted according to size classes. On the basis of the data thus obtained, the contents of the forests in sound teak trees over 1 foot 6 inches girth were calculated. They were as follows : — Class I. over 7 feet girth = 31,523 II. 6 feet to 7 feet „ == 18,114 „ III. 4 feet 6 inches to 6 feet „ = 42,768 „ IV. 3 feet to 4 feet 6 inches „ = 101,737 V. 1 foot 6 inches to 3 feet „ = 150,910 To determine the rate of growth, countings on 198 trees and logs were made, which gave the following averages : — Girth. 1 foot 6 inches 3 feet 4 feet 6 inches 6 feet 7 feet Age in Years. 31 ; 60 93 J 130 j 156' Years required to pass through each Class. 29 33 37 26 125 Hence, the rotation was fixed at 160 years, and divided into five periods of 32 years each. From observations made in this and other forests in Burma, it was ascertained that the following percentages of sound trees are likely to survive and be available for utilisation : — Class I. over 7 feet girth = 95 per cent. „ II. 6 feet to 7 feet „ = 85 „ III. 4 feet 6 inches to 6 feet „ = 70 „ IV. 3 feet to 4 feet 6 inches „ = 50 „ V. 1 foot 6 inches to 3 feet „ = 25 „ giving the following numbers of trees available for utilization : — Class I. = „ II. = 29,947 15,397^ III. = 29,938 1 IV. = 50,869 j 133 ' 932 - V. = 37,728] Total 163,879 288 DETERMINATION AND REGULATION OF THE YIELD. As it requires 125 years to pass a tree of 1 foot 6 inches girth into the first class, the average number of trees passing annually into the first class would . 133,932 . ._. , be — tv^ = 1,0/1 trees a year. 12o J There is evidently a surplus of trees over 7 feet girth, as it is not necessary to keep more than half the average yield of a period of such trees standing in the forest, or 1,071 X 16 = 17,136. The balance, 29,947 - 17,136 = 12,811 trees, might be removed in addition to the actual increment. Assuming that the surplus of growing stock in the first class were removed during the first period of 32 years, or 400 trees annually, the theoretically correct yield would amount to : — Yield representing the annual increment = 1,071 trees „ „ removal of surplus stock = 400 ,, Total permissible yield, annually = 1,471 trees. As a rule, it is desirable, for other reasons, not to work up to the full theoretical yield. On the one hand, certain trees never reach a girth of 7 feet, while, on the other hand, trees of 8 or 9 feet girth yield much higher prices per cubic foot than smaller trees. In many cases, some mature trees must be left standing to provide seed for regeneration. Hence, the actual yield has, in this instance, been fixed at 1,000 trees annually, for a term of 32 years. 3. Division of the Forest into Fixed Annual Coupes. Under this method the area of the forest, or working section, is divided into as many annual coupes as there are years in the rota- tion, and each coupe is marked on the ground. Every year one coupe is cut over, giving the annual yield of final returns, to which must be added the necessary thinnings in the other coupes. The A size of each annual coupe is = — if the area is at once restocked, A or = — — — if each coupe lies fallow for s years. In either case, the area of the coupes should be so fixed that all have the same yield capacity (see page 245). The system was introduced into French and German State forests about the middle of the eighteenth century. The merits of this method are small. It aims more directly than any other method at the establishment of a regular series of age gradations, which becomes normal after one rotation if the division of the area is based upon the reduced area of the several parts. It achieves this object only by heavy sacrifices, because ALLOTMENT OF WOODS TO PERIODS. 289 the returns during the first rotation must be very uneven, unless at the outset a proper proportion and distribution of the age classes existed. The method takes no notice of disturbances, nor of the state of the market ; hence, it is very rigid. Above all, it neglects to a considerable extent the fundamental principle that the most important measure must always be the establishment of the normal increment within the shortest possible period of time. The method is applicable to coppice woods, coppice with standards, and, with modifications, to selection forests ; for all other methods of high forest it is unsuited, except perhaps for clear cutting with a short rotation. 4. Allotment of Woods to the Different Periods of one Rotation. In order to remove the great rigidity of the fixed annual coupes, and to obtain a method which is suitable for the treatment of high forest, especially if managed under one of the shelterwood 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 contains from 10 to 30 annual coupes. In this way, the forest is divided into as many lots as there are periods in the rotation ; during each period one of these lots is dealt with. Thus, operations extend over the whole area once in each rotation. 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 compartment uniform. It is evident that during the first rotation the total yield is represented by the growing stock which happens to stand in the forest at the commencement of operations, plus that part of the increment which is added to it during the course of the first rotation ; it may be equal to, smaller or larger than, the normal yield. An essential part 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 to be cut over. The allotment can be made according to area, volume, or the two combined, so 290 DETERMINATION AND REGULATION OF THE YIELD. that practically three different methods exist, which must be described separately. The regeneration of the woods placed in each period can be effected by clear cutting and planting, or by natural regeneration under a shelterwood. a. The Method of Periods by Area. (First developed by H. Cotta in Saxony early in the nineteenth century.) The woods of a forest are so allotted to the several periods of one rotation that each contains the same or approximately the same area, called the " periodic coupe." Where few or no differences exist in the quality of the locality in the different parts of the forest, the size of each periodic coupe will be = — , where t represents the number of periods in the rotation. If 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 arrange- ment 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 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 volume calculated, and the increment for half the number of n years in the period, -5, added. The total of the volume thus A obtained is divided by the number of years in the period n, so as ALLOTMENT OF WOODS TO PERIODS. 291 to obtain the average of the final annual yield during the first period. To this amount the thinnings must be added. For an example, see Appendix V., A„ where the working plan for the communal forest of Krumbach, a village in Hesse-Darmstadt, is given. This working plan has been actually followed 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 uneven returns during the first rotation, though this can to some extent be avoided by suitable shif tings. Although the method is much less rigid than that of fixed annual coupes, it is often difficult to produce during the first rotation a proper grouping of the age classes. Another disadvantage is that a surplus of growing stock 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. The method gives only a limited latitude to the forester to hold over vigorous woods, or to cut over at an early date those which are deficient in increment. For a financial management, the method is only moderately adapted, except in so far that it intro- duces order into the management. b. The Method of Periods by Volume. This method was developed by G. L. Hartig during the end of the eighteenth and the beginning of the nineteenth centuries. The woods of a forest are so allotted to the several periods of a rotation that each yields the same or approximately the same volume. In some cases, only the final returns are thus regulated ; in others, the intermediate returns are utilized to equalise the yields of the several periods. The allotment is based upon the table of age classes ; then shift- ings are made, so as to bring woods which have a poor increment early under the axe and establish, as far as practicable, a suitable grouping of age classes ; then further shiftings are made, so as to equalise the periodic returns. The result represents the general working plan for the first rotation. It will be found that, in the majority of cases, the areas placed in the several periods 292 DETERMINATION AND REGULATION OP THE YIELD. will be uneven, resulting in uneven returns during the second rotation, unless a fresh allotment is made. Example. — In Appendix V., B., only the final returns have, for sim- plicity's sake, been equalised. The data are those of the Krumbach communal forest given in Appendix V., A. As the future returns have to be estimated for a whole rotation, it is evident that yield tables must be used ; accordingly, the above general working plan has been based upon the returns for beech high forest, given at page 361. After making the shif tings indicated in the general working plan, the volumes allotted to the several periods stand as follows : — Periodic Yield. Annual Yield. Area in the Period. Cubic Feet. Cubic Feet. Acres. Period I. = 201,740 10,087 340 II. = 207,421 10,371 32-5 „ III. = 210,932 10,547 30-5 „ IV. = 206,180 10,309 300 V. = 212,286 10,614 330 Total = 1,038,559 1600 Mean periodic area — 320 An attempt to equalise the returns further would necessitate the cutting up of compartments, which is not desirable. The areas placed in the several periods are uneven, and fresh shiftings may have to be made later on, so as to equalise the returns during the second rotation. 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 genera- tion more fully. On the other hand, the estimate of the future returns is more or less problematic, so that the equalisation 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. It may also drag a surplus or deficit 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 generally takes several rotations to accomplish this, but the difference from the normal state is very small by the end of the first rotation. As regards its financial aspect, it stands on about the same footing as the method by area. THE AUSTRIAN ASSESSMENT METHOD. 293 c. 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 equalisation of the periodic areas and returns is effected, either by adding columns for the volume to the general working plan used for the method 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. It will be easily understood that such an equalisation is a difficult operation, especially in a very abnormal forest ; hence, more than an approximate equalisation cannot be attempted. The method shows some of the advantages and disadvantages of the two previous methods of which it is a combination. Its principal disadvantage is that a suitable grouping of age classes is still more difficult than in the case of each of the two component methods. In practice, various modifications of the above three methods have been evolved which sometimes partake more of one and sometimes more of another of the methods. THE FORMULA METHODS. The next four methods, numbers 5, 6, 7, and 8, determine the yield by a formula, based on the increment laid on and any difference between the real and normal growing stock. Having thus ascertained the yield, the woods for cutting during the next period are selected in accordance with silvicultural considerations and other requirements. No provision is made in them for the drawing up of a general plan of operations for a longer period than suits the special requirements of each case. Of a considerable number of methods coming under this heading, only the four mentioned above need be described here ; the others are either modifications of these, or of limited practical value. 5. The Austrian Assessment Method. In the year 1788 (during the reign of the Emperor Joseph II., one of the most enlightened sovereigns known in history) the 294 DETERMINATION AND REGULATION OF THE YIELD. Austrian Government issued instructions regarding the assessment of forests for the purpose of taxation. In these instructions refer- ence 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 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 estab- lish the normal growing stock — in other words, to remove 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 for a time ; if the real growing stock is smaller than the normal, less than the real increment should be utilized, 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 increment of a series of years. (2.) The normal growing stock is placed equal to the normal 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 G n = I x-y, calculated for the middle of the growing season. Here I represents the normal annual increment of all age gradations, which is equal to the volume of the oldest age gradation. (3.) The real growing stock is obtained by multiplying the real THE AUSTRIAN ASSESSMENT METHOD. 295 final mean annual increment by the present age of each age gradation. For this purpose it is necessary to determine for each wood the real final age and the volume at that age. (4.) The difference between the real and normal growing stock is removed during such period as the owner, or forester, may determine according to the circumstances of each case, more especially the conditions of the market. (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 : — . 1V . ,. . T . . real Gr. Stk.— norm. Gr. Stk. Annual Yield = real Increment -\ Y = I re al + wr real tr normal If G T <.G n , then the last position becomes negative. 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 most other 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 incre- ment, whenever the normal growing stock is present. (3.) It distinguishes in the yield between increment and growing stock ; in other words, between the removal of genuine annual increment and that of surplus capital. On the other hand, the method, as above described, has serious drawbacks : — (1.) The calculation of the real and normal growing stock, based upon the final mean annual increment, is not correct and not even safe. As, however, both are calculated in the same manner and one is deducted from the other, the error is to some extent eliminated. (2.) As the yield is determined by a formula, the method, if rigidly applied, may lead to absurd results : for instance, it may happen that a full increment takes place, that numerically the real growing stock is equal to the normal 296 DETERMINATION AND REGULATION OF THE YIELD. growing stock, and yet there may not be a single mature wood in the forest available for cutting. The method is, however, one of considerable merit, provided it is somewhat modified, that is to say, if : — (1.) The real growing stock is taken as that actually existing in the forest, and the normal growing stock is calculated from a suitable yield table. (2.) The yield as calculated with the formula is modified to suit the special conditions of each case — in other words that final cuttings are reduced, or even suspended for a time, if the area of mature woods is below the normal amount. The method gives to the forester full liberty to arrange the cuttings in accordance with the silvicultural requirements of each wood, and to arrange the grouping of the age classes and cutting series in the most desirable way. The method is applicable to all silvicultural systems, but the determination of the increment involves much labour, if it is to be accurate. Under it a forest is gradually lead over to the normal state, though perhaps not for a considerable time ; the difference between the real and normal state will be very small at the end of the first rotation. The sample working plan given in Appendix VI. is based upon the formula of this method. The plan has actually been carried out in a part of the Herrenwies Range in Baden. 6. Heyer's Modification of the Austrian Method. This method was originally designed by Carl Heyer ; it rested on the Austrian method. Subsequently it was further developed, especially by Gustav Heyer, until it became a combination of the Austrian method and the allotment of woods to periods by area. It is generally known as " Heyer's method." Its theory is as follows : — (a.) To arrange all woods into a general working plan according to periods, so that each period contains the same or approxi- mately the same area. The object of this arrangement is to equalise the increment during the second and subse- quent rotations. (6.) To equalise the real and normal growing stock, if any heyer's modification. 297 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 series of years, plus or minus the quota of growing stock determined under (6). It is obvious that these objects can be realised only by a com- plicated procedure, and even then only approximately, because changes in one direction disturb the balance in another. 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 equalise the areas by suitable shiftings, as indicated under the method of periods by area ; care being taken to allot the woods, as far as this is practicable, with due consideration to silvi- cultural requirements, and a proper distribution of age classes. (b.) The real increment is placed equal to the real final mean increment, for which purpose it is necessary to determine the final age of each wood (which may differ from the normal final age) and its probable volume at that age ; the latter divided by the former gives the mean annual incre- ment. In order to avoid having to calculate the increment year by year, it is generally calculated for a number of years, which may be called a'. If an abnormal wood is cut over during the a' years at an age differing from the normal, and a normal wood grows up in its place, the incre- ment 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 = — » — > where / represents the normal final mean 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. 298 DETERMINATION AND REGULATION OF THE YIELD. (d.) The theoretical yield is then fixed by the formula — y _ Real Increment of a' years .G re ai — G , norm. a 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 formula goes over into — v & real ~r ^ real — & tiorm. (e.) The next step is to ascertain, whether the woods pre- liminarily placed in 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 shif tings 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 requirements of the method are realised, that is to say, until each period contains the same area, and at the same time the volume necessary to meet the yield as calculated under (d.) As already indicated, the forester must, in this respect, be satisfied with approximate results. (/.) The regulation of the yield is restricted to final returns. The intermediate returns are estimated only for the first period, or part of it, by means of yield tables, or past experience, and added to the final yield. The method is one of great precision. On the other hand, it is very complicated, and it calculates the increment, as well as the normal and real growing stock, incorrectly, as in the case of the Austrian method. The latter objection could be removed by using suitable yield tables, instead of the final mean annual incre- ment, 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. hundeshagen's method. 299 7. Hundeshagen's Method. Hundeshagen's method of determining the yield is based upon the idea that the real yield must bear the same proportion to the real growing stock as that existing between the normal yield and normal growing stock ; he thus obtains the equation — J- real ' 0» real == J- norm. • tr norm and * r == «> X "7=r. (r„ In words, the real yield is equal to the real growing stock multi- plied by the normal yield and divided by the normal growing Y n 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, whereas the ... . Y„ utilization per cent, is -^- X 100.) 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 ; by the real growing stock Hundeshagen understands that which is actually standing in the forest. In applying the method, Hundeshagen prepares a general working plan, for a limited number of years ; he determines the species, silvicultural 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 5 or 10 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 remeasure the growing stock every year, but, as the changes are slow, Hunde- shagen considers it sufficient if the remeasuring is done once every 20 or 30 years. Hundeshagen determines, in the manner above described, only 300 DETERMINATION AND REGULATION OF THE YIELD. the final returns ; he adds the intermediate returns, estimated in a summary manner, or calculated according to average data obtained locally. The principal assumption of Hundeshagen is not quite correct ; at any rate, there is no justification for maintaining that the real yield bears the same proportion to the real growing stock as the normal yield to the normal growing stock, because the rate of increment is not determined by the quantity of growing stock which stands in a forest. On the contrary, a large growing stock consisting of defective old woods may give a small increment, while a small growing stock consisting of vigorous young woods may show a large increment. The method, if applied rigorously, may lead to absurd measures, just in the same way as the original Austrian method ; it pre- scribes a definite annual yield, while not a single mature wood may be present ; or it prescribes too small a yield, whenever a con- siderable portion of the area is stocked with decrepit old woods which ought to be cut over as quickly as possible and replaced by vigorous young woods. In all such cases, the yield, as fixed by the formula, must be modified in accordance with the requirements of each case. The method does not distinguish in the yield between incre- ment and surplus growing stock, and in this respect it stands below the Austrian method. Moreover, it may drag a surplus of growing stock over an undefined period. Hundeshagen assumes that, with the yield calculated according to his method, the normal growing stock will be established automatically, 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 in all circumstances. If, for instance, both the increment and growing stock are deficient, the yield may be greater than the increment, so that the growing stock is still further reduced, at any rate for a time ; hence, the establishment of the normal state may be considerably delayed. On the other hand, Hundeshagen 's method has this great advantage, that the increment need not be determined, such an operation being at all times beset by difficulties and uncer- tainty. All that the method requires is a suitable yield table, and von mantel's method. 301 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 yield determined by the formula need not be rigorously cut. It may reasonably be assumed that Hundeshagen himself expected this. 8. von Mantel's Method. Von Mantel, in arranging for the speedy determination of the yield of certain forests in Bavaria, laid it down that this should be done according to the formula — Real Growing stock of the forest _ G rea i Half the number of years in the rotation r ~2 It is based on the assumption that approximately twice the growing stock is removed in the course of each rotation, as has been mentioned above. This formula rests upon the same basis as Hundeshagen's method, if for the latter the normal growing stock is calculated with the final mean annual increment as in the Austrian assess- ment method. Hundeshagen's formula — Y n J- == Ixreal X 77- in that case goes over into — •* == y^real X i- n l^real r r The cutting of the yield according to von Mantel's formula will gradually lead to the establishment of the normal growing stock, as the following considerations will show : — Supposing the real growing stock, by which von Mantel under- 302 DETERMINATION AND REGULATION OF THE YIELD. stands that actually present in the forest, is equal to the normal growing stock, then his formula goes over into — Y = The formula gives, therefore, the correct yield, provided the increment is normal. If the actual growing stock is smaller than the normal, say Great = — ~ x, then r X I —5 x r = -? =i-l r r 2 ¥ which means that less than the increment is cut. Supposing that the real growing stock is greater than the normal : G rea i = ~ h x ; then, r X 2 - 7 +. = / + X r ~2 r 2 Y = more than the increment will be cut, so that the surplus of growing stock will gradually disappear. All these assumptions depend, however, on the supposition that the normal increment is laid on. If the increment is deficient, the abnormal state may be further increased until the increment has reached its normal size. The merits of the method are approximately those of Hun- deshagen's method. The normal growing stock and normal yield need not be determined ; in other words, the method can do without yield tables. It is only necessary to measure the growing stock and to determine the rotation ; hence, the method is very simple in execution. the compartment, or uniform, system. 303 9. The Compartment, or Uniform, System. Selection of Woods for Cutting according to Silvicultural Requirements and the Objects of Management. The system was developed by degrees in Saxony from Cotta's time onward, and put into a definite shape by Judeich. It is known as Judeich's " Bestandswirthschaft." By " Bestand " is understood a part of a forest of about the same description which ordinarily is treated in a uniform manner ; it may comprise a sub- compartment, or a compartment, or more than one compartment. The main character of the system is that each " Bestand," or wood, is treated on its own merits throughout its life, and that the yield of the whole forest represents the sum total of the returns prescribed for the several compartments (or other units of division). In introducing the system, the first step is to divide the forest into a suitable number of compartments, including an appro- priate system of roads and rides ; the latter need not be all con- structed at once, but can be taken in hand as they are required by the progress of the work. In designing the system of roads and rides, special attention must be paid to a suitable arrangement of the age classes, both in size and grouping. Next, each compartment is examined and its future treatment for a limited number of years indicated, with due consideration for its silvicultural requirements. The estimates of the projected final cuttings in the several compartments are added up, and they represent the final yield during the next, say, 10 years, unless considerations for a sustained yield in the future demand certain modifications. The method aims chiefly at the establishment of a full increment and a proper arrangement of the age classes ; these given, the normal growing stock comes of itself. An important point is to determine the working only for a short period, and to improve it at each revision in the fight of past experience. The requirements of each compartment can be reconsidered, and the establishment of the necessary cutting series developed. The latter point is of special importance in coniferous forests. It provides a sufficient number of points of attack, and gives the forester a free hand to deal with each wood at the right time. 304 DETERMINATION AND REGULATION OF THE YIELD. If the area of the forest is considerable, or consists of pure woods worked under different rotations, the forest may be divided into two or more working sections. Each of these should be dealt with separately, and a special account kept of it. The system is equally applicable to the method of clear cutting and to that of regeneration under a shelterwood. a. Short Description of the Two Methods. Under the method of clear cutting, the new wood is originated on an area clear of trees, by direct sowing of seed or by planting, or occasionally by seed coming from adjoining woods. The trees on each gradation are all of the same age and height, or nearly so. From the time when the branches begin to interlace, they form an uninterrupted leaf canopy overhead throughout life, favouring the formation of trees clear of branches to a considerable height. The extent of this depends on the original degree of density, the species, the quality of the locality and the degree of thinning. The effect of protection given by the wood to the producing factors of the locality differs with the age. During early youth, the soil is exposed to the full effect of the sun and air currents. Subse- quently, when the leaf-canopy has been established, its beneficial effect is of a high degree, but when, with advancing age, the crowns have been elevated, air currents pass through the wood and may reduce the activity of the locality, chiefly through the loss of mois- ture in the soil (see Fig. 52, page 209). The clearings should be of moderate extent, and one should not adjoin a previous one except after the lapse of several years. Frost, drought, insects and air currents are likely to do much damage during the early years of the wood. The production of wood compares favourably with that of other high forest systems, and the quality of the timber is of a high class, provided that the thinnings are carried out in a judicious way. Under the shelterwood method, the wood is regenerated under the shelter of the whole or part of the old crop, which is retained until the new crop has established itself and is safe against in- jurious external influences peculiar to early youth. The regenera- tion is effected by the seed falling from the shelter trees, assisted, if necessary, by sowing or planting. In some cases the latter may THE COMPARTMENT, OR UNIFORM, SYSTEM. 305 be done at once without waiting for a seed year. In many cases there is a difference in the age and height of the new crop, which, however, is no longer discernible by the time the wood has reached middle age. This system has the advantage over the clear cutting system in providing good protection to the young crop during early youth against frost and drought and, in many cases, also against insects. When once that period is passed there is prac- tically no difference between the two systems. The shelter trees generally increase rapidly in diameter or girth, owing to their more open position ; on the other hand, the shelter trees are liable to be thrown by wind, and their ultimate removal frequently does some damage to the new crop. b. The General Plan of Operations. This plan gives the division of the forest into units of working, generally called compartments. They should be numbered con- secutively — that is to say, by one series of numbers throughout each working section, if not throughout the whole forest. The compartments are marked off by natural or artificial lines, of which one at least should, if possible, abut on a road, or other means of transport. This plan enables the forester to determine, in a general way, the order and direction in which the cuttings should proceed, and the grouping together of compartments into suitable cutting series, especially in the case of clear cuttings. In some cases, temporary cutting series may have to be designed which, at the time of revision, will be changed into more permanent groupings. c. Determination of the Rotation. The method of determining the rotation has been explained on pages 188 to 195. It differs from that followed by Judeich, who adopted the financial rotation for the Saxon forests. Experience has shown that short rotations, in connection with clear cutting, lead to a reduction of the yield capacity of the locality, except on really fertile lands, and these are rarely placed at the disposal of the forester. The rotation should be fixed with due regard to local conditions and the class of produce which the proprietor desires to grow. At the same time, it is desirable to inform the pro- prietor of the temporary financial loss due to a departure from the jh. x 306 DETERMINATION AND REGULATION OF THE YIELD. financial rotation. Such loss is, as a rule, in the long run, more than recovered by the maintenance, and even improvement, of the fertility of the locality. d. Determination of the Final Yield. The woods in which final cuttings during the working plan period are to be made should be selected with due consideration for the desired cutting direction and the establishment of suitable cutting series. No woods should be selected the removal of which would expose adjoining woods to damage by windfalls, unless they are also to be cut during the working plan period. Subject to these considerations, the following areas would be selected : — (1.) Areas to meet silvicultural or other necessities, such as the establishment of severance cuttings, woods interfering with the establishment of a proper grouping of age classes or cutting series, proposed road lines, etc. (2.) All decidedly ripe woods, as determined by the objects of management. (3.) Woods the ripeness of which is doubtful, or 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 being 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, the regular supply of markets, or the occupation of the staff and workmen necessitate an approxi- mately even annual out-turn. Here, the yield, as determined above, must be subjected to a modifying regulator, either as regards the area to be cut or the volume to be removed during the working plan period. This regulator can take any suitable shape, such as the size of the mean annual or periodic coupe, or the yield calculated accord- ing to volume and increment, or both. 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 THE COMPARTMENT, OR UNIFORM, SYSTEM. 307 under a general rotation of 80 years, the mean annual coupe would be equal to -^— = 25 acres. During a working plan period of 10 years, the normal cutting area for it would amount to 25 X 10 == 250 acres. In other words, during a period of 10 years, 250 acres should be cut over or taken under regeneration, and the areas selected as indicated above should be brought within that limit. This, however, is desirable only if the propor- tion of the age classes is fairly normal. In all cases where con- siderable deviations from the normal proportion exist, such a narrow limit cannot be drawn, because in some cases it is highly desirable to deal with more than the normal area, if, for instance, too large a proportion of old or defective woods exists, or regenera- tion proceeds slower than expected. In other cases, the cuttings should be below the normal area, if, for instance, the area of mature woods is deficient. Hence, the regulator should give merely the maximum and minimum area or volume to be dealt with. In the above case, the area might be given as 200 to 300 acres, or corresponding volumes. As long as the total area determined under (1.) to (3.) falls between these limits, it may be accepted as the area to be dealt with during the first 10 years. If it is larger than the maximum, then some of the most suitable areas enumerated under (3.) should be held over until the second period of 10 years ; if smaller than the minimum, then possibly some further woods may be found which could be added to those already placed under (3.). In extreme cases, the yield may be kept for a number of years below the proper minimum. Example. — Let the age classes in the above example be as follows : — Age Class. Nonrjal Distribution of Areas. Acres. Real Distribution of Areas. Acres. 1—20 500 22) ™ 21—40 500 41—60 500 Z\ wo" Over 60 500 Total = 2,000 2,000 As there is a considerable excess of old woods, the area to be cut, or taken under regeneration, every 10 years should be more than -^ — = 308 DETERMINATION AND REGULATION OF THE YIELD' 250 acres. Indeed, for the next 20 years up to 300 acres might be cut or placed under regeneration during every 10 years. The result would be as follows : — After 10 Years. After 20 Years. Age Class. Acres. Acres. 1-20 =5001 =5501 975 21-40 =350/ 850 =425/ *' & 41-60 =500) , 150 = 425) . Q2 Over 60 = 650/ U5 ° = 600/ 1j ° 25 Total = 2,000 2,000 After that, 250 acres might be put under regeneration during every 10 years, so that, at the end of 30 years in all, the distribution of the age classes would be : — After 30 Years. Age Class. Acres. 1-20 = 525) 21—40 = 487 J lf °" 41-60 = 4251 Over 60 = 563/ 2,000 The deviations from the normal distribution still existing will disappear by continuing to cut about 250 acres every 10 years. e. The Intermediate Yields. The limit between final and intermediate yields is not always easy to define. 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. (b.) All returns from other woods which, in consequence of unforeseen causes, are so large that the regenera- tion of the woods becomes necessary, whether it is done during the working plan period or later on. (2.) Intermediate yields comprise all other returns derived from — (a.) Cleanings. (6.) 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 THE COMPARTMENT, OR UNIFORM, SYSTEM. 309 put down for regeneration during the working plan period, or are of such extent that they come under sub-head (1 &.), above. The woods to be cleaned and thinned are put down according to their areas. The quantity of intermediate yields is best esti- mated according to past local experience, with due consideration of the condition of the several woods. Where the necessary local data are not available, the most suitable average data obtained elsewhere must be used, or an estimate made in accordance with the condition of the woods. 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 regu- lated by the final cuttings. At the same time, the intermediate yields may be utilized to equalise any unavoidable inequalities of the final yield. In any circumstances, 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. The total yield of the working plan period is suitably divided amongst the years comprised in it. /. Separation of Yield into Classes of Produce. The yield should be separated according to classes of produce as it is brought into the market, say as timber and firewood, or large timber, poles, mining props, faggots, etc., each being given in cubic feet. This separation should be based upon locally- obtained proportional figures. It is also desirable to give separately the yield of the important species — as, for instance, oak, other broad-leaved species, larch, other conifers, etc. In India, teak, sal, deodar, and some other valuable species should always be given separately. g. Example. Given an area of 4,000 acres stocked with spruce = 90 per cent., silver fir = 4 per cent., beech = 2 per cent., and blanks = 4 per cent. The latter are due to the necessity of allowing the cut areas to He fallow for two years, 310 DETERMINATION AND REGULATION OF THE YIELD. on account of the presence of pine weavila. The silver fir and beech are found over the whole area in single trees, so that the forest repre- sents practically an almost pure wood of spruce. The forest has been divided into 100 compartments, with an average area of 40 acres each. As the work proceeds it is proposed to arrange these into 25 cutting series of an average area of about 160 acres (see Figure No. 53, on page 211). This arrangement will enable the forester to select at all times for regeneration those parts of the forest which are in the greatest need of treatment. The age classes are represented in the following proportion : — Age Classes. Normal Area. Actual Area. 1—20 21-hH) 41—60 Over 60 Blanks Total area . . 1,000 1,000 1,000 1,000 Lioo] 1800 700 f 1 ' 800 800 12 100 1,300 [ A1UU 100 4,000 4,000 The local value of the soil was ascertained to be £10 per acre. An examination of the average height growth of typical woods showed that the soil must be classed as I. quality, to which the following normal yield table would apply : — Age. Years. Mean Height. Feet. Mean Girth. Inches. Yield in Cubic Feet, Per Acre. Timber. Total. Mean Annual Forest. Per Cent. Final. Thinnings. 30 40 50 60 70 80 51 66 80 91 100 106 23 33 42 50 56 60 3,500 5,250 6,760 8,020 8,960 9,400 410 925 960 860 665 500 3,910 6,175 7,720 8,880 9,625 9,900 2-4 3-7 40 41 40 3-9 Total t hinnings .. 4,320 From the data given above, the mean annual forest per cent, has been calculated and placed in the last column. It will be noticed that the maxi- mum mean annual forest per cent., 4-1, is realised under a rotation of 60 years, which is, therefore, the financial rotation. Under it the average girth of the trees comprising the final crop amounts to 50 inches. The proprietor desires, however, to secure a mean girth of not less than 60 inches^ for which a rotation of 80 years is required. In adopting that rotation the proprietor reduces the mean annual forest per cent, by 4-1 — 3-9 = -2 per cent. THE COMPARTMENT, OR UNIFORM, SYSTEM. 311 The normal annual coupe amounts to ' = 50 acres, that for the first OK) period of 10 years to 50 X 10 = 500 acres. On a detailed examination cf all compartments, it was found that, for silvicultural and protective reasons, the following areas require to be dealt with during the first 10 years : — (1.) Silvicultural and protective necessities. . 90 acres. (2.) Woods ripe and over -ripe .... 400 „ (3.) Woods of doubtful ripeness or woods which may become ripe during the first period . 50 „ Total 540 acres. This is 40 acres more than the normal area ; hence, the area given under (3.) above may be kept back for treatment during the second period of 10 years. As there is, however, a surplus of 100 acres of woods over 40 years old, the area of 540 acres may stand to be dealt with during the first 10 years. The yield during the next 10 years consists of the following items : — (1.) The volume standing on the 540 acres to be finally cut and re- generated. (2.) Five years increment on these 540 acres. (3.) The estimated receipts from thinnings in the remaining areas during the 10 years. The total number of cubic feet obtained from these three items, divided by 10, gives the average annual yield. These data are obtained by actual measurements in the forest. To explain the process in this place, the above yield table is used. Assuming that each wood at time of cutting is 80 years old, the final cuttings during 10 years would amount to 9,900 x 540 = 5,346,000 cubic feet. The sum of 9,900 cubic feet includes the thinnings between the years 70 and 80 (as well as 10 years increment) which would ordinarily be made. The area to be thinned in 10 years may be estimated as that stocked with timber between the ages of 20 and 70 years old, namely : — Area in the age class 21 — 40 == 700 acres. „ 41—60= 800 „ „ over 60 = 760 (being 1,300 - 540). Total area to be thinned in 10 years = 2,260 acres. Assuming that one-fifth of this area, or 452 acres, is thinned at each of the ages of 30, 40, 50, 60 and 70, the total yield of thinnings would be estimated as follows : — 10 Thinnings at the age of 30 years = 410 X 452 = 185,320 cubic feet. 40 „ = 925 X 452 = 418,100 50 „ = 960 X 452 = 433,920 60 „ = 860 X 452 = 388,720 70 „ = 665 X 452 = 300,580 Total of estimated thinnings . . 1,726,640 cubic feet. 312 DETERMINATION AND REGULATION OF THE YIELD. Repetition : — Final cuttings. Total = 5,346,000 Annual average . 534,600 Thinnings . „ = 1,726,640 „ „ . 172,664 Grand Total = 7,072,640 Annual average = 707,264 This is equivalent to an average annual return of 177 cubic feet, represent- ing an efficiency of 100 per cent. With an efficiency of 80 per cent., which can easily be obtained in spruce woods of I. quality, the return would be reduced to 142 cubic feet, and with one of 70 to 122? cubic feet per acre and year. ' *f h. Notes. Under the uniform or compartment system, as described above, the regulation of the yield is effected by area, with due considera- tion for the proportion between the several age classes. The method is extremely simple, and leads to the establishment of the normal state of the forest. Other methods of regulation are, however, not excluded, as long as they lead to a sustained yield. A method frequently employed is to compare the yield calculated by area with the increment, and, if the two differ, to take the mean of the two and adjust the area to be regenerated accordingly. In other cases, the Austrian method is used for the calculation of the yield, and a corresponding area selected for regeneration. The calculation of the yield for the uniform, or compartment, method with natural regeneration is practically the same as that for clear cutting, provided that the regeneration is completed during the working plan period. As a rule, this is not the case, and a part of the shelterwood has to be carried over into the next period ; on the other hand, a corresponding quantity has been taken over from the previous period ; it may be assumed that the one makes up for the other. It may occur that the regeneration period extends over two, three, and even more periods of 10 years. In all such cases the yield during the first period of, say, 10 years is calculated as follows : — (1.) Yield calculated as in the above example, 7,072,640 cubic feet. (2.) Plus amount of shelterwood taken over from previous periods, say 150,000 cubic feet. (3.) Minus amount of shelterwood likely to remain at end of the period, and to be carried over into second period, 200,000 cubic feet. a. (4.) Yield during first period = 7,012,640 cubic feet. MODIFICATIONS : THE QUARTIER BLEU SYSTEM. 313 The total amount, divided by 10, gives the average annual yield during the period 70t,'264 cubic feet. For an example of such a calculation see Appendix Y.A, . j* £ 8? 10. Modifications of the Compartment System. In the course of time a considerable number of modifications of the compartment system have been elaborated. Some of these try to obviate certain disadvantages of the uniform system, others to meet special local conditions, and others are the outcome of personal fancies. The more important modifications will here be shortly described. They are : — (a.) The French System known as the Quartier Bleu. (b.) The Group System. (c.) The Strip System. (d.) The Strip and Group System. (e.) Wagner's Blendersauinschlag. (/.) The Wedge System. With the exception of the first, the determination of the yield is effected in the same way as in the case of the compartment system. a. The French Quartier Bleu System. This modification of the shelterwood compartment system is based on the same principle as has been explained above, but differs somewhat in the manner of selecting the areas to be placed under u.ilurnJ regeneration. Instead of placing every 10 years a proportionate area under regeneration, under the quartier bleu system the average duration of regenerating a compartment is estimated. In dividing the rotation by that figure, the proportion of the area to be placed under regeneration is obtained, and that portion is kept up throughout the rotation. Taking the latter at 100 years, and the average duration of re- generation at 20 years, the regeneration area would be = -^ = the fifth part of the area. If, for instance, the forest has an area of 1,000 acres, the regeneration area would amount to = 200 acres. That area is selected and painted blue on the forest map (hence the name), while the rest of the area remains uncoloured. From time to time — say, every 10 years — the 200 acres are 314 DETERMINATION AND REGULATION OP THE YIELD. examined, any parts on which regeneration is complete are taken out of the blue quarter, and a corresponding area from the uncoloured part added to it. It is essential that regeneration should proceed at such a rate that it passes over the whole area of the forest in the course of one rotation. The determination and regulation of the yield is done in some cases by area with a volume check, in others according to the French Ordinance of 1883. The latter was really designed for selection forests ; its principle is as follows : — The exploitable girth, say 60 inches (representing the rotation), is divided into three equal parts or classes : Class I. = 1 — 20 inches, Class II. = 21 — 40 inches, Class III. = 41 — 60 inches. If the volume of the three classes were in the proportion of 1 : 3 : 5, the forest would be considered to be in a normal condition, and the volume in Class III. would represent the normal yield during the next 20 years. To test the matter, the trees of the II. and III. classes are enumerated and the volume in each of the two classes calculated. If their contents are found to be in the proportion of 3 : 5, the forest is assumed to be normal. If the proportion differs from 3 : 5, a sufficient number of trees is transferred from one to the other until that proportion is established. If the stock of the II. and III. classes are found to be above normal, the excess must be removed and the probable deficiency in the first-class trees made good, until the proportion between the three classes becomes as 1 : 3 : 5. It appears that in most of these cases the yield has been much underestimated in the past, probably the result of the somewhat uncertain method of calculation. The following five systems owe their origin to the endeavour to obviate certain shortcomings of the uniform system of regenera- tion if applied to a considerable area, say a whole compartment, at one and the same time. If in such cases seed years come at the time when they are wanted, all goes well ; but if there is much delay in their arrival, or if (for other reasons) the regeneration should not be successful, the forester has left on his hands an opened-out area deteriorating under the effects of sun and air currents. Such areas have frequently to be restocked artificially. To avoid this disadvantage, or at any rate to minimise it, it is desirable to reduce the area taken in hand in the first place to a number of small groups or a narrow strip, or the two combined. TEE GROUP SYSTEM. 315 b. The Group System. With a view to reducing the area opened out in a wood under regeneration to a minimum, only small or moderate-sized groups are taken in hand, and when these have been regenerated others are taken up, and so on until the whole compartment, or wood, has been regenerated. An alternative method is to remove the old wood over any groups of advance growth and enlarge them from Fig. 59. — Showing a group with its height decreasing from right to left, joining a second group on the left. time to time until the several groups join. In most cases both methods are combined. The regeneration period under this system is generally much longer than under the uniform system, extending frequently to 30, 40, and even more years. Consequently, the regeneration area must be correspondingly increased (see page 306 of this volume). c. The Strip System. Instead of groups scattered over the compartment, a strip is taken in hand at starting. Its breadth should not be more than 316 DETERMINATION AND REGULATION OF THE YIELD. twice the height of the wood and frequently not more than once ; it may, however, be of any length. The first strip should be situated at that end of the compartment where it is best sheltered either against wind or the sun, or both if possible, according to local conditions. North. u p s f West. Direction of prevailing wind. East. South. Fig. 60. u p s f North. West. East. Direction of prevailing wind. u p s f South. Fig. 61. THE STRIP AND GROUP SYSTEM. 317 In the first year a preparatory cutting (if necessary) is made. A few years afterwards a seeding cutting is made, and a prepara- tory cutting in a second adjoining strip. In the following years the first strip is in the final stage, the second in the seeding stage, and a preparatory cutting is made in a third strip. There are always three strips under regeneration, and in this manner the regeneration proceeds until it reaches the other end of the compartment. d. The Strip and Group System. Under this combined system a strip is taken in hand to begin with, but, instead of dealing with it in a uniform manner, only groups are opened out in it as described for the group system. While these are being enlarged, a series of further groups are com- :h: m m ■ I fl ' if Fig. 62. — Group and strip systems combined. Regeneration commenced on the right and proceeded towards the left. The strip on the extreme right has been cleared of shelter trees. menced in a second strip; in other words, the groups march somewhat ahead of the final clearing of the previous strip. This procedure continues until the further end of the compartment has been reached. e. Wagner's Blender saumschlag. Blendersaumschlag may be rendered in English as " Selection Border Coupe." The method attempts regeneration by a series of narrow strips, each of which is situated at the border of the old wood. In this way regeneration begins at one end of the wood and moves gradually through it until the further end is reached. In this respect the system does not differ from the ordinary strip system described above. There are, however, differences in the nature of the cuttings. Instead of having three distinct stages — the preparatory, seeding, and final — Wagner employs a series of selection fellings which produce a new crop of somewhat uneven 318 DETERMINATION AND REGULATION OF THE YIELD. age in each group. As the system aims at a very high degree of efficiency, it is desirable to give some further details. Wagner, as a decided advocate of natural regeneration under a shelterwood, was much impressed by the shortcomings of the natural regeneration under the uniform compartment system, especially as regards the effect of the sun and climatic factors upon the soil and the young growth, as well as the damage done to the young crop by the removal of the shelter trees. With a view to establishing an improved strip system, he started a long series of experiments and observations, so as to define the extent to which the above-mentioned agencies affected the progress of regenera- tion, and to devise measures for reducing their damage to a minimum. In his inquiry, Wagner paid special attention to the following points : — (1.) The direct effect of the sun on the desiccation of the soil and on the destruction of seedlings. (2.) The desiccating effect of dry east and north-east winds. (3.) The accessibility of light rain (especially from the west) to the regeneration area. (4.) The formation of dew and the length of its retention on the ground. (5.) The exposure of the regeneration area to strong winds. (6.) The removal of the shelter trees without injuring the young growth which has sprung up under their shelter. On the basis of the information thus obtained, Wagner arrived at the following conclusions as regards the effect of exposure from the various points of the compass : — (a.) East and south-east are altogether unfavourable ; the sun penetrates into the inner part of the strip ; light rains from the west do not reach it ; dew is at once dried up by the morning sun; there is much danger from frost; desiccating winds from the east are very injurious. (6.) South and south-west are nearly as unfavourable, but dry east winds do less harm ; south-west sides benefit by light west rains, but receive the full effect of the afternoon sun and suffer from strong west winds, (c.) West is somewhat more favourable ; the midday sun is kept out of it, but it suffers from the afternoon sun and wagner's blendersaumschlag. 319 from western strong winds and gales ; light rains enter it freely. (d.) North-west sides are very favourable ; they give access to light western rains, and are protected against the midday sun and dry east winds, but only partially against western gales ; dew is freely formed and retained. (e.) North sides are very favourable ; they are protected against the sun ; dew forms freely and is retained for a long time ; they rarely suffer from strong winds and only moderately from dry east winds ; light westerly rains, however, reach only the outer part of the strip. (/.) North-east sides are sheltered against the sun during the whole day, except in the early morning ; during the latter time dew is liable to be dried up ; they do not receive light rains from the west, and are exposed to north-east winds. To sum up, Wagner considers, on level and gently sloping ground, aspects between north-west and north-east as favourable for regeneration, those between east and south-west as unfavour- able, while west holds an intermediate position. He proposes that the regeneration of each individual strip should proceed from north to south, and that the progress of the whole operation should proceed from east to west, or from north-east to south- west, as indicated in Figs. 63 and 64. In hilly country the cutting direction depends to a great extent on the local wind direction. To make sure that the border of the old wood, where regenera- tion is expected, points to the north, Wagner gives the edge of the old wood a broken-up shape. If the forward movement is from the north-east to the south-west, the edge presents the shape of a series of steps ; if the movement is from east to west^ the edge consists of a series of triangular openings or bays, as shown in the appended illustrations, Figs. 63 and 64. While regeneration in the first strip is proceeding, the first selection felling in the second strip works somewhat ahead of the strip actually under regeneration, and so on. The number of fellings in each strip is not fixed ; it depends on the progress of regeneration. The removal of the felled trees is effected through the old wood, all trees being thrown in that direction, as shown in the illustrations. In this way, practically 320 DETERMINATION AND REGULATION OF THE YIELD. no damage is done to the young generation.* It remains to add that the determination and regulation of the yield is based on area, as in the ordinary uniform compartment system. Wagner's main object is to reduce the desiccating effect of the III Regeneration from N. to S. [fir Direction in which trees are thrown. milUiWUIIIIIIIII Where regeneration should take place. ^ Where selection fellings are made. S. Fig. 63. — Wagner's Blendersaumschlag Cuttings in the shape of Steps. (After Wagner.) sun on young regeneration to a minimum and to secure as favour- able a degree of moisture in the soil as possible, especially during the growing season. The importance of this has, of late years, been more fully recognised in consequence of unfavourable * Readers who desire further information on the method will find it in Wagner's two works : " Die Grundlagen der raeumlichen Ordnung im Walde " and " Der Blendersaumschlag und sein System," both published by H. Haupp, Tuebingen. THE SYSTEM OF WEDGE FELLINGS. 321 results in attempted regenerations. It has been recognised by foresters that, in order to obtain the best possible results, the soil must be kept under continuous protection in all cases where the rainfall is not favourably distributed over the year ; in other words, that regeneration under a shelterwood, whether natural or artificial, gives, in the long run, better results than clear cutting with subsequent planting or sowing. In Saxony, for PROGRESS OF REGENERATION FROM E. TO W. N. *WW 2 7 4 / 6 , w. .— • / /ndfll^HjIM^/; ... . .-'. -_ ; 5 ,' S —. S I „„ 3 , 5 ,' .^mmM 1 *-- -, - ■-/■- ^^T^^r Si,,, u,n\tnu Fig. 64. — Wagner's Blendersaumschlag Cuttings in the Shape of Bays. (After Wagner.) instance, detailed investigations carried out during the last three years have shown that the woods raised during the last 100 years by clear cutting and planting have produced considerably smaller volumes per acre than those reared formerly under shelterwoods. /. The System of Wedge Fellings. This method, elaborated by Dr. Eberhard at Langenbrand in the Black Forest, is a modification of the strip system, in which the chief objects are : — (a.) To expose the longest possible front to regeneration. (6.) To prevent damage by wind. 322 DETERMINATION AND REGULATION OF THE YIELD. (c.) To avoid damage during the felling and extraction of the produce. Dr. Eberhard produces these effects in the following manner : — On level or gently sloping ground, in each compartment a number of long narrow wedges are felled against the prevailing wind direction. These wedges are from 10 to 15 feet wide, and of any length, but leaving a protection belt at each end of the JL DR. EBERHARDS SYSTEM OF WEDGE FELLINGS. N. L_ w. 8. r Early Stage. Advanced Stage. Fig. 65.— Wedge Fellings. (After Troup.) wedges. Subsequently these wedges are widened by narrow cuttings on each side as soon as regeneration has appeared on the first opening, and this process is repeated from time to time until the borders of the compartment are reached ; at the same time the apexes of the wedges are advanced towards the wind direction until they reach the further edge of the regeneration area. In this way, the several wedges join up and, after the protection belts have been treated in a similar way, the whole area becomes regenerated (see Fig. 65). The produce is removed through the unregenerated parts to the nearest road. It is assumed that if wind enters the wedges it THE COPPICE SYSTEM. 323 escapes as through a funnel towards the east ; also that the wedge-form disperses and reduces the force of the wind. On steep slopes the wedges run down-hill, to facilitate the sliding of the logs to the lower edge of the strip. In this case, the openings are made broader on the east than on the west side. It is said that regeneration is very complete under this system, but the method is of a very complicated character, requiring the constant attention of the forester. The yield is regulated by area. 11. The Coppice System. Character of the System. — When a wood, chiefly consisting of broad-leaved species, has been cut over near to the ground, the stool or roots, or both, produce shoots which develop into a new crop called simple or ordinary coppice. Generally, several shoots spring from the same stool, and these stand in clumps forming a complete cover earlier than in the case of seedling woods. When this has been established, the wood presents the appearance of a thicket in high forest. It grows up into poles and, under favour- able conditions, into trees. This method of regeneration can, as a rule, be repeated as long as the stool and roots live. Coppice woods suffer more than seedling crops from late and early frost, because the shoots are more succulent, and they require during the first year a longer growing season to ripen before autumn frosts set in. On the other hand, damage by frost is more easily healed. Coppice also suffers much from damage by game, especially deer and rabbits ; mice also do much damage. In other respects, coppice is less affected than high forest. Coppice woods yield chiefly firewood and small timber. Oak coppice gives bark for tanning, which has, however, been much superseded by other materials. The number of cubic feet of wood produced per acre and year is generally much smaller than in the case of high forest. Owing to the rapid growth of the shoots during the first few years, a complete cover overhead is quickly established which protects the soil well ; on the other hand, the latter is more frequently laid bare than in the case of high forest. Determination of the Yield. — In the first place, the rotation must be fixed in accordance with the class of produce which it is desired 324 DETERMINATION AND REGULATION OF THE YIELD. to grow. By dividing the total area (real or reduced) by the num- ber of years in the rotation, the size of the annual coupe is obtained. In the case of extensive areas, or for the purpose of supplying markets in different directions, it is frequently desirable to divide the forest into two or more working sections, allotting to each a number of coupes equal to the number of years in the rotation. In some cases, different rotations for the several working sections are indicated. A separate account should be kept for each work- ing section. The 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 and dividing them by the number of years in the period. Intermediate returns consist of the cuttings made in all areas not put down for regeneration during the working plan period ; they are, as a rule, not of much importance. Their amount should be estimated according to average local figures obtained in the past. 12. The Coppice with Standards, or Combination, System. (See pages 202—207.) Character of the System. — The system is a combination of simple coppice with standards of uneven age treated under the high forest selection system. The coppice forms the underwood, and the standards the overwood, the two being treated under different rotations. Generally, cuttings are made in both underwood and overwood in the same year ; that is to say, when the underwood has arrived at the end of its rotation, it is cut over, and at the same time those standards are removed which have reached the end of the rotation fixed forjihe overwood, or which it is desirable to remove for other reasons. New standards are then introduced, which, as a rule, should be seedlings and not coppice shoots. The rotation of the overwood should be a multiple of that fixed for the underwood. The number of that multiple depends on the size of timber which it is desired to produce. As a matter of fact, the latter consideration is, in the majority of cases, the deciding factor. The actual proportion of standards in each age gradation de- pends on the objects of management. The numbers form a falling THE COPPICE WITH STANDARDS SYSTEM. 325 series from the youngest to the oldest gradation. The total num- ber of standards must not be so great that the coppice is deprived of the necessary light ; hence, it is smaller than the number of trees in a regulated selection forest. Generally, the standards are scattered over the area by single trees, but in some cases they are in small groups. As regards external dangers, the system partakes of the advan- tages and disadvantages of the simple coppice and selection systems, according as it approaches the one or the other. If properly treated, the system acts beneficially upon the factors of the locality, though not to the same extent as the regulated selection forest. The production of wood is smaller than that of high forest. On the other hand, it permits the production of exceptional dimensions of trees without endangering the activity of the producing factors of the locality. Determination of the Yield. — The first step is to effect a division into compartments or annual coupes, and to allot them to as many working sections as may be required. There should be as many coupes in each working section as there are years in the rotation of the underwood. This regulates the yield as far as the underwood is concerned. The determination and regulation of the yield of the overwood is effected on the same fines as those explained for the regulated selection forest. Each compartment, or coupe, is treated on its own merits. In selecting the standards for cutting, the forester is guided, subject to the objects aimed at by the proprietor, by silvicultural considerations and the degree of ripeness of the several trees. Whenever a sustained yield is aimed at, not more should be cut during the working plan period than the increment laid on during the same period, but allowing for a deficiency or surplus of growing stock. At starting, the forester should make the best possible estimate of the incre- ment during the first period of r years, remeasure the stock of standards at the end of the first period and thus obtain a more accurate estimate of the expected increment during the second rotation of r years (see Selection Forest above). By adding the yields of the underwood and of the standards, the total yield is obtained. To that amount should be added the produce obtained by any thinnings made in other compartments, the amount of which should be estimated on the basis of local experience. 326 DETERMINATION AND REGULATION OF THE YIELD. SECTION II.— AUXILIARY SYSTEMS. A variety of auxiliary systems are practised. They are generally dealt with in Silviculture, and, as regards the regulation and deter- mination of the yield, they do not differ from the principal systems upon which they are grafted. Hence, a few remarks on some of the more important suffice in this place. 1. High Forest with Standards. During the regeneration of a high forest, single trees or small groups of trees are left standing, with the object of producing trees of a larger size than can be obtained in one generation. The length of time during which these standards are retained differs, according to the required size, from a limited number of years to a full second regeneration, and in some cases even more. In former times, masts of ships used to be produced in Europe by this system. From an economic point of view, the system has considerable drawbacks. In the first place, it is financially unre- munerative. Secondly, the standards interfere considerably with the development of the new crop, unless they consist of a thin- crowned, light-demanding species ; and if they are removed before the end of the second rotation, they are liable to do much damage to the second crop. Standards of broad-leaved species are liable to develop epicormic branches, which may reduce the quality of the timber ; they must be removed by pruning. Unless the standards are very wind-firm, they are liable to be thrown prematurely. 2. The Two-storied High Forest. In a wood consisting of one or more light-denianding species, a time arrives, at a comparatively early age, when the leaf canopy becomes interrupted, so that it can no longer preserve the factors of the locality. In such a case, a fairly heavy thinning is made, removing all inferior or otherwise undesirable trees, and a second crop, consisting of a shade-bearing species, is introduced, generally by sowing or planting. The two crops are then allowed to grow up into high forest with a difference in age ranging from 15 to 60 years, according to species and local conditions. FORESTRY COMBINED WITH FIELD CROPS. 327 Of interesting examples of this kind the following are mentioned : — (a.) At Novar, Scotland, 15 to 20 years old larch have been underplanted with silver fir, spruce, Douglas fir, and various other shade-bearing species (see Fig. 66). (6.) In the Spessart, Weiserstein, and elsewhere, oak at the age of 50 to 60 years is underplanted with beech (see Fig. 67). (c.) In the forests of the Vosges, France, Scots pine, about 60 years old, has been undersown with silver fir. In some cases the two species are cut over at the same time, followed by a fresh start on the same lines. In other cases, the older wood is removed when the trees have reached the desired dimensions, and the younger wood is allowed to grow to maturity. In the Spessart, where the object is to produce specially large oaks, the beech is cut over when mature, and a second crop of beech is grown and cut with the oak. In these cases the determination and regulation of the yield is done on the lines described for the uniform system, but for each story separately. 3. High Forest with a Soil-protecting Wood. When the leaf canopy of a high forest begins to become inter- rupted, an underwood is introduced for the protection of the soil. This must be dense and not too old ; hence, it should be replanted from time to time, or, better still, coppiced periodically ; it must consist of a species which can stand the shade of the overwood, the latter consisting of a thin-crowned species. The effect on the factors of the locality is highly beneficial. The system has been largely used in the oakwoods of Britain. 4. Forestry combined with the Growing of Field Crops. The practice of growing field crops on forest land is very old. There is evidence to show that it was extensively practised in Ceylon more than 1,000 years ago, and probably much earlier — in fact, ever since the human race commenced cultivating the soil. The original method consisted in cutting down the crop on a piece of forest, allowing the wood to dry and then burning it. After the ashes had been scattered over the area, rice, other grains and vegetables were grown for one or two seasons, after which 328 DETERMINATION AND REGULATION OF THE YIELD. the soil was allowed to recover itself with forest growth. The system is still practised in most parts of the British Empire. In India it is known under a variety of names, such as jhooming, dhya, kumri, taungya cultivation, etc. In European countries, in the course of time, some order was brought into the system ; the timber, instead of being burnt, is utilized, only the twigs and other inferior pieces being burnt. The system is practised in two distinct forms, in connection with coppice woods or with high forest. Fig. 66. — Larch, 25 years old, as Overwood, and Tsuga hederophylla, aged 8 years, as Underwood. In the case of coppice woods, after the twigs and other pieces of wood, frequently mixed with turf, have been burnt, the soil is generally used for the cultivation of buckwheat and rye between the stools of the previous crop. In some cases, the two seeds are sown together, say, in June, the buckwheat is harvested in August and the rye in the following summer. In other cases, they are cultivated one after the other. The cultivation of field crops in connection with high forest has been practised in Europe for a long time past. In France it is known by the name of " sartage," and much practised in the 329 Oak. Oak. Fig. 67.— Oak Wood, 110 Years Old, with Beech Underwood, 53 Years Old (Weiserstein ; Spessart). Number of oaks per acre = 240. Total production of oak timber, quarter girth measurement = 5,670 feet. Production per acre and year = 52 cubic feet, valued at £4, apart from the beech. Soil a sandy loam of only middling quality, overlying old red sandstone. Oaks clear of branches for 50 feet. 330 DETERMINATION AND REGULATION OF THE YIELD. regeneration of coniferous woods. In Germany, large areas have been restocked under this system with Scots pine, oak, and other species during the last 120 years. After the old wood (timber, firewood and stools) has been removed, the soil is worked, planting or sowing of seed is done in lines, and between the lines cereals, potatoes and other crops are grown for two, three, and even four years. In Burma, the system has been used in the cultivation of teak since the year 1866. The author saw one of the earliest attempts in 1867 in one of the forests near Toungoo. Since then many thousands of acres have been stocked with flourishing teak woods. During the last few years, the system has been adopted in the regeneration of sal and other species in India proper. 5. Forestry combined with Pasture. Pasture lands are widely planted with forest trees, which yield a certain return and also improve the value of the pasture by moderating cold and dry winds, thus affording shelter to the cattle. Broad-leaved species may also be lopped for fodder in cases of necessity. Strong seedling plants are used for the estab- lishment of the woods, which should be protected until their crowns have grown beyond the reach of the cattle. 6. Forestry combined with the Rearing of Game. A forest which is fenced and stocked with deer or other game is called a " deer forest " or " game preserve." All inside areas which are under regeneration must be separately fenced. Species which produce food for the deer, especially oak or chestnuts, should be represented in deer forests. Scottish deer forests are, as a rule, not fenced. They consist chiefly of extensive open areas ; at the same time it is desirable that the deer should have access to some forest areas, as it improves their development, especially the size of their antlers. Pheasant preserves are found in all parts of Britain. Any form of forest can be used for the purpose, but the most suitable system is coppice with standards. The underwood should consist of fairly shade-bearing species, such as beech, hornbeam and hazel, but ash is also extensively used, as it is more profitable and stands a moderate amount of shade while young ; even birch is used in THE CHOICE OF SYSTEM. 331 fairly open parts. The overwood should consist of fairly thin- crowned species, such as ash, oak, larch, poplars and perhaps some pines. Fenced rabbit warrens also occur in woodlands, but they, naturally, end in the destruction of the forest. SECTION III.— THE CHOICE OF SYSTEM. The choice of system depends on a variety of considerations, the details of which are dealt with in Silviculture. In this place it will suffice to draw attention to some of the most important aspects. These are :— (1.) The objects of the proprietor, whether he aims at indirect effects, or the production of the greatest volume, the highest quality, a special class or size of produce, or a high financial return, etc. (2.) The local conditions, such as the nature of soil and climate, the configuration aspect and gradient of the locality. (3.) The species best suited to realise the objects of the pro- prietor and also suitable to the local soil and climate. (4.) The dangers which may threaten a particular class of forest growth, such as frost, drought, insects, fire, wind, weeds and disease. The preservation and, if possible, improvement of the fertility of the soil is the most important consideration ; hence, the choice between regeneration on clear-cut land and under a shelterwood must be carefully considered. The former is, generally speaking, admissible only on land which is not only fertile, but also subject to a sufficient rainfall favourably distributed over the several seasons of the year. In all other cases, the exposure of the soil to the full effect of the sun and air currents extending over a number of years leads invariably to a reduction of its fertility. To prevent this, a system must be chosen which provides for a regeneration under a shelterwood. Then arises the question : which of the latter class systems is preferable ? There cannot be any doubt that of these the regulated selection system gives the best protection, and next to it the uniform system or one of its modifications. Of the latter, Wagner's modification may be specially recommended. The Austrian, Hundeshagen's and von Mantel's systems deter- 332 DETERMINATION AND REGULATION OF THE YIELD. mine the yield by a formula and give full liberty in other respects, so that they can be applied to the clear-cutting or shelterwood systems. They can also be used as a check on the determination of the yield by area. Heyer's method combines the determination of the yield by volume with one by area, which makes it somewhat complicated. The system of the division of the area into fixed annual coupes is applicable only to coppice and coppice with standards ; it is too stiff for other purposes. The comparative volume production and the value of the returns is of great importance in the selection of the system. They can be decided only by statistical data derived from the results of experiments, which are generally brought together in volume- and money-yield tables. Much has been learned in that way, but not all that is required to arrive at final conclusions in many respects. So far it may be said that the uniform system and its modifications give the highest volume production, but that of the regulated selection forest should not be much below it, if at all. The value per unit of volume produced in even-aged woods under the uniform system is generally somewhat higher than in the case of selection forest. On the other hand, the general expenses of the former system are likely to be higher than those of the latter ; hence, it is questionable which of the two systems is the more profitable — in other words, which of the two gives the higher mean annual forest per cent. The qualifications of the managing forester are of importance in the selection of the system. Where a thoroughly qualified staff is available, as in India, in Great Britain and in some parts of the Colonies, any system can be adopted which may be advisable under the existing local conditions. Where such a staff is not yet available, a simple system may give better results than attempt- ing a more complicated method. Generally speaking, the choice of the system depends on the degree of intensity of management which has been reached. In the greater part of the British Empire the selection system is as yet indicated. As the staff and the intensity of management improve, the regulated selection system will probably be the next stage, to be followed in many cases by the uniform system or some of its modifications. CHANGE OF SYSTEM. 333 SECTION IV.— CONVERSION FROM ONE SILVICULTURAL SYSTEM TO ANOTHER. As a general rule, the returns during the period of conversion are likely to be uneven in amount. If the new system requires a higher rotation than that to be abolished, the returns will be smaller, until the conversion has been completed, and possibly even longer. Hence, before a change of system is undertaken, it should be carefully considered, whether the advantages expected from the change are likely at least to compensate for the unavoid- able disadvantages. The number of conversions from one silvicultural system to another which are conceivable is considerable, and it is impossible to give any general rules of procedure. Whatever the nature of the conversion may be, the only sure basis for the determination of the expected yield is the annual cutting area. Hence, the consideration of a few special cases will bring out the essential points to be considered in each conversion. 1. Conversion of the High Forest Selection System into the Uniform, or Compartment, System. This conversion necessitates the substitution of even-aged for uneven-aged woods, and it frequently involves the cutting over of trees at an age differing from that which is most advantageous. To justify this sacrifice, the compartment system must offer decided advantages over the selection system. It is usual to fix one rotation for the conversion, to divide the rotation into periods of even lengths, and to allot to each period a corresponding portion of the total area, with due consideration of the condition of the several woods. As a rule, the several age classes are not evenly distributed over a selection forest ; gene- rally, more old wood is found in some parts of the area, and more young wood in others. This fact is taken advantage of in the allotment — that is to say, Period I. receives those woods which contain most old trees, especially those with deficient increment} Period II. receives the woods which are richest in middle-aged trees, and so on. In effecting this allotment, a proper grouping of the future age classes and cutting series must not be overlooked 334 DETERMINATION AND REGULATION OF THE YIELD. Example. — Assuming the rotation to be 120 years and the whole area allotted to three periods of 40 years each, the working during the first rotation would be as follows : — During Period I. — Part A, approximately equal to one-third of the total area, will be regenerated, either naturally or artificially, or by a combined method. From part B any over-mature trees are removed by selection, the necessary thinnings made, and blanks, if any, stocked. In part C over- mature trees are removed, blanks stocked, incomplete young woods filled up, and others thinned. During Period II. — Part B will be regenerated. In part A any remain- ing shelter trees will be removed and probably thinnings commenced. In part C over-mature trees will be cut and thinnings made wherever necessary. During Period III. — Part C will be regenerated. In part B any remaining shelter trees will be cut and thinnings commenced. In Part A the necessary thinnings will be made. The following table will further illustrate the procedure : — Period. Part A. Part B. Part C. I. 1—40 years. Regenerated. Over -mature trees removed. Thinnings made. Blanks stocked. Over-mature trees removed. Thinnings made. Blanks stocked. Incomplete woods filled up. II. 41—80 years. Any shelter trees removed. Probably thinnings commenced. Regenerated. Over-mature trees removed. Thinnings made. III. 81—120 years. Thinnings made. Any shelter trees removed. Probably thinnings commenced. Regenerated. 2. Conversion of Coppice into High Forest. This conversion may be effected by one of two methods : (a) Thin the coppice once or twice, leave the most vigorous, well- shaped shoots, let them grow until they have reached a market- able size and are capable of producing good seed ; then regenerate. As coppice shoots do not produce, as a rule, the same class of trees as those grown from seed, the regeneration of the former should be effected at a comparatively early age — say, when the annual increment has reached its maximum. The method has the dis- advantage that no final yield is obtained for a considerable num- CHANGE OF SYSTEM. 335 ber of years ; even the thinnings may be of comparatively small value, (b) Cut the coppice when it has reached the usual age, and interplant the stools with seedling plants, preferably of a species of rapid growth. The fresh stool shoots will have to be cut back once or twice, until the seedling trees have reached a sufficient height to hold their own against the coppice shoots, which will then become an underwood or gradually die. In all cases where, in the future, a sustained annual or periodic yield is desired, the area should be. divided into a corresponding number of annual or periodic coupes of equal yield capacity. If the new wood consists of a coniferous species, it is necessary to arrange suitable cutting series. The determination and regulation of the yield is done by area. 3. CONVERSION OF COPPICE WITH STANDARDS INTO THE COM- PARTMENT System. This conversion can be effected by gradually growing so much overwood in each coupe that it represents a full high forest. For this purpose, the coppice with standard system is continued for a time, but as little as possible overwood cut, and as many poles as possible left standing, until the area is fully stocked with overwood. The poles thus left should, if possible, be seedling trees and not stool shoots. Another method is to grow the high forest direct out of the underwood, provided the latter contains a sufficient number of seedling trees, and has not suffered by too much cover overhead. In either case, a good deal of planting or sowing may be necessary. To prevent a great unevenness of returns during the first rota- tion, the conversion will be effected only gradually, as indicated under 1 . Conversion of a Selection Forest. Example. — If the future rotation of the high forest be 120 years, the work would be distributed as follows : — During Period I., of, say, 40 years. — Convert one-third of the area ; cut very sparingly in the second part of the area ; cut as usual in the third part. During Period II., of 40 years. — Convert the second part ; cut sparingly in the third part. Thinnings will be commenced in the first part. During Period III., of 40 years. — Convert the third part. Thinnings in the first part will be in full swing. Thinnings will be commenced in the second part. 336 determination and regulation of the yield. 4. Conversion of a Forest of Broad-leaved Species into a Forest of Conifers. An irregularly stocked forest of broad-leaved species, partly high forest, partly coppice, and partly coppice with standards, is to be converted 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 compartments 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 had been completed. Supposing 60 years were chosen for the period of conversion, then at its close the oldest coniferous wood would have an age of 60 years. By dividing the total area by 60, the area is ascertained which should be converted annually. In selecting the areas to be taken in hand year by year, two con- siderations present themselves : — (1.) A suitable arrangement of the future cutting series. (2.) To begin with cutting over the woods which are poorest in increment. A consideration of both decides the allocation of the annual coupes over the forest area. Example. — A coppice with standard forest of 1,200 acres shall, in the course of 60 years, be converted into a coniferous forest. Every 10 years ' o = 200 acres must be taken in hand for conversion. In that case, the yield would consist of : — CHANGE OF SYSTEM. 337 During the first 10 years — (1.) The clearing of 200 acres. (2.) The treatment of 1,000 acres as coppice with standards. During the second 10 years — (1.) The clearing of 200 acres. (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. And so on. It is evident 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 any cuttings in the area of coppice with standards which will come under conversion during the next period of 10 years — in other words, by letting the material become 10 years older than it otherwise would. A similar arrangement should be followed during the third period of 10 years. After that time the thinnings in the young conifer woods should equalise the annual yield. The expected yield is determined by estimating the returns from the area to be converted during the first period and adding thereto the necessary cuttings on the rest of the area ; the latter should be sparingly done, so as to equalise the cuttings as much as possible. 338 CHAPTEB V. CONTROL OF EXECUTION AND RENEWAL OF WORKING PLANS. It is not sufficient to prepare a working plan ; it is also neces- sary to see that its provisions are carried out ; and when the period for which it lays down the management of a forest has come to an end, a new, or rather a revised, plan must be prepared. As the preparation of a first working plan is to some extent based upon incomplete data, it is of importance to keep a careful record during its execution, so as to eliminate in the course of time all doubtful elements. Apart from this, changes in areas or in other respects may occur which must be noted. The work of control and renewal comprises, therefore, three distinct opera- tions : — (1.) The record of changes as they occur. (2.) The record of works. (3.) The preparation of revised working plans from time to time, or renewals. Table of Yield, Receipts, Year. Area, Acres. Wood Sold, in Solid Cubic Feet. Receipts, Shillings. Expenses, Timber. Fire- wood. Bark. Total. From Wood. From Minor Pro- duce. Total. Har- vesting of Wood. Har- vesting Minor Produce. 1891 1892 1900 Total .. Annual ) Average j 253 12,300 7,000 100 19,400 7,600 400 8,000 1,200 100 253 130,000 13,000 70,000 7,000 1,000 100 201,000 20,100 75,000 7,500 4,000 400 79,000 7,900 14,000 1,400 900 90 KECORD OF WORKS. 339 1. Record of Changes. (a.) All changes in the areas must be recorded. Part of the area may be sold or exchanged, or additional areas bought ; areas hitherto used for the production of wood may be set aside for other purposes, or vice versa. The progress of the cuttings may cause alterations in the allotment of areas ; natural phenomena may produce changes, such as floods, landslips, fires, etc. All such changes should be noted at the close of each year, in the maps as well as in the tables of areas. (6.) 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. (6.) To give the means of comparing the provisions of the work- ing plan with the execution or actual results. The special form to be adopted depends on local circumstances, but information on the following points is required : — (1.) Result of each cutting according to quantity and amount realised by its sale. AND Expenses. Shillings. Net Result, in Shillings. Forest Capital, Shillings. Per- centage given by- Forest Capital during Year. Re- marks. Form- ation and Im- prove- ment. Ad- minis- tration and Pro- tection. Taxes, etc. Mis- cella- neous. Total. Total. Per Acre. Soil. Growing Stock. Total. 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 1,000 100 24,000 2,400 55,000 5,500 21-74 31,100 128,700 159,800 3-44 Z2 340 EXECUTION AND RENEWAL OP WORKING PLANS. (2.) A comparison of the estimate with the actual results. (3.) The harvest of minor produce according to receipts and, if possible, quantity. (4.) The data showing the net results of management. For a sample see the table on pages 338 and 339. (5.) The means of following up the history of each wood or compartment, as illustrated in Appendix VI., page 378. 3. Renewal of Working Plans. The renewal may in some cases amount to an entirely new plan ; but in the majority of cases much of the work done on the first occasion can be used again, only subsequent changes being noted. The most important part of what remains from the provisions 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 much easier than on the previous 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. (6.) Investigation of the extent to which the provisions of the former working plan were judicious and appropriate, (c.) Proposed changes, especially as regards the silvicultural system, species, method of formation, tending, and any other important operation. (d.) Preparation of a new working plan, based upon — (1.) The old working plan. (2.) The corrected records and maps. (3.) The results of past yields in material and money. (4.) The account of past works of formation, tending, and improvement. (5.) Approved changes. 34] APPENDICES. APPENDIX I. A. Area of circles for diameters ranging from 1 inch to 60 inches. B . Sum of the areas of circles for diameters ranging from 1 inch to 48 inches, or, Volume of cylinders for diameters ranging from 1 inch to 48 inches and any length. Example : Find the area of 24 circles of 15 inches diameter. Square Feet. Area of 20 circles = 10 X 2-4544 = 24-544 Area of 4 circles = 4-9088 Total = 29-4528 or, Find the volume of a log 24 feet long with a mean diameter of 15 inches. Cubic Feet. Volume of a log 20 feet long = 10 X 2-4544 = 24-544 Volume of a log 4 feet long = 4-9088 Total = 29-4528 342 APPENDIX I. A. AREA OF CIRCLES FOR DIAMETERS Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft.' Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft. 10 0-0055 20 00218 30 00491 40 0-0873 50 0-1364 1 •0067 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 •0107 4 •0314 4 •0631 4 •1056 4 •1590 5 •0123 5 •0341 5 •0669 5 •1105 5 •1650 6 •0140 6 •0369 6 •0707 6 •1154 6 •1710 7 •0158 7 •0398 7 •0747 7 •1205 7 •1772 8 •0177 8 •0428 8 •0788 8 •1257 8 •1835 9 •0197 9 •0459 9 •0830 9 •1310 9 •1899 110 0-6600 120 0-7854 130 0-9218 140 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 •6965 3 ■8252 3 •9648 3 11153 3 1-2768 4 •7089 4 •8387 4 •9794 4 1-1309 4 1-2936 5 •7214 5 •8523 5 •9941 5 1-1467 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 1-3444 8 •7595 8 •8937 8 1-0387 8 1-1946 8 1-3616 9 •7724 9 •9077 9 1-0538 9 1-2108 9 1-3789 210 2-4053 220 2-6398 230 2-8852 240 31416 250 3-4088 1 2-4283 1 2-6638 1 2-9103 1 31679 1 3-4361 2 2-4514 2 2-6880 2 2-9356 2 31942 2 3-4636 3 2-4745 3 2-7122 3 2-9610 3 3-2207 3 3-4911 4 2-4978 4 2-7366 4 2-9864 4 3-2471 4 3-5188 5 2-5212 5 2-7611 5 30120 5 3-2748 5 3-5465 6 2-5447 6 2-7857 6 3-0377 6 3-3006 6 3-5744 7 2-5684 7 2-8104 7 30635 7 3-3275 7 3-6024 8 2-5921 8 2-8352 8 30894 8 3-3545 8 3-6305 9 2-6159 9 2-8602 9 31154 9 3-3816 9 3-6587 40 8-7266 41 9-1684 42 9-6211 43 10-0847 44 10-5592 50 13-6354 51 14-1863 52 14-7480 53 15-3207 54 15-9043 60 19-6350 The circles of full inches were calculated with logarithms APPENDIX I. 343 OF 1 INCH TO 60 INCHES. Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft. Diam. in inches. Area of circle in square ft. 60 01963 70 0-2673 80 0-3491 90 0-4418 100 0-5454 1 •2029 1 •2750 1 •3579 1 •4517 1 •5564 2 •2096 2 •2828 2 •3668 2 •4617 2 •5675 3 •2164 3 •2907 3 •3758 3 •4718 3 •5787 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 160 1-3963 170 1-5763 180 1-7671 190 1-9689 200 2-1817 1 1-4138 1 1-5949 1 1-7868 1 1-9897 1 2-2036 2 1-4314 2 1-6136 2 1-8066 2 20106 2 2-2256 3 1-4492 3 1-6324 3 1-8265 3 20316 3 2-2477 4 1-4670 4 1-6513 4 1-8465 4 20527 4 2-2699 5 1-4849 5 1-6703 5 1-8666 5 20739 5 2-2922 6 1-5030 6 1-6894 6 1-8869 6 20952 6 2-3146 7 1-5212 7 1-7087 7 1-9072 7 21167 7 2-3371 7 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 260 3-6870 270 3-9761 280 4-2761 290 4-5869 300 4-9087 1 3-7154 1 4-0056 1 4-3067 1 4-6186 31 5-2414 2 3-7439 2 40353 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 110447 46 11-5410 47 120482 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 by interpolation. 344 APPENDIX I. B. TABLE OF THE SUM OF CIRCLES FOR DIAMETERS OF Diameter in Inches. Number o Circles, or Length of Cylinder. f 1 2 3 4 5 6 7 8 1 00055 00218 00491 0-0873 01364 01963 0-2673 0-3491 2 •0110 •0436 •0982 •1746 •2728 •3926 •5346 •6982 3 0165 •0654 •1473 •2619 •4092 •5889 •8019 10473 4 •0220 •0872 •1964 •3492 •5456 •7852 1-0692 1-3964 5 •0275 •1090 •2455 •4365 •6820 •9815 1-3365 1-7455 6 •0330 •1308 •2946 •5238 •8184 11778 1-6038 2-0946 7 •0385 •1526 •3437 •6111 •9548 1-3741 1-8711 2-4437 8 •0440 •1744 •3928 •6984 1-0912 1-5704 21384 2-7928 9 •0495 •1962 •4419 •7857 1-2276 1-7667 2-4057 3-1419 17 18 19 20 21 22 23 24 1 1-5763 1-7671 1-9689 21817 2-4053 2-6398 2-8852 31416 2 31526 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 120265 131990 14-4260 15-7080 6 9-4578 10-6026 11-8134 130902 14-4318 15-8388 17-3112 18-8496 7 110341 12-3697 13-7823 15-2719 16-8371 18-4786 20-1964 21-9912 8 12-6104 14-1368 15-7512 17-4536 19-2424 211184 230816 25-1328 9 14-1867 15-9039 17-7201 19-6353 21-6477 23-7582 25-9668 28-2744 33 34 35 36 37 38 39 40 1 5-9396 6-3050 6-6813 7-0686 7-4667 7-8758 8-2958 8-7266 2 11-8792 12-6100 13-3626 141372 14-9334 15-7516 16-5916 17-4532 3 17-8188 18-9150 200439 21-2058 22-4001 23-6274 24-8874 26-1798 4 23-7584 25-2200 26-7252 28-2744 29-8668 31-5032 33-1832 34-9064 5 29-6980 31-5250 33-4065 35-3430 37-3335 39-3790 41-4790 43-6330 6 35-6376 37-8300 40-0878 42-4116 44-8002 47-2548 49-7748 52-3596 7 41-5772 441350 46-7691 49-4802 52-2669 55-1306 580706 61-0862 8 47-5168 50-4400 53-4504 56-5488 59-7336 630064 66-3664 69-8128 9 53-4564 56-7450 601317 63-6174 67-2003 70-8822 74-6622 78-5394 1 APPENDIX I. 345 1 IN. TO 48 IN., AND OF THE VOLUMES OF CYLINDERS. Number oi Circles, or Length of Cylinder. Diameter in Inches. 9 10 11 12 13 14 15 16 1 0-4418 0-5454 0-6600 0-7854 0-9218 1-0690 1-2272 1-3963 2 •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 31416 3-6872 4-2760 4-9088 5-5852 5 2-2090 2-7270 3-3000 3-9270 4-6090 5-3450 61360 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 111704 1 9 3-9762 4-9086 5-9400 7-0686 8-2962 9-6210 110448 12-5667 25 26 27 28 29 30 31 32 1 3-4088 3-6870 3-9761 4-2761 4-5869 4-9087 5-2414 5-5851 2 6-8176 7-3740 7-9522 8-5522 9-1738 9-8174 10-4828 111702 3 10-2264 110610 11-9283 12-8283 13-7607 14-7261 15-7242 16-7553 . 4 13-6352 14-7480 15-9044 171044 18-3476 19-6348 20-9656 22-3404 5 170440 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 390957 8 27-2704 29-4960 31-8088 34-2088 36-6952 39-2696 41-9312 44-6808 9 30-6792 33-1830 35-7849 38-4849 41-2821 44-1783 47-1726 50-2659 41 42 43 44 45 46 47 48 1 9-1684 9-6211 100847 10-5592 110447 11-5410 120482 12-5664 2 18-3368 19-2422 201694 21-1184 22-0894 23-0820 24-0964 25-1328 3 27-5052 28-8633 30-2541 31-6776 331341 34-6230 361446 37-6992 4 • 36-6736 38-4844 40-3388 42-2368 44-1788 461640 48-1928 50-2656 5 45-8420 48-1055 50-4235 52-7960 55-2235 57-7050 60-2410 62-8320 6 550104 57-7266 60-5082 63-3552 66-2682 69-2460 72-2892 75-3984 7 64-1788 67-3477 70-5929 73-9144 77-3129 80-7870 84-3374 87-9648 8 73-3472 76-9688 80-6776 84-4736 88-3576 92-3280 96-3856 100-5312 9 82-5156 86-5899 90-7623 950328 99-4023 103-8690 108-4338 L130976 346 APPENDIX II. TABLE OF QUARTER GIRTHS IN INCHES, FEET AND SQUARED. Inches. Feet. Squared. Inches. Feet. Squared. Inches. Feet. Squared. i 4 3 f 1 •0208 •0417 •0625 •0833 •0004 •0017 •0039 •0069 51 5* 5| 6 •437 •458 •479 •500 •1914 •2101 •2296 •2500 10i 10J 10} 11 •854 •875 •896 •917 •7296 •7656 •8025 •8403 n if 2 •104 •125 •146 •167 •0109 •0156 •0213 •0228 7 .521 •542 •563 •583 •2713 •2934 •3164 •3403 Hi 11* 111 12 •937 •958 •979 1-000 •8789 •9184 •9588 1-0000 2| 3 •187 •208 •229 •250 •0352 •0434 •0525 •0625 8 •604 •625 •646 •667 •3650 •3906 •4171 •4444 12* 12* 12| 13 1-021 1-042 1063 1-083 10421 1-0851 1-1289 11736 3J H H 4 •271 •292 •313 •333 •0734 •0851 •0977 •1111 8i 9 •687 •705 •729 •750 •4727 •5017 •5317 •5625 13i 134 13| 14 1104 1125 1-146 1-167 1-2192 1-2656 1-3129 1-3611 H 5 •354 •375 •396 •417 •1234 •1406 •1567 •1736 9i 9| 10 •771 •792 •813 •833 •5942 •6267 •6602 •6944 144 1*4 14} 15 1-188 1-208 1-229 1-250 1-4102 1-4601 1-5109 1-5625 APPENDIX II. 347 TABLE OF QUARTER GIRTHS IN INCHES, FEET AND SQUARED. Inches. Feet. Squared. Inches. Feet. Squared. Inches. Feet. Squared. 15i 1-271 1-6150 201 1-688 2-8477 251 2104 4-427 15J 1-292 1-6684 20£ 1-708 2-9184 25J 2-125 4-516 15£ 1-312 1-7227 20J 1-728 2-9900 25| 2146 4-605 16 1-333 1-7778 21 1-750 3-0625 26 2167 4-694 16|r 1-354 1-8338 211 1-771 31359 261 2-188 4-785 16* 1-375 1-8906 211 1-792 3-2101 26* 2-208 4-877 16| 1-396 1-9484 21| 1-812 3-2852 26| 2-229 4-968 17 1-417 2-0069 22 1-833 3-3611 27 2-250 5-062 17i 1-438 2-0664 221 1-854 3-4379 271 2-271 5157 m 1-458 2-1267 22J 1-875 3-5156 27£ 2-292 5-251 17| 1-479 2-1879 22f 1-896 3-5942 27J 2-312 5-348 18 1-500 2-2500 23 1-917 3-6736 28 2-333 5-445 181 1-521 2-3129 231 1-938 3-7539 281 2-354 5-541 18J 1-542 2-3767 23£ 1-958 3-8351 28J 2-375 5-641 18f 1-562 2-4414 23| 1-979 3-9171 28f 2-396 5-741 19 1-583 2-5069 24 2-000 4-0000 29 2-417 5-840 19J 1-604 2-5734 241 2-021 4-0838 291 2-438 5-941 19* 1-625 2-6406 24£ 2-042 4-1684 29£ 2-458 6044 19| 1-646 2-7085 24| 2-062 4-2539 29| 2-479 6-145 20 1-667 2-7778 25 2083 4-3410 30 2-500 6-250 348 APPENDIX III. TABLES OF COMPOUND INTEREST. Instead of solving the subjoined formulas with the help of logarithms, these tables convert the operations into simple multiplications. A. Amount to which a capital of 1 accumulates with compound interest in n years : — C n = C x l-0p n . Example : — C = £50 ; n — 30 years ; p = 4 per cent. Then — C 30 = 50 x 3-2434 = £162-17. In order to economise space, the tables give the multiplicators from 1 to 10, year by year, and afterwards only for intervals of 5 and 10 years ; hence, for intermediate years two multiplications are required. If in the above example n were = 32 ; C 32 = 50 X 104 30 X 104 2 = 50 X 3-2434 X 1-0816 = £175-403. This holds good for all the tables. B. Discount, or present value, of a capital of 1 realisable n years, hence — C = l-0p n ' Example : — C» = £80 ; n = 40 years ; p = 4 per cent ; Co = 80 X •2083 = £16-665. C. Present value of a perpetual rental of 1 due every n years : — R Co I0p n — V Let R = £100 ; n = 50 years ; p = 4 per cent. ; C =» 100 X -1638 = £16-38. D . Present value of a rental of 1 due at the end of every year altogether n times : — 10^ n X -Op' Example : — Rental i? = £10 ; n = SO years ; p = 4 per cent. ; C = 10 X 17-2921 ; C = £172-921. APPENDIX III. 349 2 PER CENT. No. of Years. A. C n = C x 10p». B. 10p n C. c R D. c R(10p n -l)_ 10p n X Op No. of Years. ^° l-0p n -l' 1 10200 0-9804 50-0000 0-9804 1 2 10404 •9612 24-7525 1-9416 2 3 1-0612 •9423 16-3377 2-8839 3 4 1-0824 •9238 121312 3-8077 4 5 11041 •9057 9-6079 4-7135 5 6 11262 •8880 7-9263 5-6014 6 7 11487 •8706 6-7256 6-4720 7 8 1-1717 •8535 5-8255 7-3255 8 9 1-1951 •8368 5-1258 8-1622 9 10 1-2190 •8203 4-5663 8-9826 10 15 1-3459 •7430 2-8913 12-8493 15 20 1-4859 •6730 20578 16-3514 20 25 1-6406 •6095 1-5610 19-5235 25 30 1-8114 •5521 1-2325 22-3965 30 35 1-9999 •5000 1-0001 24-9986 35 40 2-2080 •4529 0-8278 27-3555 40 45 2-4379 •4102 •6955 29-4902 45 50 2-6916 •3715 •5912 31-4236 50 55 2-9717 •3365 •5072 331748 55 60 3-2810 •3048 •4384 34-7609 60 65 3-6225 •2760 •3813 361975 65 70 3-9996 •2500 •3334 37-4986 70 75 4-4158 •2265 •2928 38-6771 75 80 4-8754 •2051 •2580 39-7445 80 85 5-3829 •1858 •2282 40-7113 85 90 5-9431 •1683 •2023 41-5869 90 95 6-5617 •1524 •1798 42-3800 95 100 7-2446 •1380 •1601 43-0984 100 110 8-8312 •1132 •1277 44-3382 110 120 10-7652 •0929 •1024 45-3554 120 130 131227 •0762 •0825 46-1898 130 140 15-9965 •0625 •0667 46-8743 140 150 19-4996 •0513 •0541 47-4358 150 200 52-4849 •0190 •0194 490473 200 350 APPENDIX III. 3 PER CENT. No. of Years. A. C x 10p n . B. 10p»" C. R D. R(10p n -1) 10p n x -Op ' No. of Years. 1-Qp" - 1 1 2 3 4 5 10300 10609 1-0927 11255 11593 0-9709 •9426 •9151 •8885 •8626 33-3333 16-4204 10-7843 7-9676 6-2785 0-9709 1-9135 2-8286 3-7171 4-5797 1 2 3 4 5 6 7 8 9 10 1-1941 1-2299 1-2668 1-3048 1-3439 •8375 •8131 •7894 •7664 •7441 51533 4-3502 3-7485 3-2811 2-9077 5-4172 6-2303 7-0197 7-7861 8-5302 6 7 8 9 10 15 20 25 30 35 1-5580 1-8061 20938 2-4273 2-8139 •6419 •5537 •4776 •4120 •3554 1-7922 1-2405 0-9143 •7006 •5513 11-9379 14-8775 17-4131 19-6004 21-4872 15 20 25 30 35 40 45 50 55 60 3-2620 3-7816 4-3839 5-0821 5-8916 •3066 •2664 •2281 •1968 •1697 •4421 •3595 •2955 •2450 •2044 23-1148 24-5187 25-7298 26-7744 27-6756 40 45 50 55 60 65 70 75 80 85 6-8300 7-9178 9-1789 10-6409 12-3357 •1464 •1263 •1089 •0940 •0811 •1715 •1446 •1223 •1037 •0882 28-4529 29-1234 29-7018 30-2008 30-6312 65 70 75 80 85 90 95 100 110 120 14-3005 16-5782 19-2186 25-8282 34-7110 •0699 •0603 •0520 •0387 0288 •0752 •0642 •0549 •0403 •0297 310024 31-3227 31-5989 32-0428 32-3730 90 95 100 110 120 130 140 150 200 46-6486 62-6919 84-2527 369-3558 •0214 •0159 •0119 •0027 •0219 •0162 •0120 •0027 32-6188 32-8016 32-9377 33-2431 130 140 150 200 APPENDIX III. 4 PER CENT. 351 No. of Years. A. C x l-Op". B. c n 1-Op"' C. R D. R(10p n - 1) 10p n x -Op No. of Years. l-0p n - 1 1 2 3 4 5 10400 1-0816 11249 11699 12167 0-9615 •9246 •8890 •8548 •8219 25-0000 12-2549 8-0087 5 8873 4-6157 0-9615 1-8861 2-7751 3-6299 4-4518 1 2 3 4 5 6 7 8 9 10 1-2653 1-3159 1-3686 1-4233 1-4802 7903 •7599 •7307 •7026 •6756 3-7690 31652 2-7132 2-3623 2-0823 5-2421 60020 6-7327 7-4353 8-1109 6 7 8 9 10 15 20 25 30 35 1-8009 2-1911 2-6658 3-2434 3-9461 •5553 •4564 •3751 •3083 •2534 1-2485 0-8395 •6003 •4458 •3394 11-1184 13-5903 15-6221 17-2920 18-6646 15 20 25 30 35 40 45 50 55 60 4-8010 5-8412 71067 8-6464 10-5196 •2083 •1712 •1407 •1157 •0951 •2631 •2066 •1638 •1308 •1050 19-7928 20-7200 21-4822 22-1086 22-6235 40 45 50 55 60 65 70 75 80 85 12-7987 15-5716 18-9452 23-0498 28-0436 •0781 •0642 •0528 •0434 •0357 •0848 •0686 •0557 •0453 •0370 230467 23-3945 23-6804 23-9154 24-1085 65 70 75 80 85 90 95 100 110 120 34-1193 41-5114 50-5049 74-7597 110-6626 . •0293 •0241 •0198 0134 •0090 •0302 •0247 •0202 •0136 ■0091 24-2673 24-3978 24-5050 24-6656 24-7741 90 95 100 110 120 130 140 150 200 163-8076 242-4753 358-9227 2550-7498 ■0061 •0041 •0028 •0004 •0061 •0041 •0028 •0004 24-8474 24-8969 24-9303 24-9902 130 140 150 200 352 APPENDIX III. 5 PER CENT. No. of Years. A. Co x 1-Qp n . B. 10p" ' C. R D. R(10p n - 1) l-0p n x -Op No. of Years. l-0p n - 1 1 10500 0-9524 200000 0-9524 1 2 1-1025 •9070 9-7561 1-8594 2 3 1-1576 •8638 6-3442 2-7322 3 4 1-2155 •8227 4-6402 3-5459 4 5 1-2763 •7835 3-6195 4-3295 5 6 1-3401 •7462 2-9403 5-0757 6 7 1-4071 •7107 2-4564 5-7864 7 8 1-4775 •6768 20944 6-4632 8 9 1-5513 •6446 1-8138 7-1078 9 10 1-6289 •6139 1-5901 7-7217 10 15 2-0789 •4810 0-9268 10-3797 15 20 2-6533 •3769 •6049 12-4622 20 25 3-3864 •2953 •4190 140939 25 30 4-3219 •2314 •3010 15-3725 30 35 5-5160 •1813 •2214 16-3742 35 40 70400 •1420 •1656 171591 40 45 8-9850 •1113 •1252 17-7741 45 50 11-4674 •0872 •0955 18-2559 50 55 14-6356 •0683 •0733 18-6335 55 60 18-6792 •0535 •0566 18-9293 60 65 23-8399 •0419 •0438 19-1611 65 70 30-4264 •0329 •0340 19-3427 70 75 38-8327 •0257 •0264 19-4850 75 80 49-5614 •0202 •0206 19-5965 80 85 63-2544 •0158 •0161 19-6838 85 90 80-7304 •0124 •0125 19-7523 90 95 1030347 •0097 •0098 19-8059 95 100 131-5013 •0076 •0077 19-8479 100 110 214-2017 •0047 •0047 19-0966 110 120 348-9120 •0029 •0029 19-9427 120 130 568-3409 •0018 •0018 19-9648 130 140 1925-7674 •0011 •0011 19-9784 140 150 1507-9775 •0007 •0007 19-9867 150 200 17292-5808 •0001 •0001 19-9988 200 APPENDIX III. 6 AND 7 PER CENT. 353 6 Per Cent. 7 Per Cent, A. B. C. A. B. c. No. of Years. Co x 10p»- 10p» R C u x 1 Qp n . 10p« R No. of Years. 10p' 1 - 1 l-0pn — 1 1 1-0600 0-9434 16-6667 1-0700 0-9346 14-2857 1 2 11236 •8900 8-0906 11449 •8736 6-9013 2 3 11910 •8396 5-2346 1-2250 •8163 4-4444 3 4 1-2625 •7921 3-8096 1-3108 •7629 3-2175 4 5 1-3382 •7473 2-9568 1-4026 •7130 2-4839 5 6 1-4185 •7050 2-3872 1-5007 •6663 1-9972 6 7 1-5036 •6651 1-9857 1-6058 •6227 1-6507 7 8 1-5938 •6274 1-6841 1-7182 •5820 1-3924 8 9 1-6895 •5919 1-4503 1-8385 •5439 11926 9 10 1-7908 •5584 1-2645 1-9672 •5083 10339 10 20 3-2069 •3118 0-4531 3-8697 •2584 0-3484 20 30 5-7427 •1741 •2109 7-6123 •1314 •1512 30 40 10-2840 •0972 •1077 14-9750 •0668 •0716 40 50 18-4160 •0543 •0574 29-4570 •0339 •0351 50 60 32-9790 •0303 •0313 57-9470 •0173 •0176 60 70 59-0570 •0169 •0172 113-9930 •0088 •0081 70 80 105-7600 •0095 •0095 224-2440 •0045 •0045 80 90 189-4700 •0053 •0053 441-1230 •0023 •0023 90 100 339-3120 •0029 •0030 867-7600 •0011 •0012 100 110 607-6590 •0016 •0016 17070230 •0006 •0006 110 120 1088-2280 •0009 •0010 3357-9920 •0003 •0003 120 D. D. r R(10p n - 1) ° ~ l-0p" X Op c _R(10p n -l) l-0p" - -Op No. of Years. Yalue. No. of Years. Yalue. No. of Years. Yalue. No. of Years. Yalue. 1 0-9434 20 11-4699 1 0-9323 20 10-5928 2 1-8334 30 13-7648 2 1-8043 30 12-4071 3 2-6730 40 150463 3 2-6228 40 13-3300 4 3-4651 50 15-7619 4 3-3857 50 13-8000 5 4-2124 60 161611 5 4-0986 60 140371 6 40173 70 16-3845 6 4-7657 70 14-1585 7 5-5824 80 16-5091 7 5-3886 80 14-2200 8 6-2098 90 16-5787 8 5-9700 90 14-2514 9 6-8017 100 16-6175 9 6-5143 100 14-2685 10 7-3601 110 16-6392 10 7-0228 110 14-2757 120 16-6513 120 14-2800 354 APPENDIX IV ABSTRACTS FROM BRITISH AND CONTINENTAL YIELD TABLES. A. Tables based upon measurements made in Great Britain and Ireland : — (1.) European larch. (3.) Scots pine (in Scotland). (2.) Norway spruce. Preliminary data on — (4.) Oregon Douglas fir. (6.) Japanese larch. (5.) Corsican pine. B. Continental yield tables, given in the absence of British tables : — (7.) Silver fir. (9.) Beech. (8.) Oak. (10.) Sal = Shorea robusta, India. No data are as yet available for Sitka spruce. The data refer only to timber over 3 inches diameter at the small end, for an area of one fully stocked acre. The measurements of the volume were taken " under " bark for the British tables, and " over " bark for the Continental tables. The British tables are prepared according to the quarter girth system ; the Continental tables give the volume in the round. To convert the latter into the former, multiply the data in them by •785. The British tables can be converted into metric tables by the following operations : — Feet multiplied by -3048 = metres. Inches in quarter girth X 3-234 = centimetres in diameter. Number of stems per acre X 2-471 = number of stems per hectare. Square feet quarter girth X -2922 = square metres per hectare. Cubic feet quarter girth per acre X -0891 = cubic metres per hectare. The following number of quality classes were distinguished : — For larch, 5 ; spruce, 5 ; Scots pine, 3 ; Douglas fir, 4 ; Corsi- can pine, 3 ; Japanese larch, 2 ; silver fir, 4 ; oak, 5 ; and beech, 5, APPENDIX IV. 355 l. LARCH. Age in Years. Mean Height, Feet. Main Crop. Mean Quarter Girth at 4' 3'. Number of Stems per Acre. Basal Area, Square Feet per Acre. Form Factor. Volume under Bark, Cubic Feet per Acre. Thinnings. Volume under Bark, per Acre. Sum of Thinnings. Quality Class I. (Mean height at age of 50 = 80 feet.) 10 20 30 40 50 60 70 80 18 40 4 900 98 •398 1,560 80 58 6 520 126 •397 2,900 265 71 7-5 350 140 •390 3,880 465 80 9 260 148 •386 4,570 560 87 10-25 205 153 •383 5,130 645 94 11-5 170 157 •382 5,630 615 100 12-25 150 159 •382 6,070 460 80 345 810 1,370 2,015 2,630 3,090 Quality Class II. (Mean height at age of 50 = 70 feet.) 10 20 30 40 50 60 70 80 14 31-5 3-25 1,160 82 •348 900 60 48 5 640 113 •387 2,100 210 61 6-75 410 131 •382 3,050 380 70 8-25 310 141 •375 3,700 460 77-5 9-5 240 148 •370 4,250 510 84-5 10-75 190 153 •368 4,760 525 90 11-75 165 156 •368 5,170 410 60 270 650 1,110 1,620 2,145 2,555 Quality Class III. (Mean height at age of 50 = 60 feet.) 10 20 30 40 50 60 70 80 11 26 39-5 4-25 800 100 •370 1,460 70 51 5-75 510 119 •377 2,290 235 60 7-25 370 132 •367 2,910 360 67-5 8-50 285 141 •362 3,440 400 74 9-75 220 147 •359 3,910 430 79-5 11 185 152 •356 4,300 360 70 305 665 1,065 1,495 1,855 30 40 50 60 70 80 40 50 60 70 80 Quality Class IV. (M ean height at age of 50 = 50 feet.) 31-5 3-25 1,100 84 •340 900 100 41-5 5 640 105 •360 1,570 200 50 6-25 440 120 •360 2,160 240 57-5 7-50 330 131 •353 2,660 260 64 9 255 139 •348 3,100 350 69-5 10 200 144 •347 3,470 325 32 3-5 1,010 87 •338 940 65 40 5 620 105 •348 1,460 100 47-5 6-25 425 119 •343 1,940 215 53-5 7-50 320 128 •340 2,330 265 59 8-75 250 136 •335 2,690 285 100 300 540 800 1,150 1,475 Quality Class V. (Mean height at age of 50 = 40 feet.) 65 165 380 645 930 A A 2 356 APPENDIX IV. Age in Years. 2. NORWAY SPRUCE. Main Crop. Mean Height, Feet. Mean Quarter Girth at 4' 3". Number of Stems per Acre. Basal Area, Square Feet per Acre. Form Factor. Volume under Bark, Cubic Feet per Acre. Thinnings. Volume under Bark, Cubic Feet per Acre. Sum of Thinnings. Quality Class I. (Mean height at age of 50 years = 80 feet.) 10 20 30 40 50 60 70 12 31 51 5-75 710 171 •401 3,500 410 66-5 8-25 410 194 •407 5,250 925 80 10-50 280 211 •401 6,760 960 91 12-50 210 223 •395 8,020 860 100 14 175 231 •388 8,960 665 410 1,335 2,295 3,155 3,820 10 20 30 40 50 60 70 Quality Class II. (Mean height at age of 50 years = 70 feet.) 10-5 27 43-5 5 920 160 •408 2,840 220 58 7-5 500 189 •410 4,490 620 70 9-5 325 207 •407 5,890 700 79 11-5 240 220 •399 6,940 670 87 13-25 190 229 •392 7,800 565 220 840 1,540 2,210 2,775 Quality Class III. (Mean height at age of 50 years = 60 feet.) 10 20 30 40 50 60 70 9 22 .. 36-5 4 1,310 146 •402 2,140 49 6-25 665 177 •424 3,680 390 60 8-25 410 198 •415 4,930 510 68 10-25 300 212 •409 5,910 540 75 11-75 230 224 •401 6,730 440 390 900 1,440 1,880 40 50 60 70 Quality Class IV. (Mean height at age of 50 years = 50 feet.) 40 4-75 1,000 157 •427 2,690 100 50 6-75 590 183 •426 2,900 270 56 8-5 400 201 •419 4,890 375 64 10 300 214 •410 5,660 360 100 370 745 1,105 40 50 60 70 Quality Class V 31 40 47-5 53 3-5 5-5 7-25 8-75 (Mean height at age of 50 years < 1,500 130 -414 1,670 765 162 -435 2,820 500 183 -427 3,700 375 197 -422 4,400 40 feet.) 200 280 315 200 480 795 APPENDIX IV. 357 3. SCOTS PINE (Scotland). Age in Years. Mean Height, Feet. Main Crop. Mean Quarter Girth at 4' 3'. Number of Stems per Acre. Basal Area, Square Feet per Acre. Form Tactor. j Volume under I Bark of | Cubic Feet I per Acre. Thinnings. Volume under Bark, Cubic Feet per Acre. Sum of Thin- nings. 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Quality Class '. . (Mean height at age of 50 years = 60 feet.) 13 .. 26 40 4-5 960 137 •354 1,940 110 51 6-25 630 165 •371 .3,120 265 60 7-75 450 185 •369 4,100 330 67 9 340 197 •366 4,840 415 72-5 10-25 275 206 •364 5,440 485 77 11-5 230 212 •362 5,920 515 81 12-5 200 218 •360 6,350 470 84-5 13-25 183 223 •357 6,720 385 Quality Class II. (Mean height at age of 50 years = 50 feet.) 10 20 31 3-75 1,280 116 •361 1,300 85 41-5 5-25 795 152 •393 2,480 100 50 6-75 550 174 •397 3,450 240 57 8 410 188 •396 4,250 305 62-5 9-5 325 199 •392 4,880 365 67 10-5 270 207 •389 5,400 395 71 11-5 230 213 •387 5,850 380 74 12-25 207 218 •384 6,200 335 Quality Class III. (Mean height at age of 50 years = 40 years. 8 16 24 32-5 4-25 1,030 130 •395 1,670 100 40 5-75 700 155 •410 2,540 110 46 700 510 171 •412 3,240 250 51 8-25 400 185 •404 3,810 280 55 9-25 330 194 ■401 4,280 315 59 10-25 275 202 •398 4,750 325 62 11-25 237 208 •395 5,100 300 110 375 705 1,120 1,605 2,120 2,590 2,975 85 185 425 730 1,095 1,490 1,870 2,205 100 210 460 740 1,055 1,380 1,680 358 APPENDIX IV. 4. DOUGLAS FIR. Preliminary Yield Table. Quality Class I. Quality Class II. Quality Class III. Quality Class IV. At 50 Years = 110 At 50 Years = 100 At 50 Years = 90 At 50 Years = 80 Age in Feet High. Feet High. Feet High. Feet High. Years. Volume Volume Volume Volume Mean under Mean under Mean under Mean under Height Bark, Height Bark, Height Bark, Height Bark, in Feet. Cubic Feet per Acre. in Feet. Cubic Feet per Acre. in Feet. Cubic Feet per Acre. in Feet. Cubic Feet per Acre. 10 24 19 13-5 9 20 53 2,840 44 2,030 37 1,360 29 660 30 78 5,100 68-5 4,240 59 3,380 51 2,630 40 95 6,630 86 5,800 76-5 4,950 67-5 4,150 50 110 8,000 100 7,090 90 6,170 80 5,265 6. CORSICAN PINE. Preliminary Yield Table. Age in Years. Quality Class I. Height = 70 Feet at 50 Years. Quality Class II. Height = 60 Feet at 50 Years. Quality Class III. Height = 50 Feet at 50 Years. Mean Height in Feet. Volume under Bark, Cubic Feet. Mean Height in Feet. Volume under Bark, Cubic Feet. Mean Height in Feet. Volume under Bark, Cubic- Feet. 10 20 30 40 50 12 29 45 58-5 70 1,440 2,940 4,200 6,280 9 23-5 38 49-5 60 920 2,260 3,370 4,340 7 18-5 31 41 50 1,600 2,570 3,410 6. JAPANESE LARCH. Preliminary Notes. Age in Years. Quality Class I. Quality Class II. Mean Height. Volume under Bark. Mean Height. Volume under Bark. 5 10 15 20 25 9-5 23-5 35 44-5 52 1,095 1,930 2,580 5-5 16 25 33 39-5 470 1,205 1,820 Percentage of OVER -BARK VOLUME consisting of Bark. Quality Class. Larch. Spruce. Scots Pine (Scotland). 80 70 60 50 40 18 19-5 21 22 22-5 10 10 10 11 12 13-5 15 16-5 APPENDIX IV. 359 7. Lorey's Yield Tables for SILVER FIR, for South Germany. Age, Years. Main Crop. Thinnings. Mean Mean Number Basal Area, Form Factor. Volume. Cubic Feet per Acre. Volume, Sum of Height, Feet. Diameter at 4' 3". of Stems per Acre. Square Feet per Acre. Cubic Feet per Acre. Thin- nings. Quality Class I., or Best. 10 3 20 9 i-3 35 30 18 2-5 71 •39 500 40 30 40 1,460 126 •45 1,700 'eo 60 50 45 5-6 990 171 •48 3,670 360 420 60 58 7-5 660 205 •48 5,700 570 990 70 71 9-6 460 233 •48 7,960 1,000 1,990 80 82 11-7 340 255 •49 10,350 1,290 3,280 90 91 14-2 250 273 •51 12,550 1,430 4,710 100 98 16-2 200 288 •51 14,290 1,360 6,070 110 104 17-3 180 300 •51 15,780 860 6,930 120 109 18-3 170 310 •50 16,990 710 7,640 130 112 191 160 320 •50 17,850 600 8,240 140 115 20-1 150 330 •50 18,840 310 8,550 Quality Class II. — III., or Avei iAGE. 10 2 20 6 •7 18 30 13 1-3 36 40 22 2-3 2,700 75 •39 650 50 33 3-4 2,000 127 •45 1,880 140 iio 60 44 4-7 1,330 159 •50 3,530 330 470 70 55 6-2 880 182 •51 5,070 510 980 80 65 7-9 590 203 •51 6,750 740 1,720 90 73 9-8 420 220 •52 8,540 900 2,620 100 81 11-8 310 235 •53 10,140 940 3,560 110 87 13-4 250 246 •54 11,470 950 4,510 120 92 14-3 230 255 ■53 12,500 750 5,260 130 96 151 210 262 •52 13,180 570 5,830 140 99 15-7 200 268 •52 13,830 230 6,060 Quality Class IV., c r Lowes T. 10 2 .. 20 5 '•'6 30 9 10 10 40 16 1-5 23 •41 150 50 24 2-4 86 •48 1,000 60 33 3-3 2,ioo 124 •49 1,990 70 70 70 42 4-2 1,480 145 •50 3,060 210 280 80 51 5-3 1,060 162 •51 4,190 400 680 90 59 6-4 780 175 •52 5,370 630 1,310 100 66 7-8 570 188 •52 6,430 790 2,100 120 76 10-4 350 205 •51 7,890 1,430 3,530 1 360 APPENDIX IV. s. Wimmenatjer's Yield Tables for OAK (Chiefly for Low Lands). Age in Years. Main Crop. Thinnings. Mean Height in Feet. Mean Diameter at 4' 3". Number of Stems per Acre. Basal Area, Square Feet per Acre. Form Factor. Volume, Cubic Feet per Acre. Volume per Acre, Cubic Feet. Sum of Thinnings. Quality Class 1 ., or Best. 10 12 20 30 2-4 1,920 70 •27 560 30 46 4-3 820 89 •41 1,700 100 ioo 40 60 61 510 103 •48 2,930 290 390 50 71 8-2 320 115 •49 4,000 390 780 60 79 9-9 236 125 •50 4,960 440 1,220 70 86 11-4 187 133 •51 5,790 470 1,690 80 92 12-8 157 140 •51 6,530 490 2,180 90 97 14-2 133 145 •51 7,220 500 2,680 100 101 15-3 114 149 •52 7,800 500 3,180 110 105 16-9 98 153 •52 8,320 490 3,670 120 108 18-4 85 157 •52 8,790 490 4,160 130 111 19-6 76 160 •52 9,220 460 4,620 140 113 21-0 68 163 •52 9,620 460 5,080 150 115 22-3 61 166 •52 10,010 440 5,520 QtJ ality Class III., or Average. 10 10 20 21 i-7 3,590 57 •08 100 30 32 30 1,185 75 •32 700 40 43 4-5 820 91 •42 1,630 90 90 50 52 61 510 103 •47 2,520 200 290 60 60 7-4 370 112 •49 3,260 270 560 70 67 8-9 280 120 •49 3,940 310 870 80 72 101 230 127 •50 4,600 320 1,190 90 77 11-4 190 134 •50 5,200 340 1,530 100 81 12-5 160 139 •51 5,770 350 1,880 110 85 13-7 140 144 ■51 6,290 360 2,240 120 89 150 120 148 •51 6,750 360 2,600 130 92 16-2 105 151 •52 7,170 360 2,960 140 95 17-4 93 154 •52 7,570 350 3,310 150 98 18-4 85 156 •52 7,960 330 3,640 Q cality Class V., or Lowest. 10 5 30 19 i-8 3,300 59 50 33 3-9 1,010 85 •36 990 30 30 60 39 51 670 96 •41 1,540 100 130 70 45 6-3 480 104 •45 2,120 130 260 80 51 7-4 380 112 •47 2,670 160 420 90 56 8-4 310 118 •48 3,200 190 610 100 60 9-4 255 124 •50 3,690 210 820 110 64 10-4 220 129 •50 4,140 230 1,050 120 68 11-4 190 134 •50 4,570 230 1,280 130 71 12-4 165 139 •51 4,990 230 • 1,510 APPENDIX IV. 361 9. Schwappach's Yield Tables for BEECH in North Germany. Years. Main Crop. Thinnings. Mean Height. Feet. Mean Diameter at 4' 3". Number of Stems per Acre. Basal Area, Square Feet per Acre. Form Factor. Volume, Cubic Feet per Acre. Volume, Cubic Feet per Acre. Sum of Thin- nings. Quality Class L, or Best. 10 6 20 18 1*7 2,550 40 30 31 30 1,550 74 •30 690 40 45 4-5 940 105 •41 1,940 130 iio 50 56 6-3 600 131 •45 3,330 400 530 60 67 8-0 423 148 •46 4,370 590 1,120 70 76 9-5 316 156 •48 5,640 740 1,860 80 85 10-9 249 161 •48 6,560 830 2,690 90 92 12-2 201 165 •48 7,360 830 3,520 100 98 13-5 166 166 •49 8,050 960 4,380 110 104 14-6 142 167 •50 8,630 840 5,220 120 107 15-6 126 166 •51 9,120 830 6,050 130 110 16-5 112 165 •52 9,520 830 6,880 140 113 17-3 100 165 •53 9,850 820 7,700 Quality Class III., or Average. 10 5 20 13 i*3 28 30 23 2-2 2,070 53 •07 90 40 33 3-3 1,390 81 •35 940 50 43 4-4 970 104 •45 2,000 90 90 60 52 5-5 930 121 •46 2,920 270 360 70 60 6-4 580 131 •47 3,720 330 690 80 67 7-4 460 137 •48 4,430 360 1,050 90 73 8-3 370 138 •49 4,960 460 1,510 100 79 9-2 300 138 •49 5,340 560 2,070 110 84 100 250 136 •49 5,620 600 2,670 120 88 10-9 210 135 •49 5,860 570 3,240 130 91 11-8 175 134 •49 6,070 530 3,770 140 93 12-7 150 132 •51 6,260 490 4,260 Quality Class V., or Lowest. 10 3 20 7 ■9 18 30 13 1-6 34 40 20 2-3 2,000 57 •35 400 50 28 31 1,510 80 •42 930 60 34 3-7 1,200 98 •46 1,530 70 39 4-4 1,000 108 •48 2,040 80 44 5-0 830 115 •48 2,410 70 70 90 47 5-5 700 117 •49 2,670 130 200 100 50 60 610 118 •49 2,860 150 350 120 54 6-7 470 116 ■49 3,030 330 680 140 57 7-3 390 114 •50 3,220 290 970 362 APPENDIX IV. 10. Smythies' and Howard's Yield Tables for SAL (Shorea robusla). Age, Years. Main Crop. Mean Height, Feet. Mean Diameter at 4-5". Number of Stems per Acre. Basal Area, Square Feet per Acre. Form Factor. Yolume, Cubic Feet per Acre. Thinnings. Volume, Cubic Feet per Acre. 20 30 40 50 60 70 80 90 100 Quality Class I. (Maximum height over 110 feet.) 51 60 433 85 •417 1,810 1,120 67 8-7 257 107 •423 3,030 820 79 11-2 180 123 •427 4,150 820 90 13-2 137 132 •411 4,880 770 98 15-2 108 136 •408 5,440 690 106 16-8 89 137-5 •410 5,980 645 111-5 18-5 74 138-5 •415 6,405 610 116-5 201 63 139 •421 6,810 580 120 21-6 55 139-5 •429 7,170 565 20 30 40 50 60 70 80 90 100 Quality Class II. (Maximum height betw ;en 110 — )0 feet.) 40 4-2 780 77 •316 970 600 53 6-4 390 87 •383 1,765 600 63-5 8-7 252 104 •423 2,800 600 72 10-8 184 116 •418 3,490 560 80 12-5 145 123 •399 3,930 545 87 140 118 126 •398 4,360 540 92 15-4 98 127 •403 4,710 515 96-5 16-8 82 127 •413 5,065 470 100 18-1 71 127 •423 5,375 460 20 30 40 50 60 70 80 90 100 Quality Class [II. (Maximum height between 90 — 70 feet.) 31 2-5 .. 52 •149 240 .. 43 4-5 652 72 •349 1,080 440 51 6-7 359 88 •415 1,860 440 59 8-6 250 101 •427 2,540 445 65 10-2 192 109 •398 2,820 320 69 116 154 113 •387 3,015 365 73 12-8 128 114 •391 3,255 375 76 140 107 114 •402 3,480 360 78 15-2 90 114 •415 3,690 335 The above yield tables refer only to the United Provinces. The volume refers to timber down to 2 inch diameter, but the trees were measured at 4-5 feet from the ground, instead of 4-25 ft., as is done in Europe. 363 APPENDIX V 364 APPENDIX V. A. General Working Plan of a High Forest of Beech A. — Allotment of Woods to the several Com- part- ment. Area in Acres. Present Age. Final Age before Shifting. Allotment of Woods to Periods Before Shifting. I. Period II. Period. III. Period. IV. Period V. Period. Acres. Acres. Acres. Acres. Acres. With Over- wood. With- out Over- wood. 1 19 80 110 19 2 8 60 110 8 3 6 60 110 6 4 11 40 110 11 5 9 15 105 6 3 G 3 130 140 3 7 7 10 100 7 8 9 50 100 9 9 4 75 105 4 10 11 75 105 11 11 9 75 105 9 12 13 75 105 13 13 3 80 110 3 14 7 16 106 7 15 7 16 106 7 16 7 65 95 7 17 4 70 100 4 18 5 70 100 5 19 5 75 105 5 20 10 82 92 10 21 3 13 103 3 20 Total 100 13 80 23 11 13 1 33 Total Area =160 acres. Average per Period = 32 acres. APPENDIX V. A. 385 with a Moderate Admixture of Oak, Ash, and Conifers. Periods According to AREA. — Rotation = 100 Years. Com- part- ment. Final Age after Shifting. Allotment of Woods to Periods After Shifting. Remarks. I. Period. Acres. II. Period. Acres. III. 1 IV. Period. Period. Acres. Acres. V. Period. Acres. With Over- wood. With- out Over- wood. 1 2 130 110 19 8 Shifted, as the wood is of good growth, to relieve II. Period. 3 130 6 Shifted, to fill up IV. Period. 4 110 11 5 105 6 3 6 140 3 7 100 7 8 120 9 Shifted, to fill up IV. Period. 9 145 4 10 105 11 11 105 9 12 13 85 90 13 3 Shifted, to provide for I. Period. Shifted, to provide for I. Period. 14 106 i 15 106 7 16 95 & 115 3-5 3-5 17 100 4 18 100 5 19 85 5 Shifted, to provide for I. Period. 20 92 10 21 103 3 34 32-5 30-5 30 13 3 20 3 366 APPENDIX V. A. Lists of Woods already under Regeneration, and Age. Trees to be Left as Standards. Serial Compart- ment. Present. At the Time of Cutting (mean). Species. No. 1 Woods already tinder 1 5 9 Beech Scots Pine 104 104 107 107 Oak 16 2 7 7 Beech 116 119 Total 16 2. 1 Voods to I e Cut and Regenerated 1 6 3 Beech 130 140 Oak 3 2 12 13 Beech 75 85 Oak 71 81 Oak 150 Conifers 70 80 3 13 3 Beech ■ 80 90 Oak 11 4 19 5 Beech 75 85 5 20 10 Beech Scots Pine 82 82 92 92 Oak 54 Total 34 APPENDIX V. A. 367 Woods to be taken under Regeneration during the I. Period. Serial Num- ber. Yield in Solid Cubic Feet. Estimate. Present Volume. Incre- ment. Total. Mean per Acre. Actual Result. Regeneration. Natu- ral, Acres. Artificial. Manner of Formation. Species. Area, Acres. Remarks. Regeneration. 1 5,238 151 5,389 ) r 625 5 Planting Oak L 232 7 239 Spruce 1 r Oak U-50 2 8,091 209 8,300 1,186 4-50 Planting J Ash 9-50 { Spruce J 13,561 367 13,928 6-50 X3= Increment 5238 104 151 cub. ft, 232 104 X 6 ~ 7 cub. ft. 8091 X3= 116 209 cub. ft. during the I. Period. 1 19,827 1,525 21,352 7,117 2 Sowing Oak 1 2 33,237 4,432 37,669 ) / Scots ) 4,444 626 5,070 - 3,350 8 Sewing i Pine 1 Larch '- 706 101 807 ) ( Spruce ) 3 14,575 1,822 16,397 5,466 2 Sowing Oak 1 4 30,400 4,053 34,453 6,891 3 Planting f Oak \ Larch h 5 36,279 1,384 4,422 169 40,701 1,553 • 4,225 6 21 Planting / Larch ! Spruce ] Scots ( Pine ) s* 140,852 17,150 158,002 4,647 13 X10 Increment. 19,827 130 = 1,525 cub. ft. etc. 368 APPENDIX V. A. Calculation of Yield for the I. Period. Sources of Yield. Solid Cubic Feet. Yield. Grand Total. Mean Annual Yield. Detailed. Total. a. Thinnings* say b. Other intermediate yields c. Balance in woods already under regeneration d. Final yield of woods to be re- generated .... f To be deducted as remaining to be carried over into the II. period. e. Balance of d to be cut /. Total of c. and e . . . Total of all yields 50,000 50,000 50,000 2,500 7,369 13,928 13,928 133,450 158,002 24,552 147,378 197,378 9,868 * See next page. f The calculation is made as follows : — Regeneration period = 10 years ; mean volume per acre of woods in I. period = 4,647 cubic feet. There remain, when the seeding cutting has been made = 4,647 X -6 = 2,788, say, 2,790 cubic feet. It is assumed that these 2,790 cubic feet are cut away in annually equal instalments of ^th, = 279 cubic feet ; hence, the ten coupes, each of -wr = 1-6 acres, will, at the end of the I. period, have volumes per acre equal to : Coupe 10 = 2,790. „ 7 = 1,953. „ 4 = 1,116. „ 1 = 279. Coupe 9 = 2,511. „ 6 = 1,674. „ 3 = 837. Coupe 8 = 2,232. „ 5 = 1,395. „ 2 = 558. thus forming an arithmetical series, the sum of which is = (2,790 + 279) X 10 15,345. This sum must be multiplied by 1-6, the size of the coupe, making the volume to be carried forward into the II. period = 15,345 X 1-6 = 24,552 cubic feet. ^ APPENDIX V. A. 369 Local Yield Table for Thinnings. Age Class. Yield of Thinnings c' solid per acre. 21— 30 . 170 31— 40 . 200 41— 50 . 230 51— 60 . 245 61— 70 . 260 71— 80 . 230 81— 90 . 200 91—100 .... 155 This table has been used to calculate the expected yield of thinnings during the next 20 years. The full details have been omitted ; the total volume amounts to 50,000 cubic feet in round figures. Examples. — Taking Compartment 1, now 80 years old, the thinnings would amount, during the next ten years, to 19 x 200 = 3,800 cubic feet. In the case of Compartment 9, now 75 years old : 230 For the first 5 years = 4 x -=- = 460 cubic feet For the second 5 years a 200 Ana 4 x -p- = 400 Total = 860 cubic feet. 370 APPENDIX V. B. B.— General Working Plan for the Method by VOLUME, The Final Yield has been taken from the Yield Com- Area ment. Acres. 1 19 2 8 3 6 4 11 5 9 6 3 7 7 8 9 9 4 10 11 11 9 12 13 13 3 14 7 15 7 16 7 17 4 18 5 19 5 20 10 21 3 Total 160 Present Age. Final Age before Shifting. 80 110 60 110 60 110 40 110 15 105 130 140 10 100 50 100 75 105 75 105 75 105 75 105 80 110 16 106 16 106 65 95 70 100 70 100 75 105 82 92 13 103 Final Yield per Acre before Shitting. Allotment of Final Yield in C" Before Shifting. Period. 6,590 6,590 6,590 6,590 6,455 7,300 6,320 6,320 6,455 6,455 6,455 6,455 6,590 6,482 6,482 6,125 6,320 6,320 6,455 6,008 6,401 21,900 60,080 81,980 II. Period. 125,210 25,820 71,009 58,095 83,915 19,770 42,875 25,280 31,600 32,275 ill. Period. 52,720 39,540 56,880 IV. Period. 515,849 V. Period. 72,490 58,095 44,240 149,140 72,490 45,374 45,374 19,203 212,286 Grand total of yield = 1,031,745 cubic feet. Average per period = 206,349 „ APPENDIX V. B. 371 based upon the data given in the Table at pages 364 — 65. Table for Beech, III. Quality, including Fuel. Compart- ment. Final Age after Shifting. Final Yield per Acre after Shifting. Allotment of Final Yield in C After Shifting. I. Period. II. Period. III. Period. IV. Period. V. Period. 1 130 7,090 134,710 2 110 6,590 52,720 3 130 7,090 42,510 4 110 6,590 72,490 5 105 6,455 58,095 6 140 7,300 21,900 7 100 6,320 44,240 8 120 6,840 61,560 9 145 7,405 29,620 10 105 6,455 71,009 11 105 6,455 58,095 12 85 5,665 73,645 13 90 5,930 17,790 14 106 6,482 45,374 15 106 6,482 45,374 16* 95 & 115 6,125 & 6,715 21,437 23,502 17 100 6,320 25,280 18 100 6,320 31,600 19 85 5,665 28,325 20 92 6,008 60,080 21 Total . . 103 6,401 19,203 201,740 207,421 210,932 206,180 212,286 Grand total of yield = 1,038,559. Average per period = 207,712. Average annual yield in I. period = 10,087. „ V. „ = 10,614. * Half of the compartment will be cut in the II. period, and the other half in tho III. period. 372 APPENDIX VI. General Working Plan drawn up according Rotation, Compartments. Number. Total . Normal state under a rotation of 120 years Comparison of real I + and normal state I — DISTRIBUTION' jf Age 1 — 40 years old. 41—60. 61—80. 81 — 100. Cubic feet. Acres. Cubic feet. Acres. Cubic feet. Acres. Cubic feet. Acres. 48,030 41 70,630 20 200,945 117 169,514 40 192,117 40 15,892 2 19,072 34 21,189 38 109,479 87 201,299 37 423,787 67 353,156 49 26,487 24 46,617 11 25,074 5 494,418 49 28,605 51 35,316 5 42,379 5 13,420 48 105 467,227 440 488,060 108 676,294 117 905,845 Calculation of the Yield. This is done according to the formula : — Gre.d — G vorimil Annual yield = I rm i + The real increment, I re „i = 102,696 cubic feet. The real growing stock, G rea i = 8,939,771 ,, ,, The normal growing stock, G mm ai = 7,456,200 ,, ,, The surplus of growing stock = 1,483,571 cubic feet. Assuming that this surplus is to be removed in the course of 50 years, the yield would be— Annual yield = 102,696 + l, ^l^ U = 102,696 + 29,671 = 132,367, or, during the first 10 years = 1,323,670 cubic feet. APPENDIX VI. 373 to the Austrian Assessment Method. 120 Years. Classes. Increment. Volume per Acre, Cubic Feet. Compart- ments. Over 100 Years. Total. Annual, per acre. Total in 10 Years. Number. Cubic feet. Acres. Cubic feet. Acres. Normal. ■Real. Normal. Real. 1 34,250 4 152,910 65 2,352 85 70 55,250 45,500 2 118,662 12 697,130 211 3,304 85 75 179,350 158,250 3 381,408 37 400,480 71 5,641 70 61 49,700 43,310 4 1,606,861 148 1,628,050 186 8,753 85 71 158,100 132,060 5 1,522,104 133 1,522,104 133 11,444 100 71 133,000 94,430 6 540,329 43 1,628,050 283 5,753 100 78 283,000 220,740 7 365,870 49 958,466 138 6,945 85 85 117,300 117,300 8 459,103 34 565,403 95 5,952 100 71 95,000 67,450 9 1,373,758 124 1,387,178 172 8,365 100 86 172,000 147,920 6,402,345 584 8,939,771 1,354 6,603 76 1,026,960 7,456,200 5,507 92 1,242,700 1,483,571 1,096 16 215,740 The yield for the next 10 years having been fixed, the forester decides where it is to be cut. He selects in the first place all silvi- cultural necessities, such as severance cuttings, the removal of shelter trees over young regeneration ; next he adds all woods which are poor in increment, especially those which have suffered from natural phenomena ; finally he makes up the total yield by adding the oldest woods, with due consideration of a proper dis- tribution of the age classes over the area. In this way, the Special Working Plan on the next two pages has been obtained. A detailed record of the work done in each compartment is kept (see page 378) ; from these data, and those on pages 374 — 75, the Summary on pages 376 — 77 is prepared, which compares the provisions of the working plan with the actual results. 374 APPENDIX VI. Special Working Plan. Compart- ment*. Description of Cuttings, Cultivation, etc. Cuttings. Cultiva- tion. Acres. Draining, Ditches. Feet, Road Construc- tion. Feet. Final. Cubic Feet. Inter- mediate. Cubic Feet. 1. 2. 3. 4. 5. Final cutting in regenerated part . . . ■ ■ Filling up blanks with spruce Thinning, and cutting can- cerous silver firs Total *a. Thinning of shelter-wood and partial final cutting. Filling up blanks with spruce and Scots pine . a & b. Thinning and removal of cancerous trees Total a. Seeding cutting, and partly final cutting b & c. Rest. Total a. Thinning of 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 34,000 10,000 3 34,000 10,000 3 35,000 53,000 10 35,000 53,000 10 53,000 53,000 341,000 341,000 19,000 19,000 4,900 19,000 19,000 4,900 a, b, c refer to sub-compartments. APPENDIX VI. 375 Special Working Plan— •continued. Compart- ments. Description of Cuttings, Cultiva- tion, etc. Cuttings. Cultiva- tion. Acres. Draining Ditches. Feet. Road Construc- tion. Feet. Final. Cubic Feet. Inter- mediate. Cubic Feet. 6. 7. 8. 9. a. Cutting of all old standards and cancerous trees Thinning .... b. Thinning of shelter-wood and partially final cutting . Filling up blanks with spruce. c. Cutting out of old defective 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 : thin- ning of shelter-wood and partially final clearing ; in the rest seeding cutting Filling up blanks with spruce . Construction of an export road. Total Continuation of regeneration cuttings and removal of can- cerous trees Thinning in fully stocked parts . Filling up blanks with spruce and Scots pine Construction of an export road Total 45,000 198,000 14,000 3,000 12 9,500 257,000 3,000 12 9,500 47,000 25,000 47,000 15,000 5,000 72,000 62,000 5,000 103,000 3 3.500 163,000 3 3,500 195,000 7,000 8 3,000 195,000 7,000 8 3,000 376 APPENDIX VI. Summary of the Provisions of the Compartments. Provisions of Working Plan. Cuttings. Cultiva- tion. Acres. Draining. Feet. I Road Construc- tion. Feet. Final. Cubic Feet. Inter- mediate. Cubic Feet. Total. Cubic Feet. 1. 34,000 10,000 44,000 3 2. 35,000 53,000 88,000 10 3. 53,000 53,000 4. 341,000 341,000 5. 19,000 19,000 38,000 4,900 6. 257,000 3,000 260,000 12 9,500 7. 72,000 62,000 134,000 5,000 8. 163,000 163,000 3 3,500 9. 195,000 7,000 202,000 8 3,000 Total . . 1,169,000 154,000 1,323,000 36 25,900 Note. — The excess was due to heavy windfalls; it will not derange future APPENDIX VI. 377 Working Plan and of the Execution. Com- part- ments Results of Actual Work Done. Cuttings. Final. Cubic Feet. 33,034 54,517 132,900 177,169 86,606 342,444 95,852 111,049 197,660 Inter- mediate. Cubic Feet. 12,549 75,000 Total. Cubic Feet, 45,583 129,517 132,900 177,169 68,301 154,907 Culti- vation Acres 4-4 50 Drain- ing. Feet, 21,635 Total 1,231,231 177,485 364,079 95,852 111,049 197,660 1,408,716 8-4 18-9 Road Con- struc- tion. Feet. Comparison of Proposed and ex- ecuted Cuttings Cut too much. Cubic Feet. 1,583 41,517 79,900 5,003 9,679 5,299 3,691 2,953 26,625 Cut too little. Cubic Feet. 116,907 104,079 85,716 163,831 Remarks. 38,148 51,951 4,340 Excess due to windfalls and snow-break. Excess due to windfalls and snow-break. Held back, on account of ex- tra fellings in other compts. Excess due to windfalls. Excess : wind- falls. Thinning held over. Held back on account of ex- cess in other compts. arrangements, as there is a considerable excess of growing stock in the forest. 378 APPENDIX VI. Sample Page of the Detailed Control Book. Compartment 1. Year. Cuttings. Cultiva- tion. Acres. Draining Ditches. Feet. Road Con- struc- tion. Feet. Description of Cuttings, Culti- vation, etc. 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 .... Total . 10,000 34,000 10,000 3 Execution. 1884 Final cutting Dry and windfall wood 14,297 813 1885 Windfalls . 665 1886 Final cutting, thinning Windfalls . 6,166 547 832 1887 Windfalls . 1,363 1888 Final cutting, thinning 7,759 11,717 .. Planting . 1-7 ii Windfalls . 82 1889 Dry wood, windfalls Planting . 649 2-2 1890 99 Windfalls . Planting . 693 •1 1891 Planting . •2 1892 Planting . •1 1893 Planting . •1 Total 33,034 12,549 4-4 379 INDEX. Age classes, distribution of, over forest, 208 ,, ,, normal, 195 ., size of, 198 table of, 256 Age of trees and woods, 74 Allotment of woods to periods, 289 Analysis of a Scots pine tree, 83 Area of circles, table of, 342 „ table of, 253 Austrian assessment method, 293 „ ,, ,, work- ing plan of, 372 B. Bark, volume of, 33 Blender saumschlag, Wagner's, 317 Block's method of volume measure- ment, 63 Boundaries, register of, 252 Branch and root wood, measure- ment of, 32 Brandis' hypsometer, 23 ,, system, 285 C. Callipers, 9 Choice of method of measurement, 67 of rotation, 193 of species, 272 ., of system, 331 Compartment, definition of, 261 ,, description of, 235 system, 303 Compass, tree, 13 Compound interest, formulas of, 117 „ tables of, 348 Conditions around locality, 251 Control of execution of working plans, 338 Conversion of system, 333 Coppice system, 323 ,, with standards, 324 Cost values of forests, 134 ,, „ of growing stock, 132 „ of soil, 120 Coupes, annual, 196 Cutting series, 265 Cylinders, volume of, 344 D. Dendrometers, 13 Diameter class system of measure- ment, 44 ,, increment, 175 Division and allotment of forest area, 260 ,, working circle, 260 ,, „ section, 262 compartment, 261 sub-compartment, 262 cutting series, 265 severance cutting, 266 system of roads and rides, 267 ,, demarcation and number- ing of the divisions, 271 Draudt's method of measuring the volume, 52 E. Estimate, determination of volume by, 72 ,, of receipts, expenses and yield, 123 Expectation value of forests, 135 „ value of the growing stock, 133 „ value of forest soil, 130 380 INDEX. Felled trees, measurement of volume, 28 „ „ measurement of stem, 28 „ ,, measurement of bark, 33 ,, ,, measurement of branch and root wood, 32 Financial results of forestry, 136 results, current annual forest per cent., 138 results, mean annual forest per cent., 142 results of forestry, profit, 136 rotation, 188 test applied to method of treatment, 161 test applied to forestry and agriculture, 158 test applied to choice of species, 160 test applied to silvicul- tural system, 160 Forest Commissioners, method of measuring volume of woods, 64 Forestry and game, 330 „ and field crops, 327 ,, and pasture, 330 Form factor tables, measurement of volume by, 56 ,, quotient, method of, 66 Formulas of compound interest, 117 G. • Girth measurement, 8 Group system, 315 Growing stock, normal, 213 „ „ volume of, 43-73 value of, 132 H. Hartig's method of volume measure- ment, 53 Height increment, 80 „ measurement of, 16 Heyer's method, 296 High forest with soil - protection wood, 327 ,, ,, with standards, 326 Hundeshagen's method, 299 Hypsometers : Brandis', 23 ; Chris - ten's, 22 ; Weisse's, 20 Increment, the, 79, 172 borer, 14 in height, 80 in basal area, 82 diameter, 81 of whole woods, 92 of whole woods deter- mined by past incre- ment, 93 „ of whole woods deter- mined by yield tables, 93 „ of volume, 172 ,, per cent., 182 Instruments used in mensuration, 8 Interest, choice of rate, 115 „ tables of compound, 348 L. Larch, yield table of, 355 Locality, 237 M. Management, objects of, 1 Maps, 257, 271 Measurement of diameter, 9 „ of diameter increment, 14 of felled trees, 28 of girth, 8 ,, of height of trees, 16 of length of logs, 15 „ of standing trees, 34 Method, silvicultural. See Systems. of treatment, 272 N. Normal age classes, 221 „ growing stock, volume of, 213 INDEX. 381 Normal growing stock, value of, 146 „ yield, 221 Notes on future treatment, 248 Numbering the divisions of a forest, 271 0. Oak, yield tables of, 360 Ocular estimate of volume, 72 P. Per cent., forest, 187 Preparation of working plans, 229 Pressler's increment borer, 15 Price increment, 186 Profit of forestry, determination of, 136 Property, value of, 114 Q. Qualities of locality, table of, 254 Quality classes of yield tables, 95 „ determination of, 242 „ increment, 184 Quarter girth tables, 346 Quartier Bleu, Le, system of, 313 R. Rate of interest, choice of, 115 ,, „ determination of, 138 Real forest compared with normal, 229 Receipts and expenses, estimate of, 123 ,, , expenses and yield, 249 Regulation of yield, 276 Relation between normal growing stock, increment and yield, 224 Renewal of working plans, 338 Rental of forest, determination of, 122 Report, statistical, 252 Rides and roads, the system of, 267 Root wood, volume of, 32 Rotation, 254 „ choice of, 193 ,, financial, 188 ,, of greatest volume pro- duction, 192 ,, of highest income, 191 ,, physical, 193 ,, technical, 192 S. Sal, yield table of, 362 Sale, or market, value, definition of, 114 ,, value, of forests, 147 ,, value of forest soil, 129 ,, value of growing stock, 132 Sample areas, volume measured by, 69 ,, trees, volume measured by, 43 „ trees, general method of, 44 Scots pine tree, analysis of, 83 „ yield table of, 357 Severance cutting, 266 Silver fir, yield tables of, 359 Soil, cost value of, 129 ,, expectation value of, 130 „ sale value of, 129 Spruce, yield table of, 356 Standing trees : measurement of, 34 „ by estimate, 34 ,, by form factors, 35 ,, by volume tables, 39 ,, by sections, 41 Statistical report, 252 Statistics, collection of, 235 Stem, volume of, 28 Sub-compartment, the, 262 Sum of circles, 344 Survey of areas, 235 System, conversion of, 303 „ choice of, 331 Systems, silvicultural, or methods of treatment according to : selec- tion forest, 277 ; Brandis', 285 ; 382 INDEX. fixed annual coupes, 288 ; allot- ment of woods to periods, by area, 290 ; by volume, 291 ; by both combined, 293 ; Austrian method, 293 ; Heyer's modification, 296 ; Hundeshagen, 299 ; von Mantel, 301 ; the compartment or uniform system, 303 ; example, 309 ; Le Quartier Bleu, 313 ; group system, 315 ; strip system, 315 ; strip and group system, 317 ; Wagner's Blender saumschlag, 317 ; wedge felling system, 321 ; coppice system, 323 ; coppice with stan- dards, 324 ; standards in high forest, 326 ; two-storied high forest, 326 ; high forest with soil- protection wood, 327 ; forest and field crops, 327 ; forest and pasture, 330 ; forest and game, 330. T. Tables of compound interest, 348 Technical rotation, 192 Tending, method of, 274 Treatment, method of, 272 „ notes regarding future, 248 Tree compass, 13 Trees, age of, 74 Type trees, measurement of volume by, 47 • U. Urich's method of measurement, 53 Utilisation value of growing stock, 132 Valuation, forest, 111 ,, of forest soil, 129 of growing stock, 132 ,, of whole woods or forests, 134 Value of normal growing stock, 146 Volume, determination of whole woods, according to methods : Diameter class method, 44 ; example, 50 ; Draudt's method, 52 ; Urich's, 53 ; Hartig's, 53 ; Examples of both, 54, 55 ; by form factors or volume tables, 56; by yield tables, 60; the volume curve method, 61 ; Block's method, 63 ; British Forestry Commissioner's method, 64 ; the form quotient method, 66 ; other methods, 67 ; accuracy and choice of method, 67 ; by sample areas, 69 ; by estimate, 72 Volume increment, 172 ,, per cent., 182 .. of bark, 33, 358 of branch and root wood, 32 of cylinders, 344 ,, of stem, 28 „ tables of larch and Scots pine, 40 W. Weisse's hypsometer, 20 Woods, age of, 74 ,, increment of, 92 ,, valuation of, 134 Working circle, 260 plan for Austrian system, 372 „ ., for periods by areas, 364 ,, ., for periods by volume, 370 „ report, 231 „ plans, control and renewal of, 338 „ ,, preparation of, 227 ,, section, 262 Yield, determination and regula- tion of, 276. (For details, see Systems.) INDEX. 383 growing between, Yield, increment and stock, relation 224 „ normal, 221 „ tables of larch, 355 ; Norway spruce, 356; Scots pine, 357; Douglas fir, 358; Corsican pine, 358 ; Japanese larch, 358 ; silver fir, 359 ; oak, 360 ; beech, 361 ; Sal, 362 Yield tables, money, for larch, 124 ; Scots pine, 126 ; Norway spruce, 127 END OF VOLUME III. MINTED IN GREAT BRITAIN BY BRADBURY, AQNEW, & CO. LD. 10, BOUYERIE STREET, LONDON, E.C.