Mttii^k €silm mm ArrrtJ«icrtt ^Ccr. 3 ^t^^ t Digitized by the Internet Arciiive in 2010 with funding from University of British Columbia Library http://www.archive.org/details/forestmensuratiOOgrav WORKS OF HENRY S. GRAVES PUBLISHED BY JOHN WILEY & SONS, Inc. Forest Mensuration. xiv+ 458 pages, 6 X 9, 47 figures. net. Cloth, S4.00 The Principles of Handling Woodlands. xxi + 325 pages, 5J XS, 03 figuics, mostly half- tone reproductions of original photographs. Cloth, S2.00 net. FOREST MENSURATION BT HENRY SOLON GRAVES, M.A. Chief Forester. U. S. Department of Agriculture FIRST EDITION FOURTH THOUSAND NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL. Limited Copyright, 1906 BV HENRY SOLON GRAVES PRESS or BHAUNWOHTH & 0(5. BOOKrjINOEHS AND PHIN BROOKLYN. N. Y. TO MY FRIEND GcovQC DuDles Sepmour PREFACE. The urgent need of a reference book in forest mensuration for class work at the Yale Forest School has induced me to publish my lectures, given during the past year, with such addi- tions as are necessary to present the material in the form of a book. This book is designed as a guide for students of forestry and as a reference book for practical foresters and lumbermen. It is not intended that it should replace the field instruction of the student of forest mensuration, for the subject cannot be mastered except through training and experience in the woods. Not only is it impossible to acquire from books the ability to estimate timber and to scale logs, but the scientific work in forest mensuration equally requires field experience. On the other hand, a systematic work describing the principles of forest measurements is of great service to a teacher in con- ducting his field instruction, and such a book should be of constant use to a forester, especially if he is engaged in research work. The material for the book has been selected with these principles in mind, and I have endeavored to furnish information which will be useful both to practical business men and to those engaged in work of investigation. I have drawn freely from the experience of European foresters, with particular reference to th^ir methods of measuring logs, determining the age of stands, and studying growth. vi PREFACE. I have made special use of the works of Dr. Franz Baur and Dr. Udo Muller. Acknowledgments are due to Mr. H. D. Tiemann for his assistance in preparing Chapters V and XVIII, to Mr. J. O. Hopwood for compiling the laws relating to the measurement of logs, and to Mr. Raphael Zon and ]Mr. Austin W. Hawes for reviewing certain portions of the work. Henry S. Graves. Yale University, New Haven, Conn., August I, 1906. CONTENTS. CHAPTER I. Introduction. &SC. PAGE 1 . Definition of Forest Mensuration i 2. Importance of the Study of Forest Mensuration 2 3 . Literature 7 4. Units of Measurement , 8 CHAPTER II. The Determination of the Contents of Logs in Board Measure. 5. Definition of Board Measure u 6. Board Measure Applied to Round Logs 12 7. Principles of Constructing Log Rules 12 8. Conditions Influencing the Contents of Logs in Board Feet. ... 13 g. Value of Board Measure Applied to Round Logs 14 10. Need of Uniformity in the Measurement of Logs 17 11. Principles of Constructing a Standard Log Rule 18 12. Selection of a Standard Rule 20 1 3 . Construction of Local Log Rules 21 14. Graded Log Rules 21 15. Log Rules Sanctioned by Statute 21 16. Which is the Best Log Rule in Common Use? 22 17. Early History of Log Rules « 22 18. Comparison of Log Rules 26 vii viii CONTENTS. CHAPTER III. Detailed Discussion of Log Rules. SEC. 'A'^^ 19. The Champlain Rule 27 Daniels' Universal Log Rule 32 The International Log Rule 35 The Doyle Rule 38 The Scribner Rule 41 The Maine Rule 42 25. The Hanna Rule 45 26. The Spaulding Rule 45 27. The British Columbia Rule 46 28. The Drew Rule 46 The Constantine Rule 47 The Canadian Rules 47 31. Miscellaneous Log Rules 48 CHAPTER IV. Log Rules Based on Standards, 20. 21. 22. 23- 24- 29. 30. 32- 33- 34- Definition of Standard Measure 53 The Nincteen-inch Standard Rule 54 The New Hampshire Rule (Blodgett Rule) 55 35. The Cube Rule 57 36. Other Standard Rules 57 CHAPTER V. Methods of Scaling Logs. 37. Instruments for Scaling Logs 60 38. Methods of Measuring the Diameters and Lengths 62 39. Methods of Making Discount for Defects 65 40. Rules for Scaling Used on the Forest Reserves 74 CHAPTER VI. Determination of the Contents of Logs in Cubic Feet. 41. Use of the Cubic Foot in America 76 42. The Measurement of Logs to Determine their Cubic Contents.. 77 43. Measuring Instruments 79 44. Principles Underlving the Determination of the Cubic Contents of Logs and Trees 85 CONTENTS. SBC. PAGE 45. Fundamental Formute 86 46. Determination of Sectional Areas 90 47. Methods of Determining the Volume of Logs by the Measure- ment of the End Diameters and the Length 91 48. Method of Cubing Logs by the Measurement of the Length and of the Diameter at the Middle 93 49. Method of Cubing Logs by the Measurement of the Length, the Top Diameter, and the Diameter at One-third the Distance from the Butt 94 50. Method of Cubing Logs by the Measurement of Two End Diameters, the Middle Diameter, and the Length of the Log 95 51. The Method of Fifth Girth 95 52. Burt's Quarter-girth Method 96 53. Other Methods Chiefly of Scientific Interest 97 54. Contents of Logs in Cubic Meters 98 CHAPTER VIL Determination of the Cubic Contents of Squared Logs. 55. Method of Quarter Girth 99 56. The Two-thirds Rule 99 57. The Inscribed Square Rule 100 CHAPTER VIII. Cord Measure. 58. The Measurement of Cord -wood loi 59. Amount of Solid Wood in a Stacked Cord 103 60. Relation between Cord Measure and Board and Standard Measures 109 CHAPTER IX. The Contents of Entire Felled Trees. 61. The Measurement of Entire Felled Trees m 62. The Computation of Volume 114 63. The Measurement of Crown, Clear Length, and Merchantable Length 116 64. Description of the Tree Measured 118 Z CONTENTS. CHAPTER X. The Determinatiom of the Height of Standing Trees. SEC. PAGB 65. Rough Methods of Measurement 120 66. Height Measures 122 67. The Faustmann Height Measure 122 68. The Weise Height Measure 129 69. The Christen Height Measure 131 70. The Klaussner Height Measure 133 71. The Winkler Height Measure and Dendrometer 137 72. The Brandis Height Measure 141 73. CUnometer for Measuring Heights 144 74. The Abney Hand Level and Clinometer 145 75. Other Height Measures 147 76. General Directions for the Measurement of Heights of Trees . . 148 77. Choice of a Height Measure 149 78. The Use of Dendrometers 150 CHAPTER XI. Determination of the Contents of Standing Trees. 79. Estimate by the Eye 152 80. Estimate of the Contents of Standing Trees by Volume Tables and Form Factors 155 81. Rough Method of Estimating the Cubic Contents of Standing Trees 155 82. Hossfeldt's Method 155 83. Pressler's Method 155 CHAPTER XII. Volume Tables. 84. Definition of Volume Tables 158 85. Volume Tables for Trees of Different Diameters 159 86. Volume Tables for Trees Grouped by Diameter and Number of Logs 163 87. Volume Tables for Trees of Different Diameters and Merchant- able Lengths 164 88. Volume Tables for Trees of Different Diameters and Tree Classes 164 CONTENTS. SBC PAGB 89. Volume Tables for Trees of Different Diameters and Heights. . 166 90. Graded Volume Tables i5g CHAPTER XIII. Form Factors. 9 1 . Definition of Form Factors jy. 92. The Use of Form Factors j-5 93. Variations in the Value of Breast-height Form Factors 176 94. Construction of Tables of Form Factors lyg 95. Absolute Form Factor 182 96. Normal Form Factor 132 97. The Conception and Use of Form Exponents 182 98. Form Height 184 99. Special Methods of Determining Form Factors 185 100. Method of Form Quotients 188 CHAPTER XIV. Determination of the Contents of Stands. 10 1. Problems of Determining the Contents of Stands 190 102. Timber Cruising i^i 103. Estimate by the Eye loi 104. Estimate by the Inspection of Each Tree in a Stand 194 105. A Method Used in Michigan 106 106. Estimating by Working over Small Squares 197 107. Estimating in 40-rod Strips log 108. Erickson's Method 1^8 109. Estimate by Use of Stand Tables 200 1 10. Estimate by the Use of Valuation Surveys 202 111. The Use of Strip Surveys 202 112. Distribution of the Strip Surveys 203 113. Data for a Forest Map 206 114. Measurement of the Trees 207 115. RecordinjT the Measurements 208 116. Number of Strip Surveys Required for an Estimate 208 117. Advantage of Strip Surveys 209 118. Accurate Plot Surveys 209 119. Instruments Used in Laying Off Sample-Plots 210 120. Necessary Precision in Laying Off Sample Plots 214 121. Shape and Size of Sample Plots 215 xii CONTENTS. SEC. PAGB 12 2. Marking the Boundaries of Sample Plots 215 123. Calipenng 216 124. The Location of Sample Plots 216 125. Computation of Volume of the Trees on Valuation Areas 219 126. Determmation of Volume of Stands by the Use of Felled Sample Trees 224 127. The Mean Sample-tree Method 224 128 Arbitrary Group Method 229 129. The Volume-curve Method 232 130. The Draudt Method 233 131. The Urich Method 236 132. Hartig's Method 240 133. Block's Method 240 134. Method of Forest Form Factor 241 135. Metzijer's Method 241 136. Method of Absolute Form Factor 242 CHAPTER XV. DETERMIN.A.TIO.NI OF THE AgE OF TrEES AND StANDS. 137. The Age of Felled Trees 244 138. Estimate of the Age of Standing Trees 246 139. The Age of Tropical Trees 248 140. Determination of the Age of Stands 248 141. Economic Age 252 CHAPTER XVI. The Growth of Trees and Stands. 142. DifTercnt Kinds of Growth 254 143. Tree Analyses 256 144. Preparation of a Felled Tree for Measurement 257 145. Determination of the Average Radius 2 58 146. Instruments for Measuring Diameter Growth 260 147. Counting the Annual Rings from the Pith Outward 261 148. Counting the Rings from Bark toward Pith 262 149. Investigations of Diameter Growth 265 150. Determination of Diameter Growth 266 151. Separate Studies Made for Trees Growing under Different Con- ditions 268 152. The Study of Diameter Growth in Even-aged Stands 268 CONTENTS. xiii SBC- PAGB 153. The Study of Maximum Diameter Growth in Even-aged Stands 272 154. The Measurement of the Minimum Diameter Growth 273 155. Stimulated Growth after Thmnmg 274 156. Rate of Growth in Uneven-aged Stands 271- 157. Determmation of the Mean Annual Growth of Trees in Uneven- aged Stands ___ 2-5 158. Prediction of Growth for Short Periods 277 159. Tables of Growth of Trees of Different Diameters 278 160. Study of the Growth of Trees in Area 282 161. The Growth in Height of Individual Trees 283 162.' Determination of the Rate of Growth of Trees in Height. . . . 284 163. Height Growth of Even-aged Stands 287 164. The Growth in Height of Trees of Different Diameters 288 165. Study of the Rate of Growth of Individual Trees in Volume. . 290 166. Graphic Method of Determining the Average Volume Growth of a Group of Trees 293 167. Modification of the Method by the Author 295 168. Determination of Volume Growth for Short Periods 298 169. Pressler's Modification 299 170. Determination of the Growth in Volume by Means of Form Factors 300 171. Estimate of Volume Growth in the Future 300 172. The Rate of Growth Percent 301 173. Determination of Volume Growth Percent of Standing Trees . . 304 1 74. Pressler's Method 304 175. Schneider's Method 307 176. The Increment of Stands 309 177. Prediction of the Increment of Even-aged Stands for a Short Period 310 178. To Determine the Growth in Volume of an Entire Forest 3J4 CHAPTER XVII. Yield Tables. 179. Definition of Yield Tables 316 180. Yield Tables for Even-aged Stands 316 181. European Yield Tables 317 182. Normal Yield Tables 318 183. Contents of Normal Yield Tables ,^ 320 184. Uses of Normal Yield Tables 321 185. Collection of Data to Construct Yield Tables . 322 »V CONTENTS. SBC. WLGg i86. Selection of the Sample Plots 323 187. Necessary Number of Sample Plots 324 188. Thinning of the Stand before Measurement 324 189. Measurement of the Plots 324 190. Description of the Sample Plots 324 191. Construction of the Tables 325 192. Normal Yield Tables in this Country 326 193. Normal Yield Tables for Unthinned Pure Stands 327 194. Yield Tables for Thinned Stands 328 195. Normal Yield Tables for Mixed Forests 331 196. Yield Tables for Many-aged Stands 334 197. Necessary Field Work 335 198. Construction of Yield Tables 337 199. Indian Yield Tables for Many-aged Stands 338 200. Empirical Yield Tables 341 201. Periodic Measurement of Permanent Sample Trees and Plots.. 344 302, Permanent Sample Plots in this Country 345 CHAPTER XVIII. Graphic Methods Used in Forest Mensuration. 203. The Use of Graphic Methods 349 204. Plotting of Values on Cross-section Paper 350 205. Construction of Curves 352 Appendix. Legislation Regarding the Measurement of Logs 359 List of the Most Important Works Dealing with Forest Mensuration . 368 Tables Showing the Contents of Logs 375 Volume Tables for Standing Trees and Tables of Form Factors 402 Tables of Growth and Yield 416 Miscellaneous Tables 429 FOREST MENSURATION. CHAPTER I. INTRODUCTION. I. Definition of Forest Mensuration. — Forest mensuration deals with the determination of the volume of logs, trees, and stands, and with the study of increment and yield. As usually defined it includes the measurement of standing trees, logs, and other parts of felled trees, but not the measurement and grading of any form of lumber, such as boards, shingles, staves, heading, etc. It does not deal with the measurement of such products of trees as resin, gum, sugar, tannin, etc. Forest mensuration could be extended to include the measurement and grading of lumber, but in the author's opinion this subject, hke the determination of the money value of stumpage and land, should be considered under the head of lumbering. In a systematic division of the science of forestry, mensura- tion falls under forest management and is often included in text- books on that subject. Forest mensuration also touches silvi- culture very closely, for its principles are used in the determina- tion of many silvical characteristics of trees, including incre- ment and yield, form and development of fhe stem and crown, etc.; and the determination of the method of silviculture appli- cable under a given set of conditions is dependent on the results of measurements. 2 FOREST MENSURATION. 2. Importance of the Study of Forest Mensuration. — In many respects forest mensuration is the most important branch of technical forestr}-, and Hes at the foundation of all practical work in the woods. The buying and selling of logs and standing timber, the valuation of forest holdings, the determination of the prac- ticability of forestr}' as distinguished from ordinary lumbering, and all work of forest organization, depend on a knowledge of forest mensuration. The branch of the subject most interesting and valuable to the lumberman is that dealing with the measurement of the contents of logs and standing timber. The study of growth lies more within the province of the forester, who must be able to foretell the future yield of forests, as well as scale logs and estimate timber. The importance to the practical forester of a knowledge of timber cruising and scaling is obvious without discussion. On the other hand the value of the study of the rate of tree growth has not been clearly understood in this country. Forestr)' begins with the recognition that forests have a value not merely in the trees standing at any given time, but in their power by growth to produce wood and timber in the future. The practical purpose of all study of growth is to measure this producing power of forests. The forester claims that the growth of forests can be increased by certain methods of treatment, and that in the long run the yield in money will be greater when they are so treated than when handled in the ordinary way. Better conditions of growth can, however, be brought about only through some present outlay of money, labor, or time. This outlay may take the form of extra care on the part of the chopper in protecting young growth, a curtailment of present gains through leaving some merchantable trees for seed, an increased cost of cutting, or a direct outlay of money for protection against fire, marking the trees to be cut, planting, prunmg, or other work of improvement. In most cases the forester cannot tell wlicther forestry will pay until he ascertains how rai)idly the trees will grow under INTRODUCTION. 3 improved conditions, and is thus enabled to compare the results with what would take place under the usual treatment. Some forests require treatment along the lines of forestry for other than financial reasons, as, for example, in certain public reserves and private pleasure-parks. But in most cases the measures of the forester can be advised only when they can be shown to be financially profitable, and this cannot be determined except through a knowledge of growth. A forester's usefulness depends, therefore, not merely on his knowledge of the nature of tree life, and on his ability to establish the best conditions for rapid growth of forests, but also on his ability accurately to forecast, from the business standpoint, the outcome of his recommended measures. Sometimes it is obvious to the forester that the improved growth will be sufficient to justify the methods of forestry, but even then his conclusions are based on a general knowledge of the growth of the trees in question. He may not be able tc express his results in figures, but may 'still be certain that the increased growth will warrant the expenditures he recommends. As a rule, however, the forester must justify his proposals from definite data as to rate of growth rather than from general estimates. The forester to-day is heavily handicapped on account of the lack of accurate data pertaining to growth. His recommen- dations as to the advisability of forestry and his proposals for various methods of handling forest lands often fail to carry con- viction because he is unable to show what may reasonably be expected in the way of financial returns. The situation in southern New England may be taken as an illustration. The question constantly comes up whether it is worth while for the farmer to plant up abandoned pastures rather than to wait for the trees to come in by natural reproduction. Should such lands be planted at all, and, if so, with what species? The forester already knows that chestnut poles may be produced in forty years, but he does not as yet know how many chestnut trees 4 FOREST MENSURATION. to the acre would be standing in a given locality at the end of forty years, or what proportion of them would he suitable in size and quaUty for poles. Not having these accurate data, he is not in a position to forecast for the farmer, better than by a random guess, the future money returns from the venture. Again, the forester does not yet know whether chestnut will yield a greater amount of timber than white pine or other fast-growing species. These questions cannot be answered until an accurate study has been made of the increment and yield of these species. Farmers and lumbermen are frequently urged to make thinnings for the improvement of the composition and growth of their woodlands. But as yet very few private owners have under- taken such improvement cuttings and in most cases have done the work experimentally and not with confidence in increased financial returns. The majority of private owners will not intro- duce forestry until the forester, through his study of growth, can prove that planting and all other outlays of time, labor and money will result in increased money returns. An accurate knowledge of the subject of growth is necessar>' not only to decide whether the outlays involved in forest methods will yield a good financial return, but also to determine the true value of young woodlands. Their real value depends upon their power of production, and this can be ascertained in no other way than by the use of data obtained in the study of growth. At the present time cut-over land is valued in a largely arbitrar}- v^ray — by a sort of guesswork or by local custom. Often two tracts of cut-over land sell for the same price per acre without regard to whether they are correspondingly well stocked with young trees. Thus a value of $5.00 per acre may be placed upon young sprout land through custom, whereas, in fact, it may be an extremely good permanent investment at $10.00 per acre or a very poor one at $5.00. WTien a purchaser is seeking cut-over land as a permanent investment, he should have a more exact knowledge than at present of its real capability for growth. Many owners have disposed of cut-over lands which they INTRODUCTION. S certainly would have held, had they known how quickly a new crop would follow. On the other hand many owners have held land for a second cutting with the expectation of securing the second crop sooner than the land is capable of producing it. Water companies and railroads often pay excessive prices when purchasing land, because they have no knowledge of tree growth. The study of forest growth is of value in damage suits. As far as the writer is informed, damage based on the future growth of trees has never been awarded by an American court for injury to woodlands. Railroad companies are frequently sued for the recovery of damages caused by the burning of immature timber. In such cases it is apparent that the real damage is not repre- sented by the sale value of the immature timber destroyed, but by its prospective value. Young woodland has a prospective value to its owner as truly as a young orchard of fruit-trees has to its owner; the only difference is in the character of the product. In suits against railroad companies for burning young woodland the damages awarded are at present based on guesswork rather than on the real value of the property injured. An illustration of the destruction of young timber which has value through its capacity for growth may be taken from the pine region. Suppose that a stand of white pine, 20 years old, is destroyed by fire from a railroad. When the railroad company is sued it will contend that the damage should be based on the sale value of the standing timber destroyed, probably about 15 cords to the acre, worth not over $15.00. The owner, on the other hand, will contend that the damage should be based not on the present but on the future value of the timber. He may justly claim that he expected to hold the property until the timber is 50 years of age, when it would yield about 50 to 55 cords of wood per acre. Of this about three fourths would be suitable for lumber and the remainder for fire- wood, worth all together $160.00 per acre, at a conservative estimate. The true present value of the property would be determined by discounting to the present time $160.00 and deducting therefrom the present value of all 6 FOREST MENSURATION. expenses which would have been incurred before the maturity of the timber, including the annual outlay for taxes, protection, supervision, and risk. This method of valuing woodlands has for a long time been in use in Europe. It has never been used in this country, first, because of the abundance of forests, and, second, on account of the lack of knowledge of the rate of growth of our native trees. As soon as foresters are able confidently to predict the future value of immature timber, litigants will be able to recover the true value of young woodlands when destroyed by fire or other- wise. A knowledge of forest growth is of paramount importance to large lumber companies. Many pulp and paper companies already recognize that young spruce lands have a value on account of the future crops which they will produce. There are, in this country, many opportunities for profitable investment in second- growth timber lands. Such lands are now cheap because their value as a permanent investment is neither recognized nor under- stood. Thus burned-over lands in Maine may frequently be bought at a very' low price. If a full crop of white birch and poplar follows the burning, an extremely profitable return would be obtained in 40 to 50 years. Of course this would be a long in- vestment and would appeal only to stable companies of large capital, such as many of our lumber and paper companies. Cases are already on record where private owners have bought young poplar land at a very low rate and have made a large profit. It is obvious that the capacity of young timber lands for future production can be determined only through a study of tree growth. Lumbermen seeking investments in young timber lands are entirely unable to judge of the wisdom of buying any given tract until provided with an estimate of its capacity for future production. When better understood the question of tree growth will be the prime factor in the settlement of cases arising out of the INTRODUCTION. 7 violation of contracts to cut timber to a specified diameter. Thus contracts are often made in the spruce sections for the cutting of trees above lo or 12 inches in diameter. Frequently these contracts are broken by cutting all trees down to 6 or 8 inches in diameter. The owner of the land, according to the present custom, is able to collect as damages no more than the stumpage value of the trees wrongfully cut, and he receives nothing what- ever for the injury to the producing power of his forest, although such wrongful cutting may have reduced the growth of the desired timber on his land 50 per cent. If the contract had been faith- fully performed, his timber might have grown, after lumbering, at the rate of 100 board feet per acre per annum, whereas the growth has been reduced by wrongful cutting to 50, or even less, board feet per annum. The real damage to the land in such a case can be reached only through a knowledge of growth. To meet these demands foresters will spcciahze and become recognized as experts in determining the prospective value of timber lands, and as such will be called on to testify in court in damage cases and also consulted by would-be investors in timber lands. 3. Literature. — EngHsh literature on forest mensuration is very meagre. Several works on general forestry and on forest management devote a few chapters to the subject, as, for example, Schlich's Manual of Forestry, MacGregor's Organization and Valuation of Forests, The Forester, by Brown and Nisbet, and Green's Principles of American Forestry ; but none of these works treat forest mensuration fully. By far the best discussion of the subject is contained in the third volume of Schlich's Manual of Forestry. The information of most value to American foresters is con- tained in miscellaneous books, pamphlets, bulletins, and forest periodicals, but the material is scattered and often not available when desired. The German and French text-books-^re excellent. The aver- age American forester, however, cannot read German and French 8 FOREST MENSURATION. with sufficient facility to use these works. Moreover, these books do not contain a great deal of matter which an American forester must know. Every forester engaged in research should learn to read German and French in order to follow the results of foreign work in forest mensuration, much of which is of great value to us, but which cannot be entirely included in text-books. The best foreign books are the following: Die Holzmesskunde, by Franz Baur, Lehrbuch der Holzmesskunde, by Udo Miiller, Leitfaden der Holzmesskunde, by Adam Schwappach, Cubage et Estimation des Bois, by Alexis Frochot. Of these Schwappach's book is the rfiost useful to the average beginner. Surprise is often expressed that the British foresters in India have not developed a more extensive literature, and that what has been written has so little reference to the practice in India. The reason why there is so little Indian literature on forest mensuration is that there has been relatively little work of research carried on in the study of growth. There is in India no central department of research, and practically all that has been done in the study of growth has been in the preparation of working plans; and as a rule the data of growth are based on relatively few measurements. The methods of mensuration, working plans, and silviculture in India are of great value to American foresters in the rhihppincs. It is unfortunate that a more complete account of these methods has not been presented together in a scries of books. A list of books on forest mensuration is given in the Appendix. 4. Units of Measurement. — The ordinary American units are used in the work of forest mensuration in the United States. The diameter measurements arc taken in inches. Lengths of logs and trees arc measured in feet. For ease in averaging and comparing the results of measurements, inches are divided into INTRODUCTION. 9 tenths instead of eighths, and feet are divided into tenths of feet instead of into inches. It is not necessary or desirable at the present time to use the metric system in forest work in the United States. Although clumsier than the metric system, the ordinary American units may be made fully to answer the requirements of the most exacting scientific work. The metric system has many advantages over the present American system, but the results of measurements taken in the woods, if expressed in the metric units, would be unintelligible to most persons for whose practical use the figures are designed. This does not apply to the Philippine Islands, where the metric system has already been introduced with success. The unit of volume most commonly used in America in the lumber industry is the board foot. In small transactions, standing timber is often sold by the lot or for a specified amount per acre. Standing trees which are to be used for lumber are occasionally sold by the piece. Hoop-poles and other small wood are sold by the hundred or thousand. Ties, poles, piles, and mine props are sold by the piece, the price varying according to specifications as to diameter, length, and grade, or by linear feet. Fire-wood and wood cut into short bolts, such as small pulp- wood, excelsior wood, spoolwood, novelty wood, heading, etc., are ordinarily measured in cords. • In the Adirondack Mountains the 19-inch standard, or as it is often called, "market", is a common unit of log measure. In some localities a log 22 inches in diameter at the small end, and 12 feet long, is used as a standard log and is the unit for buying and seUing timber. In other sections standards are used which are based on logs of other dimensions, as explained in a later chapter. In New England wagon stock is sometimes sold by the cubic foot, but the unit is not commonly used in commercial transac- tions in this country. WTien used, it is employed to measure long timber, and the results are calculated for the square sticks rather than for the full contents of the round logs. The cubic lO FOREST MENSURATION. foot, however, is commonly used in measuring precious woods imported from the tropics. Such timbers are also sold by the ton. Formerly the Spanish cubic foot was used in the Philip- pines, but the cubic meter is now the standard unit, as estab- lished by the Forest Act of 1904. CHAPTER II. THE DETERMINATION OF THE CONTENTS OF LOGS IN BOARD MEASURE. 5. Definition of Board Measure. — The unit of board measure is the board joot, which is a board one inch thick and one foot square. The contents of a board one inch thick are equal to the number of square feet of surface of the board's side; hence the term superficial contents which is applied to the number of board feet in lumber. Board measure is used also for measuring the contents of Umber of other thicknesses than one inch and other widths than one foot, as plank and scantling. The ex- pression superficial contents, which originally was applied to inch boards, is now popularly applied to the number of board feet ii lumber of any dimensions whatever, and also to the contents, board measure, of round logs. The number of board feet in any piece of lumber is obtained by multiplying the product of the width and thickness in inches by the length in feet and dividing by 12. It is necessary to divide by 12 because the width of the board is expressed in inches instead of feet. Thus a 2X4 scant- /2X4.Xr2\ ling, 12 feet long, contains ( 1=8 board feet. Tables are constructed to show the contents of boards and scantling of all commercial dimensions. Such tables are published in a variety of forms, usually in so-called Ready Reckoners, such as those mentioned on page 369. In some localities board meas- ure is based on boards | of an inch in thickness. In this case the unit is a board one foot square and } of an inch thick. Con- 12 FOREST MENSURATION. siderable confusion has resulted from this deviation from the usual unit. 6. Board Measure Applied to Round Logs.— In America the contents of round logs are usually measured in board feet. This measure does not show the entire contents of logs, but the amount of lumber which it is estimated may be manufactured from them. The contents of any given log are determined from a log table showing the estimated number of board feet which can be cut from logs of different diameters and lengths. Such a table is called also a log scale or log rule. The method of constructing a log table or rule is to reduce the dimensions of perfect logs of different sizes, to allow for waste in manufacture, and then to calculate the number of inch boards which remain. 7. Principles of Constructing Log Rules. — There are, in general, five m.ethods of constructing log rules. 1. The method of diagrams. Full-sized circles of all diam- eters are drawn on large sheets of paper. Lines are drawn across to represent the boards, each being separated by a narrow band representing the saw-kerf. As many boards are fitted into the diagram as possible, assuming a specified minimum width of board and a reasonable width of slab. The contents in board feet are then calculated from these diagrams for logs of all lengths and diameters. 2. Mathematical formulae. In this method a mathematical formula is used which reduces the dimensions of the log by an amount proportionate to its size, to cover the loss in slabbing, edging, and sawdust, and gives directly the amount of lumber in board feet. As described later these formula? are, with a few exceptions, mathematically incorrect, and tables derived from them are of little value except as a rough approximation which is little better than the ocular estimate of a trained sawyer. 3. By the results of actual experience at sawmills. A number of log rules have been constructed from the results of actual tests at the mill. Logs of (h'fTcrcnl sizes are followed through the mill CONTENTS OF LOGS IN BOARD MEASURE. 13 and the product of each ascertained. The results of a large number of such measurements are averaged together in the form of a log table. 4. By correcting existing log rules. Lumbermen frequently change some log rule which has proved unsatisfactory, by apply- ing corrections to make the results conform with what their own mills actually yield. 5. By first constructing a rule in standards (see page 53) and then translating to board measure by applying a uniform converting factor to each of the values in the standard rule. As shown later, this method is incorrect. 8. Conditions Influencing the Contents of Logs in Board Feet. — The amount of lumber which actually can be cut from logs of a given size is not uniform because the factors which determine the amount of waste vary under different circumstances. These factors are as follows : 1. The thickness of the saw. A thick saw causes a greater waste in sawdust than a thin one, as, for example, a modem band- saw. The old-fashioned rotary saw cut a kerf J or A inch thick, while the modem band-saw cuts out J inch. 2. The width of the smallest board which may be used. The narrower the board that can be utilized, the greater will be the total product of a specified log in board measure. If the width of the narrowest board that can be used is 6 inches, there is greater waste in slabbing than if 3-inch boards can be taken. In the former case a thick slab is thrown away which at its center is thick enough, but which is not wide enough, to make a board 6 inches wide. It is obvious that such slabs often would saw out a 3-inch board. 3. The thickness of the boards. A log sawed into 2-inch plank will yield a greater number of board feet than if sawed into inch boards, because there are fewer cuts and hence less waste in sawdust. If the boards are cut less than one inch in thickness, there would be even a greater sawdust waste than by sawing i-inch boards. 14 FOREST MENSURATION. 4. Skill of the sawyer. Great judgment is required to cut timber in such a way as not to waste any material besides the absolutely necessary slab and saw-kerf. As a rule the sawyer must decide very quickly how a given log should be sawed, so that he must be a man of clear head, quick perceptions, and great experience. Mill-owners find it economy to hire the best available sawyers, e^•en at very high wages. 5. The efficiency of the machinery. It is obvious that a saw which is poorly set and filed will waste more material in saw- dust than one properly handled. Cheap machiner}' often pro- duces boards thicker at one end than at the other. This means that the total product from a given lot of logs will be less than could be obtained from better machiner}-. 6. Defects in the timber. .Very few logs are perfect. In the majority of logs there is more or less waste due to crooks, rot, knots, worm-holes, or other defects. . 7. Amount of taper. It is evident that logs having consider- able taper will yield more than those with little or no taper, since some short boards may be cut from the wider portion of the logs. 8. Shrinkage. Boards shrink to a certain extent after sawing. 9. Value of Board Measure Applied to Round Logs. — The lack of uniformity in the conditions influencing the contents of logs in board feet has led to wide differences of opinion as to how log rules should be constructed. It is obvious tliat a rule based on a ^-inch saw-kerf and a given allowance for waste by edging does not give accurate measure when used with a saw of different gauge and in a mill which wastes less wood in edging than allowed by the rule. Many luml)ermen have not been satisfied with such log rules as have been constructed, and have devised new rules to meet their s]xrial local re(]uirements. The multiplication of rules has conlinui'd unlil tlu-rc arc now over forty in use in this country and Canada, The large number of rules, their inconsistencies, and the incorrect methods used CONTENTS OF LOGS IN BO/IRD MEASURE. 1$ in applying some of them have led to great confusion and incon- venience; and in some cases landowners have been defrauded through the use of defective rules. One of the sources of difficulty in log measurement is the lack of uniformity in applying any given rule. Most rules require the measurement of diameter at the small end of a given log, on the assumption that the increase at the other end is lost in slabbing. Inasmuch as the taper is thus left out of consider- ation, a single long log will show a different product, with a given log rule, according to the lengths and arrangement of the short logs into which it may be cut. In some cases, of course, a long log may be divided only in one way because of crooks or other imperfections which have to be avoided. But with a perfectly straight long log there may be a dozen or more methods of arranging the short lengths, and in almost every case a different product will be obtained from the log rule. This is well illustrated by the example of two pitch pine trees measured in Pennsylvania, each having a merchantable length of forty-two feet (see table, page i6). This table shows a variation of the scale of tree No. i between 149 and 181 board feet, and of tree No. 2 between 136 and 167 board feet, according to the method of cutting. The largest scale is obtained by cutting four logs. In practice, however, it would frequently be more profitable to cut three logs with a smaller scale, because of the greater expense in handling the larger number of logs. Appreciating the facts explained above, one is inclined to advocate the abolishment of the board foot as a unit in measuring round logs. The board foot is, however, an exceedingly convenient unit. It is much simpler for the millman to know at once the actual product of logs than to be obliged to calculate the product by applying converting factors to some other unit like the cubic foot or the standard. In estimating the^yield of a given tract in saw timber, in purchasing stumpage to supply a mill for a given length of time, in valuation of . forest land and similar work, i6 FOREST MENSURATION. Tree 1. Tree H. Tree L Tree H. Log No. Length of Log, Feet. Total Scale, Bd. Ft. Log No. Length ot Log, Feet. Total Scale, Bd.Ft. Log Ko. Length of Log, Feet. Total Scale. Bd. Ft. Log No. Length of Log, Feet. Total Scale, Bd.Ft I 2 3 i6 14 12 153 I 2 3 16 14 12 153 I 2 3 16 16 10 157 I 2 3 16 16 10 157 I 2 3 14 i6 12 149 I 3 14 16 12 12 14 16 149 136 I 2 3 10 16 16 157 I 2 3 10 16 16 143 I 3 3 12 14 i6 lO lO lO 12 lO lO 12 lO 162 I 2 3 I 2 3 16 10 16 153 I 2 3 16 10 16 144 I 2 3 171 175 I 2 3 4 I 2 3 4 10 10 10 12 161 I 2 3 14 14 14 157 I 2 3 14 14 14 144 4 I 2 3 16 12 14 159 I 2 3 16 12 14 I 2 10 10 12 10 10 12 10 10 165 167 148 3 4 I 2 3 14 12 16 151 I 2 3 14 12 16 I lO 12 lO lO 12 lO lO lO 179 I 3 4 140 2 3 4 I 2 3 12 16 167 I 2 3 12 16 14 140 I 2 3 4 181 I 2 3 4 12 10 10 10 158 board measure has proved a very useful unit of contents and m\\ not be given up. While board measure is practical for mrasuring logs used for lumber, it is an unsatisfactory and incorrcci unit for comput- ing the contents of logs in shingles, lath, staves, r.hakes, and so on. At present lumbermen estimate roughly the nunbcrof shingles, lath, and staves contained in a thousand feet of lu^ibcr. It would be a great advantage if there were log tables showing the })roduct in shingles, staves, etc., of logs of different diameten and lengths, just as board-foot tables show the contents of logs in inch boards; CONTENTS OF LOGS IN BOARD MEASURB. i? but as far as the author is informed, no attempt has ever been made to construct such tables. Board measure is extremely unsatisfactory for measuring the product of trees or logs in pulp-wood. Practically the whole log is used in making pulp. A solid measure should be adopted, like the standard or the cubic foot for the measurement of pulp- wood, dye-wood, etc., where the whole log is utihzed. As the value of wood increases the use of the cubic foot will undoubtedly be increased and eventually to a large extent replace the board foot as a unit for measuring logs. 10. Need of Uniformity in the Measurement of Logs. — The large number of log rules and their inconsistencies have led to a wide-spread demand for a reform which will lead to uniformity in the methods of measuring logs. There is a demand for a standard log rule which may be used in all cases of dispute and which will replace the present rules in purchasing and selling logs and timber. A universal log rule is needed not only in commercial transactions, but also in scientific work of forestry, notably in investigations of the volume, growth, and yield of trees. The Government has in recent years published volume tables of standing trees, tables of growth in volume of different species, and tables showing the yield per acre of timber in different regions. Some tables are based on the Doyle, some on the Scribner, some on the Maine rules, etc. A scientific comparison of these tables is impossible because differences in results may be due to the variable differences in log rules used in computing the contents of the trees, rather than to differences in laws of growth. It will be impossible to construct a single log rule for com- mercial use which would be satisfactory to all lumbermen, with- out modifications to meet local conditions of the forest and of manufacture. Such a rule is not proposed by the author. It is, however, perfectly possible and practical to construct a log rule showing the product of logs under the best conditions, to serve; I. As the recognized commercial rule under the best con- ditions of lumbering. 1 8 FOREST MENSURATION. 2. As a standard in cases of dispute. 3. As a standard of comparison in all scientific work. 4. As a foundation for local commercial rules. Local rules can never be altogether dispensed ^Yith as long as the board foot is used as a unit in measuring logs. A local rule showing the average yield of logs of a certain species from a certain region under given conditions of manufacture is very useful in estimating timber, and it is probable that many lumber- men will insist on local rules for buying and selling logs. Thus it woull he necessary to have a local log rule for the hardwoods of the southern Appalachians, another for the second-growth timber of New England, and so on. Local log rules are necessary just as local volume tables are necessary, as an aid in estimating and, if desired by the parties concerned, for use in timber sales; but there should at the same time be a standard which is just as definite as would be a recog- nized method of measuring logs in cubic feet or cords. II. Piinciples of Constructing a Standard Log Rule. — Numer- ous attempts have been made to standardize a log rule, as is shown by the State legislation on the subject. These attempts have tended to increase the confusion because the States have adopted different rules. So far the efforts have been to select a rule from those in common commercial use. Each of these rules, however, has serious defects which makes it unfit to be a standard, and it is these defects which have prevented lumbermen from reaching an agreement as to which is ihe best rule. The question will not be settled until lumbermen agree as to the purpose and the requisites of a standard rule for measuring logs. The requisites of a satisfactory standard rule arc, in the author's opinion, the following: 1, It should show the product of logs in boards one inch thick. 2. It should be based on the use of a saw cutting a specified kerf, for example \ inch. CONTENTS OF LOGS IN BOARD MEASURE. 19 3. It should include boards down to a specified minimum width, for example 3 inches. 4. Its construction should presuppose the use of good machinery and skilled sawyers. 5. It should be based on logs normally straight and sound. Logs are seldom absclutely perfect, there being nearly always some loss by crook or hidden defect. Logs normally straight and sound are then the best which are commonly found, in con- trast to ideal logs which are scarcely ever encountered. An allowance in the rule should, therefore, be made to cover this loss wdiich is practically always present. 6. It should be based on correct mathematics. This point is mentioned because many rules are mathematically unsound, as explained in the discussion of the various rules. 7. It should be based on a formula rather than on diagrams or mill scales. The objections to the use of diagrams are: (i) the values in the table increase from diameter to diameter by irregu- lar differences; (2) the values cannot be easily corrected to conform to new or special conditions of manufacture; (3) the values cannot be easily checked as to correctness. The method of constructing log rules by tallies from a mill scale is undesirable, because it would be almost impossible to conform to the con- ditions and requisites mentioned above. Such a rule would almost inevitably bear the impression of local quality of timber and local conditions of manufacture. It would have temporary and only local value; and when it should become necessary to alter it to meet new conditions, the work would have to be done all over again. The rule should be based on a mathematical formula by which the volume of the whole log, the loss by saw-kerf, slabbing and edging, and the loss by normal defects, are separately deter- mined. The amount allowed in the formula for loss in manu- facture should not be determined theoretically, but by tests at the mill. Such a formula can be corrected for different widths of saw, special dimensions of the product, and so on. At any 20 FOREST MENSUR/iTION. time one can check the values in the table or himself construct a table. But the most satisfactory feature of the method is that the exact allowance for waste in slabbing, saw-kerf, crook, etc., is known, and there is an opportunity to discuss and agree on these points, so vital to the success of a universal rule. 12. Selection of a Standard Rule. — None of the rules now in use met the requirements of a satisfactory standard rule. Two independent investigations, however, have recently been made which have clearly demonstrated the correct method of con- structing log rules, and which should lead to the desired harmony in log measurement. The studies of Prof. A. L. Daniels of Bur- lington, Vt., and Prof. J. F. Clark of Toronto, Ont., constitute the most valuable contributions to the subject of log measure- ments that have been made. Each has proposed a formula to construct a standard log rule, based on the same general mathe- matical principles and designed to accomplish the objects of a standard rule described in the preceding section. The formulae differ mainly in that Prof. Daniels makes no allowance for loss by crooks and disregards the taper of logs, and Prof. Clark makes a greater allowance for defects, including normal crook, and provides for a taper of one-half inch in every four feet of length. The differences between the two rules are not great, but in the author's opinion neither can be definitely proposed as the universal standard without some further study. Thus Prof. Clark's table appears to meet the requirements of the standard rule so far as pine is concerned; but it remains to be proved whether his allowance for crook and taper are applic- able to southern hardwoods, cypress and other trees than pine. Prof. Daniels allows less for normal defect than Prof. Clark and this point in his formula would have to be proved by mill tests which have not yet been made in sufficient numbers. The points of difference between the two rules are capable of proof by tests. The establishment of one of these rules or of some other rule as a universal standard can 1)c brought about only by agreement among the lumbermen and foresters, and by sub- CONTENTS OF LOGS IN BOARD MEASURE. 2X sequent enactm&nt of the necessary legislation giving legal sanc- tion to the rule. 13. Construction of Local Log Rules. — It was explained in section 10 that local log tables will be required in estimating and valuing timber and for many commercial transactions. At the present time the old rules are used for this purpose. The mill-scale studies which are being made by the U. S. Forest Ser- vice are, however, proving the old rules to be inaccurate, and in many cases unsuited even for local use. It is probable that nearly all the old rules will have to be superseded by new local rules. Where the necessity for a new local rule is proved, the new one should not be made directly from the average of the mill-scale tallies, but should rather be based on the universal rule by applying to it corrections which are determined in the local mill studies. Local log tables are necessarily more or less temporary in character, differing from the standard rule in the allowance for defects, crook, saw-kerf, thickness of slab, and so on, — factors which will in time be changed. Local log rules will be constructed by adding to or subtracting from the values in the standard rule a certain percent or per- cents, the latter being determined by local mill studies. 14. Graded Log Rules. — Graded log rules show the product of logs in lumber of different grades and value. A number of such tables have been made up by the U. S. Forest Service in con- nection with the preparation of graded volume tables. None have as yet been published. They promise to serve a useful purpose in the valuation of logs. 15. Log Rules Sanctioned by Statute.— There are in the United States six different log rules sanctioned by State law, as follows : The Doyle rule, which is the statute log rule of Louisiana, Florida, and Arkansas; the Scribner rule, adopted by Minne- sota, Idaho, Wisconsin, and West Virginia; the Spaulding rule, adopted by California; the Verm.ont rule; the New Hampshire rule; and the Drew rule, adopted by Washington. To this list may be added the New Brunswick, the Quebec, and the British 2 2 FOREST MENSURATION. Columbia rules of Canada. The U. S. Forest Service has adopted the Scribner rule (Decimal C). Several lumber associations give their official sanction to certain rules; for example, the Doyle- Scribner combination rule, adopted by the National Hardwood Lumber Association, and the Drew rule, sanctioned by the Puget Sound Timbermen's Association. This official approval of different log rules only adds to the general con- fusion. i6. Which is the Best Log Rule in Common Use. — From the standpoint of accuracy, the Maine rule, if used with short logs, is probably the best of the Eastern rules in common use. The present methods of using it to measure long logs give unsat- isfactory results, but this is due to the incorrect application of the rule, and not to defects in the log table. The Spaulding rule appears to give satisfactory results for the Pacific Coast con- ditions. 17. Early History of Log Rules. — The board foot as a unit of measure for sawed lumber has been used in this country for a great many years. Thus the measurement of the superficial contents of boards is described in A Complete Treatise on the Mensuration of Timber, by James Thompson, published in Troy, New York, in 1805. At that time, as shown in this same work, round logs were measured entirely in cubic feet, by the old Fifth Girth Formula, brought over from England. In the book above mentioned there is no reference to log tables or to estimating the contents of logs in board measure. The earliest mention of a log rule for board measure, known to the author, is contained in A Table for Measuring Logs, Anon., Portsmouth, ISIe., 1825. The rule, as described in this brochure, is as follows: "Cast \ of the diameter of the log and then reckon as many boards as there are inches diameter, and the width of boards the same. For example, take a log 12 feet long and 12 inches through at the top, and by casting off \ as above mentioned it leaves q inches, which I call 9 boards 9 inches wide and each board makes 9 feet; and then mnltij)ly the number of boards by the number CONTENTS OF LOGS IN BOARD MEASURE. 23: of fed in one board and the product is 81 feet; and by the same ade you may cast any log whatsoever." It will be seen that this is the same as the square of the three- fourths formula described on page 49. One of the oldest formulae for determining the board con- tents of logs is shown in The Mechanic's Assistant, by D. M, Knapcn, published in New York in 1849. The rule is as follows: "If the log be 2 feet in diameter, or less than 2 feet, allow 2 inches on four sides for the thickness of the slabs, and one-fifth for saw-calf, and one board for wane ; but if the log is more than 2 feet in diameter, allow 3 inches for the thickness of each of the four slabs, and one-fifth for saw-calf, and two boards for wane. If, however, the logs are very straight and smooth, the slabs may be thinner. " For so-called market boards the rule reads: "Market boards are usually a httle less than one inch in thick- ness; and consequently the number of feet of market boards in a log will be greater than the number of feet of inch boards. To find the number of feet of market boards, in any log, allow one- eighth for saw-calf, and apply the above rule for inch boards with this difference. " About this same time there appeared a rule giving the same results as the present Doyle rule, reading as follows : "From the diameter of the log, in inches, subtract 4 for the slabs. Then multiply the remainder by half itself, and the product by the length of the log, in feet, and divide the result by 8: the quotient will be the number of square feet." ■ This nde was published for the first time, as far as the author is informed, in Elements of Drawing and Mensuration, by Charles Davies, New York, 1846. These facts are interesting in view of the introduction of the Doyle rule between 1870 and 1880, which gives exactly the same results as this old rule and which was claimed to be new. Undoubtedly Mr. Doyle's formula was original, but an equivalent table had been used thirty to forty years before. 24 FOREST MENSURATION. COMPARISON OF LOG RULES SixTeen- Name o£ Rule. Diameter Champlain Universal Scribner * Doyle Holland or Maine Hanna. . . ; Spaulding New Hampshire Humphrey or Vermont. Bangor Cumberland River Favorite Baxter Square of three-fourths. Square of two-thirds. . . Drew Herring Quebec British Columbia New Brunswick Dusenberry Orange River Chapin Northwestern Derby Partridge Parsons f Ropp Stillwell Baughman's rotary saw Baughman's band-saw. . Saco River •)■ Ballon Wilson Wilcox Warner Boynton Carey t Forty-five White Finch and Apgar Constantine Ake Wheeler International (band-saw) 14 18 4 20 19 24 23 27 16 28 26 21 17 20 26 22 23 22 20 43 32 32 16 44 32 35 43 41 34 48 25 32 33 49 46 41 41 41 49 40 46 30 32 3S 30 67 •41 40 45 10 13 14 16 18 Board 57 54 36 68 51 50 54 66 69 47 56 75 58 49 59 55 42 64 61 75 68 64 65 70 73 75 61 67 40 60 61 51 105 6,S 6,S 70 105 89 79 64 105 So 96 100 68 64 84 108 85 80 84 96 68 76 84 77 1 10 102 100 69 96 105 1 12 108 79 lOI 66 62 90 No 90 79 74 151 95 95 105 146 127 114 100 142 117 114 106 130 137 93 98 117 147 114 No va 107 120 119 130 100 104 1 12 117 148 140 140 109 133 145 156 147 117 144 lOI 98 i-M value 125 114 112 21 Tf 128 132 150 193 172 159 144 179 160 161 139 170 182 121 142 156 192 150 lues gi 142 160 160 17 136 136 144 170 195 180 179 157 176 193 209 192 170 184 144 128 170 given 168 161 157 268 167 174 200 247 223 213 196 232 213- 216 176 217 238 153 197 200 243 192 ven 183 213 207 229 170 173 186 206 248 236 231 211 225 244 270 249 206 244 180 162 216 for 218 214 203 339 212 223 255 •Values for 6, 8, and 10 inchris are those used bv the T Values read off from a scaler's stick. CONTENTS OF LOGS IN BOARD MEASURE. 25 F0.1 BOARD MEASURE. FOOT Logs,. in Inches. 20 3S 34 26 28 30 32 34 36 38 40 Feet. 308 376 450 532 620 714 814 923 1038 1 159 1287 282 347 419 497 582 674 773 878 990 1 108 1234 280 334 404 500 582 657 736 800 923 1068 1204 256 324 400 484 576 676 784 900 1024 1 156 1296 302 363 439 507 614 706 795 900 1026 "35 1261 273 336 416 501 576 656 741 832 933 1066 1200 276 341 412 488 569 656 748 845 950 1064 1185 217 262 313 367 426 489 557 628 704 785 870 267 320 384 300 369 444 526 609 697 792 892 190 229 268 320 372 427 485 548 614 685 759 248 324 392 476 562 632 725 845 920 1037 1160 250 305 366 432 504' 582 665 754 848 300 365 432 507 588 675 768 867 972 236 285 341 400 464 533 605 684 768 854 946 below 20 fe et. 230 284 344 411 485 567 655 752 857 963 1067 280 347 420 507 580 673 760 867 947 1040 "73 261 320 386 457 535 619 708 804 906 1015 1 1 29 30G 362 432 229 285 346 414 487 567 652 744 841 945 1054 213 258 308 360 418 480 546 616 692 769 853 233 294 374 465 563 666 777 896 1027 1161 1296 248 324 392 450 536 632 725 845 920 1037 1 160 307 368 438 512 593 680 773 872 977 288 350 416 486 564 650 738 834 998 300 366 433 506 600 705 272 339 413 493 579 672 771 877 989 1 107 1232 261 320 385 456 533 588 675 768 310 382 457 540 633 722 822 934 1054 1142 1294 340 417 500 590 686 790 900 1022 1182 1286 1425 302 280 366 436 513 590 674 771 306 374 448 529 616 713 814 922 240 313 373 446 513 592 673 754 853 973 1 1 20 2t)3 258 316 372 431 490 560 630 366 322 384 450 522 logs over 15 fe et lo ng- 275 341 415 498 590 691 803 925 1058 290 338 402 492 575 649 728 797 258 318 400 474 552 624 733 840 928 1054 ii8i 416 507 603 708 821 942 1072 1210 1356 1511 1671 261 316 377 441 512 S88 669 ■ 277 337 404 475 553 636 725 320 390 470 555 645 745 850 965 1085 1210 1345 Santa Clara Lumber Company, New York. 26 FOREST MENSURATION. The exact date when J. ]\I. Scribner first pubKshed his log table is not known to the author. The fourth edition was issued in 1846. It is probable that the rule is one of the oldest used in the countr}-. ^ — It-is impossible to determine exactly when the board foot came into general use as a unit for measuring logs. Probably it was not generally used before 1820, for the works on mensuration printed before that date make no mention of log tables. It is probable that about the middle of the ccntur}^ a number of different ndes were constructed in different parts of the East, including the Younglove, the Parsons, the Saco River, and other rules. The conception of using a standard log as a unit of measure is also very old. The 24-inch standard is described in Davies' Elements of Drawing and ^Mensuration, mentioned above, and reference is made to the 19-inch, 22-inch, and 24-inch standards in Knapen's Mechanic's Assistant. This point is also inter- esting as showing the custom in the early days of cutting logs 13 feet long. 18. Comparison of Log Rules. — The different log rules are com- pared in the table on pages 24, 25, which shows the board contents of sixteen-foot logs of different diameters. This table, including as it docs all the log rules, is presented for the convenience of those wishing to make comparisons between the values obtained by different rules. It should be borne in mind, however, that some of them are really not comparable. For example, the Constantinc rule can hardly be compared to the Cumberland River rule, because the former gives the whole contents without allowance even for a sawdust waste, whereas the latter is intended to cover a special amount of defects such as occur in river lofTS. ; CHAPTER III. DETAILED DISCUSSION OF LOG RULES, 19. The Champlain Rule. — This rule was devised by Prof. A. L. Daniels of the University of Vermont. The following de- scription is based on certain portions of Bulletin 102 of the Vermont Agricultural Experiment Station, entitled " The Meas- urement of Saw Logs,'' and on private correspondence with Pro- fessor Daniels. In many places the author has used Professor Daniels' own language. The Champlain log rule is developed in the following way: It is assumed that all logs are straight, round, and free from defects, and that the loss in the manufacture of the board is due only to sawdust, slabbing, and edging, and not to crooks, knots, or other blemishes. The only portion of the log dealt with is that which will make boards. The thickness of the slab is based entirely on the diameter at the smallest end, the taper of the log being disregarded; in other words, the log is considered a cylinder whose diameter is the same as the average diameter of the top end of the log. We begin, therefore, with a cylindrical log, round, straight, and of perfect quality. The solid contents in cubic feet of such a log is determined by multiplying the area of the cross-section in square feet by the length, that is, by the formula V= XL or F = 0.7854X1)2x1,, in which V is the cubic volume, D the diameter, and L the length of the log. If D is expressed in inches and L in feet, it is necessary to divide the result by 144. If the log in question is 12 feet long, the formula reads 7 = 0.7854X2)2-- 12. 27 2S FOREST MENSURATION. This result may be translated into board measure by multi- plying by 12 on the assumption that each cubic foot contains 12 board feet, which is the case if the waste in sawdust, slabs, and edging be disregarded. The solid contents of the log in board feet is, therefore, obtained by the formula 5/=(o.7854Z)2i:^i44)Xi2, or for a twelve -foot log 5/^0.78541)2. It will be seen by reference to section 29 that this is the same as the Constantine rule. In the manufacture of boards two allowances for waste must be made, one for saw-kerf, and the other for slabs and edging which may be called surface waste. Consider first the allow- ance for saw-kerf. Suppose that the log is sawed through and through by the method sometimes called "slash-sawing," or "saw- ing through ahve"; suppose, further, that a circular saw is used which cuts out a kerf one-quarter of an inch wide. The loss in sawdust for the log will then be one-fifth of the contents. That is, for every inch board there is a loss of one-quarter of an inch. There remains, then, four-fifths of the solid contents. Since the con- tents of a 12-foot log is 0.7854X1)2, there remains after sawing IX0.7854D2 or 0.628322)2^ This represents the exact value of the untrimmed inch boards, including slabs, in a perfect log. It will be seen, however, that if the saw had cut a wider or narrower kerf, the numerical factor would have been different. In case of a band-saw which cuts a kerf of | inch, the contents would be - X or 0.0081 3Z>2,* 9 4 ^ ^ The waste by sawdust has now been accounted for, but no * Expr'^ssed mathematically, a saw of any thickness, S, wastes 3 parts in every i +5 parts, and the contents of the log after sawing is — r-^X^- D^. I -t-o 4 DETAILED DISCUSSION OF LOG RULES. 29 allowance has been made for loss in slabbing, edging, and for such slight imperfections as are present in the most perfect logs. It is assumed that logs, whatever the diameters, have an average amount of waste in slabbing, edging, etc., proportional to the amount of surface. The amount of surface is proportional to the diameter and length. That is, a 24-inch log of a specified length has twice as much surface as a 12-inch log, and therefore the waste in slabs, edging, etc., in the former is just twice as great as in the latter. In the same way, a 16-foot log of a specified diam- eter has twice as much surface, and therefore twice as much waste in slabs, etc., as an 8- foot log. In order to construct a log table, then, it is necessary to find the relation existing between the surface waste and the diameter. This proportion is obtained from the evidence of sawyers and scalers and by using diagrams as a check. After extensive investi- gation. Professor Daniels has concluded that the surface waste in perfect logs is equivalent to an inch board having a width equivalent to the diameter of the log; that is, for surface waste he subtracts as many board feet as there are inches in the top diameter. The complete formula, on the basis of a saw-kerf of \ inch, is .B/ = (0.628321)2 xL - 144) X 12 -Dx—. This formula may be used for any length and diameter, or the contents of 12-foot logs may be first determined and the values for other lengths obtained by multiplying by the length and dividing by 12. The formula for 12-foot logs is 5/ = 0.628322)2-7). The intimate connection should be noted that exists between this rule and the Constantine rule. Take four-fifths of the Con- stantine values, subtract the diameter, j.nd one has the Cham- plain rule. Or add to the figures in this rule the diameter, in- crease by one-fourth, and one has the Constantine figures, which 3° FOREST MEmURATION. i c i "^ lOvO t^X C^ 0 1 - (N ro •+ u~. >0 r-x ON 0 ►« CI ro •+ lO 1 CI CI CI CI CI 1 VO r^x ovoi d d d d CO a 60 o iJ "o •s bo c 1 C\0 O CO - vC "* " N ro "0 vO 00 1 ro Tj-X ro 0 O M -^ r^ O « « « i-i (S On " ^ ON NO (N O On CN NO CN rs n r^ ro lo r^ 0 "0 CI O Tt- On CO X •Tf T)- -^ I/-, to 1 1 ►- d vO "-i X cox re ON ■* VO NO t-^ t^X « 1 CnO "OO CO r^ On 1 X X 0 -1- O ON " -^o o\ 1 r^ t^x (N t~~ (Nt CN M <^ rO 1 •* CO Tt t-. ►- X CI NO C "^ CO ■* -^ lO "~, X t^ r^ On CO ON -r ON -* C iCvO vO I^X 1 X "O •+ Tl-O O t; « (N r^ -^ "O r^ 1 r< " (N ir-. On On ■-• <^ "0 t^ lO rO <~0 tJ-X O f^O On (n) (N CS tN CN PO CO O X X "I vO O f^ 1^ M CO 'I- ^ ^ "0 lO 1-1 X t^ On vO 1-1 "0 0 in lOvO VO t^ t^ 1-1 n ro -i- "O 1^ 1 r^ LO -t-O X X C * 1 -. ^1 Cn X X O^ 'N « " c< ro -*0 O IN On r^ r^ r-^ On O 1-1 CI CI CI On On >-i Tj- On On CI NO On CI CI re CO ro rj- lO CO d re u". VO O -^-X d rj- u-j lo "0 vO < M O - X O lO "^ r-^ -H -^ (N ro ^ uo 0 Lc - X r^ t^X O >- 1^ r^X « lo >- lO r^ O CI lo ►1 1-1 M d CI r-NO >OvC X t^ O revO ON CI CO re re re CI t^ CO 1- C coo O •+-l 1-1 CI CI NO CI OnX X lOX O revO CI N re CO CO On I- "0 On lO On revO Cv CO CO -i- ■^ rj- lo lO 0 "O IN O X X 1-1 1-1 tN r^ rO rf O 0 O NO O r^X O ■-• re 1-1 0 O CI rD "O r^ On 1-1 " « " « M ■ »o o Tt- 0 r- re lOX ►- re M CI d re CO VO >OvO X ►- vO Ov d lO O CO CO Tj- 1^ -t- © lO On -)- O r^ lO -h -H (N CI ro -f -t lOX " lO lOv^ t^ ON O 1-. r>. U-) CO CO M CO lO t^ On ce lox CI VO ►- CO lOX 0 CI CI CI d re d On r-»vo vO ceiox « -t CO CO CO -^J- Tf « -)- /j i^i X ^- "- o -1 « ri o -i- On ON O -i re lO I^ •1 d d d d On rex »e d On d T^ t^ C d CO re CO -t « -t 1- - O - X irj -. M ri ri r<^ 1^. n n r'-; -t- 1 -t lOvO t^x t- O -+ ON •+ On "- CI CO lO •-< X vp "0 lO I^X 0 - UO X On O CI ro OMO O >^ 1- -to X On ►" ►- •- 1-1 -> d CO 1-1 1-1 Hi d re lO 1^ C> ►- CI d d d ro i VI si IH 1 1-1 M re "+ lO VO t-«X On O M n M m r4 w d CO "t to N M W Ci M VO r~.oo ov c « w w w t«- DETAILED DISCUSSION OF LOG RULES. 31 « (N po ■+ in ro ro rO fO '^ rO ro fO ro ■-< M PO •^ lO 10 10 10 lO UO NO r^X On 0 lO 10 »o *o 0 1^ r^ « 0 fo a\ os 0 c - - On rO - X NO PO 'T >0 iOnO t-^ X 0 PO X -1- - 0 X NO 10 X On ON 0 - - ro >0 On 10 rj- PO PI « « PI P^; -t IONO PI PI PI PI PI PI H- PI l/^ On I^X On 0 -' 0 '-' -O fN 00 r^OO X On 0^ X t^ 0^ tN r^ PO 0^ 10 -< - PI PO -^ n PI PI PI PI povo ►- X NO 10 T 'i- PO PO IOnO t^X On 1 " ^^ 0 <~0 rl- loX 1 t^ t^X X 0^ PO 0 I^ vO ^ t^ M X "i- 0 0 0 0 '- o N 0 0 0 10 ►< t^ PO " « p) p) 1:0 0 rONO " I^ ON 10 " X ^ po -i- 1010 0 10 -+ •+NO 0 "X 10 PI 0 r^ t^X On 0 -* 0 t-. lO 10 r^ 10 PI ox PI PI PI pi' pi r-O — -• ri to t^ « 10 On f^ 100 0 0 r^ X PO On r^ lO r^ PI 0 « vo r^X X On On iOnO On CS r^ I- NO "" r^ M 0 0 -' - P) -t « 0 0 0 X Tl- Q NO (N PI rn ^ '4- IT) po r^ pt 00 10 X T)- ►- r^ Ti- lONO r-- r^x -* ^NC X PI ►- X lo n 0 On On 0 "-• M 10 0 r^ "0 ro (NO 0^ *^) r^ I 10 10 100 0 PO ■+ t^O >o " lOON -)-x t-, t^ r^x X PO I^ P) t^ P) ONON 0 0 « t-~ On pox •+ r^ PI X PO 0 « PI PI PO PO c 0 0 C i^- 10 >- r^ CO ON -t >0 IONO NO •0 On ":f C X ■ 10 — X lO ■-< r^X X On 0 --«««! ^ . „ r^ 0 '^. r^ f^ ( t^ 0 -t- t^ « -t- 10 LO LCO ONVO -*- ^ -t- -t-x moo; NO NO t^ t^X 1 1 NO On (N| t^ PO -)-X ro t^ P4 X X On On 0 | 0 t^NO NO t^ 1-^ W NO ►-I NO 0 "-I >-i H r^ PI X ro PO PO •*• "d- lO 10 PO PO PO 10 On u". ►- r^ PO 10 NO r- t-~ X 0 X X o\ « f "^. u~,ZC - "0 -1- -t- -+ "O U-, -f r^ p) r^ ^ 1 X « lOX P) 100 NO NO r^ 1 I « 0 ON 0 0 NO 0 fOX PI t^X X X On 1 pOnO 0 iO 0 1 0 0 "O On •+ 1 OnO 0 0 « 1 t-- 10 -:f rO '*• X POX POX >-< PS PI ro rO NO X PI NO " POX •;)- ON >0 TT ^ lO IONO 1 1 "" 'O -+ 'i- •* 1- 1 On On 0 " PO 1 - -tx >- •+ . 10 10 "O NO NO 1 ( r~^ .- vO IN X ' r^ •- « X « , 0 t~^ t^ r^X 1 v'^ -1- PO PO -t- 1 lO ON p^ r^ « 1 X X On ON 0 1 lox " >o 0 1 •0 On 'l-X PO 1 0 0 " - M 1 NO fO 0 ONX r^ PI r^ i-i 0 PI PO PO •+ -+ "0 "OX 0 1^1 -*■ n r^ 10 PTs 1 >OX 0 'OnO , r}- -+ lOlO 10 1 ( n PI PO -I-nO 1 On pi lOX il IOnO vO no r^ On PI NO •- f~» 1 •i-X - lOX 1 t~^ t^X X X 1 pp- 0 r^ r^vo 1 PI NT On -0 r^ 1 On On On 0 'O | r-.x c " -t - "0 0 -+x - « PI PI PI 1 - n fO -HO ( -^ ro po ro t^ 1 1 ■0 r^X ON 0 PO PO PO pO Tl- >-• PI ro •+ lO f ^ •o 1 1- PI po •-)- >o 10 10 10 "0 >o NO r^x On 0 10 10 "0 IONO 32 FOREST MENSURATlOhf. give the number of board feet in the solid log. If the number of cubic feet are wanted, it is only necessary to divide the figures of the Constantine rule by twelve. Professor Daniels has devised two short rules of thumb which give nearly the same results as the Champlain rule. They are as follows: (A) Take five-eighths of the diameter, subtract one and multiply by the diameter. (B) Subtract one from the diameter, square, and the result is the contents of a log of that diameter 19 feet long. Both these short rules give slightly less than the Champlain rule. 20. Daniels' Universal Log Rule. — In October, 1903, Professor Daniels published in Bulletin 102 of the Vermont Agricultural Experiment Station a new log rule which he called the Universal rule. The principles of constructing the Universal rule are exactly the same as for the Champlain rule, except that a greater allowance is made for waste in slabbing, edging, and for slight defects. The endeavor was to secure a rule which would give the contents of logs of average grade. The Champlain rule is made for perfect logs while the Universal rule is applicable to second-grade logs which have slight crooks or other blemishes, such as are not of sufficient importance to be made subject to a special discount by the scaler. Professor Daniels gives the name "roughage" to the material wasted by slabbing, edging, and slight defects. After careful study he has given as an allow- ance for surface waste, or roughage, an amount equivalent to a 2-inch plank, whose width is the same as the diameter of the log in question. It will be remembered that this "allowance plank," as Professor Daniels terms it, was, in the case of the Champlain rule, I inch in thickness. The Universal rule, expressed by formula, reads, therefore, L .B/= (0.628322)2x1- 144) X 12 -2l>X — L '^ = (0.628322)2 X L) -M 2 - 22) X — , DETAILED DISCUSSION OF LOG RULES. 33 or for 12-foot logs, B/=o.62832D2_2r>. Professor Daniels' argument for choosing the value 2D as the width of the allowance plank is, in his own language, as follows ; "The particular value 2, which I have chosen as the thick- ness of the allowance plank, adapts the rule to what might be called a second-class log. So far as I can find out it makes it just safe for a buyer to take a fair ordinary lot of logs without any dickering over premium or discount. If a lot of perfect logs were offered, it might be fair for the buyer to give a small premium. Just where premiums or discounts are called for must naturally be left to the experience of the men in the business. The main point and prime advantage in using this rule is that they need pay no attention to whether the logs are large or small since the rule is a level one. The choice, therefore, of this second factor {2D), whether it should be 1.5 or 2 or 2.25, is, after all, as much a matter of convenience as anything in the actual business of buying and selling lumber in the log. The Universal log rule is so constructed, however, that it is very easy to get from it the figures which would have been shown if any one of these other factors had been used. Assume, for example, a log 24 inches in diameter and 12 feet long, which scales by this rule 314 board feet. In order to find what the amount would have been with the factor 1.5, we have only to add a number of board feet equiv- alent to one-half the diameter, expressed in inches. Thus in this case one-half of 24 equals 12 and 3 14 -f 12 = 326 board feet. In the same way a 12-inch log is credited by the Universal rule with 66 board feet; but if the factor were 1.5 it would scale 72 feet. This is just what the present Vermont rule allows for ^uch a log, an amount which is considered by sawyers to be more than they can get from any but an exceptionally perfect log by careful sawing. "In order to show the precise effect of choosing different thicknesses for the allowance plank I subjoin a small table for a 34 FOREST MENSURylTlON. 1 2-foot log, and different diameters, with allowance plai-ks of different thicknesses. Diameter Thickness of Plank. in Inches. 2.5 in- 2 in. I 5 in. I in. 6 12 24 36 Board feet 8 60 302 724 II 66 314 742 14 72 326 760 17 78 338 778 "I am convinced that no buyer would consent to use a rule with such figures as stand in the last two columns under 1.5 inches and i inch, and that no seller would want to use the column under 2.5 inches. I make this comparison for the convenience of readers and in order to give the fullest opportunity for candid criticism. First-class logs carefully sawed would probably yield the amounts scheduled under the 1.5 inches caption; but the fairness and wisdom of such a rule for general use on tne generality of logs is another matter." * * Prof. A. L. Daniels has shown in Bulletin 102 of the Vermont Agricul- tural Experiment Station how any given rule may be expressed by a formula as follows : " For logs of the same length the total vohiinc varies as the square of the diameter, and the trimmings, for reasons mentioned above, as the first power of the diameter The amount of board feet, therefore, is a quadratic func- tion of the diameter, a function of the form B = aD'' + bD + c. " When now the proper values are assigned to the constants a, b, and c, the scale can be computed by arithmetic. These values are easily determined when the printed scale is given, as follows: Take, for example, from Doyle's rule the amounts for a 12-foot log corresponding to the diameters 10 inches, 20 inches, 30 inches, successively, and we have: 27= looa-l- 106 4- c, 192 = 400a 4- 20^ 4- c, 507 = 900a 4- 306 4- c, from which we can easily deduce the values fl = o.75, 6= —6, c=i2, and Dovle's formula reads. Z^ = o.7sD'— 6D4- 12. DETAILED DISCUSSION OF LOG RULES. 35 21. The International Log Rule. — This log rule is the result of recent investigations by Professor Judson F. Clark, Forester of the Department of Lands and Forests, Ontario. It is designed for use with a band-saw, cutting a saw-kerf of -J- inch. The rule is based on the formula: B} = o.22D^-o.'jiD, in which the first term, o.22D^, represents the contents in board feet of a log 4 feet long, after deducting the loss in saw- kerf and shrinkage in season- ing, and the second term, o.jiD, is the waste due to square edging and to normal crook. The principles underlying the derivation of this formula are as follows: 1. An allowance of J inch is made for saw-kerf, and A inch for shrinkage and unevenness in sawing. After deducting for 16 ~D^ this loss, the contents in board feet of a 12-foot log are — X = 19 4 o.66Z>2j a.nd for a 4- foot log, 0.22 D-. 2. The minimum board is 3 inches in width, containing not less than 2 board feet. A 3-inch board must, then, be at least 8 feet long to be included; a 4-inch board, 6 feet long; a 5-inch board, 5 feet long; a 6-inch board, 4 feet long. 3. An allowance is made for a taper of ^ inch for each 4 feet of length. Professor Clark has shown that this is a conservative allowance for merchantable logs of all species so far studied in this country, including white pine, loblolly pine, spruce, balsam- fir, chestnut, and northern hardwoods. 4. Provision is made for the loss due to normal crook and that due to human and mechanical imperfections. By normal crook " In the same manner we obtain the others, which are subjoined. Universal B = o.62St,2D'^-2D. Doyle B = o.75D^-6D+i2. Vermont B = o.5oD^. New Hampshire B=o.4iD^—o.iD + i. Hanna B = o.6iD^-i.7D-6. Bangor B = o.62D^ — i.iD — i. Holland, or Maine B='o.6t,sD^ — i .45D + 2. Drew of Puget Sound 5 = 0.615^^ — 4.i25D-f 29. Scribner j5 = o.555£)'-o.55D-23." 36 FOREST MENSURATIOS. s 5 " N ro >*• to vo t-00 O O .1 i-i 1-1 i-i n I- N CO tJ- "0 ts ts M M M »0 r-00 On 0 CI CI M M fe C M C ►J 1 0 0 O >o 0 "^ »o lo o "^ lo lo « „ « N, JS O lO 0 O 0 vO On <^ r- " (N M r^ CO ■^ lO O 0 O 0 IT! O "^ O "^ ■^ lO >OnO no lO ID uo I/; O 0 nO CI X "0 t— UOX 00 On 1 0 lO 0 0 "^ O 0 - « f^ -i- lO i^ a^ O O "0 >o "O „ « « « >o o O O fN fN re ro (^ 0 lO 0 lo lo ro r- cj vO - T)- ^ U-, I/: vO 0 "^-0 lO »o t^ CI X CO On NO t- r-x X 1 ) 0 >0 lO to O "O lO 1- « M ro >OVO 00 ID >0 »0 ID O O r< "^ t^ O ■^ >H t^ M C^ O O >D O ID rOvO On re vO M (N (N re PC "~, ic O i^. 0 O "i- O^ reoO 0 O "~. 0 "0 re X fe o- Tj- NO nc r- r-x 1 O lo lo lo >o 0 "^j J „ « M rO rl-O t^ 1/5 lO 0 O lO Cs ~ Tj-o 00 H M l-l M lO T) iO O "^ 1-1 Tj- r- « Tj- M N M CO ro 0 0 O 0 "-- 00 c< vO o ■* fO 1^ Tj- lo in "^ C C C "O ON Tf o^ Tt ON "OvO vc t— r- 1 « ! 11 ri re -r "^ t^ 0 >r> o o >o o O f^ "^ f^ Q "0 >o 0 0 0 tH lO On 4- tJ- lio "0 o uo lo uo lO O ■* On 'l- iOnC nO nO t^ 1H ""/ 0 0 O O O lO M M rO -+ LO O O O 0 o o 00 O ^. O 0 •'J covo O 'I- t— CO re Tl- Tf rf 0 O •^ 0 "0 CI vC C >0 On uo U-, sc NO vC 1 lO O O >0 lO O O «« M n ro lOO •oo o o o r^ 0\ 1-1 ro lO O >o O 0 lO r— On (N lO r— 1-1 « ct n f) ir; o 0 lO "-. C -+ r- 0 'I- o vC 00 O CO u-, >- ■-■ M (N M ir; \/5 i/^ lO 0 oc « Ti- r-- - M CO CO CO ■^ Tt Tj- lO lOvC U-) 0 "^ 0 O O O PH i-i cs ro -^ >0 lO T! O O "0 vO l^ Ov 11 P) HH (-1 >o lo >o o "^ •*0 00 - <~0 « « « N fs Q XT) \ri \r, \ri NO 00 - '*■ r- C< C4 rO CO CO i^ 0 "^ 0 0 O '1- r- - >o -f Tj- ■<*- ID lO 1 lO ^O lO O lO lO lO w M D O >o o >o "0 r^ X C - O O 0 C "-- re IA-. r^ CN - lo O "^ "> "^ O >^; ir 0 0 r- O CO r- 0 re -1- •^ ■^ "^ 1 O « « »N ro •+ O >o >o 0 "O lOvO t^ O^ 0 O <0 lO U-) lO (S ro lO t— On >o lo 0 >o 0 - rOO 00 - ITN UO "0 l/^ "^ r'vC ON CI UO fe re CO -r -^ 1 05 lo 0 'O 0 0 "> ID ID lO O O -I- io\o 00 ov lO o >o "0 o O ri t- O O O "-' "-• On «" re uo r-- >- C« M CI M 0 >A C C ''^ 0 CI 1/-X C ce re re co Tt K lO 0 "^0 i^J o »- ►. (N o 0 'O O On O <^ CO lo O lO lO uo >o t— 00 O c< -^ ■1 « N N r< lo r o ''^ 0 vO ON - cOnO N PI CO CO CO 0 "5 :> 'I „ ^, ro -^ ir. NO t-30 On 0 — CI CO •*• >n CI CI CI N M ^^3^i^ DETAILED DlSCUSStOU OP LOG RULES. 37 w N to Tf lO CO to fO fO f^ \D t^oo On 0 r^ PO CO ro Tl- « M ro -+ >0 Tl- ^ Tf rt ^ NO r^OO On 0 ■^ ■<*• -1- -+ >o w r< o Q « 30 lO N 0 0 O -" f^ f^ lo »ri »o o ^ i^ in n (N o fO rt- iOnO r^ « « « « - lo lo lo o "o Onoo r^ i^nO l^ 00 On O "- ►H HI l-l (N M lo lO 0 lO 0 NO NO r^ l^co (N rO Tl- IT) NO M r( (N (N CS O lo lo lo o O' O •-* I^ On 0 "■ O 0 0 1-^ ON N lOOO rO tJ-nO t^OO fO rO <0 fO fO O >ri O 0 o Ov 0 O " IN lO O •O "0 lO 0 00 lO ro « ro ro T^ iOnO O >0 0 0 O 0 00 r^NO lO r^ t--oo On 0 »-t >^ 1^ HH 04 "0 O 0 O 0 'i- rt- T(- -+ rt- « (N ro •+ >0 tN M CS (N) ts lo 0 0 O >o -+ lONO t^co NO 1-^00 ON 0 (N (N M M ro 0 lo >o lo 0 O « ro lOOO (N ro -i- uOnO ro fO ro rO fO lo lO 0 lo O O MD ro OnvO On C^ 0 0 '-' O O >0 0 "O CS rO rO ■ 00 ON C> 0 0 O >0 lO lO >o NO (N OnnO CO >-i ri c< ro -f 0 >o >o "o lo ►- 00 NO ^ ir: lo "O -t -+ T^ rO -t- >OnO t^ M (N fN) tS 0 0 0 i^ rl- On >0 0 lO t^ r^CO 0^ 0^ lO ID lO lO 0 ■1 t^ ro OnnO 0 0 « - P' "-> 0 O 0 O IN OnnO fO O rO rO -f- "OnO lO O O "0 lO t^ lO rO 0 CC NO r^oO On on O 0 >0 U-) 0 t^ uo ro (N 1-1 O >- 0 IONO t^co (N M rt (N CN| « « « « - "-) 0 0 O 0 0\ •* 0^ -t- On lO 0 "^ 0 o ON 0 0 - " O >o O >o 0 rO ONNO (N ON fN) (N rO •^- •^- 0 O 0 lO O NO O O i^ "O IONO t^ r^oo lO lO lO lO lO N 0 00 NO ^ On O O ►- CN >- (N) M CM M O "^ >o O O ro " O Onoo ro Tj- lO lONO CS CS M n o 0 "0 0 "5 >o NO vo r^ r^oo •O vo lO O "0 t^ M r^ r^oo 00 On On O O -t O NO 0< 00 P-. (N n (-0 ro lO O "0 "0 lO rt- lO lONO t^ lO lO O lO o 00 >0 to 0 CO t^OO On O 0 0 O 0 O 'T NO Tl- (N 0 00 " P) <0 T)- -t (S M Pt CS M IN 0 0 0 >o lO On ro r^ 1- >0 i0\0 NO r^ t^ 0 O "0 >o "0 O -O ON Tf On 00 00 00 On On 0 0 lO >o 0 Q « 1-1 (N D 0 0 0 0 lO (-0 On lO « 1^ <-0 ro ^- lO lO O 0 >o lo lo NO t^ t^CO On lo 0 lO 0 0 00 NO fO >-■ On ON 0 '-' M PI 1- (S -l NO On O 0 « - lO O "0 lO 0 « r^ M CO ^ (N 0 lO 0 "O 0 NO (N On »0 lO iono no r^ 0 lO lO lO lO (N 00 lO (N On 00 CO On O O "0 0 "^ 0 "^ 00 M lO ON W ■^ lO lO uOnO lO lO 1^ *o »o NO O TfOO ^ 0 O lO O lO "- « M (N< P) ro O 0 "O 0 0 NO n r^ ro On f) ^ Tj- lo lO O O "0 lO O lO " r^ ro o NO r^ t-^oo 0~ lo in lo 0 0 fO ^ On fO ^O Tl- Th -4- lO lO lo 0 >^ "^ 0 ON fONO o 1- u-)0 NO t^ r^ 00 0 0 •+ r^OO CO On On O "O 0 >0 lO On <~OoO r< r^ On 0 0 ^ '-I lO >o >o "-> o N (N ro fO tJ- O "O 0 0 >^- 00 ro On lO O Tj- lo lovo r^ lO 0 O 0 "2 00 « -J- t^ o< f^ -f "^ 't rt- >o 0 O 0 "^ r» \0 On fN lO lO lO uo vO NO o >^ o 0 "5 On 'Ni \0 0 *0 NO «^ r^oo 00 o >o o o t^ " lO O •* CO On On p O lO ID o 0 "^ 00 M t^ « NO 0 ►" "" (N r4 lo 0 0 0 0 - VO - NO - rO PO •<*-■+ »0 " " " " " « f-l rO -t lO rO fO fO ro fO NO r^ CO On O rO ro rO ro •^ " M ro -+ lO 'f T)- ^ T*- rh NO r^co On O ■<1- 'i- Tt Tl- lO M N ro Tf lO lO »0 UO lO *o NO r^oo O O lO »0 »0 u*:vO 38 fOREST MENSURATION. is meant the average crook of first-class logs accepted at tiic average mill. The average crook allowed in the rule is about 1.5 inches, and does not exceed 4 inches in 12 feet. Any crook more than 4 inches would have to be specially discounted by the scaler. Professor Clark first estimated this loss theore:;ically and then proved his computations by extensive tests at the mill. His studies showed that the waste due to crooks and surface imperfections is, like the waste in square-edging, directly pro- portional to the diameter of the log. The necessary allowance for waste in edging, crooks, etc., amounts altogether to 2.12D for 12-foot logs, or o.-jiD for 4-foot logs. This allowance was determined by mathematical com- putations and by tests at the mill. With these principles estab- lished, the log table was compiled by first computing the content? of logs 4 feet long and then of logs of other lengths, allowing a taper of i inch in 8 feet. The International rule may be applied in mills which use saws cutting kerfs of other widths than ^ inch, by adding to or subtracting from the total scale a certain percentage, as indicated in the following table: For s'j - inch kerf add 1-3% " t^ " subtract 5-0% " i < ( it 11 9-5% " A f ( i C (I 13-6% " f I C it 1 ( 17-4% " ^ ( ( < ( i I 20-8% 22. The Doyle Rule. — This rule is known in some sections as the Connecticut River rule, the St. Croix rule, the Thurber rule, the Vannoy rule, the Moore and Beeman rule, Ontario rule, and the Scribner rule. It is often called the Scribncr rule because it is now ])rintcd in Scribncr's Lumber and Log Book. The Doyle rule is used ihrouglioul the entire country and is more gcnerallv employed than any other rule. It is the statute rule of Arkansas, Florida, and Louisiana. DETAILED DISCUSSION OF LOG RULES. 39 It is constructed by the following formula: Deduct 4 inches from the diameter of the log as an allowance for slab; square one-quarter of the remainder and multiply the result by the length of the log in feet. This formula does not explain the principle of the rule as well as that published over 50 years ago, giving the same results, namely : Deduct 4 inches from the diam- eter for slabs, then squaring the remainder, subtract \ for saw- kerf and the balance will be the contents of a log 12 feet long, from which the others may be obtained by proportion. The principle is first to deduct a 2-inch slab regardless of the size of the log; then to square the diameter to obtain the number of the square inches on the end of the stick; deduct ^ for saw-kerf, then divide by 12. The result is the number of board feet in a log I foot long. If the last division by 12 be omitted, the contents of a 12-foot log will result. The important feature of the formula is that the width of slab is always uniform regardless of the size of the log. This waste allowance is altogether too small for large logs and exces- sive for small ones. The principle is, therefore, mathematically incorrect. The product of perfect logs of different sizes follows an entirely different mathematical law from that of the Doyle rule. It is astonishing that this incorrect rule which gives ridicu- lous results for very large and very small logs, should have such a general use. Without doubt the rule has happened to yield fairly accurate results where the loss by defects in the timber and waste in milling have accidentally about balanced the inaccuracies of the rule. Generally millmen recognize the failings of the rule and make corrections to meet their special conditions. The opinions of a number of millmen regarding the rule are pertinent at this point. The following are selected from letters from a very large number of men all over the country. It should be added that the reason for such wide differences in the per- centage of inaccuracy is on account of dTfferences in local defects of the timber sawed. 40 FOREST MENSURATION, "The saw bill will overrun the scale when the log is 20 inches and under in diameter and will begin to fall short of the scale when it reaches 24 inches in diameter, and the larger the log the more it falls short." — Mill located in Ohio. " Large logs have to be very straight and good to hold out, and according to our experience Doyle's Rule might be increased 10% to 16 or 17 inches diameter, and from that up to 24 inches remain as it is and about 24 inches reduce 2 to 5%." — Mill in Indiana. "Pine, spruce, and tamarack overrun the scale 20%; maple, ash, hemlock 5/c." — Massachusetts. "Small logs overrun 20*7^; large logs lose 20%." — West Virginia. "Fir: large logs fall short of scale 5%, small overrun io%." — Washington. "Logs 12 inches and less overrun the scale about 40% for straight, clear logs. "Logs 12-20 inches overrun the scale about 15-20% for straight, clear logs. "Logs 20-24 inches overrun the scale about 10-20% for straight, clear logs. "Logs 24-30 inches overrun the scale about 5-10% for straight, clear logs. "Logs 30-36 inches about hold up the scale. "Logs 36 and over fall below the scale." — Mill in Ohio. "Poplar, chestnut, spruce, hemlock hold out. Cherry under- runs about 5%. Sycamore underruns 12^%. White oak cut into car stock overruns 12%. Red oak cut into lumber under- runs 5%. Rock oak underruns 10%. " — West Virginia. The Doyle rule may be found in: Scribner's Lumber and Log Book. G. W. Fisher, Rochester, N. Y. The Woodsman's Handbook, by Henry S. Graves, Bull. No. 36, Bureau of Forestry, Washington, D. C. The instructions given in Scribner's Lumber and Log Book are to measure the log at the middle. In practice the logs are measured at the small end inside the bark, except long logs, which arc measured at the middle. One of the writer's corre- spondents measures the diameter of a long log at one-third the DETAILED DISCUSSION OF LOG RULES. 41 distance from the small end. Long logs arc those containing two or more short logs of merchantable length. 23. The Scribner Rule. — This is the oldest log rule now in general use. It was originally published in The Ready Reckoner, by J. M. Scribner. It is now usually called the "Old Scribner Rule." It is used to some extent in nearly every state, and is the statute rule of Idaho, Minnesota, Oregon, Wisconsin, and West Virginia. The rule was based on computations derived from diagrams drawn to show the number of inch boards that can be sawed from logs of different sizes after allowing for waste. The following description of the rule is taken from the edition of 1846: "This table has been computed from accurately drawn dia- grams for each and every diameter of logs from 12 inches to 44, and the exact width of each board taken after being squared by taking off the wane edge and the contents reckoned up for every log, so that it is mathematically certain that the true con- tents are here given, and both buyer and seller of logs will un- hesitatingly adopt these tables as the standard for all future con- tracts in the purchase of saw logs where strict honesty between party and party is taken into account. In these revised computa- tions I have allowed a thicker slab to be taken from the larger class of logs than in the former edition, which accounts for the discrepancy between the results given in these tables and those in former editions. " The diameter is supposed to be taken at the small end, inside the bark, and in sections of 15 feet, and the fractions of an inch not taken into the measurement. This mode of measurement, which is customary, gives the buyer the advantage of the swell of the log, the gain by sawing it into scantling, or large timber, and the fractional part of an inch in the diameter. Still it must be remembered that logs are never straight and that oftentimes there are concealed defects which must be taken as an offset for the gain above mentioned. It has been my desire to furnish those who deal in lumber of any kind with a set of tables that can 42 FOREST MENSURATION. implicitly be relied upon for correctness by both buyer and seller, and to do so I have spared no pains nor expense to render them perfect ; and it is to be hoped that hereafter these will be preferred to the palpably erroneous tables which have hitherto been in use. If there is any truth in mathematics or dependence to be pkced in the estimates given by a diagram, there cannot remain a particle of doubt of the accuracy of the results here given." The judgment of most sawyers with whom the author has talked is that the Scribner rule gives very fcir results for small logs, but that for large logs, for example those above 28 inches, the results are too small if the logs are free cf defects. It often hap- pens that defects are greater with large logs than with small ones because the former are from trees which are elder and m.ore apt to be mature or overmature than small trees. Scribner's rule is fairly satisfactory in such cases. The rcsuLs for the small sound logs are fairly accurate and the defects of the larger logs is balanced by the deficiencies of the rule. Som.etimes the Scribner rule is converted into what is known es the Scribner Decimal lulc by dropping the units and rounding the values to the nearest tens. Thus 107 board feet would be written 11 in the decimal rule; 104 would be written 10. The Hyslop rule is practically the same as the Scribner Decimal rule. The ori:rin:.I rule did not give values bebw 12 inches. A number of lumber companies have interpolated for' their own use the values for small logs. Thus the figures for small diam- eters in the table on page 24 are those u;ed by a comj)any in the Adirondacks. The Lufkin Rule Company publishes three tables for the scale of small logs by the Scribner rule. These arc called Decimal A, B, and C. The lule is now published in tlie following books: Scribner's Rule for Log IMeaiiurenxnt. George \V. Fisher, publisher, Rochester, N. Y. Price 30 cents. The Wccdsmnn's Handbook, by Henry Solon Graves. Bulletin No. 36, Bureau or Forcstr}', Wnshinglon, D. C. 24. The Maine Rule. — This is also known as the roll nd rule, DETAILED DISCUSSION OF LOG RULES. 43 and as Fabian's rule. Its use is restricted to northern New Eng- land, chiefly to Maine, where it has long been the principal log rule. The Maine rule was constructed by the use of diagrams representing the small ends of logs of all diameters from 6 to 48 inches. The inscribed square of the logs was first determined, and the contents of the logs were then computed by allowing I inch for each board and one-fourth of an inch between the boards for saw- kerf. The boards outside the square were reck- oned, if not less than 6 inches in width; otherwise the whole slab was discarded. In judging this rule it must be remembered that it was devised for the measurement of short logs and not for long logs, to which it is now so frequently applied. Millmen very generally agree that the Maine rule is extremely satisfactory for short logs. In fact, it probably comes nearer satisfying the present require- ments of a modern sawmill than any of the other rules in com- mon use. It gives considerably larger results than the Scribner, Hanna, and Spaulding rules. Like the Scribner rule the values in the Maine rule run irregularly. It is a very simple matter to correct these irreg- ularities by graphical interpolation. Mr. H. D. Tiemann has prepared a corrected form of the Maine rule as given in the table on page 44. The chief trouble with the rule is not due so much to defects in the values as to the present method of applying it. As explained in section 37, logs over 30 feet are measured as two logs, the diameter at the small end being measured and the diameter at the middle being estimated. An illustration of the working of the rule is given by Mr. Austin Gary in the Report of the Forest Commission of Maine, 1896: "Even when the present method of scaling by the Maine rule is conscientiously applied it leads to wasteful lumbering. A good example is that of a spruce log, cut in Maine, 32 feet long and scaled as 169 board feet by the Maine ruie. If the loggers had cut this particular log 40 feet long the scale would have 44 FOREST MENSURATION. MAINE RULE. (A'^alues Made Regular by Interpolation.) Length in Feet. Diameter. 10 12 14 16 IS ( 20 23 24 Inches. 1 Board Feet. 6 13 15 17 20 22 25 27 29 7 19 23 36 30 34 38 42 45 8 26 31 36 42 47 52 58 63 9 34 41 47 54 61 68 75 82 lO 43 51 59 68 76 85 93 102 11 52 62 73 83 93 104 114 125 12 62 75 87 99 112 124 136 149 13 73 88 102 "7 132 146 161 176 14 85 102 119 136 153 170 187 204 15 98 118 137 157 176 196 216 235 i6 112 135 157 180 202 225 247 270 17 128 154 179 205 231 256 282 307 18 145 175 204 233 262 292 321 350 19 164 197 230 263 296 329 362 395 20 184 221 258 295 332 369 406 443 21 205 247 288 329 370 411 452 494 22 228 274 319 364 410 455 501 547 23 252 302 352 403 453 503 554 604 24 277 332 387 443 498 553 609 664 been only 168 board feet, or i foot less, although 8 feet longer and containing 5 cubic feet more. The contractor gained by wasting 8 feet of wood entirely suitable for saw lumber or pulp. Other facts about this tree are shown in the table below and illustrate the tremendous range of results depending on the dif- ferent methods of applying a single specified rule : Log as cut, 32 feet long; contents with bark, 31 cubic feet; scaled as two 16-foot logs, giving butt log i inch rise 169 ft. Scaled as two 16-foot logs, giving butt log actual rise 185 " A 16-foot log above, that might have been taken, scales 31 Log if cut 40 feet long; contents with bark, 36 cubic feet; scaled as two 20-foot logs, giving butt log 2 inches rise 168 Scaled as two 20-foot logs, giving butt log actual rise '95 " Scaled as four lo-foot logs, using actual top diameter of each 216 " Whole tree, sawed down at \\ feet from ground and taken up to 6 inches diameter; contents, 43 cubic feet; scaled in 16-foot lengths from butt up with actual diameter 226 " Total contents of the tree's stem, 46 cul)ic feet." DETAILED DISCUSSION OF LOG RULES. 45 This illustration is sufficient to show what absurd results may be obtained if the rule is loosely applied, as is customary in prac- tice. The Maine rule may be obtained from V. Fabian, Milo Junction, Maine. 25. The Hanna Rule is used in Pennsylvania, Tennessee, Vir- ginia, New York, and Massachusetts, and locally elsewhere. It was computed from diagrams drawn for every size of log from 8 to 50 inches in diameter. Practical millmen were consulted by the author of the rule to check the results. This rule was con- structed on the same general principles as the Scribner, Maine, and Spaulding rules and its results, like those rules, are fairly satisfactory for logs of average size. The use of the rule among practical millmen is on the increase. The rule follows closely the Scribner rule, but is less erratic. When the two are compared the Hanna rule appears like an attempt to correct the eccen- tricities of the Scribner rule. 26. The Spaulding Rule. — This is the statute rule of Cali- fornia adopted by an act of the Legislature in 1878. The revised statute is quoted in the Appendix. This rule was constructed from diagrams. Its author has given no adequate description of how the results were obtained. The only description of the construction of the rule as published by its author is as follows : "Each sized log has been scaled so as to make all that can be practically sawed out of it, if economically sawed. Each log to be measured at the top or small end, inside of the bark, and if not round, to be measured two ways — at right angles — and the average taken for the diameter. Where there are any known defects, the amount to be deducted should be agreed upon by the buyer and the seller, and no fractions of an inch to be taken into the measurement." "In the foregoing table I have varied-the size of the slab in proportion to the size of the log, and have arranged it more par- ticularly for large logs by taking them in sections of 12 feet and 46 FOREST MENSURATION. carrying the table up to 96 inches in diameter. As there has never been any in use for scaling over 44 inches, it has been my purpose to furnish a table for the measuring of logs that can be implicitly relied upon for correctness by both the buyer and seller; and to do so, I have spared no pains or expense to render it perfect." The rule gives very fair results for logs which are sound. Where the run of logs is defective, the scale overruns the saw bill. As far as the author can learn, the millmen are satisfiec with the rule. It may be obtained from N. W. Spaulding Saw Company, 17 Freemont Street, San Francisco, California. 27. The British Columbia Rule. — The province of British Columbia has established a statute log rule which is based on the following mathematical formula: For logs up to 40 feet in length deduct i| inches from the diameter at the small end inside the bark; square the result and muLipiy by the decimal 0.7854; from the product deduct three-elevenths; multiply the remainder by the length of the log and divide by 12. For logs over 40 feet in length an allowance is made on half the length of the log in order to compensate for the increase in diameter. This allow- ance consists of an increase in the diameter at the small end of the log of I inch for each 10 feet in length over 40 feet. Thus for logs 51 to 60 feet long the contents of half the log are com- puted by the diameter at the small end. The other half is con- sidered to have a diameter i inch larger. The British Columbia log table is published in a small booklet entitled The British Columbia Log Scale, and may be secured in Victoria, B.C., at the cost of S2.00. 28. The Drew Rule. — This rule has been adopted as a statute rule in the State of Washington. The law establishing it is given in full in the Appendix.. It is also the official log rule of the Puget Sound Timbermen's Association. It is used only in the north- western states and is confined chiefly to Washington. No infor- mation is given in the puljlished rule as to how the values were DETAILED DISCUSSION OF LOG RULES. 47 derived. The rule may be obtained in the form of a small leather bound booklet for $2.50 in Seattle. 29. The Constantine Rule. — This is a theoretical rule, which gives the solid contents, expressed in board feet, of logs without any reduction for waste in sawdust, slabbing, edging, etc. The principle of the rule is to determine, first, the sohd contents, in cubic feet, of cylinders of ditTerent diameters. These results are then translated into board feet by multiplying by 12, on the principle that if there is no waste in sawing, there will be in. each cubic foot 12 board feet. Of course, it is really not proper to express the solid contents of a log in board feet, because the board foot represents a manufactured product, and it is impos- sible from a cubic foot of round timber to saw 12 board feet. As it stands, therefore, the Constantine rule can hardly be considered a log rule, but only a mathematical step in the derivation of a log rule. The formula for constructing a table for this rule is as follows : Square the diameter of the small end of the log inside the bark and muhiply by the decimal 0.785; multiply the result by the length of log and divide by 12. Expressed algebraically, B/=[-j-Xi:-i44jxi2, jB/ = 0.78541)2 XL -1 2. A practical board rule is sometimes made from the Constan- tine table by deducting a third or fourth from the figures for saw-kerf and other waste. This rule is also used as a founda- tion for the Champlain and Universal rules of Professor Daniels. 30. The Canadian Rules. — A number of the American log rules are used in Canada, but those recognized by statute or custom are the Quebec rule, the New Brunswick rule, the British Columbia rule, and the so-called Ontario rule, which is the same as the Doyle rule. The British Columbia rule has already 48 FOREST MENSURATION. been discussed in connection with the Pacific Coast rules. The author has been unable to learn exactly how the Quebec and New Brunswick rules were constructed. As far as the author is informed, the Canadian rules, except, of course, the Doyle rule, have never been used in this country. 31. Miscellaneous Log Rules. The construction of the Vermont Rule is described in the Appendix. It still has some use in the northeastern states, being retained chiefly because it is a State rule. An effort is now being made to replace it by a new rule, it being considered unsatisfactory' by most lumbermen. It is also called the Humphrey rule and the Winder rule. The Baughman Rules. — These rules, devised by H. R. A. Baughman, of Indianapolis, have been constructed to show the full contents, in board measure, of perfect logs manufactured by modem machinery; one to be used with a rotary saw, and the other with a band saw. They are based on diagrams. As in other diagram rules, the values increase by irregular differ- ences. It is, however, one of the few rules which do not allow an excessive amount for waste. Its values are, for small logs, almost identical with those of the Champlain rule. The Baugh- man rules are contained in Baughman's Buyer and Seller, Indian- apolis, Ind., 1905. Price $1.50. The Baxter rule is used chiefly in Pennsylvania. According to Prof. J. T. Clark it is based on the formula: Subtract i from the diameter inside the bark at the small end, square the re- mainder and multiply by 0.52, and the result is the contents of a 1 2 -foot log. The Dusenberry Rule is used in Pennsylvania, New York, Ohio, and Indiana. It was made originally for white pine, but is now Used also for other timbers. The Favorite, or Lumberman's Favorite Rule, is used in Vir- ginia, West Virginia, Michigan, New York, Texas, Tennessee, Indiana, Pennsylvania, North Carolina, and Missouri. It is probably based upon diagrams. The Square of Two-thirds Rule, which is also known as the St DETAILED DISCUSSION OF LOG RULES. 49 Louis Hardwood rule, the Two-thirds rule, the Tennessee River rule, and the Lehigh rule, is used in Tennessee, Pennsylvania, North Carolina, Kentucky, lUinois, Indiana, New Jersey, Virginia, and West Virginia, and probably in some other states. It is based on the following formula: Deduct one-third of the diameter at the small end of the log inside the bark for saw- kerf and slab, square the remainder, multiply by the length, and divide this product by 12. The result is the contents in board feet. The Square of Three-jourths Rule, whose other names are the Portland scale, the Noble and Cooley rule, the Cook rule, the Crooked River rule, and the Lumberman's scale, is occasionally used in the northeastern states. The formula upon which it is based is as follows: Deduct one-fourth of the diameter at the small end of the log inside the bark for saw-kerf and slab, square the remainder, multiply by the length of the log, and divide this last product by 12 for the contents in board feet. The Cumberland River Rule is known in some parts of the country as the Evansville rule and the Third and Fifth rule. It is used in Tennessee, Kentucky, Indiana, Ohio, Michigan, Illinois, Massachusetts, and probably in some other states. It is based upon the following formula: Deduct one-third from the diameter at the small end inside the bark to reduce the round log to square timber. Then from one side of the square thus obtained deduct one-fifth for saw-kerf; multiply the remain- der by the side of the square and the product will be the contents of a log 12 feet long. For logs of other lengths multiply by the length and divide by 12. This rule was constructed for the measurement of hardwood logs in the water in the Mississippi River and its tributaries. These logs are often defective and in the water it is impossible to distinguish the defects which are hidden by the water itself, by mud, sand, plugs, etc. The log rule is supposed to allow for all such hidden defects. The Herring Rule, which is also called the Beaumont rule, is used in Texas. It was first published iniSyi by T. F. Herring, Beaumont, Texas, and afterwards enlarged by W. A. Cushman 50 FOREST MENSURATION. of Beaumont. No intimation is given of exactly how the table was constructed. It is probable that it is based partly on the actual cut of the logs at the mill and partly on diagrams. The rule may be obtained from Mark Weiss, Beaumont, Texas. Price $i.oo. The Orange River Rule is also known as the Ochiltree rule and as the Sabine River rule. It is used in Texas. It is based on the following formula : Multiply the square of the diameter of the small end of the log inside the bark by the length of the log and divide the product by 30; the result is the contents in b'.ard feet. The Combined Doyle and Scrihner Rule. — This is a combina- tion of the Scribner and Doyle Rules. It is used in New York, New Jersey, Pennsylvania, Virginia, Tennessee, Kentucky, Ala- bama, Louisiana, Arkansas, Mississippi, Missouri, Indiana, Illi- nois, Michigan, Ohio, Iowa, Wisconsin, Montana, Idaho, South Dakota, and probably elsewhere. It has been adopted as the official scale of the National Hardwocd Lumber Association, St. Louis, and is published in their " Grading Book." The values for diameters under 28 inches are taken from the Doyle rule; those for 28 inches and over from the Scribner rule. The effort seems to have been to find a rule which gives very small results, in order to cover loss in defective timber. The principal use is with the hardwoods, which arc apt to be unsound. It is to be counted as one of the rules designed for a special class of timber. The Chapin Rule is based on measurements of logs actually sawed into lumber. It is claimed that it gives the greatest amount of lumber which can be manufactured from straight smooth logs. It is a comparatively new rule and has not yet come into very general use. It may be purchased from the .Xmerican Lumber- man, Chicago. A number of other rules are in local use. They are as follows: The Northwestern Rule, used to some extent in Michigan and Illinois. DETAILED DISCUSSION CF LOG RULES. 51 The Derby Rule, also known as the Holdcn and Robinson rule, which is used in Massachusetts. The Partridge Rule, also called the Murdoch and Fairbank rule, which is used rarely in Massachusetts and which is based on I inch boards. The Preston Rule. This is based upon the principle that one- fifth of the contents of a log should be deducted for saw-kerf. The waste in slabs is calculated by deducting if inches for small logs and i^ inches for large logs. The results are given in board feet and inches. The Parsons Rule, used in a few places in Maine. The Ropp Rule, used in Illinois. It is based on the following formula: Subtract 60 from the square of the diameter of the small end of the log inside the bark, multiply the remainder by half the length of the log, and point off the right-hand figure. The StiUwell Rule, known as the Stillwell Vede Mecum rule, used by its author in Georgia. The Saco River Rule, used in Maine. The Wilson Rule, used in Massachusetts. The Ballon Rule, used by M. E. Ballon & Son, of Becket, Mass., in measuring small hardwood timber, such as basket ash. The Wilcox Rule, used locally in Pennsylvania for softwood timber. The Warner Rule, used locally in New York. The Boynton Rule, based upon a compromise of the Vermont and the Scribner rules and adjusted by sawyers' tallies. It is used in Vermont. The Carey Rule, used in Massachusetts. The Forty-five Rule, used in New York. It is based upon the following rule: For a 24-inch log multiply the square of the diameter, namely 24, by the length of the log and the result by 45, then point off three places. The figures at the left of the decimal point will represent the contents in board feet. For every variation of 2 inches in the diameter from the standard 52 FOREST MENSURATION. 24-inch log add or subtract i from the number 45 in the formula, according as the diameter is larger or smaller than 24 inches. The White Rule, used to a limited extent in Montana. The Finch and Apgar Rule, pubHshed in the Excelsior Log Book Table, New York. The Ake Rule, used locally in Clearfield County, Pa. It is based upon the following rule of thumb: jSIukipIy the diameter of the log, measured at the small end inside the bark, by 0.7; square the resuk ; mukiply the product by the length of the log and divide by 12. The final resuk will be the contents in board feet. The Younglove Rule is a very old rule formerly used in New England and probably still occasionally employed in Massa- chusetts. Other rules may be in existence, but they are unknown to the author. CHAPTER IV. LOG RULES BASED ON STANDARDS. 32. Definition of Standard Measure. — It was shown on page 26 that the custom of using a standard log of specified dimensions as a unit of volume has been used for over fifty years. A table of standards is based on the principle that the contents of logs vary directly as their lengths and the squares of their respective diam- eters. To obtain the volume of any given log in terms of a specified standard, square the diameter at the small end and divide by the square of the diameter of the standard log; then divide by the length of the standard log and multiply by the length of the log measured. Thus if the standard is a log 12 feet long and 24 inches in diameter at the small end, the square of the diameter of the log measured is divided by the square of 24 and then multiplied by a fraction whose numerator is the length of the given log and denominator the length of the standard. Expressed algebraically, the rule for determining the volume of a log in standards is in which V is the volume of the log, D its diameter at the small end, L its length, d and / the diameter and length of the standard. It will be noticed that in this formula the full contents of the standard and of the log are not compared, but the contents of cylinders having diameters equal to the diameters of the respec- tive logs at the small end. If the full contents of the logs were 53 «;4 FOREST MBmU RATION. to be compared, it would be necessary to take the measurements of diameter at the middle. This will be clear by reference to the formula for determining the solid contents of logs described in section 47. 33, The Nineteen-inch Standard Rule. — One of the standards in most common use is the so-called 19-inch standard, or market. The unit is a log 13 feet long and 19 inches in diameter at the small end inside the bark. On the principle that the contents of logs vary as the squares of their diameters, a lo-inch log 13 feet long contains 0.28 standards (the square of 10 divided by the square of 19). Expressed algebraically the formula for deter- mining the contents of a given log by the 19-inch standaid rule is F=-^x— , in which V represents the volume in standards, D the diameter inside the bark at the small end, and L the length of the log. This log rule is most commonly used in the Adirondack Mountains of New York. It is particularly popular in measuring pulp wood because the rule is based on volume and not on board measure. It is sometimes called the Glens Falls Standard rule. It has been called by some the Dimick rule because it is published in Dimick's Ready Reckoner. This booklet, edited by L. Dimick, may be purchased for 25 cents from Crittenden and Cowles, Glens Falls, N. Y. Standard measure is commonly translated into board measure by multiplying the volume of a given log in standards by a con- stant. In the case of the Nineteen-inch Standard rule, it is assumed that one standard is equivalent to 2CX3 board feet, and the number of standards in a log, regardless of its size, is multiplied by 200 in translating from standard to board measure. This procedure is emphatically incorrect, because the contents of logs measured in standards vary as the squares of the diameters, while the contents of logs measured in board feet vary by a totally LOG RULES B/1SED ON STANDARDS. 55 different rule (see sections 19-21). When a standard table is converted into board measure by multiplying throughout by a constant, as for example 200, it incorrectly is assumed that the board contents vary as the squares of the diameters of the logs. When logs of different diameters are scaled both in standard measure and board measure, the results are not the same as when the logs are scaled in standard measure and converted into board measure by muLiplying by 200. It is true that the average of a very large lot of logs when measured by the two scales will run about 2co feet to the standard (based on Doyle's Rile). This is the only way that the converting factor can correctly be used. It should not be used when applied to individual diameters. The table on page 56 shows that, taking logs separately, there are not 5 standards to the thousand, but from 4 to nearly 14 standards to the thousand, according to the diameters of the logs. 34. The New Hampshire Rule (Blodgett Rule), Although usually not recognized as a standard log rule, the Blodgett rule, which has been adopted as the statute rule of New Hampshire, is nothing more nor less than a standard rule based on the same principles as that of the Adirondack market described above. The Blodgett standard, as fully described on page 363, assumes as a unit a log i foot long and 16 inches in diameter. The contents in so-called cubic feet (more correctly standards) of a log of any dimensions is found by the following formula : in which V is the volume in standards, D the diameter in inches, and L the length of the log in feet. This rule is now being very generally introduced in the spruce region of northern New England for the measurement of long logs which are cut for pulp. The reason for its popularity is because it i§ a volume rule. In the manufacture of wood pulp 56 FOREST MENSURATION. COMPARISON OF 13-FOOT LOGS SCALED IN STANDARDS AND BOARD MEASURE. (From Report of N. Y' . Forest Commission, 1894). Standard Measure. Number of Number of Number of Number of Diameter, Inches.* Logs to a Feet. Log Logs per Standards per Standard. Measure. t 1000 Feet. 1000 Feet. 8 ■177 5.6 13 76.9 13-7 9 .224 4 5 20 50.0 II I 10 ■277 3 6 29 34-5 9 6 II •335 3 0 40 25.0 S 3 12 •399 2 5 52 19.2 7 7 13 .468 2 I 66 15. 1 / 2 14 •543 8 81 12.3 6 8 15 .623 6 98 10.2 6 4 16 .709 J 4 117 8.5 6 I 17 .800 2 137 7-3 5 8 iS .897 I 159 6.3 5 7 19 I .000 0 183 5.5 5 5 20 I . loS 9 208 4.8 5 3 21 1 . 221 8 235 4-2 5 2 22 I. 341 7 263 3-8 5 I 23 i^465 7 293 3-4 5 0 24 1-595 6 325 31 4 9 25 I-73I 6 358 2.8 4 8 26 1.872 5 393 2-5 4 7 27 2.020 5 430 2^3 4 6 28 2.172 5 468 2. I 4 6 29 2.330 4 508 2.0 4 6 30 2.493 4 549 1.8 4 5 31 2.662 4 592 1.7 4 5 32 2.836 3 637 1.6 4 4 33 3-OI7 3 683 I .5 4 4 34 3.202 3 731 1^4 4 3 35 3 • 393 3 781 1-3 4 3 36 3 590 3 832 1 . 2 4 3 * At top end of log, inside the bark. t Doyle's Rule the entire log is utilized, there being very little waste. Land- owners are therefore demanding a unit of measure which will take into account the entire contents of the logs. Another reason for the adoption of the New Hampshire rule is the widespread dissatisfaction with the Maine rule as it is now used. The reader is referred to the discussion of the New Hampshire rule in sections 37 and 38. Just as in the case of the Adirondack standard, lumbermen are accustomed to convert the Blodgett rule into board measure. LOG RULES BASED ON STANDARDS. 57 The Statute states that the ratio of the Blodgett standard to the thousand feet shall be as 100 is to 1000, or 10 feet in every cubic foot. In practice the lumbermen consider that there are 115 Blodgett feet in 1000 board feet when the diameter measure- ment is taken at the middle of the log and 106 Blodgett feet per 1000 boaid feet when the measurement is taken at the small end of the log. These are fair average figures and in practice are applicable in converting the scale of a large lot of logs lumped together from one measure to the other. It is not, however, fair to construct a log table for board measure by dividing the values in the Blodgett rule by the constants 106 or 115. Such a log rule for board measure still remains a volume rule, although expressed in board feet. The values in the table are not proportional to the board measure of the log, but to the cubic volume measure. 35. The Cube Rule. — Another standard rule is the so-called Cube rule of the Ohio River. This is based on the hypothesis that a log 18 inches in diameter is the smallest one from which a 12-inch square piece can be cut. To use local phraseology, an 1 8- inch log will cube once, meaning that for each linear foot .there will be one cube. To estimate the contents of a log, square the diameter in inches, multiply by the length in feet, and then divide by the square of 18. Algebraically, J)2 Ordinarily 1 2 board feet are allowed for one cube. This rule is known also as the Big Sandy Cube Rule. 36. Other Standard Rules. — The Twenty-two Inch Standard Rule is slill used to some extent in New York State and probably elsewhere. The unit is a log 12 feet long and 22 inches in diam- eter at the small end inside the bark. The rule is used in the same way as the Ninetecn-inch Standard rule, and a table may be constructed on the same principle. The 2 2- inch standard log s^ FOREST MENSURATION. _U SCRIBNER'ST 1 ^- Kt^ 4i)| 64 i JJJ^ .10 11, 12 13 i4 • "}? SCRIbNER 'ifl'-'-* Fig. 1. — Different Forms of Scale Rules. LOG RULES BASED ON STANDARDS. 59 contains 252 board feet (Scribner rule). Common usage gives tour standards to the thousand board feet. The Twenty-two Inch Standard rule is sometimes called the Saranac River Standard rule. The Twenty-four Inch Standard rule is based on a standard log 24 inches in diameter inside the bark at the small end and 12 feet long. The standard log contains 300 feet, board measure, according to the Doyle Rule. In the use of this rule timber is usually sold by the standard or by the 300 feet, instead of by the thousand feet, as commonly ; the logs are scaled by the Doyle rule and the total number of feet divided by 300, the unit of sale being a certain sum per standard. To obtain the value of the odd number of feet, the latter are divided by 300 and multiplied by the price per standard. The Canadian standard rules are based on logs 12 feet instead of 13 feet in length, and 21 and 22 inches, respectively, in diameter. These rules are used in the same way as the Amer- ican standard rules already described. CHAPTER V. METHODS OF SCALING LOGS. 37. Instruments for Scaling Logs. — The measurement of logs to ascertain their contents is called scaUng. The instrument used for measuring logs is called a scale stick, scale rule, or log rule. A number of different types are manufactured. The most com- mon type of scale rule consists of a stick, square or flat, which may be placed on the end of a log and shows, by two sets of figures on its face, both the diameter of the log and its contents in board feet. At each inch-mark is indicated the volume in board feet, by a specified rule, of a log of that diameter. Each line of figures represents the. results for one length of log, the lengths being indicated at the left-hand end of the stick. It is exactly as if a printed log rule were wrapped about the stick. The flat type of stick is most commonly used throughout the country. These rules arc generally made of hickory and tipped with a plain binding of brass or by a head of iron. There arc in use a variety of such heads for the measurement of logs of difi'crent forms. Fig. i shows a number of forms made by the Lufkin Rule Co., Saginaw, Mich. The ad- vantage of a head is that the rule may be i)l:iccd quickly and accu- rately on the end of the log. If there is no such guide, inaccuracies arc frequent through carelessness in not placing the end of the rule exactly at the edge. This type of rule, however, is applicable only where the log has been peeled. Where logs are scaled with the bark on, the plain rule with no guide-herd must be used, or a reduction in the measure made for the thickness of the bark. 60 METHODS OF SCALING LOGS. 6 1 Sometimes logs are " nos'?d " ; that is, the sharp edges are rounded off with the axe to prevent sphtting ("brooming") of the ends in transportation. In scahng such logs a long guide-head on the scale-stick is needed. Occasionally scale-sticks are made hexagonal instead of tlat or square. The old Gary and Parsons scales of Maine were formerly constructed in this way. Where scaling in the woods consists merely in measuring the diameters of the logs, a flat rule graduated in inches and half inches is used. These rules are often made by the scalers themselves, or for them by the camp blacksmith. A common type consists of a flat steel rule i inch wide attached to a wcoden handle. Several firms manufacture a caliper scale for the Scribner rule. CaUpers are used also where the diameter is meas- ured at the middle or at one-third from the end. The New Hampshire rule requires a measurement at the middle of the log. Therefore a caliper rule is used. The most common form is one in which there is a depression on the inside of each arm, so that the recorded diameter is less than the real diameter. This is the allowance for bark. These calipers are constructed for use with spruce, and an allowance is made on the calipers equivalent to the average thickness of spruce bark at the middle of an average log. The scaler is thus saved the trouble of chipping off the bark or of measuring its thickness. It is, of course, a rough method to assume that on all logs the thickness of bark is the same. For measuring the lengths of logs a wheel is often used. It consists of ten spokes, each tipped with a spike, mounted on a small hub which is attached to the caHper scale. The spokes are all painted black except one, which is yellow, and this one is weighted with a band of lead, so that it always points down- ward when at rest. When the wheel is placed on a log, the yellow spoke touches the log first. The construction is such that the tips of the spokes are 6 inches apart. When the wheel is run along a log, each revolution, easily counted by the yellow spoke, measures 5 feet, and as the distance between the spokes is 6 inches, 62 FOREST MENSURATION. the length of a log may quickly be determined to within 6 inches. (Fig. 2.) Fig. 2. — Wheel for Measuring Lengths of Logs. 38. Methods of Measuring the Diameters and Lengths. — The methods of scaling logs differ in using different rules and accord- ing to local differences in the character of timber, in the market requirements, in the habit of the individual scalers, etc. In regions where the logs are cut into short lengths and piled on skidways for winter hauling, as in the Adirondacks, the scaling is done in the following way: Ordinarily two men constitute the scaling crew. They are provided with a rule for measuring the diameters of the logs, a note-book, tally-sheets or a "scale-paddle" for recording the measurements, a special marking-hammer, and crayons for marking the logs. One scaler measures the diameters of the logs inside the bark at the small end; the other records the results. Only the smallest diameter is recorded, since the log tables are based on length and on diameter at the small end of the log. It is not necessary to measure separately the length of each log, for there are usually only a few standard lengths, as, for example, 10, 12, 13, 14, and 16 feet. The scaler can tell at a glance the correct length. If a log is slightly longer than the standard, ihe extra length is disregarded. For example, METHODS OF SC/tLlNG LOGS. 6;^ a log 16.5 feet long is scaled as a 16-foot log. If 18 feet is the next standard length, a log 17.5 feet long is scaled as a 16-foot log. Therefore, a log may be slightly longer than the specified leng.h bat never shorter. If a log is shorter than the length of the shortest speciiication (ordinarily 8 or 10 feet) it is discarded entirely. A great deal of waste is caused by choppers through careless measurement of log lengths. In measuring the ends of logs, the diameters are rounded to whole inches. If a diameter is nearer 7 than 6 inches,' the log is tallied as 7 inches. If the diameter is exactly between two whole inches, as, for example, 9.5 inches, the scaler usually tallies it under the lower inch class, in this case 9. Sometimes scalers endeavor to throw about half of such logs into the inch class below and half into the class above. Very conservative scalers record all diameters falling between two whole inches in the lower inch class, even if it is within one-tenth of an inch of the next class (for example 6.9 inches would be called 6-inches), When logs are evidently not round, the rule is usually placed at a point on the cross -section where the diameter is about an average between the largest and smallest dimensions. Some scalers always take the smallest diameters, a precaution necessary in measuring veneer logs. The field records are taken on special forms prepared by the company owning or buying the logs. Often the scalers use a blank-book or wooden scale-paddle in the woods, and then trans- fer the figures to regular forms at the camp. There are two methods of recording the measurements. The most common way is to tally the logs by diameter and length, and then afterwards compute the volume in the office. The other way is to record the board contents of each log as shown by the scale-stick. When a log has been scaled, the end is chalked to prevent its measurement a second time. Logs which are to be discarded receive a special chalk-mark. At this time or later the logs are stamped with the special marking-hammer of the purchaser of 64 FOREST MENSURATION. the logs. It is customary in many places to blaze a tree near each skidway, and mark the number of the skidway and number of logs tallied. Thus -^^^ would mean that there are 460 logs on skidway number 23. The description of scaling given in the previous pages applies to the northern regions where logs are cut short and where ror.ds are used for hauling. The principles of scaling are practically the same in other sections where short logs are cut. When the logs areloaded on cars in the woods, the scaling is generally done on the cars after loading. Where logs are to be driven, they may be scaled on the bank before rolling into the river, or, where slides are used, at the side of the slide before they are started. Naturally the accuracy of the different scalers varies tremen- dously. Some guess at the dimensions of many of the logs with- out measuring them, and even estimate the total run of a pile without bothering to measure any of the logs in it. In Maine and also in some parts of New Hampshire, spruce is cut in long logs, that is, the entire merchantable part of the tree is taken out in one log. The scaling is sometimes done as the logs are hauled to the skidways or yards, and sometimes at the landing if they are to be driven. If the Maine Log rule is used, the scaler's outfit consists of the ordinary Maine scale- stick, a measuring-pole or tape, marking-hammer, and chalk and note-book. The small end of the log and its length are measured. The results in board feet are read directly from the stick and recorded on special tally-blanks or in a note-book. The Maine rule gives figures for lengths only up to 30 feet, so that if a log is longer than that, it must be scaled as two logs. Ordinarily the diameter at the small end alone is measured, the scaler estimating the diameter at the middle. Thus if a log is 36 feet long, the small diameter 7 inches, and the diameter at the center estimated at 9 inches, the contents of two 18-foot logs, respectively 9 and 7 inches in diameter, arc read from the stick as the contents of the whole log. The scaler guesses at the middle diameter of the log after measuring the top. The increase in size from top to center (called the "rise") may be estimated METHODS OF SCAUhlG LOGS. 65 very accurately by experienced scalers. Sometimes a scale-stick is used which gives the contents of whole logs over 28 feet long, constructed on the principle that logs 28 to 32 feet long have a rise from tip to center of i inch, those 32 to 36 feet long a rise of 2 inches, those 36 to 40 feet long a rise of 3 inches. The rise of logs over 40 feet long is left to the scaler's judgment. The stick thus constructed is called the regular five-line rule. Deductions for crooks and other defects are made according to the judgment of the scaler. There are no rules, the discounting being entirely a matter of experience. In common practice it is mostly customary to reduce the total scale of a lot of logs by a certain percentage as a factor of safety. This is particularly the case where the quality of logs is extremely poor. For example, the disease of cypress called "peckiness" is so difficult to dis- cover from external signs that a general reduction for safety is necessary. The growth of the pulp industry in Maine has introduced a new factor in the scaling of spruce. Inasmuch as the whole log is used in making pulp, a solid measure is more appropriate than board measure. For this reason many operators are now using the Blodgett rule. This requires the measurement of the middle diameter of a log instead of the end diameter. The measurement is taken with calipers of the type described before. The length of the log is measured and the middle point located by a wheel. The diameter is taken outside the bark, the calipers being con- structed to allow for an average bark width. The contents of the log are read directly from the beam of the caliper. The deduction for defects is made as with the Maine rule. In scaling long logs by the Doyle rule, the diameter is measured at the middle or the two ends are averaged. Better results are obtained if long logs are measured in short lengths and the diameters taken at the points where the cuts would be made. 39. Methods of Making Discount for Defects. — If all the logs on a skidway were sound and straight the operation of scaling would be largely mechanical and would not require much skill. But many logs are cut and piled which are partly rotten, crooked, 66 FOREST MENSURATION. or seamy. They must be entirely discarded or reductions must be made for imperfections when the contents are calculated. Skill is required in deciding what logs should be thrown out. The obviously rotten logs are not piled on the skidway at all. The contractors include many which are doubtful, and which they think may be accepted by the purchaser. The final decision rests with ihe scalers. There are many logs having center rot or rot only on one side, seamy, shaky, and crooked logs, which contain enough good lumber to pay for the hauling, but cannot be given a scale equivalent to straight sound logs of equal di- mensions. When such a log is measured, a deduction is made to compensate for the loss through the imperfection. If the scaler is recording only the diameters and lengths of the logs, discount for defects in a specified log is usually made by reducing the measured diameter sufficiently to cover the loss. Some- times, chiefly in the South, the allowance for defect is made by reducing the log's length. If the contents of the logs are reduced in the woods, the discount in board feet is made when the log is measured. The experienced scaler who has worked at a saw- mill is able to estimate the loss through certain imperfections merely by inspecting the log. It requires skill and experience to recognize defects and to know how much they affect the quality of the limber. It also requires good judgment to determine how much the dimensions of a defective log should be reduced to scale what can actually be manufactured from it. The best scalers have this experience and judgment. Many, however, make deductions for defects largely by guesswork. The writer has encountered a few rules for special cases, but there is apparently no uniformity in practice among different scalers. This lack of uniformity is unfortunate, and while it is impossible to lay down rules which are universally applicable, it is possible to classify ihc principal problems met by scalers. It would be entirely practicable for lumbermen to follow a uniform system of handling these problems, making modifications as required in special cases. Discount for Center Rot. — If a log has a rotten spot at the center, and there is enough good wood to pay for hauling, a dis- METHODS OF SCALING LOGS 67 count for the defect is made in the scale. Several incorrect methods for computing this discount are in use. One method requires the subtraction of the diameter of the rotten core from the diameter of the log for the rec|uired diameter. Thus if a 12-foot log were 20 inches in diameter, and the rotten core had a diameter of 6 inches, this method would make the new diam- eter 14 inches. The loss (using the Champlain Rule) would be 122 board feet, which is ridiculous. Another method is to scale the log as sound, compute the contents of a log the size of the core, and subtract this from the scale of the log. In case of the 20-inch log with a 6-inch center rot the loss would be 17 board feet. Another scheme is to add 3 inches to the diameter of the rotten core, square this and deduct from the gross measure- ment. The result, if the method be applied to the example above, would show a loss of 81 feet. The actual loss, as shown by a diagram, would be 2,Z board feet. This shows that some of the methods of scaling in practice are thoroughly incorrect. The writer has for some time considered the possibility of "cull tables" to assist scalers in making discounts for specified sorts of defects in logs. In pursuance of the idea of basing such " cuLi tables" on diagrams, the writer secured the services of Mr. H. D. Tiemann, of the U. S. Forest Service, to experiment with the construction of the tables. In the first place Mr. Tie- mann constructed a series of diagrams representing the cross- sections of logs of different diameters and calculated the actual loss occasioned by center holes of different sizes. In construct- ing the diagrams, \ inch was allowed for saw-kerf and 4 inches as the width of the narrowest board. It was assumed that the logs would be sawed so as to yield the greatest possible output. Experiment showed that the most is obtained by "sawing through and through" up to a certain point where the holes are large enough to make "sawing around" necessary. It was recog- nized also that in sawing through and through there might be a difference whether the log is cut so as to have an inch board from the center or to have the saw pass exactly through the center. In every case the maximum yield was used. 6S FOREST MENSURATION. Mr. Tiemann's study established the fact that in logs o] the same length, the loss due to holes of any specified size is practically uniform, regardless of the diameter of the log. This law is clearly shown in the table below. It happens that for 1 2-foot logs this loss is almost exactly expressed by the formula — (D + i)^, where D is the diameter of the hole. 5 LOSS BY CENTER-ROT IN TWELVE-FOOT LOGS OF SELECTED DIAMETERS AS SHOWN IN DIAGRAMS. *0 . . 4) I 2-inch Log, Loss when Sawed 16-inch Log, Loss when Sawed 24-inch Log, Loss when Sawed 36-inch Log, Loss when Sawed 48-inch Log Loss when Sawed ti 0 .ax c Thro gh Around Throgli Ground Thro'gh Around Thro'gh Around Thro'gh Around Ins. Board Feet. . Board Feet Board Feet. Board Feet. Board Feet. 2 3 6 9 14 14 6 9 12 12 4 9 12 12 2 9 16 26 4 6 28 53 14 34 13 29 20 30 II 27 12 32 12 27 26 44 II 8 lO 69 50 76 112 52 82 45 70 54 92 47 65 70 80 51 12 132 120 106 132 186 1 10 173 132 194 lo8 175 t6 221 20 314 306 276 306 272 Note. — The double lines are drawn at the points where the loss is greater by sawing through than by sawing around. In practice, logs which have holes are apt to have more loss from hidden defects than others. Therefore it is wise to allow a further loss of 5%. This gives the very simple formula of loss in board feet due to center holes: Loss=§(Z)-fi)2. A table showing the loss in board feet for logs of different sizes and holes of different diameters has been constructed by METHODS OF SCALING LOCS. 69 this formula, first for 12-foot logs and then for 10-, 13-, 14-, 16-, 18-, and 20-foot logs, and is given on page 71. This table is applicable to all center defects, such as holes, cup shake, rot, etc., which are four inches or more from the bark. (Fig. 3, D, E, and F.) To apply the table, measure Fig- 3- — Methods for Discounting the Scale for Defects. the longest diameter of the defect, find the loss in board feet from the cull table, and deduct from the gross scale of the log. If the defect runs through the log, or if it appears only at the large end, measure the defect at the large end, otherwise at the small end. The table should be used only with short logs. Some may naturally ask how one is to determine the length of a hole if it appears at only one end. 'It is assumed that, if a defect appears at one end, there will be a loss to the center board 70 FOREST MENSURATION. throughout the length. If short pieces can be utilized, that is the gain of the millman, and the fact is an element of conserv- atism in the rule. The same principle holds good for the suc- ceeding cull rules. Discount for Defects near the Edge of Logs. — Under this head may be included rot, splits due to careless felling, super- ficial shake due to fire scars, sun scald, frost, or any other defects which require the removal of a wide slab, as shown in Fig. 3, A, B, and C. Cull Table B has been constructed, by the use of diagrams, to show the loss by cutting slabs of different widths from logs of different diameters and lengths. The scaler measures the width of the slab which would obviously have to be cut off, finds in the table the loss in board feet, and deducts this from the gross scale of the log. If the defect runs through the log, following the grain, and does not extend deeper at the large than at the small end, the measurement is taken at the top. If the defect appears only at the Mrge end, or extends relatively nearer the center than at the small end, the scaler must estimate the width of the slab, at the small end, which would have to be taken off. Cull Table C is designed to meet the case of defects on the side of a log, which the sawyer eliminates by cutting around them, rather than by taking off a wide slab. These arc narrow defects running rather deep into the log, such as are indicated in Fig. 3, G and H. The loss in sawing around such a defect was found by Mr. Tiemann to be equivalent to removing a wedge- shaped piece, a sector, fully enclosing the defect, though this principle docs not exactly indicate the sawyer's method of sawing the log. On this principle Cull Table C was constructed, by diagrams, to show the loss by cutting around sectors of different sizes from logs of different diameters and lengths. To use the table, estimate wht'ther the dcfectixc sjx)! is entirely included within one-sixteenth, one-eighth, etc., as represented by a frac- tion of the circumference of the end of the log, then find the loss from the table and deduct from the gross scale. Just as in the case of cutting a wide slab, the scaler must estimate, with refer- ence to the small end, the jKJition of the log wasted. METHODS OF SCALING LOGS. 7« CULL TABLE A. Loss BY Defects of Different Diameters near the Center OF Logs. (Good for defects more than 4 inches from the bark.) Diameter Length of Logs in Feet. of Defect. 10 12 13 14 16 18 20 Inches. Board Feet. 2 5 6 6.5 7 8 9 10 3 9 II 12 13 15 16.5 18 4 14 17 18 20 23 25.5 28 5 20 24 26 28 32 36 40 6 27.5 33 36 38.5 44 49.5 55 7 36 43 47 50 57 65 72 8 45 54 58.5 63 72 81 90 9 56 67 74 78 89 100 112 10 67 81 87 93 107 120 133 II 80 96 104 112 128 144 160 12 94 "3 122 132 151 169.5 188 13 109 131 142 153 175 196.5 218 14 125 150 162.5 175 200 225 250 15 142 171 184 218 226 255 283 CULL TABLE B. Loss BY Cutting Slabs from One Side of Ten-foot Logs. Diameter of Log in Inches. Width of Slab. Inches. 6 8 10 12 14 16 18 20 22 24 26 Board Feet. I 2 3 4 I 0 3 7 0 4 8 14 I 5 9 15 22 I 5 ID 17 24 33 2 6 1 1 19 26 35 45 2 7 13 20 28 38 49 60 3 8 14 22 30 41 52 65 77 3 8 15 23 33 43 55 68 82 97 3 8 15 25 35 46 59 73 86 102 119 4 10 16 26 37 49 62 76 91 107 124 141 4 10 17 28 39 52 65 80 8 9 10 96 1 1 •-" 129 148 167 12 13 72 FOREST MENSURATION. CULL TABLE B. Loss BY Cutting Slabs from One Side of Twelve-foot Logs. Diameter of Log in Inches. Width of Slab, Inches. 6 8 10 13 14 16 18 20 23 24 26 Board Feet. I 2 3 4 5 6 0 4 9 I 5 10 17 I 6 1 1 19 27 2 7 13 21 29 39 2 7 14 23 32 43 55 3 8 15 24 34 46 59 73 3 9 16 26 37 49 63 78 93 4 10 18 28 39 52 67 82 98 "7 4 1 1 19 30 42 56 71 87 104 123 142 5 II 20 31 44 59 75 92 no 129 149 170 5 12 21 33 47 62 7 8 79 97 "5 135 155 178 9 ID I 2 13 200 CULL TABLE B. Loss by Cutting Sl.\bs from One Side of Fourteen-foot Logs. Diameter of Log in Inches. Width of Slab. Inches. 6 8 10 12 14 16 18 20 22 24 1 26 Board Feet. I 2 3 4 5 6 0 4 10 I 5 12 19 I 6 13 22 31 7 i,S 24 34 46 2 8 16 26 37 50 64 3 9 t8 28 40 53 68 85 4 10 19 30 43 57 73 9' 108 4 1 1 20 ?,2 46 61 78 96 114 ■36 5 12 22 34 48 f>5 82 U12 I 21 •43 166 6 13 23 3^' 51 68 87 107 128 '50 >73 >97 6 '4 25 39 54 7 8 92 "3 ■34 •57 181 9 10 1 1 1 2 207 234 1 1, METHODS OF SCALING LOGS. CULL TABLE B. Loss BY Cutting Slabs from One Side of Sixteen-foot Logs. 73 Diameter of Log in Inches. Width of Slab, Inches. 6 8 10 13 14 16 18 20 22 24 26 Board Feet. I 2 3 4 5 6 O 5 II I 6 '3 22 I 7 15 25 35 2 9 17 27 39 52 3 lO i8 30 42 57 73 3 1 1 20 32 45 61 78 . Q7 4 12 21 35 49 65 83 103 123 5 13 23 37 52 69 8^ 109 131 155 5 14 25 39 55 74 94 116 138 163 189 ■ 6 15 26 41 59 78 99 122 146 171 198 226 7 16 28 44 62 83 105 128 7 8 9 ID 153 179 207 237 268 ir 12 13 Discount for Crooks. — Usually logs are supposed to be straight, and the scaler does not make any discount for crooks when he measures the logs. When logs are piled on skidways, it is obvi- ously impossible to take crooks into consideration. Often, however, a small percentage is deducted from the total scale to allow for this imperfection. To make allowance for the loss by crooks in a specified log, the scaler sights over the surface and calculates how much the small end must be reduced to circum- scribe the square piece which really can be cut from the log. Discount for Wormy or Rotten Sap. — The diameter measure- ment is taken inside the sap, that is, the heart-wood alone is scaled. Discount for Seams and Shakes. — Seamy and shaky logs are usually culled altogether. Sometimes in a tree with straight grain, a seam causes only the loss of one plank in the center. This loss may be calculated by the rule: Multiply the thickness of the plank to be discarded by the diameter of the log, multiply by the length and divide by 12. Usually th^ grain of the log is not Straight and it has to be discarded altogether. 74 FOREST MENSURATION. CULL TABLE C. Loss FROM Defects contained in Sectors representing Fractions OF Logs. Part of Diameter of Log in Inche Length of Circle 6 8 10 12 14 16 18 20 22 24 26 Log. Re- Feet. moved. Board Feet. lO ^ 2 3 5 6 8 1 1 14 17 20 25 30 1 4 6 8 1 1 14 18 22 28 33 41 49 1 4 7 10 15 20 25 32 40 49 61 75 90 f -• 14 22 30 39 49 62 77 94 "4 134 h 7 14 22 33 45 60 77 97 119 141 167 12 ^ 2 4 6 S 10 13 17 20 25 30 36 i 5 ~ 10 13 17 21 27 33 40 49 59 i 9 13 18 24 30 39 48 59 73 90 108 f 9 17 27 36 47 59 75 93 113 136 160 * 9 17 27 39 55 73 93 117 142 170 200 14 ^ 2 4 6 9 12 15 20 23 29 34 42 1 8 6 8 12 15 19 25 31 39 47 57 69 \ 10 15 20 27 35 45 56 69 85 105 126 10 19 31 41 54 69 87 108 132 159 187 i 10 19 31 46 64 85 108 136 166 197 234 16 A 3 5 7 10 13 17 23 27 33 39 48 i 7 9 13 17 22 28 35 44 53 65 79 1 1 1 1 17 23 31 40 51 64 79 97 120 144 f II 22 35 47 62 79 99 123 151 181 213 h II 22 35 52 73 97 123 155 1 89 226 268 Shaky logs arc usually valueless. If the shake is confined to the center, the cull rule for center-rot may be used. 40. Rules for Scaling Used on the Forest Reserves. — The following rules * have been issued to the Federal forest officers to govern the scaling in timber sales on the forest resen'cs: All timber must be scaled by a forest officer before it is removed from the tract or from the points where it is agreed that scaling shall be done. Each stick of sawlogs, timbers, poles, and lag- ging must be scaled separately. Rough averaging of diameters or * From The Use of the National Forest Reserves, U. S. Dept. of Agri- culture, Washington, D. C, 1905. METHODS OF SCALING LOGS. 75 lengths is not allowed. The Scribncr rules will be used in all cases. Ties may be actually scaled, or reckoned as follows: Eight-foot ties, standard face, 2,2)h feet B. M., each; 6-foot ties, standard face, 25 feet B. M., each. Shake and shingle-bolt material is measured by the cord. Squared timbers are scaled by their actual contents in board feet with no allowance for saw-kerf. Thus, an 8 X 12-inch 16-foot stick contains 128 feet B. M. Unsound or crooked logs will be scaled down to represent the actual contents of merchantable material. All partially unsound but merchantable stuff must be scaled, whether removed or not. In ground-rotten timber, butts which, though unsound at heart, contain good lumber toward the outside, are frequently left in the woods. Where such material will pay for sawing, the forest officer will scale it at what he considers its true value and include it in the amount purchased. Logs which are not round will be scaled on the average diam- eter; flats and lagging on the widest diameter. In the absence of a log rule, or where the position of logs in the pile makes its use difhcult, the diameters and lengths may be tallied and the contents figured from a scale table later. When possible, the purchaser will be required to mark top ends of logs to avoid question when they are scaled in the pile. The forest officer should insist on having one end of piles or skidways even, so that ends of logs may be easily reached. When the lengths of piled logs are hard to get, two men should work together. When scaled, each stick of sawlogs, timbers, ties, lagging, posts, poles, or piles must be stamped with the United States mark on at least one end, and on both when possible. Cord material, such as wood or bolts, must be stamped at both top and bottom of piles, and at least 12 pieces in each cord must be stamped. All scaling is inside of bark. CHAPTER VI. DETERMINATION OF THE CONTENTS OF LOGS IN CUBIC FEET. 41. Use of the Cubic Foot in America. — The cubic foot is already used extensively in forestry in the United States. Many of the most useful tables of contents of standing trees, of growth, and of yield, have been obtained by the use of the cubic foot. Although most figures of volume are finally expressed in board feet or other unit common in commerce to have practical value, the cubic foot is often the basis for these results. Board measure, cord measure, and standard measure are useful only in buying and selling wood and timber. These units can never be used satisfactorily in scientific work where the exact contents of logs and trees are required. The uses of the cubic foot in preparing volume tables for standing trees in cords, board feet, and standards, and in determining the laws of growth of trees under different circumstances are explained in later chapters of the book. The cubic foot is but seldom used in this country for buying and selling round logs. It is, however, used with high-priced imported woods, occasionally with hickory and oak, and with squared timber. The cubic foot will unquestionably be used more and more, as the value of timber increases, and eventually in large measure replace the present rough unit, the board foot. The American forester must, therefore, be familiar with the principles and methods of determining the cubic contents of logs and trees. 76 CONTENTS OF LOGS IN CUBIC FEET. 77 42. The Measurement of Logs to Determine their Cubic Con- tents.— All the methods of cubing logs require the measurement of the diameter at one or more points and the measurement of the length. Ordinarily the diameter measurements are taken with calipers. Formerly in India and in Europe the circumference was measured with a tape. In this country a tape is only used when calipers cannot be obtained, and in work with the trees of the Pacific Coast which are too large for ordinary calipers. A rule is sometimes used where ends of logs are measured inside the bark, as when a study of growth is being made. Generally the measurements for volume are taken in the fol- lowing way: Two measurements are taken with the calipers, one Fig. 4. giving the greatest and one the smallest diameter. (Fig. 4a.) The average is considered the average diameter of the log at the point measured. If the log appears to be perfectly round, only one measurement is taken. Some attempt to measure one average diameter, even when the log is not round. (Fig. 4b.) Sometimes the log is in such a position that it is difficult to measure accu- rately the longest and shortest diameters, as when it is lying on a flat side or is sunken in a depression. In such cases the log must be moved or rolled over, if an accurate measurement is to be taken. If the measurement of diameter inside the bark is sought, the bark may be chipped off or its average width may be determined by 78 FOREST MENSURATION. separate measurements and deducted from the diameter outside the bark. Sometimes the diameter outside the bark is desired at a point where the bark is torn away altogether or in part. Then the diam- eter inside the bark is measured and the average width of bark added, the latter being determined from a neighboring part of the log. Where volume measurements alone are sought, the common practice is to measure the diameter outside the bark, and to de- termine the inside measurements by deducting the bark width. This method is not so accurate as measuring first inside the bark and adding the bark width. The reason for this is that there are apt to be irregularities of bark which make the measure- ments of diameter too large, or pieces are broken off and the diameter is too small. This is particularly true with trees with soft scaly bark like the yellow pines. With hardwoods the common method of measuring outside the bark is accurate enough for most purposes. In determining the average thickness of bark, several measure- ments should always be taken at different sides of the log, unless the bark is thin and obviously uniform in thickness on the entire circumference. Where the bark is deeply cut, like that of an old pine, each measurement of width should show the thickness between the wood and a line tangent to the log, as the arm of a caliper fitted to the log at that point. Sometimes there is a swelling due to a knot or other cause at the point where it is desired to take the measurement of diam- eter. In this case the calipers must be i)laced just above or below the swelling} or measurements may be taken both just above and below and the average called the correct diameter. Many inaccuracies arise from the careless use of calipers. They should always be placed at right angles to the log. Inas- much as the sliding arm of the calipers when moved bends toward the stationary arm, as explained on page 8i, care must be taken that it rest tightly against the log and is at right angles to [he graduated beam when the reading is taken. Whenever possible, the calipers should be i)laced so that the l)eam touches the log. CONTENTS OF LOGS IN CUBIC FEET. 79 The measurement should not be taken with the tips of the arms, except in extreme cases, because the measurer is apt not to have the sUding arm brought to a perpendicular position with the beam, and because any inaccuracies of the calipers due to warping or wear are greater at the tip than near the base of the arms. The forester should continually test his calipers to guarantee their accuracy. In all scientific work diameter measurements are taken in inches and tenths. Foresters are sometimes tempted to round the measurements to half or to whole inches, especially when a large number of logs are being measured. If the cubic foot were used in commerce, the diameter measurements would probably be rounded to the half or whole inch, as is the case where logs are scaled in board measure. At present in this country the measure- ments of cubic volume are chiefly for scientific purposes, as in the preparation of volume tables, the study of growth, etc., and require diameter measurements to tenths of inches. It is frequently asserted that there are apt to be inaccuracies due to irregularities of the bark, and that in consequence it is incon- sistent to take such fine measurements. It is true that there are chances for errors in measuring logs with rough or ragged bark, but this is no reason for deliberately adding to the errors by a rough method of taking the readings from the calipers. Moreover, the rounding of diameter measurements to half or whole inches leads invariably to carelessness on the part of the measurer, who may soon estimate certain diameters without using his calipers, or in other measurements give figures which are estimates rather than true readings from the instruments. 43. Measuring Instruments. — In work on very large logs like redwood logs, circumferences are taken with tapes. A special tape is made for such work, which shows not only the cir- cumference in inches or in feet, but also the diameter correspond- ing to every circumference. The readings, therefore, may be recorded as diameters, thus avoiding the laborious work of after- wards calculating the diameters from circumference readings. So FOREST MENSUkylTlON. The end of the tape is provided with a pin which may be inserted in the bark, enabling one person without assistance to measure a large log or tree. (Fig. 5.) Usually the tape gives a larger result than calipers, because every swelling or abnormal protuberance of bark is included in the tape measurement. It is impossible to bring the tape close against the trunk at all points. Care should, therefore, be taken in using the tape to avoid irregularities on the log which may affect the measurements. Where the diameters of the ends of the logs are measured, a rule may be used. This is often done in taking full tree Fig. 5. — Tape for Measuring Girths and Diameters. analyses. The diameters inside the bark are measured with the rule on the smooth cross-cut, and the outside dimensions obtained by adding the bark width. For these measurements the cross- cut must be made at right angles to the axis of the log, otherwise the fjgurcs will be too large. A number of different forms of calipers arc made. American foresters generally use the type of calipers developed by the Forest Service, U. S. Department of Agriculture. This form is extremely simple, and has been found to be light, strong, and durable, as well as very accurate, the qualifications necessary for a satisfactory instrument. These calipers consist of a beam CONTENTS OP LOQS IN CUBIC FEET, Si having scales on both sides graduated in inches and tenths. This beam is provided at one end with an arm held in place by a bolt and nut, which permit it to be detached for convenience of transportation. The beam is provided with a sliding arm fitted loosely so as to slide easily over it, but constructed so that when pressure is applied to its inner edge, as when it is brought against a tree-trunk, it swings into position in which it is at a right angle to the beam. For use in eastern forests the most convenient caliper has a beam measuring 36 inches and arms one half that length. In forests where trees over 3 feet in diameter occur, ib'H'4 i.D'i e IT iS'i.'j •^ — m- ""lytiiii.iiBiiii'iiiiiiiiiiiiiipiiiiiiwuiiil Fig. 6. — American Type of Calipers. calipers having a beam measuring 50 inches and proportionately long arms are used. The 36-inch calipers weigh i .9 pounds. The upper and lower edges of the opening in the sliding arm are lined with metal to prevent wear. The metal strip lining the upper edge is movable at one end, being held in place by a screw {A in Fig. 7). This device enables the perfect adjust- ment of the arm with reference to the beam of the calipers. The chief disadvantage of the American type is that the space for the beam in the sliding arm is made so narrow that the 82 FOREST MENSURATION. latter does not run smoothly or it actually sticks when the beam swells, as often occurs if used in the rain. The same thing hap- pens if the beam becomes slightly coated with pitch, which cannot be avoided when working with pine logs; and again the sliding arm is apt to be clogged by damp snow and seriously interJ.'ere with winter work. This disadvantage is obviated in the calij)ers used in Germany, described below. The German calipers are, however, heavier and for most work in this country less convenient than the American type. This form of calipers is manufactured Fig. 7. by Keuffel & Esser Co., No. 127 Fulton Street, New York City, listed at $4.50 each. The calipers used in ordinary forest work in Austria are very similar to the American type just described. The device for adjusting the sliding arm differs only in the position of the rctain- ing-screw. The graduations on the beam are marked in depres- sions, about an inch wide, in order to protect the marks from the wear of the sliding arm. As ordinarily constructed, the calipers are heavier than those made in this country and have the disadvantage of not taking down. A number of different kinds of calipers are used in practice in Germany. Simple calipers like the .Austrian type above described are used by many foresters. A common form is that made by Staudinger & Co., in Giesscn, which has a special con- CONTENTS OF LOGS IN CUBIC FEET. ^3 struction designed to obviate the difficulty caused by the sweUing and consequent sticking of the movable arm. In these calipers the measuring-beam is beveled on the edges so that the cross- section is a regular trapezium. Fig. 8 shows a section of the movable arm A A, including a cross-section of the measuring-beam M. The construction is such that at the points a, a', and a" the measuring-beam fits closely to the sliding arm, but does not come in contact with it at any other points. The sliding arm is further fitted with a metal wedge shown in cross-section as N. This wedge is held in place by the screw o, and whenever the screw turns is moved toward or away from the measuring-beam. The screw 0 is turned by means of a key, which is provided with Fig. 8. Fig. 9. two points made to fit the shallow holes in the head of the screw. By loosening or tightening the wedge the sliding arm may be adjusted to suit the condition of the beam. If it is swollen by moisture or coated with pitch, the wedge may be loosened so that the arm will move with ease. The disadvantage of the calipers is that there is a separate 84 FOREST MENSURATION. key, which is easily lost. The construction being less simple than in the forms described above, the weight is necessarily greater. Fig. 9 shows another adjusting arrangement, some- times found on the sliding arm of German calipers. A number of folding calipers are constructed for convenience in packing and in carrying to and from work. The author has never seen any folding calipers which were serviceable for prac- tical woods work. They are not so strong as the regular forms, and with use they soon become inaccurate. A caliper which may be taken down like that first described has every advantage of the folding caliper except that it cannot be readily taken apart for transportation to and from daily work. This last advantage is too insignificant to require any sacrifice in the strength and durability of the instrument. Every European text-book on Forest Mensuration contains descriptions of calipers constructed on other principles, as, for instance, like a carpenter's caliper-gauge. The author has never found any such calipers in extensive practical use even in Europe. The length of logs is usually taken with a tape graduated in feet and tenths. The length is taken along the surface of the log. If the log is considered a frustum of a cone or paraboloid, this represents the slant height and not the true length of the axis. The error is, however, very minute and may be disregarded. On an average this amounts to only 0.1%, as has been proven by European experiment. It was explained on page 63 that in scaling logs for board feet the length is usually rounded to feet and always to the foot below the actual measure, as, for example, 16 feet, if the actual measure is 16.7 feet. In all scientific work with the cubic foot, the measurements are rounded to tenths of feet or to inches, preferably the former. For general work of forest measurements a steel tape, measui- ing 50 feet, is the most satisfactory. It is convenient in size and weight, and is more durable than any olhcT form of tape. A CONTENTS OF LOGS IN CUBIC FEET. 85 metallic tape, that is, the cloth tape which has several strands of copper wire running through it, is satisfactory in every respect, except that it frays after a short time when used in the woods, A steel tape will last several years in constant use, provided it is not allowed to rust. After using a steel tape in wet woods, it should always be wiped and oiled, A number of different forms of steel tape are constructed. The best type has a band | inch wide, and costs $6,50, A cheaper tape with a band \ inch wide costing $4.45 answers every purpose, but will not stand as rough wear as the more expensive form. With careful treatment the smaller tape should satisfy the requirements of most foresters. Metallic tapes cost $2.75. Cloth tapes are impractical for ordinary rough work in the woods. Tapes may be purchased from any dealer in survey- ing instruments, 44. Principles Underlying the Determination of the Cubic Contents of Logs and Trees. — For many years European foresters have endeavored to discover a mathematical formula by which the cubic contents of logs may accurately be calculated from a few measurements. Great difficulty has been encountered, because the forms of different logs differ so much under different con- ditions. The form of a specified log depends on its relative growth in diameter at different points. The growth in diameter at different parts of logs varies widely, and in consequence their forms are not uniform. If the diameter growth on the trunk at certain distances above the ground were always the same for a given species, the form of the trunks of all trees of that species would be constant. But the form of a tree changes from decade to decade, different individuals nearly always differ in form, and logs from different parts of the same tree have different forms. At first sight the surface lines of a log appear to be perfectly straight, as on the section of a cone. Experiment has shown that on most logsthe longitudinal surface lines are slightly convex, as on the section of a paraboloid. Sometimes, however, they are slightly concave, in which case 86 FOREST MENSURATION. the log approaches the form of a Neilian paraboloid or neiloid. Usually the form of the log is between that of a cone and a paraboloid. A number of formulee have been devised which enable the cubing of logs with almost perfect accuracy, the error amounting to less than one percent. The most accurate formulae, however, require for their use too many different measurements on the logs, or they involve too many calculations, to be of use in practical work. In ordinary work in the woods extremely simple formulae are used, which are accurate enough for commercial purposes, although they are subject to an error in individual cases of 2 to 4 per cent. 45. Fundamental Formulae. — It is customary to assume that logs and other parts of felled trees have the form of some known geometric body, as the frustrum of a cone or paraboloid, and to cube them by formulae applying to these bodies. The methods will be clearer if prefaced by a statement of the most impor- tant formulae for cubing a cylinder, paraboloid, cone, and neiloid. These formulae are as follows: FORMULAE FOR DETERMINING THE VOLUME OP A CYLINDER, CONE, PARABOLOID, AND NEILOID. The Cylinder. Let F= volume of the cylinder; i7 = altitude of the cylinder; i? = radius of the base; Z> = diameter of the base; 5 = area of the base; I. F= ?:/?'•//; 2. V= •//; 4 Fig. 10. 3. V=BH. CONTENTS OF LOGS IN CUBIC FEET. 87 The Full Cone. Fig. II. Let F = volume of the cone; £r = altitude of the cone; i? = radius of the base; Z> = diameter of the base; 5 = area of the base; Z)i = diameter at ^H; B^ = area of cross-section at ^H] B\ = area of cross-section at \H\ I. F= 2. F= 3- V- 3 ' 12 ' BH 4. V=j-Di-H; 5. V^^-Bi-H; 6. V=(B + 4Bi)^; Frustum of a Cone. 7. F=o.75-^i-^; V = B^-H+ BH Let F= volume of the frustum; h = altitude ; /? = radius of the lower base; Z? = diameter of the lower base; jB = area of the lower base; r = radius of the upper base; = diameter of the base; J5=area of the base; 5j = area of the cross section at ^H. I. V- nRm 2. F= nD'^H BH 3. F= — ; 4. F=2Bifl"; H 5. F=(5-f45i)y, Fig. 13. 90 FOREST MENSURATION. Fustriim oj a Neilian Paraboloid or Neiloid. Let T' = volume of the frustum; 27 = altitude of the frustum; /;: = radius of the lower base; r = radius of the upper base; 5 = area of the lower base; 6= area of the upper base; 5j = area of the cross -section at \h. ^=- {R' + ^R^^ + '^'Rh'+r^; h V={B + 4Bi + b)^. 46. Determination of Sectional Areas. — Most formuL^ for determining the cubic contents of logs are based on the length and the area of one or more cross-sections. Ordinarily the area of a cross-section is considered equivalent to that of a circle whose diameter is the average diameter of the cross-section. The area is computed bv the formula, B= , in which B is the area, 4 and D the diameter of the cross- section. Usually the cross- sections of logs are not perfect circles; but if two or more diam- eters are measured and averaged, the area of a circle having as a diameter this average will be found to be very close to the real area of the cross-section. If the circumference were taken, the area would be determined by the formula, B = ^, in which Ij is the area and C the circumference of the cross- section. This last method would not be so accurate as that of using an average diameter unless the cross-section were a perfect circle. If the cross-section were not a circle, the result would be too large because with a given perimeter the circle has the largest area of any plane surface. Moreover the irregularities of bark, tend also to give too great a result. Tables are constructed which show the areas of circles corresponding to different diameters, so that no special computations arc necessary. Such a table of areas of circles is given in the Appendix. CONTENTS OF LOGS IN CUBIC FEBT. 91 If a cross-section is elliptical, its area may be accurately deter- mined by the formula for an ellipse, namely, ^ = 0.7854/) . 51. II 43-50 30 5700 5300 4 1 . 0(.> 5500 47-00 Feet. 3 68.50 63.00 50.00 65-75 56.50 4 88.92 82.42 63.62 85.67 73.02 5 108.50 101.50 78.00 105.00 89.75 6 128.50 120.00 92.30 124.25 106.15 7 14955 138-05 106.41 143.80 122.23 8 170.00 165.00 II 9 . 90 167.50 142.45 9 190.00 175.00 133-50 182.50 154-25 10 21 1 .00 193.00 147-50 201 .00 170.25 II 230.00 210.50 16 1 . 20 220. 25 185.85 12 250.00 228.00 175.00 239.00 201 .50 13 269.00 245 - 50 189.00 257-25 217.25 14 287 . 50 262.50 203.00 275.00 232.75 class wood; in the .second class, 5%. Low, crooked, and branchy trees would reduce the solid contents 10% and 5% respectively, and so on. As can easily be seen from this, these tables are not absolute for all conditions. To be perfectly correct, such tables should be made for a limited locality. The merit of the tables given, therefore, lies in pointing out tin- relative solid contents in cords of sticks of different length and diameter, and as such CORD MEASURE 109 they ought to prove of value to all industries which buy timber for its actual solid volume, like pulp and extract manufacturers. " By giving the actual solid volume in cords of different length and diameter, these tables help to establish just and uniform prices, and ought, therefore, to be the basis of all specifications in contracts for pulp-, extract-, or fire-wood." 60. Relation Between Cord Measure and Board and Standard Measures. It is customary in many localities to compute the contents of logs both in cords and in board feet. Fire-wood is not measured in this way, as it is too small and inferior to use for timber. But pulp- wood and other wood, which is cut into short bolts and is large enough to scale in board measure, is sometimes sold by the cord and sometimes by the thousand board feet. Many persons are accustomed to measure timber by the thousand and are unable readily to reckon by the cord, so that it is convenient to have a converting factor to trans- late from one measure to the other. Still again,' it is often con- venient to estimate standing timber entirely by the cord and to calculate the board measure separately. Therefore there have come into use rough converting factors, analogous to the factors for converting board measure to standards and vice versa. In this case, however, there is a great divergence of opinion as to the board contents of a stack of timber. This is natural, because the board contents of stacks differ according to the size and length of the logs, the character of the surface, and, what is often overlooked, the log rule used and the method of scaling. Ordinarily the attempt is made to show into how many cords a given lot of logs will stack when cut into short bolts. The logs are scaled before cutting into bolts; they are scaled by their top diameters; the butts may vary enormously in diameter and irregularity; no regard whatever is taken of the size of the logs. A lot of logs from large virgin trees would yield totally different results than small second growth. It has been shown that the cubic contents of a stack increases with the size of the sticks. The board contents of logs increase with their size in a very much more no FOREST MENSUR/ITION. rapid rate than cubic feet. The use of the same converting factor with small and with large timber is, therefore, totally in- correct. All that can be done is to obtain the average amount of board feet in stacks of timber cut in a certain locality where the average size of the sticks, the average form, and irregularities of surface of the timber are uniform. The use of this factor in other localities where the species, the size of timber, and even the method of scaling in board feet are different, would prove inaccurate. This explains why some give 300 and others 1000 board feet as an equivalent of a cord. In spruce of the New England States 560 is the ordinary translating factor used by many companies. For average-sized timber 550 board feet per cord is a conser\^ative estimate. The conversion of standards to cords is simple because the standard is a unit of solid volume. Ordinarily the Nineteen- inch Standard is considered equivalent to one-third of a cord, or, more exactly, 2.92 standards to the cord. A fair average ratio between board feet and cubic feet is 6 board feet to each cubic foot. This ratio is consistent with the figures given in the preceding paragraph. CHAPTER IX. THE CONTENTS OF ENTIRE FELLED TREES. 6i. The Measurement of Entire Felled Trees. — The foregoing sections show how to determine the contents of logs. Many investigations, however, require the contents of trees. The cruiser measures the merchantable contents of felled trees to aid him in estimating the volume of standing trees. Volume tables showing the contents of standing trees of different sizes are based on the measurement of felled trees. When the growth of trees in volume is studied, the contents of whole trees and not merely of individual logs must be determined. The measurements usually taken are the diameter breast-high, diameter at each cross-cut inside and outside bark, stump height, length of each log, and the length of the top above the last cut. These data enable the computation of the volume of the whole stem and the merchantable volume. If the percent of sapwood is required, the width of sap is measured at each cross-cut. It has been a common custom in the United States to take measurements for volume in the lumber woods where timber is being cut for the market. The forester measures the trees as soon as cut and before the logs are drawn away from the stumps, and in this way saves the expense of hiring choppers and of paying for the privilege of cutting trees, which often have to be purchased outright. Young trees below merchantable size and trees which cannot be sold for other reasons must be felled spe- cially. In the latter case the forester cuts the trees into such lengths as Slit the special requirements of the investigation. When the 112 FOREST MENSURATION. forester measures trees cut for the market, the lengths of sections must conform to the regular log lengths. In many cases this varies, as, for example, when logs are cut lo, 12, 14, 16 feet, and per- haps also other lengths. The data secured are of less scientific \-alue than where the logs are all the same length. For most prac- tical purposes of study in old timber, the measurements of logs cut for the market yield satisfactory results. It is the custom of foresters to classify trees by the diam- eters at breast-height. Lumbermen more often refer to the stump diameter when speaking of the size of trees. The stump diameter is unsatisfactory because of the varying height of the stump and also because the stump cut is usually within the base swelling of the tree, and is much more variable than the diameter measured above this swelling. Sometimes specifications of trees bought on the stump call for certain diameters at 6 feet above the ground. This is an awkward point to measure, par- ticularly for a short man. The plan of the forester to classify all trees by the diameters at breast-height is the most practical. This point is above the root swelling, and it is the natural place to caliper a standing tree. In America 4^ feet has usually been accepted as the breast-height point. In Germany breast-height is 1.3 meters, or about 4 feet 3 inches. The English have chosen 4^ feet for their work in England and India, and this has been adopted in this country. It is slightly above true breast-height for a short man, but is just right for a man of average height. In measuring felled trees, therefore, the diameter at breast- height is obtained with the calipers. If the tree is not round, the largest and smallest diameters are averaged as the true diam- eter. Sometimes the measurer is able to take this diameter before the tree is felled. Otherwise it is necessary to measure it at the proper point on the butt log. To find the breast-height point on the butt log, the average stump-height is measured, and then this amount deducted from 4.5 feet for the distance which must be measured from the base of the log to the breast-height point. There is often confusion as to where to take the measurement THE CONTENTS OF ENTIRE FELLED TREES. 113 of the height of the stump. Thus on a side-hill, on a hum- mock, or other irregularity of ground, the height of the stump is much greater on one side than another. The simplest method is to imagine the same tree growing on level ground and place the lower end of the rule at the point which would represent the plane of the level ground. When the stump cut is slanting or uneven on account of bad chopping, care must be taken to measure the average height and not the distance from the ground to the highest point or the lowest point of the stump cross-cut. In the same way in measuring from the base of the butt log to the breast-height point, one must be careful to locate the breast-height point exactly 4J feet above the ground as the tree stood before felling. The scarf at the base of the log often leads to errors by careless measurers. After measuring the diameter at breast-height, the length and the diameters at the ends of each merchantable log are measured. These figures enable the determination of the merchantable con- tents of the whole tree in board feet, standards, or cubic feet. Frequently the trees measured are classified both by diam- eter breast-high and also by height. In this case the distance from the uppermost cross-cut to the tip of the tree is measured. The sum of the lengths of the logs, plus the stump-height, plus the distance from the uppermost cut to the tip, is the total height of the tree. The distance above the last cut is measured with a tape or a measuring-rod, usually the former. The measurement is apt to be taken carelessly, because the tape must be stretched in among the branches. It requires some time and patience to stretch a tape through the crown of a tree and secure an accurate measure- ment. In scientific work an accurate measurement is necessary. In some rough work it is sufficient to take the measurement on one side of the crown, calculating the limits by the eye, or even to pace beside the crown to obtain the length of the top piece. For clas- sification of trees by height classes a rough'estimate of height may suffice. In the study of growth and similar work the total length 114 FOREST MENSUR^TJON. of the trees must be determined accurately. Sometimes young foresters are confused in locating the tip of a hardwood tree which has an irregular top. If the crown is rounded, imagine a tangent perpendicualar to the tree's axis and let this be the top. If the crown is very irregular the highest point is taken as the tip. Sometimes the computed height is slightly greater than the true height of the tree because the result is the sum of the lengths of several sections, some of which bend from the perpendicular line of the tree. The effort should always be not to measure abnormal trees. Ordinary trees offer no practical dilhculties. An accurate determination of volume of the whole stem is required in certain scientific investigations. Sometimes volume tables are based on the entire stem contents, as explained later. The form of trees may be compared better when the entire stem or the stem down to a certain fixed diameter is cubed than when simply the merchantable contents are determined. Certain studies of growth also require the stem contents. The measurements in the field are the same as described above, except that diameter measurements are taken above the uppermost merchantable cut. Ordinarily in measuring timber trees, the top, i.e., the portion of the stem above the last merchant- able cut, is divided into lo-foot sections and diameter and length measurements taken, just as on the merchantable logs. Where small trees which are not large enough for sawlogs arc measured for volume, the sections are made lo feet in length. If there is a cord-wood market for 4-foot sticks, the sections are made 8 feet long. If very exact data are required, diameter measure- ments are taken on the stems every 4 feet. 62. The Computation of Volume. ^The contents of an entire stem are determined as follows: Each log or bolt is cubed as the frustum of a paraboloid; in this country usually by the end diameter method (Smalian's method). The top piece, i.e., the small piece from the last cut to the tip, is ordinarily cubed as a cone, i.e., by the formula, V= , in which V is ihc volume, THE CONTENTS OF ENTIRE FELLED TREES. 115 B the area of the kist cross-cut, and h the length of the top piece. If the stump is included, it is generally considered a cylinder with a diameter equal to the diameter of the stump. The formula is V = Bli, in which V is the volume, B the area of the stump cut, and h the stump-height. Naturally this method of cubing the stump does not include all of the wood because there is a con- siderable flare on every stump. It has been found, however, that this root flare is so variable that better results are obtained by disregarding it and considering all stumps as cylinders. In investigations in this country, the cubic contents of branches are determined only in the case of old hardwoods with large branches, which will make merchantable cord- wood. Only such parts are measured as are salable. The limbs are cut into regu- lar lengths, usually 4 feet, and diameter measurements taken as on the sections of the stem. Inasmuch as there is often only one stick in a limb and the pieces are in consequence isolated indi- viduals, the middle diameter and length are taken and the pieces cubed by the middle-diameter formula (Ruber's). In this country no studies have ever been made of the contents of the smaller parts of the branches or of the roots. In Europe such material is often salable. It is doubtful if American forestry will need any such studies for a long time. Even scientific studies com- paring the contents of trees growing under different conditions will probably be based on measurements to a fixed diameter of branch, say 2 inches, instead of including the twigs. In Europe the contents of very small and irregular parts of trees are cubed by means of the xylometer. This consists of a large cylindrical vessel, which is graduated inside, or by a tube outside, to show the volume of water contained in it. The volume of irregular sticks or pieces of roots may be obtained by immers- ing them in the xylometer and determining the amount of water displaced. Another form of xylometer has a spout from which water flows when the wood is immersed, -the water being caught and measured in a separate vessel. When considerable quan- tities of wood are measured, the whole is weighed, then a small II 6 FOREST MENSURATION. portion, w-hich is weighed separately, is cubed by the xylometer; and then the entire mass cubed by assuming that the weight and volume are proportionate. If W is the weight of the whole, w the weight of the small portions selected for cubing, V the volume of the whole, and v the volume of the portion cubed, W V : v = W : w or F= — v, w 63. The Measurement of Crown, Clear Length, and Merchant- able Length. — The measurements described in section 61 may be summarized as (a) diameter breast-high, (b) diameter at each cross- cut, (f) stump-height, {d) length of each log and the top above last cut. Other measurements often required by investigations of volume are as follows (letters to continue the measurements above summarized): (6') Clear length. — The purpose of this measurement is to enable the estimate of the amount of each tree which has clear lumber. The figures obtained are averaged together to assist a cruiser in estimating the percentage of clear in a specified forest, or to assist in the valuation of timber and an estimate of the classes of lumber for which a specified lot may be used. In this case clear length means the length of the trunk yielding clear lumber. Often, however, the purpose of the measurement is to study natural pnming, in which case clear length may refer to the length of trunk clear of branches or branches of a certain size. In all cases the records should make it j)lain to what clear length refers. (/) Merchantable length. — This is the distance from the stump to the point on the stem where it is no longer of a merchantable size or quality. Ordinarily the measurement is taken without regard to the cutting of the stem into short logs. It is as if the stem were to be cut at the highest possible point in the tree and then be taken out whole, as is often done with spruce. Certain studies require as the merchantable length the sum of the lengths THE CONTENTS OF ENTIRE FELLED TREES. I17 of the merchantable logs. The term used length is employed for the length which can be utilized. Often it is desirable to know what the tree contains, on the assumption of cutting to a lower limit. For example, if the average limit were 8 inches, one might wish to know the contents, were it possible to use the timber down to an average of 4 inches. In that case the pos- sible merchantable length would be the distance from the stump to the 4-inch point, or as near that point as the timber continued to be of merchantable quality. When the contents of trees are taken to a fixed limit, as, for example, 3 inches, regardless of whether the upper part is of merchantable quality, the measure- ment of length from the stump or ground to this minimum point should not b3 called the possible merchantable length, but the "Icxigth to 3-inch point" or similar clear phrase. The con- fusion arising regarding the meaning of merchantable length may in this way easily be avoided. (g) Length of crown. — Just as in the case of the merchantable length, foresters have not in all cases agreed regarding the exact meaning of the length of crown. The crown is measured for descriptive purposes alone. It is entirely to explain the form of the bole as indicated by its volume, and in case of full tree analyses to explain the rate of growth found. The character of the stem must be ascertained by the clear length and special description. The length of crown, then, refers to the length of the crown proper, and not necessarily to the distance from the tip of the tree to the lowest green limb. It may happen that a green limb is isolated from the crown proper and some 5 to 15 feet below it. If the distance from the tip to the lowest green limb is called the length of crown, it would indicate that this is all crown, whereas the extra limb plays an insignificant part in wood pro- duction. The measurer should regard the crown by itself, as the part of the tree affecting the growth, and take its length by itself, throwing out the occasional branches which are of but little importance, and which if included would mislead in the conception of the assimilating surface of the tree. ii8 fOkEST MENSURATION. Qi) Width of Crown. — This measurement is often omitted, but is crcactly as important as the length of crown. The two measure- meats together give an admirable mental picture of the crown, and are necessary v\'hen comparing the volume of trees of the same size from different places. It may be measured by a tape or estimated. Being a measurement primarily for description, exactness is not an essential. 64. Description of the Tree Measured, (i) The Tree Class. — If the tree grows in a stand which is even-aged or approximately so, the tree should be distinguished as dominant, intermediate, or suppressed. In an uneven-aged stand this distinction may not ^s^' >E Fig. 14. always be made. The rule is that the tree class is named when possible. If it clearly cannot be assigned to any class, as, for instance, a thrifty twenty-year-old tree among, but not crowded by, eighty-year-old trees, a full description of the tree may suflkc. THE CONTENTS OF ENTIRE FELLED TREES. 119 (2) Crown Description. — This is designed to supplement the measurements of the crown. It may be expressed in words, but still better by a diagram, showing the shape of the crown. If a crown is one sided it requires a number of words to give a clear description of the shape. Fig. 14 shows a sketch of a vertical section of a crown, together with the measurements. It shows also the shape of the trunk, answering the purpose of word description. (3) Description 0} the Stem. — Usually the stem is described as round or elliptical, straight, crooked, with a sweep at butt, tapering or full boled, etc. (4) Thrift and Vigor. — Note should be made whether the tree is vigorous and thrifty, or sickly, apparently rapid-growing or slow-growing. If there is anything unusual about the tree it is described, as for instance a dead top, dead limbs in the crown, a swollen butt, shaky at butt, rotten at heart, etc. The measurements of felled trees are recorded on special forms, like that shown below, which is used by the forest officers of Massachusetts. The U. S. Forest Service uses for this pur- pose the regular tree-analysis blank, described on page 264. Locality, Milford, Pike Co., Penn. Date, July 28, 1905. No. 31. Type, Chestnut, Qual. II. Species, Chestnut. Total height, 53.6 Feet. D. B. H.* 8 Inches. Class, Dominant. Length Crown, 26.6 Feet. Width Crown, 19 Feet. Length of Section. D. 0. B.t Width of Bark. D. I. B.t Voli'tne with Bark. Feet. Inches. Cubic Feet. 0.8 8.0 0.4 7-2 10. 6.8 0-35 6.1 3.0 ID. 6.2 0.4 5-4 2.3 10. 4-2 0.25 3-7 1-5 10. 2.6 025 _ 2. 1 0.7 12.8 ♦ Diameter breast-high. t Diameter outside bark. t Diameter inside bark. CHAPTER X. THE DETERMINATION OF THE HEIGHT OF STANDING TREES. 65. Rough Methods of Measurement. — It is often necessary in forestry to determine the total height of a standing tree, its merchantable length, clear length, length of crown, or the height above the ground of a certain point on the trunk. In the practi- cal work of timber cruising an estimate of height is often suffi- ciently accurate. A height measure is valuable to the cruiser chiefly in training his eye to estimate heights, and in testing his judgment by an occasional exact measurement. A woods- man can train himself by practice to estimate the height of a tree within 5 to 10 feet. Some are able to make this estimate merely by looking at the tree. Others find it easier to divide the shaft, mentally, into lo-foot sections, and to estimate the number of these sections. There are several methods of measuring without an instru- ment the height of a standing tree. One of the simplest is to measure the shadow of the tree and the shadow of a straight pole of known length set perpendicular to the earth. Multiply the length of the shadow of the tree by the length of the pole and divide the product by the length of the shadow of the pole. The result will be the height of the tree. A method used when the sun is not shining is to set two poles in a line with the tree. (See Fig. 15.) From a point on one pole sight across the second pole to the base and to tlic top of the tree. Let an assistant note the points where the lines of DETERMINATION OF THE HEIGHT OF STANDING TREES- 121 vision cross the second pole and measure the distance between these points. Also measure the distances from the sighting-point on the first pole to the base of the tree and to the lowest vision- Ar^. Fig 15. point on the second pole. Multiply the distance between the upper and lower vision-points on the second pole by the longer of the other two measurements and divide by the shorter; the result will be the height of the tree. Example: Let &c = 6; ylc = 4; and AC=Tp\ then height of tree. 6X30 = 45» 122 FOREST MENSUR/1TI0N. Another method sometimes used is as follows: The observer walks on level ground to a distance from the foot of the tree about equal to its estimated height. He then lies on his back, stretched at full length, and an assistant notes on a perpendicular staff erected at his feet the exact point where his Hne of vision to the top of the tree crosses the staff. The height of this point from the ground is measured and the observer's o^^Tl height. Then the height of the tree is the product of the distance meas- ured on the staff and the distance from the observer's eye to the tree divided by the observer's height. There are other rough methods of measuring heights, based on the principle of similar triangles. They are not of sufficient value to justify a description in this book. 66. Height Measures. — Many instruments have been devised for measuring the height of a standing tree. In Miiller's Holz- messkunde, about thirty different height measures are described; and since the publication of that work, several new ones have been invented. A complete description of all these instruments seems to the author unnecessar}'. Therefore only those which are likely to be of value to the American forester are described in full. Mention is made of others which are on the market, with their cost and the firms manufacturing them. Height measures, often called hypsometers, are based either on the geometric principles of similar triangles or on the trigono- metric principle of measuring angles. The principal geometric instruments are the Faustmann, Weise, Klaussner, Winkler and Christen height measures. The trigonometric instruments arc the Brandis, Abney and Goulicr height measures. 67. The Faustmann Height Measure. — This instrument, shown in Fig. 1 6, consists of a skeleton rectangular metal frame having two cross-bars at one side of its longitudinal center, the frame and bars being in one piece, A slide, reversible end for end and having beveled edges, works in undercut grooves formed in the inner edges of the cross-bars. This slide is provided at its ends with thumb-notches, and \\\X\\ transvcrsclv arranG:cd index marks. DETERMINy4TlON OF THB HEIGHT OF STAN DING TREES. 123 designated I and II. A plumb-line carrying a plummet is attached to the slide in the center of the index mark 11, A retaining spring secured to the back of the frame and bearing against the inner face of the slide holds it in any position in which it may be set Fig. 16. — The Faustmann Height Measure. The left-hand end -bar of the frame is furnished with an eyepiece, and the right-hand end -bar with an objective, both of metal, and hinged so as to be folded down out of the way when the device is not in use. A long, narrow mirror is hinged to the 124 FOREST MENSURATION. frame at a point below the objective, so as to reflect a right-hand horizontal scale and a left-hand horizontal scale engraved upon the lower bar of the frame, and meeting at a zero-point, which is intersected by a line passing through the longitudinal center of the slide. The right-hand scale runs to 75 and the left-hand scale to 225, the latter scale continuing upward on the left-hand end-bar of the frame. ./ ./ V C ,-. FiG. 17. The right-hand cross-bar is provided with a vertical scale running upward from zero to 100, and continued on the left-hand cross-bar with a scale running ui)ward to 175. These scales are divided in fifths and numbered. The lines forming the scales are equally separated from each other and represent units of distance under any system of measurement that may be adopted. The handle of the device is attached to the left-hand cross-bar. DETERMINATION OF THE HEIGHT OF STANDING TREES. 125 A cheaper form of the instrument has a solid wooden frame and slide, and the scales are stamped on inlaid white com- position. The operation of this instrument is based on the geometric principle of similar triangles. To take the simplest possible case first, suppose the eye of the observer is exactly on a horizontal plane with the base of the tree. When the instrument is sighted to the tip of the tree a triangle is formed by the intersection of ^^. '••;= .--V- Fig. 25. The theory of the Klaussner height measure is clear from Fig. 25. The instrument is set so that Ac represents the number of feet, yards, or other units in the distance AC. The triangle, formed by the base- and sigh ting- rules and the altitude scale, is similar to ABC, and -7— = . Ac has the same number of DC ac units as AC, so that the number of units in he is the height of the tree. The chief advantage of the instrument is that it is fitted to a tripod and is therefore not subject to the^error due to the shaking of the hand or to an unsteady eye. It is, therefore, the most accurate of all the small instruments. A second advantage is 136 FOREST MENSURATION. that only one observation is required. It is not so compact as the instruments already described and it is more easily thrown out of adjustment. It is particularly well suited to work of a scientific character which requires accuracy. In most rough Fig. 26. — The Winkler Height Measure. forest work, hand -instruments are preferred on account of the burden of transporting a tripod. The Klaussner height measure may be purchased from KeufTel & Esscr Co., N. Y., for $26.00, or from Wm. Sporhasc, Giessen, Germany for 40 marks. DETERMINATION OF THE HEIGHT OF STANDING TREES. 137 71. The Winkler Height Measure and Dendrometer. — This instrument consists of a shallow box 5I inches long, 3 inches wide, and i inch deep. Against one face of the box is attached a metal plate on which are marked off vertical and horizontal lines, making a series of squares. The horizontal lines are further subdivided and constitute a series of altitude scales. Each horizontal line has a right-hand and left-hand scale meeting at a zero-point to the left of the center of the instrument. The vertical line passing through the zero-point of the altitude scales is graduated as a distance scale. Suspended from the zero- point of this distance scale is a narrow flat metal pendulum bevelled on one side to a sharp edge and carrying at the end a short line and plummet. A scale is graduated on the pendulum in the same units as the altitude scales. On the upper edge of the instrument are two upright plates, the one having a peep- sight and the other fitted with cross-hairs, constituting together a line of sight. The instrument is mounted on a jointed stand- ard, which may be fitted on a tripod or held in the hand. By the construction of the instrument the observer must stand at 20, 40, 60, 80, or 100 feet from the tree. There is no sliding distance-scale, as in the Faustmann height measure, but the different horizontal lines correspond to specified distances from the tree. If the observer stands 100 feet away from the tree the IOC-foot altitude scale is used. If the observer is 80 feet from the tree, the 80-foot altitude scale, that is, the second one from the bottom, is used. When the instrument is sighted to the tip of the tree the intersection of the right-hand scale with the metal strip marks the distance from the level of the eye to the tip. The distance from the level of the eye to the base of the tree is obtained from the left-hand scale by sighting to the foot of the tree. If this instrument did not have the box construction necessary for its use as a dendrometer, it would be one of the most practical of all height measures. As it is ordinarily constructed, the graduations of the altitude scales are made for every five units, giving readings which are too rough for precise work. This I3S FOREST MENSUR/iTION. objection could be easily obviated by a finer division of the scales. Another objection to the instrument is that the observer has a choice of only a few specified distances at which he must stand. This could be obviated by adding other horizontal Hnes, one for each lo feet instead of 20 feet. -Q]L_^_iai Fig. -The Winkler Instrument used as a Dcndrometer. When the Winkler instrument is used as a dcndrometer, a special line of sight is used. The ocular consists of a minute hole in the metal plate which covers the right end of the instrument. At the other end of the instrument and inside the box is an objective opening in which are fitted, per- pendicular to the axis of the instrument, two metal plates, M and N (Fig. 27), of which N is stationary and M may be moved by means of the thumb-screw B. Attached to the plate M is a DETERMINATION OF THE HEIGHT OF STANDING TREES. I39 vernier plate which moves over a diameter scale marked on the face of the instrument and indicates the distance between the two plates M and N. When used as a dendrometer the instrument is placed on a tripod in a horizontal position, as shown in Fig. 27. A station is chosen at 20, 40, 60, 80, or 100 feet from the tree, where the point on a tree whose diameter is required can be distinctly- seen. The observer then tips the instrument and sights through the box to the point to be measured. The thumb- screw is turned Fig. 28. until the two objective plates exactly enclose the trunk of the tree at the required point, and the distance between the metal plates is read on the diameter scale. The instrument is then turned over and used as a height measure. The oblique dis- tance from the eye to the observed point on the tree is determined by means of the scale on the pendulunT The desired diameter is then obtained by the formula: diameter equals oblique dis- I40 FOREST MENSURATION. tance from eye to trunk multiplied by the distance between M and A^ on the instrument, divided by lo. tv D= — , where D is the desired diameter, / is the oblique lO distance from the eye to the tree where D is measured, and v is the distance between the objective plates if and N. The theory of the instrument is shown by reference to Fig. 28. PQ is the desired diameter, pq the measured interval between the plates M and N on the instrument, and OP is the obhque distance from the eye to the tree. Two similar triangles are ^ OP formed in which PQ = jrr X P9.- The instrument is so constructed that the distance between the peep-sight and the objective plates M and N is exacdy 5 inches. Twenty units of the diameter scale measure f inch ; each part being, therefore, -j-f „ of an inch. Substituting in the above formula, / for OP, (•^Xxf 0) for pq, and ^V for Op: 120 /v Diameter = — ^ — = — . 1% 10 Unfortunately the instrument which is in the market is made in Austria and based on the Austrian foot and inches. The Austrian foot equals 1.04 English feet, the inches having the same ratio. In measuring the distance from the tree, therefore, it is necessary to use the following distances to conform to the Austrian measure, Austrian. English. 20 feet 20.8 feet 40 " 41-6 " 60 " 62.4 " 80 " 83.2 " 100 " 104 " DETERMINATION OF THE HEIGHT OF STANDING TREES. 141 The results obtained are in Austrian inches, which may be translated into English inches by multiplying by 1.04. With proper handling the Winkler instrument gives accurate results. The degree of accuracy falls off with the increase in the height above the ground of the point measured. There is danger of inaccuracy in dark woods where the edges of the tree are not sharply defined. The instrument is much better for general woods work than any other on the market because of its compactness and simplicity. 72. The Brandis Height Measure. — This instrument consists of a square tube about five and one-half inches long, with an Fig. 29. — The Brandis Height Measure. ocular slit at one end, and a single cross-wire at the other end as an objective. To the left-hand side of this tube is attached a weighted wheel about two and one-half inches in diameter, swinging between two pivots and enclosed in a circular metal 142 FOREST MENSURATION. case. A small opening is cut in the periphery of the case, and directly opposite this opening a small lens is attached at the ocular end of the tube just to the left of the sighting-slit. The rim of the wheel, which can be seen through the opening in the case, is graduated in degrees, with plus and minus scales meeting at a zero-point, which, when the instrument is horizontal, is exactly opposite the slit. When the instrument is pointed upward or downward, the wheel remains stationary and the angles may be easily read through the lens attached to the eyepiece. On t<< Wllf^.iW^'U. Fig. 30. the side of the metal case is a retaining-spring, which clamps the wheel in any desired position, and which may be released by the pressure of a small button. The theory of the instrument is illustrated in Fig. 30. AB represents the line of vision from the eye to the toji of the tree; V the upper angle obtained by sighting to the tree top; AC the line bETERMINATION OF THE HEIGHT OF ST/INDING TREES. 143 of vision to the base of the tree ; and / the lower angle obtained by sighting to the base. Then BC:AC=- sin {u +/) : sin h 5CXsin6 = ^CXsin (m+/) but sin 6 = cos w; substituting, ^CXcos w = ^CXsin (w+/) or ^CXsin (w+/) BC = cos u For convenience a table has been constructed which gives the value of the expression for all values of u and ^ cos u I which are likely to be required. This table accompanies the instrument. Most instruments have on the face of the metal case enclosing the wheel a small table giving the value of 20 cos a, 20 sin a, and tan a for different angles up to 30 degrees. This table enables one to compute heights when the distance from the tree is 20 meters, yards, or other units. A very complete table is published in Calcutta, entitled Tables for Use with Brandis' Hyposometer, by F. B. Manson and H. H. Haines. Price in India, 8 annas. To use the instrument, the distance from the tree is first meas- ured, then the tip of the tree sighted through the instrument and the angle read from the wheel. Then the base of the tree is sighted and the corresponding reading taken. The value in the table corresponding to the upper and lower angles is then multi- plied by the distance from the tree, for the desired height. The height of the tree may also be obtained by reducing the degrees to tangents and multiplying by the distance, as explained in the next section. The Brandis height measure is an admir- able clinometer for measuring slopes. 144 FOREST MENSURATION. The chief value of the instrument lies in its compactness. The objections to it are that it does not give direct readings of height, but requires special computation and the use of a separate table; and that in dark woods it is difficult to read the gradua- tions on the metal rim of the wheel. It may be purchased from Max Wolz, Bonn, Germany, price (in Germany), 22 marks. 73. Clinometer for Measuring Heights. — This instrument, shown in Fig. 31a, consists of a square panel of wood recessed to receive a metal disk and a glass which protects it. The disk has Fig. 31. — Goulier's Clinometer. a curved right-hand scale and a curved left-hand scale engraved upon it below its center. These scales meet at a zero-])oint, and correspond to each other in their graduations, which run outward in opposite directions from the zero-point to 100. The graduations of these scales represent percentages of angles instead of degrees of angles, as do the graduations of most clinometers. These two scales are swept by a pendulum ball, the lower half of which is beveled and brought to an edge having a central index mark. The upper end of the j^enduluni rod is formed into an eye through which a movable screw-stud passes, continu- DETERMINATION OF THE HEIGHT OF STANDING TREES. 145 ing through the disk and panel and terminating at its rear end in a push-button. A spring secured to the back of the panel engages with the button and draws the head of the screw against the eye of the rod, thus holding the pendulum fixed. When the button is pushed inward, the pendulum is free to swing by gravity when the instrument is held in a vertical plane. The instrument is only about three inches square and may be easily carried in one's pocket. To use the instrument the observer sights along its upper edge to the top of the tree and releases the pendulum by pressing the push-button. When the pendulum comes to rest over the right-hand scale, the pressure on the push-button is removed, permitting the spring to hold the pendulum until the reading can be taken. The number now opposite the index mark is the percentage of the angle formed by a line running from the ob- server's eye to the top of the tree and a horizontal line running from him to its trunk. This percentage is the ratio between the height of the tree above the level of the observer's eye and the horizontal distance from the observer to the tree. This value is multiplied by the horizontal distance from the observer to the tree, and the result is the height of the tree above the level of the observer's eye. The observer then sights the instrument to the base of the tree, operates it as before, takes the reading from the left-hand scale, multiplies the value thus secured by the horizontal distance from him to the tree, and adds this result to that previously obtained, for the total height of the tree. These computations may be greatly simplified by taking all observa- tions at a distance of loo feet or loo yards from the tree. A more elaborate form of the instrument is furnish(;d with a hinged cover having a mirror on its inner face, and w ith two sights located at the upper corners of the panel. (Fig. 31 i.) The instrument is sometimes called Goulier's clinometer. 74. The Abney Hand Level and Clinometer. — This instrument (shown in Fig. 32) is a telescoping surveyor's hand-level of ordinary construction, except that its spirit-tube is located above 146 FOREST MEhlSUR.4TI0N. instead of in its main tube, which, however, contains the usual inclined steel mirror and sigh tin pr cross- wire. Fig. 32. — The Abney Hand Level and Clinometer. Combined with the hand-level is a clinometer comprising a plate screwed to one side of the main tube of the hand-level and having engraved upon it a curved right-hand scale and a curved left-hand scale. These scales are struck from the same center and meet at a zero-point, from which they are graduated outward in degrees to 90. A measuring-arm, w'ith a spatulate lower end beveled to receive vernier graduations, sweeps these scales. This arm is carried by a short shaft journalcd in the upper edge of the plate and concentric with the two curved scales. The outer end of the shaft is furnished with a nurled hand-wheel, by which the clinometer is operated. The inner end of the shaft carries a frame which supports the tubular case containing the spirit- tube of the hand-level. The center of the case is cut away to show the bubble in the tube. On the extreme inner end of the shaft is a jam for setting the instrument, which, when turned inward, holds the shaft against turning. The measuring-arm and frame are rigid with the shaft. The case stands at a right angle to the measuring-arm, so that when the arm is placed at the zero-point of the two scales the case will be exactly ])arallel to the longitudinal axis of the hand-level. Immediately below the exposed portion of tlie s]iiril-tube a slot is cut in the top of the main tube. A small mirror is fixed DETERMIN/ITION OF THE HEIGHT OF STANDING TREES. 147 at an angle inside the main tube directly underneath the slot. This mirror is so narrow and is placed so close to the side of the main tube that it does not obstruct the line of vision through the tube. The observer can thus see at the same time the cross- wires at the objective and the reflection in the mirror of the spirit-bubble. In measuring the height of a tree the observer sights the instrument at the tip and turns the hand-wheel until the bubble shows that the case is level. The measuring-arm, which swings with the case, then indicates upon the right-hand scale in degrees an angle formed by a line running from the observer's eye to the top of the tree and a horizontal line extending from his eye to the trunk of the tree. He then consults a table of natural tan- gents, which gives him the value of the angle secured, expressed as its tangent or percentage. The tangent or percentage of this angle is multiplied by the horizontal distance from the observer's eye. He then sights to the base of the tree, and in the same manner ascertains the angle formed by a horizontal line running from him to the tree and a line running from his eye to the base of the tree. He now consults his table again for the value of this angle expressed as its tangent or percentage, and multiplies this value by his horizontal distance from the tree, which gives the height of the tree from the ground to the level of his eye. The figures thus secured are added together, giving the total height of the tree. The scales of the instrument are sometimes graduated in tangents or percentages of angles instead of in degrees, in which case the table of tangents is not needed. 75. Other Height Measures. — Below are listed those other instruments which, by reason of cost, rarity, or serious disad- vantages for practical use, seem to the author unlikely to be used in the United States. Students who may wish to make a special study of these instruments are recommended to consult the German books on Forest MenstlTation, notably Miiller's Holzmesskunde. 148 FOREST MENSURATION. 1. Rueprechfs Height Measure. Sold by A. Rueprecht^ Vienna, Favoritenstrasse 25. Price 50 Crowns. 2. Havlick's Staff Height Measure. Sold by Gebr. Fromme, Vienna. Price 32 Crowns. 3. Havlick's Hand Height Measure. Sold by Gebr. Fromme, Vienna. Price 9 Crowns. 4. Fricke's Nasenkreuz Height Measure. Sold by Alechaniker Fentzloff, Hann.-Miinden. Price 1.50 Marks. 5. Stotzer's Height Measure. Sold by E. Bischoff, Meinin- gen. Price 40 Marks. 6. Ed. Heyer's Height Measure. Sold by W. Sporhase, Giessen. Price 90 Marks. 7. Trumbach''s Height Measure. Sold by Triimbach, Kgl. Bayr. Forstamtsass't, Obernburg a. M. Price 90 IMarks. 8. The Oninimeter. Sold by Keuffel & Esser Co., N. Y. Price $15. 9. Base's Height Measure. Sold by Mechaniker Weingarten, Darmstadt, Germany. Price 6 ^larks. ID. Mayer's Height Measure. Sold by L. Tesdorpf, Stutt- gart. Price 45 Marks. II. Tiemann's Height Measure. Must be made to order. Keuffel & Esser Co., N. Y. Price about $50. The dendrometers described in section 78 may all be used as height measures. 76. General Directions for the Measurement of Heights of Trees. — It is important to select for observation a station whence both the tip and the base of the tree may be distinctly seen. The tip of a coniferous tree is easily distinguished; but on a hard- wood with a round top it is often difficult to distinguish the true tip from a side branch. If one should mistake a side branch on the near side for the tip, the measured height would be too large. The true tip may usually be seen by standing at some distance from the tree. The general rule is to choose an observation station at a distance approximately equal to the licight of the tree; or if this is impractical, at a greater rallier than a less dis- DETERMINATION OF THE HEIGHT OF STANDING TREES. M9 tance. On a slope one should stand above rather than below the base of the tree. It is often difficult to distinguish the true base of a tree on account of brush, grass, or other obstacles. It is necessary to get a clear vision to the base; and if it cannot then be easily seen, a handkerchief or some other bright object may be used as a distinct point for sighting. If a tree is leaning, one should choose a position in a line perpendicular to the vertical plane of the tree. The result of the measurement is then the distance from the ground to the tip of the tree and not the length of the tree itself. To determine the exact length of the stem of a leaning tree one would have to calculate the degree of inclination and from this reckon by trigo- nometry the true length. The object of taking a position at right angles to the direction of inclination is to avoid a possible mistake in measuring the distance from the tree. If one were in line with the lean of the tree and measured the exact distance to the base a false result would be obtained. With most instruments the horizontal distance from the observer to the tree is required. In the case of the Klaussner hypsometer the oblique distance from the eye to the base of the tree and not the horizontal distance is measured. In all cases the distance should be measured, not paced. In using the Klaussner instrument a beginner sometimes has difficulty with a leaning tree whose tip is not in vertical line with the base. The best plan is to sight to an imaginary point on a level with the true tip. If the instrument were per- fectly leveled it would be possible first to take an observation to the base of the tree and then to turn the instrument enough to sight the tip. There is, however, no way of leveling the Klauss- ner height measure, and therefore the first method is the best. 77. Choice of a Height Measure. — Inasmuch as the choice of two equally good instruments depends on individual taste, opin- ions differ among foresters as to the be&t'height measure. In the opinion of the author the Klaussner height measure is the best 150 FOREST MENSURATION. of the small instruments for accurate scientific work. For general forest work where accuracy is desirable, but great precision is not necessary, the Faustmann height measure gives the most satisfactory results. 78. The Use of Dendrometers. — A considerable number of instruments have been manufactured for measuring the diameter of standing trees at different points. Several of these instru- ments are accurate, and may be used to great advantage in scien- tific work. They will probably not be much used in general forest work, for the following reasons: first, a good instrument is rather expensive; second, most dendrometers are delicate and easily thrown out of adjustment; third, as a rule they are rather large and cumbersome to carry, in addition to recjuiring a tri- pod; fourth, an observation, if properly made, is time-consuming; fifth, only the diameter outside the bark can be measured directly, the inside measurement being that usually required. The dendrometer of Winkler described in section 71 is, in the judgment of the author, the best instrument for foresters from the standpoint of simplicity of construction, compactness, rapidity of measurement, and cost. The Wimminaur dendrometer has been recommended by several American authors. It is, however, much more expensive than the Winkler instrument, and, on account of the delicate construction of certain parts, is less adapted to rough forest work. It may be purchased from W. Sporhase, Giessen, Ger- many, for about 75 marks. The best instruments for purely scientific work are those of Joseph Friedrich, head of the experiment station at Maria- brunn, Austria, and of A. R. von Guttenbcrg, of the forest school in Vienna. These are instruments of great precision, and may be used in taking periodic measurements in studying diameter growth. They have to be made to order, and arc therefore very expensive. Other dendrometers arc: Peltzman's dendrometer, which can be secured from Gcbr. Frommc, \'ienna, price in Vienna 80 crowns; Starke's dendrometer, sold by Starke o: Kam- DETERMINATION OF THE HEIGHT OF STANDING TREES. 151 merer, Vienna ; Sanlaville's dendrometer, sold by Ncuhofer & Sohn, Vienna, price 70 crowns. A special attachment for measuring diameters is made for the Klaussner height measure. For a detailed discussion of the different dendrometers, see Miiller's Holzmesskunde. CHAPTER XL DETERMINATION OF THE CONTENTS OF STANDING TREES. 79. Estimate by the Eye. — Persons who have constant prac- tice in measuring logs and trees are able to estimate the contents of standing trees by a mere superficial inspection. Practiced timber cruisers attain an astonishing degree of accuracy in such estimates. The estimating of contents of trees at a glance is possible only by a trained eye. The inexperienced cruiser or one who is estimating an unfamiliar species must calculate the contents of standing trees from measured or estimated diameters and by the use of a log rule. It is necessary first to determine the lengths of the logs; then the diameter inside the bark at the top of each log. The scale of each log is obtained from a log rule and the results for the different logs added together for the total scale of the tree. This method involves the ability to estimate diameters at different points up the tree and involves also a knowledge of the thickness of the bark, which varies at different points. For one not practiced in estimating diameters, a good method is to use a light lo-foot pole, attaching across one end a small stick marked off in inches by prominent notches. An assistant holds the pole against the trunk with the cross-stick at the point where the top of the first log would come. The diameter can be de- termined very accurately from the notched rule. From a diam- eter measurement at the base, taken with calipers, and another at the top of the first log obtained as just explained, it is possible 153 DETERMINATION OF THE CONTENTS OF STANDING TREES. 153 to estimate by comparison the diameters at the tops of the other logs. The average thickness of the bark at different heights must be allowed for. After one has taken a few measurements of bark on felled trees, it is possible to estimate fairly well by its general appearance the thickness of bark on standing trees. After sufficient practice in estimating diameters, the lo-foot pole may be discarded. This method of determining contents works extremely well with trees having not over three or four logs. The butt log, since it has the largest scale, requires the most accurate estimate. If the contents of this log is correctly determined, a slight error in estimating the diameters of the others will not materially affect the total scale ; except, of course, in tall trees with more than four logs. Naturally the work of estimating the diameters can be done more accurately with a good dendrometer. The time consumed in using a dendrometer, however, is so great that the method just described is more applicable to our con- ditions. One method often used is to estimate the length of the mer- chantable portion of the tree, then estimate its top and base diameters, average these diameters, and determine the con- tents by the Doyle rule. If the length of the merchantable por- tion of a tree is 40 feet, the top diameter 6 inches, and the base diameter 14 inches, the average diameter would be assumed to be 10 inches, and the volume of the log would be, by the Doyle rule, 90 board-feet. A number of rules of thumb are in existence for estimating the number of board-feet in standing trees. The following is a good illustration: Subtract 60 from the square of the estimated diameter at the middle of the merchantable length of the tree, multiply by 0.8, and the result is the contents in board-feet of the average log in the tree; multiply by the number of 16-foot logs for the total scale. A rule of thumb proposed by Dr. Schenck for estimating tall 154 FOREST MENSURATION. sound trees by the Doyle rule is: to square the diameter, breast- high, muhiply by 3, and divide the resuh by 2. Still another rough method of Dr. Schenck is as follows: Assuming that the tree is to be cut into 16-foot logs and the taper is 2 inches per log, multiply the breast -height diameter of the butt log inside bark, by the number of logs, and multiply the result by the same diameter less 12. h quick and fairly accurate method of estimating the volume of white pine in cubic feet is as follows: Square the breast-height diameter (in feet) and multiply by 30. The rule gives excellent results for trees 10 to 14 inches in diameter and 80 feet high, 16 to 20 inches by 85 feet, 22 to 28 inches by 90 feet, and 30 to 36 inches by 95 feet. For other heights add or subtract for each 5 feet of length 6*^ for trees 10 to 20 inches, 5.5% for trees 22 to 28 inches, and 5% for trees 30 to 36 inches in diameter. Suppose, for example, a tree is 18 inches in diameter and 90 feet high, the rule would be: Square 1.5, multiply by 30, and increase the result by 5.5%, or (1.5)2X30 + 5.5% = 71.2 cubic feet. The volume table in the Appendix gives 71.9 cubic feet for such a tree. A similar rule* is used in Germany to obtain the volume of standing trees in cubic meters, as follows: Square the diameter, breast-high, in centimeters, and divide by 1000. The rule holds good for pine 30 meters high, beech, oak, and spruce 26 meters high, and fir 25 meters high. For other heights add or subtract the following amounts for each meter of length, accord- ing as the tree is taller or shorter than the above heights: Pine, add 3%, subtract 3%. Beech, "5% " 5%. Spruce, " 3% " 4%. Fir, "3% " 4%. * Called Denzin's method. DETERMINATION OF THE CONTENTS OF STANDING TREES. 155 80. Estimate of the Contents of Standing Trees by Volume Tables and Form Factors. — X'olumc tables are used by foresters in this country more extensively than any other method of esti- mating the contents of standing trees. In Europe the method of form factors, as well as that of volume tables, is used. These methods are described in the next chapters. 81. Rough Method of Estimating the Cubic Contents of Standing Trees. — The cubic contents of the stem of a tree may roughly be obtained from the measured diameter at breast- height by the formula -?. in which V is the volume, B the area at breast-height, and H the height. By reference to page 88, it will be seen that this is for- mula No. 3 for cubing a paraboloid. 82. Hossfeldt's Method. — On page 94 it was shown that a log may be cubed by the formula, V = {sB,+bA 4 in which V is the volume, B^ the sectional area at one- third the distance from the butt, b the sectional area at the top, and h the length of the log. In case of an entire stem b is o, and the formula becomes V = iB^Xh. To determine the cubic contents of a standing tree, the length of the stem above the probable stump is measured with a height measure, and the diameter at ^ this length is estimated or is measured with a dendrometer. These measurements furnish data for the application of the Hossfeldt formula. 83. Pressler's Method. — In 1855, G. Pressler, a professor in in the Forest School in Tharandt, devised the following formula for cubing a standing tree: <--?). v=^^b(h+''^ ' 156 FOREST MENSURATION. in which V is the volume of the tree, B is the sectional area meas* ured just above the butt swelling, H is the distance from the stump to the point on the stem where the diameter is exactly one-half that measured at the butt, and M is the distance from the stump to the point where B is measured. Ordinarily B is taken at breast-height. The stem of a tree is cubed as two sec- tions, (i) the portion above the point where the diameter is taken, considered as a paraboloid or a cone; (2) the portion between the stump and the point of diameter measurement, considered as a cylinder with a diameter equal to that at the upper end of the section. The stump and branches are disregarded. The main part of the stem is cubed by the formula, in which h is the distance from B to the one-half diameter-point. This holds good for both the paraboloid and the cone, as may be seen in the following demonstration : In a paraboloid the point at which the diameter is \ that at the base, is f the altitude. If this distance is h, the total altitude Hy the basal area B, then li = lH, and H = \h Substituting in the formula F = ^, then F = -x4 = ^M. 2 233 The same process of reasoning will show the formula correct also for the cone. The lower part of the tree is cubed as a cylinder by the formula, V = B M. The volume of the whole stem is then V = lBh+BM ■■A"'"y DETERMINATION OF THE CONTENTS OF STANDING TREES. 157 A dendromelcr may be used to determine the point where the diameter is one-half that at the base. Pressler devised a special instrument for this purpose, consisting of a small paste- board telescope with an eyepiece at one end and with two pins or screws at right angles to the axis of the instrument at the other end. In use the telescope is first closed and the tree is sighted where the base diameter is to be taken. The pins or screws are adjusted so that the stem appears to occupy the space between the points. The instrument is then drawn out to twice its former length, and sighted up and down the stem to find the point exactly fitting between the pins. The diameter of the tree at this point is one-half that at the point first measured CHAPTER XII. VOLUME TABLES. 84. Definition of Volume Tables. — \^olume tables sliow the average contents of standing trees of different sizes. They may be made for any desired unit — the cubic foot, board foot, standard, cord, or cubic meter — or they may show the contents of trees in ties, poles, shingles, or other product. They are used to estimate the yield of wood and timber standing on speci- fied tracts. Volume tables are intended only for estimating a large number of trees. Compiled from the average of a number of measurements, they are necessarily inaccuraie as applied to a single tree. The volumes of individual trees of the same species and same dimensions may vary 20 percent, or more. On the other hand, the average volume of a large number of trees of the same species, having the same height and diameter and growing under the same conditions, is very uniform; and tables showing the average volumes of a large number of felled trees give satis- factory results in estimating the contents of a large number of standing trees. Volume tables may Ix^ local or general. Local volume tables are based on the measurement of trees growing in a restricted locality and usually under specified conditions of mixture, density, etc. General volume tables are based on the average volume of trees growing in a variety of conditions o\er a large region. In (iermany general volume tables are usually made. In this country the forests arc so irregular in age, density, and form tliat VOLUME TABLES. I 59 loral volume tables are the rule; and often there must be separate tables for areas as small as townships or counties. The best rule is to make sej)arate tables at least for every forest region. 85. Volume Tables for Trees of Different Diameters. — The simplest and most convenient volume tables show the average contents of trees of different diameters. These are the tables in most common use in estimating the merchantable contents of standing timber. The total contents of trees of any given diam- eter are computed by multiplying the number of trees by the average volume given in the volume table for that diameter. (See page 219.) The tables are based on the measurement and computation of volume of a large number of felled trees. These data are usually secured where lumbering is in progress. A crew of two or three men follow the cutters and measure the trees as they are felled. If the investigation includes only the preparation of volume tables, the following measurements are usually taken on each tree: diameter at breast-height; diameter at each cross-section, inside and outside the bark; length of each log; length of the top above last cut, and height of stump, giving total height; length of crown, and width of crown. With these measurements, the merchantable or full contents of the stem, with and without bark, may be computed. The measurements of the length and width of crow^n serve as an excellent description of the tree. In addi- tion, it is usually desirable to add a descriptive note regarding the form of the trunk, soundness, general thrift, approximate age, the form of the stand, the trees in mixture, and the soil and situa- tion. Where a volume table is constructed for diameters alone, a full description of the tree and forest is not essential. A crew of three men is most effective for work in collectino- measurements of volume. One man selects the trees, directs the work, and records the measurements. The others do the measuring. The proper equipment of 5uch a crew is a pair of calipers, tape, scale rule, and record book or tally-sheets. Before undertaking the field work of collecting material tv. i6o FOREST MENSUR./tTlON. volume tables, it is desirable to examine the forest where the tables are to be used in estimating, in order to determine what type of trees ought to be measured. It is then decided how many trees to fell and measure, and in general how they should be distributed among the different diameters. Ordinarily the aim is to measure at least looo trees as a basis for volume tables; but where the timber is very uniform, as with most conifers, 500 trees give exceedingly good results. If the tables are to be used in careful cruising, at least 500 trees should be measured. In reconnaissance work and rough cruising, or where the trees are extremely regular in form, 100 trees may suffice. Care is required in the selection of the trees for measurement. It is the rule to measure only sound trees, because volume tabbs show the full contents of sound trees. It might appear that the tables would be more practical if based on average trees, including those partially defective. But a table made up in this way would be extremely unreliable, for it is well known that the defects of trees differ greatly in different situations; so that a table based partly on defective trees would be useless in estimating trees whose defects are different from those of the trees observed in its construction. Again, any such defect as injury by ffre, insects disease, wind, or ice, would entirely vitiate a table constructed for trees showing another defect than the particular one in ques- tion; whereas a table based on sound trees may be reduced in any given case, just as log rules are reduced for unsoundness in logs. Care should be exercised to select for measurement trees representative in form. The temptation usually is to measure only the best trees; but it must be remembered that the figures will represent the average tree of each diameter, regardless of difference in the number of logs, total height, or tree class. There- fore each tree should be a good representative of its class, and normal in height, size of crown, form of trunk, etc. Different classes of trees should be represented about as they occur in the forest; that is, there should be aljoul the same percentage of VOLUME TABLES. l6t one-log trees, two-log trees, three-log trees, etc., as ordinarily occur in the particular forest under observation. This point is to be especially observed when the number of trees measured is limited. If looo trees are to be measured, it is ordinarily suffi- cient to measure trees as they are cut by the lumbermen, taking care that the diameters are well distributed and that the trees are not abnormal. Abnormal trees are those with forked trunks, those with swollen butts, and diseased or distorted trees. The first work of computation is the calculation of the volume of each tree measured. The work can be done most rapidly by two persons, one handling the data collected in the field and the other the log tables, tables of areas, or other tables neces- sary in determining the contents of the logs in the unit chosen. The computing work may, with economy of time and mental effort, be divided between the two. The trees measured are grouped according to breast-height diameters in inch classes. Thus the 6-inch class comprises all trees with a diameter between 5.6 and 6.5 inches. In judging the diameter class the five-tenths goes to the lower rather than the higher number; that is, a tree 12.5 inches in diameter is counted as a 12 -inch tree, not a 13-inch tree. The volumes of all trees in a single-diameter class are averaged together and the exact average diameter also determined, the last being usually not a whole inch, but a few tenths, above or below the whole number. The data may then be arranged in five columns, as in the table on page 162. The first column shows the inch-diameter classes, the second column the exact average diameters of the trees in each diameter class, the third column the number of trees used, the fourth column the average volume of the trees in each diameter class, and the fifth column the results of the fourth column made regular by graphic interpolation. To construct the curve used in obtaining the values in column five, the volumes from column four are plotted on cross-section paper as ordinates, with the average diameters in columiT two as abscissa?. The values in column three show what points are to receive most em- l62 FOREST MENSURATION. phasis in drawing the curve. For the final results in column five, the values for the whole inches are read from the curve. CHESTNUT— VOLUME TABLE FOR TREES OF DIFFERENT DIAMETERS. Based ox the Measurement of ioi Trees at Milford, Pa. Diameter Class. Breast-high, Inches. Average Diameter of Trees Measured, Breast-high, Inches. Number of Trees Measured. Average Volume ot Trees Measured, Cubic Feet. Average Volume, Results of Column 4 Evened Off by Curve, Cubic Feet. 6 6.25 2 4-7 4-5 7 7 10 5-4 5-4 8 8.1 13 7.2 7 9 9 16 9-4 9-3 lO ID 15 II. 7 II. 7 II II 14 14-9 144 12 12 18 16.2 17. 1 13 12.9 9 20.2 20.2 U 14. I 3 23.6 23-4 15 14.9 I 27 27 Another method of averaging together the volumes for different diameters is as follows: The volumes of all trees are plotted on cross-section paper as ordinates, the abscissas being the diameters breast-high. After the volumes of all trees have been plotted, an average curve is drawn through the points. From this curve are read the average volumes for the different diameters. Volume tables for trees of different diameters give very satis- factory results in cruising, particularly when the tables have been prepared for special conditions. They are not, however, applicable to forests where the conditions of growth differ from those pre- vailing where the data were gathered. If, for example, the tables were based largely on tall trees, they could not be used where the trees are, on an average, shorter. This objection is largely obviated by making local tables for restricted areas, on which the general conditions for growth are fairly uniform. Volume tables for trees grouy)ed by diameters alone arc de- signed primarily for commercial estimating in board measure. yOLUME TABLES. 163 A further grouping of the trees is necessary for very close deter- mination of volume, as described in the succeeding sections. 86. Volume Tables for Trees Grouped by Diameter and Number of Logs. — In the method just described all trees are averaged by diameters regardless of height or length of mer- chantable timber. Thus one-log trees are averaged with three- log trees, or even five-log trees, of the same diameter. In order lo secure greater accuracy, volume tables based on trees grouped by diameters and number of logs were devised. Such tables are in actual use by cruisers. They are used in tall timber where a standard log-length — as, for example, 16 feet — may be used in the estimate of the number of logs. To construct a volume table for trees grouped by diameters and number of logs, a large number of felled trees are measured and their volumes computed as described for the previous method. The trees having the same number of logs are then grouped together, and the average volumes of one-log trees of different diameters are determined, then of two-log, three-log trees, etc. If the volumes do not increase regularly with increase of diameters, the irregularities are evened off by graphic interpolation. The results are expressed in a form like the following: VOLUME TABLE FOR TREES OF DIFFERENT DIAMETERS AND NUMBER OF LOGS. Length of Standard Log Feet. (Based on the Measurement of Trees.) Diameter, Breast-high, Inches. Volume of One-log Trees, Board Feet. Volume of Two-log Trees, Board Feet. Volume of Three-log Trees, Board Feet. Volume of Four-log Trees, Board Feet. The objection to this method is that trees are not always cut into logs of the same length. Even with very tall trees it is seldom that all the logs are the same length. A tall white pine may 1 64 FOREST MENSURATION. for example, yield three-sixteens, and one twelve. If the volume tables are based on sixteen-foot logs, an inaccurate estimate would result if this were classed as a four-log tree. These tables are, therefore, not much more accurate than those first described. 87. Volume Tables for Trees of Different Diameters and Mer- chantable Lengths. — On account of the defects of the previous method, it has been proposed to base volume tables on trees grouped by merchantable length as well as by diameter. The length classes should be such as would be actually used in practice. When short logs are used, the merchantable length of a given tree would be the sum of the log lengths. In this case the length classes would have to correspond to all the possible combinations of short logs. Two-foot classes would meet this requirement, and would also be small enough for the conditions where the whole merchantable part of the tree is taken out as one log. To construct such a table, the measurements of felled trees are first obtained in the ordinary way. The computed volumes are grouped by the diameters and merchantable lengths of the trees, each length class comprising two feet. ,A preliminary table of averages is made, giving the average volume of trees of different diameters with a merchantable length of 10 feet, those with a merchantable length of 12 feet, those with 14, 16, 18, 20, 22 feet, and so on. Under ordinary circumstances it will be found that this table has irregularities not only in the vertical columns, but also in the horizontal lines. These irregularities are then evened off by a scries of harmonized curves. The final table may be expressed in a form like that shown on page 165. As far as the author is informed, no such volume tables have been made. They should, however, yield very accurate results, although more difilcult in application than the volume tables based on diameters alone. Their use in estimating stands is described on page 222. 88. Volume Tables for Trees of Different Diameters and Tree Classes. ^ — These are designed for use where the trees have grown under varying conditions of density and form of the stand, miUMe TABLes. i6s VOLUME TABLE FOR TREES OF DIFFERENT DIAMETERS AND MERCHANTABLE LENGTHS. Based on the Measurement ok Trees. Merchantable Length in Feet. Diameter, Breast-hieh, Inches. 10 13 14 16 18 30 34 38 30 Board Feet. as in very irregular forests. Such tables are particularly useful in estimating cord-wood in second-growth hardwood forests. The author has found that volume tables based on diameter alone are not accurate for cordwood work; when large branches are merchantable, a table based on merchantable length is out of the question. On the other hand, a table which gives sepa- rately the volume of the trees with large crowns, those with medium crowns, etc., yields very good results. No rules can be laid down for the formation of classes. Under some circumstances, it might be desirable to make three classes — dominant, interme- diate, and suppressed trees. Elsewhere a grouping of trees with large crowns, medium crowns, or small crowns would be proper. In second-growth hardwoods the following classifica- tion will be found to be useful: Trees in the open. Large-crowned forest trees (maximum in stand). Trees in crowded stand, crowns narrow and about 15-20 percent of the length of stem. Overtopped and partially suppressed trees. Badly suppressed trees. In selecting the trees for volume measurement, much greater stress is placed on the description of the'trees than with the other kind of volume tables. It is particularly important to describe i6(j FOREST MENSURATION. ihe conditions of density, form of surrounding stand, and shape and dimensions of the crown, because these are the factors which determine the class to which a particular tree is assigned. After computing the contents of the trees, they are separated into classes, and then for each class a table is constructed in the ordinary manner, showing the volume of trees of different diameters. These separate tables are then combined in the following form: VOLUME TABLE FOR TREES OF DIFFEREN1' DL\METERS A\D TREE CLASSES. Based ox the Measurement of Trees. Tree Class. Diameter. Breast-high, Inches. I. II. III. IV. V. Cords. 89. Volume Tables for Trees of Different Diameters and Heights. — These are usually considered the most accurate kind of volume tables. The European volume tables, which are used with satisfactory results, even where considerable accuracy is required, are based on this principle. In Europe, liowever, the ordinary volume tables are used in estimating regular forests and separate tables are made for different age classes. Even when used in very irregular stands, where the trees differ largely in age and development of crown, they are more accurate than volume tables based on diameter alone. They are probably not as accurate as those based on (Hameter and nH'rcliantal)k' length, because the merchantable length is a better inde.\ of the volume of a tree of a given diameter than the total height. Volume tables based on diameter and height have been constructed for several species in this country and used in i)rac- tical work of estimating. They give good results with trees of VOLUME T/1BLES. 167 regular form like the pines and spruces, but with the liardwooda they are not entirely satisfactory unless separate tables are made for different tree classes. The construction of volume tables for trees of different diame- ters and heights is based on the measurement and computation of volume of a large number of felled trees. European volume tables are based on tables of form factors. In this country a number of tables have been constructed by averaging together directly the volumes of the measured trees, grouped by diameters and height classes. The procedure in this method is as follows: The computed volumes of the measured trees are grouped by inch diameters and five-foot height cUsses. Figures of each diameter and height class are then averaged together and the results compared in a preliminary table. This preliminary table, even if based on a very large number of measurements, usually is irregular in both the horizontal and vertical directions. All values are then evened off by a series of harmonized curves. The final form of the table is illustrated by the following example : CHESTNUT— VOLUME TABLE FOR TREES OF DIFFERENT DIAMETERS AND HEIGHTS. Based ox 99 Trees Measured at Milford, Pa. Height in Feet. Diameter, Breast-high, Inches. 40 45 50 55 60 Merchantable Cubic Feet. 6 i 8 9 10 II 12 3-9 4.8 6.2 7.8 9-7 12.0 4-2 5-1 6.6 8.3 10. 2 12.6 15.1 17.8 20.9 4.6 5-7 7.3 9.0 II . I 13.6 16. 1 18.9 22.0^ 8.1 10. 0 12.2 14.8 17-4 20.2 23-4 16.3 18.9 21.7 25.0 28.8 13 15 1 68 FOREST MENSURATION. Another method, and the one most commonly used in Europe, is first to make a table of form factors and then convert this into a volume table by multiplying each value by the product of the corresponding height and basal area. The conversion of a form- factor table into a volume table should present no difficulty to the student after reading the next chapter, which describes the theory and use of form factors. This last method is applicable only to cubic measure. Often it is desirable to make a volume table in cubic feet as a founda- tion for a table in some other unit. One of the best ways, from the standpoint of accuracy, of making a volume table for mer- chantable timber is first to construct a table of cubic contents of the entire stems of trees and then reduce this to a table of merchantable contents. It is a good method because the con- tents of whole stems do not vary so much as the merchantable volume and a table of averages may be constructed with less interpolation. A table showing the ratio of merchantable to total contents may then be constructed and applied to the first volume table to reduce the values to merchantable terms. Suppose that a table of cubic contents of the stems of white pine has been constructed, like that in the Appendix, and one wishes to convert it to board feet, the procedure is as follows: The volume of each of the trees measured is computed in cubic feet and also in board feet and the ratio between the two determined. The cubic volume in each tree is multiplied by 12 and the board feet divided by this product. The result represents an artificial but convenient ratio between the cubic and board feet of each tree. A table of factors is then constructed for trees grouped by diameters and heights or by diameters alone. Such a table was made by the author in constructing volume tables for white pine, and may be used as an illustration (sec page 169). The cubic volume table is then converted into board measure. Each value is multiplied by the factor in tlu' table corresj)on(ling to the diameter, and the result multiplied by 12 in order to con- vert back to board feel. VOLUME TABLES. 169 RATIO BETWEEN THE BOARD CONTENTS AND TOTAL VOLUME OF WHITE PINE. Board Feet Board Feet Board Feet Reduced to Reduced to Reduced to Diameter, Breast-high, Inches. Cubic Feet in Percentage of the Total Volume of Diameter, Breast-high, Inches. Cubic Feet in Percentage of the Total Volume of Diameter, Breast-high, Inches. Cubic Feet in Percentage of the Total Volume of Wood and Wood and Wood and Bark. Bark. Bark. 10 12 22 35 34 46 12 18 24 38 36 47 14 23 26 40 38 48 16 26 28 42 40 49 18 29 30 44 20 32 32 45 90. Graded Volume Tables. — The volume tables described in the preceding pages give the contents of trees in a given unit, but they do not indicate the quality of the product. Graded volume tables show for trees of different sizes the amount of timber of different grades and enable the determination of the money value of standing trees better than the ordinary volume tables. The U. S. Forest Service is at present studying the yield, in timber of different grades, of all the important trees. Already investigations of long-leaf pine, loblolly pine, yellow poplar, white oak, chestnut, ash, and other hardwoods in the South, and maple, birch, and beech in the Adirondacks, have been initiated. The results of such studies are expressed first as graded volume tables, and second as tables showing the money value of trees of different sizes. The method of constructing a graded volume table is as follows:* A large number of trees are measured as soon as they are cut by the saw crews. The length and top diameter of each log are measured and a mark placed on the end. Each tree is given a number and each log in that tree an additional number or letter. Thus, for example, 576^ indicates the second log * From the Determination of Timber Values, by E. A. Braniff, Year book of the U. S. Dept. of Agriculture for 1904. lyo FOREST MENSURATION. (counting from the butt) of tree 576. The logs are then sawed at the mill and their exact yield in graded lumber determined. The measurements at the mill are taken in the following way: A man stands near the slab-carrier. As each piece of siding from a marked log is dropped on the rollers, the number of the log is chalked on it. \\lien a siding has passed through the edger and trimmer, it is graded and measured and a record made of the log number, grade, and dimensions. These data for all boards cut from the marked logs enable the computation of the exact product in graded lumber of each log, and by com- bining the products of all logs having the same tree number, the total yield of each tree is computed. The data taken in the woods serve a check on the work at the mill. When the volume of all the trees has been determined, the trees are grouped together by inch-diameter classes and the average contents of trees of each diameter computed. Any irregularities in the resulting table are evened off by curves. The form of these tables is well illustrated by the Graded Volume Table for Yellow Birch as shown on page 171. This is the result of an investigation in the Adirondacks by the U. S. Forest Service. This table shows the yield of choice grades of birch advancing rapidly with the growth of the tree. The choice grades are firsts and seconds red, and firsts and seconds. The amount of red birch in a tree under 18 inches in diameter is too small to consider. An 18-inch tree contained 2 board feet of this high- priced lumber, a 19-inch tree only 4 feet of it, a 20-inch tree 8 feet, but in a 21-inch tree the amount rose to 23 board feet, showing a gain of almost 200 percent, over the product of the previous diameter. The exj)lanation for the exceptional increase is that the rules of the National Hardwood Lumber Association, under which llu' lumber was inspected, rt'(|uire red birch 4 or 5 inches wide to show one face all red; over 5 inches, one face must be not less than 75 percent red. Red birch is heart-wood, and it liappens that the heart-wood is not wide enough to jxiss the VOLUME TABLES. 171 GRADfiD VOLUME TABLE FOR YELLOW BIRCH. Diam- eter, Breast- high. Inches. 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Firsts Firsts and Seconds. Shipping Mill Culls Sound and No. I CullsCNo. (No. 3 7"Xo" Total. Seconds Red. Common. 2 Com- mon). Com- mon). X 8' Ties. Bd. Ft. Bd. Ft. Bd. Ft. Bd. Ft. Bd. Ft. Bd. Ft. * Bd. Ft. 3 5 6 20 25 59 7 7 7 37 37 95 II 10 8 41 55 125 16 12 8 38 72 146 22 14 8 35 84 163 2 28 17 9 36 94 186 4 36 20 10 45 102 217 8 44 24 II 55 108 250 23 54 28 13 65 114 297 26 66 31 15 74 119 331 36 78 33 16 82 118 363 48 86 36 18 88 112 388 62 92 38 19 93 104 408 81 97 42 20 98 96 434 lOI 103 47 22 106 91 470 116 no 53 22 118 86 505 128 120 59 23 134 81 545 139 132 64 24 155 74 588 150 144 68 25 180 52 619 Number of Trees Tallied. 7 16 23 32 32 57 50 39 40 46 25 37 30 24 28 16 * To obtain number of ties divide board feet in this column by 42. severe inspection in considerable quantities in trees under 21 inches in diameter. The increase of red birch goes on steadily from the 21 -inch to the highest diameters. The next best grade, firsts and seconds, not graded by color, is contained in practically all sizes of merchantable trees. The increase of this grade goes on steadily, but is greatest between 18-inch and 23-inch trees, because the inspection rules, which favor wide boards, show their greatest effect here. Narrow boards from small trees grade lower than wide boards from large trees. Wlien we compare the choice grades (firsts and seconds red, and iirsts and seconds) with the common ones (No. i common, shipping culls, and mill culls) we find that the choice grades increase, on the whole, much more rapidly with the growth of the tree than do the latter. In the case of firsts and seconds red there was a rise between a 13-inch'and a 31 -inch tree from o to 150 feet, and in the case of firsts and seconds from 3 to 144 172 FOREST MENSURATION. feet. Contrast this with No. i common, which rises from 5 to 68 feet; with shipping culls, which rise from 6 to 25 feet; and with mill culls, which rise from 20 to 180 feet, and the tendency of the better grades to outstrip the poor ones becomes apparent. The fact must not be overlooked, however, that a considerable amount of what would have made inferior grades went, in this instance, into railroad ties. The table given on page 171 may be used to determine the money value of trees of different diameters. If the value of each grade of lumber is known, it is a simple matter to convert a graded volume table into a money value tabic. According to prices obtained from the Boston and New York markets for yellow birch, the table given above may be expressed as follows: VALUE OF YELLOW BIRCH. Diam- eter, Breast- high. Inches. Graded Volume. Value per Tree. Value per 1000 Diameter, Breast- high. Graded Volume. Value per Tree. Value per 1000 Bd. Ft. Bd. Ft. Inches. Bd. Ft. Bd. Ft. 13 59 So. 55 $9 32 23 363 $5-19 $14-30 14 95 0.89 9-37 24 388 5.80 1495 15 125 I . 22 9.76 25 408 6.39 15.66 16 146 1-52 10.41 26 434 715 16.48 17 163 1.78 10.92 27 470 8.03 17.09 18 186 2.13 "•45 28 505 8.80 17-43 19 217 2.56 II .80 29 545 9-57 1756 20 250 3.06 12.24 30 588 10.34 17-59 21 297 3 98 J 3 • 40 31 619 10.99 17-75 22 331 4-51 13-^)3 This tabic illustrates how the value of trees increases with increase of diameter. Not only do the trees increase in value, but their value per thousand feet increases as they grow larger. These tables may be used not only to determine much more closely than ordinarily the value of timber land, but when com- bined with a knowledge of growth they enable an owner to determine what trees should be cut and what should be left to Accumulate increment. Graded volume tabli's must necessarilv be made for restricted VOLUME Ty^BLES 1 73 regions or localities. The methods of manufacture differ not only in different localities, but also at different mills. The quahty of the timber varies in different regions, due to differences in the character of the soil, exposure, and other silvical factors. Graded volume tables should be made, therefore, to apply to a specified set of conditions. In the same way tables of timber values must be local in character, and in constructing them, one should consider the changes in price of the different grades. The graded volume tables now being made are based on diameter alone. It would, of course, be possible to make more elaborate tables for different tree classes, trees of different heights, etc. It is, however, proba- ble that the present method will answer the present needs of forestry. The principle of graded volume tables may be extended to comprise other products than lumber. Thus tables may be constructed to show the volume of chestnut trees of different diameters in ties of different grades, in posts, and in cord-wood. Volume tables may also be made for poles. Thus it would be of great practical value to have tables showing the average length and top diameter of poles yielded by chestnut of different diameters, or the length and middle diameter of piles contained In pitch pine trees of different sizes. CHAPTER XIII. FORM FACTORS. 91. Definition of Form Factors. — The form factor of a tree is the ratio between its volume and that of a cyHnder having the same diameter and height. Expressed mathematically, F = ^Jl^ or V^^BHF, in which F is the form factor, V the volume, B the basal area, and H the height of the tree. The form factor is, then, a reducing figure by which the volume of a cylinder having the same diame- ter and height a*s the tree must be multiplied to obtain the volume of the tree. Inasmuch as .the tree has a smaller volume than the cylinder, this reducing figure is a fraction. It is customary to distinguish between hrcast-hcight jorm jaclor, absolute jorm jactor, and normal form jaclor. The breast- height form factor is obtained by the use, in the above formula, of the sectional area at breast-height; that is, the diameter of the cylinder to which the tree is compared is the same as the breast-height diameter of the tree, as shown in Fig. t,^. The breast-height form factor is the one most commonly used, and in this book the term form factor will always mean breast-height form factor unless otherwise indicated. If a tree is compared to a cylinder ha\ing a diameter equal to the diameter at the base of the tree, the absolu/c jonii jactor results. According to the usual conce])tion, the absolute form factor is based on a sectional area taken at the ground, as shown 174 FORM FACTORS. 175 in Fig. 34. If the volume used in the form-factor formula comprised only the portion of the tree above the stump, the sectional area would be taken at the stump in computing the absolute form factor. In the same way the absolute form factor Fig. 33. Fig. 34. Fig. 35- is sometimes used to compare the portion of the stem above breast-height with a cylinder having a diameter equal to the breast-height diameter and having a height equal to the height of the tree minus 4.5 feet (Fig. 35). In this case the portion below breast-height is disregarded or considered separately. Still another kind of form factor is obtained when the basal area is determined not at a fixed distance from the ground, but always at a distance having a fixed ratio to the height of the tree. The resulting form factor is called the normal or true form factor. A still further classification of form factors is usually made. If, in the form-factor formula, the merchantable volume of the tree is used, the form factor is called the merchantable or timber jorm factor. If the volume of the stem alone (including the top above merchantable wood) is used, the stem form factor is obtained. The tree form factor results when the endre volume of the tree, including branches, twigs, and all, is used in the formula. In this country only merchantable and stem form factors are used. 176 FOREST MENSURATION. 92. The Use of Form Factors. — Form factors are used to determine the contents of trees. If the basal area, height, and form factor of a tree are known, the volume is obtained by the formula V = BHF. Tables are constructed showing the average breast-height form factors of trees of different dimen- sions, for use in estimating the cubic contents of standing timber. Just as volume tables, form-factor tables are designed for use in estimating the volume of a large number of trees and not of a single tree. European foresters constantly use form-factor tables in estimating standing timber. Convenient tables for different species are published in pocket handbooks like the Forst u. Jagd Kalendars of Prussia, Bavaria, and Austria. In this country form factors will be used chiefly in scientific wurk, as a basis for volume tables in cubic feet and other units, and as a method of comparing the form of trees of different species and of the same species growing under different conditions. They will not be used much in estimating timber because it is just as easy to construct volume tables, which are much more convenient for practical use in the field. 93. Variations in the Value of Breast-height Form Factors. — The term " false " form factor is sometimes applied to t".e breast-height form factor because it is not a true expression of form. This is best illustrated by comparing the breast-height form factors of two perfect bodies (as, for example, two Appolo- nian paraboloids) which have different heights and different diameters. Inasmuch as the two bodies have the same geo- metric form, the form factors, if true expressions of form, should be the samc-yBut in our illustration the breast-height form factor of the paraboloid with the greater height is the smaller. The reason for this is that the sectional areas are taken at tl:c same distance from the ground, a point which in relation to total height is relatively higher on the shorter paraboloid. In consequence the volume of the cylinder to which the shorter paraboloid is compared is relatively smaller than in the case of the larger paraboloid, and tlie form factor is the larger. In FORM FACTORS. I77 Other words, the breast-height form factors of trees of exactly the same form decrease with the increase of height. One would naturally conclude that tables of form factors would be constructed to show average values for trees of different heights without regard to the diameters. In fact such tables were made in Europe — as, for example, those of Dr. Koenig — for Spruce and Fir.* But when the form factors of trees are com- pared, it is found that they do not always vary by the height alone, but sometimes by both height and diameter and some- times by diameter alone. The explanation of this lies in the fact that trees vary so much in form that the tendency of the form factors to decrease with increasing height is often counter- balanced. Influence of Density on the Size oj Form Factors. — The forms of trees are distinctly influenced by the character of the forest in which they grow. It is a matter of common observation that trees growing in the open are apt to be more tapering than those growing in dense forests. Expressed in another way, forest trees are full-boled and the stem or merchantable form factor of a forest tree is ordinarily greater than that of a tree growing in the open. On the other hand, very old trees which stand ini the open frequently have a greater stem form factor than those in the forest. In view of the variation in form factors due to differences in density of stands, it is desirable, particularly in this country where the forests are very irregular, to make separate form-factor tables for different tree classes. In 1864 the proposition was made by Dr. Koenig of Germany to make separate tables of form factors for the following classes of trees: First-class trees in crowded stand, slim and with narrow crowns. Second-class trees in stands of moderate density, more sturdy and wind-firm. * Hilfstabellen der Forstmathematik, by Dr. G. Koenig, 1864. I7« FOREST MENSURATION. Third-class trees in rather open stands, with full crowns. Fourth-class trees in open stands, with heavy crowns. Fifth- class trees standing singly. A similar classification is often desirable in this country. In much of our work, however, it may be better to make only three classes, as suggested for classifying trees in constructing volume tables (see page 165). Influence 0} Situation on the Size 0} Form Factors. — It has been long a matter of controversy whether the average form factors of a given tree var}^ in different localities and in different classes of soil. Without question the form factors are some- what influenced by the climate and by the character of the soil. Other factors, particularly^ density, are of much greater impor- tance, and usually trees from different forest types and different classes of soil are averaged together in a single table. If the tree classes are kept separate, variations due to situations may be disregarded. Influence of Age on the Size 0} Form Factors. — Old trees have more cylindrical trunks than young ones. It is a saying among foresters that when a tree carries its diameter well up into the crown and has a full- bole, it is old. This fact would indicate that the form factors increase with age. »- This is well illustrated in the case of the Norway spruce, whose stem form factor for trees 20 centimeters in diameter ' and over 90 years old is 0.559, but for trees under 90 years old and 20 centimeters in diameter is 0.534. Taking investigations of the different European trees as a whole we find no regular variation of stem form factors with age. This seems contra- dictory to the statement just made. But it is probable that only great differences in age affect the stem form factors and the trees used in the European investigations do not vary enough in age to be affected by this influenQC. Dr. Franz Baur of Ger- many proposes that separate tables of form factors be made for different age classes, each com])rising 40 years. While it is a FORM FACTORS. 179 matter of contention whether differences in age have much influ- ence on the form factors of trees after they are 90 or 100 years old, it is certain that 40-ycar age-classes are small enough. In our work with form factors it is desirable to make separate tables for young and for old trees. No rule can be given for the Hmits of the age-classes because these would differ under different circumstances. Thus it might be best to group the trees 50 to 100 years, or those 60 to 120 years of age. Ordinarily groups of 50 to 75 years will sufhce for the present requirements of our investigations. Influence of Change in Diameter on the Size of Form Factors. — There is no uniform relation between form factors and diameters of trees. The form-factor tables given in the Appendix illustrate the lack of uniformity in the variation of form factors of the different species. 94. Construction of Tables of Form Factors. — To construct a table of form factors a large number of trees are felled and measurements of volum.e taken. The volume and form factor of each tree are then computed and the results for trees of like diameter and height averaged together. Thus the form factors of all trees rounding to 6 inches and 25 feet are averaged together, the form factors of the trees 7 inches by 25 feet, those 8 inches by 25 feet, and so on. A convenient form for averaging the values is that on page 180, in which the number in the center of each square is the average form factor, the number in the upper left-hand corner is the average diameter of the trees measured, the number in the upper right-hand corner the number of trees averaged, and the number in the lower right-hand corner the average height of the trees measured. The next step is to inspect the values in this preliminary table to see how the form factors vary. If the form factors are found to vary regularly with the increase of diameter and height, it is necessary to make a table for both- diameters and heights. If upon inspection of the first table of averages of the form factors, it is found that there is a distinct change in their values with FOREST MENSURATION. Diameter, Breast-high, Inches. Height in Feet. 50 Average Merchantable Form Factors. 6 6 0.470 40 6.2 I 0.465 45-7 6.3 I 0.463 49 7 7-3 2 0. 461 39-5 7 5 0.457 44.8 6.8 2 0.441 51.2 7 2 0.438 55 8 8.1 4 0.457 41 8.0 7 0.450 46 8.2 3 0.440 50 8.0 2 0.430 56 increase in diameter, but no appreciable change with increase in height, the final table is made by averaging together the form factors of trees of different diameters without regard to heights. In the same way, if the values of the form factors are found to change with increase in height, but not with increase in diameter, the form factor table is based on heights alone. It usually hap- pens, however, that there is a certain amount of irregularity in the horizontal and vertical column, even when the table is based on a large number of measurements. These irregularities may be evened off by a series of curves. As a rule, tables of stem form factors for coniferous trees are based on diameter alone. Behm's tables for Norway spruce, European fir, and larch over 90 years old are constructed on the basis of the average form factors of trees of different diameters without regard to height. The tables for silver fir and larch 60 to 90 years old are constructed in the same way, but the talkie for spruce 60 to 90 years old is based on both diameters and heights. The table of tree form factors for Scotch pine is constructed on a basis of heights without regard to diameters. Bchm gives also a table of tree form factors for beech over 90 years old, based FORM FACTORS. l8l on diameters and heights, while that for beech 60 to 90 years old depends on heights alone. In spite of the opinion of many European authors that tables of stem form factors for mature coniferous trees should be based on diameters alone, the most important hand-books of Germany and Austria give, for use in practical estimating, stem form factors of these trees averaged by heights without regard to diameters. This lack of uniformity in construction of tables of form factors in Europe is extremely confusing to the student. It is best, in making a table of form factors, not to try to follow any rule, but to determine, by an inspection of the preliminary table of averages, whether the final tables should be based on diameters alone, heights alone, or both diameters and heights. /Tables of form factors are considered worthless by European! foresters unless founded on a very large number of measure- ments, and, indeed, the form of individual trees varies so much that a satisfactory average cannot be obtained unless several thousand trees are measured. The Bavarian volume and form-factor tables, begun in 1846, were based on 40,000 trees. The tables for pine elaborated by Schwappach depend on 17,000. Baur's spruce tables are based on 22,000 trees and Schuberg's fir tables on 5643 trees. These German tables are designed to show the laws of the form of trees throughout large areas. This does not mean that in this country the practical use of form factors is excluded under cir- cumstances where it is impossible to make such an extensive study. Local volume tables may be based on a relatively small number of measurements. The accuracy of such tables is, however, in direct proportion to the number of measurements used in their construction. But in the preliminary work of forest organization in this country the forester must often be satisfied with tables which give only approximate results. Local tables of volume and form factors based on 100 trees are often used in this country with fairly satisfactory results. They must, 1^2 PORBST MENSURATION. of course, eventually be replaced by tables based on more thorough investigations. If the trees are separated into classes, loo trees for each class will often suffice for volume and form-factor tables ta be used in estimating standing timber. 95. Absolute Form Factor. — As explained above, the abso- lute form factor is obtained by dividing the volume of a tree by the product of its height and the basal area taken at the true base. Naturally the absolute form factor is not applicable to the full contents of a tree because of the difficulty of measuring the diameter at the ground. It is, however, sometimes applied to the portion of the tree above breast-height.* In this case the absolute form factor is found by dividing the volume of the tree above breast-height by the product of the breast-height sectional area and the height of the tree above that point. \\Tien this factor is used in cubing trees, the portion below breast-height is con- sidered a cylinder having the same diameter as that at breast- height. 96. Normal Form Factor. — This is a theoretical formula which was at one time used in practice by its inventor, Pressler. The normal form factor is the volume of the tree divided by the product of height and the sectional area at a height in fixed proportion to the height of the tree. This proportion is generally assumed as 1/20. Then V Normal form factor = HXB [ taken at — ) 20/ 97. The Conception and Use of Form Exponents. — Analytical geometry teaches us llic mallu'malical expression for tlie curves whose revolution about an axis will form a cone, an Ajjpolonian paraljoloid, a Neilian paraboloid, etc. The straight line parallel to the axis is rej)rcsented by the equation y = p-x. * Sometimes called Rinniker's absolute form factor. FORM FACTORS. 183 The curve generating an Appolonian paraboloid, by the equation y'~=p2'^'- The curve generating a cone, by the equation y^ = P3X^. That generating a Neilian paraboloid by the equation in which x is the abscissa, y the ordinate, and p, P2, pz, pi are constants, the so-called parameters. The general expression applicable to any one of these curves is y^ = px'^. The form of the body produced depends on the exponent r, vi^hich is called the form exponent or form coefficient. It is possible to determine the form exponent of a stem or log by a few measurements. Suppose that it is desired to find the exponent of form of a log such as that shown in Fig. 36. Let .-Vi be the distance Fig. 36. from the tip of the tree to the base of the log, X2 the distance from the tip of the tree to the top of the log, yx the radius of the base, and y2 the radius of the top. Then yi^ = pxi'' and y^='pX2^. If the first equation is divided by the second, then J'^ X2''~\X2r from which r(log xx -log X2) = 2(log yi -log y2), FOREST MENSURATION. I0gj'i-l0gj2 log Xi^ -log X2 Example. — Suppose that the two measured diameters are i8 and 15 inches,* and the lengths are 61 and 45 feet. log>'i=log 1.5 =0.176091 log :ri=log 61 =1.785330 log >'2 = l0g 1.25=0.086910 log .T2=log 45 = 1.653213 Difference = 0.0891 81 Difference = 0.1 321 17 0089181 r = 2X '■ = 2 Xo.675 = i.^5 0.132117 The cubic contents of the stem of a tree may be determined by the formula r+i 4 in which V is the volume, D the diameter at the base, H the length and r the form exponent. In this formula the diameter is taken at the base of the tree. For the breast-height diameter the fol- lowing formula must be used: r+1 4 -\H-4h/ Space does not permit a full mathematical explanation of the derivation of these formula?. An algebraic derivation of the formula is described in Aliiller's Holzmesskunde, page 12, and a proof by calculus is contained in Lehr- und Hand- buch der Holzmesskundc, by Langcnbacher und Nosseck, page 68. 98. Form Height. — By form height is meant the product of the form factor by the height of a given tree. The (jcrnian tabk's of form heights are constructed for convenience in determining the cubic contents of trees by the use of form factors. * In practical calculations it is immaterial whether the diameters or radii 4re used. FORM FACTORS. 1 85 99. Special Methods of Determining Form Factors. — riiilipfs Method. — In 1896 Karl Philipp of Baden published, in a pamphlet entitled Hilfstabellen fiir Forst-taxatorcn, a new formula which serves as a mathematical expres- sion for all forms of the stems of trees. The equation representing any stem curve is as follows: In using this formula, the form factor is based on the volume and height of the stem above breast-height (1.3 meters). The form factor is expressed n by the fraction — . Suppose that the form factor is 0.47, expressed as a vulgar 47 fraction , then n = A'] and ni = ioo, and the equation reads: 100 ^ y^' = px''\ The formula is used to determine the form factor of a tree in the follow- ing way: Let D be the breast-height diameter, d the diameter at a point on the stem representing a fixed and arbitrary proportion of the height (usually 0.4 of the height), H the height above breast-height, and h the distance from the point where d is measured to the tip. Then n I m Sirzelecki's Method. — The following method was described by Forst- director Heinrich Rittcr von Strzelecki, a Galician forester, in the Central- blatt fiir das gcsammte Forstwesen, 1883. It is interesting and may in some cases prove of practical value. With a paraboloid as a model, it is assumed that, if d is the diameter at one-half the height and D is the basal diameter, then /— d d = v. 1,7) =0.7070, or —=0.707. d The quotient — is greater or less than 0.707, according as the trunk of Lhe tree is greater or less than a paraboloid, and in the same proportion as tJie form factor will be greater or less than 0.50. Expressed in a formula, d ^ d o-7°7-J^ = o-5-F, or ^ = 0.707—. i86 FOREST MENSURATION. The volume of the tree would then be d F =0.707 -XBXH, in which V is the Volume, B the basal area, H the height. To obtain the volume of a tree, measure the height, the diameters at the base and at the middle point, the latter with a dendrometer, and apply the above formula. Pressle/s Method. — As explained on page 156, Pressler's formula for cubing standing trees is: r=,s(H+f). V Substituting this value of V in the formula F = --—, then j(-?) H The Form Factor Determined from the Form Exponent. — The formula for cubing a tree when the form exponent is used is as follows: V^BXHX r + fiVH-4.5/ The form factor is therefore F- + i\H-4.5/ r + i\H-4.s/ When the basal area is taken at the true base, and not at breast-height, V = BXHX . r + i The absolute form factor is then F=-^. r + i Nossek's Method. — As explained al)ovc, the absolute form factor may be expressed by the formula "-rh FORM Factors. 187 in which F is the form factor and r is the form exj)onent of the tree. The volume formula would then read r + i ' wricTfe 2 is the basal area at the stump cut. If now the breast-height diameter is D, m the distance from the stump to breast-height, and d the diameter at H-m , , then d':D' = l j :{H-m)r = 1:2^, d_ I D~V2r' If this equation is multiplied by ■, then d "^2^ I — X = = Absolute form factor. D /-+! r + i If B is the area at breast-height the formula would read: d ^2" Form factor (breast-height) =— X X D r + - I / my A table was prepared by Nossek showing the value of the above equa- te tion for all values of — and of H which might be required. In practice one determines D, d, and H by measurement, and then looks in Nossek's tables for the corresponding value of /. The volume of the tree is then readily obtained. Schaal's Method. — Forstmeister Schaal of Griinthal, Germany, published in the Allgemeine Forst und Jagd Zeitung, August 1885, the following simple method of determining the form factor of a tree: An observer determines the angles formed by sighting a clinometer to the tree-tip and to the point on the trunk where the diameter is one-half that af breast-height. The form factor of the stem is then obtained by the formula ^ 2 tangent b 3 tangent a i88 FOREST MENSURATION. in which F is the stem form factor, a and b are the angles obtained by sight- ing to the tip and the half-diameter point of the tree. This method gives only approximate results. 100. Method of Form Quotients. — It has already been explained that there is a great difference in form factors of different trees of the same diameter and height, and that this difference pre- vents the use of average form-factor tables with single trees. The method of form quotients has been devised to enable the quick computation of the form factor and the volume of a single tree. The form quotient is the ratio between the diameters at the middle of the stem of the tree and at breast-height. Expressed algebraically, q= j:, d being the diameter at the middle of the stem, D the diameter at breast-height, and q the form quotient. This ratio is an excellent expression of form, because the form quotients of trees vary directly with the volumes. It is a con- venient expression because it is easily determined, even for a standing tree, and enables the rapid computation of volume. The form quotient has a close relation to the stem form factor of a tree, and the difference between the form factors and form quotients of a number of trees of the same species is very uni- form. Thus, for example, it has been found that the constant difference between the form factors and form quotients of Scotch pine is 0.2, of Norway spruce 0.21, of beech between 0.22 and 0.23. These constants may be used to determine the form factors and the volumes of standing trees in the following way: The diameter at breast-height is measured with calipers; then the total height and distance of the middle point above the stump are determined with a hciglU measure; then by estimate or measurement with a dendrometcr, the diameter at the middle point is determined. The form factor is then found by sub- tracting from the form quotient the constant difference between form factor and cjuolicnt for the species in question. Plxpressed FORM FACTORS. 189 as a formula, F = q — c, F being the form factor, q the form quo- tient, and c tli^eenstant. The constant for a given species varies slightly with the height of the tree. The variation is not great, particularly for trees between 40 and 100 feet. As the trees whose volumes are required are usually within this range of height, an average value for c may be used in practice. Prof. Judson F. Clark has made a study of form quotients of balsam fir in the Adirondacks, which indicates that the method can be successfully applied in practice in this country. CHAPTER XIV. DETERMINATION OF THE CONTENTS OF STANDS, 10 1. Problems of Determining the Contents of Stands.— The purpose of studying the volume of single trees, of making volume tables and tables of form factors, is to facilitate the com- putation of the contents of stands. Occasionally a single tree is sold and its volume desired, but ordinarily the single tree is of interest to the forester only as it forms a part of a whole stand or forest. In general, there are two distinct sets of problems in deter- mining the volume of stands: First, those requiring an estimate of merchantable volume, used in valuing forest land for possible purchase or sale and in making plans for lumbering. Second, those involving an accurate determination of volume, used in studying increment and future yield. Various methods of estimating the contents and value of timber have been developed in different parts of the country. These methods differ in the degree of accuracy of the results and each is designed for a particular region and set of conditions. The methods of accurate determination of the volume of stands are mostly adopted from European practice. The problems of studying the volume of stands are so varied under different con- ditions in this country that in a general book on forest mensura- tion it is desirable to describe all the more important methods of work. An explanation is given, with each method, of the kind of problem for which it is specially designed, in order that the student may not be confused by their large number. 190 DETERMINATION OF THE CONTENTS OF STANDS. 191 102. Timber Cruising. — The determination of the merchant- able volume and value of standing timber is called Timber Cruising or Timber Estimating. In this country and Canada there is a body of professional cruisers (also called estimators, land-lookers, or land-valuers) who make a business of estimating the value of forest land and its possibilities for profitable lumbering. These men are so skilled that they can estimate, merely by inspection, the merchantable contents of a standing tree or the approximate yield per acre. The most experienced cruisers can estimate pretty closely the yield of an entire township or section without taking a single measurement. It is absolutely impossible to learn from books how to esti- mate timber, for it is not a matter of method, but of judg- ment, which can be acquired only through experience and prac- tice in the woods. A cruiser is able to judge by the eye the mer- chantable contents of a tree because he has seen trees of the same character and size cut and used, and he knows what they produced. In the same way a cruiser can estimate the con- tents of a stand by comparing it to similar stands whose actual product he knows. The cruiser must understand the local conditions of lumbering in order to know what trees are mer- chantable from the standpoint of size and condition. He must be able to recognize the external signs of defect and judge the amount of loss through hidden imperfections; and in order to place a value on the timber he must be able to judge the cost of lumbering. This is not a matter of information which can be given in a book, but of field training. It is, however, possible to describe the general methods of the cruiser in different kinds of problems and the aids which he uses to guide and check his judgment. 103. Estimate by the Eye. — This method was formerly used almost universally to determine the value of standing timber. The available timber was so plentiful and cheap that a very accurate estimate of the amount on any-specified tract was not essential. Usually the cruiser's guess, based on a superficial 192 FOREST MENSURATION. examination of the land, was sufficient for the purchaser. In recent years, as the value of land has increased, greater accuracy is required, so that in many sections the estimates are now based on very careful methods which involve actual counts of trees. Purchasers were formerly satisfied if the estimate underran the real product of the land. But now very close estimates are required because a considerable underestimate might cause a buyer to lose a chance for profitable investment; while an over- estimate might cause the purchase of land at too high a figure. Nevertheless transactions in land are to-day constantly made on the basis of ocular estimates by cruisers. There is no uniform method of work in making an ocular estimate of timber on a given tract. Each cruiser does the work in his own way. Suppose that a township of timber is to be estimated. The cruiser goes over the tract examining the char- acter of the timber with more or less care and then guesses at the total yield or the yield per acre. If the timber is fairly uni- form in size and evenly distributed over the ground the esti- mate may be made in a short time. Usually the timber is not uniform, but has a different yield in different portions of the township, so that each portion must be estimated separately. Thus if there is a mountain on the tract, the north slope may be estimated separately from the south slope, the lower slopes separately from the upper slopes, the different water-sheds, swamps, or other special types of land, also separately. Some cruisers guess at the total contents of a township or part of a township in million and fractions of million feet ; others estimate first the yield per acre, multiplying by the known or supposed num- ber of acres in the area. The estimate by the eye is being rapidly replaced by methods dependent, at least in part, on counts of trees on the whole area or on small sample areas. The esti- mate by the acre is more reliable than the general guess, Ixxause the cruiser constantly checks his judgment by laying off samj)Ic areas and estimating the contents of standing timber on them. There are several methods of laying off rough sample areas DETERMINATION OF THE CONTENTS OF STANDS. 193 without measurement. One way often used by cruisers is to count the trees in a circle having an estimated radius of 7 rods, which covers an area of about one acre. In the spruce forests of the Northeast this is about as far as one can distinguish a tree by its bark. After counting the trees the cruiser estimates the contents of an average tree and muhipHes by the number of trees for the yield per acre. A quicker way is to count the trees in a circle of 60 feet radius, which covers an area of approxi- mately one-quarter acre, or a circle of 85 feet radius, covering an area of about one-half acre. If the forest is very open, one should use a whole acre if possible, as a smaller area may not represent average conditions. Another method is to count the trees in a narrow strip. One paces off ID yards, stops and counts the trees for a distance of 2 rods on each side, then paces another 10 yards, again count- ing the trees, and so continues until he has paced 165 feet, which comprises an area of one-quarter acre; or he paces off enough to make a half or a whole acre. There are several ways of estimating the volume of the aver- age trees required in these methods of rough sample areas. Some estimate by the eye the average yield per tree. Some estimate the average number of logs per tree, and knowing from the experi- ence at the local sawmills the average contents of the logs, deter- mines the average yield of the standing trees. Another way is to select several trees of average size, estimate their volume, and use the average of these as the required average yield per tree in the forest. Cruisers often have rules of thumb for esti- mating the volume of certain species. (See page 153.) Sometimes cruisers lay off square plots by pacing the sides and measuring the corner angles with a pocket compass. The laying out of measured plots is described in connection with the accurate determination of the contents of stands. A convenient form for use in estimating timber is used by the forest oflEicers on the federal reserves. The forest reserves are divided into so-called blocks, districts, and divisions. Scpa- r94 FOREST MENSURATION. rate estimates of standing timber are made for each of these divisions, the forest officer being allowed to choose his own method of making the estimate. Usually the forest officer estimates by the yield per acre, judging this by the eye or by rough sample areas, such as have been described. The data secured are entered in the following form, which has been filled out to make it clearer. ESTIMATE SHEET. Estimated stand per acre on Block 5, District 8, Division 3. (Here state whether for entire block, portions of block, or tract applied for only.) Covers entire block. LIVIXG TIMBER. Species (to be written in). Number of trees above 8 ins. per acre . . Average height of trees Average number of trees per M Average stand, B. M., per acre Percent deduction for defect Bull Pine 55 16 4400 Total DEAD TIMBER SOUND ENOUGH FOR USE. Number of trees above 5 inches per acre Average stand, B. M., per acre Cords down timber per acre Cords standing timber per acre, suitable for fuel only. . . 70 55 16 4400 5% What percent of total was actually estimated and what system wa used? 10 percent of the timbered area (155 acres). \ acre, circle methoti John Doe, Head Ranger 104. Estimate by the Inspection of Each Tree in a Stand. — Most of the more accurate methods of estimating used l)y cruisers in this country are based on an inspection of every merchantable irce in a given stand. The simi)k'st method is to court & DETERMIN/tTION OF THE CONTENTS OF STANDS. 195 merchantable trees, then determine the volume of an average tree and multiply this volume by the total number of trees. In mountain districts where the land is rugged and there is a constantly changing topography, the merchantable trees are often scattered or in small groups. It is then comparatively easy to count the merchantable trees without danger of including any one tree twice. If there is danger of counting trees more than once, each one, when it is inspected and counted, is blazed or otherwise marked. A method requiring greater skill is to estimate the contents of each tree as it is inspected. When each water-shed or secondary water-shed, ridge, plateau, or other type of land is finished, the figures are added together for the total. A third plan is to measure each tree with calipers and deter- mine the contents of the stand by volume tables. This method is described in section iii. The following is a description of how the method described above was applied in estimating the timber in Pisgah Forest, North Carolina.* 1. Each tree is approached individually, its diameter measured, and its defects, especially its hollowness, examined by "sounding." The diameter measure and the estimated volume are entered on a tally-sheet opposite the number of the tree, which is inserted in the stump of the tree by a stroke of the "revolving numbering hammer." 2. One cruiser and one helper tally 400 trees per day. 3. The method allows of ready control by the owner, the forester, and the buyer. It is adapted to hardwood forests in a rough mountainous coun- try where the merchantable trees per acre are few and where practically no tree is free from defects. Where the trees are counted and not measured, it is more con- venient to record the count on a tally register than on a tally- sheet or note-book. '^ Forest Mensuration, by Dr. C. A. Schenck, page 42. 196 FOREST MENSURATION. This instrument consists of a metal box or case about 2 inches in diameter and J inch thick, containing a mechanism including three numbered wheels the edges of which are exposed through a small glass disk set in the center of the front of the case. The wheels are turned step by step by a plunger project- ing through the edge of the case in posi- FiG. 37. — Tally Register, tion to be operated by the thumb. The box is carried within the palm of the hand and held by a ring through which the middle finger is passed. It counts from i to 999 and costs $2.50. (See Fig. 37.) 105. A Method Used in Michigan. — In a flat countr}' — as, for example, in the Lake States — it is more difficult than in the moun- tains to keep track of the counted trees and not to go over the same ground twice. In such regions a number of systematic methods, which differ in detail with different cruisers, have been developed. The method described in the following paragraph is used by a Michigan cruiser and is given as a typical example: In Michigan the land has been subdivided into square quarter- sections of 160 acres, each of which is further divided into plots of 40 acres. A "forty" is 80 rods square. The cruiser who uses the method now to be described has found by trial that 500 of his natural paces are required to go 80 rods. He begins at the corner of a "forty" — say, at the southeast corner — and steps off 125 paces on the south line, and so covers one-quarter of the side of the "forty." (See Fig. 38.) He then stops, and, facing north, counts the trees first to an estimated distance of 125 paces on the right hand, and then to an estimated distance of 125 paces on the left hand, and in each case to a distance of 100 j)aces in front of him, thus including the area represented in the diagram as Plot I. He then ste])s north 100 paces, and in the same way counts the trees on Plot II, and repeats the o])eralion successively for Plots III, IV, and V. This gives a complete count of the trees on the eastern half of the "forty." He then walks DETERMINATION OF THE CONTENTS OF STANDS. 197 west 250 paces along the north line of the "forty." Facing south he now counts all the trees in Plots VI, VII, VIII, IX, and X in the same way as before, and thus compleies counting the trees on the entire "forty." As he goes over the ground he constructs a rough map, locating the ridges, streams, swamps, and windfalls. He also makes notes of the general character of the timber and of any other information useful to the owner of the land. When the work h completed the cruiser has a practical working-map for carrying on lumber operations in addition to the other material secured. It is obvious that this method can be used only on comparatively level ground. Another similar method is described by A. S. Williams in the Forestry Quarterly, Vol. II, No. 3. Plot' VI 1 Plot V PlotjVII Plot'lV Plot; VIII 1 Plot; III 1 Plot! IX 1 1 Plotlll 1 PlotI X 1 1 Plot; 1 125 paces Fig. 38, 106. Estimating by Working over Small Squares. — ^.\nother method of cruising which gives good results is to divide each "forty" into 16 small squares of 2^ acres and to estimate the timber on each square separately. This method and the one following were described in an article in Rod and Gun of Canada, November, 1901, by A. Knechtel. The following description is essentially the same as given in that article: The cruiser begins at one corner of a "forty"; for example, 19^ FOREST MENSURATIOhf. at the southeast corner. He paces along the south line lo rods east and then turns and paces lo rods north. This brings him to the center of a square 2^ acres in extent, or one-sixteenth of the "forty." Standing at this point he locates by the eye the boundary-lines of the square and then estimates the timber upon it, usually by counting the trees and determining their contents from volume tables. In dense stands where the trees cannot be readily counted, a 5ag may be placed at the center of the square to guide the »ruiser. He then paces 5 rods south and then 5 rods west, which brings him to the center of the southwest quarter of the square. He estimates this small plot and then paces 10 rods north, where he stands and estimates the northwest quarter of the 2|-acre square. He then paces 10 rods east and estimates the northeast quarter of the square and then paces 10 rods south and estimates the southeast quarter. Having completed the estimate of one 2J- acre square, he returns to the flag and paces from this point 20 rods north, which is the center of the second 2j-acre square which he estimates In the same way as before. This operation is continued until four squares have been estimated. The cruiser then takes in hand the tiers of squares directly east of the first series until the 16 squcires, or the entire "forty," have been cov- ered. (See Fig. 39.) 107. Estimating in 4c/-rod Strips. — \ method sometimes used in ^Michigan is to estimate the timber in strips 40 rods in width and one-half mile long, which cover exactly 40 acres. The cruiser is' assisted by a lineman, who runs a compass line along one side of the strip, measuring its length by pacing. The cruiser passes back and forth over the strip estimating the timber. He paces the distance when going away from the line- man, who guides him, when returning, by a policeman's whistle, When a strip of one-half mile, or 40 acres, has been completed, an adjacent strip is cruised in the same manner. 108. Erickson's Method. — An excellent method of cruising is that devised by M. L. Erickson of the U. S. Forest Service. DETERMINATION OF THE CONTENTS OF STANDS. 199 It consists in gridironing a given tract by strips 4 rods wide and usually \ mile apart, and recording the estimated breast-height diameter of each tree and the estimated top diameter of each mer- chantable log. If there is a crew of two men, one directs the strip on a compass-line and paces the distance, the other records the diameters of the trees and logs. The compassman first paces off a short distance — for example, ten yards — and waits until the tallyman records the trees in that distance and ^1 ll 10 Rod Fig. 39. comprised within a 4-rod strip. The tallyman records on a tally-sheet, like that shown on page 200, the estimated breast-height diameter of each tree and the estimated top diameters, inside the bark, of each 16-foot log. The compassman keeps track of the distance paced, and makes a note of roads and streams crossing the strip, and of any other information required in the cruise. The strips, together with the roads, streams, and other features, may later be plotted on a map. A separate tally-sheet is used for each strip, or part of strip, for which a separate estimate is required. Thus a new record is made when a different water- shed is reached, when the compass direction of the strip is changed, when a diflerent forest type is encountered, etc. The records enable the determination of the contents of the 200 FOREST MENSURATION. logs by any desired log rule, the determination of the total num- ber of trees, the average number of logs per tree, the number of trees or logs per thousand board feet and the yield per acre. One of the advantages of the method is that each tree is scaled for what it will yield, and crooked and defective logs discarded. The only deduction required in the final total scale of a tract is a certain percentage for hidden imperfections not apparent on the standing trees. In the spruce forests of New Hampshire one crew of two men can work over in a day a strip ij miles long. If the strips are laid off \ mile apart, this means a cruise of 300 acres per day. The method requires not only a knowledge of what con- stitutes a merchantable log, but also the ability to estimate diam- eters. It requires a trained eye and cannot be practised by a novice. RECORD OF ESTIMATED DIAMETERS. Locality, Waterville, N. H. Block, Snow Brook. Compartment, II. Species, Spruce. Strip, No. 17. Course, N. 8° E. Length, 120 rods. 1) u 0 E Top Diameter of Logs Inside Bark, in Inches. 4/ ^ « E ax. 6 7 8 9 10 11 13 13 14 15 NumbtT I f Logs. ,S 9 10 1 1 12 13 14 15 16 I 2 17 12 22 30 35 15 '12 10 91 «3 68 59 44 ,V^ 16 8 8 109. Estimate by Use of Stand Tables. — Stand tables show the average volume per acre of stands of dilTercnt character. DETERMINATION OF THE CONTENTS OF STANDS. 20 1 When the yield per acre is shown for fully stocked even-aged stands at different ages, stand tables are the same as normal yield tables (described on page 318). When stand tables show the actual average yield of even-aged stands in a specified locality or region, they are the same as empirical yield tables. Most of the stand tables so far made in this country show the average number .of trees of different sizes and the volume per acre of the timber growing on specified tracts, and are used in estimating the total present yield and future growth on given tracts. Stand tables are valuable as a standard of comparison in estim.ating timber. Suppose, for example, that one were esti- mating a stand of chestnut and oak sprouts thirty years old; suppose, also, that average stand tables have been made for the region showing the average yield of oak-chestnut sprout stands at thirty years of age to be 27 cords per acre, one judges by the eye whether the stand in question is better or poorer than the average in the region and estimates the yield of the stand by using the 27 cords as a standard of comparison. The timber cruiser has such average yields in mind; that is, stand tables are merely a tabulated statement, resulting from actual measure- ments, of the information constantly used by the cruiser. Normal yield tables are, however, somewhat different, because they are based on the yield of fully stocked stands. They are applicable in estimating only to even-aged and usually only to pure stands. . Suppose, for example, that one were estimating a stand of 50-year-old white pine, such as often is found in New England. Suppose, also, one has a normal yield table which shows a yield of 55 cords per acre for a normal stand of pure even-aged white pine. The stand is inspected and the deviation from normal stocking estimated. Suppose that it were estimated that it has only 80 percent of what might be growing. Then the yield per acre is 55X0.8, or 44 cords. Such a plan of estimating is especially useful in very small growth. It is used constantly in Europe to estimate the growing stock of^oung stands in making working-plans. 202 FOREST MENSURATION. 110. Estimate by the Use of Valuation Surveys. — By valua- tion survey is meant the measurement of the diameters of the trees or other detailed study on a known area. Tlie counting of treeL, on an estimated circle or paced plot described on page 193 is a form of valuation survey, though the term is applied usu- ally to the work on measured areas where the trees are calipered or their diameters estimated. The area upon which the measure- ments or other detailed studies are made is called the valuation area, sample area, or sample plot. A strip survey comprises the measurement of a stand on a narrow strip, usually one chain wide. If the valuation area is a square or any other shape than a narrow strip, the work on it is called a plot survey. Valuation sur\^eys are used extensively in estimating timber, not only as checks to ocular estimates, but when a large num- ber are taken, as a complete mathematical basis for the compu- tation of the volume of a given tract. Their use in estimating timber and in exact studies of the contents of stands is described in the succeeding sections. 111. The Use of Strip Surveys. — ^The principle of this method is to measure the trees on narrow strips distributed systematically over the forest and covering in the aggregate a specified per- centage of the total area. These strips arc knowTi as strip valua- tion surveys, or strip surveys. In the practice of the U. S. Forest Service the strip surv^cys are one chain in width, and for each ten chains of length, that is, for each acre, the tree measure- ments and forest descriptions are kept separate. The work of laying-off the strips requires a crew of at least three men. One, called the tallyman, carries a note-book or tally-sheets, and records the species and their diameters as they are called out by two calipermen, and also makes the required descrii)tive notes. The strip is measured off in length with a surveyor's chain in the following way: Tlie cliain is stretched on the ground in the chosen direction, the tallyman carrying the forward end and one of the calipermen the other end, and tlie trees within an estimated distance of 33 feet (one-half chain) DETERMINATION OF THE CONTENTS OF STANDS. 203 on each side of the chain arc then calij)cred. Then the crew moves forward another chain length in the direction indicated by the tallyman, the chain laid on the ground and the trees calipered on each side of it as before. This same operation is repeated until ten chains have been measured. If there are four men in the crew, one man determines the direction of the strip with a compass and carries the forward end of the chain, two men caliper the trees, and the fourth makes the records. The compassman directs the work of the crew, seeing that the calipering is accurately done, that no unsound trees are measured, that the calipermen keep within 2)Z feet on each side of the chain, and he makes observations required for the descriptive notes which he dictates to the tallyman. As it is difficult for the compassman to direct the course and at the same time make observations of the character of the forest and over- see the work of the other men, a fifth man is sometimes added to the crew. This enables the leader of the crew to devote his whole attention to directing the work and making the descriptive notes. If the trees are to be counted and not measured, two men in a crew are sufficient, one to do the counting, the other to man- age the compass and the forward end of the chain, record the counts, take notes on the forest, lumbering, topography, etc. 112. Distribution of the Strip Surveys. — ^There are two gen- eral methods of distributing the strip surveys over a given tract; first, to lay them off in long strips running across the tract, parallel and equidistant; and second, to locate them as isolated sample areas. The U. S. Forest Service uses the strip method not only to obtain estimates of the merchantable timber, but also to secure a count of the trees not yet merchantable, to make forest maps, and to gather other detailed information necessary for a prac- tical forest working-plan. Under thesg. circumstances lines of strip surveys are usually laid off parallel and equidistant, and run across the entire tract. Suppose, for example, that a town- 2 04 FOREST MENSURATION. ship in a region like the Adirondacks is to be estimated. The first step is to determine the percentage of the area to be included in the valuation surveys and to make a plan for the distribution of the strips over the area under investigation. Usually one side of the tract is chosen as a base-line and the strips are laid off at right angles to it and at equal distances apart. Stations are marked along the base-line to indicate the location of the strips. The crew starts at the first station, which is close to the end of the base-line, and runs a line of lo-chain strip sur- veys across the tract in a direction determined upon in advance. Upon arrival at the farther side of the tract, the crew paces along the line the distance which is to separate the strips. Then a second line of strip surveys is laid off parallel to the first and running in the opposite direction to station No. 2 on the base- line. As soon as the base-line is reached the crew paces the distance to the third station, whence a new strip is started parallel to the other two, and so on until the whole tract has been covered. Inasmuch as the lines are run with a pocket compass, it is diffi- cult in rough country to exactly meet, on the return courses, the fixed stations on the base-line, as, for example, station No. 2. Most investigations do not require that the strips be precisely equidistant, so that often there are no fixed stations; but the crew starts at a predetermined point near one end of the base- line and lays off strips as nearly parallel and equidistant as pos- sible, not trying to reach upon the return strip any fixed point. The exact location of the strips is, however, carefully recorded on the map. This plan gives a little more elasticit}- to the method, often desirable in rough country. As the strip method is ordinarily used, tlie chaining is not done very carefully. Thus, it is often customary for the com- passman to attacli tlie chain to liis hv\{ at tlie back and to mark off the distances merely by scratching the surface of the ground with the heel and not to mark by a ])in or slake. The chaining is usually not done on the horizontal, l)ul tlie Icngtlis are measured along the ground regardless of \\\v sloj)e. A valuation survey DETERMINATION OF THE CONTENTS OF STANDS. 205 run up and dawn a steep slope covers an acre of surface, but is less than 10 chains long when projected on a map. On account of the errors from this inaccurate method of chaining, the strips often do not fit precisely into the map. There is not, however, any considerable error in an estimate arising from this lack of precision in chaining because the errors in laying off single acres largely compensate each other. It is only when the chaining is used for a topographic map as well as an estimate that accu- rate chaining on the horizontal is necessary. It often happens, in running a line of strip surveys across a given area, that the last strip is less than 10 chains in length. Strictly this should be regarded as a fraction of an acre. Thus, for example, if the last strip is 4I chains in length, it comprises 0.45 of an acre. When the results of the measurements on this short strip are used, it is necessary to express them in terms of whole acres by dividing by 0.45. In practice, however, where the forest is uniform, the whole acre is completed, either by continuing over the line or by turning and finishing inside the line in another direction, in order to facilitate computation and avoid fractional acres whose results must be converted into terms of whole acres. It is easy to see that the systematic gridironing of a tract, as above described, would not always be the best plan of dis- tributing the strip surveys. Thus, for example, in mountain country, where the merchantable timber is located in certain types of land or in certain portions of a tract, and on small or very irregularly shaped tracts, it is usually better to lay off strip surveys more or less irregularly, and often as isolated sample plots, in such a way as to obtain an average yield per acre of the type or area under immediate examination. Suppose that the timber in a small water-shed is to be estimated and that the yield per acre differs materially along the stream from that on the slopes, isolated strip surveys are taken and the yield per acre determined separately for each'type of forest. In less mountainous regions the strips are sometimes laid off radially 206 FOREST MENSURATION. from a central point, or run in a zigzag fashion over a given area. The strips are, therefore, laid off by judgment and not by rule, as in the gridiron method. In general the gridironing plan is used in level, rolling, or moderately mountainous country and where a forest map is required in addition to an estimate of the volume of the timber. The method of isolated strip surveys is preferable in very rugged regions where the merchantable timber is confined to certain types of forest or to certain areas of the tract and where a separate estimate is required for each type or area; and on small tracts or those very irregular in shape. 113. Data for a Forest Map. — The preparation of the forest map is often combined with the estimate. In most cases a con- tour map is not designed, but rather a map which will show the distribution of the timber, the forest types, the location of the roads, streams, and main ridges. Such a map is prepared in the following way: When a strip intersects a road or stream the tallyman notes the point of intersection and also the direc- tion of the road or stream, so that it can afterwards be located on the map. If a road or stream crosses several strips the points of intersection are connected on the map and the exact location thus indicated. When a stream or road is crossed, the tally- man takes any necessary notes as to its character and width. The description of each acre includes the general direction of the slope, and if there is a marked change in the degree of slope in the middle of the acre, that fact and the point where the change occurs are noted. The location of ridges may thus be determined from the descriptions of each acre and sketched on a map. It is possible, also, to make a map of the forest types because the description of each acre includes a statement of the type. If an acre crosses from one type into another, this fact is cx])lained on tlie tally-sheet and the point indicated where the change occurs. The outlines of the different types may be sketched on the map in the same way as tlic roads and streams. bETERMlhlATlON OF THE CONTENTS OF STANDS. 207 114. Measurement of the Trees.— The strip method may be used without calipering the trees, but by counting them or estimating the contents of each merchantable tree as it is inspected^ Usually, however, the trees are calipered at breast-height to the nearest inch. Sometimes the trees are thrown into diameter classes of two or more inches. Ordinarily only one measure- ment of each tree is taken unless it is obviously eccentric, when two diameters at right angles are measured, the average being recorded as the diameter. (See section 43.) Care should be exer- cised not to take the measurements below breast- height. It is very easy for a tired man to drop his calipers and measure at 3 or 3-I feet instead of 4^ feet. The author has made tests of the possible error occasioned by low measurements. With small timber averaging 6 to 10 inches in diameter the error is practically negligible, but with large timber it may seriously affect an estimate. In old spruce, the writer found that care- less calipering adds i inch to the diameters of 20 percent of the trees. This means for every 1000 trees an overestimate of 8000 feet, or on an average, on spruce and hardwood lands, about 300 feet per acre. Care should also be exercised to place the calipers at right angles to the axis of the tree. It is obvious that a considerable error may result if the calipers are placed obliquely on the trunk. When there is a bulge or other normal swelling at breast-height the measurement should be taken just above the obstruction. In tropical countries, where many of the trees have buttresses, the measurements cannot be taken at breast-height, but special methods of grouping are used. Where an estimate of merchantable timber is being made, only the apparently sound marketable trees are included. Errors in estimating often come from counting unsound trees. Inex- perienced or careless men often measure trees which at first sight appear sound and merchantable, but which are really defective. Great care must be exercised to scrutinize each tree for signs of defect. Usually decay manifests itself by some external sign, as punk knots, white resin, unhealthy crown, 2o8 FOREST MENSURATION. broken top, dead limbs, moss, and so on. A cruiser must know these signs. If he is working in a new country he should asso- ciate with him some local woodsman who is familiar with the character of the timber. In a great deal of government work trees below the merchantable size and sound trees of species not yet merchantable are measured in connection with prepa- ration of working-plans. The principles governing the measure- ment of small trees is discussed on page 335. The methods of determining the volume of the trees on the strip surveys are described m later sections. 115. Recording the Measurements.— The diameter measure- ments are recorded in a note-book or on a special tally-sheet. The tally-sheet is ruled in columns, the first showing the diameter classes, by inches or groups of two or more inches, the other columns being for the different species of trees. A special form of tally-sheet is used by the U. S. Forest Service, with columns sufhciently broad for subdivision. These tally-sheets may be fastened to a th^n board by thumb tacks or carried in a special holder, made to contain approximately fifty sheets. This device is tray-like in form, and consists of a rectangular board or panel provided on three sides of its upper face with wooden cleats, the inner edges of which are grooved to receive the edges of the sheets, which are held in place by a narrow hinged leaf secured on its fourth side. A spring hook holds the leaf in its closed position. These holders may be purchased from Keuffcl & Esscr Co., New York. The trees are tallied by dots and lines, in blocks of ten, as in- dicated in the following tabic, which shows the marks correspond- ing to different numbers: 123450789 10 * •••::: r. n n n la s This method is economical of space, and cna^ Ics the recording of a large number of trees on a single sheet. 116. Number of Strip Surveys Required for an Estimate.— It is the usual aim to make the sample strips comprise from 5 to 10 percent of the total area. Sometimes it is possible to include DETERMINATION OF THE CONTENTS OF STANDS. 209 20 or 30 percent, .but ordinarily on large tracts, from 5 to 10 per- cent, is considered sufficient. On very large areas of 100,000 or 200,000 acres the strips cover 2 to 3 percent. Recent work in the U. S. Forest Service has been done on a basis of running the strips one-quarter or one-half of a mile apart. . Under ordinary circumstances a crew of four men should be able to measure off 30 to 50 acres a day if only the merchantable timber is included. In very open woods this number may be increased. Where small trees are measured and special care taken in laying off the strips, 20 acres a day are about all that a crew can measure. 117. Advantage of Strip Surveys. — The chief advantage of the strip method is that the sample acres represent a good average, inasmuch as they are run straight through the forest and include whatever may be in the course, whereas square plots are more apt to be located in the best areas and hence to give too large results. A second advantage is that the strip surveys may be taken very rapidly and a much larger number of sample areas obtained than is possible with carefully surveyed plots. The third advantage is that the systematic location of the strips enables the preparation of a map. The disadvantage of the method is that there is always a chance of error in estimating the width of the strips. This is not a serious matter provided the caHpermen are careful and the method is used only in measuring large timber. The esti- mating of the boundaries is hazardous in small timber, as an error of a few feet may result in including or excluding a con- siderable number of trees. 118. Accurate Plot Surveys. — -Accurate plot surveys are used principally in the study of growth and the preparation of yield tables. Occasionally an accurately measured valuation area is used in timber estimating, but, if the merchantable trees alone are measured, rough valuation surveys like the strips and esti- mated plots described in the previous sections usually suffice. Plot surveys are used in estimating sr&all growth, as, for ex- ample, second-growth hardwoods in southern New England, birch 2IO FOREST MENSURATION. and poplar in Maine, etc. Rough plot surveys and strip sur- veys are unsatisfactory and unreliable in this small timber because a slight error in guessing at the boundary-lines of the rough valuation area often results in considerable errors in the esti- mate of the volume of the stand. Stands of small timber are usu- ally more uniform than large and old timber and it is much easier to select plots which represent an average of the forest. For the same reason it is generally not necessary to take as many valuation surveys to secure a good average of a specified area and the plots need not be as large as in older and larger timber. 119. Instruments Used in Laying Off Sample Plots. — The sides are measured with a chain or tape and the angles with a small compass, staff head, angle mirror, or other instrument which is compact, light, and suited to rapid work. Instru- ments like the transit or railroad compass are not used in this work because great precision is not necessary and because these instruments are expensive, delicate, and difficult to carry in the forest. In the following sections the common instruments for measuring angles of sample plots are described. Of these instruments the compass is best where the ground is very irregular, and where frequent offsets have to be taken to avoid trees or other obstructions. Under ordinary conditions the staff -head is the most satisfactory, especially for plots of half an acre or more. For quarter-acre plots or smaller ones the angle mirror is most rapid. The compass and staff-head have the dis- advantage of being more clumsy than the angle mirror and of requiring a staff or tripod. Ordinarily, however, where accuracy requires the larger instruments, the extra trouble of carrying them is a small consideration. Stajj Compass. — This instrument (shown in Fig. 40) con- sists of a compass set into a shallow, circular metal box, having two sights hinged to its edge. A removable support, screwed into the bottom of the box, terminates in a socket, adapting the instrument to be mounted upon a staff or upon a tripod. The support also comprises a ball-and-socket joint, by which DETERMINATION OF THE CONTENTS OF STANDS. 211 the compass is leveled with the aid of spirit- tubes located in its bed, a s\vi\el, which permits the compass to be turned in sighting it, and a set-screw for securing it against turning after sighting. When not in use the sights are folded down and the support unscrewed from the box. When taken apart the entire Fig. 40. — Staff Compass. instrument is in compact form for transportation. It is made in different sizes, with needles from 2I to 4 inches long. The price varies from $10.50 to $13; without spirit-tubes, from $8 to $11.50. Cross Stafj-head. — This instrument consists of a small metal box, octagonal in form, mounted on a socket which may be fitted to a staff or tripod. Four of the faces have simple diopter slits; 212 FOREST MENSURATION. each other face has a short narrow slit to serve as the ocular, and a wide slit fitted with a hair as an objective. The socket may be unscrewed and fitted in the head for compactness in transportation. In use the staff -head, mounted on a staff or tripod* is placed on a kno\\'n line, at a point where it is desired to lay off a new line at right angles to the first. A sight is taken along the known line and then without moving the instrument the observer uses the line of sight perpendicular to the first and de- termines the direction of the second line. This instrument may be purchased from Keuffel & Esser Co., N. Y., for $4. A handy staff -head is manufactured in Fig 41. — Cross Staff- q^j-j^^^v. It is cylindrical instead of head. ' . octagonal and revolves m a metal rim, which is graduated in degrees, enabling the measurement of any angle. This instrument may be purchased for 30 marks from \V. Sporhase, Giessen, Germany. Other simple instruments based on the same prmciple as the staff -head are manufactured, such as the surveyor's cross. It is possible to manu- facture a rough surveyor's cross by fastening two narrow strips of wood together at right angles and driving short nails near the ends to serve as the ocular and objective. This mounted on a staff serves well to measure right -angles. The Angle Mirror. — This handy instrument consists of an open triangular metal box contain- ing two small mirrors mounted in frames secured to the sides of the box and set at an angle of 45° to each other. Rectangular sight-openings are Fig. 42.— An- formed above tlie mirrors in the sides of the box. ^'^ Mirror. The device is provided with a handle, ]ireferably made re- DETERMINATION OF THE CONTENTS OF STANDS. 213 movable for convenience. The observer looks directly into the box through its open sides and sights the instrument through one or the other of its two sight-openings at some given ob- ject. At the same time an object at a right-angle to the object sighted is visible to him in the mirror below the sight-opening through which he is looking, and is in the same vertical h'ne as the object sighted. The principle of the device is that the reflected object is first imaged through the open side of the box in the mirror opposite the sight-opening through which the observer is looking and then reflected across from one mirror to the other and thus brought into his vision. Fig. 43.— Adjustable Angle Mirror. In laying off a square, the forester runs out one side and then takes a position at the point where he wishes to determine a right-angle. With the instrument in one hand he looks througn one of its sight- openings at an object in the predetermined Kne, such as stake or pole. An assistant in the approximate location of the desired new line now moves about until his image appears in the mirror below the sight-opening being used, and exactly in line with the stake or pole. The assistant is then standing in a line at a right-angle to the predetermified line and establishes the new line. 214 FOREST MENSURATION. An adjustable form of the angle mirror is shown in Fig. 43. One of the mirrors is movable and the inclination is determined by an arc graduated from zero to 100°. The instrument may, therefore, be set to determine any desired angle. It is of special value in running out irregular plots. Determination oj Right-angles with a Tape. — A right-angle may be determined with a tape. Suppose that a stake has been set on a predetermined line at a point where a corner is to be established, set a second stake 4 feet from the first stake on the line already established, determine the general direction of the required new line, and set a third stake which is exactly 3 feet from the first or corner stake and 5 feet from the second stake. A line of sight from the corner over this last stake will establish the new line exactly perpendicular to the first line. Use 0} a Pocket Compass. — A square plot may be roughly laid out with a pocket compass, but usually where plot surveys are used greater accuracy is required than is possible with a pocket compass. A good compass for general forest use is the D. W. Brunton compass which is manufactured by \Vm. Ainsw'orth of Denver, Colo. The instrument which carries a 3-inch needle is very strong and is fitted with a stout cover. The instrument is fitted with a line of sight, and the observer is able by means of the mirror in the lid to take a sight and the compass reading without removing the instrument from the eye. A clinometer attachment enables the determination of slopes, heights of trees, etc. 120. Necessary Precision in Laying Off Sample Plots. — ^The plots are surveyed off accurately. In practice, however, it is diflicult, with such instruments as have been described for deter- mining the angles, to lay off a j)Iot with such precision as is rcf|uircd in most work of land-surveying. In an open forest of old trees a slight error in determining an angle or measuring a line may not be serious, Ijul in small growth where the trees stand very close together such a mistake may result in includ- ing or excluding a large number of trees which in reality are DETERMINATION OF THE CONTENTS OF STANDS. 215 outside or inside, the plot respectively. Wliere the forest is open and the plot covers as much as an acre, an error of 2 feet in tying up the lines may ordinarily be allowed. On all small plots, and if there is considerable small growth to be counted, on all large plots, an error of not over 6 inches may be allowed. 121. Shape and Size of Sample Plots. — Accurate plots are generally square or rectangular in shape. In some cases irregu- lar polygons are laid off, as, for example, where it is desired to determine the volume of a specific patch of timber. The shape of the plot IS not of so much importance as the knowledge of its exact area. As a rule acute angles in plots are to be avoided. Triangles are therefore not as good as polygons with wider angles. When possible, plots of one acre or multiples of one acre are laid off, because a smaller area does not give as good an aver- age and because the final results are always expressed in acre terms. Nevertheless half-acre plots are used a great deal where it is inconvenient to lay off a whole acre, where a half acre represents better the required average conditions, or where a stand is very uniform. In very small timber and where the timber is exceptionally uniform, quarter acres are frequently used. In estimating cord-wood, the author has successfully used plots 52 feet square, which comprise an area of one-sixteenth of an acre. A sixteenth-acre plot may be run out very rapidly and accurately with a 50-foot tape and angle mirror, and a short time only is required to measure the trees. Sometimes in small timber, where the forest types or ages of the stands vary con- siderably on a relatively small area, eight or ten sixteenth-acre plots give better results than one or two large surveys, such as could be obtained in the same length of time as the eight or ten small ones. 122. Marking the Boundaries of Sample Plots. — In laying off a plot the boundaries should be clearly marked, so that no trees outside the line will be measured %or any inside the plot be omitted. Stakes are set at the corners and a number of trees 2i6 FOREST MENSURATION. along the lines are blazed. A good method of marking the boundaries is to lay string along the lines. 123. Calipering. — WTien the boundaries have been marked o£F, the trees are cahpered. In calipering, a crew of three proceeds as follows: One man records the figures, the other two measure the trees, working over the plot in strips about 50 to 75 feet broad. The cahpermen mark enough trees to enable them to follow the line back, and to prevent measuring any trees twice. Ordinarily it requires about J to i hour to run out an acre and about h hour to do the calipering if only merchantable trees are measured. If small growth is counted or measured a longer time is required to caliper a full acre. The description just given applies to a crew of three micn, which is the most convenient number. If there are two men, one records the figures and the other calipers the trees, moving back and forth over the area in narrow strips. The tallyman assists in keeping the strips uniform and the count accurate. Scratchers (or as they are also called bark-blazers, tree-scnbes gouge-blazes) are used by the calipermen for marking the trees Several forms of scratchers are sho^\^^ in Fig. 44. Scratchers may be purchased in Europe at a cost of from 50 cents to $1 each. The European instruments, however, are too small and weak for use in old timber or with trees having hard bark like the hickory. A blacksmith of ordinary skill can make a satisfac- tory scratchcr. An important consideration in making a scratcher, is to set the gouge at the proper angle to the axis of the instru- ment. The gouge should be about \ inch across at its widest point. A band of metal over the handle, as shown in most of the scratchers in Fig. 44, is important to protect the knuckles from the bark. 124. The Location of Sample Plots. — Sample plots are se- lected to represent an average of a larger area. The selection of the sample plots depends on the object of the investigation, the form, age, composition, and degree of uniformity of the forest, and the character of the land. The location of plots DETERMINATION OF THE CONTENTS OF STANDS. 217 depends, therefore, on judgment and not on rule. Some guiding principles may, however, be given which will assist the beginner. Two problems may be distinguished when plots are used in estimating. I. The plots are to be used as a check to an ocular estimate, as, for example, in making compartment descriptions in a work- ing-plan. In this case the plots are located wherever the esti- mator is in doubt as to the yield per acre. If more than one type of forest occurs, or there is a difference in age or character Fig. 44. — Different Types of Scratchers. of the forest, one or more plots are laid off in each stand and used as a standard for comparison. Each stand must, however, first be carefully examined, in order that the estimator may select thoroughly representative plots. 2. An estimate is to be based entirely on the valuation 3lir» veys. Suppose that a tract of 1000 acres in southern New Eng- land is to be estimated, that there is considerable variation in the topography and the forest types, age, density of stands, etc. The estimator determines first how many plots are necessary and in general how they are to be distributed. The number is determined by considerations of expense and required accuracy. The general distribution is determined by the impression obtained 2i8 FOREST MENSURATION. from a reconnaissance of the tract, for which not over one day would be required. Beginning at one end the estimator sketches on a map the boundary of a restricted area, as, for example, a slope, a swamp, a ravine, or other well-defined area having a fairly uniform stand. One or more representative plots are used to compute the acre-yield of the area which is determined from the map. Then another arbitrarily restricted area is marked off on a map and estimated separately, and so on until the whole tract is covered. If there is no map, the forester estimates the approximate area occupied by each type of stand and then estimates the volume of each type separately bv the use of representative plots located in different places and averaged together to give the average acre-yield. Suppose, for example, that it is estimated that on the looo-acre tract 20 percent is mixed chestnut, oak, and other hardwoods 40 to 50 years old, growing on first-quality soil; 20 percent the same species, also 40 to 50 years old, on second-quality soil; 30 per cent swamp land, with red maple and other swamp trees 20 to 30 years old; and the rest old grown-up pasture land 20 to 50 years old. Suppose, further, that 50 sample acres, or 5 percent of the area, are to be taken. These are distributed over the tract proportionately among the dift'crcnt types. The largest num- ber are taken in the irregular stands, while only a few need to be taken in the youngest and most uniform stands. AH the surveys in the 40- to 50-year-old oak-chestnut type are averaged together and multiplied by the number of acres in the type, and in the same way each of the other types is estimated sepa- rately. A natural suggestion often made by students is to aver- age together all the ])lots and multi])ly by the total area of the tract. This plan is good provided the plots have been propor- tionately distributed among the different types. But it is very difficult to make such a correct distribution, and one would also be ])revented from taking a larger number of plots where most needed on account of the irregularity of the stand or for other reasons. If the forest is uniform over the entire tract, all plots bETERMlNy4TJ0N OF THE CONihNlS Of STANDS. 219 would be averaged together for the average acre-yield of the whole area. The location of plots used for studies of growth and for the preparation of yield tables is explained in Chapter XVII. 125. Computation of Volume of the Trees on Valuation Areas. — The volume of the trees measured in the surveys is determined from volume tables or by means of felled sample trees. In strip surveys the volume is usually computed from volume tables which show the contents of trees of different diam- eters. (See page 159.) This computation may be made very simply and rapidly in the following way: Make four columns of figures as shown below. In the first column place the diameters, in the second column the number of trees of each diameter measured on the acre, in the third column the average contents of trees of different diameters, from the volume table, and in the fourth column the total contents of all trees of each diameter, which are found by multiplying together the values in the second and third columns. The figures in the fourth column are then added together for the total con- tents of the stand. CONTENTS OF CHESTNUT ON A SAMPLE PLOT AT MILFORD, PENN. Diameter, Breast-high, Inches. Number of Trees. Contents from Volume Tables, Cubic Feet. Total Contents, Cubic Feet. 6 2 2.7 5-4 7 10 5-4 540 8 13 6.9 89.7 9 16 9-3 148.8 10 15 II. 7 175-5 II 14 14.4 201 .6 12 18 17. 1 307.8 13 9 20.2 181 .8 14 3 23-4 70.2 15 I 27.0 '■' Total 27.0 1261.8 22 0 FOREST MENSURATION. If the contents of trees on the valuation areas are to be computed by the use of volume tables which are based on diameters and heights, it is necessary in the field to determine the heights as well as the diameters of the trees (See page i66). Usu- ally the heights of a few representative trees of different diame- ters are determined and the heights of the trees of other diame- ters estimated by interpolation. Thus the heights of three to ten trees of each species are determined, care being taken to select trees of different diameters, including small, medium, and large trees. Care is taken to select for measurement trees each of which appears to be of about an average height in its particular class. Suppose, for example, that the following measurements of white pine have been taken : Diameter in inches lo 15 19 24 Height in feet 75 85 93 114 With these data a height curve for trees of different diameters may be made. In a system of rectangular coordinates in which the abscissae represent diameters and the ordinates represent heights, plot the four heights given above, then draw a regular curve through or as near the points as possible. The height corresponding to any diameter may then be read off from this curve. This method is used to find the contents of a valuation sur- vey in the following way: Make a table of five columns. In the first column place the diameters; in the second column, the number of trees of each diameter given in the first column; in the third column, the average height of trees of each diameter, these average heights being obtained from a curve such as has been described; in the fourth column, the contents of an aver- age tree from a volume table; in the fifth column, tlie total con- tents of all trees of each diameter; then add the figures in the fifth column and the result will be the total contents of the stand. The following is an example of such a table: DETERMINATION OF THE CONTENTS OF STANDS. WHITE PINE. 221 Diameter Breast-high, Inches. Number of Trees. Height, Feet. Contents of Average Tree from Volume Table, Board Feet. Total Contents. Board Feet. :o a2 -4 b i8 20 22 10 II 3 4 4 5 2 75 78 82 86 91 97 lo.S 30 69 120 185 272 383 549 300 759 360 740 1088 1915 1098 6260 In some investigations a calculation of heights for every valuation survey is made. In this case a separate crew of two men accompany those taking the survey and measure the necessary heights. More often in strip surveys the average heights of trees of different diameters are obtained for different forest types or for specified portions of a tract and used in applying the volume tables to all the valuation surveys in those types or specified areas. Sometimes the height of each tree is estimated when the diameter is measured. The trees are then recorded by diame- ters and by height classes, the tally-sheet being specially ruled like the followino: form: White Pine. Diameter, Breast-high Inches. Height Classes. 20-30 30-40 40-50 50-60 The volumes are computed by using a volume table for trees of different heights and diameters. 222 FOREST MENSURATION. Instead of grouping the trees by diameters and heights, it is possible to group them by diameters and merchantable lengths. The application of this method is almost exactly like that just described. The diameters are first measured, and then the average merchantable lengths of trees of all diameters deter- mined from the measurement of a few trees and interpolation by a curve; or the merchantable length of each tree is estimated when the diameter is taken. In the last case the measurements are recorded on a tally-sheet ruled hke the following : White Pine. eter, Breast- high, Merchantable Length in Feet. Inches. 10 13 14 16 18 20 34 38 33 36 40 The volume table, like that described on page 164, is used to compute the contents of the stand. If volume tables based on diameters and number of logs are used in computing the contents of timber on the valuation areas, the field work must include the determination of the num- ber of logs as well as the diameters of the trees. The simplest way is first to measure the diameters as ordinarily and estimate the average number of logs in a few representative trees of differ- ent sizes, and then by interpolation estimate the number of logs in trees of any desired diameter, just as (exj)lained on page 220) is done with heights. Usually it is sufficient to determine the average number of logs for separate forest types on specified portions of a tract and use this average for all plots wiiliin that type or area. Knowing the number of trees of cacli cHamctcr and the average number of logs in each tree, the volume of an acre may easily be calculated from the volume table. DETERMINATION OF THE CONTENTS OF STANDS. 223 If specially accurate results are required, the calipermen give not only the diameter and species, but also the number of logs of each tree. The tally-sheet is ruled in the following way for the record of the measurements: Diameter. Breast-high, Inches. White Pine. One-log Trees. Two-log Trees. Three-log Trees. Four-log Trees. Hemlock. One-log Trees. Two-log Trees. Etc. The volume table may then be used to compute the contents of the valuation survey. Some investigations require a separation of the trees into special classes. Thus in some of the valuation survey work by the Government the dominant, intermediate, and suppressed trees have been recorded separately. With second-growth hard- woods it is often desirable to separate the trees into three or more classes, which are usually based on crown develop- ment. In such cases the volume of the trees calipered, is determined by using a volume table which shows the contents of trees of different diameters and tree classes, (See page 164.) The field data are recorded on a tally-sheet ruled like the follow- ing: Diameter. Breast- White Oak. Chestnut. high, Inches. Class I. Class II. Class III. Class IV. Class V. Class I. Class 11. Etc. It may happen that the volume is desired, not in cubic feet or board feet alone, but in special products. Thus it may be desired to note the number of poles, ties, posts, or mine timbers 224 FOREST MENSURATION. of certain dimensions. In this case a special ruling of the tally- sheet must be made. Sometimes merely the number of poles is indicated; at other times the diameter of the tree which yields I tie, 2 ties, 3 ties, etc., is shown. In work in second-growth hardwood forests where the computation of the cord-wood left after taking out the ties is desired, it is necessary to note the diameter of the trees as well as the number of ties. A form like the following mav be used: Diameter, Chestnut. high. Inches. One Log. Two Logs. Three Logs. Pole. One Tie. Two Ties. Three Ties. Cord- wood. The total amount of cord-wood is determined from volume tables which show the contents, in cords, of trees of ditTerent sizes and which show also the cord-wood left after taking from trees of different sizes a pole or a specified number of logs or ties. 126. Determination of Volume of Stands by the Use of Felled Sample Trees. — The volume of the trees on a given sample plot may be determined by the use of volume tables in the way described above. But if no reliable volume tables exist, or if ver}- accu- rate results arc required, it is necessary to fell and measure a certain number of sample trees and from them calculate the volume of the whole stand. A number of different methods of computing the volume of stands by means of sample trees have been devised. The methods likely to be of special interest to AmiCrican foresters are described in the following pages. 127. The Mean Sample-tree Method. — The princi|)le of this method is to calii)cr the trees on a given \Ao{, then determine the diameter of the average tree, fell and measure test trees hav- ing this average diameter, determine their contents, and from them estimate the contents of the whole stand. DETERMINATION OF THE CONTENTS OF STANDS. 225 As explained later this method is not applicable to the board- foot unit, but to the volume units like the cubic foot and cord. In practical work in the United States it is most used for com- puting the contents of second-growth timber in cubic feet and cords. Determination oj the Diameter oj the Average Tree. — There are several conceptions of the average tree and the ways to deter- mine its dimensions. One way is to determine the arithmetic mean of the diameters represented in the stand. Each diameter is multiplied by the number of trees of that size and the sum of the products divided by the total number of trees in the stand. Expressed algebraically, . ,. d\ni+d-^no + dsns + . . . d^n Average diameter = ^r^: > where di is the smallest diameter measured in inches and «i is the number of trees of that size, d2 is the next inch-diameter and W2 the number of trees, and so on; and A^ is the total num- ber of trees. It has been explained that the principle of the mean sample- tree method is to determine the average tree and then obtain the whole volume of the stand by multiplying this average tree by the total number of trees represented. In other words, the average tree is the tree of an average volume, and if the arith- metic average diameter is determined as just described, it is assumed that the contents of trees vary as their diameters. The contents of trees do not vary as their diameters, but more nearly as the squares of their diameters. The diameter of the average tree is, therefore, more accurately determined by com- puting the average basal area of the stand and from this the corresponding diameter. The average basal area is obtained by the formula bifli + 62»2 + ^3«3 + . . T + bxUx ■ ^ = N ' 2 26 FOREST MENSURATION. in which B is the average basal area, hi, &2j ^3> etc., are the areas of circles of different diameters. If z'l, Vo, Vs, etc., are the volumes, ni, n^, nz, etc., the number of trees, hi, hj, hi, etc., the heights, / , jo, /a, etc., the form factors, and 5,, b^, bs, etc., the basal areas of the trees of different diameters; and v, b, h, j are the volume, basal area, height of the average tree, and A' the number of trees on the given area, then _Vini + v^n^ + vma + . . .+vxnx n' and bJiifxTi, + 62^2/2^2 + Wz3/3n3 + . . .+bxhx}xnx bhj^- N In even -aged stands, provided there is not too great a range of diameters !\j=hiji=h2J2 = hiJ3'=hxlx, and then the above equation becomes 61M! + boJio + bzHs + . . . + bxtix B= ^-^ r- . If there is a ver\' wide range in the diameters of the trees on an area, then the products of the form factor and height in the different diameter classes are not equal, and the volumes do not varj' as the basal areas. la this case the mean sample-tree method is not appHcable. The calculation of the average basal area is simplified by tables which give the product of areas of circles and different numbers-such as are likely to be met in the field. (See page 430.) After calipering the trees on a given plot one uses this table to obtain the product of the area and number of trees of each inch- diameter class, then adding these products divides by the total number of trees. The result is the average basal area, and the corresponding diameter is easily determined from a table of areas of circles. Selection oj Test Trees. — Wlicn the average basal area and the corresponding diameter have been determined, the test trees are selected, felled, and measured. The forester enndeavors to find trees within a half inch of the ideal size. He chooses aver- age trees; that is, those which have an average crown develop- DETERMINATION OF THE CONTENTS OF STANDS. 227 ment and normal trunk form. No rules can be laid down for this selection. The forester judges entirely by the eye after inspecting the stand, which presumably has been done during the calipering. The amateur nearly always selects the best trees of the required diameter. Normal and average do not mean the tallest, straightest, roundest, and fullest bolcd trees. Herein lies the greatest drawback of the method. Inexperienced or careless men are apt to overestimate the stand by selecting abnormally good trees as average. The method is more easily applied and more accurate when trees are even-aged and fairly uniform and the variation in height is not great. Number of Test Trees Required. — This depends on the char- acter of the forest and nature of the investigation. Ordinarily 3 to 5 test trees of a given species are considered sufficient for work in a fairly uniform stand. In an extremely accurate investi- gation this method would not be used at all. Compulation 0} Results. — The volumes of all the test trees are first determined and averaged together. If the basal area of each is exactly the same as the average basal area in the stand, the product of the average volume of the test trees by the total number of trees in the stand gives the total volume. If, how- ever, the basal areas of the test trees are not exactly the same as the average basal area in the stand; the total volume is obtained by the following formula, which corrects the slight error caused by using the volumes of test trees whose basal areas are not exactly equal to the average basal area in the stand: V:v = B:b or F = ^^, in which V is the desired volume of the stand, v is the average volume of the felled test trees, B is the total basal area of the stand, and b the average basal area of the test trees. Problems in which the Method willjbe Used. — This method will be used chiefly in estimating the volume of small timber and uniform stands, Wliere the range of diameters is very 228 FOREST MENSURATION. small it may be used in the preparation of yield tables in cubic feet. It is not accurate in irregular stands where there are large differences in the diameters and tree classes. It is inapplicable to board measure, but in the study of cord-wood it finds a very practical use. In second-growth hardwoods the stands are often relatively even-aged and the difference in diameter of the mercrs-ntable trees of a single species not great. This is par- ticularly true in young stands. In very irregular stands it is necessary to make diameter groups as in the methods described in the succeeding sections. The mean sample-tree method is sho\\Ti in the follo\^'ing computation of 336 spruce trees in the Adirondacks. The trees were growing in a relatively even-aged stand, 100 to 130 years old, of spruce, mixed with scattering fir, birch, and maple. All trees on 14 sample plots were felled and analyzed, and of the total number, 336 were chosen at random for the computation by different methods. The actual contents of the trees, obtained by adding together the volumes computed indindually, are 2150 cubic feet. The mean sample-tree method gives 2197.8 cubic feet. COMPUTATION OF VOLUME OF A SPRUCE STAXD BY THE MEAN SAMPLE-TREE METHOD. Diam- eter, Inches. Number of Trees. Basal Area, Sq. Ft. Average Basal Area, Sq. Ft. Diameter Average Tree, Inches. Diameter Test Trees, Inches. Basal Area Test Trees, Inches. Merchant- able Vol- ume Test Trees, Cu. Ft. 5 6 7 8 9 0 I 12 15 48 77 63 50 38 31 10 3 I 2.040 9.408 20.559 21.987 22. 100 20.710 20.460 7 • 8.50 2.766 1 . 069 ■0.384 8.4 8.S 8.4 8.4 8.5 8.2 0-394 0.385 0.385 0.394 0 . 3<'7 6.90 6.67 6.32 6.98 5-94 13 14 Totals.. . 1.925 32.81 Totals. . . ,T,T,G 128.949 DETERMINATION OF THE CONTENTS OF STANDS. 229 ^•925 If one test tree, and in this case the first in the list, were used, the resu'*" would be 6.9Xi2Q.g49 ^ ,- c 4. V = — — = 2260 cubic feet. 0.394 If the first three trees were used as test trees, the result would be ^^ 19.89X128.949 u- r . ' F= — 7 =220!; cubic feet. 1. 164 In this calculation the volume has been obtained by the formula for the sake of illustration. Usually when the basal area of the test trees are so nearly identical with tiie average basal area of the stand, the formula is not used, but the volume obtained by multiplying the average volume of the test trees bv the number of trees in the stand. In the above example the average volume of the five test trees is 6.56 cubic feet. This multiplied by 336 is .^204. 16. 128. Arbitrary Group Method. — If the trees in a given stand vary considerably in diameter, the mean sample-tree method is inaccurate, because of the difficulty in selecting average test trees in an irregular stand. More accurate results are obtained by grouping the trees into diameter classes and determining separately the volume of each class. The method has the advan- tage of greater accuracy than the preceding, because it enables the determination of the volume of different parts of the stand separately. Thus, for example, the volume of the merchantable trees and of those which are not merchantable may be deter- mined separately. This method may be used to determine the contents of stands in board measure. In the arbitrary group method the sizes of the different diam- eter groups are determined arbitrarily. There is no rule as to the number of inches to be included in .each group and the differ- ent groups do not necessarily contain the same number of inches. 230 FOREST MENSURATION. Usually at least 3 inches are comprised in one group, although sometimes a group of 2 inches is used. Suppose that a second- growth stand of fir is calipered and all trees taken; suppose, also, that trees under 6 inches are salable for cord- wood and that no trees under 10 inches will yield merchantable boards; then the trees under 6 inches are included in the first group, those 6 to 10 inches in the second separate group, and above this each 4 inches are taken as a separate group, unless there are only a few trees of the larger diameters when one wide group of 5 or more inches is made. After fixing the groups, the diam- eter of the average tree in each group is determined exactly as the diameter of the average tree was determined for the whole stand in the preceding method. The principle of selection of the test trees is the same as in the preceding method, namely, to find trees of the required diameters, each having an average form and average height of its class. A good way is to select for inspection a number of trees of the desired diameter and compare their height and form and then from these make the final selection for felling. Frequently satisfactory test trees of the desired diameters cannot be found on the sample plot under examination. In this case one may use test trees which are growing just off the plot provided the conditions of growth are the same as on the plot. A good test tree off the plot is better than a poor one on the plot. Test trees cannot be selected offhand. The writer has seen young foresters choose as average trees, and as rep- resentatives of the same class, specimens which proved to differ in volume 20 percent. A careful scrutiny and comparison of the trees before felling would have shown the dilTcrcnce and prevented a bad selection. Ordinarily three trees of each diameter group are considered enough even where very accurate results are required. In many investigations one tree for each group is suflicient. If the data are for the study of volume growth and for yield tables, the forester should cut, when possible, three trees for each group of over DETERMINATION OF THE CONTENTS OF STANDS. 231 20 trees, 2 for groups containing 10 to 20 trees, and i tree for groups of less than 10 trees. When the trees have been measured and later in the office the volumes ascertained, the contents of the whole stand are determined. The volume of each diameter group is computed separately and then the results added together for the total volume of the stand. In most work, as when the board-foot unit is used, the aver- age volume of the test trees is multiplied by the number of trees in the group. In exact work with cubic feet the formula described in section 127 is used, viz., V:v = B:b, in which F and B are the volume and area of the group and v and b are the average volume and area of the test trees. COMPUTATION OF VOLUME OF A SPRUCE STAND BY THE ARBITRARY GROUP METHOD. a ^ s 1 <« m 2i^ kl ■ S • H 3 . > £1 . Lh <,S . 2 V . S-C <^fe i volume of the stand exactly like the volume tables explained in section 125. The advantages of the volume-curve method are: that it enables the computation of the volume of trees of each diam- eter separately and may, therefore, be correctly used with board measure; that field work is simple and rapid, no computing work in the woods being necessary; and that it is very accurate because each volume used in the computation depends on the values of all the test trees and hence any abnormal values are corrected, which is not the case in the arbitrary group and simi- lar methods. COMPUTATION OF THE VOLUME OF A SPRUCE STAND BY THE VOLUME-CURVE METHOD. Diameter, Inches. Number of Trees. Diameter of Test Trees, Inches. Volume of Test Trees, Cu. Ft. Volume from Curve, Cu. Ft. Volume of all Trees, Cu. Ft. 5 6 7 8 9 10 11 1 2 15 48 77 63 50 38 31 10 3 I I .2 2. I 3-7 5-8 8.0 10.,^ 12.6 14.9 17.3 19.8 Total 18 0 6.4 2.4 100.8 284.9 365 . 4 400.0 390.4 390 . 6 149.0 51 9 19.8 8.1 9-3 10.7 1 1. 5 6.4 8.57 12.47 12.86 13 '4 2170.8 130. The Draudt Method. — This method is often used in Europe in work requiring an accurate determination of the con- tents of stands. It is applicable only ^o research work where it is possible and desirable to fell a large number of test trees. It is used only with cubic measure. In this method the number of test trees in each diameter class bears a constant ratio to the total number of trees in the class. Thus if it is decided that the number of test trees in a plot be 10 percent of the total number of trees standing on the 2 34 FOREST MENSURATION. plot, the number of test trees in a given diameter class is lo per- cent of the number of trees in that class. In theory the volume of all the test trees multiplied by the quotient of the total num- ber of trees in the stand by the number of test trees gives the total volume of the stand; that is, if lo percent of the indi- viduals in a stand are felled and these felled trees are propor- tionately distributed among the different sizes, their total volume will be one-tenth of the volume of the stand. When, however, one attempts to determine the number of test trees of a single diameter or diameter class, it is very rare that the result will be a whole number, but is usually a fraction. If, for example, there are twenty-two trees in a group, lo percent of them is. two trees and two-tenths. If two trees are cut, their contents cannot represent the yield of two and two-tenths trees, but only of two trees. In practice the numbers are rounded off to whole trees, all fractions up to 0.5 being disregarded. It may happen then that several of the diameters have no representative test trees whatever. In this case it is sometimes customary to group together two or more diameters which have few trees repre- sented, and to assign one test tree to the group. This rounding off of the figures disturbs the perfect distribu- tion of the test trees, and in this case the sum of the volumes of the test trees does not represent one-tenth the total volume of the stand. The total volume is, therefore, not determined by the formula V:v = N\n, but by the formula V.v = B:h, in which V is the total volume of the stand, v the sum of the volumes of the test trees, B the basal area of the stand, and b the sum of Jhe basal areas of the test trees. In practice the trees are calipered as usual, tlic j^ercentagc of the total number to be felled as test trees fixed upon, and the tally of calipering arranged as shown on page 237. The diameters are entered in the first column; the number of trees, in the second column; the basal areas of the trees, in tlie tliird column; in the fourth column, the product of the number of the trees by the percentage factor for determining ihc number DETERMmATION OF THE CONTENTS OF STANDS. ^35 of test trees; and in the fifth column, the values of the fourth colrmn lounded off to whole numbers. Column five is then inspected to see that the total number of trees is the correct percentage of the whole number on the plot. It often hap- pens that in rounding off the figures in column five, the total number of trees is too large or too small. Exactly this thing occurred in the computation shown on page 237. A total of 12 instead of 13 trees, was obtained. Therefore 2.5 (column 3) opposite 8 inches was called 3 and 1.5 opposite 10 inches was called I. Test trees are then selected, and felled, and measured for volume. After computing the volumes of the test trees, the data obtained are entered in the form described above, the basal areas in the sixth, and volumes in the seventh columns. After adding the columns for totals, the volume of the stand is obtained by the formula V:v = B:h. It may be desirable to use an arbitrary number of test trees rather than a specified percentage of the number of trees as test trees. Suppose, for example, that it is desired to cut 1 5 trees. If N is the total number of trees in the stand and w, Uy, ^2, etc., the number of trees of each diameter, the number of test trees for any specified diameter x is — v~^' '^^^^ trees are arranged in a form similar to that shown on page 237. In column 4 is entered for each diameter the value of the expression ^- As in the other case fractions will result. These fractions are rounded off to whole numbers in column 5, A larger number of diameters may be left without representation than in the other method. If among the larger or smaller diameters a considerable number are left without test trees, one or more groups are made to bring the total number of test trees up to 15. The method from this point is carried out exactly as before. Another modification of Draudt's method is to make diam- eter groups on the same principle as in the arbitrary group method. 236 FOkBST MENSUk/iriON. The diameter of the average tree is then determined for each group. The number of test trees is decided upon as a specified number or as a certain percentage of the total number in the stand and apportioned to the diameter groups. If 10 percpnt" is chosen the number of test trees for each group is 10 percen of the total number of trees in that group. The required num- ber of test trees for a given group are then felled, all of the same diameter as the average tree of the group. The method is carried through from this point exactly like the arbitrar}^ group method. The only difference between this and the arbitrar}' group method is in the determination of the number of test trees for the different groups. The Prussian Forest Experiment Station has adopted the following rule for making diameter groups: Four classes of 100 trees each are made of the 400 largest trees in a specified hectare plot; three classes of 200 each of the 600 next largest trees and if any trees remain they are grouped into classes of 400 each. As the Draudt method is applied, all the material may be worked up together. When cord measure is used this is a great advantage, because it is impractical to make stacks where each test tree has to be kept separate. On the other hand, the method is very slow and laborious, involving a large amount of work on paper in the field and the felling of many test trees. The gain in accuracy is not sufficient to counter- balance this objection. The use of diameter groups simpli- fies the method and brings it within the range of most investi- gators. 131. The Urich Method. — The ])rinciple of this metiicd is to divide the trees in a stand into a s])ecificd number of diam- eter groups, so arranged that each group contains the same num- ber of trees. The test trees arc then equally divided among thi different diameter groups. By tliis plan test trees are dis- tributed in correct proportion to different parts of the stand, whereas in the arbitrary group method a diameter group com- DETERMIN/iTION OF THE CONTENTS OF STANDS. 237 prising 20 trees often has as many test trees as one comprising 80 trees. COMPUTATION OF THE VOLUME OF A SPRUCE STAND BY THE DRAUDT METHOD. Diamete'', Incnes. Number of Trees. Basal Area, Sq. Ft. Percent. [ = 4%] Multiplied by Number of Trees. Number Rounded to Whole Trees. Basal Area Test Trees. Sq. Ft. Volume Test Trees, Cu. Ft. 5 15 2040 0.6 I 0.147 1-57 6 48 9408 1-9 2 0.419 4 66 7 77 20559 31 3 0.850 13 45 8 63 21987 2.5 3 I . I 19 19 47 9 50. 22100 2.0 2 0.875 17 0 10 38 20710 1-5 I 0.579 9 97 11 31 20460 1 .2 I 0.625 12 47 12 10 7850 0.4 0 13 3 2766 0.1 0 14 I 1069 0.04 0 Totals .... 336 1 28949 13 4.614 78 =;q 78.59X128.949 ^ r = -^—-: ^^ = 2 196.4. 4.614 After the cahpering is completed, the total number of trees is first determined, and by inspection of the tally-sheet the necessar}^ number of diameter groups fixed upon. The total number of trees in the stand divided by the number of groups gives the number of trees to be included in each diameter group. If the total number of trees is not exactly divisible by the num- ber of groups it is necessary to assign one or two more trees to some groups than to others. The tally record is then transferred to a new sheet. Beginning with the smallest trees, the diameters and number of trees are entered as ordinarily, except that some inch classes are split in order to include in each group the correct number of trees. In the example given on page 237, it was necessary to split diameter inch class 7,^and to include 49 trees of this size in the first part and 28 trees in the second part. The inch class 9 is split in the same way. After arranging the 238 FOREST MENSURATION. diameter groups, the diameter of the average tree of each group is ascertained. A specified number of test trees for each group is then selected for felling and measurement. From this point on the computation is exactly the same as in the arbitrary group method. This method is ver\' accurate and has practically replaced Draudt's method in much of the scientific work in Europe. It has nearly all the advantages of Draudt's method and is much simpler and more rapid. In practice 3 to 5 classes are usually made. The German Association of Forest Experiment Stations prescribes for yield- table studies a division of the stands in 5 groups and for each group 5 test trees. When extremely accurate results are required, 7 classes are sometimes made. For work in this countr}' a good rule is to use such a number of groups that a single group among COMPUTATION OF THE VOLUME OF A SPRUCE STAND BY THE URICH METHOD. Diam- eter, Inches. Num- ber of Trees. Total Num- ber of Trees. Basal Area. Sq.Ft. Total Basal Area, Sq. Ft. Aver- age Basal Area, Sq. Ft. Diam- eter Aver- age Tree. Inches. Diam- eter Test Trees, Inches. Basal Area Test Trees, Sq. Ft. Vol- ume Test Trees, Inches. 5 6 7 15 48 49 112 2040 9408 13083 24531 0. 219 0.34: 0.586 6.3 7-9 10.4 6.2 6.4 8. I 8.0 10.3 10.2 0.2IC 0. 223 0.376 0.349 0.567 0.579 2 ■ 304 2.47 2.43 7 8 9 28 63 21 1 12 7476 21987 9282 38745 6.74 6.84 9 10 II 12 13 14 29 38 31 10 3 I 1X2 12818 20710 20460 7850 2766 1069 65673 9.62 II . 10 Totals. . 336 128949 39.20 30-2 y 1 28.949 2.304 -=2194 cubic feet. DETERMINATION OF THE CONTENTS OF ST/fNDS. 239 the diameters best represented will not include over 4 inches. Ordinarily 3 test trees for each group is sufficient for the studies made under our present conditions, except in the work of per- manent sample plots, when at least 5 test trees should be measured. The advantages of Urich's method are that it is very accurate, because the test trees are proportionately distributed among the different diameters, and it permits of a separation of the classes of timber, as in the arbitrary group method. The chief disadvantage is that a transfer of the field data to a new sheet and considerable other computation are necessary in the field before the test trees can be felled. A modification of the method, also proposed by Urich, is to arrange the groups so that the most trees are included in the medium-sized diameter groups, to which a proportionately larger number of test trees are allotted. Suppose, for example, that there are 250 trees on the plot; that 10 test trees are to be felled, and an inspection of the tally record shows that the smallest number of trees are among the small diameters, and that the largest diameters are also poorly represented, though better than the smallest trees. Suppose, further, that four diameter classes are to be formed. Then the trees would be distributed in the diflferent classes in the ratio 2:3:3:2. Since the total number of trees is 250, then 25o-^ 10 = 25, ^^d th^ number of trees in each group would be 50:75:75:50. The advantage of this plan is that the most important trees are grouped together and the less important are kept in separate groups. Another slight modification of the method proposed by Urich is the following. After calipering the trees and arranging them in groups contain- ing the same number of trees, the average diameter is estimated by inspec- tion of the tally record; a uniform number of test trees are cut in each group, and from their volumes the total volume of the stand is calculated by the formula ^ , , Volume of all test trees X total number of trees lotal volume = — ; ;: . Number of test trees Tests of this modification of Urich's method have shown a very high degree of accuracy when the number of diameter groups is large; that is, when the diameter range of each group is so small that the average tree may be easily estimated. ^ The object of the method is to save the time required to calculate by 240 FOREST MENSUR/ITION. basal areas the diameter of the average tree in each group. This saving of time is, however, extremely small, not over fifteen minutes on each plot. It seems to the author to be inconsistent to use an elaborate method of arrange - ing the classes and a loose method of calculating the diameters of the sample trees. 132. Hartig's Method. — In this method the trees on a sample plcL are arranged in such a way that all diameter groups have equal total basal areas. An equal number of test trees are then assigned to each diameter group. The method is designed to make diameter groups in which the volumes are about equal. In the other methods the total volumes of the groups differ widely. By the Hartig method the volumes are brought nearer together, but still are not always equal, because the heights of the trees in the separate classes are usually different. After the trees have been calipered, the tally record is examined to determine the number of groups to be formed. The data are entered from the tally record upon a new sheet. The total basal area of the whole stand is determined and divided by the number of diameter groups. The result of this division represents approximately the basal area which each diameter group should have. In forming the diameter groups one begins with the smallest diameters and adds together the corresponding basal areas until the sum is approximately the same as the quotient of the total basal areas by the number of classes. It is usually necessary to split certain diameters in order to approach this figure, just as it was necessary to s])lil diameters in Urich's method. A specified number of trees of each group are then selected for felling and the computation of final results is carried out as in the arbitrary group method. XZZ- Block's Method. — This method is peculiar only in the manner of forming the diameter groups. After calipcring, the trees are arranged in diameter groups, usually of 50 trees each, beginning with the largest. The last group may contain less than 50 trees. If there arc over 500 trees on the plot, classes of 100 trees each arc made. The average diameter of each group is then computed and at least one test tree cut for each. DETERMINATION OF THE CONTENTS OF STANDS. 241 134. Method of. Forest Form Factor.— The total volume of a stand in cubic feet may be obtained from the product of the total basal area of all the trees, the average height of the stand and an average form factor, called the forest form factor. The forest form factor is calculated by the formula BH' in vi^hich V is the volume, B the total basal area, and H the average height of the stand. With such tables in hand, the contents of a sample plot may be readily obtained in the following way: First caliper the trees to ascertain the total basal area, then measure (with height measure) or estimate the average height, and then multiply the product of the total basal area and average height by the average form factor, shown in the table, for the given species and character of forest. One way to determine the forest form factor is to use the average of the form factors of the individual test trees. Since the form factor is an expression of volume, the form factor of the average tree of the stand is approximately the forest form factor. If, therefore, forest form factors are not available, the average tree of a stand is determined; representatives are felled and their form factors computed, averaged, and used as the forest form factor to calculate total volume of the stand. Instead of felling test trees, the form factor of the average tree, taken from a form- factor table, is sometimes used as a forest form factor This is, however really another form of the mean sample-tree method. Studies in Europe have shown that the average tree — that is, the tree having an average volume, form factor, and height — in an even-aged stand is so related to the others that 60% are smaller and 40% are larger. To find the diameter of the average tree, therefore, one may count off 40% o\ the trees in the tally record beginning with the largest. This average tree is used as described in the two previous paragraphs. A modification of the method just described is that involving the use of the form height. In section 98 it was explained that the expression form height refers to the product of the form factor and height of a tree. The forest form height of a stand may be found by multiplymg the forest form factor by the average height of the stand. In Europe average form-height tables are often constructed. With such tables at hand the volume of the trees on a plot is computed as follows: The total basal area is determined by calipering; the average height of the stand is then determined with a height measure or by estimate; and the total volume of the stand is obtained by multiplying the total basal area by the form height given in the table corresponding to the average height of the stand. 135. Metzger's Method. — This method is sometimes used in Denmark 5or estimating timber. It is applicable to stands which are even-aged or nearly 242 FOREST MENSURATION. so, mature or nearly mature, and which have been properly thinned; in other words, to timber tracts of even-aged stands which have been under forest management. Such forests occur abundantly in Europe, but the method cannot be used for estimating in this country' because of the irreg- ularity of our stands. Applied to the spruce stand mentioned with the pre- ceding methods, a total volume of 2506 cubic feet was obtained, or 17% too much. Briefly the method is to take a block of forest (not necessarily a sample plot, but any specified area) and count the trees. As the trees are enumerated the forester keeps in mind the general run of their sizes, but does not measure them. After counting, the forester, who from his observation knows about how the sizes run, selects for felling and measure- ment of volume three of the largest and seven of the smallest trees. The volume of the stand is then obtained by the following formula: ,, vol. ? max. + vol. 7 min. V=NX ' . 10 In other words, the volume of the stand is equal to the total number of trees multiplied by one-tenth the sum of the volume of three ma.ximum and seven minimum test trees. 136. Method of Absolute Form Factor. — The principle of this method is to determine separately the contents of the portions of the trees above breast-height and then add the contents of the portions between this point and the stump. In the first part of the computation breast-height is con- sidered the base of all trees just as if a plane were passed through the stand at that point and as if the butts of the trees below this imaginary plane did not exist. After the contents of the trees above breast height have been ascertained, the contents of the butts are computed and added to the first result for the total volume of the stand. The volume above breast-height is obtained by an average absolute form factor in the following way: If V is the volume, // the height of the average tree above breast- height, and B the basal area, the absolute form factor of the upper portion of the tree is obtained from the formula V = FBH or P = ^- The total volume of a stand (above breast-height) may be obtained by multiplying the product of the total basal area and the average height (above breast-height) by the average absolute form factor as defined above. The jjorlion of the average tree below breast-height is treated as a cylin- der. If its length is designated as S, then its volume is tlu- product of 6' and B. DETERMINATION OF THE CONTENTS OF STANDS. 243 In computing the volume of a stand it is assumed that the average value of S is equal to that of the average tree or the average of the test trees. Knowing the average value S, the volume below breast height of the stand is found from the formula V = BXS, in which V is the total volume below breast-height. If no studies of absolute form factors have been made and hence no tables of average values are available, the method is applied in the following way: The trees on a given plot are calipered in the ordinary manner, then test trees are selected by one of the methods described in the preceding sec- tions. For simplicity, stippose that the mean sample-tree method is used. After obtaining the diameter of the average tree, 3 to 5 test trees are selected, felled, and measured for volume. By averaging together the measurements of the test trees, one obtains an average value of the height above breast-height [H), the absolute form factor (F), and the distance between the stump and breast-height (5). The total volume of the stand then is obtained from the formula V = {BXFXH) + {BXS), in which B is the total basal area of the stand. If branch wood is to be included in the computation it is reckoned as a certain percentage of the total volume. This percentage is obtained from the study of the test trees. The method as described above has no special advantages over several other methods. Its chief value lies in its application to estimating. Numer- ous tests of the method in Europe in second -growth hardwoods have shown that the average absolute form factor usually lies between 0.4 and 0.5, and in a normal stand is about 0.45. If after a practical study of absolute form factors in a specified forest region the average of a given species lies within certain definite limits, as 0.4 and 0.5, and is most often a certain number, say 0.45, one can soon train his eye so that he can tell by an inspection of standing timber approximately what the absolute form factor will average. As soon as a forester becomes suflficiently expert to estimate the absolute form factor, the cutting of test trees may be dispensed with. The trees are calipered to obtain the total basal area B, then the average height above breast-height H and the average value of S are estimated, and the total contents of the stand computed by the formula given above. This method is specially applicable to the measurement of cord-wood. It has already been used in this country in a few instances. CHAPTER XV. DETERMINATION OF THE AGE OF TREES AND STANDS. 137. The Age of Felled Trees. — A tree increases in diameter by the formation of a new layer of wood each year between the old wood and the bark. These annual layers of wood make the concentric rings seen on stumps and ends of logs. The number of rings on the cross-section of a tree indicates the age of the tree at that point. To find the correct age of a tree the rings must be counted at the ground. The number of rings at a cross- cut, made at some distance above the ground, as, for instance, at the top of a sawlog, would show only the number of years re- quired by the tree to grow above that point, for the reason that the tree cannot begin to form rings at any point until it has grown up to it. Therefore the number of rings on the stump of a tree usually does not represent its correct age, because most forest trees require several years to grow up to the stump-height. In many cases it is difficult to determine with certainty the cor- rect age by counting the rings at the ground because the growth of the seedling is small and the first few annual rings are very difficult to distinguish on an old tree. The increased accuracy resulting from cutting trees at the ground docs not pay for the expense and trouble involved. For many purposes the age at the stump is considered close enougli, but in most scientific studies a greater degree of accuracy is refjuired. In such work the rings are counted on the stunij), and to this figure is added the average number of years required 244 DETERMIN/ITION OF THE AGE OF TREES AND STANDS. 245 by the species in question to grow to the height of the stump. This extra number of years is estimated or is obtained from a study of small seedlings. To ascertain the average height growth of small seedlings, a large number are cut at the ground and their rings are counted; and from these figures a table is constructed showing the average age of seedlings of different heights, like the folio wing: Age, Height of 3 I 6 2 12 3 18 4 24 5 Suppose, for example, that a tree with a two-foot stump is cut, its age would be found by adding five years to the age shown by the rings at the stump, since the above table shows that five years is the average period required for a tree of the species to grow two feet above the ground. It is often difficult to count accurately the annual rings on a stump or other cross-cut. In some species, as, for example, the maples and beech, the rings are not distinct from each other. Again, when the growth has been slow, the rings are very narrow and difficult to distinguish and count. Sometimes when the growth is interrupted early in the year, on account of a drought or for some other cause, and later on during the same season new leaves are put forth, a second or false ring is formed. As a rule, however, the dividing marks between two growths of a single season are not so distinct as between the growths of sepa- rate seasons, and the careful observer can detect the so-called false rings. \Vlien the rings are not easily distinguished from each other a perfectly smooth surface should be made with a knife or axe; a chisel may also be used. If then the- rings cannot be readily distinguished and counted, a lens is used. A little fine dirt 246 FOREST MENSURATION rubbed on the cut makes the rings somewhat more distinct. Care should be taken not to count the inside layer of bark, which sometimes has the appearance of a layer of wood. 138. Estimate of the Age of Standing Trees. — The exact age of a standing tree cannot be determined with certainty unless there is a record showing when it was planted. It is often possible to estimate the age of standing trees near enough for the purpose of general forest description, in cases where it is not practical to fell any trees. One method of estimating the age of a tree is to count the whorls of branches. This can be done only with the conifers and with relatively young trees. ]\Iany conifers form each year at the base of the new leader a distinct whorl of branches which marks clearly the annual growth in height for the year. These whorls, or traces of them, may be distinguished in trees growing in the open or in open stands, often to the sixtieth or eightieth year. In forest-grown trees the branch stubs are apt to be overgrown before that time. White pine, spruce, fir, and other conifers having persistent branches show the traces of the annual shoots the longest. Very intolerant trees like the yellov*- pines and larch soon lose all traces of the branch whorls. If traces of the branch whorls can be found from the ground upwards, the age of a tree may be estimated with a fair degree of accuracy. In estimating age by whorls it is necessary to make a full allowance for the age of the seedling when no branches were formed of sufficient size to show in later years. Another way to estimate the age of standing trees is by using the Pressler borer. This instrument, shown in Fig. 45, con- sists of three parts: (a) A hollow augur. A, about four inches long, tapering and threaded at one end, and square in cross-section at the other end. (b) A hollow metal handle, B, with a square opening in the center into which the augur fits when in use. At the ends of this handle are detachable caps. DETERMINATION OF THE AGE OF TREES AND STANDS. 247 (c) A narrow wedge, C, furnished at one end with a flat head, and incised on one side at the other end. The wedge and the augur are carried inside the hollow handle when the instrument is not in use. To use the instrument one bores into a tree to a depth of 2 to 3 inches, then inserts the wedge through the augur with the incised side turned inward. The wedge is jammed down, thus / AA/VAA^^VviZ Fig. 45. — Pressler's Increment Borer. holding tightly in place the core of wood within the augur. The handle is then turned sharply to the left, severing the core from the wood. The cylinder of wood is then drawn out, and the rings counted or measured. To determine the age one bores into a tree to the heart at breast-height, counts on the extractcdtore the number of rings, and then adds the probable age from the ground to breast-height. 248 FOREST MEhSURATION. Inasmuch as it is practical to make a boring of only about 3 inches, the method is not applicable to trees over 6 inches in diameter at breast-height. The author has used the instrument satisfactorily in investigations in second-growth forests. The practiced forester can estimate in general terms the age of a tree simply by inspection. He can estimate trees under 100 years of age within 20 years and above this age to within 50 years. Many external signs indicate age to one vrho has studied the age of felled trees. The size of the tree under a specified condition of growth, the form of the cro\\Ti, the shape of the bole, and the texture and color of the bark indicate to the prac- ticed eye the approximate age. 139. The Age of Tropical Trees. — It is impossible to deter- mine the age of trees in those portions of the tropics which do not have a marked annual change of season such as is occasioned by dryness. Trees growing in the Philippines, for example, may show concentric rings, but these do not mark annual growth ; and usually it is impossible to distinguish the rings clearly. The forester is obliged to use studies of growth which already have been made and estimates the age from the probable mean annual growth of the tree. If the investigations show that the average mean annual growth of a specified species is one inch in four years, the age of a tree 40 inches in diameter is called 160 years. As shown later, the growth of tropical trees which do not shov.' annual rings must be studied by taking periodically measure- ments of the diameter of selected standing trees. 140. Determination of the Age of Stands. — By the age of a stand IS meant its average age. The average age of a stand has no practical value if there is a very wide dilTercnce between the age of the youngest and the oldest trees. In an all-aged stand (selection forest) it is customary to describe the range of ages and the representation of the different ages. Thus a northern virgin hardwood forest might be described as having an age range from young seedlings to 150-year-old veterans, willi 7o'~(- over 100 and the remainder under 50 years old, the intermediate DETERMINATION OF THE AGE OF TREES AND STANDS. 249 ages lacking. If there is considerable variation in age in a given stand, but it is not all-aged, the age range and the general average age are estimated. The age of such a stand is expressed by a fraction, in which the range of age is in the numerator and the 60 — 100 average age in the denominator. Thus, for example, — years means that there is a range of 60-100 years in age and the average age is about 70 years. If a stand is exactly even- aged or nearly so, the average age is often determined with care, as, for example, in making yield tables. Strictly speaking, an even-aged stand is one which has been established in a specified year. The term is, however, not used very strictly and a stand which does not show wide differences in age in the main crop is called even-aged. The age of such a stand is the average age of the principal crop. If an occasional old specimen of advance growth occurs, it is disregarded in con- sidering the age. Again, if small specimens of a tolerant species occur under the mam crop, they are disregarded or considered by themselves. It is nearly always possible to determine by inspection whether a stand is exactly even-aged or not. If it is obviously even-aged, like a plantation, the age is found by cutting down one tree of average size. It is much better to cut a tree of average size than a small one, because on small trees the rings are apt to be very close together, leading to mistakes. Frequently on sup- pressed trees which are dying the growth of the last few years is not represented at all at the base. It is best not to judge the age of a stand from a large tree because it may have been advance growth and hence would be a few years older than the prevailing crop. Ordinarily it is best to determine the age of several average trees, rather than only one, even when the stand appears very even-aged. ' It often happens that exact records exist when a given stand was established. Of course it is then unnecessary to fell any trees'for an age study. Nearly all so-called even-aged forests in this country are 2 50 FOREST MENSURATION. only approximately even-aged because they have originated from natural reproduction. The period of reproduction on an opening is usually lo to 30 years, or even more, resulting in rather uneven-aged stands. A stand having a range in age of even 20 or 30 years forms a fairly even crown canopy when it reaches middle age — that is, 40 to 60 years — and is classed as an approximately even-aged stand. Such stands are used in con- structing normal and empirical yield tables and their average age exactly determined. The German conception of the average age of stands which are not strictly even-aged is that age which would be necessary to produce an even-aged stand of the same volume as that of the uneven-aged stand in question. There are several ways of obtaining the average age of approximately, but not exactly, even- aged stands. Ordinarily when an average age is desired it is in connection with a sample plot where test trees are cut for volume computation. If the mean sample-tree method is used, the average of the ages of the test trees is considered the average age of the stand. This method is sufficiently accurate for any in- vestigation which permits the use of the mean sample-tree method for the computation of volume. When a method of diameter groups with the felUng of test trees is used, the simplest though not the most accurate method of ascertaining the average age is to take the average age of all test trees. The only objection to this plan is that in a method like the arbitrary group method diameter groups having a small volume are given relatively as much weight in the average of age as those with a larger volume and therefore the condition of the definition of average age given above is not carried out. To overcome this difficulty the following formula has been suggested: nXa-\-n\ Xai -f ^2X^2+ . . . Age = -^ . in which w, Wi, W2, etc., are the numlxT of trees, a, a^, Oo, etc, the average age of the test trees in the diameter grouj)s, and N is DETERMINATION OF THE AGE OF TREES AND STANDS. 25 1 the total number of trees. But even by this plan an average age is not obtained which satisfies the requirements of the definition on page 250. This represents an arithmetic rather than a geo- metric average age. If there were in a stand a very large num- ber of small trees which do not contribute largely to the volume and which are correspondingly younger than the larger diam- £ter classes, the average age calculated by the above method ivould show the stand to have reached the present volume in too short a time. The most exact results would be obtained by a geometric formula based on volume. The volume method (so-called Sjialian method) is based on the principle that the true aver- ag-j age of a stand is found by dividing the total volume by the mc5.n annual growth, in which A is the average age required, V the total volume, and M the mean annual growth. If a stand has been calipered and the trees divided into diameter classes, test trees felled, and so on, the mean annual growth of each diameter group is the volume of the group divided by the average age (the average of the ages of the test trees). The age of the stand may be obtained by the forij^ula 4 = V Vi Vo V3 - + -4-- + - + a ai a2 (I3 in which v, Vi, V2, Vs, etc., are the volumes and a, Oi, ao, 03, etc., are the ages of the diameter groups. Theoretically this formula gives the most accurate results of all the methods. The objection usually made to it is that it is clumsy and time-consuming. This is not a proper objec- tion because it is designed only for vc-fy accurate investigations such as the preparation of \i<:ld t*ibles. 252 FOREST MENSURATION. Another geometric method is by the basal-area formula ba + biOi +^2^2+ • ■ • A = B in which A is the age, h, hi, &2 are the basal areas of the diameter groups, o, Qi, 0-2 the ages of the diameter groups, and B the total basal area of the stand. This method is theoretically correct if the form heights of the diameter groups are equal. The method has no particular advantage over the previous, because neither would be used except where sample plots are taken and the volume of the separate diameter groups is to be calculated. 141. Economic Age. — This cenception of age was used by T. Lorcy with the silver fir, because silver fir usually starts under very unfavorable circumstances and is often suppressed for many years.* At the center of the stem there is, then, usually a small cylinder of very hard wood where the growth is extremely small. The total age of a tree does not at all represent its possibihty for growth, because a number of years were passed in deep shade. As soon as released, the tree shoots ahead and makes a rapid growth. The economic age of such a tree is not repre- sented by the total number of years from the seed, but by the number of years after its release from suppression plus the average period of suppression in the forest under examination. To ascertain the number of years to be added, a separate study is made, involving the analysis of a large number of trees and the determination of the period of suppression of each. Then a table of the following form is constructed showing the average number of rings in central cores of suppression of difi'erent diameters: Diameter of Average Core. Age. * Ertragstafcln fiir die ^\'eisstannc, liy T. I.orcy, 'luhiiigcn, 1SS4. DETERMINATION OF THE AGE OF TREES AND STANDS. 253 To obtain the economic age of a given tree, the rings are counted outside its central core of suppression, the diameter of the core is measured, and from the table the number of years corresponding to this diameter is taken and added to the age after suppression. Suppose, for example, that the diameter of the core of sup- pression of a given tree is 2 centimeters, the number of rings out- side the core 70, and the number of rings inside the core 25; and that the table shows for a core 2 centimeters in diameter an average age of 14 years. The economic age of the tree is, then, 70 + 14 or 84 years, and not 70 + 25 or 95 years. CHAPTER XVI. THE GROWTH OF TREES AND STANDS. 142. Different Kinds of Growth. — In forest mensuration it is customary to distinguish between the growth of trees in diameter, sectional area, height, and volume. The increase in volume of a tree or stand is technically called increment; the increase in diameter, sectional area, and height is called accretion. Some authors use the expressions diameter increment, height incre- ment, volume increment, etc. In practice, however, foresters use the term growth instead of increment or accretion, as diameter growth, height growth, etc. Diameter growth is determined for single trees. Growth in volume and sectional area is studied for stands as well as for single trees. Studies of height growth are made for single trees, and for stands provided they are even-aged or nearly so. Quality growth or increment is the increase in value per unit of volume as applied to a single tree or stand. Price growth or increment is that resulting from an increase in the price of forest products independent of quality growth or increment. Forest mensuration is not concerned with the growth of trees and stands in weight, by which is meant the increase in pon- derable substance measured in pounds or other unit of weight. This subject belongs rather to forest technology. The growth of a tree or stand may further be distinguished as: Current Annual Growth, or the growth of a specific year. 254 THE CROIVTH OF TREES AND STANDS. 255 Periodic Growth, or the growth during a specified period of years. Mean Annual Growth, which is obtained by dividing the total growth during the life of the tree by its age. Periodic Annual Growth, which is obtained by dividing the growth during a specified period by the number of years in that period. Some German authors use the term total growth, referring to the total product of growth from the seed or stump. This is, however, really the same as periodic growth, except that periodic growth is generally taken only for a decade or two and not for the whole life of the tree. In the United States many tables of growth are made which show the number of years required for a tree of a specified size or age to grow i inch in diameter. This is the same as periodic growth. Another common, method of expressing growth is to show the average age of trees of different sizes, which is a way of expressing total final growth. Growth may be calculated for a certain year or period in the past life of a tree, or may be prophesied for a future year or period. For example, the growth in diameter for the past few years may be measured with the Pressler increment borer. This is called reckoning backward. The same figures may be used to estimate the growth during a future period. This is called reckoning forward. In many computations the relative rate of growth is required; that is, the ratio between the present condition of a tree or stand and the growth occurring in the succeeding year. This is expressed as growth percent and is calculated by the ordinary simple-interest formula. Suppose, for example, the growth in diameter to be in question. Let Z) = the diameter now, a = the growth expected next year, and P = the growth percent, then ^ aXioo ' 256 FOREST MENSURATION. In most work periodic annual growth is used instead of cur- rent annual growth. The reason for this is that it is difficult and laborious to measure separately the growth of single years in the life of a tree. It is comparatively easy to measure the growth of a period of years; for example, a decade. In addition, more satisfactory results are usually given by the periodic annual growth, because the annual variations of growth due to unusual conditions, such as cold season, drought, defoliation by insects, etc., are more or less eliminated by the averaging. In general the curreht rate of growth of trees, as well as of stands, is small in early youth; later on, at a period differing with different species and under different conditions of site, the rate of growth increases, and then in late life it decreases as the life energy of the trees falls off. This is true of the rate of growth in diameter, height, and volume. When the current annual growth of a tree or stand is compared to its mean annual growth, it will be seen that the latter is at first the smaller, it increases more slowly, and begins to fall off at a later period. The mean annual growth reaches its maximum at the point wiien it is equal to the current annual growth. This relation between the two kinds of growth must be considered, for the forester frequently has occasion to determine both the mean annual and current annual growth of a tree or stand, or to choose which kind of growth should be used in a given problem. 143. Tree Analyses. — The measurement of a felled tree to determine its growth is called a tree analysis. Tree analyses vary with their purpose, and may include all measurements required to compute the growth in diameter, area, height, and volume, or only a part of them. A complete tree analysis com- prises the following measurements: Length of each section, diameter inside and outside the bark at each cross-cut, the total age, the age and width of the sapwood, the diameter growth at each cross-cut, the diameter breast-high, the total height, the clear, used, and merchantable lengths; and a full description of the trees is also made. THE GROIVTH OF TREES /iND STANDS. 257 Tf the diameter growth Is measured only at the stump, a siump analysis is made. A section analysis includes measure- ments of diameter growth at more than one section. A partial stump or section analysis is one in which measurements of diam- eter growth include only a part of the rings, as when one measures the growth for the last ten years. Only sound trees should be selected for tree analysis. It is not possible to measure the annual growth accurately on a cross- section which is unsound. Rotten spots may prevent the cor- rect determination of the age, and even if the rings can still be distinguished, often cause inaccuracies on account of the shrink- age of the unsound rings. Wounds which have been healed over cause a distortion of the rings and prevent a fair measure- ment of the annual growth. The trees should be as nearly straight and round as possible, unless irregularity of shape is characteristic of the species or group of trees under investiga- tion. Each tree should be representative of its class. In all cases one should avoid the selection of trees with abnormal crowns, because an abnormal crown means abnormal growth. The size of the trees selected for measurement depends on the specific problems under investigation, 144. Preparation of a Felled Tree for Measurement, — ^Where merchantable trees are analyzed, they are cut into regular mer- chantable log lengths, as described on page in, and the age and measurements of diameter growth taken at the stump and at the tops of the logs. If there is a long piece above the last cut, it is usually cut into 10- foot lengths and the rings counted and measured at the new cross-sections. When second growth is studied and the trees are cut primarily for tree analysis, greater care may be taken to cut the stumps at an equal height or to make their heights proportional to the diameter. The German cus- tom is to make the stump-height one- third of the diameter meas- ured at the point where the principal root swelling begins. When possible the logs are made a uniform le»gth, usually determined by the local market conditions. For example, if the average log- 258 FOREST MENSURATION. length for the species in question is 12 feet, that length is chosen for the analysis work. If, on the other hand, ties are the principal product, 8 feet would be chosen. If pulp is to be manu- factured and 4-foot bolts used, a multiple of four would be taken as the log-length. In some studies of growth it is desirable to use a uniform length of log, but this is not always necessary, as will appear in the discussion of special problems. The cross- cuts should be made, when possible, with a saw in order to obtain an even surface for the measurement of the rings. The cross-cut should always be brought to a right angle to the axis of the tree, since diameter measurements taken on a slanting cross-cut would give too large results. 145. Determination of the Average Radius. — After a cross- section has been made perfectly smooth, so that the rings can be counted, the average radius from the bark to the pith is deter- mined. If all cross-sections were perfect circles and the pith were exactly in the center, the measurement of rings could be taken at any point. But this is seldom the case. Therefore, in order to obtain a true measurement of the diameter growth, the rings are measured along an average radius. An average radius of a section is equal to the radius of a perfect circle whose area is the same as the area of the cross-section. Theoretically the average radius should cut each ring perpendicular to a tangent at that point, which would be the case if the cross-section were a perfect circle and all the concentric rings were perfect circles. This is often not the case, and even when the cross-section is a circle, some rings are irregular and the average radius intersects them slightly at an angle. This method gives, however, the average width of the rings very closely, and is the only practical way to obtain the ring measurements, which, all taken together, exacdy equal the average radius. The average radius is one half the average diameter. The usual rule given for obtaining the average diameter is to aver- age together the longest and the shortest diameters, taking these, where possible, at right angles to each other. In this case one THE GROIVTH OF TREES AND STANDS. 259 measures first the longest diameter and takes the other at right angles to it. This method works very well where cross-sections are oblong or elliptical, but with lop-sided cross-sections or those flattened on four sides the best results are obtained by measuring the longest and shortest diameters, even if they are not at right angles to each other. Another method is to measure first what appears to be an average diameter and then take the second diameter at right angles to it. The best rule for studying growth is to measure only trees which are fairly reg- ular in form and then to use the first rule, namely, to average together the longest diameter and that taken at right angles to it. Sometimes it is a characteristic of a species to have irregu- lar stems. For example, red cedar often has a very irregular trunk and the periphery in cross-section is wavy or even scalloped. In this case one measures several diameters which appear to be average and takes their mean. The average diameter of a cross-section should be taken inside the bark. Erroneous results are often obtained by meas- uring with calipers the diameter outside the bark and then deduct- ing the width of the bark. This is particularly true at the stump, where the bark's thickness is very uneven or so much bruised that an accurate measurement of diameter cannot be obtained. If a cross-section is irregular in shape, care must be taken that the short- est diameter is a true diameter, passing through the true center (not necessarily the pith) of the cross-section. This can be judged by the eye or the measurement may be made with the calipers (inside the bark), which guarantees that the diameter lies between two parallel lines tangent to the circumference of the cross-section. A more accurate radius is obtained by determining first the average diame- ter than by averaging together directly the longest and shortest radii. With the steel calipers a very quick method is to place the point of the stationary arm on the pith, swing the instrument around To the nearest, and then the farthest, point of periphery, average the measurements, and then by setting the instrument at this average figure find the average radius. The result 26o FOREST MENSURATION. on an eccentric cross-section might, however, be inaccurate, as is clear from the following extreme illustration: Suppose that a cross-section has the form of an ellipse, and the pith is located on the axis of the ellipse, half-way between the center and one end. The average radius, determined with the increment calipers, would be equal to one-half of the major axis of the ellipse. It is obvious that the area of the corresponding circle would be greater than that of the ellipse. WTien the average diameter has been determined, it is divided by 2 for the average radius. A place on the cross-section is then found which measures, from the pith to the bark, exactly the average radius, and a line is ruled off with a pencil at this place. Then the rings are counted and measured along this average radius. 146. Instruments for Measuring Diameter Growth. — It is cus- tomary in this country to measure the width of the annual rings in inches and tenths. Usually a simple flat scale rule 6 or 12 inches in length is used. A good rule is made of boxwood, with edges covered with a hard white composition resembling ivory, which strengthens it and makes the graduations easy to read. Steel scale rules are often used. A capital instrument for measuring diameter growth is the steel calipers shown in Fig. 46. This consists of a beam of steel l„„i,.!l„.,i„:l„„i„^l„ .,„,Jl„„,.„^l,.„,„'l„„ ,.l,.i„!l„„,,„!i°„ nn'ifn,,,,,: :.,.„.\!„,„.!^„....,'^,..,.,„ \ / Fig. 46. — Steel Increment Calipers. or other metal having the usual graduations and furnished with two arms, one of which is fixed, the other movable. The fixed arm is at one end of the beam; the movable arm depends from a sliding head furnished with a set-screw. The ends of these arms are not square, but are cut away at the corners so as to bring tlie ends to a sharp point, the outer comer of tlic fixed THE GROIVTH OF TREES /IND STANDS. 261 arm and the inner corner of the movable arm being thus cut away. In measuring growth- rings, the point of the iixed arm is placed upon one edge of the ring and the movable point brought to bear upon the opposite edge. In this way the rings can be measured, not only with all the accuracy of caliper work, but with great rapidity. Sometimes narrow strips of stout paper are laid on the cross- section and the widths of the rings marked on them. They are afterwards measured in the office by a scale rule or by the increment calipers already described. A number of attempts have been made to secure prints of the annual rings of cross-sections by means of carbon paper, which may be studied afterwards in the office. On trees which have a very porous grain it is possible to obtain a print of a cross-section by placing a piece of carbon paper between the wood and a sheet of ordinary paper, and rolling the surface with a rubber roller. Better results are obtained if the surface of the wood is washed with a chemical preparation which eats the soft portion of the annual rings, but does not affect the dense wood. The method is impractical, because it is not possible in the woods to make a cross-section of a tree smooth enough to secure a perfect print which will include all the rings. The method is, however, admirable to secure prints of sections of wood desired for special illustration, as for a publication, when time can be taken to prepare perfect opecimens in the office. 147. Counting the Annual Rings from the Pith Outward. — Whether the rings should be counted from the bark inward or from the pith outward depends upon the character of the investi- gation. When the forester wishes to determine merely the average rate of growth in diameter, but does not intend to study the growth in volume, the simplest method is to begin at the pith and count outward, marking each tenth ring. He then lays his ruler along the pencil line' and first measures the distance from the pith to the first ten-year mark, then from 262 FOREST MENSURATION. the pith to the second ten-year mark, then from the pith to the third ten-year mark, and so on; and finally from the pith to the bark. The last measurement must correspond to the average radius. If each of these measurements is multiplied by 2, the results are the diameters at 10, 20, 30 years of age, and so on. 148. Counting the Rings from Bark toward Pith. — In most investigations the rings on a cross-section are not counted from the pith outward, as just described, but, beginning at the bark, are counted inward. The reason for this is that tlie forester generally uses the measurements for volume growth, as well as for diameter growth, and wishes to determine the dimensions (and from these the volume) of the tree as it now is, as it was 10 years ago, 20 years ago, 30 years ago, etc. The dimensions 10 years ago may best be determined by deducting from the diameters at different cross-sections the diameter growth at those sections for the last 10 years. Accordingly the rings at the different sections are counted along the average radius beginning with the bark and proceeding toward the center, each tenth ring being marked to facihtate the measurement by decades. Fig. 47 shows the theoretical cross-section of a log 49 years old. The rings are counted on a chosen radius, beginning with the periphery and working inward, and each tenth ring is marked. Between the pith and the inside mark there are nine rings. When the rings have been counted, the following measure- ments are taken on the average radius: First, distance from pith to inside decade mark, i in Fig. 47. Second, distance from pith to second mark, 2. Third, distance from pith to third mark, 3. Fourth, distance from pith to fourth mark, 4, and finally, distance from pith to periphery, which is tlie average radius. These figures of growth arc usually c-ntcrcd in a special form. The form used by tlie U. S. Forest Service is shown on page 264. It THE GROJVTH OF TREFS AND STANDS. 263 will be noticed that there is space for the measurement of diam- eter growth at 10 cross-sections and that the form may be used for trees up to 300 years of age. Usually an accurate tree description accompanies each tree Fig. 47. analysis. This tree description should include the tree class, the form of crown (preferably by a sketch), the length and width of crown, the clear length, merchantable length, health, and form of bole. It is customary also to make a forest description^ especially where the trees occur in different types of forest and 264 FOREST MENSURATION. ^ ~ u S ci s w 00 m H m w 0!, 0 to w 0 Di >- P H h-r D 0 c^ 0 < 0 to 0 r^ H z w < s H < c 0 c a 0 N en flj (5a Mg £" 1 "3 4J . 0 0 n 00 1H -t t» I5£ ^- 0 Width of Sap, Ins. 10 lO <^- ro t^ r^00 0 a^ 0^3C CO 1 Diam. Out- side Bark, Ins. 000 vO ■<*•-<" Width of Bark, Ins. to 10 c d 6 6 6 N Diam. Inside Bark, Ins. 00 1^ M rM 6^ 0 >o 'i- n 1 1 1H Le'tith of Sec- tion, Ft. " 0 0 0 0 lo 0) c 5 0 u c a> B ^ II < C 0 OJ u § 0 w GO OS N r. CO N to X5 10 000 ^ 10 m m 0 10 CO 10 10 oo 0 <^^ 0 n M n N N 10 -i ^ -'"'000 « 1 ■uo -s 103S SOJ3 ■uop -V oas SOJ3 1 - (N r'. -r "^"C l> --I THE GROJVTH OF TREES AND STANDS. 265 in sites of dillercnt quality. These descriptions assist in the classihcation and grouping of the different tree analyses and explain any pecuharities of growth. A full description of the site and the stand should include the situation, absolute and relative altitude, slope and aspect, rock, soil, humus, litter, brush and herbaceous growth, reproduction, forest type, form of stand, size and age of trees, trees in mixture, density, quality of site, silvical condition, merchantable condition and estimated yield per acre. In some studies of the growth of individual trees, however, a full forest description is unnecessary; or if one were measuring a large number of trees in one place, it would be neces- sary to make only one forest description to cover all of the trees in the stand. 149. Investigations of Diameter Growth. — The purposes of the study of diameter growth may be: 1. To determine at what age a given species under given conditicns will become merchantable. 2. To compare the rates of growth of two species, or of the same species under difi'erent conditions. 3. To illustrate the results of certain kinds of treatment. 4. To serve as a step in the determination of volume growth. It is seldom that the specific objects of an investigation can be accomplished by the measurement of trees selected in a hap- hazard fashion. Thus some foresters make a practice of measur- ing the growth on stumps whenever an occasion is offered. A miscellaneous lot of such measurements would have little value for statistical purposes, though they assist the forester him- self to a better knowledge of the hfe of the tree and are of value in estimating growth in the absence of more elaborate data. General growth studies, which aim to give the average re- sults of trees growing under a number of different conditions, are not valuable for practical work. Therefore the data for diameter growth should be collected according to a definite plan, and with the proposed uses of the results of the investigation constantly in mind. 266 FOREST MENSURATION. Almost every question of diameter growth can be better answered by a study of volume growtli. But investigations ot volume growth are very slow and expensive compared to those of diameter growth; so that when possible the latter have been used in this country. 150. Determination of Diameter Growth. — By growth of a tree in diameter or sectional area is meant the growth at breast- height or at the stump. The most useful tables of diameter growth show the rate of growth at breast-height outside the bark. These tables are the most useful because standing trees are measured and classified by the diameters at breast-height. As a rule, however, measurements of grovAth cannot be taken at breast- height because such a high cut wastes valuable timber. There- fore the diameter growth inside the bark on the stump is first determined, and the diameters outside the bark at different ages are estimated by a study of the average ratio between the stump diameter inside the bark and that at breast-height outside the bark, obtained from a large number of trees of different sizes. The average rate of growth in diameter of a number of trees is obtained by means of a diameter curve. The diameter measurements of each tree are first plotted on cross-section paper, on whose horizontal lines are laid off the ages and on the vertical lines, the diameters. Suppose that there are 53 rings and that they have been counted from the bark inward. One enters first the growth of the innermost three years; that is, twice the dis- tance from the pith to the inside decade mark; then the diam- eter growth for 13 years, then for 23, 2>Z^ 43, and 53 years, the last being the average diameter of the tree. An average curve is drawn through the points and from this curve a table is con- structed showing the average diameter of the trees at 10, 20, 30, 40, and 50 years of age. The results from the curve show the average diameter of the trees at different ages inside the bark at the stump. But when one wishes to know tlie diameter of a tree at a specified age, it is the diameter at breast-height outside the bark, and not that at THE GROIVTH OF TREES AND STANDS. 267 the stump inside the bark. To be sure, tables of growth at the stump for different species show comparative rates of growth very well. It should be borne in mind, however, that the rate of growth at the stump is greater and is less uniform than at breast-height. The breast-height diameters of the trees at different ages are determined in the following way: The difference, in inches, be- tween the diameter of each tree at breast-height, outside bark, and its stump diameter, inside bark, is calculated; then the trees are grouped by diameters inside the bark at the stump; and for each inch class the average difference between stump and breast-height diameters is computed and arranged in a table like the following: Diam. inside bark at stump, inches. . . 5 6 7 8 etc. Difference between diam. inside bark at stump and outside bark at breast-height, inches 0. 1 0.2 0-3 0.4 etc. These figures may then be applied to the stump diameter curve as reducing factors to construct a breast-height diameter curs'e. Thus one finds where the 5-inch ordinate intersects the stump curve and makes a mark on this ordinate o.i inch below the curve; then makes a mark on the 6-inch ordinate 0.2 inch below the curve, and so on. These new points are joined by a curve which represents the growth at breast-height as nearly as it is possible to determine it without actually measuring the rings of the trees at that point.* * Some may object to this method on the ground that the average difler- ence between the stump and breast-height diameters is determined for trees of different sizes without regard to age. It would, of course, be possible to first ascertain from the stump curve the average age of the 5-inch trees and then use only 5 inch trees of that age to determine the difference between the stump and breast-height diameters; and in the same way use trees of specified ages to determine the reducing fa^or for the other diameters. The author does not know of any investigation having been carried out in this way. 268 FOREST MENSURATION. If the rings are counted and measured at breast-height, a diameter growth curve is made, just as was described for the growth on the stump. This curve shows the rate of growth inside the bark at breast-height, and to be really useful must be corrected to show the diameters at different ages outside the bark. To accompUsh this, it is necessary to measure the \\ddth of the bark, at breast-height, of trees of different sizes and ages. Thus one would determine from the diameter curve the age of 6-inch trees and then measure on a number of trees of approxi- mately that size and age the thickness of bark at breast-height, and do the same for the other sizes. The average bark thick- nesses may then be apphed to correct the iirst curve, and a new curve may be drawn showing the diameter growth at breast- height outside the bark. 151. Separate Studies Made for Trees Growing under Differ- ent Conditions.- — The rate of diameter growth of trees varies so greatly that a study of average growth under a great variety of conditions has little practical value. Almost every practical question of growth has to do with a particular set of conditions, for which a separate table of growth must be made. In tlie first place it is necessary to distinguish between trees grown in even-aged and uneven-aged stands. Usually separate growth tables also have to be made for different forest types and for differ- ent soil classes, and sometimes separate tables of diameter growth should be made for stands of different density, as, for example, for dense, interrupted, and open stands. The most important problems are discussed in the succeeding pages. 152. The Study of Diameter Growth in Even-aged Stands. — One of our important problems is to determine the rate of growth in diameter of trees growing in even-aged stands. Even-aged, or approximately even-aged, stands arc very common in many sections, occurring usually where the land has been cleared by cutting, windfall, or fire. Conspicuous examples of even -aged stands are: The bulk of sprout stands; birch, poi)lar, and other THE GROIVTH OF TREES AND STANDS. 269 second growth on extensive burns in northern New England; spruce in old pastures, on burns, and on areas cleared by wind- fall; white pine on burns and abandoned land; second-growth white cedar (chamajcyparis) near the coast; pitch, short-leaf, loblolly, Virginia pine, and practically all other pines in the Central and Southern States, coming up as second growth on abandoned fields and burned land; white, jack, and red pine in the Lake States on old clearings and burns; lodge pole pine, yellow pine, red fir, and many other conifers, which follow fires or occupy clearings in the far West. In other words, an important part of the second growth of the whole country is in the form of practically even-aged stands. Inasmuch as all plantations and all clean-cutting systems of natural reproduction furnish even-aged stands, the study of growth of trees in this character of forest requires special considera- tion. Generally the average diameter growth of even-aged stands is sought to answer such questions as: What are the mean and current rates of diameter growth at different ages ? How long does it take on an average to produce a merchantable crop? How soon will a specified young stand become merchantable ? Such a study must, however, presuppose a certain method of management, particularly in the matter of making improvement thinnings. If the purpose is to show the rate of growth of even-aged stands in which improvement thinnings are not made, then one takes the measurements of growth in volunteer stands, which represent, as nearly as one can judge, the conditions which will obtain where the figures of growth are to be applied. Sup- pose, for example, that an investigation is made of diameter growth in second-growth sprout stands. Usually separate tables of growth are made for different forest types. One would select the trees for analysis in a given forest type in stands which repre- sent the average prevailing conditions in that type. The resulting tables of growth may be applied to similar land where presumably the trees will grow as on the area studied. After locating repre- 2 70 FOREST MENSURATION. sentative stands, the trees are selected for tree analysis, "^'ith due regard to their form and health, as explained on page 257, and also with regard to proper size. Several methods of determining the size of the trees to be analyzed are distinguished: {a) By the Analysis 0} all Trees on Selected Plots. — By this plan selected sample plots are laid off and all the trees on them analyzed and the measurements of their growth averaged together. Generally only such trees are included as will probably reach merchantable size; the owner is not so much interested in the trees which die through suppression. The best way is to use for the study stands which already are of merchantable size, and not to include for analysis any suppressed trees. This method is practicable in forests where timber is being clear-cut, as in sprout forests. It is a simple matter to follow the choppers and analyze the trees before they are removed. Several plots judiciously located in each forest type would yield enough mate- rial for most practical purposes. If stands are used which . have not reached merchantable size, only such trees should be analyzed as later will probably become merchantable. (b) By the Analysis 0} Average Trees. — In this method one lays off sample plots, as in the preceding method, then calipers the standing trees on each plot and determines the diameter of the average tree. A number of trees of average diameter on each plot are measured for growth. The measurements of all trees analyzed in a single forest t}-pe are then averaged together. This method gives fairly good results when average trees from merchantable stands alone are used. The resulting tables show the average rate of growth of the trees which reach maturity, without regard to the gro^^1h of tlie trees whicli die before the stand is mature. In this connection it must be borne in mind that an average tree in a mature stand has not always been the average tree. A tree which at 60 years of age has an aver- age diameter will not necessarily have an average diameter THE GROJVTH OF TREES /iND STANDS. 271 when the stand is 80 years of age. In any even-aged stand changes are constantly taking place, one of the most important being the reduction in the total number of trees and in the num- ber constituting the dominant crop. If a stand is measured at 30 years and again 20 years later, it will be found that a large number of trees have died and that the tree which repre- sented the average at 30 years is below the average at 50 years, because some of the trees which were used in deter- mining the average diameter at 30 years have died within the period. The trees which died were naturally among the smallest and their absence proportionately increases the average diameter when the stand is 50 years of age. The growth of average trees in a merchantable stand represents fairly well the average growth of the trees which are standing at the present time. (c) By the Average Diameters of Standing Trees. — One of the objects in the study of diameter growth is to determine for differ- ent ages the diameter of the average tree whose volume, mul- tipUed by the total number of trees in the stand, will give the volume of the stand. When this object is to be attained the method just described is not strictly applicable, because it gives for different ages only the average diameter of the trees which reach maturity, not the average diameter of all the trees in the stand. The simplest method is to compare the diameters of average trees in stands of different ages without making any tree analyses at all. In this method sample plots are taken in even-aged stands of different ages, as, for example, stands about 20 years old, 30 years old, 40 years old, and so on, up to maturity. The diameter of the average tree and the average age of each stand are obtained. These figures are then compared and averaged by a diameter curve based on age in the following manner: On a sheet of cross-section paper, whose horizontal lines represent years and whose vertical lines represent diameters, are plotted the average diameters for -stands of different ages. An average curve is then drawn through the different points. i'j2 FOREST MENSURATION. From this curve is obtained a table giving the diameter of the average tree of stands at different even decades. The advantage of this method is that it gives results directly in terms of the breast-height diameter, and thus answers one of the practical questions of the study of diameter growth. Measuring one hundred plots in each forest type gives excellent results. {d) By Averaging Together Selected Trees 0} Different Sizes.— \ common method of selecting trees in even-aged stands is to fol- low the choppers, taking the trees just as they come. No plots are taken and there is no rule regarding the size of the trees measured, except that the forester sees to it that the different sizes are well represented. If enough trees are used, a very good average result is obtained. A thorough investi- gation would ordinarily include at least 100 trees in each forest type. 153. The Study of Maximum Diaxneter Growth in Even- aged Stands. — The methods just described permit the deter- mination of the average rate of growth in diameter in volunteei stands which are not thinned. It is a well-known fact that judi cious thinning of a forest increases the rate of growth. Tht maximum rate of growth compatible with good form of bole and quahty of wood is obtained by thinning stands when young and repeating the thinnings at intervals throughout life. It is of importance to determine the rate of growth of stands in which thinnings are begun at the proper time and repeated at proper intervals. Of course this question may best be solved by the use of data collected in stands which have been under manage- ment throughout life. But in America very few stands of this character exist. Therefore the growth of systematically thinned stands must be determined by studying individual trees which have had favorable conditions of light and growing space such as are furnished by thinnings. It is fair to assume that by thin- nings all of the dominant trees in a given stand can be made to grow as rapidly as the jastcst gnnting dominant trees in an TH£ GROIVTH OF TREES AND STANDS. 273 unthinned stand, the qualities of site being equal. Reference is here made to normal maximum trees, and not to occasional stragglers with wide crowns and large rough trunks. The object of forestry is not to produce rough trees, but rather trees with full, vigorous crowns and trunks which will yield satisfactory timber. On the principle, then, that by thinnings one can make the majority of trees grow as fast as the best found in an unthinned stand, the largest trees which have satisfactory stems are selected for analysis. Thus, in a sprout chestnut stand one would usually select for measurement about ten of the largest trees (not in- cluding abnormally developed trees). In this way a large num- ber of maximum trees are measured; and their growth meas- urements, when averaged together, represent the average rate of growth of the trees which reach merchantable size in a sys- tematically thinned forest. The trees which die or are removed by the thinnings are not considered. The determination of the possible number of such trees per acre, which could be produced, under certain methods of treatment, is described in section 194. If the trees are selected, as described under {a) or {d) of the previous section, the maximum rate of growth may be deter- mined by means of a maximum diameter curve. Suppose that the growth measurements were all plotted on cross-section paper, then a curve is drawn through the highest diameter points. If some points are exceptionally high, and evidently represent abnormal growth, they are excluded. The curve forms an upper boundary of the main body of points and represents the average maximum growth, 154. The Measurement of the Minimum Diameter Growth. — It is frequently desired to know what the diameter of the small- est trees will be at different ages, and especially at maturity. Suppose, for example, a study of growth shows that the average trees in an even-aged stand of oak sprouts will reach merchanta- ble size at 50 years of age, what will be the size of the small- est trees at that age and how soon will they be merchantable? 274 FOREST MENSURATION. The minimum diameter growth may be determined by drawing a minimum curve in the same way as the maximum curve; that is, a curve is constructed through the lowest points represented on the cross-section paper, taking care that no abnormally low values influence its shape and direction. A good way to deter- mine the minimum rate of growth in a thinned forest is to con- struct a minimum curve for a group of maximum trees selected from an unthinned stand in the manner described in the previous section. 155. Stimulated Growth after Thinning. — It has already been explained, on page 272, how to determine the growth of even-aged stands in w^hich the diinnings are begun at the proper time and repeated at proper inter\als. Suppose, however, that the thinnings are not begun at the proper time, but still it is desired to know what the rate of growth will be after the thin- nings. Thus, for example, a volunteer even-aged stand of white pine may be thinned for the first time when 30 years old. How will the average rate of growth in diameter after thinning compare with that which would have taken place under ordinary treatment? This question is difiicult to answer because it is very difficult to find stands of difierent ages which have been properly thinned. In the absence of such stands the author recommends the following method to be used until the growth after thinnings can be determined em- pirically. While it is often not possible to find a whole stand which has been thinned properly, small patches occur which by acci- dent have been given exactly the right treatment. Thus it is possible to find tnritty trees about which poor individuals have been remoxed and which ha\e been gi\en tlie benefit of just the right amount of light for their best develoi)ment. Such trees are analyzed to determine their rate of growth. The analyses are then grouped on the basis of diameter and age, and the aver- age growth of trees 30 years old and 10 inches, 11 inches, 12 inches, etc., in (Hameler, is computed. In tlie same way one THE GROIVTH OF TREES /IND STANDS. 275 determines the growth of the 4o-year-ol(l trees of different diam- eters, and that of other ages. These figures are llien applied to correct tl:e tables of average diameter growth. Thus if the lo-inch trees in the above-mentioned 30-year-old white pine stand were growing at a rate of 2 inches in 10 years, and the study of stimulated increment showed an increase of 50 percent by thinnings, then one may count on 3 inches in the next decade. It may then be assumed that after a decade the trees will grow at the rate of the 40-year-old trees and a decade later at the rate of 50-year-old trees, etc., presupposing, of course, that thinnings are repeated w^henever desirable. In studying increased growth after thinnings it is desirable to select for analysis trees from stands where thinnings have been made at least 5 to 10 years before, for several years are usually required by the tree to adjust itself to the new conditions, and the growth of the first year or two after thinning may not represent the normal increase. It is also desirable to take the measurements at breast- height because the increase of growth at the stump is greater than at breast-height. . 156. Rate of Growth in Uneven-aged Stands. — The condi- tions for growth in uneven-aged stands are much less uniform than in even-aged stands. In many-aged forests the rate of growth of the different individuals of the same species varies so much that usually no attempt is made to average their growth at different ages. Sometimes, however, studies are made of the average mean annual growth of such trees at maturity, as ex- plained in the next section. Frequently the average rate of growth is determined for special classes of trees growing in uneven-aged stands. Thus one might wish to determine the average diameter growth of the advance trees of a certain species growmg upon abandoned fields, as, for example, the chestnut trees which first come in on open fields and develop large crowns and short trunks. Special groups might be made of red cedar growing in the open, red 276 FOREST MENSURATION. cedar growing in crowded pure stands, and red cedar starting in the open and later being overtopped; of hemlock growing under pine; tamarack growing over balsam and spruce; white pine among spruce, hemlock, and balsam. A great number of illustrations could be given of special classes of trees which would naturally be grouped together for diameter growth. Such investigations are made whenever some practical question regarding the growth of a particular class of trees has to be answered. The selection of the trees for tree analysis is not difficult if the purpose of the study and the principle of classi- fication of the trees is understood in advance. The method of studying diameter growth most commonly used in uneven-aged stands is to compare and average the current rate of growth of trees of different diameters without regard to their ages. This method of study is described on page 278. 157. Determination of the Mean Annual Growth of Trees in Uneven-aged Stands. — It was explained in the preceding section that trees in many-aged stands grow under such variable con- ditions that a comparison of their growth at different ages has no practical value. It is often desirable to determine how long, on an average, it takes certain species growing in certain forest types to reach maturity or merchantable size. Suppose that, in the work of organizing a certain forest which is managed on the selection system, it has been decided to cut the trees to an average diameter limit of 12 inches. It is of interest to know what rotation this diameter limit represents. Therefore one determines how long it takes, on an average, in the forest under examination, for the given species to reach 12 inches. This is done by measuring a large number of 12-inch trees and counting the annual rings at the base. The average age of the 12-inch trees re[)rcsents the rotation on which the forest is being managed. In many-aged forests it is customary to use size classes rather than age classes, since the former roughly corresjiond to the latter. Suppose, for example, that 12 inches is established as a (h'ameter THE GROWTH OF TREES AND STANDS. 277 limit, and for Ihc particular purposes of organization it is desirable to use 3-inch size classes. If the average age of 12-inch trees were 100 years, then each size class roughly corresponds to an age class of 25 years. It is customary in many investigations in uneven-aged stands to make tables showing the average age of trees of different diam- eters. Sometimes these tables are used to indicate the current rate of growth in diameter. More satisfactory results, however, are obtained from tables based on the measurement of the growth for the last 10 years, such as are described in the succeeding sections. 158. Prediction of Growth for Short Periods. — There are two methods of determining the probable growth of a tree for the immediate future: first, by measuring its recent growth with an increment borer, and, second, by the use of tables showing the average rate of growth of trees of the same size under similar conditions. It may be assumed that a tree will grow in the immediate future at the same rate as during the last year, or as the average during the last 5 or 10 years. This assumption is not absolutely correct, because the growth may be decreasing from year to year, in which case the estimate of growth would be too large. In the same way the result would be too small if the annual growth were increasing. As a rule, however, the prediction of growth is made at a period in a tree's life when the rate of growth is not changing rapidly from year to year. For all practical pur- poses, therefore, the recent growth may be used to predict the future growth for a short period, as, for example, a decade. The measurements of growth for the last 5 or 10 years are taken with an increment borer, at breast-height. It is, of course, impossible to determine exactly where the average radius is, so that the measurement of growth is not so accurate as if it were taken on a cross-section. For thir reason, therefore, one should select trees which are round. If perfectly round trees 278 FOREST MENSURATION. cannot be used, two borings should be taken from a single tree. These may be in Hne with the longest and shortest axes, or at points where the growtli is probably about average. Three or four borings from the same tree will, of course, give better results than only one or two borings. . The measurements of the borings should always be taken immediately after their extraction from the tree. One should not hold borings for measurement later in the office, because of the shrinkage by drying. One objection often advanced to the use of the increment borer is that the rings are apt to be some- what jammed together, particularly with soft wood. With a good instrument skilfully handled this objection is not serious. A second method of predicting the gro^^1:h of a tree is by the use of tables of growth of trees of different diameters. These tables and their use are described in the succeeding section. 159. Tables of Growth of Trees of Different Diameters. — Many practical investigations require the current rate of growth of trees of certain diameters, but do not require the age of the trees. Thus, in many of our irregular forests, it is customary to cut the large trees and leave the small ones. If it is known how fast these small trees grow, the owner can tell how soon he can return for a second crop. To meet these conditions tables are constructed to show the rate of growth of trees of different sizes, instead of the rate of growth of trees of different ages, as described in the previous sections. Such tables show how fast trees 5, 6, 7, 8, 9, etc., inches in diameter grow, instead of how fast trees 20, 30, 40, etc., years old grow. In our many-aged virgin forests, trees of the same size, even if of different age, have more uniform gro\\1;h than trees of the same age. Thus, a spruce tree 12 inches in diameter and 100 years old probably grows more nearly like the average of 12-inch trees of the forest than like the average of the 100-year-old trees. It is assumed that 12-inch trees grow at the rate sliown for that diameter in the table, until they are 13 inches, when they grow like tlie average 13-inch trees. THE GROIVTH OF TREES AND STANDS. 279 To construct such a table, one first analyzes a large number of trees. As a rule the work is done where lumbering is being carried on, and the trees are analyzed as they are cut by the saw- crews. The measurements required for each tree are the diameter at breast-height and the measurement of the growth at breast- height or on the stump for the last 5 or 10 years. The total age of the tree is not determined unless required for some other purpose. The trees are then grouped together by diameters, and the growth of the trees in each diameter class averaged together. Thus the measurements of growth of the lo-inch trees for the last 5 or 10 years are averaged together; then that of the 1 1 -inch trees, the 12-inch trees, the 13-inch trees, etc., is obtained in the same way and the results arranged in a table. Usually it will be found that the growth increases or decreases more or less regularly from the small to the large diameters. Any irregularities which may occur in this first table are evened off by a curve. Separate tables are made for different forest types and classes of soil. Usually all trees analyzed in a given forest type are averaged together by diameters regardless of differences in height and crown development. This is not always fair. Thus, for example, it is hardly fair to average together the rate of growth of a lo-inch tree 50 feet high and having a thrifty crown, with one which is 25 feet high and has altogether a different crown de- velopment. Under these circumstances a much more accurate investigation of growth is made if the different classes of trees of each diameter are kept separate. Thus spruce growing in a virgin forest may be divided into three tree classes. Class one comprises the tall thrifty trees with full crowns, class three the short trees with inferior crowns, and class two the inter- mediate trees. This classification may extend to trees of any specified diameter. Other methods of classification may be used, depending on the species and character of the forest. The method of constructing tables of growtlr is just as described above, except that instead of one figure of growth for each 2 8o FOREST MENSURATION. diameter there are three; that is, one for each class. A table of growth, made on this principle, can be expressed in the follow- ing form: CURRENT GROWTH IN DIAMETER OF TREES OF DIFFERENT DIAMETERS. Diameter, Breast-high, Inches. Annual Growth for Last Ten Years, Inches. Class I. Class II. Class III. The number of trees required for a study of growth of trees of diiferent diameters depends on the uniformity of the forest. Where there are a number of forest types, one usually endeavors to measure at least looo trees. Where the growth is measured for the last lo years and at one cross-section, it should be pos- sible to measure looo trees within two weeks, provided that number of trees is available for measurement. In selecting trees for measurement, one naturally must see to it that each diam- etei is about equally represented. It will be noticed that in the discussion of this method no mention has been made of stimulated growth after cutting. The assumption has been made that the growth for the immediate future will remain the same as during the past few years. Experi- ence has shown that after lumbering, the trees whose crowns are freed by the removal of the old trees show a decided increase in growth. If, therefore, the lumbering is fairly heavy, figures taken from trees growing in the virgin forests do not give a cor- rect and satisfactory result. If the lumbering is very light — that is, a few trees removed per acre — a large number of the trees remaining may not be at all benefited by the cutting. An average THE GROIVTH OF TREES AND STANDS. 281 cut of 15 to 20 trees per acre usually affects the rate of growth of a large number of those remaining, but not of all. The spruce forests of the Adirondacks furnish a good illustration of this principle. When the merchantable trees are cut, there usually remain some large non-merchantable trees, such as unsound or crooked birch, beech, maple, or other species which continue to shade a por- tion of the small spruce left standing. Only a portion of the young trees, therefore, show a stimulated growth. A study of the growth of trees in unthinned forests would give too small results and measurements of trees showing stimulated growth too large results. The true average rate of growth may, therefore, be obtained by making two tables of growth: first, a table showing the rate of growth of trees of diiTerent diam- eters in the virgin forests, where no cutting has taken place; and second, a table showing the rate of growth of trees of differ- ent diameters, all of which have had their crowns more or less freed by the lumbering. The second table is made up in the following way: The forester finds cut-over land in which old trees have been cut and small ones left standing. Near the stumps of the old trees may be found younger ones whose crowns have been more or less released by the cutting. It is often possible to tell at a glance which have been benefited or likely to have been benefited by the cutting. These are selected for measurement. The measurements are worked up in the same way as described before. By a separate study the average per- centage of the trees which will probably be benefited is esti- mated. Sometimes this is merely estimated by inspection of the forest where the figures are to be applied. A better plan is to survey a few plots and make a record of the trees which by their proximity to merchantable trees are likely to be bene- fited by the cutting. From this enumeration the forester is able to make a table of percentages of trees of dilYerent sizes which show an increased rate of growth. With the table of percent- ages he combines the two previous ta-bles of growth. If his table of percentages shows that 20% of the trees will probably 2S2 FOREST MENSURATION. be benefited by the removal of the old timber and 80% of them will not, then his combined average table of growth will be made up of 80% from the first and 20% from the second table. This average table can then be applied directly to the growth of trees of different diameters. The following table was con- structed in this way: AVERAGE RATE OF GROWTH IN DIAMETER AT THE STUMP OF SPRUCE. [Based on 1593 Trees on Cut-over Land at Santa Clara, N. Y.] Number of Trees showing Increased Growth after Cutting. Annual Annual Average Diameter Diameter Annual Number Diameter Number Growth Growth Diameter of Years Breast- high, Inches. of Trees of Trees not of Trees Growth, Required Measured. showing an Increase, showing an Increase, mcluding all Trees. to Grow One Inch. Inches. Inches. Inches. 5 8 I •095 . 100 .09 I I 6 158 16 .080 . 180 10 ID 7 329 63 .090 .185 109 9 8 350 77 .105 .205 125 8 9 277 59 .120 .205 140 7 10 226 50 •135 215 '50 7 II 135 18 .130 .210 160 7 12 64 7 .165 .240 170 6 1.3 30 2 .165 .170 178 6 14 II I -150 . 200 185 6 15 I .080 192 6 16 4 .200 .20 200 5 Average .112 ■137 7 160. Study of the Growth of Trees in Area. — By growth of a tree in area is meant the increase at a given cross-section, expressed in square feet or other unit of square measure. Tables of growth in area are not commonly made in this country, not having been required in many of our practical prob- lems. The growth in area for short periods is, however, fre- quently used in predicting the increment in volume. In reality the area growth shows the real capacity of the tree THE GROIVTH OF TREES AND STANDS. 283 better than the diameter growth. Diameter growth shows the energy of radial cell division, but the area growth gives a measure of the actual amount of wood produced at a given cross- section. This is well illustrated in a comparative study of the growth at different parts of a tree. Thus in a forest tree which is growing in a crowded stand the growth in diameter increases from breast-height up to the base of the crown, whereas the growth in area remains practically the same. This increase in diameter growth is due to the fact that the stem tapers and a given amount of material produces wider rings than where a greater surface must be covered. The amount of material pro- duced at different points is, then, shown better by the increase in area than by that in diameter. A study of the rate of growth in area involves no difficulties because the results are obtained from a study of diameter growth by substituting for all diameters in the final tables the areas of corresponding circles. 161. The Growth in Height of Individual Trees. — The rate of growth in height is used in computing the rate of growth in volume. There are many occasions when one desires the rate of growth of a specified group of trees, as, for example, the growth of white pine over spruce, spruce under pine, hemlock under oak, spruce in swamps compared with that on slopes, and so on; an immense list of problems. In establishing plantations the forester has to know the relative rate of height growth of the different trees in order to mix the species which will best thrive together. For example, a slow-growing intolerant tree would not be planted with a more rapid-growing species. Thus, if pitch pine and white pine were planted together, the former would eventually be overtopped and die. A knowledge of the relative height growth would prevent such an error. The forester requires also a knowledge of height growth in the work of improve- ment cuttings. There are many occasions when the selection of a tree in making thinnings depends on its growth in height. This is particularly true in young growth, for example, where 284 FOREST MENSURATION. it is a question of saving a slow-growing tree which stands among more rapid-growing ones. Frequently one has to make a heavy opening of the stand in order to save such a tree. Again, a forester, ignorant of height growth, might often expend labor in trying to save a tree growing among other species, when, if left alone, it is capable of growing rapidly enough to hold its own. Experiment has shown that under ordinary circumstances the height growth of trees is an excellent index of the quality of a given site; that is, where the conditions of climate and soil are most favorable for the life of a species, there the height growth is the greatest, unless some modifying factor checks the develop- ment of the trees. The average growth in height of trees is, there- fore, determined to assist in judging the quality of the site. (See page 325.) Care should be exercised in constructing and using tables of height growth of individual trees designed to aid in judging the quality of the site. Where trees are scattered individually among others the height growth may vary consider- ably, even on the same class of soil. For example, a red oak in mixture with pine might grow differently than when mixed with white oak or hard maple, or a pine in mixture with oak might grow in height differently than when growing in pure stands. It is well known that trees grow in height somewhat differently in very open and in crowded stands. This is particularly true in early youth when the height growth is frecjuently checked by overcrowding. A too-open stand also acts as a check to lieight growth. Separate tables must therefore be made, not only for different soil classes, but also for other conditions where there is a characteristic height growtli. In making tables of height growth of indi\idual trees, their practical purpose must always be kei)t clearly in mind, exactly as in the study of diameter growth. Haphazard figures of height growth are not suited to general conclusions. 162. Determination of the Rate of Growth of Trees in Height. — It has been explained that the age at a given cross-section of THE GROiVTH OF TREES yiND STANDS. 285 a tree represents the number of years required to grow from that point to the tip. The age at the stump may not be the age of the tree from the seed, but only the age of the portion of the tree above the stump, and in the same way the age at the top of the first log is less than at the stump. The ages at different cross-sections from the base toward the tip are, therefore, sue- DIgtence from ground 46 ft. grown in 63 jeari ' ^Distance from ground ^i ft. growniin^oS-ycara Distance from eround HI ft. grown in 39 years /^Isiaoce from ground ' ^1 ft. grown in V3 years Distance from ground (11 ft. -grown in 13 years Xo. rings 40 No. rings SO Distance frodi ground . 1 ft. grown in 3 years {(- The growth for the last year is then r.D'hj - 4 The growth percent is -7(-^)'^'^7^(^-^)- : — ( — ; I =100: p, 4 4 \ n «7 ^' 400 400 THE GROH^TH OF TREES AND STANDS. 309 If the growth be calculated on the basis of £)+— instead of D-— then n n' the following formula will result: 400 400 ^ nD nW^' The average between the two formulae is taken, namely, 400 Inasmuch as Schneider's formula assumes that there is no change in height and no change in form factor, the results are very conservative. An attempt has been made to adapt the formula to rapid-growing trees by increasing the value of 400, but the resulting formulas have httle practical value. The methods just described are satisfactory only with mature or nearly mature trees. There is no good method of determining the rate of growth percent of a rapid-growing tree except by cutting it down and analyzing it. Fully as good results are obtained by using average-growth tables as by applying Schneider's or Pressler's methods to fast-growing trees. 176. The Increment of Stands. — The increment of individual trees is studied chiefly to enable the determination of the increment of stands. The American forester is now confronted by a multitude of practical problems which require the deter- mination of the future yield of stands in timber and in money returns. Three main groups of problems may be distinguished: first the prediction of the increment of even-aged stands for short periods; second, the prediction of the yield of stands established on clearings by planting or by natural reproduction; and third, the prediction of the yield after lumbering in many-aged forests. The first problem is discussed in the following sections of this chapter; the second and third problems'are considered under the head of Yield Tables. JIO FOREST MENSURATION. 177. Prediction of the Increment of Even-aged Stands for a Short Period. — Frequently in making a working-plan it is necessary to predict the increment for one or several years or for a decade. One of the most common problems is to determine whether a stand is adding increment rapidly enough to pay to leave it stand- ing. In certain European countries, for example in Austria, the policy is to cut and reproduce a stand as soon as it ceases to yield a satisfactory rate of interest. This is called the financial maturity of the stand. To ascertain whether a stand is finan- cially mature, one determines its value now and one year ago. If the difference represents a rate of interest less than what the owner demands, the stand is past maturity. If the interest is equal to the minimum required by the owner, it is just mature. Another problem is where a stand is to remain for a certain number of years and the owner wishes to know what the yield will be at the end of that period. In organizing a forest under a -s^'orking-plan it is customary to predict the yield of certain stands, which are to remain a decade or m.ore, by computing their present volume and adding the increment for the period in question. In the w^orking-plans of some European countries it is cus- tomary to predict the yield at maturity of every portion of the forest. The final yield of stands which are young or middle- aged are estimated by the help of yield tables (to be described later), but the final yield of the nearly mature stands is deter- mined by studying their present current increment. The method of determining the current increment is best explained by an example. Suppose a pure stand of red maple sprouts covering 25 acres is to be cut clear in 12 years, what will be the final yield ? If the stand is uniform in age and density over the whole area, one sam})le acre is selected to represent the whole. If there is some variation in the character of the tim- ber, enough plots are taken to guarantee a good average. The plot is accurately laid off and the trees calipered, then the volume computed by one of the methods involving the felling of sample trees. Suppose that the mean sample-tree method is choseo THE GROIVTH OF TREES y4ND STy4NDS. 3H and that three test trees are cut. The rate of growth percent in volume is determined for each test tree by the formula V — V 200 The average growth of the test trees is assumed to be the aver- age growth of the stand. The volume growth of the stand for one year is, therefore, obtained by multiplying the stand's present volume by the growth percent. The volume growth for 12 years added to the present volume of the stand gives the yield at the proposed time of cutting. If it is impractical to fell test trees on account of the lack of time or because great accuracy is not necessary, the rate of growth percent is determined from standing trees. The trees are calipered as before and the diameter of the average tree com- puted. Volume tables are used to compute the volume of the whole stand (see page 219). Three test trees are selected as before, but instead of felling them the forester determines the rate of growth of each for the last few years with an increment borer, and after measuring the diameter computes the growth percent by the formula p= —jj or by Pressler's method. This plan is, however, very inaccurate in second-growth hardwoods, as the trees are usually growing in height and changing in form. It is therefore better to determine the growth percent from sample trees whenever possible, unless one is working in mature forests. If a stand is composed of several species the growth of each is computed separately. Thus in southern New England the sprout forests are nearly always mixxd, and frequently as many as ID species are represented on a single sample plot. The survey shown on page 312 is a representative plot taken in Connecticut. To estimate the growth of such a stand accurately one should deter- mine separately for each species the diameter of the average tree, then feU one to three test trees of each kind and calculate the 312 FOREST MENSURATION. growth as described above. This would give a very good esti- mate of growth for the particular stand in question, but the accuracy would not pay for the time required t>y such a long operation. One would determine the growth of such a mixed stand in order to estimate the growth of a larger area, using the plot as an average. But mixtures of trees vary so much that PLOT SURVEY IN MIXED HARDWOODS. Diameter, Breast- high, Chestnut. Red Oak. Rock Oak. Red Maple. Black Birch. Bjech. Poplar. Inches. 2 2 4 60 5 3 3 I 4 24 35 2 I 4 2 7 31 19 2 I 5 7 15 13 13 I 6 22 9 6 I 3 2 7 34 13 16 I 8 20 19 9 9 5 13 3 lO 8 I II 6 12 3 13 I 14 2 15 I it is almost impossible to select a stand in which the percentage of each species in mixture is exactly an average of the whole area. It is therefore impractical to keep all the species sepa- rate in the estimate of growth of a mixed forest. The growth of each of the ruling species is determined separately and the rest arc lumped together or are considered a part of the ruling class. In the examjle given above the red and rock oak and clicstnut are kept separate. Together they constitute 65 percent of the stand. The other species are lumped together as a single species and one or more test trees used of a species which represents, in the forester's judgment, about an average. In tlie above example red majile would show about an average growth, so that after determining the average diameter of tlic various s])ccics taken together, one or more red maples are cut and used to THE GROIVTH OF TREES AND STANDS. 313 estimate growth. The volume of the several species which are lumped together may be determined from the maple test trees or from volume tables for the separate species. In most cases tlie mean sample-tree method is the simplest for determining the growth of even-aged stands. Sometimes however, the trees are not sufficiently uniform in growth to use this method. For example, one may wish to keep separate the dominant and suppressed trees. Then two or more groups are made instead of one. If a stand is even-aged, but on account of its broken character has several distinct tree classes, then it is desirable to estimate the growth of each class separately. In the same way, if a stand is not strictly even-aged, the different age classes may be kept separate and by felling separate test trees for each class the growth of each may be determined. An illustration of stands in which it is necessary to esti- mate the growth of several classes separately is found on old pastures in New England which have grown up to hardwoods. One often finds old chestnut trees which started in the open, and in the same stand groups of younger trees whose growth is quite different. Usually these tree classes differ in diameter so m.uch that the arbitrary group method may be used in the study of their growth. But if the diameters overlap, then the classes must be tallied in separate columns when the stand is calipered. Another method of determining the future growth of a stand is to assume that it will grow in the future at the average rate it has grown during its entire past life; that is, instead of basing the future growth on the periodic growth for the past 5 or ID years, it is based on the average growth during the whole past hfe of the tree. In other words, the mean annual incre- ment of the stand is assumed to remain the same for a specified number of years. To determine the mean annual growth of a stand the total volume is computed and then divided by the average age. This method gives only approximate rcsuItsT During the period of rapid growth, the mean annual growth is less than the current 314 FOREST MENSURATION. annual growth, and in later life it is greater. The method gives accurate results only at the period when the mean annual growth is equal to the current annual growth. Nevertheless it serves as a ready way of estimating increment and is often used. Thus in the sprout region of New England the yieW of stands is sometimes predicted by a study of the mean annual growth. More often, however, yield tables are used, as they are much easier in application, and if applied judicioo.ily, are fully as accurate as the method just described. 178. To Determine the Growth in Volume of an Entire Forest. — One of the important problems in organizinj^ a forest, which is to be managed on the principles of forestry, is to deter- mine its annual production. Usually two questions must be answered, namely, what is the rate of growth in volume over the whole tract ? What will be the merchantable yield of the tract in a specified period? The rate of growth in volume over the whole forest is used in determining the amount of timber which can be cut annually or periodically without reducing the productive capacity of the forest. In practice the mean annual rather than the current annual growth is used. If the forest is composed of even-aged stands, as in the mixed hardwoods of Connecticut, the procedure is as follows: The tract is divided and subdivided into so-called compartments and subcompartments, enabling the study of each part of the forest separately. The final yield at maturity of each subcompartment is estimated and the mean annual growth computed by dividing this yield by the final age. The mean annual production of all subcompartments taken together constitutes the annual production of the forest. In a many-aged forest, managed on the selection system, the yield of each division of the forest at the end of a specified cutting period is calculated. This yield divided by the number of years in the period is the mean annual growth. The total annual production of the whole forest is the sum of the results found for the separate divisions. The method of determining the yield in many aged stands at THE GROH^TH OF TREES AND STANDS. $1$ the end of a specified period is described in section 198. The appHcation of these studies of growth in regulating the annual or periodic cut constitutes a part of forest management and its discussion is not germane to the present work. The other question, namely, what amount of timber can be cut in a specified period ? involves the prediction of future yield for separate portions of a forest based on periodic growth for the last five or ten years. The divisions which are likely to become merchantable within the specified period are studied and the future yield predicted by the methods described in sec- tion 174 for even-aged stands and in section 198 for many-aged stands. The prediction of yield in different parts of a forest is made in the preparation of working plans and is discussed in books on fo"rest management. CHAPTER XVII. YIELD TABLES. 179. Definition of Yield Tables. — A yield table is a tabu- lar statement of the yield per acre, at different periods, of a forest of a specified character growing on a specified class of soil and treated under a specified method of managcnent. Usually yield tables show t'.e future product of stands, and in this book the term when used alone will have that meaning. The Society of American Foresters has adopted the terms juture yield table for one showing future products, and present yield table for one showing the present stand. In this country we also distinguish between yield tables jor even-aged stands and yield tables jor many-aged stands. The first show the product, at different ages, of stands wl ich have been established on clearings, and which are e\en-aged or nearly so. The second class of yield tables show the yield per acre of many-aged forests after the large trees have been rcm.oved under a specified system. The last are often also called incre- ment or growth tables. They are, l^.owever, properly called yield tables because they show the product j^er acre at diflerent periods of a forest treated under a specified system of manage- ment. 180. Yield Tables for Even-aged Stands.— -As yet only one or two attemj)ts liave been made in tliis country to construct yield tables for even aged stands. On tlie other liand, the yiild tables abroad are altogether for even aged forests, because the bulk of the forests are the result of jJanting or systematic natural rej)ro- duction on areas cleared at one time or within a short period. 316 YIELD TABLES 317 American foresters have been inclined to regard such tables as less important than the yield tables for many-aged forests. It should be remembered, however, that there is in the aggregate an enormous area of second-growth forest throughout the country which is even-aged or approximately even-aged, and that this area is being constantly increased through fire, cutting, abandon- ment of old fields, and planting. The forester is handicapped on all sides by the lack of yield tables, both in deciding upon the introduction of forestry on given tracts and also in the work of making thinnings and in making working-plans. The first yield tables of this character in this country were made in 1894 for the white pine by Gift'ord Pinch ot and the present writer. Since that time conditions of lumbering have changed, and the tables shoul 1 be replaced by a more exhaustive study. The list of instances in which trees are growing in even-aged- stands would include not only all plantations, but the old clear- ings made by fire, windfall, clear-cutting, and the abandoned fields. Nearly every species which has light seed may be found in even -aged stands of greater or less extent, and many of the heavy-seeded trees occur as even-aged sprout stands after clear- cuttings, as, for example, in southern New England. The methods used in making yield tables for such stands will necessarily be very similar to those used in Europe. The Ameri- can should, therefore, understand European methods, and it is then a simple matter to make such modifications as are required by the circumstances. 181. European Yield Tables. — It is customary to distinguish between Normal or Index and Empirical Yield Tables. By a Normal or Index Yield Table is understood a table showing the yield, at different ages, of fully stocked stands. Empirical Yield Tables are based on stands which represent an average of the whole forest, including the poorly stocked as well as the best areas. -^ Yield tables are further distinguished as local and general. Local yield tables are based upon data gathered in a restricted 31 8 FOREST MENSURATION. locality, and have only a local value. General yield tables are based upon data from a large area, such as a State or whole country. For example, Wm. Weise's yield table for Scotch pine is a general yield table based on data from all over Ger- many and designed for general use. On the other hand, Lan- dolt's yield tables for the Zihlwald are based on Zihlwald figures and are not strictly applicable elsewhere. In Germany the question of the correctness of general yield tables has been frequently discussed. The general yield tables for entire Germany are now distrusted, and the tables for more restricted regions are substituted for them. It is sometimes difficult to decide whether the results of studies in different regions differ because of the different factors of growth or because of the difference in silvicultural treatment or difference in methods of investigation. It is almost without doubt, however, that even in Germany the conditions for growth differ enough to make separate yield tables advisable. For example, the yields of spruce in central and southern Germany differ by a consid2rable amount; and Schwappach found marked differences in the growth of pine in different parts of Germany. If this is true for Ger- many, it must be doubly important in the United States, where there are wide climatic and geological differences which cause a variation in yield of a given species. It is a good rule in this country to make separate yield tables for different forest regions. Thus normal yield tables for white pine should be made separately for New England, the Appalachian region, and the Lake States; and investigation may show a still further re- stricting of the localities to be necessary. 182. Normal Yield Tables. — Normal yield tables show the product of fully stocked stands. By a normal or fully stocked stand is meant one witli the average maximuni yirhi actually obtainable with a given species under a given method of treat- ment in a given quality of site. Normal yield tables show the average maximum yield which results on an area fully stocked by planting or natural seeding, and undisturbed during the stand's YIELD TABLES. 319 life by fire, wind, cutting, insects, or other causes. It is there- fore a yield actually obtainable if the forest be successfully pro- tected from disturbing factors, instead of a theoretical yield, which can seldom be secured. It is very difficult to determine by the eye whether a stand is normal or not. One who has had experience with the species in question can, however, judge of the normality of a stand with sufficient degree of accuracy for purposes of general description, and in order to use normal yield tables. In gathering data for yield tables, it is not always possible to determine in the field whether a stand is normal or not. There- fore the forester measures such stands as seem to him as jully stocked as possible. These stands are later compared at the ofiice, and those which deviate too far from the average are dis- carded as not normal. The rule given by Professor Baur to determine whether stands are normal is as follows: Stands M'hich have the same age and average height are compared, and all are considered normal whose total basal area lies within a range of 15 percent; that is, the basal area of the best- and poorest- stocked stands must not differ more than 15 percent. Nearly always there are some stands whose total basal area is too great; that is, which are abnormally well stocked. These are considered abnormal, just as those which are not sufficiently stocked. This rule is based on the assumption that a comparison of the basal areas of the stands is equivalent to a comparison of the volumes. As explained in section 127, the volumes of trees in even-aged stands vary so nearly as their basal areas that errors due to deviations from this law are negligible. The actual number of trees per acre cannot be taken as a measure of normality, because two stands of the same height and the same age may be normal, but have a different number of trees. On the other hand, if normal, they would have approximately the same basal area, at least within 15 percent. The standard normality represents The best that actually exists and not the best that might exist under ideal conditions. 320 FOREST MENSURATION. Normality of stand is, therefore, relative rather than absolute, and as the yield of forests is improved by scientific management, the conception of normality of a given species changes. Thus the normal yield of plantations which are to be thinned through life is larger than the normal yield of stands which will not be thinned at all or not often enough. In preparing normal yield tables, one presupposes a specified system of management and aims to show the average maximum yield of fully stocked forests under those conditions. It is, therefore, entirely proper that there should be two sets of normal yield tables in this country: first, for fully stocked stands which are correctly thinned, and second, for stands not thinned. 183. Contents of Normal Yield Tables.— The most important part of the tables is the yield in timber at dift'erent ages. In addition, the tables contain the average number of trees per acre, the total basal area, the average height, and diameter of the average tree. Generally they contain also the growth per- cent and the forest form factors. Most European yield tables give the total cubic contents of the main crop, including all wood 7 centimeters and over in diameter, and also the volume of the subordinate trees which ma}- be removed by thinnings. The average height is included chiefly as a guide to the forester in judging the quality of the site of given stands. It has been found that the best qualities give the greatest height, and, vice versa, the poorest qualities give the poorest height growth. The only cases where this is not true are where a stand is too much crowded or is too open. If a forest has been tliinned like those in Europe, this stagnation of heiglit growth by overcrowding does not occur. The average diameter is given as an indication of the class of timber produced. It difi"crs so much with different stands that it cannot be used as an index of the quality of the site. It is of value to know the number of trees required to secure the total product, and it is a lielp in estimating the j)robable cost of cutting the timber. The number of trees per acre enables a YIELD TABLES. 321 comparison of the relative tolerance of side shade of different species and rapidity of the reduction of trees from period to period. The total basal area is used in practice to test the normality of stands. If a wind has entered a stand and it is found by calipering that the basal area is only 40 percent of the yield table, the volume will also be about 40 percent of the volume in the yield table, on the principle that the volumes of stands vary approximately as the basal areas. The forest form factor is used to estimate volume of stands. The contents of a specified stand is found by multiplying the total basal area by the product of the height and the form factor (taken from the yield tabic). In the Appendix several yield tables for European species are given. A number of columns have, however, been omitted as unnecessary for the purposes in hand, namely, the yield of material below 7 centimeters in diameter and the annual growth in height and volume. 184. Uses of Normal Yield Tables. — The practical uses of normal yield tables are as follows: 1. The prediction of the future returns on an investment in planting. The tables show what may be expected at different ages, provided no damage is suffered from fire or other adverse causes. They show how soon merchantable timber mav be obtained, and by allowing a reasonable amount for damages, one may make a conservative estimate of the money returns on an investment. 2. The prediction of the future yield of young or middle-aged stands. The value of immature stands lies chiefly in their pos- sibihty for future returns. Yield tables enable the prediction of the future returns and hence the correct valuation of such stands. This is of great use in the purchase and sale of second growth, and in damage suits where young grou'th has been injured or destroyed. In applying the tables a discount must be made if the immature stands are obviously not fully stocked. The forester estimates the degree of stocking and assumes that the 32 2 FOREST MENSURATION. ratio of tlie stocking to the normal will be the same at maturity as now. 3. An estimate of the contents of stands. This is done l)y estimating the age and the degree of stocking and then taking the yield per acre from a yield table. If an even-aged stand of loblolly pine is 0.8 stocked and is 30 years old, the yield per acre is 80 percent of that shown in the yield table for 30-year- old stands. 4. The determination of the quality of a specified site for the growth of timber. The volume, basal area, or height of normal stands indicate the quaHty of the site. Suppose one owns a forest and wishes to determine the quality of site, as is often necessary in making a detailed working-plan. The height and age of a portion of the stand which is fully stocked is compared with the heights for the age in question in the yield tables, and the quality which has the nearest height ascertained. The total basal area or volume of a sample plot would serve still better than the height to determine quality of locality, but this would take too much time unless sample plots were taken for some other purpose. 5. The determination of the financial rotation of forests, their expectation value, and their normal yield and growing stock, and the solution of many other problems of forest management. 185. Collection of Data to Construct Yield Tables. — Normal yield tables are based on the measurement of a large number of sample acres in fully stocked stands of different ages, grow- ing in different sites. The most satisfactory results are obtained by taking repeated measurements, at intervals of about five years, of permanent sample plots. We require, however, yield tables at once, and cannot wait for 10 to 30 years for the results of the periodic measurements. Therefore a large number of sample j^lots arc measured in normal stands, as they are to-day, and from them the yield tables are constructed. This method is described in the following pages with particular reference to the European practice. The plan of work is as follows*. I YIELD TABLES. 323 First, to select a large number of sample plots of dilTerent ages which are normally stocked. Second, to determine accurately the contents of these sample plots. Third, to determine the quality of the site to which each plot belongs. Fourth, to construct curves for the contents per acre of stands of different ages in sites of different quahty. Fifth, to construct curves for height, basal area, and num- ber of trees per acre, and to compute any other information desirable for the table, such as the forest percent and the form factor. Sixth, to tabulate all results in the final yield table. i86. Selection of the Sample Plots. — The plots are located in fully stoclvcd stands of diff'erent ages and sites of different quality. As explained in section 182, it is difficult to determine by the eye whether a stand is fully stocked or not. Two trained investigators would often differ in their judgment of the nor- mality of a stand, and sometimes a plot which appears at first fully stocked proves defective upon further examination. There- fore the fieldmen select for measurement plots which appear to them fully stocked. The final decision as to the normality of the stands is reserved until their total basal areas can be com- pared. In Europe it is easy to find normally stocked stands, for most of the state forests have been under management for many years, and even the mature forests were in most cases established under a forester's care. The plots are distributed among stands of different ages from 10 years up to maturity. The greatest proportion of plots is located among the old and middle-aged stands. Those under 30 years old are less important, because, even in intensively managed forests, the product of thinnings is small before that time and the final yield is seldom used^ in practice. The plots are located in sites of different quality. The forester cannot always determine by the eye the quality of a given site, 324 FOREST MENSURATION. but he can estimate it closely enough to enable him to include all qualities in the valuation areas. 187. Necessary Number of Sample Plots. — In general 150 plots are considered a minimum number, when five quahties of site are distinguished, and where the tables are designed for a r.^la- tively small State or county. For general yield tables more must be used. Modern European yield tables are based on it,o to 450 valuation surveys, a part being repeated surveys of permanent sample plots. 188. Thinning of the Stand before Measurement. -European yield tables show tb.e product of thinnings as well as of the yield of the main stand. Before the trees are calipered, a thinning is marked, so that the two classes of trees may be kept separate in the tally and their volumes computed separately. 189. Measurement of the Plots. — The rule in Europe is to lay off whole hectares, but in practice a portion of the plots used are J and \ hectare. The plots are usually square, and are surveyed out with accuracy, with boundaries distinctly marked. The calipering is done with great care, each tree being measured two ways or half the trees measured east and west and the other half north and south. After the calipering, test trees are felled for the computation of volume. Usually the Urich method is used, but recently the volume curve method has been introduced, notably in Austria. The number of test trees ranges from 9 to over 20. 190. Description of the Sample Plots. — As a rule in Europe the description is considered subordinate. This is because pure stands are chosen which are even-aged, normally stocked, and in good thrifty normal condition. There is, then, really nothing to describe except the soil. And since the quality of tlie site is judged entirely by the product, and not by the soil's aj)pearance, the descrii)tion is not absolutely necessary. It is only where one is trying to separate regions of growth tliat this becomes neces- sary. In Schappach's tables for the Scotch pine, there is no description whatever. Other tables generally contain the follow- YiBLD Tables. 325 ing points: Elevation, aspect, degree of slope, geological formation, kind of soil, its depth, consistency, and degree of moisture. When tables are published the results of the measurements and elso the description are given in a tabulated form, so that the results from the ligures can be traced back by students and exj:eits if desired. 191. Construction of the Tables. — The first work in the oflEice after collecting the field data is to compute for each plot (in vv^hole hectare or acre terms) the total yield, basal area, num- ber of trees, average age, height, diameter, and form factor. The next step is to assign the different ]jlots to their proper quali- ties of site. And it is exactly this point about \vl ich many authors disagree. The simplest method is that of Baur, called ,the method of bands. The total yield in cubic measure of each stand is j lotted on cross-section paper, whose ordinates represent hnal yield of the main crop in cubic measure and whose abscissee represent the average age of the stands. As each point is j lotted, the number of the valuation survey is also entered near it. Then regular curves are drawn through the maximum and minimum points, confining all the points in a comet-shaped band whose outer edges represent the maximum and minimum yield. Tl en the ordinates at each decade lying between these curves are divided into five equal parts, and the dividing points are connected by curves which separate the points representing the yield of the different plots into five divisions. The points lying in a single band indicate plots which belong to the same quality of si'e. A modification of the method just described is to use heights instead of volumes to determine the quality of the si'e. After the heights on all the plots have been determined they are entered on cross-section paper whose abscissae represent age and ordinates height. A maximum and minimum curve are drawn and then intermediate curves are interpolated just as in the other method. All plots whose heights l"ic in a given narrow band are assumed to have the same quality of site. This method is 326 FOREST MENSURATION. based on the principle that the height of an even-aged stand is a reliable index of the quality of site. It has been proved by repeated experiment that the classification of sample plots by this method and by that just described in the precedmg para- graph leads to practically the same result. Sometimes the average height of the stand is used, but some authors advocate the determination of the quahty of site by moans of the maximum height. Still another plan is to judge the quality of site by the volume or height of a specified number of the largest trees instead of by the total volume or the height of the stand. Thus one might use the volume or height of the 200 or 300 largest trees on each plot. The purpose of this plan is to eliminate all possible errors arising from differences in thinning, that is, from the presence of more or less small suppressed trees. Still another plan sometimes suggested is to base the quality of site not on the largest trees but on the second 100 trees, in order to eliminate errors due to the presence of abnormally large trees, such as occur in most stands which have been established by natural reproduction. The plots which are of the same quality of site are then grouped together and average curves constructed for volume, height, diameter, basal area, number of trees, and so on, and the results tabulated as a part of the yield table. 192. Normal Yield Tables in this Country. — Some maintain that it is not feasible to construct normal yield tables in this country, because of the irregularity of our even-a^ed stands, most of which have originated from natural reproduction and are generally composed of a number of species in mixture. This claim is due to a false idea of what constitutes a normal stand. It is entirely possible to make tables of the yield of fully stocked stands which have started under a specified set of conditions and have been managed in a specified way. Such tables show the maximum yield under certain conditions and serve as an index or standard of comparison. They are, therefore, true index or normal yield tables, although their results are not so high YIELD TABLES. 327 as the European tables. In other words, the standard of the highest average yield actually obtainable in many of our forests is not so high as that in Europe, because the systems of manage- ment are not so intensive. There are three problems of yield tables for even-aged foiests in this country: i. Yield tables for unthinned pure stands. 2. Yield tables for unthinned mixed stands. 3, Yield tables for thinned stands. 193. Normal Yield Tables for Unthinned Pure Stands. — These tables are required now in many sections of the country where clearings made by fire, cuttings, wind, or otherwise, come up to pure stands approximately even-aged, and where it is impractical to make improvement thinnings at present and probably not for a considerable length of time. The method of constructing the tables is, in general, to take a large number of plot surveys in pure, fully stocked stands of different ages occurring in different situations, and average them together as explained for the European forests. The chief diffi- culty in this country is to find plots which are pure and fully stocked. If none exist, then it is unnecessary to make yield tables for pure forests, but tables for mixed forests are made instead. With many species such plots do occur and in suffi- cient amounts to make tables which will meet the requirements of our present problems. It is often difficult to find whole acres which are in every way satisfactory. In this case irregular plots, if necessary less than one acre in size, may be taken. The adjust- able staff -head, adjustable angle-mirror, or staff -compass, may be used to lay out irregular plots, which give satisfactory results provided the angles are not acute. The plots should be pure and fully stocked. It is an unsat- isfactory method to use plots which are not pure or fully stocked, and by estimating the degree of density convert the measure- m.ents into terms of full stocking. This was done by the author in an • investigation of the white pine, with results which have proved unsatisfactory. 328 FOREST MENSURATION. The trees on the plots are carefully calipered in the ordinary way and then test trees cut to enable the accurate determination of volume. One of the diameter group methods, like the arbitrary group or volume curve method, should be used, and 6 to lo test trees used for each plot, except in the young stands, where 3 to 5 test trees ordinarily suffice. If it is impractical to take test trees on account of the necessity of buying the trees or for other reasons, volume tables are used. The test-tree method is, how- ever, to be used when possible. In many investigations it is desirable to keep separate the main stand and the trees which ought to be removed by thinning. This necessitates marking for an improvement thinning before the calipering is done. The diameters of the marked trees are recorded in a separate column and test trees cut to enable a separate computation of volume. The yield tables will then show how much would be obtained if thinnings were made and enable the owner to judge of their practicability. The yield tables should show for the whole stand (or in some instances for the main and subordinate stands separately) the number of trees per acre, the basal area, average minimum and maximum diameters, the average height, the total cubic volume, the merchantable volume in board feet or cords or both. Other information, such as the forest form factor, growth percent, etc., may be added if needed Ijy the investigation in question. 194. Yield Tables for Thinned Stands. — The method described above cannot be used for stands which are thinned, because by proper thinning much larger trees can be produced in a given time, and the total merchantable timber will be considerably greater. By tliinning, the period from the establishment of a stand to merchantable size can be often reduced by 10 to 20 years. In this country there are practically no stands which have been thinned from youth to maturity, so that the estimate of yield must be made by a different method from tliat described in the previous section. As explained in section 153, it is fair to assume that by thin- YIELD TABLES. 329 nings the growth of the trees may be so much increased that all will be as large as the average maximum obtained in an unthinned stand. That is, if a stand is fully stocked at the beginning, the forester can, by thinnings, govern the development of the crowns of the leading trees and produce timber of such a size as be desires up to the maximum capacity of the species,- as represented by those standing in the open with entirely free crowns. The develop- ment which the forester usually desires is that of the maximum trees in an unthinned stand, for these represent rapid growth combined with good quality. This is particularly true in this country, where the stands are seldom so overcrowded as to make the maximum trees too small for use in this method. The forester studies the diameter and volume growth of the maximum trees in stands of different ages, and studies the development of crown, in length and width, necessary to pro- duce such trees. He first determines the size of trees which can be produced at maturity. Suppose, for example, that this size is at 60 years 15 inches at breast-height, 70 feet high, 19 cubic feet in volume, with a crown 30 feet long and 20 feet wide. The growth of the trees on which these data are based show the dimensions at previous periods. These dimensions are com- pared with those of maximum trees in younger stands, and the probable dimensions of the crowns at different ages, which are necessary for the production of the trees 15 inches in diameter in 60 years, are determined. The next step is to determine how many trees can stand on an acre at different ages. This cannot be done merely by squar- ing the diameter of the crown, as, for example, 20 feet, and dividing the area of an acre by the result, for it may happen that a greater amount of space is required for the development of a crown of the size in question, or that the crowns may inter- lace to some extent and fit together more compactly than would be represented by this method. A silvical study is necessary to determine how close together trees maA' stand at different ages to produce crowns of certain sizes. Direct observation and 330 FOREST MENSURATION. measurements of small groups of trees will answer this question. The required average crown space is determined for all ages and not merely at maturity, so that the number of trees and volume per acre may be shown from decade to decade up to the merchantable period. Such a table shows the yield of the lead- ing trees, it being assumed that the subordinate ones are removed by the thinnings. The tables are not so complete as the regular normal yield tables. But they furnish the important information required in our present problems, and will serve until there are forests which have been under treatment long enough to be used as a basis for the tables. The product of thinnings and their cost and returns must be estimated. The cost of the first thinnings can be definitely determined by sample plots. The later thinnings would, usually at least, pay for themselves, and may often be disregarded for the sake of conservatism. The study furnishes, in any case, sufficient information to make a conservative estimate of the returns in thinnings. Inasmuch as the tables show the crown development and space required for the leading trees at different ages, they serve as an aid in making the thinnings, for the forester can see that as soon as the required crown space is reduced by the closing together of the branches and the necessary length of crown is falling off, by too heavy shade, a thinning is needed. In making such a yield table, it must be borne in mind that too heavy thinnings may be injurious by drying out the roots or allowing the ground to run wild with forest weeds. The present method, however, is based on the maximum trees of a forest, and therefore represents a condition which does not require excessive thinnings. This method may be used also to determine the yield of mixed stands which are thinned. It is more difficult to deter- mine the number of trees jjcr acre than in j)ure stands. The mu- tual effect of the mixture must be stU(Hed, a delicate silvical (]ucs- tion, but one which may be worked out by a skilled investigator. YIELD TABLES. 33 1 One problem is met that is not answered by any of the yield tables described above, namely, What will be the yield of stands thinned in middle or late Hfe? The previous methods assume that thinnings are begun in early youth and are repeated at proper intervals. Thinnings are just being introduced into this country, and many unthinncd stands 40, 50, 60 years and over, occur for which thinnings are advocated and a knowledge of whose future yield is desired. In the absence of available stands of this kind which have been thinned, the following plan is recom- mended: A study of volume growth of individual trees is made in stands which are thinned, as described for diameter growth in section 155. Thus the volume growth is determined for stands which are thinned for the first time at 30, 40, 50 years, etc. This growth is expressed as a percentage and is compared with that in stands unthinned, the difference representing per- centage of increase in growth. Assuming that thinnings will be made later, sufficient to maintain the growth, the yield tables for unthinned stands may be corrected in the following way: Suppose that by thinning, the current rate of growth of a 30- year- old stand is increased 20 percent, the volume curve for the yield tables of the species and quality of site in question is at the 30- year point raised to show an increase in volume of 20 percent. A curve is then drawn from this new point parallel to the old curve and a new set of values introduced into the yield table. This same thing is done for stands thinned for the first time in 40 years, 50 years, etc. It is probable that the successive thin- nings will cause an increase in each case, which would really cause the new curves to diverge from the old. The present assumption is, however, conservative, and serves the immediate needs of investigation. 195. Normal Yield Tables for Mixed Forests. — As far as the author is informed, practically no studies have been made of the yield of mixed forests. A few local yield tables for mixed stands have been made in Europe, but most authors avoid mentioning the subject, or state that it is impractical to construct them. 332 FOREST MENSURATION. Nevertheless, European foresters advocate the establishment of mixed stands for the reason, among others, that the yield is greater than in pure forests; and yet no information is available as to what may be expected from such mixed stands. This lack is due to the difficulty of constructing yield tables for mixed forests. One perplexing question is whether a mixed stand 30 years old had the same percentage of mixture when estab- lished, and whether the mixture can be maintained as now until maturity. Another difficulty is to find stands with a uniform percentage of the species in mixture. Other problems, such as the manner of mixture, whether by groups or singly, and how the data are to be arranged to be of practical value, add to the difficulties, and have probably prevented investigators from attempting to construct such yield tables. Therefore to esti- mate the yield of a mixed forest in Europe one has to use }'ield tables for pure forests, allowing the correct percentage for each species in mixture. But mixed forests often yield more than pure forests. One example is quoted of the growth of a mixed spruce and pine forest in Silesia \Ahich in 80 years had a mean annual growth 18 percent greater than pure spaice and 28 per- cent greater than pure pine, on the same class of soil. By using yield tables for pure forcsis, and supposing each species to consti- tute 50 percent, the mixture would be assumed to have a yield less than pure spruce, whereas really it would be greater. It is probable that normal yield tables for mixed stands can- not be made so com])lete as those for pure stands. Tlie infor- mation of practical importance can, however, be furnished. Although the author has had no opportunity to use the method proposed below, he believes that it can be employed in a prac- tical way in this country. To simplify the description, a speci- fied ])r()l)k'ni will be assumed. Su])j)Ose that it is desired to make a yiekl table for white ])ine mixed with oaks. This is a common forest type in eastern Massachusetts, and the yield at different periods is of j)ractical im])ortancr to the forester. \'ield tables would show first the j^rochict of \\\\\[v pine in this lyi)e YIELD TABLES. 333 of forest when it forms 25^0 50^0 and 75^, respectively, of the mixture. The ordinary yield table shows the product of pure stands. Then the table should show the product of the other ruling species of the type for certain percentages in the mixture, and finally the yield of the miscellaneous species taken together. The mode of procedure is as follows: A large num- ber of sample plots are taken in the specified type, comprising a variety of ages from 20 years to maturity. If the same per- centage of mixture occurs in more than one quahty of site, separate tables are made for each site. To take white pine first, its volume in each plot is determined, and also the percentage in mixture based on the total volume of the main crop. Then all values are entered on cross- section paper whose abscissse represent age and ordinates volume. As each volume is entered, the per- centage of white pine in mixture is entered above the point. Wlien all points are plotted, there will naturally be an immense number of different percentages represented. Points having the same percentages are joined together by light pencil lines as far as possible, to show the trend of the curves. Then, guided by these lines, a curve is drawn for the yield, when the percentage of white pine in mixture is 25%, '^0%, and 75%. The same operation is repeated for other ruling species and finally for the miscellaneous species taken together. The form of the table would be as follows: YIELD PER ACRE OF MIXED SPECIES. White Pine. Red Oak. Black Oak. Miscel. Species. i Percentage in Mixture. Percentage in Mixture Percentage in Mixture. Percentage in Mixture. < 25% SO% 75% 25% So% 75% 25% 50% 75% 25% 50% 75% Yield in Board Feet. Yield in Board Feet. Yield in Board Feet. Yield in Board Feet. 334 FOREST MENSURATION^. Suppose one owns a stand of pine and oak 15 yeais old, what will the yield be in 30 years? Suppose, further, the per- centage of mixture is estimated to be pine 50^, red oak ^0%, miscellaneous trees 20^0- The yield of pine is taken directly from the table; the yield of red oak is taken by proportion as one-fifth the difference between the yields from 25% and 50%. So also the yield for the miscellaneous trees may be obtained by proportion. 196. Yield Tables for Many-aged Stands. — These tables show the future yield of many-aged stands at different periods after a portion of the trees have been cut under a specified method of selection. The tables under consideration contain the mer- chantable yield per acre of a given species before the selection cuttings and the predicted future yield in 10, 20, and 30 years after cutting. Other information may also be given, such as the number of trees per acre, the number of years rec^uircd to obtain the original yield, and the mean annual increment. The tables are based on the assumption that the timber will be cut to a specified diameter limit. This does not mean that the method is appUcable only where a rigid diameter limit is used in the selection cuttings. On the other hand, in using the selection system it is often necessary to leave some large trees for seed and to remove some which have not reached maturity. It is, however, generally customary, at least in this country, to use a certain diameter hmit as a guide in making the selection cuttings, leaving where necessary trees above the limit and cutting certain others below that size, the amount of timber above and below the limit being about cfiual. Therefore, in speaking of cutting to a certain diameter limit, one means an average limit, and does not mean that the selection cuttings are made by rule of thumb and without reference to the silvical requirements of the forest. The form and contents of yield tables for many-aged stands are illustrated in the Ajjpcndix. The uses of yield tables for many-aged stands arc as follows: YIELD TABLES. 335 1. They enable the prediction of the growth of the trees left after lumbering, and the yield in merchantable timber in the future. 2. They enable the valuation of cut-over lands, and of imma- ture timber which has been destroyed by fire. 3. They are used to determine the diameter limit which will in the long run be most profitable in lumbering. 4. They enable an owner to determine whether it will pay to hold his land for a second cut and whether he has sufficient land to supply his mills indefinitely with timber. 5. They replace the ordinary yield tables, described in sec- tions 182 to 191, in all work of forest management in many-aged forests. 197. Necessary Field Work. — Yield tables for many-aged stands are based on three separate lines of field work, namely, valuation surveys, preparation of volume tables, and a study of diameter growth. The valuation surveys are taken to determine the average number of trees per acre of different sizes which will be cut and the number which will be left standing to accumulate growth for a succeeding crop. The tables, so far made in this country, have been based on strip sur\'eys which were also used in esti- mating merchantable timber, in making forest maps, etc. In these surveys it is customary to caliper the trees down to about three inches and on an occasional acre to count the saplings and seedlings. In calipering the trees, only those are included which are either of merchantable character or likely to be mer- chantable later on. Small trees must be scrutinized carefully, and if they are unsound, crippled, or otherwise obviously defect- tive and unlikely to Hvc until the next cutting, they are discarded or recorded in a separate column. All of the small trees now standing will, however, not live until the next cut even if per- fectly sound and thrifty, because many^will be killed in the ctruggle for light and space, just as in an even-aged stand, and many will be destroyed in felling and removing the larger trees. 33^ FOREST MENSURATION. The valuation sun^eys are taken under the assumption that all the sound thrifty trees below the given diameter limit will later become merchantable, while the loss through shading and through lumbering is determined in a separate study. The following method may be used to determine the loss to young trees through lumbering: Plot sur\'eys are taken in different forest types, so located and in such numbers as to give a good average of the prevailing conditions. The trees are caiipered and those which will probably be destroyed in lumber- ing are recorded separately. One who has a knowledge of legging can determine what trees will be cut, how they will be felled and bow hauled out; and he can determine just what small trees will probably be destroyed in this operation. It is sometimes possible to determine on the ground what trees will probably die through shading. More often this loss must be estimated from a silvical study of the tolerance of the species with special reference to the new conditions of light after lumbering. This is usually a matter of judgment and obser- vation rather than of actual measurement.* The death of small trees through various causes is best ex- pressed as a percentage of the number of trees of different sizes. Thus the reduction of the trees 4 to 6 inches in diameter might be estimated at 15%, 7 to 8 inches lo'^, and 9 to ii inches 5%. The loss due to shading would naturally be greater in thirty years than in shorter periods, a fact which must be taken into con- sideration. In all cases the loss should be made large enough to include the destruction of small trees for making skids, roads, bridges, and for other lumbering purposes. * Some have recommended the calculation of the reduction in the num- ber of trees with increase of age by the use of valuation surveys. It may be seen from the valuation surveys that the number of trees in the diam- eter classes falls off with increase of size. Suppose, for example, that there are on an average fourteen trees 8 inches and twelve trees 9 inches in diameter, and that it takes ten years to grow i inch in diameter. The loss, by shading, would then be 14.3% in ten years. The assumption is, however, not fair because new and more favorable conditions are established after lumbering. Yield tables. 337 A careful forest description accompanies all valuation surveys. Special attention must be given in these descriptions to the prob- able silvical effect of cutting to different diameter limits, to repro- duction, and to the question whether it is necessary to leave seed trees above the diameter limit or to remove any below it. This information is of value in deciding on the diameter limit. Further field work consists in a local study of growth of trees of different diameters. The method of making this study is fully described in section 159 and need not be further discussed at this point. Local volume tables, for trees of different diameters, are also made, the data being usually collected at the same time as the measurements of growth. 198. Construction of Yield Tables. — The first steps in the preparation of the yield tables is to construct, for each forest type, a table giving the average number of trees of different diameters on the valuation areas. This table is sometimes called the model acre, for it represents an average of all the acres surveyed in a given type. Naturally the average number of trees of a given diameter may be a fraction, as shown in the table on page 339. The model acre enables the computation of the volume of the merchantable trees above any desired average diameter limit, by the use of volume tables. The next step is to determine the future yield of the trees left after lumbering. The model acre shows the number of trees now standing below the diameter limit. This portion of the model acre is corrected to show the number of trees which probably will be standing at the time of the second cut. This is done by using the reducing factors for loss in lumbering and death by shade, determined as shown in the preceding section. The table of growth of trees of different diameters is then used to determine the size of the trees in 10, 20, and 30 years after the cutting. In using the growth table it is asi.umed that a tree of a specified diameter will grow at'the rate shown in the growth table for that diameter until it becomes one inch larger, 33* FOREST MENSURATION and that it will then grow at the rate shown in the table for that larger size. Thus a tree now ii inches in diameter will grow at the rate of an ii-inch tree until it becomes a 12-inch tree, when it will grow at the rate given for that diameter in the growth table. Another assumption is made, that as soon as a tree of a speci- fied diameter, say 11 inches, has grown i inch it will have the volume shown for a 12-inch tree in the local volume table. Sup- pose it takes live years for an 11 -inch tree to grow an inch, at the end of five years it has grown to have a volume equal to the aver- age of the 1 2 -inch trees now standing in the forest. The volume growth for five years is assumed to be the same as the difi'erence in volume of an 11- and a 12-inch tree in the volume table. This is an assumption that has never been verified. A better method would be to use a table of volume growth of trees of different diameters instead of a table of diameter growth. With the above principles in mind a table is made showing the condition of the stand now, in 10 years, 20 years, and 30 years after lumbering. An illustration of such a table is shown on the next page. From it the yield table in its final form may readily be constructed. In this computation an allowance has been made for death during and after the first cutting, of 5% in 10 years, 7% in 20 years, and 10% in 30 years. The original cut of 1979.5 board feet could be obtained in 28 years. To obtain this result, sub- tract 1289. 1 from 2143.2, divide by 10 to determine the mean annual growth between 20 and 30 years after cutting, then add enough years' growth to approximately equal 1979.5. Fractions of feet would be dropped in the fmal table. In our illustration the computation has been made for a i2-inch-diameter limit. Most yield tables show the yield for other diameter limits to enable the determination of the method of cutting which in the long run will be most profitable. 199. Indian Yield Tables for Many-aged Stands. — The foresters in British India use a method similar to that just described, YIELD TABLES. 339 (J~. o S O "^ ^ CI > 1 ^ 2: ^ 0 On lO LO -1- rO 3 n .2 6 ir 1 (N O fN O n o d (S (U >< o _c c _o ■o c 0 u Total Vol- ume, Board Feet. 00 <~0 -1- CO Volume Aver. Tree. Board Feet. On Li NO lO c _o -d c 0 O c Si a, Annual Growth in Diam- eter, Inches. OsO q « d d ONiOOOOOoOiori O ^ •+ lOvO t^ f^OO On 0 MI-ll-ll-lhHI-ll-ll-ll-lCS d d d d d d d d d d Total Vol- ume, Board Feet. on-c^O^ r^oo Ti- tN ^ o "0 o 0 On ON >- Tj-Ost^t^r<^csvOCO woo NVO O 0^(N O O r-^'^OOO t^t^^Tj-io M(S(N(NCN>->>-ii-i Vol. Av. Tree, from Vol. Table. Bd. Ft. ; ; ; ; ; . [i-i^i-ioofo rooo vo -+ r^ o "o o o OO Os (N rO r^ On rovo On >o Os HNC4r(frifO^'^lO 1 ^ W O NO (T) Tf rj- rOOO vO NO OviO M OnnO ■* rO P) M ii « w NO 00 OOOOOOt--'OlO<^r^;M>HH-wOOOOOOOOO rflONO t^OO C Own <~0 -t iOnO t^OO On O « N fO tJ- iT) 340 FOREST MENSURATION. to predict the future yield of many-aged stands of teak, sal, and other species cut under the selection system. These studies of yield are made in connection with the preparation of working plans for specified ^^■orking areas, and the resulting tables of yield are apphcable only to the tracts studied. Valuation sur- veys, in the form of strips, are taken to determine the number of trees of different sizes. The trees on the valuation areas are calipered and recorded in broad diameter or circumference classes. Thus Class I may include all trees over two feet in diam- eter, Class II trees i8 inches to 2 feet, Class III trees 12 to 18 inches. Class IV trees 6 to 12 inches, and Class \' those below 6 inches in diameter. The forests are so irregular that 20-30% of the area must often be covered by the surveys, and some maintain that, in order to obtain satisfactory data for the prediction of future yield, this should be extended to 50% in sal and similar forests. The valuation surveys are used to construct tables showing number of trees, by classes, standing on the tract in question. The following table, taken from a working plan for the Pozaun- daung Reserve in Burmah, illustrates the procedure. ESTIMATED NUMBER OF TEAK STANDING, IN 1901, ON THE TOTAL AREA OF 51,728 ACRES. Class I. Above 7 Feet in Circum- ference. Class 11. 6 to 7 Feet in Circum- ference. Class III. 4i to 6 Feet in Circum- ference. 13,100 9,300 21,068 The allowance of loss by death is, for Class I 5%, Class II 15%, Class III 30%. A study of growth of the species in question is made to deter- mine how long it takes for the trees to grow from one diameter class to the next higher. In the Pozaundaung working plan above referred to, the growth was based on the mcasurcm.cnt of rings on 121 stumps, and the results arrafigcd in the fol- lowing table: YIELD T/iBLES. 341 NUMBER OF YEARS REQUIRED TO PASS FROM A GIRTH OF: 0 to 3 Feet. 3 to 4i Feet. 4i to 6 Feet. 6 to 7 Feet. Number of Years to Reach Matiority. 64-5 53-7 42.7 32 193 The annual production of the forest is represented by the average number of trees which reach merchantable size each year. Thus in the above example the minimum circumference limit is 7 feet. The growth table shows that 32 years are re- quired for the second-class trees to become first-class, that is, in 32 years all the second-class trees will be 7 feet or over in circumference. The annual production may then be considered 9300, less 15%, divided by 32, or 247 trees. The method of using these data to determine the number of trees which should be cut annually is described in D'Arcy's Preparation of Working Plans. The discussion of that problem belongs to forest manage- ment and is beyond the scope of this book. 200 Empirical Yield Tables. — This term has been adopted by the author to designate tables showing the yield per acre, at different ages, of even-aged stands having an average degree 0} stocking, in contrast to normal yield tables, which represent fully stocked stands. The expression "empirical" has been chosen because the tables are based on the average yield actually found on areas of considerable extent. The tables are useful in many investigations in even-aged or approximately even- aged stands where it is not feasible or not necessary to construct normal yield tables. Such tables necessarily have only a tem- porary value, for, as the forests improve or deteriorate, the yield will later on be different from that now found on the areas under consideration. Empirical yield tables are used to determine the value of second growth, to predict future yield, and to serve as a guide and check in estimating standing timber.^ If they truly represent the average degree of stocking of a given tract or region, they are 342 FOREST MENSURATION. of greater use in the work just mentioned than normal yield tables, as their values may be used directly without discount. If, how- ever, a forest is more or less fully stocked than the average shown in the yield tables, it is not so easy to make the proper corrections as is the case with the normal tables. Empirical yield tables will doubtless be constmcted in con- nection with working plans for areas which are managed under one of the methods of clear cutting. In many cases the tables will have to be made for mixed stands. Where fuel alone is the product, all species could be lumped together with no further separation than an indication of the percentage of hard and soft wood, body-wood and limb-wood, etc. Such a table would enable the prediction of the future value of the crop. If logs, ties, etc., were to form a part of the crop, the results could still be expressed in cords, but there should also be shown the per- centage of timber suitable for logs, poles, ties, or other products. In predicting future values a different price per cord would be used for the different products. The work of constructing empirical yield tables is similar to that required for normal yield tables, the chief difference being in the selection of the sample plots and in the grouping and cla„^sifying the plots in the office. In general the following method may be used to construct the tables: A series of plot sur\'eys is made in the different forest types. The plots are distributed in each t}^e so as to include different age classes up to the maximum required in the investigation. The plots are located so as to represent average conditions, with respect to density of stocking, development of trees, etc. Each survey comprises calipering of the trees, measurement of test trees for the computation of volume, and a detailed forest descrip- tion. The ffrst work in the office is to separate the sur\-eys into groups according to the forest types they represent, the assignment of a survey to a given type being based on the forest description. The next step is to determine the volume and average age of each stand. A table is then constructed showing the average volume of stands of different ages. This is done by YIELD TyiBLES. 343 means of a volume curve based on age. The volume of each survey is plotted on cross-section paper whose horizontal lines represent age, and vertical lines volume. An average curve is then drawn through the points and the values for every ten years are read off and tabulated. Sometimes the volumes of stands of the same age vary so widely that it is difficult to draw an average curve. If the variation is too great, a satisfactory table cannot be made. Usually the forester can judge in the field W'hether the conditions in a single forest type are uniform enough to construct a useful empirical yield table. If the volumes of the different surveys differ very widely, a table may often be constructed by using the mean annual incre- ment. The table shown below was constructed in this way. There were not enough surveys to construct volume curves in the ordinary manner. Therefore the mean annual growth in volume was determined for each survey and the average obtained for all stands lo to 20, 20 to 30, 30 to 40 years old, etc. An average table showing the mean annual growth in volume was constructed, irregularities being evened off by inter- polation. The total yield in cords was then computed by mul- tiplication. The following table was constructed by this method, for use in a working plan for 12000 acres in southern New York. EMPIRICAL YIELD TABLE FOR DIFFERENT FOREST TYPES ON A TR,\CT OF 12,000 ACRES IN SOUTHERN NEW YORK. [Based on 167 Plot Surveys.] Mixed Hardwood Type, Quality I. Mixed Hardwood Type, Quality 11. Mixed Hardwood Type. Quality III. Chestnut Type Quality I. Age. Years. Yield per Acre, Cords. Mean Annual Growth per Acre, Cords. Yield per Acre. Cords. Mean Annual Growth per Acre, Cords. Yield per Acre, Cords. Mean Annual Growth per Acre, Cords. Yield per Acre, Cords. Mean Annual Growth per Acre, Cords. 8 7 0. s8 4.2 II .5 0.28 10.6 20 to 30 20 0 0.80 0.46 7.-0 0.28 25.0 I .00 30 to 40 25 9 0.74 17.8 0.51 12.9 0.37 36.7 1.05 40 to 50 29 ?, 0.65 17. I 0.38 "J 0.26 40.5 0.90 50 to 60 ?,o 8 0.56 17.0 0.31 II .0 0.20 40.7 0.74 60 to 70 30 5 0.47 16.9 0.26 10.4 0. 16 38.3 0.59 344 FOREST MENSURATION. 201. Periodic Measurement of Permanent Sample Trees and Plots. — There are a large number of problems in forest mensura- tion which cannot be satisfactorily solved by the methods described in the previous page*-,, but which require repeated measurements and observation cf specified trees or stands. The yield tables in Europe are now based in part, and will eventually be based almost entirely, on repeated measurements of permanent sample plots. The German government has established a very large number of plots throughout the State forests which are visited annually or every few years, and the necessary observations and measurements are taken for the study of the development of the stands. The method is briefly as follows: Stands are chosen which are fully stocked, and ordinarily only those which are composed of a single species. The plots are not smaller than a quarter hectare each. Permanent posts are set at the corners and the boundary-lines are marked by shallow ditches or by painting the boundary trees. Surrounding each plot is a so-called "isolation-strip," 50 to 100 feet wide, which is under the same treatment as the plot. Before calipering the trees a uniform thinning is made on the plot and isolation-strip. The trees are then calipered, and are usually numbered so that the diameter of each tree at the present time may be compared with that found later on. After calipering, the volume of the stand is computed by the use of the Urich or a similar method. The test trees are cut from the isolation-strip and not from the plot. After from 3 to 5 years the trees are again calipered and the volume deter- mined as at first. When three to five periodic measurements covering 15 to 20 years have been taken on each plot, the con- struction of yield tables becomes much simpler and the results are much more reliable than when they are based on one measure- ment of each plot. The study of permanent sample plots was begun in Ger- many in i860 and since then enough time has elapsed to enable the construction of accurate yield tables for a number of species. YIELD TABLES. 345 202. Permanent Sample Plots in this Country. — At the present time in this country foresters are handicapped by the lack of results derived from experience. Many of our operations in silviculture are based on the judgment of the forester as to what probably will happen, rather than on what has been known to occur in some specific instances. In order to secure definite data of the results of different kinds of treatment in different types of forest, the United States Government is now establishing a large number of sample plots for repeated observation.* The purpose of these plots is not only to study the rate of growth of individual trees and of whole stands after cutting, but also to study the reproduction of various species under different conditions, their tolerance in youth, and other silvical characteristics. In general the following classes of plots have so far been established: I. Plots of one-half acre or more in even-aged stands, estab- lished to determine the results of different degrees of thinning. These plots are similar to those established in Europe. Permanent stakes are set at the corners, the boundaries permanently desig- nated, and the trees numbered. The numbering is first done with chalk when the trees are calipered, and later the permanent numbers are put on in paint. Each tree is calipered two ways and a small paint spot is made at the point where the beam of the caliper touches the tree. This enables the forester to cahper the tree at exactly the same place when measurements are taken in later years. The diameters are recorded in the form shown below, and when a tree is recorded the caliper man gives also the estimate of the height and tree-class. A very careful description is made of each plot which is indicated on a map in order that it may later on be readily located. The records thus show the con- dition of each tree. A later measurement in 3 to 5 years will show the increase in diameter of each tree, its estimated height, and whether or not it belongs to the same class as previously. The results of different degrees of thinnmgs may be determined * This work was organized for Ihe Government in t904 by Mr. G. H. Myers and the author. 346 FOREST MENSURATION. by such plots in a way that would be impossible with the ordinary means of observation. Experiment No. Location Tallied by. . . Measured by. Date. Tree No. Species. Diameter, Breast-high. Class. Height 2. Plots of one acre in many-aged stands, to test the effect of the removal of the old trees on those left standing. In many- aged forests, like those in the spruce region of the northeast, there is a lack of definite information as to how the small trees will develop after the older ones have been removed under different methods of selection. Sample plots of one acre each are laid off in selected places, and enough are established to include the different local problems of silviculture. In addition to the records of diameter, height, tree-class, and the forest description described in the previous paragraphs, an accurate map is made locating each tree. This is done in the following way: A traverse board is set up in the middle of the plot, and the location of each tree is determined by means of a small alidade and by measuring the distance with a tape. The number of ench is also entered on the map. A horizontal sketch represcnt'»)g the projection of the crown is made in the case of the trees whose development is to be specially observed. 3. Reproduction plots of about a square rod each, to study the natural reproduction and the development oi the young trees under given conditions. These small plots are la:d out in great number where re[)roduction cuttings arc to be made or ha\e been made. Permanent posts are set at the corners and then all YIELD Tables. 347 growth on the plot is counted. Seedh'ngs and other small growth are recorded in the form shown below. A sketch is prepared showing the projection of crowns of all trees, above the seedling stage, which shade the plot. A careful forest description is made as in the previous cases. Experiment No. Date Location Tallied by . Counted by Species. 0-3 In Age. 3-6 In. Age. 6-12 In. Age. 12-18 In. Age. Species. 18-24 In. Age 2-3 Ft. Age. 3-4 Ft. Age. 4-5 Ft. Age. 4. Single-tree plots, comprising single trees or small groups of trees definitely located and numbered, for the observation of their behavior under specified conditions. There are many cases where American foresters are in doubt as to the exact effect on a given tree of the removal of one or more of its neighbors. The repeated observation and measurement of individual, trees or groups of trees growing under certain conditions would answer many of these questions. Such trees are designated by one or several permanent posts and their location indicated on the map. The trees are numbered and the point of measurement marked as described for the other plots. Vertical and horizontal sketches are made of the trees under observation, as well as of the neighboring trees, which may influence their development 348 FOREST MENSURATION. Single-tree plots are required in the study of tropical trees whose growth cannot be determined by annual rings. 5. Description plots, comprising areas of diSerent sizes chiefly located in the lumber woods, to observe the results of different kinds of lumbering. These areas are usually from 10 to 100 acres each. No measurements of trees are taken as in the preceding plots, but a very detailed description is made of the woods before and immediately after the lumbering. The areas are inspected every two or three years and the changes which occur on them are noted. On these plots there are usually located a considerable number of reproduction plots. CHAPTER XVIIL GRAPHIC METHODS USED IN FOREST MENSURATION. 203. The Use of Graphic Methods. — The results of scientific work in forest mensuration are expressed in tables of averages, based on widely varying values. These tables are constructed by the use of the simplest statistical method, namely, graphic interpolation. This method consists in representing graphically on cross-section paper a series of variable values and correlating them by a curve. The advantages of the graphic method of compiling statistics obtained in forest mensuration are as follows: First, it presents clearly to the eye the proper relationship of the quantities concerned, showing results in a way that a set of numerical figures in tables only indicate by prolonged study or fail entirely to indicate. Second, it offers a means of averaging data much more quickly than by ordinary mathematical calculations. Third, the results are accurate, errors which might otherwise escape detection being visible to the eye. For the same reason it gives the best means of culling out data which maybe abnormal. Fourth, it is an excellent method of determining a general law of variation of quantities. In work of forest mensuration it is difficult to secure enough field data to arrive at the law of variation of values without some interpolation. It is usually the average values which are sought, rather than the actual salues as obtained in the field. Suppose, for example, that a thousand trees are measured in the field to show the relation between 349 35© FOREST MENSUR/iTJON. height and diameter in a specified forest. If these are grouped by diameters, and the average height of each group is determined arithmetically, the heights of difierent diameters ^\ill follow each other more or less irregularly in the table, which evidently is not true of the natural law sought after. But the results \\\\\ approach nearer to this law and the irregularities be correspondingly less, the greater the number of trees measured. It is not feasible in practice to secure enough data to construct a perfectly regular table by merely averaging together the figures taken in the field, and there must be some interpolation to obtain the natural law of variation of heights with diameters. Therefore, the numerical averages are plotted on cross-section paper and the various values coroUated by means of a regular curve. The points on this curv^e will approach nearer to the natural law than any of the original points plotted, except as far as the latter happen to be on the curve. Then the value of any point upon the curve is not based merely on the field measurements which it represents, but is dependent for its value upon all of the original data. If looo trees were measured in the field, each point on the curs-e depends for its value on looo trees; whereas each original point on the cross-section paper may have depended only on a few trees. 204. Plotting of Values on Cross-section Paper. — Cross-section paper, with its series of perpendicular lines, represents a system of rectangular co-ordinates. Any two lines perpendicular to each other, as two of the heavy lines on the paper, may be taken as co-ordinate axes Any two other lines, parallel respectively to these axes and at known distances from them, will intersect in a point whose position is definitely fixed. The horizontal distance of this point from the vertical axis is called the abscissa of the point and the vertical distance from the horizontal axis is called the ordinate. A given value may be graphically repre- sented as a point, if its ordinate and abscissa are known. Sup- pose, for example, that it is desired to represent on cross-section paper the height (A a tree of a given dianutcr. Let the horizontal GRAPHIC METHODS USED IN FOREST MENSURATION. 35 1 lines or abscissas represent diameters and the vertical lines or ordinates represent heights. Then one measures off on the horizontal axis a distance corresponding to the diameter, accord- ing to an arbitrary scale, and on the vertical axis, a distance corresponding to the height. The intersection of the perpen- dicular lines erected at these two points fixes the position of the point which represents the height in question. Suppose that a large number of trees have been measured and a regular table is required, showing the average heights of trees of different diameters. This may be made by plotting the heights on cross- section paper as just explained, and correlating the values by a curve. The measured trees are classified by diameters and the heights of trees of the same diameter averaged. The results are arranged in a table like the following: AVERAGE HEIGHTS OF TREES OF DIFFERENT DIAMETERS. Diameter Class, Inches. 6 7 8 9 lO II 12 '5 Average Diameter of Trees Measuied, Inches. 7 8.05 9 13 13.8 14.9 Average Height of Trees | Measure d, Feet. 54 5 60 66 5 68 73 79 5 80 84 Number of Trees Measured. Average Height from Curve. Feet. 49-5 54-5 59-75 64-5 69 73 76.5 79-5 81.5 83.4 Examination of this table (column 3) shows that the heights increase with the diameters by irregular differences. If the heights are plotted on cross-section paper, these irregularities are very apparent. In plotting the points one lays off the diameters on the horizontal lines and the heights on the vertical lines, the scales being chosen arbitrarily. (Fig. 52.) In general the aim should be to choose such scales that thr curve will be neither very fiat nor very steep. This is accomplished if the largest 352 FOREST MENSURATION. ordinate is not less than one-half or greater than one and one- half of the greatest abscissa. This arrangement of scales makes the construction of the curs^e easier and more accurate. In the illustration given above one large square subdivided into tenths is given the value of one inch on the abscissae and ten feet on the ordinates. The basis of the table in our illustration is diameter. The diameters arc, therefore, the independent variable quantities and the heights are dependent variable quantities. It is custom- ary to lay off the independent quantities on the abscissae, so in the present case the latter represent diameters. The points are marked by a sharp pencil or draughtsman's pin-point. Beside each point is indicated, in light pencil, the number of trees on \vhich the value is based. This is given because in locating the cur\'e the consideration given to a single point is in direct pro- portion to ^h& number of trees on which its value is based. 90 Iso % "50 4 _^ 1 - ,^ i--^ ■^ ' 3 z^ '^ o3 y ^ 9 10 11 Vi 13 Diamutcr iu IncUes 14 15 Fig. 52.- -Carve showing Height of Trees of Different Diameters. 205. Construction of Curves. — After plotting the points, they are joined by straight lines in light pencil. This shows the trend of the curve and assists in its location. After careful inspection of the series of points, the curve is drawn free hand through the points, or as near them as possible. In locating the curve the weights of the various points arc considered, and it is drawn through or nearest to those representing the largest number of GRAPHIC METHODS USED IN FOREST MENSURATION. 3$ 3 measurements. The curve must be regular and smooth as dis- tinguished from wavy and broken. The curve should be located by the eye and first drawn free hand. Then the irregularities of the free-hand curve may be smoothed off by a spline or similar device. The resulting curve represents the heights of trees of all diameters, in their proper relation to each other, and from it the height, corresponding to any diameter, may be determined. Thus, to find the height of a 6-inch tree, measure, to scale, the vertical distance from the 6-inch mark on the horizontal axis to the curve. The heights, correspond- ing to each inch diameter, may thus be determined and a table of averages constructed, as shown in column 5 in the table on page 351- When the data are based on a large amount of field measure- ments, it is a simple matter to draw such a curve, for the values are so regular that a curvT may readily be drawn through or near most of the points. But when the data are rather meagre, more interpolation is necessary, and the construction of the curve requires a high degree of skill. In the illustration given above, the trees were grouped accord- ing to diameter, and the heights of all trees of a single-inch diam- eter class averaged together. Theoretically in this problem it would be possible also to work out a table of the variation of diameters based on height. In that case the trees would have been grouped by heights and the diameters of all trees of the same height averaged together. At first thought it would seem that two curves representing values worked in the two principles would coincide. They are, however, quite different. This will be clear from a graphic illustration, using diameter and age as the variables. Suppose, in Fig. 53, curves A and B represent the growth in diameter of two trees. In averaging the values of these cun-es, it makes a difference whether the average age of trees of different diameters or the average diameter of trees of different ages is sought. In the first case, ages are the dependent variables, and therefore are averaged together. Graphically, points on 354 FOREST MENSURATION. the same abscissae are averaged and curve C results. In the second case, diameter is the dependent variable and points on the same ordinates are averaged, giving curve {D) In finding the average of two curves, that is, to interpolate a curve exactly between them, one should not bisect the angle, but divide the vertical lines between the curves and draw the average curve through these dividing marks. The explanation in the foregoing pages shows how to con- struct a table giving the relation between two series of variable quantities. In many problems, however, there are three vari- ables. Thus, for example, in constructing a log rule, one has to deal with three variables, diameter, length, and volume. Suppose that looo logs have been sawed at a mill, and the diameter, length, and actual volume of each determined. The average contents of all logs having a common diameter and length are then deter- mined and the results tabulated in a form like the following: TABLE A. Average Contents of Logs. Length in Feet Diameter 8 10 13 14 16 Inches. Contents in Board Feet. 8 i6 18 23 27 34 9 19 24 33 36 44 lO 24 26 43 48 56 II 30 36 53 57 66 12 38 45 67 70 8i 13 47 55 76 86 94 14 56 64 96 102 118 15 67 80 114 124 135 i6 67 92 126 140 159 17 93 no 146 160 184 i8 106 122 164 188 215 The values in this table are then correlated by a series of harmonized curves. Separate curves are first made to correlate GRAPHIC METHODS USED IN FOREST MENSURATION. 355 the values in the vertical columns of the table. These curves may be best constructed on a single sheet of cross-section paper, for this enables a certain harmonizing of their forms. If a table (Table B) is constructed from these curves, the values in the TABLE B. Average Contents of Logs. (Vertical columns made regular by a series of curves.) Length in Feet. Diameter 8 10 13 14 16 Inches. Con ents in Board Feet. 8 16 iS 23 27 34 9 19 23 33 36 44 10 24 29 43 47 55 Ik 30 36 55 58 67 12 38 45 67 71 8i 13 47 55 80 86 97 H 57 66 94 102 "5 15 68 79 no 120 135 i6 80 92 127 140 •59 17 93 107 146 162 186 18 106 122 166 188 215 vertical columns will be regular; but the table may be irregular when read across, that is, the volumes of logs of the same diameter will increase with length by irregular differences. Expressed in another way, the curves in Fig. 54 are all perfect in themselves, but they are not at proper distances apart. Therefore it is necessary to construct a second series of curves on another sheet of cross-section paper, showing the contents of logs of different lengths for given diameters. For this series of curves, the second and not the first table is used. Fig. 55 shows the manner of constructing such a series of curves. A tabic is then constructed from this second set of cur\^es. This table will generally be found regular when read in any direction (Table C). If, however, there are still any irregularities, a third series of harmonized 356 FOREST MENSURATION. curves may be constructed to even oS any irregularities in the vertical columns caused in the construction of the second series. Such a table is more accurate for use in scaUng a large number of logs than the original table representing the arithmetical average of the field measurements. The reason is, that individual variations and accidental features are thrown out and the values are all brought into proper relation to each other. Each value in the final table depends on ever}' log measured, while in the first table each value depended only on the average of a few logs. TABLE C. Average Contents op Logs. (Obtained by evening off the horizontal lines in Table B by a series of curves.) Length in Feet. Diameter. 8 10 13 14 16 Inches. Contents in Board Feet. 8 i6 19 22 2 / 3^ 9 19 25 31 37 43 ID 24 32 40 47 55 II 30 40 50 58 67 12 38 50 62 72 . 81 13 47 61 74 86 97 ij. 57 72 88 102 115 15 68 86 103 120 135 i6 80 100 120 140 159 17 93 115 138 162 186 i8 106 }^^ i6q 18S 215 I GRAPHIC METHODS USED IN FOREST MENSURATION. 357 12 a & a Curv ? A ^ y^ y y uive D y y ^^^ ^^^ 3ur\ eC ^ / ^^ ^-^' •'' ^ 'urv eB / ^ ^y^ J-^' ^ / yy <^ ^ /. ./' y'' / /. V > / \y / '^ y ^ r ^ ^ ]0 20 30 -10 , 50 uo ro 80 Age Fig. 53. — Method of Averaging Two Curves. 200 ^180 "gieo "£140 .0 cq cl20 CO 1 100 "c o O 80 60 40 20 0 / » 16-f 0 >t Cur ve / -^7 14-fo< tCur -e /, /I .12-fo It Cur ■e '^/'J / ^ ^ k^ ,j ,10-fo( t Cur 'e ^y ^ / y ^8-foc tCur ■e ^ V ^ y > ^ /* ^ n- [^ X J Lff. 19.64 23.76 28.27 ^^ ■ 1 8 38 . 48 44.18 37 16.35 20. 18 24.42 29.06 34- 10 39 55 45 41 TABLES SHOIVING THE CONTENTS OF LOGS. 379 CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL ARUAS—iContmued) . Diameter in Inches. Length, Feet, or Number 9 10 11 13 13 14 15 of Trees. Contents of Cyhnders in Cu bic Feet, or Basal Areas in Square Feet. 38 16.79 20.73 25.08 29.85 35 03 40.62 46.63 39 17-23 21.27 25.74 30.63 35-95 41.69 47.86 40 17.67 21.82 26.40 31.42 36-87 42-76 49.09 41 18. II 22.36 27.06 32.20 37.79 43-83 50.31 42 18.56 22 .91 27.72 32-99 38.71 44.90 51-54 43 19 .00 23-45 28.38 33-77 39.64 45-97 52-77 44 19-44 24.00 29.04 34-56 40-56 47.04 54-00 45 19.88 24-54 29.70 35-34 41.48 48. 1 1 55-22 46 20.32 25.09 30.36 36.13 42.40 49.17 56.45 47 20.76 25-63 31.02 36-91 43-32 50.24 57.68 48 21.21 26.18 31.68 37.70 44.24 51.31 58.90 49 21.65 26.73 32.34 38.48 45-17 52.38 60.13 50 22.09 27.27 33.00 39-27 46.09 53-45 61.36 51 22.53 27.82 33.66 40.06 47-OI 54-52 62.59 52 22.97 28.36 34-32 40.84 47-93 55 - 59 63.81 53 23-41 28.91 34-98 41-63 48-85 56.66 65.04 54 23.86 29-45 35-64 42.41 49-77 57-73 66.27 55 24-30 30.00 36-30 43-20 50.70 58.80 67.49 56 24-74 30-54 36-96 43-98 51.62 59.86 68.72 57 25-18 31.08 37-62 44-77 52-54 60.93 69 -95 58 25.62 31-63 38.28 45-55 53-46 62 .00 71.18 59 26.07 32.18 38.94 46-34 54-38 63-07 72.40 60 26.51 32.73 39.60 47.12 55-31 64.14 73-63 61 26.95 33-27 40.26 47-91 56.23 65.21 74.86 62 27 -.39 33-82 40-92 48.69 57-15 66.28 76.09 63 27.83 34 - 36 41.58 49.48 58.07 67-35 77-31 64 28.27 34-91 42.24 50-27 58.99 68.42 78.54 65 28.72 35-45 42.90 51 05 59.91 69.49 79-77 66 29. 16 36.00 43-56 51-84 60.84 70-55 80.99 67 29.60 36-54 44.22 52-62 61.76 71 .62 82.22 68 30.04 37 09 44-88 53-41 62.68 72.69 83-45 69 ,^0.48 37.63 45-54 .H-r9 63.60 73-76 84.68 70 30. 'A3 38.18 46.20 54-98 64-52 74-83 85.90 71 31-37 38. 72 46.86 55 76 65-44 75-90 87-13 72 31.81 39-27 47-52 56-55 66.37 76.97 88 . 36 73 32.25 39-82 48.18 57 . 33 67.29 78.04 89.58 74 32.69 40 . 36 48.84 58. r3' 68.21 79.11 90.81 75 33.13 4.0.91 49 50 58-91 69.13 80.18 92.04 3^0 FOREST MEmU RATION. CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL AREAS— (CoTC/mMr^. Diameter in Inches. Length, Feet, or 16 17 18 19 20 21 22 Number of Trees. Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet. I 1.40 1.58 1-77 1-97 2.18 2.41 2.64 2 2.79 3-15 3.53 3.94 4.36 4.81 5.28 3 419 4-73 5 30 5.91 6.54 7.22 7.92 4 5-59 6.31 7.07 7.88 8.73 9.62 10.56 5 6.98 7.88 8.84 9.84 10.91 I 2 . 03 13-20 6 8 . 3S 9.46 10.60 II. Si 1 3 . 09 14.43 15-84 7 9-77 11.03 12.37 13. 78 15.27 16. 84 18.48 8 II. 17 12.61 14.14 15 75 17.45 19.24 21 . 12 9 12.57 14.19 15.90 17.72 19-63 21 .65 23 76 lO 13-96 1576 17.67 19.69 21.82 24.05 26.40 II 15-36 17-34 19.44 21.66 24.00 26.46 29.04 12 16.76 18.92 21.21 23.63 26.18 28.86 31.68 13 18.15 20.49 22.97 25.60 28.36 31.27 .34 - 32 14 1955 22.07 24.74 27.57 30.54 33.67 36 . 96 15 20.94 23.64 26.51 29-53 32.72 36 . oS 39.60 i6 22.34 25.22 28.27 31.50 34-91 38. 48 42.24 17 23-74 26.80 30.04 33-47 37.09 40 . 89 44.88 i8 25-13 28.37 31.81 35 ■ 44 .39-27 43-30 47.52 19 26.53 29-95 33-58 37.41 41-45 45 70 50. 16 20 27 -93 31 -53 35-34 39 . 38 43.63 48.11 ■ 52.80 21 29 32 33.10 37-11 41.35 45.82 50 . 5 1 55 44 22 30.72 34.68 38.88 43-32 48.00 52.92 58.08 23 32.11 36.25 40.64 45-29 50.18 55 ■ 32 60.72 24 33-51 37.83 42.41 47 ■ 25 52.36 57.73 63.36 25 34-91 39.41 44-18 49.22 54.54 60 . 1 3 66.00 26 36 . 30 40.98 45 • 95 51.19 56.72 62.54 68.64 27 37 ■ 70 42.56 47.71 53. 16 58.90 64 . 94 71.27 28 39.10 44.14 49. 4S 55. 13 61 .09 67, ^5 73.91 29 40.49 45.71 51.25 57. 10 63.27 69.75 76 55 30 41.89 47.29 53.01 59.07 65.45 72.16 79 19 31 43-28 48.86 54-78 61 .04 67.63 74 56 ^1.83 32 44.68 50.44 56.55 6^.01 69.81 76.97 ^4.47 33 46.08 52.02 58.32 64.98 71-99 79 . 37 87.11 34 47.47 53-59 60.08 66 . 94 74.18 81 .78 89 -75 35 48.87 55-17 61.85 68.91 76.36 84.18 92 . 39 3fi ,■50.27 56 75 63.6.' 70.88 78.54 <,G . 50 95.03 37 51.66 5'^ 3-' 65 . 38 72.85 80.72 S9 . (X> 97.67 TABLES SHOIVING THE CONTENTS OF LOGS. 381 CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL KRU AS— {Continued). Diameter in Inches. Length, Feet, or 16 17 18 19 20 21 22 Number Cti Trees. Contents of Cylinders in Cu jic Feet, or Basal Areas in Square Feet. 38 53-06 59 90 67- 15 74-82 82.90 91.40 100.31 39 54-45 61.47 68.92 76.79 85.08 93.81 102.95 40 55 85 63.05 70.69 78.76 87.27 96.21 105.59 41 57-25 64.63 72.45 So. 73 89. 45 98.62 108.23 42 58.64 66. 20 74-22 82.70 91.63 loi .02 110.87 43 60.04 67.78 75-99 84.66 93-81 103-43 113.51 44 61.44 69-36 77-75 86.63 95-99 105-83 116.15 45 62.83 70.93 79-52 88.60 98.17 108.24 118.79 46 64-23 72.51 81.29 90.57 100.36 110.64 121.43 47 65.62 74.08 83-06 92.54 102.54 113-05 124.07 48 67.02 75-66 84.82 94.51 104.72 "5-45 126.71 49 68.42 77.24 86.59 96.48 I 06 . 90 117.86 129-35 50 69.81 78.81 . 88.36 98.45 109.08 120. 26 131-99 51 71 .21 80.39 90. 12 100.42 III .26 122.67 134-63 52 72.61 81.97 91.89 102.39 113-45 125.07 137-27 53 74.00 83-54 93-66 104-35 "5-63 127.48 139-91 54 75 40 85.12 95-43 106.32 117. 81 129.89 142-55 55 76.79 86.69 97-19 108.29 119.99 132.29 145-19 56 78.19 88.27 98.96 110.26 122.17 134-70 147-83 57 79.59 89.85 100.73 112. 23 ' 24 - 35 137.10 150.47 58 80.98 91.42 102.49 1 14.20 1 26 . 54 1 39 - 5 1 153-11 59 82.38 93.00 104.26 1 16. 17 128.72 141.91 155.75 60 83.78 94-58 I 06 . 03 118.14 1 30 . 90 144-32 158.39 61 85.17 96.15 107.80 120. II 13308 146.72 161.03 62 86.57 97-73 109.56 122.07 135.26 149-13 163.67 63 87.96 99 - 30 I " ■ 33 124.04 137.44 151.53 166. 31 64 89.36 100.88 113.10 126.01 139-63 153.94 168.95 65 90.76 102 .46 114.86 127.98 141 .81 156.34 171.59 66 92.15 104.03 116.63 129.95 143-99 158.75 174.23 67 93-55 105.61 1 1 8 . 40 131.92 146.17 161.15 176.87 68 94-95 107.19 120. 17 133-89 148.35 163 56 179.51 69 96 - 34 108.76 121.93 135-86 1 50 . 5 ^> 165.96 182.15 70 97-74 110.34 123.70 1 37 -S3 152.7- 168.37 1S4.79 71 99-13 III .91 125.47 1 39 . 80 154.90 170.77 187.43 72 100.53 "3-49 127.23 141 .76 ^57.08 173.18 1 90 . 07 73 101.93 115.07 1 29 . 00 143-73 159.26 17559 192.71 74 103.32 1 16.64 130.77 M5-70 161.44 177 -99 195.35 75 104.72 118.22 132.54 147.67 163.62 1 80 . 40 19799 382 FOREST MENSURATION. CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL A.'R.'E AS— {Continued). Diameter in Inches. Length, Feet, or 23 24 25 26 27 28 29 Number of Trees. Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet. I 2.89 3-14 3-41 3 69 3.98 4.28 4.59 2 5-77 6.28 6.82 7-37 7-95 8.55 9-17 3 8.66 9.42 10.23 11 .06 11.93 12.83 13-76 4 "•54 12.57 13-64 14-75 15.90 17. 10 18.35 5 1443 15-71 17.04 18.44 19.88 21.38 22.93 6 17-31 18.85 20.45 22 . 12 23.86 25.66 27.52 7 20. 20 21.99 23-86 25-81 27-83 29.93 32-11 8 23.08 25-13 27.27 29.50 31-81 34-21 36.70 9 2597 28.27 30.68 33.18 35-78 38.48 41.28 . 10 28.85 31-42 34-09 36.87 39.76 42.76 45-87 II 31-74 34 56 37-50 40.56 43.74 47 -04 50.46 12 34.62 37-70 40.91 44.24 47.71 51-31 55.04 13 37-51 40.84 44-31 47.93 51.69 55.59 59.63 14 40-39 43-98 47-72 51.62 55-67 59.86 64.22 15 43-28 47.12 51.13 55.31 59.64 64.14 68.80 16 46.16 50.27 54-54 58-99 63 . 62 68.42 73-39 17 49-05 53-41 57-95 62.68 67-59 72.69 77-98 18 51-93 56.55 61.36 66.37 71-57 76.97 82.56 19 54-82 59-69 ' 64-77 70.05 75-55 81 .24 87-15 20 57-71 62.83 68. 18 73-74 79-52 85.52 91-74 21 60.59 65 -97 71-59 77-43 83.50 89.80 96.33 22 63.48 69. II 74-99 81. II 87-47 94.07 100.91 23 66.36 72.26 78.40 84.80 91.45 98.35 105.50 24 69 . 25 75-40 81.81 88.49 95.43 102.63 1 10.09 25 72. 13 78-54 85.22 92. 18 99.40 106.90 114.67 26 75 02 81 .68 88 . 63 95.86 103.38 111. 18 1 19.26 27 77-90 84.82 92.04 99.55 107.35 115-45 123.85 28 80.79 87.96 95-45 103.24 III- 33 119.73 128.43 29 83.67 91. II 9^.86 106.92 115.31 124.01 133.02 30 86.56 94-25 102. 27 110.61 119.28 128.28 137.61 31 89.44 97 - .^9 105.67 114.30 123.26 132.56 142.20 32 92 - 33 100.53 109.08 117.98 127.23 1 36 . 83 146.78 2>2, 95 - 2 1 103.67 112.49 121 .67 131. 21 141 . 1 1 1 5 1 - 37 34 9S. 10 106.81 115.90 i25-;<6 135- 19 145-39 155-96 35 100. 9S 109.96 "9 3' 129.05 139.16 149.66 160.54 36 103.87 113. 10 122.72 132.73 143.14 153.94 165.13 37 106.75 116. 24 126.13 136.42 147.11 158.21 169.72 TABLES SHOIVING THE CONTENTS OF IOCS. 3^3 CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL AREAS— (Co n/mwd). Dia meter in In ches. Length, Feet, or Number 23 24 25 26 27 28 29 f 'p- Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet. 38 109.64 119.38 129-54 1 40 . 11 151.09 162.49 174-30 39 112.52 122.52 132-94 143-79 155-07 166.77 178.89 40 115-41 125.66 136-35 147-48 159-04 I 7 I . 04 183.48 41 1 1 8 . 30 128.81 139-76 151-17 163.02 175-32 188.06 42 121. 18 131-95 143-17 154-85 167.00 179-59 192.65 43 124.07 135-09 146.58 158.54 170.97 183-87 197.24 44 126.95 138-23 149.99 162 23 174-95 188.15 201.83 45 129.84 141-37 153-40 165.92 178.92 192.42 206.41 46 132.72 144-51 156.81 169.60 182.90 196.70 211 .00 47 135-61 147-65 1 60 . 2 2 173-29 186.88 200.97 215-59 48 138-49 1 50 . 80 163.62 176.98 190.85 205.25 220. 17 49 141.38 153-94 167.03 180.66 194-83 209.53 224.76 50 144.26 157-08 170.44 184.35 198.80 213.80 229-35 51 147-15 160.22 173-85 188.04 202.78 218.08 233-93 52 150.03 163.36 177-26 191.72 206.76 222.35 238.52 53 152.92 166.50 180.67 195 41 210.73 226.63 243-11 54 155.80 169.65 184.08 199. 10 214.71 230.91 247.69 55 158.69 172.79 187.49 202.79 216.68 235-18 252.28 56 161.57 175-93 1 90 . 90 206.47 2 2 2.66 2.39-46 256.87 57 164.46 179-07 194-30 210. 16 226.64 243-73 261.46 58 167.34 182.21 197.71 213-85 230.61 248.01 266.04 59 170.23 185-35 201 . 12 217-53 234-59 252.29 270.63 60 173-12 188.50 204-53 221 .22 238.56 256.56 275-22 61 176.00 191.64 207.94 224.91 242-54 260.84 279.80 62 178.89 194.78 211.35 228.59 246-52 265.12 284.39 63 181.77 197.92 214.76 232.28 250-49 269-39 288.98 64 184.66 201 .06 218.17 235-97 254-47 273-67 293 56 65 187.54 204 . 20 221.57 239.66 258.45 277-94 298-15 66 190.43 207 - 34 224.98 243 • 34 262.42 282.22 302 . 74 67 193-31 210.49 228.39 247-03 266 . 40 286.50 307-32 68 196.20 213-63 231.80 250.72 270.37 290.77 311.91 69 199-08 216.77 235-21 254-40 274-35 295-05 316-50 70 201.97 219.91 238.62 258.09 278.33 299.32 321.09 71 204.85 223.05 242.03 261.78 282.30 303 - 60 325-67 72 207 . 74 226. 19 245-44 265.46 286.28 307 . 88 330.26 73 210.62 229.34 248.85 269.15 :-e90.25 312.15 334 - 85 74 213-51 232.48 252.25 272.84 294.23 316.42 339 - 43 75 216.39 235-62 255-66 276.53 298.21 320.70 344 02 384 FOREST MENSURATION CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL MLEKS— {Continued). Diameter in Inches. Length, Feet, or 30 31 32 33 34 35 36 Number of Trees. Cont£ nts of Cylinders in Cui)ic Fe'-t, or Basal Areas in Sqr.are Feet. I 491 5-24 5-59 5-94 6.30 6.68 7.07 2 9. 82 10.48 II . 17 11.88 12.61 13.36 14-14 3 14-73 1572 16.76 17.82 18.92 20.44 21 .21 4 19-63 20.97 22.34 23-76 25.22 26.73 28.27 5 ^4-54 26.21 27-93 29 . 70 31-53 33.41 35 ■ 34 6 29-45 31-45 33-51 35-64 37 -S3 40.09 42.41 7 34 - 36 36.69 39.10 41-58 44.14 46.77 49.48 8 39-27 41-93 44.68 47-52 50.44 53.45 56.55 9 44. iS 47-17 50.27 53-46 56.75 60.13 63.62 10 49.09 52.41 55-85 59-40 63.05 66.81 70.69 11 54.00 57-66 61.44 65-34 69 . 36 73-49 77-75 12 58.90 62 .90 67.02 71.27 75.66 80.18 84.82 13 63.81 68.14 72.61 77.21 81.97 86.86 91.89 14 68.72 73.38 78.19 83-15 88.27 93-54 98.96 15 73-63 73.62 83.78 89.09 94-58 1 00 . 2 2 106.03 16 78.54 83.86 89.36 95 03 100.88 106.90 1 13. 10 17 83-45 89. 10 94-95 100.97 107 . 18 113.58 120. 17 18 88.36 94-35 100.53 106.91 "3-49 120.26 i27.23 19 9327 99-59 106. 12 112.85 119.80 126.95 134.30 20 98.17 104.83 111 .70 118.79 126. 10 133-63 '41.37 21 103.08 110.07 117.29 124-73 132-41 140.31 148.44 22 107.99 115-31 122.87 130.67 138.71 146.99 155-51 23 1 1 2 . 90 120.55 128.46 136.61 145.02 153.67 162.58 24 1 17 .81 125-79 134.04 142-55 151-32 160.35 169.65 25 122.72 131.04 139.63 148.49 157-63 167.03 176.71 26 127.63 136.28 145-21 154-43 1 63 . 93 173-71 183.78 27 132-54 141-52 150.80 160.37 170.24 1 80 . 40 190.85 28 137.44 146.76 156.38 166.31 176.54 187 .08 197.92 29 142.35 152 .00 161.97 172.25 182.85 193 76 204.99 30 147.26 157-24 167-55 178. 19 189-15 200.44 2 I 2 . 06 31 152.17 162.48 173.14 184-13 195-45 207. 12 219.13 32 157-08 167.73 178.72 190.07 201 .76 213.80 226. 19 33 161 .99 172.97 184.31 196.01 208 . 06 220.48 233.26 34 1 66 . 90 178.21 189.89 201 .95 214-37 227.17 240.33 35 171 .81 183.45 195-48 207.88 220.68 233 . 85 247.40 36 176.71 188.69 20 I . 06 213.82 226.98 240.53 254.47 37 181 .62 193-93 206 . 65 219.76 233.28 247.21 26 I . 54 TABLES SHOIVING THE CONTENTS OF LOGS. 385 CUBIC CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF BASAL ARUAS— (Continued). Diameter in Inches. Length, Feet, or Number 30 31 33 33 34 35 36 of Trees. Conte nts of Cylii flers in Cu' ic Feet, or Basa! Areas in Square Feet. 38 186.53 199.17 212.23 225.70 239-59 253.89 268.61 39 191.44 204.42 217.82 231.64 245-89 260.57 275.67 40 196.35 209.66 223.40 237.58 252.20 267.25 282.74 41 201 .26 214.90 228.99 243.52 258.50 273.93 289.81 42 206 . I 7 220.14 234.57 249.46 264.81 280.62 296.88 43 211.08 225.38 240 . I 6 255.40 271. IJ 287.30 303 . 95 44 215-98 230.62 245-74 261.34 277.42 293.98 311.02 45 220.89 235.85 251.33 267.28 283.72 300 . 66 318.09 46 225.80 241. II 256.91 273.22 290.03 307 . 34 325.15 47 2 ^,0 . 7 I 246.35 262.50 279.16 296.33 314.02 332.22 48 35 62 251.59 268.08 285.10 302 . 64 320.70 339-29 49 2 +0 . 53 256.83 273.67 291.04 308 . 94 327.39 346 . 36 50 24544 262.07 279.25 296.98 315.25 334 - 07 353-43 51 250-35 267.31 284.84 302.92 321.55 340.75 360.50 52 255-25 272.55 290.42 308 . 86 327.86 347-43 367 . 57 53 25o.i6 277.80 296.01 3 1 4 . 80 3,34.16 354-11 374.63 54 265.07 283.04 301.59 320.74 340.47 360.79 381 .70 55 269.98 288.28 .307.18 326.68 ,346.77 367.47 388.77 56 274.89 293.52 312.76 332.62 353.08 374.15 395.84 57 279.80 298.76 318.35 338.56 359 . 38 380.84 402.91 58 284.71 304.00 323.93 344.50 365 • 69 387.52 409.98 59 289.62 309 . 24 329.52 350.43 371.99 ,394.20 417.05 60 294-5-' 314.49 335.10 356.37 378.30 400 . 88 424.11 61 299-43 319.73 340.69 362 . 34 384.61 407.54 431.21 62 304-34 324.97 346.27 368.28 390.91 414.22 4.38.28 63 309-25 330.21 351.86 374.22 397.22 420.80 445-35 64 314-16 335.45 357.44 380.16 403.52 427.58 452.42 65 31907 340.69 363.03 386.07 409.82 434.29 459-46 66 323-98 345.93 368.61 392.04 416.13 440.95 466.55 67 328.89 351.18 374.20 397.98 422.44 447.63 473-62 68 333-79 356.42 379.78 403.92 428.74 454.31 480.69 69 338.70 361.66 385.37 409 . 86 435.05 460.99 487-76 70 343.61 366 . 90 390.95 415.77 441.35 467.69 494.80 71 348.52 372.14 396.54 421.74 447 . 66 474.35 50 I . 90 72 353.43 377.38 402. 12 427.68 453-96 481.03 508 . 97 73 358.34 382.62 470.71 433.62 460.27 487.61 516.04 74 363.25 387 . 87 413.29 439.56 '^66. 5 7 494.39 523. II 75 368.16 ,393 - 1 1 418,88 445-47 472.87 501.10 530.14 386 FOREST MENSURATION. w Q t-H >^ O O H O o o s a " M ro Tt 1/^ 0 r^X C^ C - (S fO rj-ul ve f^oo ON 0 « « « « (S| 1 c u u I c cc u.' c 0 r'.LC X " Tf 0 0 C 0 0 6 On 0 CN| lOX !N 10 »■ fi re I/:; NO IN ri (N C-4 CJ d N - r< re lO I^ - ri rr; -t lO C 0 0 0 0 6 Cs i-i i^ X - t^ ON C " f^O 0 r- 0 0 - 0 C 0 " " 0 -)- t^ 0 '^.nO ■rt 1/", r^ X On (N re "+ 100 d C re NO ON IN "■ rj re rJ-NO X On 0 -1 IN ■I >-i n N cs d - >o 0 Lc C "^ O c^x X r^ O - -• 0 0 •ONO t^X On M d l-l HH 1^ d O r^ U-) re «- O 0 - M rO 1^ q 0 0 0 0 d " 0 X t^ lo I^ lO rt ox -t- 100 i^ r^ 00000 6 -1- M - 0 X 0 "+ (N 0 r>. X CNO - « 0 0 « « " 0 r^ I/; rt- fs i-i 10 re •-■ On r^ N re 'J- ■* IT) d c: -)- r^ - -t-X C H C 0 0 d M 10 On re 0 X -to 1^ ^. re -t- 10 lOO q 0 0 c 0 d 0 ^' r^ - -t- C 0 n On T; r^ r^X X On 0 0 0 0 0 d X I-I l/l On (N - X Tt 0 r- 0 0 " r^ " d 1 ao 0 - - - « LO c lo 0 "0 0 0 0 0 0 M (-) ri rj re C lO 0 lO 0 re re -f -t- U-, q 0 0 0 0 d ro re Tj- Tj- -t- 10 0 m 0 lo lOVC NO t^ I^ 00000 0 •i- le 10 i^ 10 0 "~. 0 lo 0 X X ON CN c C 0 0 0 " 0 i> X r^ lo ■:^ ri 0 8 O 0 0 d q 0 0' 0' 0 d re ri 0 CN t^ cs 0 0 re r^ T^ --^ 10 le »o 00000 d NO - re _ c «- 10 ON re r^ NO NO NO r^ r^ q 0 c 0 0 d V) 00 t^ "0 rO " 08800 6 0 X 0 '^ rO t^ On M lOX •1 •-■ >0 10 00000 d U5 0 c> 0 000 n re 10 r^ On 0 0 0 c 0 c c 0 c 0 0 >-' re 10 t^ ON q 0 0 0 0 NO NO IC "^ •* ►- re i/~, t^ On M "-I i-i ^1 fN« 0 0 0 0 0 d Tj- ^ re re re Mi re 10 r^ On re re re r'. re 0 0 c c c ^ e 10 X 0 ^^ 5 S 8 8 8 lOX " r^,0 r^X 0 "" f^ 08000 X i-i revo On r^ lONO r^oo 00000 ~ Tj-NO On - 0 •- r^ re 10 fH IN N r< p) q 0 0 0 0 d « 1^ -1- - X U-. 0 - n ri re S 8 8 8 8 0 n 0 1- -r - 88888 0 X 10 N OnnO t^X On ON 0 88880 0 re 0 1^ ■* " I-i fN) PI re 'J- 00000 f» §§§88 On fN >OX ►- "■ N n (s re 8 8 8 8 8 d «ooo - "+ r^ re re "i- -t -f 8 8 8 8 8 d 0 re t^ 0 re 10 »0 »OnC vO 88888 6 »- "1 (N re -t d >r ^o 0 1^ X d ON On 0 - N §§888 re re Tt- lA^ NO 88888 r ■5 2 ^2 — ri re -l- 10 >C I^X ON 0 « (N re -t 10 NO l-X O' 0 M M n i_i 01 TABLES SHOmNG THE CONTENTS OF LOGS. 387 s 8 u tn Pi Q ,— ^ G HH QJ h4 > >, 0 C/J 0 to IH 0 0 vo t^X On 0 M 0) fO ■+ 'O vo r^x On 0 ►- M 1-1 1- 04 1 1 1 S N 0 '.3 0 _c M c lU « ri ro Tf "0 10 0 lO - 0 Q « « (N (N 6 NO i-^ r^X On X - -1- r- 0 rO r^- ^ rr 10 d 0 « 01 00 •+ -r i^ 0 <^-no X 00 On -1- On 10 nO no t^ t^ d "-.NO t^ X On ON Ol 10 X - rt 0 "0 Q NO 00 ON ON 0 0 d «5 1-1 M ro rO ■+ rr o> "* On -^ 0 0 " " T^- r^j M « 0 On •+ On -1- ON ri ^ r^, 'i- -t .0 0 0 ►- 0) 00 0 OnX t^vO -1- X c^. X 00 uo !/■; no NO r^ d ■* 10 NO t^ t^ 10 rt CO 01 « X COX cox t^X X ON ON 0 (N lO t^ 0 f< ir> 0 "O >H vo 't On r^oo (N 0 0"'-''^ 0 tJ- t^ On n •* ►- NO « I^ fN I~-. « NO 0 lO 0 ro fO rh rl- 6 NO On >-' f'. NO t^ 04 X OC-jOj On -fX r<-^ r^ Tf 10 u-jnO no d CO ►- 00 ir, X CO ON rt ON rt 01 NO 1-1 "0 0 t^ r-^x X On d M 10 *^ vO '^^ r^ « (-0 Ttvo t^ -tX (N 0 0 0 0 - « ft d r'iX r)- On 10 On 0 f^ <^ "2 »+ On ro r^ >- M CI CO fO -f d 0 NO " r^ 01 t^X 0 " CO 10 On H-X in rj- t:!- 10 u-j NO d X CO On rt 0 -tNO r^ On 1-1 NO 0 •too CO NO t^ t^ r^ X d N 0 0 0 " " CO NO -:!- ^^ 0 ro r^ " 10 On 0 0 " ►- - d HH HH l-l »-( «-l X NO 'i- <"< 0 (N) NO 0 '^X M IN ro CO ro d « ri n 0( 01 X NO -1- 01 0 n 10 On c<-. t^ »t -t -1- 10 10 d 01 01 01 00 CO X NO rt 01 0 0 -tX 01 NO NO NO NO r^ t^ 0 NO ro On "0 r^ -t- ON <^jOO fO rONO 0 f^ t^ 0 0 « " " 6 cc >o " r^ -t- r^ ri t^ " NO 0 -t- t^ w r^ M (N| N fO rO d 0 NO CO On "^ " 10 0 ^ On X " lOX " 00 -t ^t Tfin d 01 X rt " r^ rtX COX 01 »OX 01 10 On 10 10 NO NO NO d © « (N ^- lO t^ rOO On 01 10 0 0 0 " " d lO ON fO t^ (~l X ON ►- <"t •* 00 ►- >OX " 1-1 M Ct n (-0 d NO 0 •^X 01 10 I^ 00 On t-i rt t^ 0 CO r^ CO CO ■* rl- rj- d r^ « 1/-, On 00 01 rt "-jnO X 0 00 NO On 01 10 10 W) »OnO d OS X NO "-> rO 1- tN lOX " 't 0 0 0"- d w 10 X (N| "0 0 X NO 10 <~0 t^ On (N lOX « ►- ts n c) d ON 01 NO ON 00 M 0 X NO "0 1-1 rl-NO On 01 CO CO CO CO rt d NO 0 "* t^ 1-1 00 01 0 X r^ lOX " conO 1^ rt 10 >0 lO d 00 rt- On f^X M 10 0 NO '-I t^ n 10 r~ 0 - NO 0 lO (N X rO On -rt- 10 r^ 0 fN 10 ►1 11 01 CI M d On -tX CO t^ ON "0 0 NO " r~. 0 00 lox 01 CO 00 00 00 d 01 NO C "^ On r^ 01 X 00 X 0 CO lox 0 rt rt rt rt 10 d t^ -t " X 10 ri lOX 0 ^ n -+NO On ■"! 0 0 0 0 « d 0) On NO 00 0 NO X ►- rt- r^ ro lOX 0 0) ,_ ►, M (S 01 d r-. -)- - X 10 On 01 lo r^ 0 ■^ r^ On " rj- 01 01 01 CO CO d 01 On NO CO 0 00 lOX "■ ^- vO X 0 00 tn CO CO rt rt ■* d w i»l ro •+ 10 00000 0 On w 01 rtNO 1-1 01 01 01 01 d t^ rt "I X -^ 01 0 X "0 CO X 0 " CO 10 M CO CO CO CO d -tX M NO 0 10 0 NO " t^ « 0 Tf NO r^ 00000 d •rt-X O) lO On 01 r^ OOX CO On 0 01 ro 10 0 - «- " 1- d to t^ >- "0 On On -t 0 "O 0 --0x0 - CO 1- « ri 01 01 d CO t^ ■- >0 On 'tNC r^ ON 0 01 01 01 01 00 d 4^ ^2 « n <^; -t 10 NO r^X 0\ 0 "« 01 CO ^ "O NO t^x 0 0 « « ►, 1, M 388 FOREST MENSURATION. U W Q I— I >^ o o w H o a o C a) M P) CD •* lO vO I^X O 0 w r< PD rh lO VO r^x o 0 a; 1 U \-. B a 05 0 ox X r^ i^ ^ r^, u^ J^ O — ri r-, -p ly-; X rj r^ - vO - r^- u", I^ O t^ X O ^ " C "-. 0 ■+ o rr r', ro c-i « — re in t^ O re -t u~- O t^ rex re r^ ci - c 0 o o - re m o X o 0 >- C< re CO — CN ro ^ U-) d lO O f^. t^ '-I O ". t^ o -* X O O 'N ro vO t- O 0 - c lO O re X CI t^ O -r t^ ■- Tl-O t^X 0 (N re Tf in t^ O 0 ^X CI -^x - -^-x 1- ci T}- in o X O 0 " CI r. LO O O " o t^ lO (N O r^ 0 " M <^ <^ - (N ro ^ >0 lO ri C X lO C: r^X O 0 t^ re X re X ri 0 i^ in (N X O O C " ^ CJ re in o re O -t O. -1- O r^ >n CI o CI CI ce rf in r^x o C - ►- CI s X c -t ^1 o — rn LO I^ X C 0 c o c — IN ro -4- uo r^ l/^ r^ « O C n •+C: t^ vC r^x o C i^ in CI ox o - ^.^.<: ^ C) Cl CI C4 "- c) re -^ in O ■* o O X X 0 CI Tt in CI ce re re r'; O r^x o O CO M -+0 X - VC (N X -* ■- o OX X X O -■ M rO ^ O r^ U-, r^ O >-i r^ f. O lO n loo t^x o o re m t^ 0 ci X to t^ re m m m -+ -t 0 - c. re -1- -to X 0 CI o in - X T re re ce ci o in^o r^x o CO X ^ -^ o O O « 0) ro -i- OX t^ vC >o C >^ M re -1- X m ro >-< O -j- r-, rj « o lo O r^x o r^ in CJ w o 00 O o - - ox X r^vc O 0 - CI re r^ in re 0 X CI ce Tt m in in -t re CI - -1- ino r^x CO CO lO p-i O n U-, vC t^X ■X -i- C' -i- <:> 0 O — r^ CI ^ CI - OX O 0 ►- — CI r - in 0 m. «- o X -1- O m, O o in ce 01 ■- ce -t in o t^ CO -1- X r^. t^ " 0 O - -- f< X vC •+ n C 0 " '■1 CO Tt- •n c M-x !-i ri ro re f^ -i- X O ^ n in ino X vO '^t M O X <0 O i-i O d X CI vc - m o t^ i^x X X O "t CI o CI re ■5j- mo CO ■O 0 -1- O •+ lO - o - ^ 0 " n r^. r^ O r^.'X r^X r< X re O ^ -1- loo o i^ CI t^ re r^ CI 0 m ►- o CI re o X m re X O O 0 - r r^ re X -f- o OX in re 0 CI n re -+ in C - C C. r-. r^ -r - X ": - X lo (N o -^t o^C CD o in CI oo re t-~X X O 0 t^ -t - X o t^ X O O 0 0 r^ ce O t~« «- » CJ re CO ce o t^ ^ " ►- CI CI re Tl- — « rj ri r^ ^ 0 O fO O T) " f*^ "J- •* lOO d t^ X c' CI ce t^ re O O CI o t^x X o r ri X -t- o m mo X o - X -I- 0 O ce O 0 - ►- CJ r - •^ lOX 0 "^ 1^ -t - oo "I - 1^ n X 0 - - n P4 d lOX O ceo re. Q X in n f^ ^ -r uo lo d X " reo X O t^ -1- - X c< X 'i- O >0 O O t^X X d - re o o « O ce 0 1^ m ►- i^ rex ■* o o o O « d J3 " " rt >. 0 OT 0 to 0 (U r/3 S H Z W H Z 0 CJ 0 m ID u «MrOrt-uo vOt^oOOO '^'^^^|f? ^CT'SS'S (-1 O O '^- '^ « 10 X '■I o vo 00 o '^> "^ (^ 10 t^ On '-' r^jvO CO 0 ''I rOO 00 M -^ -:}-30 CN r^ 1-1 Q O ►« " M (N ro ro ro ■* cs Ttvo CO O »• -t r^ O fN l^ ►- lO O "^ -t 10 lO 10 \0 fj Tf^ CO O irjoo >-< -^^O vO t^ t^co CO OS C^OO CO CO « ro >0 t^ On ~ -tCO " "0 CO -I- O f^ "^J >-« rO 10 I^ O^ CO D i^ O^ n O^O M CO 10 10 10 ID •+ "+ ►H ro 10 r^ O^ >0 O^ t^O O •rt- tn rr-j r^j ri 1-4 r^j u^ r^ O^ \0 " t^ "^ On X t^ 10 •+ <^1 CO t^^ "O •* - r^; 10 r^ On -too CI r^ (^Cn'OO'O ►H0cor^>0 Ttni-'OOO — rOiOOOO OPi'+OCO ri CO rC' On "0 r^ uo -t- ri ►- I- O Cnco i-^ C ri r^. u-j t^ O On OnX CO M « ri ro -* CO NO •+ " O ►-4 r^ 10 r-» On I-^ i^nO nC O uonO r^cO On CO NO 't M O O tN TNO CO m m -^ -t '^j O l-i M '~0 't On r-- LO fO I-' On •- fO "0 t^ (^ ri rj n ►- ID NO r^ CO On On t^ *D ^ *-^ CO O t~< '*0 ID 0 "^ 0 "^ r^j 1^ O -1" i-^ 1^ -r n OnO » r'i iDvO CO 0 "DO "to -t ON Tl- ON -t CO ■- >DCO I"! O CO ID ot O On O <^< ^nO O -+ On -t On ID On CJ NO O^ r^ -i" CM OnnO (^ On " C) -^ n -tNO CO O O M CO -i- '- 10 "^ OnnO ^ 1- rn -a-NO CO !-■ (-0 ID t^ On t^ r^j On ID -1 OnvO CI OnvO On '-I CO ^nO « r^ ID t^ On CO -)- O NO ci ci OnnO ci o 00 On " CO -t O CI -i-vO 00 OMD « t^ CO 10 CJ On "D CI NO CO On !-• CO O " " c, P) On X r-. NO ID IT) ►- I^ ro On " CO -TtNO r^ ro CO CO •+ •+ -t- rO CJ ►" O ID "- r^ CO On UO ID nO nO NO OnX r^NO >D rf O NO CI CO r^ ON O CI CO r^ 1^00 D O ID O NO >- ro -tNO r- CO -t •+ ID >D CI -tNO X O w vO ^ NO CI On O CI CO ID ^O NO t — r^ X CI ^nO X O t^ CI t^ o 00 NO X On " M X O O O " CI -t r^ ON " cox cox -t -t ID t^CO O CI -tNO X i-i id o id o no "^ On cooO ci >-< CI ■* ID r^ CO "DX O CJ « vO " t^ CI t^ -' NO O "D 00 o •" CO Tt 'tNO ON « CO r^ CI t^ cox On -tX CO t^ ID r— CO O I-' ID r^ O CI -t fOOO -1- On -t CI NO '- "^ O CO -tNO t^ On ID >-< NO CI r^ CO r^ ID -t CI ro i^ ■-• ID On ►1 O -t iDnO COX -t ON -t 1-" OnX NO ID CO nO O "t CO X On — CI CO O ID i- NO C) -t CI - ONCO CI NO O CO I^ ID NO X On O t^ roX CO On NO ID CO CI O i-i ID On CO I^ CI CO -tNO r^ CI -tNO X O ""i NO On CI NO ^ CI f-O ID nO M CI CI CI CO CI -tNO X O On CI ID X ci i^ ON 0 " CO ro CO CO -t -t CI -tNO X O IDX >- -tX -t iD r-^X On -t -t "D ID ID CI -tNO X O ►H -t r^ O -1- HH CI CO ID NO O NO CO O NO -t On ID " NO ID r^ O CO ID t^X O " CI- CO O NO CO' O CI X CO On ID X O CO IDX ro iDnO t^X O NO - r^ CO — rONO X ►- O " CI CO ID ^2 ►H ri r^. -t ID NO l^X OnO i-icirO't>D no t-X Cs O 39° hOREST MENSURATION. U w. Pi w Q 2: a o H W H O O o O "5 2 " * C^ d - 0 X NO lo fo ►- (N •^NO X Ov CN IDX ►" On r^vO On cO ►- 0 X VO 10 0 M fo lo r^ lOX « -^ t^ VO Ov f^NO ON fO -i- CO "- 0 X NO On -< CO ^nO 0 "^ r^ 0 CO CO NO On covO u-j vO t o r^ 'I- « X "O ~ ro lOMD X n "^O X O r0>O On CS ^ d I . 9302 2.2519 5736 8953 3.2170 r^ Tj- - CO 10 X 0 <■< <0 "O rOvO X 0 ct lOX '1 "OX CN ON NO CO 0 r^X 0 CN -^ Tj-NC ON « ^-o >0 NO - "^j uo vo X « ri fO ':!- >0 rO\0 On M "O d 1.8703 2.1821 4938 8055 3.II72 0 t^ Tt ►- On On 0 r* "* "O a ^ lOvO 1-^ ■* t-» 0 CO NO fO rt- NO CO 0 X 10 t^ On ►- (N Tj- X On ►- CN CO On CH vO On CN -+ UO NO OnX i^\0 lO 11 r^ lO r^ ON O 0 O 0 o rOsO On CN "0 0 '-' ^ r^j rr, r^ >-■ ►1 ro 10 r^ On 00 -< -^ t^ 0 0 ONX t^vo « CN Tl-vO X CN (N ri P) CN COnO On P< 10 CO -1- lO rt- ro (N « 0 (N TJ-VC X CO CO CO CO CO X " -d- 1^ 0 'i- 10 vO (N TtO 0^ " (s lOX ■- -+ d ir> t^ 0 r^ in ro lOX 0 CN 10 -i- ro ro M r^ 0 f^vO On t^ 0 (N lO I^ ■^ t^ On " c^ " 0 ON ONX CN 10 t^ 0 CO CO ^ Ov (N Tj- r^ On "OX 0 CN ^ t^vO vO "O '^ VO On CN lOX •* 10 © t^ lo M o i^ CS lOX I-" rO X VO "* ro -< (N UOX « ^ d 10 r) On t^ 'i- NO ON - -+ l^ ON r^vo 'I- (N NO On CN lOX CN On r^ Tj- - 0 CN lOX •- >-i On r^ 10 Tj- •1 rONO On cn CO -t CnvO '^ 1 Ov COVO On CN •+ r^ C X r^ 10 10 X 0 COvO ^ \n o U o g S 'i; -l-X (N MD O r^ tJ- M onnO r* "OX O ro d « Tj-x ri vO 0 Tf « X NO fO NO On >-i -^ t->. -tcc (N NO 0 I^ 0 "* t^ 1 0 X 10 (N 0 0 OX i-i rONO CO 10 t^ On « NO 0 -rx cc 0 r^ c^. Onvc On « -rj-vc On CO 10 t^ 0 CN t^ "- 10 0 -i- rj ON lO CN X CN "I- J^ 0 CN rf 10 n -1- >o r^ On lO 0 "^ 0 "0 lo " o CI t^ 0 « (N ttvO X M VO •-• NO "- rOX ^ ON lO ON ^ CO ^ VO vo f 1 t^ CN r-- 0 NO ~ t^ P) X 0 CO "OX CN CO X 0 C^ CO >o CN X CO X CO X CO ON 't 0 0 CO »ox ►- •0 n P^O ON ri uo NO 0 « •:)- ON f^X fO . . On M -^l- CO NO On ri 10 On 10 - X -^ 0 "00 -+ On t^ On CN Tf-vO X ►- Ti- r^ 0 0 t^ CO ONvO ■^x CO r^ (N Ov " ^VO On •■' -1- vO fN t^ CO On t^ lO (s 0 r^ ro r^ « lOX (N -1- r^ On >- d lO ►■' t^ (N X 10 "* 0 NO rt t^ CO "-■' X vo ^ ►H vox (N NO NO X 0 CO 10 D ^0 CO 0 lO >- I^ - X NC ^ - 0 CO t^ - lO X 0 CN 10 t^ CO -r 0 0 " - - onx r^vo >o - n (N CO CO CO PO OvX t^vO 10 ■- '^ t^ 0 CO lOt^ On CN Tj- CN ci •* 1- ■+ Tf -i- Tj- CO (N - C VO Ov CN lOX VO X >- CO 10 CO 1- vO IN On lO "H 0 « -. (N ro "' -tvO X - d t^ ro OnvO fN ro -f -t lONO N -4-NO X 0 fO "O I^ On o t^X Ov 0 ►" r< CO -i- 10 vO t-»X ON 0 T/tBLES SHOIVING THE CONTENTS OF LOGS. 391 U en Pi w Q 1 — ' Z E >. 0 Ul y tt. 0 01 rn S H 2: W H 2; 0 u 0 1— ( CQ P 0 •512 ■-■ 0 n Tj- >o NO r^X On 0 I-I Cl CO -+ 10 NO t^X On 0 I-I H, I-I « Cl E c 0 -t- I^ -^ Cl 0 X NO -t- CI 0 r^ X rO X ro t^ CI ro Th Cl 0 On r^ 10 NO ^ ■- On r^ LO CO "< X NO Cl t^ Cl 0 ^ 1/5 NO r^ -t Cl >- OM^ 10 CO «« X NO Ti- Cl 0 t-» "^ NO ►- NO 0 >0 t^X On t^ rO 0 t^ rO LO — t^ (N 00 nO "^ OnnO tN -f- On COOO CO 6 "' ci 0 NO ro 0 NO Tf- On "0 w vO ON "0 M ON "O r- CI t^ w so CI CO Tt- CO 0 NO CO On Cl X CO On -^ M X lO ►- X M 10 0 "0 On "0 NO NO fO OnnD CO 0 NO " t^ CO "0 I- X -1- 1- 't On CO X CO t^ X o> 0 nO '^y OnnO C) c^ r^ 0 'l-oo u^ 0 NO f-i NO •:}- ON rOOO 01 0 ►- 0 11 10 On Cl NO Cl r^ Cl X CO t^ >- NO 0 >0 Cl CO 'i- " X ^ 0 t^ 0 CO t^ ►- '^ ON -t On 10 0 ON -^X COX 't^ NO rO 0 NO CO On X Cl 10 On Cl 10 ►< NO ►- 1^ Cl r-» M NO 0 t^ X ON 10 ■X 0 -+ " On « ro 10 t^OO -t-X ^ NO 0 -tX rO t^ 0 6 « ci r^ 10 CO -H On 0 Cl -1-nO t^ 10 On CO t^ I-" NO 0 T) ON Tj- ci CO -+- t^ -)- Cl OX ON I-I CO "OnO "0 0 'J-X Cl X CO t^ H-l NO -1- >0 NO NO -1- Cl o^ r^ X 0 01 ro 10 NO " "0 ON CO 0 10 On cox r-^ X 't t^ ►H n CO rO rj- c 0 0 0 0 rOO On C) 10 -1-00 fH I^ M 0 " ci "ono t^x X 00000 00 - -i- t^ 0 10 0 ^X CO Cl CO ^ On 0 I-I M CO 0 « I-' I-I " CO NO ON N IC t^ 1- lO 0 '^ -+10 NO CO -^ 10 NO r^ M I-I 11 HI »-i X I-I -rf- 1^ 0 X CO t^ M *o NO r^ X « 10 >-c VO CI t^ X t^ 10 -^ CI I-I ro 10 I^ On ■^X CI vO 0 0 11 CI Cl X cox Tf i-i OnX no "0 « Cl -t-NO X 10 On ro t^ " Cl CO -+ ON 10 0 "0 ►- CO Cl ►- OnX 0 01 ^ 10 t^ NO 0 'tX Cl t)- to ^O NO Cl f^ 01 X NO "0 CO C| 0 On -■ CO LO r^ NO — 10 0 CO NO r^ X I* CI ro iOnO X r- -t « X "0 0 >- CI CI CO •^CC CI vO 0 On - Cl -1- 10 Cl 0 t~-» ^ --I -)- 10 lOvO t^ ■rt-X Cl -O 0 t^X 0 I-I <~o X LO rO 0 r^ t^X On 0 0 -tX Cl t^ K -tNO r^ 0 0 ■^ 11 X 10 r^j 1-1 Cl 01 CO -1- 10 On CO 1^ ►- 0 l-i CI Cl rO -t -1- 10 NO NO r^ X 0 ONX X t^NO 10 HH r>» ro ON On OnX 00 t-. rO r^ i-i 10 ON 6 " LO -t -1- ro Cl 10 " t^ CO On t^ I^nO no "O CO r^ "- 10 On Cl CO K 0 On ONX 10 - NO Cl X 10 10 Tt Tl- ro ro t^ " 10 On r^NO "0 10 -h -t 0 NO 01 X CO CO Cl Cl - CO t~^ ►- "0 On NO r^ X r^ 10 -1- CI -1- ON •+ ON Th X vO 10 CO CI r^ r^ 11 10 0^ d " CnX no "0 ON rox COX ■ 0 ONr^NO -^ cOvO 0 -^X ^1 ro CO -1 0 X r^ rox CO t^ Cl CO >-i 0 X t^ Cl NO 0 CO r^ ir^ -t 01 - ON r^ 01 t^ 01 NO 10 T|- 01 I-I On M 10 ON CO NO NO r-» 05 (0 On On X r^ NO CO t^ -< 10 ON r^ -t CI ON NO CO r^ « tj-oo d « NO >0 -J- -)- CO CO t^ w 10 On •* - ON NO CO Cl NO On CO t^ Cl CO Cl I-I ►- 0 ON ro r^ I-I lOX " X NO CO 0 1-1 -^X Cl \0 X X i^nO nD 01 vO 0 'tX X 10 CO 0 r^ On CO t^ ►- -r 1/0 1^ 1^ CI CO lo r^X •"OO On ci uo NO CI X lO -" CO r^ 0 -1-X d 0 Cl CO 10 t^ On ci lOX i-i I- T}- 0 NO rO h-l 10 C\ Cl NO Cl CO X 0 Cl -t- 10 -tx ~ -t t^ On 10 Cl X -t- On CO t-^ 0 -t ro -+ >0 t^ ON 0 ^1 -t 0 ro t-- 0 -O I-I t^ r^> 0 NO X 11 10 On 01 u-iNO t-^ 0 - f^ cox n 10 r^ 0 01 10 0 "0 i-i NO CO r- 0 ■+ r^ d « -t- 0 >0 " r^ lOX 0 CO 10 I-I NO Cl r^ Cl ►H Tl-X " >0 C« ro Cl X CO On >0 X 0 CO 10 X r^ cox cox X Cl 10 On Cl CO -1- >o 0 NO Cl l^ 1-0 "- cOnO X " ■* On -t 0^ 10 NO On CO vO 0 10 N--^ r^ - ci -t- lO^ c. -i-iO X 0 -tX Cl NO i-r "^O vO 0 CO f^ 0 - I^X 0 " Cl Cl -t r-- 0^ « u-3 On CO r-~ Cl 0 CO t- 0 -t Cl CO CO -1-NO r^x CO uo t^ On « NO 0 "l-X CO r^ 1- -^ t^ w CO -1- 10 On 0 1- ro -h rO\0 X 0 oi r^ -. 10 0 -f •+X " lOX 10 NO « N fO 1+ 10 vo r^X Os 0 „ d fO -t- >o NO r-»x o^ 0 W I-I IH ». d 392 FOREST MENSURATION. T tn Pi w B B a ^ ■-^ tr, o i w o u o m •S S2 " ri <-^, •+ lo >o t^X O 0 ►I <~t re ^ lO VO r^x o 0 "- i-> — >-■ CI 0) 1 (3 OJ E a! 5 © u u c c 0 ■ f^l f^, lO t^ O ■O <-< X 1- o "-. 1^ C -1-X 0 c vC ;^X O C - CI ci -4-vo X 0 . re o C -' M X re I-, ri r^ O " "0 0 -*• O O "O lO Tj- lO - I^ re o re -1- LC 1- vO ►- vO C o rex M r^ re re CI (N — UO >- t^ re o >C t^ X LO C -T O -t - vC 0 -1- O - 0 0 OX LO 1- t^ CI X X X OX vo m -t- 0 - 0 - vo re -1- lO 0 -1- O re X C) O VO -^ " ^ O i^ -1- ~ CN X t^ O "O vC t^ X CI r^ « VO C OO •+ - O r^ Tj- - X Tj- 0 vO CI (^ re O 0 " n -h lO r^ O -t-x no O lO O vO " t^ >- ^1 -1- c X lO O f^- r^ - (N t^ re X -+ fOx ■* o lo o ^ re lo vc lO 0 ■* X CI o lo 0 LO « 0 VO (N t^ re X 0 CI -1- LO vo ►- LO o ce VO CI r^ CI X X -* o LO 0 re -1- >o vO l^ X X o o - CO X N X - (N ro ^- lO •1-X IN O 0 6 - n T -r ". loo vc r^X O 0 •rt- X Ct VO ►" CN t>. rOX "* rO rf lO 1^ 1^ ^, O 0^ - M re Tl- lO lO O f^^ t^ -" Ov •* 0 "O" >OVO t^ X 0 O - c C-, t-^X O 0 >-' lO o ce X CI vO " t-~ CJ X o d - n .-) «T lO X vC •+ ts 0 O lOX >H -^ lO O >0 >-i vo vO t^X O O X vO -^ <^ >-| vO On M >O00 w vO N r^ IN ro ^ »0 ►> r< re tT LO Ov t^ lO fO ~ O cevo 0\ c< X fOX rr> Ov lOvO t-~ VO r-. X O 0 O r^ >o re CI 't r^ 0 cevo ■<^ O lo 0 >o> X o d lO C "O — o LO 0 lO 0 lo X " T}-!-, 0 - t^ o revo On lo X rex -t- o vO X O "■ . c< r~, re X o d X c X o I"" 1- "■. c ^ ^ "1 >o X 0 fO 0 0 O « " lo 0 "O 0 "O d «' r> fN O LO n J. O - -:»■ t^ o D re re re rO lO 0 lO 0 "3 lOvC t^ L/, - X T - CI LO r^ 0 re ^ Tf- tJ- lO LO O lo 0 >o 0 x o c '1 "^ ic r^x 0 0 0 0 0 ox i^vo "o -r o -t- o ^ O - 'i O n re lO I^ ^ ^ In " O o -1- O -t O M re -f X 0 CI re LO ►- Cl c< c< c< ox t^vO >0 rex rex re >o v.e r^ r^x o CI re M o re rO re ■* ce N ►- 0 X cex fOx x o « n rO ■^- lO vo I^X o c « CI re -t- >o VO l^X O 0 TABLES SHOIVING THE CONTENTS OF LOGS. 393 W W o J3 M to " w M ro -^ >0 NO t-^X On 0 M CI ro -^ lO O t^X 0\ o " — " P-< CI u .s c u i E (5 O o 1-1 l-l 01 o 3 U .c *J c 0) c 0 -t-X MOO lO 0 vO - 1^ X r^ LO 'tt- C4 t^ lO CO ►^ On 0 " CI CO TX ci O O CI r^ cox •+ -. ONX NO LO t^ Tf CI o 00 ^co CI o 0 ON -:f- 0 "O - CO CI ►-■ CnX O ^ CI On t^ X ON o Tl-X CI O o O " r^ CI X O LO CO CI O LO CO " On r^ CI ro -1" LO C5 05 X lO ro - 00 ON On On Q^Xi O "^ O r^ •+• r^ lO CO 0 X 0 " N CO NO -t •- On t^ X X X t^ t-» >H X LO N On O CO PI Onno Tf LONO t~^ lO CI O X LO t^ I^ I^O NO O CO O r^ 't ^ CI o t^ LO X On 0 " CO ►- X o -t- O O LO LO LO >-• 00 LO CI ON CO 0 OO O CO CI ro Tt LO GC OS rOO 0^ C) lO -tx CI r^ « "0 O vo ■- r- r^ lO CI 0 t^ 0 " CI ro X - -1- t^ 0 LO 0 -tX CO CI X rOX 't lO CI 0 J^ LO Tf LOO r^ rOO X •- ■+ I^ ~ lO 0 '^ On LO O NO ii CI 0 X LO CO X On O « (--- O roo On X ro t^ « LO O CI 1^ rox O 00 >0 CO 0 CI CO rt- LO 05 O 0 ON ON ON ONX O LO •+ CO t^ « lO On t^ tJ- CI OnnO O i-i CI CO On OnX X X ro CI N- 0 On CO t^ « LOX Tt- " ONvo CO rj- LO O t^ XXX r^ r^ X I^ O LO ■+ CI o 0 ^x ■H X O CO o X On 0 " t^ r^ t^ O O ro CI " O On CI O O "+ 1^ « lO CO 0 t^ 05 05 X O lO "^J ~ ro I^ " lO On CI Tf t^ 0-. " t^ ^ - OO O 0 >-' CI fO CvX O -1- CI CI vo 0 -^X T^NO ON " rO CO 0 t^ ^ CI •* LO NO r^ " On r^ lO CO CI LO On CO t^ O X 0 CO LO ONO -+ >H X t^X On O CI 0 X O LO " LOX CI o 00 O CI LO t^ LO ro 0 r^ -+■ >- CI ro -t X O LO 1^ >- X r^O lO -t 0 " CI r^ ^ t^ Tj- >- 00 lO ONX O •+ C| CI « C OnX LOO t^ r^X CI On NO CO 0 0 CN t^ LO CO r^ lo -t CO CI On 0 -• CI CO r^ lo CI ONO "0X0-+ " O X r^o -+ LO LO O t^ ro 0 r-. -f « O " CI CO rh LONO r~» t^X On 0 - ci ro -+ 05 O 0 On CN C^ •+X « lO On OnX X t^O O CO o r^ ^ 0 ~ CI rO ONX X X 00 CO r^ — lo ON O >0 LO Tt CO ►« X LO CI On t1- loo X t^ t^ r^ r^ ro r^ « LO Cn ro CI CI p- o O CO 0 t^ •* t^X On O NO o o o o ro t^ - LO On O On OnX r^ w J^ -* p- X l-P CI CO M 05 rOO On ci lO OnX t^ t^O r^ lO CO « On O CO 0 t^ t^ 0 '-' CI CO r^ C coo On LO LO •+ CO CI r^ lO ro " On O t^ rt- i-i f^ •-I- LOO Cl LOX " •+ CI « 0 O On r^ LO ro « X Tl- « X lO " t^X On 0 t^ On C| lOX X r^ r^o LO NO -rt- CI 0 X 00 >0 M On LO 0 P-p CI ro 05 X >0 CO O X -1- On -t- On rO NO CI 0> LO CI NO CO GnnO ^ 0 " CI rO o CO « X o X <^^X CI f^ X LO « X "^ OnO CO OnO CO -t LO O -1- - ON I^ '^ CI r^ ►- O l-l ►- r^ -t 0 r^ CO OnO CO 0\ I^ X ON CI On r^ LO CI NO 0 lO 0 LO ro O NO ro ON O ro ONO CI C •-■' ci r^. 05 -tX CI vo ON LO O LO O "0 vO CO CnnO ci 0 >-* CI CO fO r^ I-" LO On ci CI ro CO CO 0 "00 lO 0 On »0 CI X LO CO T^ LO O CO r^ 0 -t X Tj- Th LO LO lO lo 0 LO o "0 w X ■* « r^ t^ X On CI O O 'tX o vTN t-- r- t-- 0 "O O >o 0 -to t^ ro O O p-p CI ro :2 2 « f< CO •* UO O t^oo On 0 ►- CI CO -t lO O r^X ON O " p-p ►- ~ CI 394 FOREST MENSURATION. •s* • 0 M Tt-\0 00 0 N ■+\0 00 0 N Tj-vO 00 0 N tvo 00 0 N ■^^ 00 0 0 1 u 1 (5 0) 4) > N © « 05 QC M N O OS CO 3 u c c c a C^O^C^a^0^c^oooooooooococo t-^t^r^r^i^t^t^t^vovo^^'O lo -t r^ O <^^ On <^< "000 « 'J- i^ O <^jVO 0^ ri loco « -1- t^ 0 ^^-^ O -f rOO ON" T|-t^ONM >OG0 O f^NO 0\~ ^i-»On(s >000 O r^-vOOO <~ "0 -H X NH (s > On M "^vO 00 r* rOiOt^O N -^t^ONM r^vo 00 On ^ fO "0 f-. O P» "+nO oO >h rotot^O CM •*nO On« PO>Ot^O cm "+^£1 r-- ,- w M M fN (N (S CS (N rO'~Oroi-0'^-^Tl--OiO iOnC NO nO VD r~. « ooooooooooooooooooocccooooc ■^ n n » M n IN ci CN CN rorCr'-, rer<^-j---f--f-f-fioiouO'OiOvC I^ ARE i^iOfN Cni^'^ci CnO •^'-i CnO ^"XnO '^-"-CCvC rOOX "Or^. C xofM'~oint->.ONO'N'-( „«i-(«i-iM(SCSM(SCN|NrorDf^rorO'^'i-'^Tj-Tl-Tl-u-) ionO D OnloOO rJX -1-OniO'-' t^CNX -fONO — r^r^ONUOONO (NX ron M NH 1-. « w « o tN CM tN cs cs rOrereooreror^Tj-T^-^f^-tl-io CNr^t^- lOONror^O ^X (N\0 O ^X i-i >OONrer--"-i u-jOnpOvOnO O X On '-' .X OnO " CN CO ^ lOO t^X OnO '-' CM -+ TlvO t^X OnO —no ««l-l»-MH-wl-ii-.i-.(NCMCNCIi — C CNX 1^^ >o-fc<:)- «Mi-iMi_i_H,Mi-i>Hi-tscNO)CMP)Cscsr4ro H t^ lO r) c t^ lO (-) C t^ -1- 01 On f^ 'I- 01 ON t^ rf oi On t^ >+ ►" OnnC ^ ~ Q O 0{ — r-.reON>OoiX -1-CvO 0) Cn'O— r^oeoo "NX tJ-QnO m Onioo 00 rO •* Th iOnO no t^X XONON0>-ii-'CMNo0'<*-O0 "OC "O 0 -1-X r^^ ONtOJ>.i- lOONOOI^'i lOONfOt^ — NO 0 MvO O "^XX oi n o< oooOoo-:t-'+>OiO "DNO nO »^ t^ t^X Xox <- \o « « 0) 0( OI oooornoo^Tj-Tj-iOiO lONO NONOvOt^t^l^Xf^XJ OO O IN -tNO X 0 M •^vO X 0 CM TfVO X 0 CM 'J-NO X O 0i0>0 lO~~ t^ Is „„„_iHCM01040)(N|OOoefOfOOO'4-r}-'4--^-1-IOlO>OlO>ONOr 1 T/tBLES SHOIVING THE CONTENTS OF LOGS. 395 U ^ . CO '^ (A O Q H « P H w 6 w w PQ bo 1 O n -d-vo 00 O N •^vo 00 0 P< "^O 00 0 P< -4-vo oo O ts ■*vO 00 O O « « M W N M M © M 05 N oc N la N f N M 1 IS d c c 0 o ooooooooooocoooooooooocoooo OoOO ■<*•(-< ooovo r)-fs Ooovo -i-^(n 0 O ^-^-lOO t^oooo OO ■-< 0\0 t^OO "' f^-*->0\000 OvO u->Pt Ot^'+'-iOO lots OI^'+i-iOO >OfS O^ •«}->-iOO lO(N O^ rriO M o N ovo rt-woc ion o t^^i-ioovo fOO r^-'+cs Ovo ct rOO t^r^O r^roO l^'l-O t^rJ-M i^rfw t^-^>-.00 't " CO »+« li-j ro Ti- Tj- lOo \0 t^oo ooOOOi-ifscsrO-J-Th lOvO vo r^oo oo O O "^ O 0 <^-0 O r^vO 0<^-v0 OCNvO 0<^tv0 On lOOP) ioO-i r^r<^0^ -iC0 -^ 0 t^OO"-" f^cOrfuoiOOvO t^OOOO OO O "-I ts (N POrOrt-iOiOvO r^r^OOOO N (S lU t^vC iriTl-Tfr<^n ft n O O OOO r^t^vO lOuO'+romn « O O OO o C c O'O'-i r'.POO'Oi-i t^fOO^-OO 0)00 -t-OO Dco -l-OO (N f^r^ 0 >OvO t^ t^oo O0000'-i'-'0<^<^^-+'t loso O r^ r^ 0 l-l«l-(Ml-l>-CI-ll-ll-ll-IH-l-ll-Cl-in u 00 r^O-+0 lOM^O M t^r^jOO ^0>00v0 "-i r-^(NO0 Tho>000 f^ t^rDOO •+0>0«vo Mt^r'loo Ti-o>0>-0 M l^rOOO ■^O'Oi-'vO t1- (S (-0 to -^ >0 lOO vO r^ t^oo O0000'-'i-'t^'^<~^r0-+-1- "TC vO O C O >-i rO'Ot^O'-i fO>Ot^OO M ^vOOO O t^ %'-vOcO O" roior^t^ vO'-'O'-ivOi-il^Nt^nt^ rooo rooo fOOrhOi-i O-+0 "OO "0>h (N roro-|--+lO>000 r^I^OOCO OOO O " " n -• ro •+ o rooo rooo oO"00'00 (N M ro rO •* -+ lO lOO O r^ I^CO 000000'-'i-'00>00>00'00'00>0 M t^ " vo O lO O -+00 POt^r-i >00 "+0 rooo p) r^ w vo O >0 t-» tS M COrO'^'^'^lOlOvOvOr^r^OOOO OOOO 0 '-' "-I (N (N toro>o OO P) -^lOt^OO N TfvO (->. O "-" c< ■^\0 t^ O >-i ro rhvO oO O " 0 O >OOfOt^^- >O0 -too MVO 0 •OO'-DI^" lOO 'too N vo 0 >ovO row OoOt^iO'^N "1 000 ^-.>r)r^p^ w O00\0"0-r)-ci >-< ooovo O OfOt^O ^00 NVO O •+t^'-i lOOfOt^O "+00 (Nvo O "^-t--."-" 10-+ " (N (s rorOrO"+rl-io>0 >OvO VO vO I^ r^oo 000000000>ii-itO CO roO'+C"0'-'VO Pf r^ fOOO -^OiOOO "-■ r^NOO tJ-OiOO^O -> ^oo w lOOO (N >o O fOvO tJ- - (s (N (N rorO'0-+--l--+->oioovDvO r^r^t^oooooo OOOO O o^(^ CI iooo>-i>ooo>-iThoo>-i-hoC'* „ „ n r< c u 0 0>OiO >0\C> t^ 396 FOREST MENSURylTION. w m S 1— ( H W Pi < D ti a J WJ ,_J Pi C) I-< Q < w a. (J vx P c M w W n rt K U Pi w HH PQ S 1— i H Q ^ P O « 5 • O N rhO 00 0 M ^vo 00 0 N Th^ 00 0 f^ 'i-O 00 K- ~ I-. CI ft CN C) ri r'; ^j r^. rr, rrj -t Ti- -t --t -r 0 N Tt-vo X 0 0 lo uo uo lo i^, o r^ o c c 6 ttf (5 & cs > N © N CS 00 r» la C5 rH N r^ C 3 O c o c 6 X HI uoondnc 0 c^r^O 'i-oc ■-•"", X ci\c ON CO NO O ■* r- ►- Tl-X NO o o f*0O O rct^O fOt^O r<^t^O <^t^O CO r^ O t^ t^X ^ t-^ O 't t^ O t^ XX o- ON ON 0 - lOX Ti- U->^ ^ I^I^X OnOnC " - CI ri 1^, T -T "-. C C: I^ i-X C^ Cl " •* t^ O <^-AC O CJ lO 0> (N lOX " -^ r- C c^.vO On CI U-. X •- t^ CI M n rocOc^rCrt--^';j-uou"yU~^vC^v£ r^I^t^t^XXX C^C ONt^T)-(N OOO ii rc« CM^-^CN OCC^O r<-. p-i On t^ "0 Cl 0 X NC re Cl rC^ Onci uot^O covOX ►- Tt-r^O ("1 lOX " M ri CI c^j r-O c^ r^ ■+ -^ Tf lO lO lO 1/", NO NO NC On Cl lO t-- C CO r^ NO f^ r^ j^x X ON t^ Cl t^ Cl t^ Cl t-^ > w '^' ^^ ^ tN lO r^O CI lor^o CI lor^O Miotic ci w CI CI Cl CI CO c^, C^ CO 'J- Tt- Tt- ^ uo u^ Cl i/-, t^ C Cl ir; r^ NO NO vC t^ t^ t^x r^, lO c«, w > J i---^- O re uox C r-, CI X v„ f. "OX C c. ic X 0 . On ■- c^NC X C CI in t-^ ™ w .1 CI CI CI CI CO CO re cc -i- -1- -i- -1- On >-■ tJ-VC X o fe lO I^X Tj- «0 ic in "Ovo vo VO vC t^ o o „„«„«„„„„„,-,«, .ti I. Cl Cl Cl Cl Cl Cl Cl Cl C; c. O N ^vO X O " -tJ-o X O X O -^ C. O 1^ "■. c-. (. CO O M Tj-^C t^ On 1-1 CO Tto X O H«cicicicic- 'ax ►- i^. ON I-. vO CO On O Cl CO UOO I~~-CnO '-' co^iOt~»X ■_i_«««i-,i-iCICICICICICICI O « Cl c-, re CO "* lOvO X O C l^ 0^ U Cl ^T ^O 1^ s,^ '-* f^ ^q-vw C'w O C^ C-, -r^ -- u •- < . "■. O X ~ Cl o lO r--cc ON O "-I t^ ■* ^^O t^oc O 0 Cl Cl Cl Cl Cl n Cl LO f* OnvO ci OnO r-;o t^-T — X "Oci OnO '•- C VC T C I- -i- - X re ^1 -f i-iONO r-r^X O^O^0 " " tN rOco-T "-. VC NO t-X X O C C -t ■Ji -t ONio>-vO Cl i^cjO^-TCn: - i^cix -r ::- >• . - vC Cl t^ c. On 1^ CI ro CO) -)■ lO >0*0 O t>. t-»X ON O^ C O '-' '-> Cl n re -^ -t ^. >ONO O On CI 1^ -vC ^ -rONc;xcii^«"". c -i-ONce X Cl t^ •- m C t o re ■/-. '1 CI CO ro -+ •+ ^ lO >0\C vO t^ t^X X X a^ On O O ►- ►- N Cl Cl re ir 1- C -r 1^ o -T 1^ o -T 1^ O -r I-- o -r 1^ - -, 1- - -, I- - T r^ ■- X w M M ci.fO)feco-^-^-*-io>0 lOvO vo vo r^ 1^ t^X C^ X On O^ On O ►- '■'"- ^f. X 0 '^. "". X C ro >/-, X O ". "". X C 'e 'e X c r' le X c re >r x 0 c. « '1 '1 ^1 '1 "-, "■. re '^. -+ -t -T -r ir ir ,r .eo C C C 1 - 1 - I - :c 2^ -1-NO X 0 Cl -to JO O Cl "l-O X 0 IN -tvc X 0 IN -nc X 0 0 H, ►, M Cl Cl Cl N N ^0c0^0^0^^•>i■^^4■Ti-•^J■'O>O>OlO lOvO t^ TABLES SHOIVING THE CONTENTS OF LOGS. 391 T w cq Q z w 0 < w •a M « w CO N M M O eo 05 N t^ e* CD N •0 N N CO N 4-' 0) IS O c c 00 - M rort-iovo rococo O^O •- ^^ "-^^lovo t^" loo^o "HvO "vo "VO i-^o "vo «t^tsr-.(Nt^r4I^ot^Mt^csoO fj - OvOO VO lO f'j (N 0 O^ t^^ Tt-f^j- OOO t^u-j-^M •-1 O^OO VO lO t^ -i- lO loo t-.00 o o ■- - I-' "^ •* "^^ <^ I^OO 0N0i-'P- ri fO -^X' 00 TTOMO-O CNOO fOO^iOOVO Nt~- -.t-»rjco -^CM-^ r^iorj o'oo lOtOOOO lOfO^cOO ->r^'4-'-'t»"i"<»"^'-;oo_"P<^"7 «' cc -i- 0 r^ <^ 00 M 00' 10 "' 00 -+0 t- "^ C>vO (N 00 10 « t-^ 0 0 0 >^ r;; ^ ;;;;j ^i;;-' 2" ;C^ 11?^ ^I:"^ 2~ ?I n « OM-O TtfO" 000 ouO'^NOoOl-iO'tcsMCh r>.vO '*" ^7 "7 n\ ir^ n X, rioo -t-O "0- r^POONiOi-iVO i^ioO rfOO 1- t-0't- M t-iiuoo Tl-ONf^jr-t^o ">oO ^00 rOt-MVO "_"P<^'^°°. ^"p ^6 '^o ^6 ^6 ^6 'o " 0 ►{^ ;r' >^' " ^' :::; ^ " ^ :i^ " {::: pj' ^ ro ^ Tf 10 10 vO Ot—t— 0000 a^C^O 0 - " " [J II?iT2^I:?IIr 10 n O^ f^.oo 0 ON ^CO "^ >- " "7 0 ri M N 0 t^ ?o •+ n- louoo vovot-r-GCGooc>a-oo|^;^p|t;;^;o ooooooooooooooooooooooooooo 0 4co ri vo d 4oo N vd 6 ^00 (n' vd d '^00 ji^ d ^'x N vd 0 d 0 ^'^ Pj'ft ^ 5^ 10 iovD vo \0 t- r-oo cOCOONONOOO-2^5 ^■-;c>?r;^^§-:i^:;>^^5^^J^r:^^^'^sg;s|2^ xT 2 ^ ?^^ 8 S cT^^ g.P^^^^^^^^'^as.i^^^S a i 398 w h4 D Oi tA c Q 0 Pi 1— c < ^- 0 0 :z 0 tT. C PO tN PI PT) -^ 100 0 CNX VO 10 t^ t^ X On 0 PO PO 0 On t^ ►« M PO P^- •^ vO PI 0 « « « n HI n M (S PI M PI M M 05 t^ lO M 0 CO t^oo 0 C 0 u-> PO M 00 vO ►H PI ro P^. ■* ■»!- PI On t^ >0 >00 VO r^X oi 0 00 >r) r0 i^. C r^ -t- C r^ -+ " 0 - « PI PO X lo PI cno rr, •* u-3 100 PC 0 VO P^ 0 t^x X ov 0 0 PI 0 « „ « « w 1-1 I- ►.! « PI f>- D CC -1- 0 VO vC 0 r^oc 00 PI 0 "^ « t^ 0 CN C ^ " PO 0> "O PI X PI PI PO -i- ■^ 'J- 0 VO PI ON lovo VO t^ r^ X 0 « W « CO 10 0 "0 — 0 10 vo vo t^ r^ PI t^ PCOO ■!*• CO 00 0 0 0 On 10 0 »0 « 0 ►- PI PI PO VO PI r^ PC X P^- T -^f "0 >o -t- NO 0 « „ « « « w •a 00 l~^, 30 P) t^ PI r^ - ^ - t^ r^ X X 0 vO - 10 0 "0 O^C G - " 0 "O ON r)- ON PI PI PI PO PO 1- 0 - - _ ►- « - - « - t n \0 0 ^+30 -^ -r 10 10 "0 PO r^ >- "0 Cn vO \0 t^ r^ r^ T)-x PI VO 0 XX On ON 0 ^ On PO r^ « 0 0 -^ - M 10 0 » H> » » „ „ « \0 0 i^. r- 0 ro ^ -a- ^ lO 10 u-jvO 0 ^O N VO ON P^.O t^ t^ t-.X X 0 -f- 1^ " -h On On Ov 0 0 X 0 0 w « ►- ■* r^ 0 ^^ r<) r^j rr> -rr -Tt- VD 0 PI "-. X -f T)- 10 lO 10 vo 0 vo r^ i~>. t^ 0 PCO On t-~X X X X ov 0 (N M CO ro (^ 0 •- Tj-^O On PO Tt -^ Tl- Tl- PI -t- t^ On PI 10 10 10 100 »o t^ 0 <^ lO VO vO i^ t^ r^ r^ t^ 0 .0 w -^.O 00 0 CN (N PI fl rn n t)-\0 X 0 C^ PO P^ PO Tj- f^ i^ r^ On ►-< T -r T ->- ^n PO lOX 0 0 vC r^X 0 0 PI rO 'i- lOvO PI p< n N r< I^X Ov w 1-1 M N M ro PC PC c 00 00 0 0 - 0 0 0 - - PI PI rr> ^ ir> lovo r^x X Ov 0 '-' P» PI ►- PI PI Pi PI PC PI 0 «0 iO\C vO r^oo 00000 X CN o> 0 0 0 0 0 - - ►> i-c PI p< rO ir> -1- 10 10 vO vO 0 ^ rn ^. -f -i- -i- 00000 10 >o 10 vo 0 00000 vO vO t^ t^ 1^ 00000 X X X On On 00000 Ov 0 0 0 « ri r--; ^ >/~j 0 I ^ X On 0 ►- PI r^. -t- CN n r< M M >ovo r^x Ov PI P4 n N N ^ T^RlhS SHOU'INC, THP. CONTFNTS OF LOGS. 399 1 w 0 PI O 00 lO CO "100 O coo O 00 O CO « ON l-i t 1^ O 00 PI (~) t-O <^^ rO r^ t t t T ID *D uoo O O O r- f^ r-oo 00 10 •-I r^ ro 0\ »r; vO 00 M coso CI 00 t o o O^ '-' t t^ o CI 00 t O O CI t r^ O CI CO On ID ►- r^ ID t^ O CO ID CO 00 CS N fO rO IT! <^ 1 1 1 t in lo "OO o O O t^ t^ t^ t^ \0 ►- \0 O Ti •rf r^ a^ CN r;t- O t O c.oc O On •- to CO t^ ci o <- On "- to On NO C ID 0 t «- to ON « O O O O t^ ON CO M (N M ro ro CO CO t t t t ID lO >0 ID » « rO "O t^ O M oo I-. too >-■ t t^ On "H t t r^ O 1 1^ O 00 1-1 CO ID O CO r^ 0 CO 00 0 CI ID t^ o On o "1 rj (N CO i-o CO c^- re t t t t >D ID ID •DO O O O — 0 (N rf ID " "TvO 00 0 r^ On i-i ce lo M t t^ On ►- O 00 O CI t CO IDOO 0 PI ID r^ On 11 CO TO 00 ►< CO ID ID o (N (N M M ro CO CO CO CO t t t t ID ID •D ID IDO O n O M ttvO 00 M o (-1 « 0 OCO 00 t^o >o t 00 0 CI to t CO PI ►. 0 00 O c to c- o-x. t^ o t^ O ^ c^ ID >D ID C U i-> (N CS M tN CI CO CO CO CO CO t t t t t t ID ID ID w QC w C> t^ lO !■'; i-i On t^ lO CO 0 O 00 0 CI TT oc O t CI o ID t^ ON f- CO OC o -tec t O « O c< OC CO ID o E ci! 5 ►^ >-• n n n CI c< CO CO ro CO CO CO t t t t t IDID vo 00 O « t^ ►- t^ t >-l t^ lOO 00 0 " t 1- 00 t "- ce iDo oc o OO t ►" 00 t ►" CO IDO 00 o ID i-i 1-1 (S N M PI M M CO CO CO CO CO CO t t t t t t f . O t C "D CO to 00 o •- o CI r^ c. M Ci t ID r^ OC t O ID - OO O ►■ CO ID o o t M i-i w M rt CI N d C| M CO CO CO CO CO ce -1- t t t T 00 r'; r- ri •^ lO t^OO O o o lo > T " CO t -O t^ Crj CI r~- ►- O 00 0 •-< CO t O ID On c- CC O t^oo 0 ►■ Cl CO t 1^ M H4 IH CS M CI M Pi CI PI CO ro CO CO CO CO fO t t 10 ceo O ceo f^- to t^oo O COO O CO o >-i CI t in O O coo O O oo On 0 PI coo O c'O CO to r^oc c 0 t CI CI CI CI CI CI CI CI CO CO CO CO CO CO CO ce lO 1^ 0 CI o rrj to t^ to O - f . (X) O O CI CO nC CC 0 CI ID t >D t^CO On t^ o- - to O " CO t ID OC o M w CI CI CI CI CI CI CI CI CO CO CO CO CO ce t lO r^ X •- CI ce -)- lO On O CI CO -1- O CO On O •- ID I^OC ON i-i CI CO t ID f^ PI C' •rt-O t^ oo On O ►- PI OC CO CO •-1 •- • 1 CI CI CI CI CI CI CI PI PI CO CO CO - ce t t t C " n <^j 1- ir: uo lo v^O NO >0 0 r^O! On O t^ J^ r^oo 0 " CI CO t OC oc OC On On IDO r^OO On 0 ci CI CI r' CI CI Ct CI CI CI 1H -T CO r<- CI ci O 0 "" CI CO - C c o o t iDO O r^ f 1^ r^ o O CO - " - ►1 >-i CI CI CI CI CI CI CI CI 0 « c< ro t >00 r^OO On O ii CI CO t PI CI PI CI PI IDO r^OO On PI PI PI P» N % 400 FOREST MENSURATION. TABLE FOR MEASURING CORD WOOD WITH CALIPERS. Length Feet. Diameter in Inches. 10 Contents in Cubic Feet of Stacked Wood (Stacked not Solid. Cubic Feet). 6 0-7 I .O '■5 2 .0 2.7 3-3 4.2 7 .8 I . 2 1.8 2-3 3-1 3-9 4.8 8 •9 1-3 2.0 2-7 3-5 4.5 5-5 9 I .o 1.6 2-3 30 4.0 50 6.3 lO I . I 1.8 2-5 2,-i 4-4 5-6 6.9 II I . 2 1-9 2.8 3-7 4.8 6.2 7.6 12 1-3 2. I 30 4-1 5-3 6.8 8.3 ^3 1.4 2-3 3-3 4-4 5.8 7.3 9.0 14 1.6 2-4 3-5 4.8 (3.2 7.8 9-7 15 1-7 2.6 3-8 51 6.7 8.5 10.4 i6 1.8 2.8 4.0 5 4 7-1 9.0 II. I I? 1-9 2.9 4.2 5-8 7-5 9 5 11.8 i8 2.0 3-1 4-5 6.1 8.0 10. I 12.5 19 2. I 3-3 4.8 6.4 8.4 10.7 13.2 20 2-3 3-5 50 6.8 > 8.8 11-3 13-8 Diameter in Inches 11 13 13 14 16 17 Contents in Cubic Feet of Stacked Wood (Stacked not Sohd Cubic Feet.) 6 50 6.0 7.0 S.2 9-3 10.7 12.0 7 5-8 7.0 8.2 9-5 10.9 12.4 14.0 8 6.7 8.0 9-3 10.8 12.5 14.2 16.0 9 7-5 9.0 10.5 12.3 14.0 16.0 18.0 10 8.3 10. 0 II. 7 136 15-6 17.8 20.0 II 9-3 1 1 .0 12.8 14.9 17.2 19- 5 22.0 12 10. r 12.0 14. I 16.3 18.8 21-3 24.1 13 10.9 130 15.3 17.7 20.3 23- ' 26.1 14 II .8 14.0 16.4 19.0 21.8 2.1.8 28.1 15 12.6 15.0 17.6 20.4 23-4 26.7 30.1 16 '3-4 16.0 1S.8 21 8 2,S.O 28.4 32.1 17 14.3 17.0 19.9 23- I 26.5 30.2 34- 1 18 151 18.0 21 . I 24 -5 28.1 32 0 36.1 19 1.5-9 19.0 22.,^ 25.8 29.7 33 8 38.1 20 16.8 20.0 23 -4 27.2 31-4 35 • 5 40. 1 TABLES SHOIVING THE CONTENTS OF LOGS. 401 TABLE FOR MEASURING CORD WOOD WITH CALIPERS— (C C M r;" 01 -j-roo O-^ONuOvO 00 "00 nvOOO >-i rOO"0 00 " O "vOvO CO OnO (n f^iOsOOO C>>- (^ — N- ri n 01 *^. rj rj r^i rr^ ^ CN 00 t^ t^oo Oi-ioOoOO '^^'-i 0"Oc^cX)oor>.-5l-0>-iioro T|-r^C^ts>o O "OO "Oil t^co ON " M '^ lo r-^c» O w ^ »-. CN 01 Ci 01 ri 01 ro 000 fOOO "0 M CT> t^ O O ■+ <^C0 O P< M rorOr-0\0 OC4 -^ 00 O .ONfCO OnQ ^ 00000 O -rfOOOOO •+ ON r>- r^oo "OnO 00 O m 404 FOREST MENSURATION. ^2 t^ t^ l^vo v0'O'^'^r0CiMP-i>H«>->-i'"'-'0000000000^aNOOO .a pi OnTiOi^" ^""jOOvO cn^OOO »Oi-iOO^ IOCS I-" "I ^ CO OC< OnCOvO , t^ONi-i ^OiOt^O\ts -^O On "- -^vD O^ (N 'I- t^ O M rorOt^ONO On(n OO "^Cnvo OnQoO ^ t^i-'OO On t^ T) O <^ <~0 rovo t^O fOt^ii «d-0 >ON00>O r^ T)-ooo O <^ l-vcc» O ^oiot^O 00 fO" <-• rcn- >O00 I- "i-r^H-o -< M CN n M M (N ror^fOnrO'^-'J-'^-^uO'OiO i/^vo vo nC ►HVOCOOOvO "Of^lOrOtN t^Tft^^CS ■^N CN'^'^ONONfON ii On 0^ lO O00 0\ r^ r- >-< O M OC t^ t^ On 'H rO Tj-NO 00 O -> >-i M o CN CN OiO'0'OvO O NO O O t^ " <~OvO 00 ■^ lOOO NO lO ►- >H O ►1 loroMoo -^Ono O •-oo r^r^t^ r^oo o i-< p« ■^lOvO r-ONO ->00o0 0 OntnO ■*0 I^<*5ror^rriONO "OOO 0*000 On ry rj- tTnO oOvO "OOnD '1 r^O O r^>0'*f*^or^r-»oooo cs OnQ -ft^ONioovr^ii ^ nOOOnOnOOnO'n Onoo in i^ fs r^ O Onvo <~0 •- Cnoo r^ r^oo r^ r-CO O^OnO <■' IN ■^'O'Or^CNO in roiOvOOO O f^ roiOt^Cv"-" n » rO-i-fTiNO ON<^j(Ni ^oc I^M -^O 'l-CNCOii —vO rOOC rOMOOOO ^ O ONt^vO "OiOiO'i-'l-NO f^" "OONfOOO O On'*->-i00vO '*- lOvOO t^oo OnO '-' f^ fO-^iOt^oo ONi-i n -^-lOr^CNO 0 lO 10»0 t^OO On O '-' I fN "1" -t^ t^ On O "' f^^ -i-\0 l>- On •-• -- O tn P^ 2 o w PQ ooo 10 t^vO cs n (N C <■ G O ir vo - CC 00 (N (N (N M- o o^ iH 01 tN vO 00 >+ 00 " r^ ►- CN N r^ <^ O \0 t^ On « o o vO r^ On O IN fO 'T i^j -i- uoo O r^ n CO 10 t^oo ON 1^ f^O M ■-• (N ON -+ O "* ON ^ UOO 00 r^ in O ON O '-' 00 M ro « O O (N O O M VO O 0-00 c^ « r^ r^ ro O 00 00 On n vO O "-- O r^ On n '^ "0 t^ 00 10 Tf 11 M rO rJ-\0 10 (N ro -1- r^ VO 00 0 M T)-vO 00 0 N ■rl-vo CO ►H l-C M N CS (S (S ro ro ro fO fO 4o6 FOREST MENSURATION. (^ O O - Tt- o m i^ " vC C "~. ^ f^/ 'T ^ i/". lO IOCX3 H^iocc rivc- Q O O <"i C C "^1 ""i Pt c o ri ri CN n ro ro (^ ^ -^ ro rt-t^O riGCO -*'i--* 1^0*0 O —r^O OCO'^ vOO^Ci lOC^c^ w o D (^ w Qi, O b CQ < t~o -r "O ^c i^ X D o C^ O - ''I TABLES FOR STANDING TREES AND FORM FACTORS. 407 VOLUME TABLE FOR SPRUCE, IN CUBIC FEET.* * From The Adirondack Spruce, by Gifford Pinchot. VOLUME TABLE FOR CHESTNUT. Dominant Trees about 50 Years Old. [Based on 99 trees measured in Milford, Pa. Height of Tree in Feet. Diameter. Breast-high, Inches. 2.5 30 35 40 45 50 55 60 65 Merchantable Cubic Feet of Pulp -wood. 5 6 7 S 9 10 I . I 1 .6 2. I I . 2 I .8 2.5 1- I 3-8 1 -3 2 . I 30 3-9 4-9 6.0 7-1 1-4 2-4 3.6 4.8 5-9 7-2 8.6 lO.O 1-5 2.8 4-2 ,5.6 6.9 8.4 10. 1 II. 7 13-4 '5 1 1.6 3-2 4.8 6.5 8.0 9.6 II. 6 '3-5 15.4 17 3 I 3 5 7 9 10 13 15 17 19 7 6 4 3 0 9 I 2 3 5 4.0 6.0 8.0 9-9 12.2 14.6 17.0 6.6 8.8 II. 0 II 13-5 16. 1 18.8 12 13 14 19.4 21.8 21 -5 24.2 Height in Feet. Diameter. . Breast-high, Inches. 40 45 50 55 60 Merchantable Cubic Feet. 6 3-4 3-8 41 7 4 7 5 2 5 6 6.0 8 6 I 6.7 7 3 7 9 9 7 8 8.5 9 3 10 0 10 9 6 10.5 1 1 4 12 3 II 1 1 6 12.7 13 9 14 9 15-9 12 15 2 16 5 17 7 19.0 13 17.8 19 4 20 9 22.3 14 20.6 22 3 24 2 259 15 25 8 27 7 29.7 4P3 FOREST MENSURATION. VOLUME TABLES FOR PITCH PINE. Dominant Trees 6o to 8o Years Old. (Based on 75 trees measured in Milford, Pa.] Fuel- wood. Diameter, Breast-high 45-54' Trees. 5S'-64' Trees. Trees of all Heights. Cubic Feet. 9 9.6 9.6 10 11.9 15 7 12.3 II 14.6 17 8 155 12 18.0 20 5 19.2 »3 22.1 23 9 23-4 »4 27.0 28 I 28.3 15 33 4 340 16 39 8 40.1 17 .... 47 8 47-3 Lumber and Fuel-wood. Diameter, Breast-high One-log Trees. Two-log Trees. Three-log Trees. Board Feet. Cords. Board Feet. Cords. Board Feet. Cords. 9 ID II 12 13 14 J5 16 '7 19 22 27 33 41 52 0.045 •059 .075 •095 . 120 28 33 41 51 64 79 97 '17 0.023 .028 •033 • 039 .047 .057 .069 43 52 63 76 93 114 141 177 0.017 .021 .026 .031 .038 .046 .056 .070 T/tBLES FOR STANDING TREES AND FORM FACTORS. 409 VOLUME TABLE FOR RED OAK. [Based on 130 trees measured at New Haven, Conn.] Height of Tree in Feet. Diameter. Breast- high. Inches. 20 25 30 35 40 45 50 55 Merchantable Cord-wood in Cubic Feet. 5 6 7 8 1-23 1.78 1. 61 2.31 I. 91 2.83 3-79 4.88 2.24 3-31 4.40 5-75 2-55 3-77 5.08 6.56 8.31 2.91 4.22 5.68 7-31 9.27 3.12 4.61 6.25 7-99 10.13 12 .62 15-70 3-40 5-04 6.79 8-75 10.97 13.64 16.87 9 10 1 1 Height of Tree in Feet. Diameter, Breast- high, Inches. 60 65 70 75 80 85 90 M srchantable Cord-wood in Cubic Feet. 5 3.66 6 5-45 5.81 6.16 7 7.32 7.81 8.31 8.78 9.27 8 9-43 10.07 10.70 II. 31 11.93 9 II .76 12.62 13-31 14.04 14. 75 10 14.63 15.62 16.52 17.42 18.30 19.20 II 18.04 19. 16 20. 18 21 . 17 22.15 2^.12 24.06 12 12.33 2^.62 24.90 26.04 27-15 28.16 29.14 13 27-33 28.85 30.34 31.62 32.98 34-21 35-40 4IO FOREST MENSUR/ITION. FORM FACTORS OF SCOTCH PINE IN NORTH GERMANY* [Based on the volume of wood above 7 centimeters.] Diameter Classes in Centimeters. Height, g Meters. 1-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 Form Factors. 12 500 13 • 495 14 491 .492 15 4«7 .488 16 4«3 .484 .487 17 479 .4S0 483 18 475 .476 479 •477 19 471 473 •475 •474 20 468 .470 .472 •471 .470 •465 21 465 .467 .469 .467 466 463 22 462 .464 .467 •465 463 461 457 23 459 .461 465 •463 462 460 457 24 456 •459 463 .462 461 459 456 455 25 453 457 461 .461 460 459 456 455 26 450 455 460 .460 459 458 456 455 27 449 454 459 459 458 458 457 456 28 448 454 458 459 458 458 457 457 29 453 457 458 458 458 458 457 30 453 456 457 458 458 458 458 31 455 457 457 457 458 459 32 455 457 457 458 459 460 33 457 458 459 460 460 34 457 459 460 461 461 35 459 461 462 461 36 460 461 462 461 * From Formzahlen und Massentafeln fiir die Kiefer, by Dr. Schwappach, 1890. STEM FORM FACTORS OF SPRUCE OVER 90 YEARS OLD.* Diameter, Diameter, Diameter, Diameter, Breast- , Breast- Breast- high, } Centime- '■' virm actor. high, J Centime- -^ 'orm actor. high. Centime- Form Factor. high. F Centime- '^' (irm ictor. ters. ters. ters. ters. 10 559 34 466 58 .414 80 370 12 544 36 462 60 .410 82 367 14 532 38 457 62 .406 84 365 16 522 40 453 64 .401 86 363 18 513 42 449 66 •397 88 361 20 505 44 444 68 •393 90 3595 22 498 46 440 70 • 388 92 358 24 492 48 436 72 •384 94 3565 26 486 50 431 74 . ^80 96 355 28 480 52 427 76 .376 98 354 30 475 54 423 78 •373 ICK) 3535 32 470 5^" 419 * From Behm's Massentafeln. TABLES FOR STANDING TREES AND FORM FACTORS. 41 1 FORM FACTORS OF EUROPEAN OAK.* [Based on the volume of wood above 7 centimeters.] Diameter at Breast-height n Centimeters. Height , Meters. 10 15 30 25 30 35 40 45 50 i& Form Factors. 6 .285 7 .298 .506 8 316 .500 •553 9 .338 ■495 •538 .548 10 361 •491 •529 •542 •555 11 ■378 .488 •524 •53S ■550 • 557 12 •395 .486 .520 • 534 •544 ■551 .565 13 .409 ■484 ■514 •530 •540 -545 •559 •564 14 •424 .482 •512 .526 .535 ■541 •555 .560 .565 ■570 15 ■437 .481 •507 •523 •531 ■536 •550 •556 .560 .566 16 .448 ■479 • 506 •521 •528 ■533 • 546 •553 •556 •563 17 ■454 ■478 •504 • 519 •525 ■530 •543 •550 •553 .560 18 .460 ■477 • 502 • 517 ■523 .528 ■541 •548 •550 •557 19 .476 •501 ■515 •521 • 526 •537 •545 •547 •554 20 ■475 ■ 500 •513 •519 •524 •534 •542 •545 •551 21 ■474 ■499 • 511 •517 •523 •531 .538 •542 •548 22 •474 .498 ■510 .516 •522 •529 •535 ■539 •545 23 •497 ■509 •515 •521 •527 •532 ■536 ■542 24 .496 .508 •514 ■ 520 • 526 •530 ■ 534 ■539 25 •495 •505 •513 •519 ■524 .528 •532 ■537 26 .496 •503 •511 .518 •523 •527 •531 .536 27 .501 .510 ■517 • 522 .526 •530 •535 28 ■497 .508 ■ 516 ■521 ■525 •529 •534 29 494 .506 •514 • 520 •523 .528 •532 30 .491 •504 ■512 ■519 .522 .526 •531 31 .488 .502 ■510 .518 •521 • 526 •530 32 .500 ■509 .516 • 520 •524 •529 33 •498 •507 •514 •519 •523 •527 34 •497 •504 • 5" .516 •521 •525 35 •495 .502 • 509 •513 •519 •523 36 ■493 .500 •505 •511 .516 •521 37 ■497 •503 .508 •514 •519 38 ■495 .500 •505 •5" •516 39 •493 • 498 • 503 ■ 509 •514 40 .490 '^496 .501 ■ 507 •512 j:- ■c:„i u,, n ,. 0»k,.,a r^^o,^V. , 412 FOREST MENSURATION. FORM FACTORS OF EUROPEAN OAK— ijContinued) . Diameter at Breast-height in Centimeters. Height, Meters. 60 65 70 75 80 85 90 95 100 Form Factors. 14 •575 15 ■570 ■575 16 .566 ■571 •570 17 •563 ■567 •571 ■576 18 .560 ■564 .568 ■572 .580 19 •557 ■ 561 ■565 ■569 ■576 .585 20 •554 ■558 .562 .566 ■571 •576 21 •551 ■555 ■559 ■ 563 ■567 •572 •577 22 •548 ■551 ■556 . !s6o •564 •569 •574 .586 23 •544 •549 ■554 ■55S • 562 •567 •572 •5S4 • 595 24 •542 •547 ■552 ■556 .560 • 565 •570 .581 • 591 25 •541 ■545 ■550 ■ 555 ■558 •563 •569 • 577 • 587 26 •540 •544 •549 ■554 ■557 .562 .568 • 574 .582 27 ■539 • 543 • 548 ■ 553 ■556 .560 .566 • 571 •578 28 •538 •542 •547 ■551 • 554 ■ 559 •564 .568 ■ 573 29 •537 •541 •545 ■550 •552 •557 • 561 .566 ■571 30 •5^5 •539 •543 •548 •551 •555 •559 • 564 .568 31 ■534 •537 ■542 •546 •549 ■554 • 556 • 562 .566 32 •533 ■536 •540 •544 •547 ■552 • 555 .560 • 564 33 •531 •534 ■537 •542 •545 ■550 •553 • 558 .562 34 ■ 530 ■ 533 ■535 •541 ■ 543 • 548 •551 •555 ■ 559 35 .52S ■532 ■ 534 • 539 •542 ■546 •549 • 553 ■556 36 .526 ■ 530 ■ 533 • 538 •541 •544 •547 ■550 ■553 37 ■524 .528 ■ 53 1 •536 . 538 •542 •544 •547 ■549 38 •522 .526 ■529 • 533 • 5?^^^ • 539 •541 •544 •545 39 •519 • 524 •527 •530 •531 •532 •534 •536 • 538 40 •517 .522 ■ 526 •529 •530 •531 • 533 • 535 • 537 4 TABLES FOR STANDING TREES AND FORM FACTORS. 4^3 ffi 0/ rj E W W ■^ pq m o ^ t^ < o Pi •n t3 o w ^ Ph <4-> o r/1 i= rt 3 O O H > r ; o; -< ^ P^ ^ o Pi .00 On O i-i N <*5 >+ >OVO r^OO 0\ O "-i P< <*5 'I- >OvO r^oo C>CT^OCOOOOOC""-"">--"" ro Tl-^ 1^00 O -'"" coOOOOC-'C-OnCOCOOOOO"'-'-""-" iot^000<"i-+Lor--000"tNr0'O 000000 O^O^C^O^C^C^O O O 0 O ^Ti-'^-T'T'^'+'t^uOlOlOlOlO O 0 CO o O 0 0 " "0 ft XCCOCCOCO 0 0-. OnO^OCnOO O O O O O O " ooocooccccoC'X asCNc:>ONOC>ONO O O O O O O I^O^O '-' '"Ti'OvO 1^0^0 " r^-1-iOt^OO O " f< "+"00 I^I^OOOOCOOCCOOOCO C?iChONCN(7vOONO O O O O O -l--t--i--t-+-1--+-|--|-'1-'^-1--|--+-^-|-LO'OlOLOLO>0 .^vO r^oc O I- tN -t-ior^oo O •-' i~o-1-"or^oo O '-' <~o-tuo . r^t^t^r^cCoCCOoOoOcooD O^C^O^a^C^C^O^O O O O O t^ r^ r^ i^ t-^ t^ t^oc 00 oc cc oc CO O O Cn O C?< O O O -+-|--t--f-t-l--1--t-t't-t-1--i--t-1--t--t--t--t't-"~^ O 1-1 fO ^O t^oo Cn O "^i '^J ^O 00 O M "^ -+ "^^ t^ r^ r^ r^ r^ r^ r^ t^OO OOOOCOCOOO C^0^0^(7^0^0^ O O O O 0 f^ '^•^ t^l^ On "H r<0 ■.rfvO CC On O .£ ■ oovOvOnOncOvCO i^r^i^t-^r^oooo , -+-i--r-t--i--t--i--i--i--t-i--i--i--t-Tt-Tf ICO r^oo Cn C '- <^ "^ ^ "^NO r-~ r^co oo g iCnOCO >-i rO>Ot^C~0 fN t^, -t-O t^OO i- -ccoo OOOOnO C O C O " -J rr-^ r^j r^j r^. ^ r^, -t -t 't -i 1 ^ 130 I lO »0 »0 lOO vC vO NO r, 01 ci ^ 'N M r< (N J3 I- •SPS a a> OS o i-( n r^'^iOO t^oo On O " ■* iOnO t^cO 414 FOREST MENSURATION. U E u W « < w fin C C^ w c Pi c O <: Height. Meters. (U E C .a CJ +-» i4 cu o E a! S <^. •^-)-'*^^-t-*-*-l-"-. 1 © »C CC O C " r-i r'. "- VC t^ CC O r^, i^. f. -t- -+ -t -t -1- -i- -t -1- -1- 1 rcmvooo OC C c-i f^, M-vC r^oo c^ fO <^, r^, <^. -*• ■* Tj- Tt- rt- ^ Tf ■;!- uo "^ lo lo u", lo u~, u-, u^ in m li^ lo r) '+•101^00 OC-C ►- r^. mvcvO r^j rc re <~0 m r^, t^, 1- -t -+ -t -1- ^ xr: \rj \r-^ \r^ ir-^ IT; \r; ir^, \/~, \r. \r, ir. xr; t » O " ft -+ U-, r^ t-~ OC O C ri re Tj- U-, tN re re re re re re re re 'I- 'I- ^ ^5- 'l- lo »o LO lo in le in u", tn in u", ic »n »n N (0 O . . . . -i-inosc O" (N re^mvcocococ ►- . . . • r^ M ri ri fi re re re re re re re re re rt Tt CO . cs (N c* nvc t^ . in in in in in lo in »n in in »n >n in in »n »n in "* ^ •GOC'-*'-'*^*^'^*^^'"'^'^*^^^^^ .invor^oooooO'-'N'^rfinvor^OO^-f^rei . ininininininininininininininininininin © i2 3 o <- M ro'+invo t^oo oc •-• <^ reTfinvo t-»oo o (NMr)CSMr((Nr«cicsrec^cOrororOtOfOfOr^ TABLES FOR STANDING TREES ANQ FORM FACTORS 415 FORM FACTORS OF EUROPEAN TREES. [Based on heights.] Spruce Scotch Pine Silver Fir Beech Height, (after Baur). (after Kunze). (after Schuberg). (after Kunze). J Meters. Tree Merch. Tree Merch. Tree Merch. Tree Merch. Form Form Form Form Form Form Form Form Factor. •97 Factor.* Factor. Factor.* Factor. Factor.* Factor. Factor.* 5 •93 .07 •97 .84 6 .89 . 10 • 84 •14 .89 .80 7 ■85 .18 .78 .21 •83 •31 •75 .01 8 .81 •27 •73 • 27 •79 ■35 ■72 .07 9 ■ / 7 ■33 .68 ■33 .76 •42 .69 .14 10 •75 .38 •65 •36 •73 •47 .66 .20 1 1 •73 .42 •63 .40 •71 ■50 .64 .28 12 •70 •45 .61 •44 .69 •51 .62 •37 13 .69 .48 •59 ■47 .68 ■52 .61 ■41 14 • 67 •49 •58 .48 .67 ■53 .60 ■43 15 .66 •50 •57 •48 •65 •53 •59 •44 16 • 65 •51 .56 •48 .65 •53 •58 .46 17 .64 •51 •55 •47 .64 •53 •58 ■47 18 •63 •51 ■54 •47 •63 •53 •58 ■47 19 .62 •51 •53 •47 •63 •53 •57 .48 20 .62 ■51 •53 .46 .62 •53 •57 .48 21 .61 •51 •52 .46 .62 •53 •57 49 22 .60 •51 ■52 .46 .61 •53 •57 •49 23 ■59 ■51 •51 •45 .60 •52 •57 •49 24 ■58 ■50 •51 ■45 .60 •52 •57 ■49 25 •58 •50 •50 ■45 •59 •52 •57 • 50 26 •57 •49 •50 ■ 45 •59 •51 ■56 • 50 27 •56 •49 •50 •45 •58 •51 ■56 • 50 28 •55 •49 •50 •45 •58 •51 ■56 • 50 29 •55 .48 •49 ■45 •57 ■50 ■56 • 50 30 •54 •48 •49 • 45 •56 ■50 .56 ■ 50 31 •53 ■47 •49 .46 •56 ■49 ■56 ■ 50 32 •52 •47 •49 .46 •55 ■49 ■56 ■ 50 33 •52 .46 ■49 .46 •54 ■48 ■ 56 ■ 50 34 •51 .46 ■49 .46 •54 •47 35 •51 .46 •53 ■47 36 •50 •45 ■52 ■47 37 •49 •45 •51 ■46 38 •49 •44 •50 ■45 39 •48 •44 ■49 ■45 40 •48 •43 .48' •44 ♦Based on the vc lume of w ood over 7 centimet ;rs in dian leter. TABLES OF GROWTH AND YIELD. The U. S. Forest Service has made extensive local studies of growth of a large number of different species, but the material has for the most part not yet been published and is, therefore, not available for this work. The author has, in consequence, not attempted to give an exhaustive list of tables of growth. A few tables have, however, been given which are likely to prove of general use. The investigations in the study of yield have not yet pro- gressed far enough to justify the pubhcation of a series of yield tables. A number of local yield tables for many-aged forests have been published, but the majority cannot be used, except in the localities where they were made. The yield tables for spruce shown on pages 422 and 424 are included for the purpose of illustration. In the absence of general yield tables for spruce they may serve a useful purpose. They have been constructed to show the future yield, after cutting to diameter limits of 10, 12, and 14 inches, of stands having an original yield, for trees 10 inches and over in diameter, of 1000, 2000, 3000 board feet, etc. They were prepared for use on a tract of 40,000 acres at Nchasane, Herkimer Co., N. Y. The author has translated portions of the German yield tables of Scotch pine, spruce, and beech. These tables will be useful as a standard of comparison when similar tables are constructed in this country. The tal)les on page 435 '^^'Ci'c used in tnmslating from the metric lo the English units. 416 TABLES OF GROWTH AND YIELD. 41 NORMAL YIELD TABLE FOR SPRUCE.* QUAUTY I. Age, Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. "^-of" Forest 10 37-2 7-5 20 2940 97-3 20.0 2.6 700 360 30 1780 168.5 35-1 4-2 2915 57 490 40 1120 205.6 51-5 5-8 5545 214 519 50 716 226.8 65-3 7.6 7746 386 519 60 500 242.0 76.4 9-4 9546 457 5" 70 380 252.3 85.3 II .0 1 1018 457 505 80 308 260.9 92.8 12.4 12247 414 500 90 256 269. 1 99.1 13-9 13305 357 495 100 220 276.5 104.3 15-2 14248 314 490 no 200 283.0 108.6 16. 1 15120 272 488 120 189 288.6 1 1 1 .9 16.7 15892 243 487 * From Wachstum und Ertrag normaler Fichtenbestande, by Adam Schwappach, Berlin, 1890. NORMAL YIELD TABLE FOR SPRUCE. Quality III. Age. Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per p Acre of Thinnings tj Cu. Ft. ^ orest ^orm actor. 10 3-6 20 61.3 10.2 30 3300 102.3 19.4 2 4 672 331 40 1924 140.8 30.2 3 7 2115 29 495 50 1216 162.4 42.0 4 9 3673 129 534 60 840 178.9 52.2 6 2 5059 229 539 70 628 189.2 61 .0 7 4 6274 243 539 80 500 200.0 67.9 8 5 7317 229 534 90 424 209.5 73-5 9 5 8217 200 528 100 380 217.7 78.4 ID 2 8960 186 522 no 346 224. 2 82.0 10 9 9632 171 520 X20 320 229.8 84.6 II 5 10232 143 520 4i8 FOREST MENSURATION. NORMAL YIELD TABLE FOR SPRUCE. QUAUTY V. Age, Years. Niimber of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per Acre of Thinnings, Cu. Ft. Forest Form Factor, lO I -3 20 38. 0 4-2 30 60.5 8.9 40 3920 86.4 151 2 .0 343 .261 50 2128 107. I 22 .0 30 957 •403 60 1356 121 .8 29 -5 41 1872 43 .516 70 988 133- I 37-1 50 2758 86 •555 80 800 142.6 43-0 5-7 3530 86 •567 90 696 150.8 47-5 6.3 4144 71 ■573 100 640 157-2 50.8 6.7 4630 71 •574 NORMAL YIELD TABLE FOR BEECH.* QUAI^ITY I. Age, Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per Acre of Thinnings, Cu. Ft. Forest Form Factor. 20 2524 39-1 18.0 I . 7 30 1526 73 4 31-5 3 0 686 .29 40 934 104 5 44.6 4 5 1943 129 41 50 598 129 6 56.1 6 3 3330 229 45 60 423 146 9 66.9 7 9 4602 286 46 70 327 159 0 76.4 9 4 5802 314 47 80 269 168 5 84.6 10 7 6903 314 48 90 228 175 8 91-5 1 1 9 7905 314 49 100 196 T82 3 97.1 13 0 8S60 286 50 IIO 174 1 87 5 102 M 0 9732 271 50 120 157 192 2 106 15 0 10518 257 51 * From Wachstum und Ertrag normaler Rothbuchenbest&nde, by Adam Schwappach, Berlin, 1893. TABLES OF CROIVTH AND YIELD. 419 NORMAL YIELD TABLE FOR BEECH. Quality III. Age, Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per Acre of Thinnings, Cu. Ft. Forest Form Factor. 30 2044 52.7 230 2. I 86 40 1372 79-9 33-5 3-3 943 •35 50 960 103.7 43-0 4.4 2001 86 45 60 724 120. 1 51-8 5-5 2915 143 46 70 572 130.0 59-7 6.5 3716 171 47 80 460 1 36 . 1 66.9 7-3 4430 1 86 48 90 380 140.0 73-2 8.2 5045 200 49 100 320 1430 78.7 91 5573 200 49 IIO 275 1456 83-3 9.8 6045 200 49 120 239 148.2 86.9 10.6 6460 200 50 NORMAL YIELD TABLE FOR BEECH. QUAUTY V. Age, Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per Acre of Thinnings, Cu. Ft. Forest Form Factor. 40 1976 56.2 20.3 2-3 400 •35 50 1496 79.1 27 9 3-1 929 42 60 II92 97.2 34 I 3-9 1529 46 70 984 107.6 39 4 4 4 2044 48 80 824 113-6 43 6 50 2415 43 48 90 696 116. 3 47 2 5-5 2672 71 48 ICO 600 117. I 49 9 6.0 28 s8 71 48 IIO 524 116. 2 52 2 6.4 2987 86 49 120 464 115-3 54 I 6.7 3073 86 49 420 FOREST MENSURATION. NORMAL YIELD TABLE FOR SCOTCH PINE.* Quality I. Age, Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per 1 „ Acre of ^^'^.^o Thinnings, t£^ Cu. Ft! Factor. lO 12 . I 20 1696 107. I 29.2 3-4 957 304 30 1076 141-7 43-6 4-9 2244 171 361 40 696 162.0 55-4 6.5 3573 214 394 50 464 175-4 65.0 8-3 4602 272 400 60 328 184.9 73-2 1.02 5459 286 401 70 256 191.4 80.1 II. 7 6202 272 401 80 218 196.6 86.0 12.8 6831 229 401 90 196 200.9 91.2 ^3-7 7346 186 398 100 179 205.2 95-8 14.4 7760 157 391 110 166 208.7 99-7 15-2 8117 143 .^87 120 154 212. 1 103 15-9 8446 129 383 * From Wachstum und Ertrag normaler Kiefembestandc, by Adam Schwappach Berlin, 1889. NORMAL YIELD TABLE FOR SCOTCH PINE Quality III. A«e, Years. Number of Trees per Acre. Basal Area, Sq. Ft. Average Height, Feet. Diameter of Average Tree, Inches. Yield per Acre, Cu. Ft. Yield per t Acre of Thinnings, J Cu. Ft. ^ ^orest ''orm actor. ID 5.6 20 2600 60.9 17.4 2.2 329 312 30 17S4 lOI . I 30.2 3 2 1200 100 388 40 I 2 28 123.6 39-4 4 3 2086 143 425 50 84S 135-6 46.3 5 4 2830 200 448 60 59^) 143-4 52-2 ■6 6 3458 229 459 70 440 149.0 57-4 7 9 3973 214 459 80 348 153.8 62.7 9 0 4387 186 452 90 292 157-7 67.3 9 9 4745 M3 443 100 255 1 60 . 7 71.9 10 7 5"45 129 433 IIO 228 162.9 75-8 1 1 5 52SS 100 425 120 205 164.2 79-1 12. 1 54'^8 86 417 TABLES OF GROIVTH AND YIELD. 4" NORMAL YIELD TABLE FOR SCOTCH PINE. Quality V. Age Number o£ Trees Basal Area Average Height Diameter of Average Yield per Acre, "^-^^ ^fS Years. per Acre. Sq. Ft. Feet. 2.3 Inches. Cu. Ft. lO 20 6.6 30 ^200 57-9 14.8 1-9 1 86 225 40 2256 81.2 21 .0 2.6 586 57 349 50 1588 93-3 25-9 3-3 1058 86 455 60 H52 100. 2 30.2 4.0 1429 86 4«5 70 828 104. 1 34.1 4.8 1744 86 492 80 640 106.3 38.1 5-5 1986 71 486 90 520 107.6 41-3 6.1 2158 57 479 100 428 108.4 44-3 6.8 2287 57 472 VIELD OF FULLY STOCKED STANDS OF SECOND-GROWTH WHITE PINE.* Age of Stand Average Height, Total Trees Merchantable Yield per Years. Feet. per Acre. Trees per Acre. Acre, Cords. lO 5 2220 15 9 1700 20 14 1600 25 ?2 1310 400 II 30 32 1090 510 21 35 45 885 620 30 40 54 690 540 38 45 62 510 460 45 50 68 400 380 53 55 72 300 300 65 60 76 260 260 80 ♦ From The Natural Replacement of White Pine on Old Fields in New England, by S. N. Spring, Bull. No. 63, U. S. Forest Service, 1905. 422 FOREST MENSURATION. W o P-, m < P o Pi o o to W PQ -< H Q ►4 8 h4 t*'3 tx ■* r^ o fO fO «r> t^ N VO CO 2 5-5 cr =^ o N CO <~0 rO •^ M- t -* lO lO rj- '^ K^fv;^ J o fe "^ w rri O a ">. = -^ = -^S r C U o CO d '^_ SO c" cs c vO Ov q q VO ^— ^ f) ■N C) n n r^ ro PO f^ CN T^ ^ [u zs-S "T _j <« o c3 0) . fo 00 00 !>. O r^ )H VO VO Cv CO o r- tr> VO t^ CO CO rD VO rO 'i- 00 00 t3 r- CO 0^ O O •o •* PO M 0 Ov 00 rt •^ *^ •"• *^ *^ •^ ^ *^ 1^ o 01 E .2 •5^ c u CJ (^ u 00 ro t^ CN lO CN P) P) q c lO •S ^^H c Ol S^^ (N IN -+ LO VC 00 d Cv 00 j^ d VO ►I ►-' " ■-> '-' •-1 r< ►- •-■ " re M u zs-g a; o n U fc u-> rn lO lO »0 0 "^ t^ VO re 0 tr; rt o ■E lO f^ (N r^ O •+ HN 1^ ov r^ v^ HH en (J_, , r< f^ r^ <~C rO -* lO •o ro rf »o t^ <« g '^ C 6> •o c 'S ' oi 0 o . 0 ■" o I. 2 s o cJ u fO 't >0 lO r^j 00 re >+ P) VO 0 0 -» ^^H (J w Eiio •o lO VC t^ t^ 00 d Cv r^ oo d re rt I. c *« jj c ^'d o . 3 1* o 2 i" '- vO n 0 oo (^ >/^ lO oc ^ Ov lO (N 3 M 00 00 M i-< Q o vO -f- Cv ov r^ u Th "^ •&■ (N rj Q •* 00 -1- 1- 0 r^ •— • M c< tn '4- lO ^0 t^ t^ Ov c M y: o rt u o . SiS"^ O fo fO -1- VO *-< t^ »~l "I- lO |M( M •"i (N M N 3 ^- 2:< « u" a>,^ c* c *-< oj ,*- C 4* . a; 3 H n E -a, « = £2.|t:S «xQ-? 5^ t-i N f^ •I- lO VO r^ 00 Ov 0 1^ N "^ " -^ ? O C C 1/1 <«-T3 _►_•- rt 3 I. ^ V. 0^ 0 rt "S o ™Hm TABLES OF GROIVTH /tND YIELD. 423 S "^ T w u PL, w w « o o < o w pq Q hJ w h4 O O he, CQ !« ?; £ < u . o > CO ro f^ fO ^ (U ," fe -+ u-j i-i ^ On 00 vn '+ 00 CO CM r^ 0 ro r^ C4 0 I^ CO >o CO 00 00 NO •0 to a^ rl- ON i-i t^ NO CN 10 n tl r^ g n M fO CO -i- '^ 10 10 in r^ 00 p "c^J 01 > 0 0 On r^ l- >o 0 C3 M On 0 >o ON »-i 10 00 n -t- 0 NO .-^ CO 0 10 ■a M M C) ro CO ^ CO CO CO 10 10 n 2; i- wJ !« Sh n n >o 10 NO 0 ON NO "O >-( M CO CM h-< U-) 00 ft CO NO CO 0 M CS c< CO C^ ^^^i: M ^ SH On On NO On NO NO On >- CO CI CN CO O 1-' O " CN -+ ^ ■5'r ON " i« S c -*; Amount 0 First Cut Trees i 2 Ii and over i Diameter Board Fee CO r^ 0 00 ^ CO NO CO CO 10 10 0 C) 0 "+ lO 00 CO r-- 10 ^ 0 0 On On NT) CO t-l n On *-" 1^ M CO rt- 10 NO NO ' — ' U C 4) . 0) 3 ,« b Cfl rt "o c c 2 S"^ ►_.,. a! 3 u T3 .DOM >0 VO t-» 00 On O •-' 4*4 FOREST MENSURATION. o 3 S - ca c 0) o 3>< O - « lO rO 00 0\ 0\ ■<4- vO O Ov T) 00 O C> VO ■J ■- ^ > E-g«T3 ^ ^ J; S= Z '- Ci 01 fO On CO ro r^ <-0 vO ^ u £ » O o o n ^ -+ r^ l-l lO "O t^ '*■ c> o fo t^ "+ (S Tf M VO ■^ '+ ? 'f Cs ro "* 00 O f) lO T^ v,0 0 •-" ►-" »-• >-i tN (N (N cs . •t rO t^ N lO t^ (N 0 0 0 c c^ VO t>. CN 0 1-4 « <*• M "t- f^ Z o s^ tU SH cO 1-0 iSfe g , -• > o gtJ „ o gT3 to <> vO 1-0 lO 00 fc^ 5 2i - '-> 3 2 „ u P 0 rt w « poTfiovo t^oo a>o " TABLES OF GROIVTH AND YIELD. 425 DIAMETER OF LOBLOLLY PINE IN DIFFERENT TYPES.* On Old Fields. In Pure In Pure Stands on Fairly Well- drained, Mixed with Hardwoods. Age. the Wet Prairie. On Well- On Poorly Light Soil. drained, Fer- Drained Soil tile Soil. (thicket). Years. Inches. Inches. Inches. Inches. Inches. 5 1-9 1-5 0.2 0.2 0.2 10 4-3 3 7 2.2 2. I 0.9 15 6.1 5 5 4.8 4.0 1.6 20 7.6 6 7 7.6 6.1 2.2 25 8.5 7 7 10.4 7-9 30 30 9-3 8 8 12.8 9-5 3-8 35 9-9 9 9 15.0 10.9 4-7 40 . 16.9 12.4 5.6 50 . 20.0 15.0 7.8 60 22.3 17.2 9.8 70 • 24.0 19-3 II. 9 * From Th e Loblolly Pine in £as1 em Tej as, by R. Zon, Bull. No. 64, U . S. Forest Ser HEIGHT OF LOBLOLLY PINE IN DIFFERENT SITUATIONS.* On Old Fields. In Pure Groups on the Wet In Pure Stands on Fairly Well- drained, Mixed with Hardwoods. Age. On Well- On Poorly Light Soil. drained, Fer- tile Soil. Drained Soil (thicket). Years. Feet. Feet. Feet. Feet. Feet. 5 18 II 6 7 5 10 34 29 21 23 13 15 50 45 35 34 21 20 62 57 45 45 28 25 69 67 53 55 34 30 74 73 60 65 39 35 78 79 67 75 44 40 82 84 73 85 49 45 89 78 95 53 50 95 83 105 57 60 88 64 70 91 72 * From The Loblolly Pine in Eastern Texas, by R. Zon, Bull. No. 64, U. S. Forest Ser- vice 1905. 426 FOREST MENSURATION. COMPARATIVE RATE OF GROWTH IN HEIGHT AND DIAMETER OF CHESTNUT FROM THE SEED AND COPPICE.* [From the measurement of 1245 trees in Marj^land.] Height. Growth each Annual Growth each Age, Ten Years. Ten Years. 1 "iears. Trees from Seed, Feet. Coppice, Feet. Trees from Seed, Feet. Coppice, Feet. Trees from Seed, Feet. Coppice Feet. 10 7 23 7 23 0.7 2-3 20 17 42 10 19 I .0 1-9 30 33 57 16 15 1.6 1-5 40 52 69 19 12 1-9 1 .2 50 64 77 12 8 1 .2 .8 60 73 83 9 6 •9 .6 70 80 87 7 4 • / •4 80 84 90 4 3 •4 •3 90 88 92 4 2 •4 .2 100 91 93 3 I •3 . I 1 ID 93 94 2 I .2 . I 120 95 95 2 I .2 . 1 Diameter, Growth each Annual Growth each Age, Breast-high. Ten Years. Ten Years. 1 Years. Trees from Seed, Inches. Coppice, Inches. Trees from Seed, Inches. Coppice, Inches. Trees frcm Seed, Inches. Coppice, Inches. 10 0.8 3-8 0.8 3-8 0. I 0.4 20 3-4 6 8 2.6 30 3 3 30 6.0 9 3 2.6 2-5 3 3 40 8.7 1 1 4 2.7 2. 1 3 2 50 II .2 13 4 2-5 2.0 3 2 60 134 15 I 2.2 1-7 2 2 70 15-4 16 7 2.0 1.6 2 2 80 17.2 18 0 1.8 1-3 2 90 18.8 19 2 1.6 1 .2 2 100 20. 1 19 8 1-3 .6 I 1 10 21 .0 20 4 .9 .6 I 120 21.6 20 8 .6 • 4 I ♦ Prom Ch< jstnut in Soi ithem Marvl and, by R. i Son. Bull. N 0. S3. U. S. Forest Ser TABLES OF GROIVTH AND YIELD. 427 RATE OF GROWTH OF CHESTNUT. [From the measurement of 68 trees in Connecticut.] A. Dominant Trees in the Forest. A.ge, /ears. Diameter on Stump Inside Bark Diameter Breast-hisrh. Outside Bark- Diameter at 10 Ft. above Stump. Diameter at 20 Ft. above Stump Diameter at 30 Ft. above Stump, Diameter at 35 Ft. above Stump, Inches. Inches. Inside Bark, Inside Bark, Inside Bark, Inside Bark, Inches. Inches. Inches. Inches. 10 2 . I 2. I 1-35 0.3 20 5-4 5-1 4-3 3-4 0.9 30 8.7 7.8 6.9 6.1 3-7 2.9 40 "•45 9-7 8.9 8.0 5-8 50 50 13-7 II-3 10.6 9-5 7-25 6..S 60 12.5 II. 9 10.7 8.55 7.6 B. Trees in the Open. 10 20 30 40 50 30 30 2. 7.8 7-4 5- 13.2 "•5 9- 18.5 15-3 13- 23-4 18.5 15- 4-5 8.0 13-4 2.5 6.0 7.9 II . 2 RATE OF GROWTH OF RED CEDAR. [Based on the measurement of 23 trees near New Haven, Conn./ A. Trees in the Open. Age, Years. Diameter, Inside Bark on Stump. Inches. Diameter. Inside Bark at 6 Ft. above Stump. Inches. Diameter, Inside Bark at i 2 Ft. above Stump, Inches. Diameter, Inside Bark at 18 Ft. above Stump, Inches. 30 40 50 5-5 6.8 7.8 4.0 51 5-9 2-3 3-5 4-5 1.6 2.6 •^.6 B. Trees Crowded, but not Overtopped. 30 4-8 3-7 2-3 1-3 40 5-9 50 3-3 2. 1 50 6.8 6.0 4-1 2.6 60 7-4 6.6 4.6 2.8 C. Trees Free in Youth, btjt Later on Overtopped. 40 4-4 3-7 2.7 1.4 50 5-1 4-5 ^ 3-4 2.2 60 5-5 4.8 3-7 30 428 FOREST MENSURATION. RED OAK. Maximum Growth of Trees in a Sprout STA^fD. [Based on the measurement of 53 trees near New Haven, Conn.] Age Years. Diameter Breast- high. Outside Bark, Inches. Height, Feet. 20 30 40 50 .60 70 3-5 5-4 7-3 8.8 10.4 II .2 36 47 57 65 70 PITCH PINE IN PIKE COUNTY, PENNSYLVANIA. Rate op Growth in Diameter. Diameter Inside the Bark. Diameter Breast- Age. Years. high, Inches. 2.7 1' High ii' High 21' High, 31' High 41' High, 51' High, Inches. 2. I Inches. Inches. Inches. Inches. Inches. 10 20 4.6 4.0 0.6 30 6.4 5-8 2.7 0.8 40 8.0 7-4 4.6 2.7 0.2 50 9-4 8.8 6.2 4-3 2.0 60 10.5 9-9 7.4 5.6 3-6 0.7 70 11.2 10.6 8.4 6.7 4-9 2.5 80 II. 6 II .0 9-1 7-7 6.0 3-7 0.6 90 II. 9 II-3 9.6 8.3 6.8 4.8 2.0 100 12. 1 II. 5 10. 0 9.2 7-4 5-7 3-2 R.\TE OF Growth in Volume. Fuel-wood. Lumber. Age. Years. Whole Trees. One-log Two-log Three -log Trees. Board Feet. Trees Board Feet. Trees, Board Feet. Cubic Feet. Cords. 40 6.5 0.073 50 10.6 .119 20.0 29.7 60 13.4 .161 24-3 36 . 9 47.2 70 16.3 .182 28.0 42.9 53.8 80 17-7 .198 30.5 47.1 58-4 90 18.8 .210 32 . 3 50 -3 61 .9 100 19.6 .219 33-8 52.6 64.4 MISCELLANEOUS TABLES. There are included under this head tables to which a forester has frequently occasion to refer and which often are not easily accessible. The forester has constant use for the table of basal areas in determining the cubic contents of logs and trees, and in using accurate methods to determine the cubic contents of stands. The tables for converting the metric into the English measure will be found useful in comparing the volume and the growth and yield of European trees with our own. The table of natural tangents is included to assist in using height measures which show angles in degrees, 429 430 FOREST MENSURATION. AREAS OF CIRCLES. < (5 41 1" 0 w 5 < i| 5 01 <5 3 0 a; < 11 S Si a < 1 .0 . I .2 •3 • 4 1-5 .6 .7 .8 •9 .006 .007 .008 .009 on .012 .014 .016 .018 .020 2.0 . I . 2 •3 •4 2-5 .6 •7 .8 ■9 8.0 . I . 2 •3 ■4 8.5 .6 • 7 .8 ■9 .022 .024 .026 .029 .031 • 034 ■ 037 .040 •043 .046 •349 .358 .367 •376 ■385 •394 •403 •413 .422 •432 30 . 1 ■3 ■4 3-5 .6 ■ 7 .8 •9 .049 .052 .056 • 059 .063 .067 .071 .075 .079 .083 4.0 . I 2 ■4 4-5 .6 ■ 7 .8 ■9 .087 .092 .096 . lOI . 106 no "5 . 120 .126 ■ 131 •545 567- •579 •590 .601 .613 .624 • 636 .648 5-0 . 1 . 2 ■3 •4 5-5 .6 • 7 .8 •9 .136 .142 • 147 • 153 •159 .165 •171 •177 •183 . 190 6.0 . I •3 ■4 6.5 .6 • / .8 •9 . 196 .203 .210 .216 .223 .230 • 238 •245 .252 .260 7.0 . I .2 .3 •4 7-5 .6 .7 .8 •9 .267 • 275 .283 .291 .299 • 307 ■ 315 • 323 • 332 ■ 340 9.0 . I . 2 •3 •4 9-5 .6 ■7 .8 •9 • 442 ■ 452 .462 ■ 472 .482 • 492 • 503 • 513 • 524 • 535 10.0 . I . 3 • 4 10.5 .6 • 7 .8 • 9 1 1 .0 . I ■4 11-5 .6 • 7 .8 •9 .660 .672 .684 696 .709 .721 • 7.U •747 • 759 • 772 12.0 . I ■4 12.5 .6 • / .s • 9 •785 •799 .812 .825 •839 • 852 .866 .880 .894 .908 130 . I . 2 .3 •4 13- 5 .6 • 7 .8 ■ 9 .922 .93^' • 95" •965 ■979 •994 1 .009 I .024 I • 039 I 054 14.0 . I • 3 •4 H-5 .6 • / .8 • 9 1 .069 I . 084 1 . 100 I . 1 1 5 1-131 1.147 1 . 1 63 I. 179 1195 1 . 21 1 150 . I •4 15-5 .6 • 7 .8 •9 1.227 1.244 1 . 260 1 .277 1.294 1.310 1.327 I • 344 1 . ^(^2 I ■ 379 16.0 . I •3 •4 16.5 .6 • 7 .8 •9 1396 1.414 I 431 1.449 1.467 I • 485 I • 503 1.521 I ■ 539 t^558 17.0 . I . 2 •3 • 4 175 .6 ■7 .8 •9 1.576 I ■ 595 1 .614 1.632 1.651 1 .670 1.689 1-709 1.728 1 . 748 18.0 . 1 .3 •4 18. s .6 _ 8 ■9 1.767 1.7S7 1 . 807 1.827 1.847 I . S67 I 887 1.907 1 .928 1.948 MISCELLANEOUS TABLES. •AREAS OF CIRChTSjS— Continued. 431 *j fc. fa fe fa fa fa "►5 6" .25 1" ^ 4" « < Q e "J 0! 2iM « rf *J 1) aw 0! (8 ry e;co Q Q < Q p < Q < 25.0 3 409 26.0 3-687 27.0 3.976 28,0 4-276 29.0 4-587 . 1 3-436 . I 3-715 . 1 4.006 . I 4-307 . 1 4.619 ,2 3-464 . 2 3-744 .2 4-035 . 2 4-337 .2 4.650 •3 3-491 •3 3 773 • 3 4.065 ■3 4.368 -3 4.682 • 4 3-519 -4 3.801 •4 4.095 -4 4-399 -4 4-714 25-5 3-547 26.5 3-830 27-5 4-125 28.5 4 430 29-5 4.746 .6 3-574 .6 3.859 .6 4-155 .6 4.461 .6 4-779 .7 3.602 .7 3.888 -7 4-185 • 7 4-493 -7 4.8H .8 3631 .8 3-917 .8 4-215 .8 4-524 .8 4-844 .9 3 659 .9 3-947 .9 4-246 .9 33-0 4-555 -9 4-876 30.0 4.909 31.0 5-241 32.0 5-585 5-940 340 6 305 350 6.681 36.0 7.069 37-0 7-467 38.0 7.876 39 0 8 . 296 40.0 8.727 41.0 9.168 42.0 9.621 43 0 10.085 44.0 10-559 450 11.045 46.0 1 1 -541 47-0 12.048 48.0 1 2 . 566 49.0 13-095 50.0 13-635 51 .0 14.186 52.0 14-748 53-0 15-321 54-0 15-904 550 16.499 56.0 17.104 57-0 17.721 58.0 18.348 59 0 18.986 60.0 19-635 , 432 FOREST MENSURATION. AREAS OF CIRCLES.* [Metric System.] el lOO lOI I02 103 104 105 106 107 108 109 no III 112 114 116 "7 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 < 0.78540 0.801 19 O.81713 0.83323 0.84949 0.86590 0.88247 0.89920 0.91609 0.93313 0.95033 0.96769 0.98520 1.00288 I .02070 I .03869 1.05683 IO75I3 I 09359 I . I 1220 I. 13097 I . 14990 1 . 16899 I. 18823 1.20763 I .22719 I . 24690 I .26677 I . 28680 I . 30698 1-32732 1-34782 I . 36848 1.38929 I .41026 -t->.tX a -^ E = u Q, .2'o Q J 35 136 137 i3« 139 140 141 142 143 144 145 146 •47 148 149 150 151 152 153 154 155 156 157 1 58 159 160 161 162 163 164 165 166 167 168 169 < 43139 45267 474" 49571 51747 53938 5'''45 .58368 . 60606 .62860 65133 .67416 .69717 •72034 •74366 •76715 .79079 .81458 -83854 .86265 -91135 •93593 . 96067 •98557 2.01062 2 03583 2 . 06 1 20 2.08672 2 . I 1241 2.13825 2. 16424 2 . I 9040 2.21671 2.24318 a c .2'0 Q 170 171 172 173 174 175 176 177 178. 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 31 u c, OJ tU (3 al il 3 . 3 . 0) E 3 . W '-' ■M.S CO h C/3 ^; en '-' V'-M a a 3 . ii s| 3 . fee 3 . Qi'-*^ to S 0'*^ W S wS 0 -S W V Is sg ^^ l| rt^ Eg ta"^ 2u . a^ .Sd £:S .S-o as .SO JiS Q < I I. 341 I Q < Q < Q < 3S0 410 13-2025 440 15-2053 470 1 7 - 3494 381 I I . 4009 411 13.2670 441 15-2745 471 17-4234 382 I I . 4608 412 13-3317 442 15-3439 472 17-4974 383 11.5209 413 13-3965 443 15-4134 473 17-5716 3S4 II. 5812 414 13.4614 444 15-4830 474 1 7 . 6460 385 II .6416 415 13.5265 445 15-5528 475 17-7205 386 II .7021 416 13-5918 446 15.6228 476 17-7952 387 11.7628 417 136572 447 15.6930 477 17-8701 388 11.8237 418 13.7228 448 15-7633 478 17-9451 389 11.8847 419 I3-7S85 449 15-8337 479 18.0203 390 "•9459 420 13-8544 450 15-9043 480 18.0956 391 12.0072 421 13.9205 451 15-9751 481 i8'.i7ii 392 12.0687 422 13.9867 452 1 6 . 0460 482 18.2467 393 12.1304 423 14-0531 453 16. 1171 483 18.3225 394 12. 1922 424 14. II96 454 16.1883 484 18.3984 395 12.2542 425 I4.IS63 455 16.2597 485 18.4745 396 12.3163 426 14-2531 456 16.3313 486 18.5508 397 12.3786 427 14.3201 457 16.40^0 487 18.6272 398 12.4410 428 14-3872 45S 16.4748 488 18.70^8 399 12.5036 429 14-4545 459 16.5468 489 18.7805 400 12.5664 430 14.5220 460 1 6 . 6 1 90 490 18.8574 401 12.6293 431 14.5896 461 16.6914 491 18.9345 402 12 .6923 432 14-6574 462 16.7639 492 19 0117 403 12.7556 433 14-7254 463 16.8365 493 19.0890 404 12.8190 434 14-7934 464 16.9093 494 19.1665 405 12.8825 435 14.8617 465 16.9823 495 19.2442 406 12.9462 436 14.9301 466 17-0554 496 19.3221 407 13.0100 437 14.9987 467 17.1287 497 19.4000 408 13.0741 438 15.0674 468 1 7 . 202 1 498 19.4782 409 131382 439 15-1363 469 17-2757 499 19 5565 MISCELLANEOUS TABLES. 435 TABLES FOR THE CONVERSION OF THE METRIC TO THE ENGLISH SYSTEM. Hectares to Acres. 1= 2.47109 2= 4-94213 3= 7-41327 4= 9-88436 5=12.35545 6= 14.82654 7 = 17-29763 8=19.76872 9=22.23981 Kilos to Pounds. I = 2 . 20462 2= 4.40924 3= 6.61386 4= 8.81848 5= II. 02310 6= 13.22772 7=15-43234 8=17.63696 9=19-84158 Centimeters to Inches. 1= -39370423 2= .78740846 3= 1 . 18111269 4=1-57481692 5=1.96852115 6=2.36222538 7=2.75592961 8=3.14963384 9=3-54333807 Meters to Feet. 1= 3.280869 2= 6.561738 3= 9.842607 4=13-123476 5=16.404345 6=19.685214 7 = 22.966083 8=26. 246952 9=29.527821 Acres to Hectares. 1= .40467 2= .80934 3=1 .21401 4=1.61868 5=2.02335 6 = 2.42802 7 = 2.83269 8 = 3-23736 9=3-64203 Cubic Meters per Hectare .to Cubic Feet per Acre. 2 = 3 = 4 = 5 = 6 = 14-291 28.582 42.873 57 164 71-455 85.746 7=100.037 8 = 114.328 9= 128.619 Kilometers to Miles. I = 2=1 3 = 1 4=2 5 = 3 6 = 3 7=4 8=4 9 = 5 62137676 24275352 86413028 48550704 10688380 72826056 34963732 97 10 I 408 59239084 Cubic Meters to Cubic Feet. 1= 35-315617 2= 70.631234 3=105.946851 4= 141 . 262468 5=176.578085 6 = 211.893702 7 = 247.209319 8 = 282.524936 9=317.840553 43<5 FOREST MENSUR/iTION. TABLE OF NATUR.\L TANGENTS Expressed as Percexts. Degrees. Minates. 0 1 1 2 3 1 4 5 6 7 Percents. o 1-75 3-49 5 24 6.99 8.75 10.51 12.28 5 15 1 89 3 64 5-39 7-14 8.90 10.66 12.43 lO 29 2 04 3 78 5-53 7-29 9.04 10.80 12.57 15 44 2 18 3 93 5.68 7-43 9.19 10.95 12.72 20 58 33 4 07 5-82 7.58 9-34 II . 10 12.87 25 73 47 4 22 5-97 7-72 9.48 11.25 13.02 30 87 2 62 4 37 6.12 7.87 9-63 ■" - 39 13-17 35 I 02 2 76 4 51 6.26 8.02 9.78 "■54 13-31 40 I 16 2 91 4 66 6.41 8.16 9.92 11.69 13-46 45 I 31 3 06 4 80 6.55 8.31 10.07 11.84 13.61 50 I 46 3 20 4 95 6.70 8.46 10.22 II .98 13-76 55 I 60 3 35 5 09 6.85 8.60 10.36 12.13 13-91 Degrees. Minutes. 8 9 10 11 1 13 1 13 1 14 15 Perce ;nts. 0 1405 15S4 17.63 19.44 21.26 23.09 24-93 26.79 5 14 20 15-99 17 78 19.59 21 .41 23.24 25-09 26.95 10 14 35 16. 14 17 93 1974 21.56 23-39 25-24 27.11 15 14 50 16.29 18 08 19.89 21.71 23-55 25.40 27.26 20 14 65 16.44 18 23 20.04 21.86 23-70 25-55 27.42 25 14 80 16.58 18 38 20. 19 22.02 23-85 25-71 27 58 30 14 95 16.73 18 53 20.35 22.17 24.01 25.86 2773 35 15 09 16.88 18 68 20.50 22.32 24. 16 26.02 27.89 40 IS 24 17-03 18 83 20.65 22.47 24.32 26. 17 28.05 45 15 30 17.18 18 99 20.80 22.63 24-47 26.33 28. 20 50 15 54 17-33 19 14 20.95 22.78 24.62 26.48 28.36 55 15 69 17.48 19 29 21 10 22.93 24.78 26.64 28.52 Degi ees. Minutes. 16 ir 1 18 1 19 1 20 1 21 1 22 23 Perec nts. 0 28.67 .30.57 32.49 34 ■ 43 36 . 40 38-39 40.40 42.45 5 28.83 30.73 32-65 34 60 36.56 38.55 40.57 42 62 10 28.99 30.89 32.81 34 76 36.73 38.72 40.74 42 79 15 29- 15 31 05 32.98 34 92 36 - 89 38.89 40.91 42 96 20 29-31 31.21 33- 14 35 08 37.06 39.06 41.08 43 '4 25 29 4'' 31-37 33 • 30 35 25 37-22 39-22 41-25 43 31 30 29.62 31-53 33 46 35 41 37 ■ 39 39 ■ 39 41.42 43 48 35 29.78 31-69 33 62 35 5« 37 • 55 39 . 56 41 -.59 43 6s 40 29.94 31-85 33-78 35 74 37-72 39.73 41.76 43 83 45 30 . 10 32.01 33 - 95 35 90 37 ■ 89 .39-90 4 1 - 93 44 00 50 30 . 26 32.17 34 • 1 1 36 07 -J8.0S 40.06 42. 10 44 >7 55 30-41 32 • 33 34 • 27 36.23 .38.22 40.23 42.28 44 35 MISCELLANEOUS T/1BLES. 437 TABLE OF NATURAL TANGENTS— (Con/mMec/)- Degrees. Minutes. 5 lO 15 20 25 30 35 40 45 50 55 24 25 26 27 28 29 30 Percents. 44 52 44 70 44 «7 45 05 45 22 45 40 45 57 45 75 45 9-^ 46 10 46 28 46 45 46.63 46.81 46.99 47.16 47-34 47-52 47-70 47.88 48.06 48.23 48.41 48-59 48.77 48.95 49-13 49-31 49-50 49.68 49.86 50.04 50.22 50 . 40 50.59 50-77 50 95 53 17 55 43 57. 51 14 53 2,^ 55 62 57. 51 32 53 54 55 81 58. 51 50 53 73 56 00 58. 51 69 53 92 56 19 58. 51 87 54 1 1 56 39 58. 52 06 54 30 56 58 58. 52 24 54 48 56 77 59. 52 43 54 67 56 96 59- 52 61 54 86 57 15 59. 52 80 55 05 57 35 59. 52.98 55.24 57-54 59 Minutes. 5 10 15 20 25 30 35 40 45 50 55 Degrees. 31 32 33 34 35 36 37 Percents. 60.09 60.28 60.48 60.68 60.88 61 .08 61.28 61.48 61.68 61.88 62.08 62.28 62.49 62 .69 62.89 63. 10 63.30 63.50 63.71 63.91 64. 12 64-32 64-53 64-73 64.94 65.15 65.36 65.56 65.77 65.98 66. 19 66.40 66.61 66.82 67.03 67.24 67 45 67 66 67 87 68 09 68 30 68 SI 68 73 68 94 69 16 69 37 69 59 69 80 70.24 70.46 70.67 70.89 71. II 71.33 71.55 71-77 71-99 72.21 72.43 72.65 72.88 73.10 73-32 73.55 73.77 74.00 74-22 74-45 74.67 74-90 75-13 75.36 75.58 75.81 76.04 76.27 76.50 76.73 76.96 77.20 77-43 77.66 Minutes. Degrees. 38 39 40 41 42 43 Percents. O 5 10 40 45 50 78.13 78.36 78.60 78.83 79.07 79.31 79-54 79-78 80.02 80 . 26 80.50 80.74 80 . 98 81.22 81.46 81.70 81-95 82.19 82.43 82.68 82.92 83.17 83.42 83.66 •\V9i 84. 16 84.41 84.66 84.91 85.16 85.41 85.66 85.91 86.17 86.42 86.67 86 93 87 18 87 44 87 70 87 96 88 21 88 47 88 73 88 99 89 25 89 52- 89 78 90.04 90.30 90.57 90.83 91 . 10 91.37 91.63 91.90 92.17 92.44 92.71 92.98 93 25 96 93 52 96 93 80 97 94 07 97 94 35 97 94 62 97 94 90 98 95 17 98 95 45 98 95 73 99 96 01 99 96 29 99 INDEX. PAGES Abney Hand Level 122, 145, 146 Accretion (see Growth) 254 Accuracy in Measurements 79 Adirondack Standard 9, 54, 56 Age, below Stump 244 Classes 178 Economic 252 Estimating, Methods of 246 External Signs of 247 Influence on Form Factor 178 Age of Stands 248 Determined by Arithmetic Method 250 " " Basal Area Method 252 " " Smalian's Method 251 Age of Suppressed Trees 249, 252 Tropical Trees 247 Age of Trees, Determination of , 244 Ake Log Rule 24, 52 Alabama, Log Rules in 50 Allowance Plank 32 Analysis, Tree 256, 264 Partial Tree or Section 257 Section 257 Stem (see Tree Analysis). Stump 257 Angle Mirror 212 Adjustable 213 Annual Rings 244 Counting of 245 Measurement of 258, 260, 261, 262, 277 Arbitrary Group Method 229 439 44° INDEX. PAGES Area Growth , 254, 282, 303 Areas of Circles 90 , 430 Cross-sections 9c, 258 Arithmetic Average Tree 225 Arkansas, Log Rules in 21, 38, 50, 359 Average Age, Detennination of 248 Average Diameter 225, 259, 271 Average Radius 258 Average Tree 15S, 160, 193, 225, 241, 249, 270 Ballon Log Rule 24, 51 Balsam Fir 35, 276 Bangor Log Rule 24, 35 Bark, Measurement of 61, 78, 153 Bark Blazer 216 Basal Area 90 Table of 430, 432 Multiple Table of 376 Baughman's Log Rules 24, 48 Baur, Franz, Investigations by 8, 103, 178, 181, 319, 325, 415 Bavarian Tables 181 Baxter Log Rule 24, 48 Beech 169, 188 Beech, Form Factors of 413,415 Yield Tables for 418 Bchm's Tables 1 80 Big Sandy Cube Rule 57 Birch 169, 268 Block's Method 240 Blodgett Log Rule 55. 65 Board Foot 9, 11 Board Measure 9, 11 Applied to Round Logs 12 Ratio to Cord Measure no " " Cubic Measure iio " " Standard Measure 55' 56, 57, 59 Value of 14 Bosc's Height Measure : 148 Boynton Log Rule 24, 51 Branches, Measurement of 115 Brandis Height Measure 122,141 Breast-height Diameter 112 Breast-height Form Factor 174 Breymann's Formula 97 British Columbia Log Rule 2 1 , 24, 46 INDEX. 441 PAGES Bmnton's Compass 214 Burt's Quarter Girth Method 06 CaUfomia, Log Rules in 4 r ^go CaHpers 65, 81, 102 European 82 For Measuring Growth 260 Use of 77, 78, 207 Canadian Log Rules 21, 24, 47 Canadian Standard Rules rq Carey Log Rule 24, 51, 61 Center-rot 55 Champlain Log Rule 24 27 ^o Chapin Log Rule 24, 50 Chestnut 162, 173, 275, 312, 407, 426, 427 Growth of 297, 426, 427 Volume Table for ^oy Christen Height Measure 122, 131 Circle Method of Estimating j q , Circles, Areas of 5,0, 376, 430 Circumference, Measurement of 77- 90 Clark's Log Rule 20, 35 Clear Length 116 Clearings, Growth on 269 Climate, Influence on Form of Trees 178 Combined Doyle and Scribner Log Rule 50 Cone 85, 87, 92, 93, 94, 95, 114, 156, 183 Connecticut River Log Rule 38 Constantine Log Rule 24, 26, 28, 47 Conversion of Volume Tables, Cubic to Board Measure 16S Converting Tables, Metric to English Measure 435 Cook Log Rule 49 Cord Foot I o I Cord Measure 9.76, loi Ratio to Board Measure 109 " " Cubic Measure 103 " " Standard Measure icg Cord-wood, Estimating 215, 217, 223, 224, 243 Measurement of 75, loi, 102 Seasoning of 105 Stacking of 105 Table for Measuring 400 Volume Tables for ^ 165, 173 Yield Tables for 343 Crook in Logs 20, 35, 73 442 INDEX. PAGES Crooked River Log Rule 49 Cross-sections, Age at 244 Area of 90 Diameter of 259 Growth of 258,261 J Cross Staff-head 211 Crown Description 119 Crown Measurement 116, 118 Cruising, Timber 191 Cube Rule 57 Cubic Contents of Logs 76, 85 Cubic Measure 9i 76 Use in America 76 Contents of Logs in 76, 77 " " Standing Trees in 155 Ratio to Board Measure 110 '* "a Cord Measure 103 Cull 75 Cull Tables 71 Culling Logs, Methods of 66 Cumberland River Log Rule 24, 26, 49 Current Annual Growth 254 Curve Drawing, 43, 162, 163, 164, 167, 180, 220, 224, 232, 266, 273, 274, 287, 292, 294, 325, 326, 331, 343, 349 Cylinder 86 Cylindrical Foot 102 Cypress 65 Damage to Forests, Estimate of 5 Daniels' Log Rules 20,24,27,32 Death of Young Trees by Lumbering 336 Death of Young Trees by Shading 335 Decimal Log Rule 42 Defects in Logs 14, 49, 65, 69, 75 Defects in Trees 207 Dendrometers 138, 150 Density, Effect on Form 165, 177 " " Growth 268,284 Denzin's Method 155 Derby Log Rule 24, 51 Description, Condition of Tree 119 Crown 119 Forest 206, 324, 337, 342, 345. 348 Stem iig Tree 118, 263 INDEX. 443 PAGES Description Plots^ 348 Diagrams Used in Log Rules 12, 41, 42, 45, 48 Diagrams of Trees 118, 119 Diameter Groups 229, 236, 237, 239, 240 Diameter Growth 254 Computation of 266 For Short Periods 277 In Even-aged Stands 268, 272, 273, 274 In Uneven-aged Stands 275, 276, 278 Investigations of 265 Maximum 272 Measurement of 258, 261, 262 Minimum 273 Of Trees of Different Diameters 278 Problems of 268 Purpose of Studying 265 Diameter, Influence on Form Factors 179 Diameter Limit 334, 337 Diameter Measurements 61, 62, 77, iii, 112, 258 Diameter Tape 80 Dimick's Standard Rule 54 Discounting for Defects in Logs 65 Dominant Trees, Growth of 271 Doyle Log Rule 21, 23, 24, 35, 38, 65, 153, 154 Draudt Method 233 Drew Log Rule 21, 24, 35, 46 Dusenberry Log Rule 24, 48 Dyewood 17 Economic Age 252 Edging, Waste by 29, 32, 38, 39 Ellipse, Area of 9^ Empirical Yield Tables 341, 343 Equivalents, Board Feet in a Cord 110 ." " "" Cubic Foot no " ""Standard.. 54,55.56,57.58 Cubic " ""Cord 103 Standards in a Cord no Erickson's Method of Estimating 198 Estimating Diameters 152 Estimating Heights 120 Estimating Timber 152. 191 By the Eye .► 152, 191 By Inspecting Each Tree 194 By Volume Tables 219 444 INDEX. PAGES Estimating Timber, Erickson's Method of 198 In 40-rod Strips 198 In Small Squares 197 Method Used in Michigan for 196 Stand Tables Used in 200 Strip Surveys Used in 205 European Methods of Scaling Logs 93 European Volume Tables 166 European Yield Tables 317 Evansville Log Rule 49 Even-aged Stands, Age of 249 Growth in Diameter 268, 272, 273, 274 " Height 287 Sample Plots in 345 Yield Tables for 315 Excelsior-wood 9 Exponent of Form 183 Extract Wood 109 Fabian Log Rule 43 Faustmann Height Measure 122, 123 Favorite Rule 24, 48 Felled Trees, Contents of 1 1 1 Measurement of 111,224 Field Records 63, 119, 208, 219, 221, 222, 223, 224, 264 Fifth Girth Method 22,95 Financial Maturity 310 Financial Returns of Forestry 2 Finch and Apgar Log Rule 24, 52 Fir 180, 181 Fire, Growth after 269 Fire-wood, Scaling of 10 1 Five-line Rule 65 Flats, Scaling of 75 Florida, Log Rules in 21, 38, 360 Forest Description 206, 265 Forest Form Factor 241, 321 Forest Management 314, 322, 335 Forest Maps 1 99. 206 Forest Mensuration, Definition of t Graphic Methods in 349 Importance of 2 Literature of 7, 368 Relation to Forest Management i Relation to Silviculture I INDEX. 445 PAGES Forest Regions 318 Forest Types 192, 343 86 74 42 74 79 74 76 77 78 75 82 86 88 75 Form Exponents 182, Form Factors 155, 168, Absolute 174, 182, 186, 187, Breast-height Construction of Tables of Definition of False Influences Affecting Value of Local or General Merchantable Normal 174, Obtained from Form Exponent Relation of Form Quotient to Stem Tables of 410, 411, 412, 413, 414, 415 Timber Tree True Use of Used in Study of A'oluine Growth Variations of Form Height Form Quotient Form of Cord-wood Sticks Form of Logs Form of Trees 155, Formula for Cubing Logs 91, 93, 94, 95, 96, Formulae for Cubing Square Timber 99, Formulae for Geometric Bodies 87 Forty-five Log Rule 24,51 France, Scaling in 96 Fricke's Height Measure 148 Friedrich's Dendrometer 150 General Growth Studies 265 General Volume Tables 158 General Yield Tables 316 Geometric Av^erage Age 251 Geometric Average Tree 225 Geometric Height Measures .^ 122 Georgia, Log Rules in 51 Germany, Scaling in 92 Girth Measurements 77 446 INDEX. PAGBS Glens Falls Standard Rule 54 Goulier Height Measure 122, 144 Graded Log Rules 21 Grading of Lumber i Graphic Interpolation, Described 349 Gridironing Method of Strip Surveys 204 Groups, Diameter 229, 236, 237, 239, 240 Growth, Defined 254 After Lumbering 338 Current Annual 254 In Area 254, 282 In Diameter 254 In Height 254, 283, 284, 289 In Volume 254, 290 In Weight 254 Mean Annual 255, 276 Mean and Current Annual Compared 256 Measurement of Diameter 258, 260, 261, 262 Of Stands 309 Of a Whole Forest ^ 313 Of Stands after Thinning 274 Of Stands for Short Periods 309 On Clearings 327 Percent 255, 301, 304, 307 Periodic 255 Periodic Annual 255 Price 254 Quality 254 Stimulated 274, 280 Total • • 25s Guttcnberg Dcndrometer 1 50 Hand Level, Abney 145. 146 Hanna Log Rule 24, 38, 45 Hardwoods, Northern 35 Southern i6q Volume Table for 165 Harmonized Curves 164. 167, 354 Hartig's Method 240 Havlick's Height Measure 148 Heading 9, 10 1 Heart-rot 67 Height, Average of Stands 287 Index of Site 284, 320, 322, 326 Height Growth 254, 283 INDEX. 447 PAGES Height Growth, Computation of 283 In E\^en-aged Stands 287 Maximum and Average 288, 289 Purpose of Studying 283 Of Trees of Different Diameter 288 Height Measures 122 Choice of 149 Height of Trees, Measurement of 120, 148 Hemlock 276, 283 Herring Log Rule 24, 49 Heyer's Height Measure 148 Hickory 76 Holland Log Rule 24 Hoop-poles 9 Hoppus' Rule 99 Hossfeldt's Method 94, 155 Huber's Method of Cubing Logs 93, 115 Humphrey Log Rule 24, 48 Hypsometers 122 Hyslop's Log Rule 42 Idaho, Log Rules in 21, 41, 50, 360 lUinois, Log Rules in 49, 50, 51 Increment (see Growth) 254 Borer 246, 300, 305 Calipers 260 India, Scaling in 99 Indian Literature 8 Indian Yield Tables 338 Indiana, Log Rules in 48, 49, 50 Inscribed Square Rule 100, 396 Instrument-makers 129, 131, 136, 144, 148, 150, 151, 212, 214 International Log Rule 24, 35, 36 Iowa, Log Rules in 5°. 360 Isolation Strips 344 Jack Pine 269 Kentucky, Log Rules in 49. 5° Klaussner Height Measure 122, 133, 134, 149. 151 Knots, Interference in Measuring Logs 7^ Konig, Studies in Cord-wood ^04 Lagging, Scaling of 75 Larch 1 80 448 INDEX. PAGES Lath 1 6 Legislation regarding Log Rules 21, 359 Lehigh Log Rule 49 Length Measurements 62, 84, iii, 113 Limb-wood , Volume of 115 Literature on Forest Mensuration 7, 368 Loblolly Pine 35, 169, 269, 322, 425 Local Volume Tables 181 Local Yield Tables 317 Location of Plots in Estimating 216 Location pf Plots for Yield Tables 327 Location of Strip Surveys 203 Lodge-pole Pine 269 Log Lengths 112 Log Rules 12 Comparison of 24, 26 Graded 21 History of 22 Local 18,21 Mathematics of 27, 35 Number of 14 Principles of Constructing 12 Statute 21 Universal 17, 18, 20 Used in Estimating 152 Log Scales (see Log Rules). Log Tables (see Log Rules) . Longleaf Pine 169 Louisiana, Log Rules in 21, 38, 50, 361 Maine, Log Rules in 43. 5*1 361 Maine Log Rule 21, 24, 35, 42, 64 Many-aged Stands 334 Growth in 275 Permanent Sample Plots in 346 Yield Tables for 316, 334 Maple 169, 284 Market Boards 23 Marking Logs 63 Massachusetts, Log Rules in 45, 49, 51, 52, 362 Maximum Growth, Studies of 272 Used in Yield Tables 329 Mayer's TTcight Measure 148 Mean Annua! Diameter Growth 276 Mean Annual Growth 355 I INDEX. 449 PAGES Mean Annual Growth of a Forest 313 of Stands 312 Used in Yield Tables 343 Mean Sample- tree Method 224 Merchantable Length 116, 164 Metric System 9 Converting Factors 435 Metzger's Method 242 Michigan, Log Rules in 48, 49, 50 Methods of Estimating in 196, 198 Mill-scale 13,29, 169 Mine Props 9, 75 Minnesota, Legislation regarding Log Rules 21, 41, 362 Mississippi, Log Rules in 50 Missouri, Log Rules in 48, 50 Mixed Stands, Yield Tables for 330, 331 Model Acre 337 Montana, Log Rules in 50, 52 Moore and Beeman Log Rule 38 Miiller, Udo, Investigations of 8, 104, 122, 184 Natural Pruning 116 Natural Tangents, Table of 436 Neiloid 86, 89, 95, 183 New Brunswick Log Rule 21, 24, 47 New Hampshire Log Rule 21, 24, 35, 55, 61, 64, 363 New Jersey, Log Rules in 49, 50 Newton's Formula for Cubing Logs 95 New York, Log Rules in 45, 48, 50, 51, 54, 57 Nineteen-inch Standard 54, 398 Noble and Cooley Log Rule 49 Normal Crook 35 Normal Form Factors 1 74 Normal Stands 3^8.319.323. 326 Normal Trees 160 Normal Yield Tables 318 Construction of 325 Contents of '321 Data for 322, 323 For Thinned Stands 328 * ' Un thinned Stands 327 ** Mixed Forests 331 In this Country 326 Uses of 321 North Carolina, Log Rules in 48, 49 450 INDEX. PAGBS Northwestern Log Rule 24, 50 Nossek's Method of Form Factors 186 Novelty Wood 9 Niimber of Log Rules 14 Oak 76, 283, 332, 333, 334 Form Factors of 411 Ocular Estimating 152, 191 Oetzel's Formulae 98 Ohio, Log Rules in 48, 49, 50 Omnimeter 148 Orange River Log Rule 24, 50 Oregon, Legislation regarding Log Rules 41 , 364 Paraboloid 85, 88, 91, 93, 94, 156, 183 Parameters 183 Parson's Log Rule 24, 26, 51,61 Partial Tree Analysis 257 Partridge Log Rule 24, 51 Pecky Cypress 65 Peltzmann's Dendrometer 150 Pennsylvania, Log Rules in 45, 48, 49, 50, 51, 52 Percents of Angles 436 Periodic Annual Growth 255 Periodic Growth 255, 277, 278 Periodic Measurements of Plots 322 Permanent Sample Plots 344, 345 In Europe 344 Philippine Islands 9 Philipp's Method of Form Factors 185 Piles 9. 173 Pinchot, "White Pine Study 316 Pitch Pine ^12>> 269, 283 Growth of 428 Volume Tables for 408 Plank Measure •' 1 1 Plot Sur\'eys 202, 209 Calipcring on 216 Instruments for Laying Out 210 Irregular 214 Necessary Precision in Laying Off 214 Plotting on Cross-section Paper 350 Pocket Compass 214 Poles 9. 173 Growth of 298 INDEX. 451 PAGBS Poplar 268 Portland Scale 49 Possible Merchantable Length 117 Posts 75, 173 Prediction of Profits of Forestry 2 Volume Growth 299 Yield 335 Pressler's Increment Borer 246, 255, 30®, 305 Method (Contents Standing Trees) 156 " of Determining Volume Growth 299 " " Estimating Growth of Standing Trees 304 ' * " Form Factors 186 Telescope 157 Price Growth 254 Profits of Forestry, Prediction of 2 Pruning, Natural 116 Pulp-wood 9, 16,65, ioi> 109 Pure Stands 327, 332 Location of Plots in 216, 327 Purpose of Yield Tables 321, 335 Quality Growth 254 Quality of Site 284 Quarter Girth Method 99 Quebec Log Rule 21, 24, 47 Radius, Average 258 Railroad Ties 9, 75, 171, 172, 173 Rectangular Coordinates 350 Red Birch 1 70 Red Cedar 275 Growth of 427 Red Fir 269 Red Maple 310 Red Oak 284, 312 Growth of 428 Volume Table for 409 Red Pine 269 Relative Diameter 305 Reproduction Plots 346 Right Angles, Obtained by Instruments a 10 Tape 214 Rise or Taper 64 River Logs 26, 49 Rock Oak 312 452 INDEX. PAGES Root Flare 115 Roots, Volume of 115 Ropp Rule 24, 51 Rough Estimating 120, 190 Rough Sample Plots 192 Rough Strips 193 Roughage 32 Rudorf s Formula 97 Rueprecht's Height Measure 148 Saco River Log Rule 24, 51 Sal 340 Sample Areas 202 Sample Plots 202, 209 Estimate by 209, 217 In Empirical Yield Tables 342 ' ' Yield Tables 323 Location of 216 Marking Boundaries of 215 Permanent 344 Selection for Yield Tables 323 Shape and Size 215 Used in Studying Diameter Growth 270, 271 " Making Yield Tables 323, 324 Sample Trees, Permanent 344 Sanlaville's Dendrometer 151 Sap, Rotten, Discount for 73 Sap-wood , Measurement of 1 1 1 Saranac River Standard Rule 59 Scale Paddle 62 Scale Stick 58, 60 Scaling 60 In Europe 92,93 Logs, Methods of 60 Rules, on Forest Reserves 74 Scantling Measure 11 Scarf, Errors due to 113 Schaal's Method of Form Factors 1S7 Schenck, Method of Cubing Trees 153 Schneider's Method of Estimating Growth of Standing Trees 307 Schuberg, Form Factor Tables 181 Schwappach Normal Yield Tables 317,417,418,419, 420 Scotch Pine iSo, 181, 188, 318, 324 Forni Factors of 410, 415 Vicld Tables for 420 INDEX. 453 PAGES Scratchers 216 Scribner Decimal Rule 42 Scribner Log Rule 21, 24, 26, 38, 41, 75 Seamy Logs 73 Seasoning 105 Second Growth, Estimate of 201 , 209 Value of 5 Yield Tables 342 Section Analysis 257 Sectional Areas 90 Selection System 334 Senkendorf , Cord-wood Studies 103 Seventeen-inch Rule 100 Shake, Discount for 70 In Logs 67 Shakes, Scaling of 75 Shingles 16, 75, loi Shortleaf Pine 269 Shrinkage 14, 35. loS Simony's Formulae 97 Single Tree Plots 347 Site, Influence on Form of Trees 178 Sketching of Trees . 119 Skidways, Scaling of 64, 75 Slabs, Taken off for Defects 70, 71 Waste by 29, 32, 38, 39 Smalian's Formula 114 " Method of Determining the Age of Stands 251 " Cubing Logs 91 , 96 Solid Contents of a Cord 103 South Dakota, Log Rules in 50 South, Scaling in 66 Spaulding Log Rule 21,24,45 Splits, Discounts for 70 Spool-wood 9 Sprout Stands 268, 269 Spruce 35. 180, 188, 269, 276, 283, 310, 317 Growth of 282 Volume Table for 406, 407 Yield Table for 417,422,423, 424 Square Measure of Boards 11 Square Plots 193. 209 Square Timber «- 9. 75- 1^> 99. 394. 39^ Square of Three-fourths Log Rule 23, 24, 49 Square of Two-thiirds Log Rule 24, 48 454 INDEX. PAGBa Stacked Cubic Foot 102 Staff Compass 210, 211 Staff -head 211, 212 Stand Tables in Estimating 200 Standard Log 9. 53. 54, 55 Standard Measure 9. 53> 76 Ratio to Board Measure 54, 55, 56, 57 " " Cord Measure log Standing Trees, Contents of 152 Estimate of Contents of 152, 155, 156 Stands, Accurate Determination of Volume of 190, 224 Contents of 190 Increment of 309 Starke's Dendrometer 150 Statistical Methods in Forest Mensuration 349 Statute Log Rules. . 21 Stem Analyses (see Tree Analyses). Stilhvell Log Rule 24, 51 Stimulated Growth 274, 280 Stotzer's Height Measure 148 Strip Surveys 202 Advantage cf 209 Calipering on 206 Distribution of 203 In Yield Tables 335 Number Used in Estimating 208 Strips in Estimating 198, 199, 202, 209 Strzelecki's Method of Form Factors 185 Study of Growth, Importance of 2 Stump , Diameter Measurements 112, 113 Height Measurements 113, 257 Volume of 115 Stump Analysis 257 St. Croix Log Rule 38 St. Louis Hardwood Log Rule 49 Superficial Measure 11 Surface Foot loi Surface Waste 29, 32, 38 Tally Board 20S Tally Record 208, 2 1 9 Tally Register 1 96 Tamarack 276 Taper 36, 64 Taper, Influence on Contents of Logs 15 INDEX. 45 5 FIGBS Tapes ' • V9.8o.84 Teak ^40 Tennessee, Log Rules in 45. 48. 49. 5° Tennessee River Rule 49 Test Trees ^^4. 232. 233. 239 In Yield Tables 328 Number of 227. 230 Selection of 226 Texas, Log Rules in 48, 49. 5© Thinnings. . ; 4 Effect on Growth. . . 274, 280 Before Measurement 328 Third and Fifth Rule 49 Thurber Log Rule 3 Tiemann's Height Measure ^48 Timber Cruising ^9^ Estimating ^9^ Ton, a Unit of Measure ^° Top Measurements Total Growth ^55 Total Height of Tree "3 Total Length ' "^ ' Tree Analysis ^5 Preparation of a Tree for 257 Selection of Trees for 257 Tree Class 118.160,163,164.177.223. 275 Tree Description 118, i59- 263 Tree Form Factor ^^5 ^ o •!_ 216 Tree Scnbe Trigonometric Height Measure ^22 Tropical Trees. Age of ^47 Growth of 348 Yield Tables for 338 Trumbach's Height Measure ^^8 Twenty-four Inch Standard Rule 59 Twentv-one Inch Standard Rule 59 Twentv-two Inch Standard Rule 57 Two-thirds Rule, Square Timber 99. 394 Uneven-aged Stands. Age of 1" * ' ' V !!« Diameter Growth m 275. 276. 278 8 Units of Measurement • Universal Log Rule. Construction of v. Need of ^7 Selection of '° 456 INDEX. TAGES Universal Rule (Daniels') 24, 32, 35 Urich Method ^^36, 324, 344 Used Length 117 U. S. Forest Service 22, 91, 169, 202, 208, 345 Valuation Area 202 Valuation of Land 2 Valuation of Second Growth 335 Valuation Survey 202 Vannoy Log Rule 38 Vermont, Log Rules in 21,48, 51,364 Vermont Log Rule 21, 364 Virginia, Log Rules in 45. 48, 49. 5° Virginia Pine 269 Volume-curve Method 232 Volume Growth 254, 290 Coinputation of 290 Determined by Form Factor Method 300 " Graphic Method 293 " " Pressler's Method 299 For Short Periods 298 Of Individual Trees 290 ' ' Standing Trees 304, 307 Prediction of 300 Volume, Index of Site 322 Volume Measurements 1 1 1 Volume of Felled Trees 1 1 1 Volume of Logs, Cubic 76, 99 Volume of Trees. Variation in 158 Volume of Trees on Valuation Areas 219 Volume Tables " . ^ 5^ Construction of 159 Data for 1 59 Definition of 158 For Chestnut 407 • ' Pitch Pine 408 • ' Red Oak 409 " Spruce 400. 407 " White Pine 403. 405 Graded 169 In Europe 1 66 " Yield Tables 335 Local or General 158, 162 Trees Grouped by Diameters. 159 «♦ " " Diameter and Number of Logs. .. 163 INDEX. 457 PAGES Volume Tables, Trees Grouped by Diameter and Merchantable Length 164 Tree Class 164 Height 166 Wagon Stock n Walter's Formula 08 Warner Log Rule 24, 51 Washington, Log Rules in 21,46, 365 Waste in Sawing Logs 12, 13, 38 Weise Height Measure 122, 129 Weise Yield Tables 318 West Virginia, Log Rules in 21, 48, 49, 366 Wheel, Measuring 62 Wheeler Rule 24 White Cedar 269 White Log Rule 24, 52 White Pine 35,269,276,283,284,317,327,332,333, 334 White Pine, Rule for Estimating 154 Volume Table for 403, 405 Yield Table for 421 White Oak 169 Wilcox Log Rule 24, 51 Wilson Log Rule 24,51 Wimminaur's Dendrometer 1 50 Winder Log Rule 48 Winkler Dendrometer 138, 150 Winkler Height Measure 122, 136, 137 Wisconsin, Log Rules in 21,41, 50, 366 Working Plans 310 Xylometer 115 Yellow Birch 169 Graded Volume Tables for 171 Yellow Pine 269 Yellow Poplar 169 Yield Tables 201, 315 Empirical 316, 341, 343 For Beech 418 " Even-aged Stands 316 " Many-aged Stands 335, 337, 339 " Mixed Forests 330, 331 ' ' Scotch Pine 420 " Spruce 417, 422, 433, 434 458 INDEX. PAGES Yield Tables for White Pine 421 Future 315 Local or General 316 Normal or Index 316, 317 Present 315 Younglove Log Rule 26, 52 Zihlwald Yield Tables 318 Zon, R. , Cord-wood Studies 106