.-ORES,iiii| MENSURATIOl HERMAN H. CHAPMAN I .\ .o^ GopightN®_ CORfRIGHT DEPOSrr. FOREST MENSURATION BY HERMAN HAUPT CHAPMAN, M.F. Harriman Professor of Forest Management, Yale University NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL, Limited 1921 5J! s5\ Copyright, 1921 By HERMAN HAUPT CHAPMAN OCT -7 7 PRESS or BRAUNWORTH & CO. BOOK MANUFACTURERS BROOKLYN, N. Y. g)CI.A624703 i X TO IN RECOGNITION OF HIS LIFELONG SERVICE IN PROMOTING FOREST EDUCATION AND IN DEVELOPING A HIGH STANDARD OF PROFESSIONAL FORESTRY IN AMERICA PREFACE This text is intended as a thorough discussion of the measurement of the volume of felled timber, in the form of logs or other products; of the measurement of the volume of standing timber; and of the growth of trees, stands of timber and forests. It is designed for the information of students of forestry, owners or purchasers of timber- lands, and timber operators. The subject matter so treated is funda- mental to the purchase or exchange of forest property or of timber stumpage, the valuation of damages, the planning of logging operations, and the management of forest lands for the production of timber by growth. The publication is intended as the successor of Graves' Forest Men- suration, and was undertaken at the request of the author, H. S. Graves, whose original text, Forest Mensuration, appearing in 1906, set a stand- ard for text-books in forestry and has been of inestimable value to foresters and timberland owners in America. The present text is not a revision of the former publication, but an entirely new presentation, both as to arrangement, methods of treatment and much of the subject matter. The author has in some instances quoted or borrowed portions of the former text and is indebted to it for many of the more fundamental conceptions and descriptions of processes used in Forest Mensuration. It is the purpose of Part I to bring out the relations of the cubic contents of logs, and their measurement, to the contents as expressed in terms of products, and to encourage the substitution of sound units of measure and methods of measurement for defective standards and methods as far as possible. The application of these standards to the measurement of standing timber is the subject of Part II. This part presents a complete analysis of the art of timber estimating as practiced in every timber region of the United States, the methods employed by skilled timber cruisers, the principles upon which these methods are based, the relative accuracy of the various systems used, the factors and averages which enter into the use of these methods, and the application of these principles and factors in practical work and in the training of men for timber cruising. vi PREFACE The object sought in Part III is to systematize the principles and problems confronting the student in the, study of tree growtlt, and to so correlate these problems that he is not diverted from the ultimate object of such/< studies, which is the determination of yields per acre, by details of methods having to do with the measurement of growth of individual trees. Research and field studies of growth per acre are rendered dif- ficult not only by the lack of an accepted unit of measure, but by the great variations in the character of the stands comprising our virgin and second growth forests, yet it is just these stands, and not planta- tions, whose growth will determine our yields of timber for the next four or five decades. Attention is called to the substitution of the International |-inch kerf log rule in the present volume, for the |-inch kerf rule in Graves' Mensuration. It is hoped that this rule will be accepted as a scientific standard for board feet since it is adapted to conditions of second growth and is conservative in values. Instead of attempting to include tables of volume or yield, a table of references is printed to such tables as are of standard quality and which are in possession of the U. S. Forest Service, Washington, D. C. The author wishes to acknowledge the many helpful criticisms received from foresters in the preparation of this book. TABLE OF CONTENTS Part I THE MEASUREMENT OF FELLED TIMBER AND ITS PRODUCTS CHAPTER I INTRODUCTION TO FOREST MENSURATION PAGE 1. Definition and Purpose 1 2. Relation between Lumbering and Timber Estimating 2 3. Relation between Forestry and Growth Measurements 2 4. Relation between Forest Mensuration, Stumpage Values and the Valuation of Forest Property 3 5. Relation of Mensuration to other Forestry Subjects 3 6. Absolute versus Relative Accuracy in Mensuration 3 7. Forest Survey 5 CHAPTER II SYSTEMS AND UNITS OF MEASUREMENT 8. Systems of Measurement used in Forest Mensuration 6 9. Piece Measure 7 10. Cord Measure 7 11. Cubic Measure 8 12. Board Measure 8 13. Log Rules 8 14. Measurement of Standing Timber Postponed till after Manufacture 8 15. Measurement of Standing Timber Postponed till after Logging 9 16. Measurement of Standing Timber in 'the Tree 9 17. Need of Standardization for both Commercial and Scientific Measurements. 10 18. Forms of Products into which the Contents of Trees are Converted 11 19. The Factor of Waste in Manufacture 13 20. Actual versus Superficial Contents of Sawed Lumber 13 21. Round-edged Lumber 14 22. Products made from Bolts and Billets 14 CHAPTER III THE MEASUREMENT OF LOGS. CUBIC CONTENTS 23. Total versus Merchantable Contents 16 24. Log Lengths 16 25. Diameters and Areas of Cross Sections 17 vii viii TABLE OF CONTENTS PAGE 26. The Form of Logs 18 27. Formulse for Solid Contents of Logs 19 28. Relative Accuracy of the Smalian and Huber Formulse 21 29. The Technique of Measuring Logs 22 30. Girth as a Substitute for Diameter in Log Measurements 24 CHAPTER IV LOG RULES BASED ON CUBIC CONTENTS 31. Comparison of Log Rules Based on Diameter at Middle and at Small End of Log 26 32. Log Rules in Use, Based on Cubic Volume 28 33. The Blodgett or New Hampshire Cubic Foot 30 34. Use of Cubic Foot in Log Scaling 31 35. Log Rules for Cubic Contents of Squared Timbers 33 36. Log Rules Expressed in Board-feet but Based Directly upon Cubic Contents 34 37. Formula for Board-foot Rules Based on Cubic Contents 35 38. Comparison of Scaled Cubic Contents by Different Log Rules 36 39. Relation between Cubic Measure and True Board-foot Log Rules 39 CHAPTER V THE MEASUREMENT OF LOGS. BOARD-FOOT CONTENTS 40. Necessity for Board-foot Log Rules 40 41. Relation of Diameter of Log to per cent of Utilization in Sawed Lumber ... 40 42. Errors in Use of Cubic Rules for Board-feet 42 43. Taper as a Factor in Limiting the Scaling Length of Logs for Board-foot Contents 43 44. The Introduction of Taper into Log Rules 44 45. Middle Diameter as a Basis for Board-foot Contents 46 46. Definition and Basis of Over-run 46 47. Influences Affecting Over-run. The Log Rule Itself 47 48. Influences Affecting Over-run. Methods of Manufacture 47 49. Standardization of Variables in Construction of a Log Rule 49 50. The Need for More Accurate Log Rules 50 51. The Waste from Slabs and Edgings 50 62. The Waste from Crook or Sweep 51 53. The Waste from Saw Kerf 53 54. Total Per Cent of Waste in a Log 55 CHAPTER VI THE CONSTRUCTION OF LOG RULES FOR BOARD-FOOT CONTENTS 55. Methods Used in Constructing Log Rules for Board-feet 58 56. The Construction of Rules Based on Mathematical Formulse 59 57. Comparison of Log Rules Based on Formulse 61 58. McKenzie Log Rule 63 69. International Log Rule for f " Kerf, Judson F. Clark, 1900 63 TABLE OF CONTENTS ix PAGE 60. International Log Rule for i" K^rf, Judson F. Clark, 1917 64 61. British Columbia Log Rule, 1902 64 62. Other Formula Rules, Approximately Accurate Both in Principles and Quantities 65 63. Tiemann Log Rule, H. D. Tiemann, 1910 67 64. Formula Rules Inaccurately Constructed. Baxter Log Rule 67 65. Doyle Log Rule 68 66. Effect of Errors in Doyle Rule upon Scaling and Over-run 70 67. The Construction of Log Rules Based on Diagrams 72 68. Scribner Log Rule, 1846 73 69. Spaulding Log Rule, 1868 75 70. Maine or Holland Rule, 1856 76 71. Canadian Log Rules 76 72. Hybrid Log Rules 76 73. General Formulae for all Log Rules 77 74. The Construction of Log Rules from Mill Tallies. Graded Log Rules 78 75. The Massachusetts Log Rule for Round-edged Lumber 79 76. Conversion of Values of a Standard Rule to Apply to Different Widths of Saw Kerf and Thicknesses of Lumber 77. Limitations to Conversion of Board-foot Log Rules 83 78. Choice of a Board- foot Log Rule for a Universal Standard 84 79. Unused and Obsolete Log Rules 85 CHAPTER VII LOG SCALING FOR BOARD MEASURE 80. The Log Scale 88 81. The Cylinder as the Standard of Scaling .■ 90 82. Deductions from Sound Scale, versus Over-run 90 83. Scaling Practice Based on Measurement of Diameter at Small End of Log 91 84. Scaling Practice Based on Measurement of Diameter at Middle of Log, or Caliper Scale 97 85. Scale Records 98 86. The Determination of What Constitutes a Merchantable Log 99 87. Grades of Lumber and Log Grades 103 CHAPTER VIII THE SCALING OF DEFECTIVE LOGS 88. Deductions from Scale for Unsound Defects 105 89. Methods of Making Deductions 105 90. Effect of Minimum Dimensions of Merchantable Boards upon these Deduc- tions 107 91. Interior Defects 108 92. Exterior Defects 113 93. Crook or Sweep 116 94. Check Scaling 117 95. Scaling from the Stump 118 96. The Scaler. . . . , . , , 119 X TABLE OF CONTENTS CHAPTER IX STACKED OR CORD MEASURE PAGE 97. Stacked Measure as a Substitute for Cubic Measure 121 98. The Standard Cord versus Short Cords and Long Cords 121 99. Measurement of Stacked Wood Cut for Special Purposes 122 100. Effect of Seasoning on Volume of Stacked Wood 123 101. Methods of Measurement of Cordwood 123 102. Solid Cubic Contents of Stacked Wood 124 103. Effect of Irregular Piling on Solid Contents 124 104. Effect of Variation in Form of Sticks on Solid Contents 125 105. Effect of Dimensions of Stick on Solid Contents 126 106. The Basis for Cordwood Converting Factors 127 107. Standard Cordwood Converting Factors 128 108. Converting Factors for Sticks of Different Lengths 128 109. Converting Factors for Sticks of Different Diameters 129 110. The Measurement of Solid Contents of Stacked Cords. Xylometers 132 111. Cordwood Log Rules. The Humphrey Caliper Rule 132 112. Discounting for Defect in Cord Measure 133 113. The Measurement of Bark 134 114. Factors for Converting Stacked Cords to Board Feet 135 115. Weight as a Measure of Cordwood 137 Part II THE MEASUREMENT OF STANDING TIMBER CHAPTER X UNITS OF MEASUREMENT FOR STANDING TIMBER 116. Board Feet — Basis of AppHcation 139 117. The Piece 140 118. Choice of Units in Estimating Timber 140 119. The Log as the Unit in Estimating 140 120. Log Run, or Average Log Method 143 121. The Tree as a Unit in Estimating. Volume Tables 144 122. Volume Tables Based on Standard Taper per Log. "Universal" Volume Tables 144 123. Substitution of Mill Factor for Log Rules in Universal Tables 146 124. Volume Tables Based on Actual Volumes of Trees 147 125. The Point of Measurement of Diameters in Volume Tables 148 126. Bark as Affecting Diameter in Volume Tables 150 127. Classification of Trees by Diameter 151 128. Classification of Trees by Height 151 129. Diameter Alone, versus Diameter and Height, as Basis of Volume Tables ... 152 130. Standard versus Local Volume Tables 153 CHAPTER XI THE CONSTRUCTION OF STANDARD VOLUME TABLES FOR TOTAL CUBIC CONTENTS 131. Steps in Construction of a Standard Volume Table 154 132. Selection of Trees for Measurement 154 TABLE OF CONTENTS xi PAGE 133. The Tree Record 155 134. Measurements of the Tree Required for Classification 156 135. Measurement Required to Obtain the Volume of the Tree. Systems Used 158 136. Computation of Volume of the Tree 161 137. Classification and Averaging of Tree Volumes According to Diameter and Height Classes 163 138. The Graphic Plotting of Data — Its Advantages 166 139. Application of Graphic Method in Consti-ucting Volume Tables 169 140. Harmonized Curves for Standard Volume Tables, Based on Diameter. . . . 169 141. Harmonized Curves Based on Height 170 142. Local Volume Tables, Their Construction and Use 174 143. The Derivation of Local Volume Tables from Standard Tables 175 144. Volume Tables for Peeled or Solid Wood Contents 176 CHAPTER XII STANDARD VOLUME TABLES FOR MERCHANTABLE CUBIC VOLUME AND CORDS 145. Purpose and Derivation of Tables for Cubic Volume of Trees 177 146. Branchwood or Lapwood 177 147. Merchantable Limit in Tops and at D.B.H 177 148. Stump Heights 178 149. Merchantable versus Used Length 178 150. Waste, Definition and Measurement 179 151. Defect or Cull 179 152. Conversion of Volume Tables for Cubic Feet to Cords 180 CHAPTER XIII VOLUME TABLES FOR BOARD FEET 153. The Standard or Basis for Board-foot Volume Tables 182 154. Adoption of a Standard Log Length 182 155. Top Diameters, Fixed or Variable Limits 183 156. Defective Trees, Measurement 184 157. Total versus Merchantable Heights as a Basis for Tree Classes 185 158. The Coordination of Merchantable Heights with Top Diameters 185 159. Construction of Board-foot Volume Tables 188 160. Data Which Should Accompany a Volume Table 188 161. Checking the Accuracy of Volume Tables 189 CHAPTER XIV VOLUME TABLES FOR PIECE PRODUCTS, COMBINATION AND GRADED VOLUME TABLES 162. Volume Tables for Piece Products 191 163. Volume Tables for Railroad Cross Ties 191 164. Combination Volume Tables for Two or More Products 193 165. Graded Volume Tables 193 xii TABLE OF CONTENTS CHAPTER XV THE FORM OF TREES AND TAPER TABLES PAGE 166. Form as a Third Factor Affecting Volume : 196 167. Taper Tables, Definition and Purpose 197 168. Methods of Constructing Taper Tables 197 169. Limitations of Taper Tables 204 CHAPTER XVI FORM CLASSES AND FORM FACTORS 170. The Need for Form Classes in Volume Tables 205 171. Form Quotient as the Basis of Form Classes 206 172. Resistance to Wind Pressure as the Determining Factor of Tree Form. . . . 208 173. A General Formula for Tree Form 209 174. Applicability of Hoejer's Formula in Determining Tree Forms 210 175. Form P'actors 211 176. The Derivation of Standard Breast High Form Factors 213 177. Merchantable Form Factors 214 178. Form Height 215 179. Form Classes and Universal Volume Tables as Applied to Conditions in America 215 CHAPTER XVII FRUSTUM FORM FACTORS FOR MERCHANTABLE CONTENTS IN BOARD FEET 180. The Principle of the Frustum Form Factor 218 181. Basis of Determining Dimensions of the Frustum 219 182. Character and Utility of Frustum Form Factors 219 183. Calculation of the True Frustum Form Factor 221 184. Calculation of the Volume of Frustums. Influence of Fixed Versus Variable Top Diameters 221 185. Construction of the Volume Table from Frustum Form Factors. A Short Cut Method 224 186. Other Merchantable Form Factors for Board Feet 225 CHAPTER XVIII THE MEASUREMENT OF STANDING TREES 187. The Problem of Measuring Standing Timber for Volume 226 188. The Measurement of Tree Diameters. Diameter Classes. Stand Tables . . 227 189. Instruments for Measuring Diameters. CaUpers, Description and Method of Use 227 190. The Diameter Tape 229 191. The Biltmore Stick 230 192. Ocular Estimation of Tree Dimensions 234 193. The Measurement of Heights 235 194. Methods Based on the Similarity of Isosceles Triangles 235 TABLE OF CONTENTS xiii PAGE 195. The Principle of the Klaussner Hypsometer 236 196. Methods Based on the Similarity of Right Triangles 238 197. Hypsometers Based on the Pendulum or Plumb-bob 239 198. The Principle of the Christen Hypsometer 243 199. The Technique of Measuring Heights 245 200. The Measurement of Upper Diameters. Dendrometers 247 201. The Biltmore Pachymeter 248 202. The d'Aboville Method for Determining Form Quotients 248 203. The Jonson Form Point Method of Determining Form Classes 249 204. Rules of Thumb for Estimating the Contents of Standing Trees 251 CHAPTER XIX PRINCIPLES UNDERLYING THE ESTIMATION OF STANDING TIMBER 205. Factors Determining the Methods used in Timber Estimating 255 206. Direct Ocular Estimate of Total Volume in Stand 256 207. Actual Estimate or Measurement of the Dimensions of Every Tree of Merchantable Size 257 208. Estimating a Part of the Timber as an Average of the Whole 257 209. The Six Classes of Averages Employed in Timber Estimating 258 210. The Choice of a System for Timber Estimating, with Relation to Accuracy of Results 261 211. Relation betTween Size of Area Units and Per Cent of Area to be Estimated 262 212. Degree of Uniformity of Stand as Affecting Methods Employed 265 CHAPTER XX METHODS OF TIMBER ESTIMATING 213. The Importance of Area Determination in Timber Estimating 267 214. The Forest Survey as Distinguished from Timber Estimating 268 215. Timber Appraisal as Distinguished from Forest Survey 269 216. Forest Surveying as a Part of the Forest Survey 270 217. The Cull Factor, or Deductions for Defects 271 218. Total, or 100 Per Cent Estimates 271 219. Estimates Covering a Part of the Total Area. The Strip Method 273 220. Factors Determining the Width of Strips 274 221. Method of Running Strip Surveys. Record of Timber 276 222. Tying in the Strips. The Base Line 281 223. Systems of Strip Estimating in Use 282 224. Methods Dependent on the Use of Plots, Systematically Spaced 285 CHAPTER XXI METHODS OF IMPROVING THE ACCURACY OF TIMBER ESTIMATES 225. The Use of Forest Types in Estimating 288 226. Method of Separating Areas of Different Types 290 227. Site Classes and Average Heights of Timber 291 xiv TABLE OF CONTENTS PAGE 228. Methods of Estimating which UtiUze Types and Site Classes. Corrections for Area 292 229. The Use of Correction Factors for Volume 293 230. Methods Dependent on the Use of Plots Arbitrarily Located 297 231. Estimating the Quality of Standing Timber 297 232. Method of Mill Rmi Applied to the Stand 299 233. Method of Graded Volume Tables AppUed to the Tree 299 234. Method of Graded Log Rules Applied to the Log 299 235. Combination Method Based on Sample Strips and Log Tally 300 236. Limits of Accuracy in Timber Estimating 301 237. The Co.st of Estimating Timber 302 238. Methods of Training Required to Produce Efficient Timber Cruisers 303 239. Check Estimating 308 240. Superficial or Extensive Estimates 308 241. Estimating by Means of Felled Sample Trees 310 242. Method of Determining the Dimensions of a Tree Containing the Average Board-foot Volume 311 243. The Measurement of Permanent Sample Plots 312 Part III THE GROWTH OF TIMBER CHAPTER XXII PRINCIPLES UNDERLYING THE STUDY OF GROWTH PAGE 244. Purpose and Character of Growth Studies 315 245. Relation between Current and Mean Annual Growth 316 246. The Character of Growth Per Cent 318 247. The Law of Diminishing Numbers as Affecting the Growth of Trees and Stands 318 248. Yields, Definition and Purpose of Study 320 249. Yield Tables 321 250. The AppHcation of Yield Tables in Predicting Yields 322 251. Prediction of Growth by Projecting the Past Growth of Trees into the Future 323 252. The Effect of Losses versus Thinnings upon Yields 324 253. The Factor of Age in Even-aged versus Many-aged Stands 325 254. The Tree or Stem Analysis and the Limitations of its Use 326 255. Relative Utility of Different Classes of Growth Data, and Chart of Growth Studies 327 CHAPTER XXIII DETERMINING THE AGE OF STANDS 256. Determining the Age of Trees from Annual Rings on the Stump 335 257. Correction for Age of Seedling below Stump Height 336 258. Annual Whorls of Branches as an Indication of Age 337 259. Definition of Even-aged versus Many-aged Stands 337 TABLE OF CONTENTS XV PAGE 260. Average Age, Definition and Determination 337 261. Determining the Volume and Diameter of Average Trees 338 262. Determining the Age of Average Trees and of the Stand 339 263. Age as Affected by Suppression. Economic Age 341 CHAPTER XXIV GROWTH OF TREES IN DIAMETER Purposes of Studying Diameter Growth 342 The Basis for Determining Diameter Growth of Trees 342 The Measurement of Diameter Growth on Sections 342 The Determination of Average Diameter Growth from the Original Data . 346 Correction of Basis of Diameter Growth on Stump to Conform to Total Age of Tree 348 Correlation of Stump Growth with D.B.H. of Tree 348 Factors Influencing the Diameter Growth of Trees Growing in Stands .... 351 Effect of Species on Diameter Growth 351 Effect of Quality of Site 352 Effect of Density of Stand .' 352 Effect of Crown Class ; . 353 Laws of Diameter Growth in Even-aged Stands, Based on Age 354 Laws of Diameter Growth in Many-aged Stands, Based on Diameter 357 Current Periodic Growth Based on Diameter Classes. The Increment Borer 358 278. Method Based on Comparison of Growth for Diameter Classes 360 279. Method Based on Projection of Growth by Diameter Classes 361 280. Increased Growth, Method of Determination 363 CHAPTER XXV GROWTH OF TREES IN HEIGHT 281. Purpose of Study of Height Growth 365 282. Influences Affecting Height Growth 365 283. Relations of Height Growth and Diameter Growth 367 284. Measurement of Height Growth 368 285. The Substitution of Curves of Average Height Based on Diameter for Actual Measurement of Height Growth 371 CHAPTER XXVI GROWTH OF TREES IN VOLUME 286. Relation between Volume Growth, Form and Diameter Growth 374 Tree Analysis, its Purpose and Application 374 Substitution of Volume Tables for Tree Analyses 375 Measurements Required for Tree Analyses 376 Computation of Volume Growth for Single Trees 377 Method of Substituting Average Growth in Form, or Tapers for Volume. . 379 Substitution of Taper Tables for Tree Analyses 382 xvi TABLE OF CONTENTS CHAPTER XXVII FACTORS AFFECTING THE GROWTH OF STANDS PAGE 293. Enumeration of Factors Affecting Growth of Stands 384 294. Site Factors or Quality of Site 384 295. Volume Growth a Basis for Site Qualities 385 296. Height Growth a Basis for Site Qualities 386 297. Other Possible Bases for Site Qualities 387 298. The Form of Stands, Even-aged versus Many-aged 388 299. Annual Increment of Many-aged Stands 390 300. The Effect of Treatment on Growth 391 301. Density of Stocking as Affecting Growth and Yields 392 302. Composition of Stands as to Species 393 CHAPTER XXVIII NORMAL YIELD TABLES FOR EVEN-AGED STANDS 303. Definition and Purpose of Yield Tables 395 304. Standards for Yield Tables 395 305. Construction of Yield Tables, Baur 's Method 396 306. Standard for "Normal" Density of Stocking 397 307. Age Classes 397 308. Area of Plots 397 309. Measurements Required on Each Plot 398 310. Construction of Yield Table, with Site Classes Based on Height Growth. . 401 311. Rejection of Abnormal Plots 404 312. Construction of Yield Table, with Site Classes Based Directly on Yields per Acre 406 313. Yield Tables for Stands Grown under Management , 407 314. Yield Tables for Stands of Mixed Species 408 CHAPTER XXIX THE USE OF YIELD TABLES IN THE PREDICTION OF GROWTH IN EVEN-AGED STANDS, WITH APPLICA- TION TO LARGE AGE GROUPS 315. Factors Affecting the Probable Accuracy of Yield Predictions 412 316. Methods of Determining Actual or Empirical Density of Stocking 413 317. Application of Density Factor, in Prediction of Growth from Yield Tables 414 318. Separation of the Factors of Volume, Age and Area 416 319. Determination of Areas from Density Factor 416 320. Application to Forest having a Group Form of Age Classes 418 321. Determination of Volume and Area for Two Age Groups on Basis of Average Age 419 322. Application of Results to Forest by Use of Stand Table and Per Cent. . . . 421 323. Determination of Volume and Area for Age Groups on Basis of Diameter Groups 422 324. The Construction of Yield Tables Based on Crown Space, for Many-aged Stands 422 325. Apphcation of Method to Many-aged Stands 425 326. Yield Tables for Stands Grown under Management 427 TABLE OF CONTENTS xvii CHAPTER XXX THE DETERMINATION OF GROWTH PER CENT PAGE 327. Definition of Growth Per Cent 429 328 Pressler 's Formula for Volume Growth Per Cent 429 329. Pressler 's Formula, Based on Relative Diameter 430 330. Schneider 's Formula for Standing Trees 431 331. Use of Growth Per Cent to Predict Growth of Stands 432 332. Use of Growth Per Cent to Determine Growth of Stands by Comparison with Measured Plots 433 333. Use of Growth Per Cent in Forests Composed of All Age Classes 434 334. Growth Per Cent in Quality and Value 435 CHAPTER XXXI METHODS OF MEASURING AND PREDICTING THE CUR- RENT OR PERIODIC GROWTH OF STANDS 335. Use of Yield Tables, in Prediction of Current Growth 436 336. Method of Prediction Based on Growth of Trees, with Corrections for Losses 436 337. Increased Growth of Stands after Cutting 438 338. Reduced Growth of Stands after Cutting 438 339. Application of Yield Tables Based on Age, to Cut-over Areas 441 340. Permanent Sample Plots for Measurement of Current Growth 443 341. Measurement of Increment of Immature Stands as Part of the Total Increment of a Forest or Period . 443 342. Comparative Value of Current Growth versus Yield Tables and Mean Annual Growth 445 CHAPTER XXXII COORDINATION OF FOREST SURVEY WITH GROWTH DETERMINATION FOR THE FOREST 343. Factors Determining Total Growth on a Large Area. 447 344. Data Required from the Forest Survey 447 345. Site Qualities, Separation in Field 448 346. Relation between Volume and Age of Stands 449 347. Averaging the Site Quality for the Entire Area 449 348. Growth on Areas of Immature Timber 450 349. Effect of Separation of Areas of Immature Timber on the Density Factor for Mature Stands 453 350. Stand Table by Diameters for Poles and Saplings; When Required 454 APPENDIX A LUMBER GRADES AND LOG GRADES 351. Purpose of Log Grades 455 352. Grades of Lumber , 455 353. Basis of Lumber Grades 455 xviii TABLE OF CONTENTS PAGE 354. Grades for Remanufactured and Finished versus Rough Lumber 456 355. General Factors which Serve to Distinguish Lumber Grades 456 356. Grouping of Grades of Rough Lumber '. . . 457 357. Example of Grading Rules 457 358. Relation between Grades of Lumber and Cull in Log Scaling 458 359. Log Grades, Determination 459 360. Examples of Log Grades 460 361. Mill-grade or Mill-scale Studies 461 362. Method of Conducting Mill-scale Studies 462 APPENDIX B THE MEASUREMENT OF PIECE PRODUCTS 363. Basis of Measurement 466 364. Round Products 466 365. Poles 467 366. Piling 470 367. Posts, Large Posts, and Small Poles 471 368. Mine Timbers 473 369. Cross Ties 474 370. Inspection and Measurement of Piece Products 477 APPENDIX C TABLES USED IN FOREST MENSURATION (see Index of Tables) 479 APPENDIX D BIBLIOGRAPHY 521 INDEX 523 44 V 48 VI 64 VII 66 VIII TABLES Article No. Title page 32 I Comparison of Results Obtained by Scaling the Cubic Con tents of Logs, at Small End and at Middle of Log 27 38 II Comparison of Per Cents of Cubic Contents of Cylinders Scaled by Various Log Rules, for Logs 18 Inches in Diam- eter at Small End, with 2-inch Total Taper 37 41 III Relation of Cubic and Board-foot Contents of 16-foot Logs with a Taper of 1 inch in 8 feet. Based on Tiemann's Log Rule ^-inch Saw Kerf 41 42 IV Comparison of Blodgett and Tiemann Log Rules for Cer- tain Logs 42 Effect of Different Methods of Scaling a Log 45 Gain in Output Secured by Sawing around Compared with Slash Sawing in Per Cent of Latter Output 48 Distribution of Waste between Slabbing and Sawdust 56 Thickness of Plank to be Deducted for Slab Waste to Coin- cide with a Collar 1.5 Inches Thick. Sawdust Allowance 20 Per Cent 61 5^ IX Deductions for Slabbing and for Saw Kerf, for 12-inch Logs, in Ten Log Rules Based on Formulae 62 Over-run, Doyle Rule, Texas 71 Over-run, Doyle Rule, Ontario . 71 Decimal Values below 12 Inches, for Scribner Log Rule 74 Conversion of International Rule j-inch Saw Kerf for Other Widths of Kerf 81 76 XIV Conversion of Log Rules with ^-inch Saw Kerf and No Shrinkage Allowance to Other Widths of Saw Kerf 82 XV Per Cent of Increase in Sawed Lumber Caused by Sawing Lumber of Different Thicknesses 82 XVI Correction in Per Cents for Contents of Logs in Superficial Board Feet, for Lumber Sawed Less than 1 Inch in Thick- ness 83 Scaling Practice, or "Scale" in Different Logging Regions. . . 94 Deductions for Crook or Sweep 116 Solid Contents of Stacked Wood 127 Standard Converting Factors for Cordwood 129 Influence of Length of Stick upon the SoUd Cubic Contents of a Cord 130 XXII Influence of Length of Stick on SoUd Cubic Contents of a Standard Cord, Balsam Fir 130 XXIII Interdependence of the Stick Length and the Volume of SoUd Wood per Cord 131 xix 66 X XI 68 XII 76 XIII 83 XVII 93 XVIII 107 XIX XX 108 XXI XX TABLES Article No. title page 109 XXIV Solid Contents of a Standard Cord Based on Diameter of Stick. Average 4-foot Wood 131 112 XXV Measurement of 4-foot Round Spruce Pulpwood, with Cull Factors Based on Solid Cubic Contents 134 123 XXVI A Portion of a Volume Table Based on Mill Factors 147 137 XXVII Preliminary Averages for Pitch Pine. Volume Table Based on Diameter and Total Height. 139 Trees. . 165 139 XXVIII Comparison of Original and Harmonized Average Volumes. . 171 140 XXIX Volumes Read from Curves of Volume on Diameter for Different Height Classes 171 141 XXX Standard Volume Table Read from Curves of Volume on Height for Different Diameter Classes 174 142 XXXI Local Volume Table, Form 175 162 XXXII Conversion Factors for Second-growth Hardwoods by D.B.H. Classes with Corresponding Diameters of the Average 4-foot Stick in the Tree or in the Stack 181 168 XXXIII Form or Taper for White Ash Trees of Different Diameters under 75 Years of Age, Giving Diameters Inside Bark at Different Heights above Ground 198 XXXIV Tapers of Loblolly Pine, Two Trees 199 183 XXXV True Frustum Ibrm Factors for Longleaf Pine, from Frus- tums whose Top Diameter Coincides Exactly with the Average Top Diameters of Trees of Each D.B.H. and Height Class 222 184 XXXVI Frustum Form Factors for 555 Longleaf Pines, Coosa Co., Alabama. Based on Average Top Diameter of 13.2 Inches for Frustums 223 XXXVII Actual Average Top Diameters of Merchantable Lengths, Longleaf Pine, Coosa Co., Ala. Basis 555 Trees. Average of all Top Diameters, 13.2 Inches 224 Errors in Using Biltmore Stick 232 Figures to be Used in Graduating a Biltmore Stick 233 Table for Determination of Form Class of Trees by Means of Position of Form Point 250 Relation of W^idth and Number of Strips to Area Covered . . 274 Sizes of Circular Plots 286 Relation between Plots and Area Covered 286 Per Cent of Total Area Required in Estimating 292 Comparative Estimates of a Tract of 40 Acres. Board Feet . 304 Estimate of Taylor 's Creek Logging Unit, Blooming Grove Tract, Pike Co., Pa., 1911 309 Growth of Jack Pine, Minnesota 318 Yield Table for White Pine 321 Yield Per Acre of Spruce, Cutting to Various Diameter Limits 322 L Height of Seedhngs at Different Ages, Western Yellow Pine, Colfax Co., New Mexico 336 LI Diameter Growth of Five Spruce Stumps 345 LII Stump Tapers Based on Stump D.I.B. for Stumps 1 foot High 350 191 XXXVIII XXXIX 203 XL 220 XLI 224 XLII XLIII 228 XLIV 238 XLV 240 XLVI 246 XLVII 249 XLVIII 250 XLIX 257 266 269 TABLES XXI UTICLE : No. LIII 278 LIV 279 LV LVI 284 LVII 288 LVIII 290 LIX 296 LX 298 LXI 314 LXII LXIII 324 LXIV LXV 337 339 LXVI LXVII AppendLx. 365 LXVIII LXIX 365 LXX LXXI LXXII LXXIII LXXIV 366 LXXV 370 LXXVI LXXVII LXXVIII LXXIX LXXX LXXXI TITLE PAGE Growth of Loblolly Pine, Old Field, in D.B.H. Based on Age of Tree. Urania, La 350 Current Growth of Spruce, Adirondacks Region, New York . 360 Shortleaf Pine, Louisiana. Growth by Diameter Classes. . . . 362 Current Growth, Loblolly Pine, by Diameters 363 Height Growth of Chestnut Oak, Milford, Pike Co., Pa 371 Growth of Chestnut Oak in Cubic Volume, from Diameter and Height Growth and Use of a Standard Volume Table 376 Stem Analysis of a Tree 378 Standards of Site Classification Based on the Height of Tree at 100 Years 387 Average Crown Spread of Loblolly Pine in the Forest at Vredenburgh, Ala 389 Normal Yield per Acre in Cubic Feet and Cords of Better Second-growth Hardwood Stands in Central New England 409 Percentage of the Various Species in Mixture from Table LXII Classified as to T>-pe and Site Class 410 Trees per Acre Based on Crown Space 425 Yields of Cordwood, for Yellow Poplar in Tennessee — Based on Crown Space and Volumes of Trees of Given Ages 426 Adirondack Spruce. Average Rate of Growth in Diameter on the Stump of 1593 Trees on Cut-over Land at Santa Clara, New York 440 Areas Remaining Stocked on Cut-over Lands 443 Relation between Circumference and Diameter for White Cedar Poles 467 Minimum Dimensions of White Cedar Poles in Inches, Circumference, Classes 468 Minimum Dimensions of Western Red Cedar Poles in Inches 470 Minimum Dimensions of Southern Yellow Pine Poles in Inches, Circumference 471 Minimum Circumference of Chestnut Poles in Inches 472 Minimum Sweep Poles, Standard 472 Minimum Sweep Poles, Country 473 Dimensions for Pihng 473 Board-foot Converting Factors for Various Products, U. S. Forest Service 478 Cubic Contents of Cyhnders and Multiple Table of Basal Areas 480 Areas of Circles or Table of Basal Areas for Diameters to Nearest ^Viiich 490 Tables for the Conversion of the Metric to the English System, and Vice Versa 492 The International Log Rule for Saws Cutting a J-inch Kerf 493 Tables for Values in Schiffel's Formula for Cubic Volumes of Entire Stems 494 XXll TABLES Article No. title page LXXXII Breast-high Form Factors 497 LXXXIII Weights per Cord of Timber of Various Species, 7- to 8-inch Wood 498 LXXXIV Tiemann Log Rule for Saws Cutting a ^-inch Kerf 500 LXXXV Tiemann Log Rule Reduced to Small End Diameters 502 LXXXVI Scribner Decimal C Log Rule 503 LXXXVII Index to Standard Volume Tables 505 LXXXVIII Index to Yield Tables 516 LXXXIX Index to Taper Tables 519 FOREST MENSURATION PART I THE MEASUREMENT OF FELLED TIMBER AND ITS PRODUCTS CHAPTER I INTRODUCTION TO FOREST MENSURATION 1. Definition and Purpose. Forest Mensuration is that branch of forestry which deals with the determination of the volume of the wood material contained in logs or portions of felled trees, in standing trees, in stands of timber and in forests, expressed in terms of cubic measure, board measure, or any other unit. It also determines the growth and future yields of trees, stands, and forests in any of the above units of volume. The measurement of standing timber is termed Timber Estimating or Timber Cruising. The commercial measurement of the contents of logs is called Scaling. Forest property is land bearing forest trees as the principal vegeta- tion. The trees may be valued for their appearance, as in parks, their protective influences, as in forests at headwaters of streams, or their wood, as in all forms of commercial use, including by-products such as naval stores and bark. In past logging operations the land has not always been regarded as true forest property, capable of growing other crops of trees; but unless such land has a higher economic value for agriculture, grazing, or other purposes than for any of the three forest uses above mentioned, it is as truly forest property as the timber. The measurement of the volume and growth of timber is an indispen- sable factor in classifying lands for their highest use, whether for agri- culture or forestry. Forest Mensuration makes possible the systematic management of forest property by ordinary business methods, which require, first, a knowledge of quantities or amount of material, and its location and 2 INTRODUCTION TO FOREST MENSURATION rate of production,^ and second, information on which to base the value of the property for the purpose of sale, exchange or the appraisal of damages. 2. Relation between Lumbering and Timber Estimating. The logging of timber is usually conducted as a business venture entirely separate from the growing of trees or management of forest property, but whether this is so, or the forest owner cuts and logs his own tim- ber, the cost of the logging will depend in a great measure on the known quantity of timber which can be brought out over a given route and by a specific method of logging. The greater the volume of standing timber, the greater the investment which is justified in roads, railroads, chutes, or flumes to cut down the expense of hauling. Overestimates cause losses through excessive investments; underestimates cause losses through not investing enough money in these transportation systems. The logger cannot wait until his timber is cut and scaled before planning his operation. Accuracy in timber estimating is therefore an under- lying factor in the successful conduct of the business of lumbering. 3. Relation between Forestry and Growth Measurements. Lum- bering as a business begins at the stump, while forest production may begin with the seedling, and may well be considered as a separate busi- ness enterprise. The growth of trees is the basis of returns on this business, no matter whether these returns are secured on the stump, or by means of the additional operation of logging. The speculator in standing timber hopes to realize a growth in unit prices such as was experienced as a result of the war. But the business of forestry depends for its profits on growth, first, in volume, and second, in quality, of the product by reason of increased sizes and improved texture, increase in prices being merely an additional guarantee of adequate returns. Since growth determines the quantity of products to be expected, any expen- diture in planting and care of the forest can be undertaken intelligently only when the probable rate of growth per acre is known. The study of growth is therefore a necessary part of the business of forestry and unless growth data can be obtained, there is no possible method of . 1 A business is an undertaking which seeks to supply a public demand. The most common form of business is that which produces raw materials and transforms them into finished products delivered as such to the consumer. Any distinct step in this process may and often does constitute a separate business. To accomplish the purpose of its existence, a business deals with three factors, quantity, location, and time. To supply forest products for the innumerable demands of modern civilization, a well-conducted business operation requires full knowledge of the quantity of raw material and finished products with which it deals, their location, and the time or periods when these quantities wall be available. Forest Mensura- tion is as fundamental to forest production as is inventory and merchandise account to a mercantile business. RELATION OF MENSURATION TO FORESTRY SUBJECTS 3 determining either the proper investments and expenses, or the probable returns and profits from such an enterprise. 4. Relation between Forest Mensuration, Stumpage Values and the Valuation of Forest Property. In determining the value of forest property for sale, exchange, or the appraisal of damages, it is necessary first to know what the mature standing timber is worth on the stump previous to cutting. This is known as stumpage value. The stumpage value of standing timber is derived from the value of the finished prod- ucts and is influenced by four factors, namely, the species of wood, its quantity, its quality, and the unit price of the product. Forest mensuration by means of a forest survey determines as accurately as possible the first three factors. By determining through an appraisal the price of stumpage for the different kinds and qualities of timber found on the area, the value of the timber may be found. The value of young timber and of forest soil can be calculated after the possible yields at given ages have first been approximated and the stumpage value has been appraised for this final yield. 5. Relation of Mensuration to Other Forestry Subjects. The rela- tion of Forest Mensuration to other subjects in forestiy is shown in Fig. 1. In the threefold division of forestry indicated, mensuration falls in the mathematical or business group, but is included in the phys- ical branch of that group which deals directly with the forest. Mathematics is the basis of Mensuration, since the latter subject deals primarily with quantities. But as both timber estimating and growth data must usually be expressed on terms of area or acreage. Mensuration rests directly on Surveying. Mensuration in turn furnishes the quantitative data required by the science of Forest Finance as a basis on which to compute the cost of production and the probable returns from forestry and to indicate the choice of methods to use in forest production. Although it falls in the business group, and is a basic subject underlying Forest Management, Mensuration is a statistical science similar to Forest Finance. Neither subject constitutes an applied science, which is the characteristic of Forest Management. Mensuration is therefore not a direct subdivision of Management, but a distinct subject preparatory to Management. 6. Absolute versus Relative Accuracy in Mensuration. Forest Mensuration attempts to secure as close an approach to mathematical accuracy as the conditions of the problem, the use to which the data are put, and the cost of the work will permit. In scaling, the volumes of logs are determined before sawing, and in timber estimating, the contents of trees and stands are obtained before felling. But no log rule will give the exact quantity of lumber which will be sawed from a given log, and no tree volume table can predict the output in boards from a 4 INTRODUCTION TO FOREST MENSURATION given tree, since these results will vary with the methods and conditions of sawing and of utilization. a si CO o C3 ti Forest Physiography Dendrology Forest Ecology Forest Entomology Wood Technology Silviculture Forest Engineering Lumbering Wood Using Industries Forest Protection ll >. 0) Geology Botany Zoology Mechanics / / to \ a u s ^ ^ I. a C14 a < \, \ >> to cj 3 to a a ►J a >> & S 2 ^ orest Econo orest Histor ■3 s u b Cl. ^ S3 plied iences onomic and chnical ■t-t HI a .£1 d d bo ^rj ® «^mH H ffl Again, in estimating timber it is seldom possible to measure every tree, on account of the time and expense involved. For this reason, FOREST SURVEY 5 only an average portion of the stand may be measured. The laws of averages, or of sampling are applied to solve nearly every problem in Forest Mensuration, in order to bring the cost of the field work within practical limits. When Mensuration deals with the growth of trees and stands, and of whole forests, its purpose is to predict what will occur in the future. It bases these predictions upon the results which have occurred in the past, under conditions judged to he similar to those which will affect these future stands. The laws of growth of trees, and especially, of stands composed of great numbers of trees competing with each other for existence and supremacy, can only be approximated on the basis of probabilities and averages. The results of living forces cannot be predicted with mathematical accuracy, and the study of growth par- takes of the nature of research rather than of routine measurement of definitely determinable quantities. Neither Forest Mensuration nor Forest Surveying produces any physical change or improvement in the forest, as does the application of silviculture, protection, and lumbering. The achievements of forestry depend upon the amount and character of the actual work done along these latter lines. Misdirected work, done at the wrong time or place and in the wrong quantity, or by too expensive a method when com- pared with results, means waste, inefficiency, and ultimate ruin and bankruptcy of the enterprise. The data supplied by mensuration and supplemented by forest finance are the balance wheel of forest industry. But the necessity of restricting the funds expended upon the mere col- lection of data to as small a per cent as possible of the total budget of expenditures, reserving the greater portion for the operations which effect actual change in the forest, is obvious and justifies the use of meth- ods based on averages rather than extreme mathematical accuracy. 7. Forest Survey. Forest Survey is the general term applied to the project of gathering all the quantitative data required regarding a specific forest property. It includes a survey and maps of the area, thus locating the property and its subdivisions, a measurement of the volume and character of the timber, and it may cover other resources such as land classification, waters, forage, game, and fish. Forest Surveying and Forest Mensuration deal with the principles and methods of accomplishing this work. The Survey itself is the enterprise or project of securing the data. Accuracy in the results of a forest survey is judged, not on an absolute standard, but in relation to the balance between utility of the results and the cost of obtaining them, and is therefore always a relative term. CHAPTER II SYSTEMS AND UNITS OF MEASUREMENT 8. Systems of Measurement Used in Forest Mensuration. Throughout the United States and Canada the EngUsh system of measure is used in all practical applications of Mensuration. In the Philippines the metric system is the standard. (Appendix C, Table LXXIX.) Efforts to substitute the metric sj^stem in the United States for the units established by custom have so far failed, though its use was sanctioned by Congress in 1866. Mensuration is applied more generally to the solution of practical problems such as timber estimating than to purely scientific research, and for the former, the results must be expressed in the customary units to be intelligible. Scientific forest measurements have also, except in a few instances, been expressed in English units. In measuring distances and areas, the chain of 66 feet, or 4 rods, is a commonly used unit. Five chains constitute a tally, or 20 rods; and 16 tallies, or 80 chains, equal 1 mile. One tally forms the side of a square 2^ acres in area. Distances are commonly measured by pacing, or counting the number of paces, the average length of the individual pace having been determined by previous tests. A true pace is the swing of one foot, or twice the length of a step. In counting, the pace rather than the step should be used, since it reduces the count by half. The acre, containing 160 square rods or 43,560 square feet, is the unit of area. In the rectangular system of survey adopted by the United States the following definitions apply: Township — a tract approximately 6 miles square containing 36 sections. Section — a rectangular tract containing approximately 1 square mile or 640 acres, but which may contain more or less than this area in irregular surveys. Quarter Section — a subdivision of a section containing approxi- mately 160 acres. " Forty " — a colloquial term describing a ygth section or quarter of a quarter section containing approximately 40 acres. Lot — a tract ordinarily containing not less than 20 or more than 60 acres, but which may contain less area, of either 6 PIECE MEASURE 7 rectangular or irregular shape, and which takes the place of the " forty " in irregular surveys or bordering lakes or streams.^ In measuring trees, the foot is the standard for height, and the inch, divided into tenths of inches, for diameter. Basal area is the cross- sectional area of a tree or stand, in square feet, measured at 4| feet from the ground. This is obtained from area of circles whose diameters equal those of the trees measured. 9. Piece Measure. Wood products which are used in the round, and logs or bolts which are barked, shaped, and reduced to standard dimen- sions where felled, are usually measured and sold by the piece. These pieces are graded by size and by quality into accepted pieces and culls, or rejects, whose defects render them unfit for the special purpose required. The standard sizes are determined by specifications, which also prescribe the species of tree and the required quality of the product. The principal products purchased on this basis are cross ties, poles, posts, piles, and mine timbers. Where bolts of uniform size are sawed or split for manufacture into special products, they may be counted and paid for by the piece. Their average volume is determined beforehand. When the number of pieces per cord, or per thousand board feet is agreed on, the payment may be in terms of these latter units. Linear measure is sometimes used for pieces of standard width and thickness but of variable length. Such products are sold by the lineai* foot. This standard is widely used for piling. 10. Cord Measure. When the pieces into which trees are sawed or split are of lengths shorter than ordinary logs, and of irregular shape, the expense of determining separately the contents of each piece is avoided by stacking them in regular piles or cording them up, and measuring only the exterior dimensions of the stack to get the total stacked cubic space occupied. This stacked cubic measure does not indicate the solid contents, which may vary widely. But if the average per cent of solid contents per cubic foot of stacked measure is known for sticks of given sizes and character, this stacked measurement becomes a practical and serviceable standard, though not well suited to scientific investigations. The cord is the standard generally adopted for stacked wood. 1 References. Manual of Surveying Instruction for the Survey of the Public Lands of the United States and Private Land Claims, Commissioner of the General Land Office, Washington, D. C, Government Printing Office, 1902. Manual for Northern Woodsmen, Austin Cary, Part I. Section VIII, 1918. Harvard University Press, Cambridge, Mass. 8 SYSTEMS AND UNITS OF MEASUREMENT The standard cord is 4 by 4 by 8 feet, containing 128 cubic feet. There are, however, other cord units in use (Chapter IX). 11. Cubic Measure. The cubic volume of trees and logs affords the only basis of accurate and permanent scientific records, and a uni- form standard of measurement. For this purpose the cubic foot should be used as the standard unit. Where cubic volume was employed by lumbermen, other cubic units, whose contents were based on cylinders of given sizes, have been adopted arbitrarily. These units possess no advantages over the cubic foot (Chapter IV). In most regions, the desire to express the contents of logs in terms of sawed lumber prevented the adoption of the cubic foot as the standard of measurement for logs. 12. Board Measure. Board measure may be defined as a cubic standard for measuring sawed lumber. A board foot is a board 1 foot square and 1 inch thick. Twelve board feet of sawed lumber equal 1 cubic foot. The board-foot contents of sawed lumber is found by multiplying the product of the width and thickness in inches by the length in feet and dividing by 12. 13. Log rules. A log rule is a table giving the contents of logs of different diameters and lengths. The unit of volume used may be based on cubic measure, or board feet. The latter form of table differs from that based on cubic contents since it indicates only the net volume of the product in boards which result from sawing the log. The use of such log rules is to measure the contents in the log before sawing, as a basis of sale of logs or for other purposes requiring such measurement. Fixed or arbitrary values are assigned or agreed upon for logs of each diameter and length. The table thus becomes a standard of measure- ment based upon a unit of volume. This method of measuring logs has consequently led to the develop- ment of numerous log rules whose construction is discussed in Chapters IV, V and VI. These rules differ, some of them greatly, for logs of the same dimensions. To secure the universal adoption of a single log rule which is at once accurate and acceptable is probably an impossible task, and several of the more widely used ones will no doubt continue as standards. 14. Measurement of Standing Timber, Postponed till after Manu- facture. This lack of standardization as to units for board-foot contents of logs inevitably reacts upon the accuracy and consistency of measure- ments of the board-foot contents of standing timber. The contents of a given stand will vary widely with the log rule used in estimating. The custom of estimating standing timber in terms of the product is not confined to measurement by board-foot log rules. Hewn ties, MEASUREMENT OF STANDING TIMBER IN THE TREE 9 poles, staves and other piece products are customarily used as units for timber estimating, when the timber is to be used for these purposes. Thus the standard commonly sought in America for measuring stand- ing timber is the net merchantable volume, which results from deducting all forms of waste in manufacture from the total contents of the tree. There is but one accurate method of measuring this net contents, and that is to postpone the measurement until the timber is logged and manufactured into boards or other products. Since a purchaser of standing timber is always conservative wherever a doubt exists, it is to the owner's interest to sell on the basis of actual mill cut of boards or output of other products, whenever this is possible. This basis is often used in regions where the timber is cut by small portable mills, located in or near the tract and where small amounts are purchased. 15. Measurement of Standing Timber Postponed till after Logging. Where the logs must be driven down streams or hauled long distances by the purchaser, this basis becomes impractical both because of the delay in settlement of account and the difficulty of checking the output of lumber. The timber owner is thus forced to substitute a log scale for a mill tally of lumber. This scale is always based on some log rule agreed upon beforehand, and may or may not give results coinciding with the actual sawed output. If the log rule is known to be inaccurate, the excess or deficiency of manufactured products can be ascertained only by a comparison of the mill tally with the log scale. Such comparisons will give an idea of over-run or under-run (§46). The owner can then adjust the price in. subsequent sales of logs according to the difference between the scaled contents of his logs and their probable output in sawed lumber. 16. Measurement of Standing Timber in the Tree. But even the log scale is inapplicable when standing timber is purchased in large amounts and a long period is required for completion of logging. The owner desires prompt payment even if based on a less accurate measure- ment of volume. The volume of the standing timber must be measured as well as possible, and since, at best, onl}^ the diameter of the trees together with a few heights can be actually determined and the rest of the work is done ocularly or by guess, the result is only a rough estimate. This method has given rise to the term Timber Estimating. The prin- cipal sources of error in timber estimating lie in the effort to arrive at the net merchantable contents minus waste, in the use of inaccurate and variable standards of log measure for this purpose, and in the difficulty and cost of determining even the superficial dimensions of standing trees. This leads to short-cut methods, approximations and guess work and calls for the development of system and of personal skill. One improve- ment in timber estimating widely used by foresters is the tree-volume 10 SYSTEMS AND UNITS OF MEASUREMENT table, which gives the average contents of entire trees of different dimen- sions, in terms of standard log rules or other units, thus eliminating a certain amount of ocular work. 17. Need of Standardization for Both Commercial and Scientific Measurements. The justification of the use of standards which give the contents of standing timber in terms of products, rather than actual cubic volume, lies in the fact that the value of the timber, standing or cut, depends upon the volume and quality of these products and not upon the cubic volume. Had it been possible to secure the adoption of a uniform standard of conversion into board feet, the use of this standard would be more serviceable than the apparently simpler cubic standard. But in prac- tice the same motives which here gave rise to standards based on products have led the French to adopt, as substitutes for cubic measurement, rules of thumb which are less accurate by far than many of our log rules. ^ The greatest drawback to the use of units intended to measure the product directly lies not in their character but in their inaccuracy and in the multiplicity of standards. It is easily seen that volume tables and measurements of growth which are based on some widely used commercial log rule may coincide with custom, but are incapable of use or comparison with other log rules (§ 77) and are inaccurate as a scientific basis of measuring growth or volume. This fact has led to endless duplication of effort and has been the chief reason for the lack of real progress in accumulating standard data on volume and growth of American trees. A continuance of such duplication of effort will hinder the progress of forestry in America, which must depend in a large part upon the accuracy of volume and growth data gathered by forest measurements. While the local value of data based on log rules sanctioned by custom will continue, these field data should be gathered in such form as to be of permanent value independent of these variable local standards. It is possible to convert all measurements to the common standard of cubic feet, which gives a basis of scientific comparison between the volumes of different trees and species, and a permanent basis for measure- ment of growth for trees and stands. It is also possible to adopt, for the purposes of permanent record, a log rule based on scientific principles which will give an equally reliable comparison of the contents of trees in board feet and the growth of stands expressed in this unit of product. But for a permanent record from which the volumes of trees may be derived in any unit of product, standard or local, the average form of the 1 Mensuration in France, Donald Bruce, Journal of Forectry, Vol. XVII, 1919, p. 686. FORMS OF PRODUCTS 11 tree is required, as expressed in diameters at different points on the stem. Investigations of tree form are therefore at the root of all per- manent progress in Mensuration (Chapter XVI). 18. Forms of Products into which the Contents of Trees are Converted. The products manufactured from trees may be classed according to the following group- ing: Group I. Manufactured products of definite form, retaining the wood structure and requiring waste in manufacture. A. Manufactured from logs. 1. Lumber a. For construction. 1'. Structural timbers. 2'. Dimension. 3'. Boards. 4'. Remanufactured or planing mill products. 5'. Special products. 6'. For export. b. For remanufacture. Scjuare edge or round edge. 1.' For mill work, furniture, fixtures. 2.' For utensils and supplies. 3.' Boxes and containers. 2. Veneers. 3. Manufactured direct from log for finished articles. B. Manufactured from bolts. Billets, flitches, squares, blocks, shingles, spokes, staves, etc. C. Manufactured from mill refuse, i.e., from slabs, trimmings and edgings. Shingles, lath, bo.xboards, etc. Group II. Bulk products in which the form or both form and structure are destroyed. 1. Excelsior. 2. Wood pulp. a. Mechanical. b. Chemical. 3. Distillates. 4. Extracts. 5. Fuel. a. Charcoal, b. Fuel wood. 6. Bark. Group III. Piece products retaining in whole or in part the original form. 1. Round products, Poles, piling, posts, etc. 2. Shaped products. Hewn cross ties. 1'. Standard ties. 2'. Mine ties. Group I. In converting round logs into lumber, there is unavoidable waste in sawing due to the difference in shape between the products desired and the log, and to the saw kerf. The per cent of waste depends upon the dimensions of the 12 SYSTEMS AND UNITS OF MEASUREMENT smallest board which is merchantable, and upon the thickness of saw used. Further intensive utilization of slabs (pieces slabbed off from the round surface of logs in sawing) and of edgings (pieces cut from the edges of boards to give parallel edges and remove bark), by manufacture into sawed products depends upon finding a market for pieces whose size is small enough to permit of their manufacture from these otherwise waste products. The waste in manufacturing articles direct from the log depends on the shape of the manufactured article with reference to the bolts from which it is made. Unless profitable use can be found for the portions so wasted, or unless antiquated methods and machinery are in use, the portions of a tree or log lost in manufacture cannot be regarded as wasted, any more than the loss in bulk of a rough block of stone in process of transformation under a sculptor's hand is considered waste. It is for this group that log rules are required. "Woods Wast 16.6i« . ^ s e Mill Waste 44.3^ Lumber 89.1;* Z' A Tops Limbs Stumps O P ■^*- a- Edgings Trimmings -^ re » » ft) 3 Seasoned L^nplaned Lumber 33.5J« •'Careless mfg. miscellaneous 2.556 5 TYPICAL INDUSTRIES Rough Lumber 100^ "1 2 ^ (D o 5^ Factory Waste Finished Product Planing Mill Products 96!« m Car Construction Boxes 82^ 255« 75^ Vehicles 755^ " ^ ea c 5 «! Fig. 2. — The percentage of utilization of the volume of a tree when manufactured into lumber. Group II. To this group belong also those waste products from Group I for which use as bulk materials can be found. The characteristics of this group are that the entire volume of the log, and a much larger per cent of the volume of the tree is utilized than in Group I. Material may be taken to very small diameters, since size is not a requisite of utility but merely a convenience in handling. For this group, cubic volume is the required standard of measurement, and the use of stacked cubic measure is customary. Group III. Nearly all the round or shaped products in this group may also be obtained from larger logs by sawing as poles, ties, fence posts, in which case they can be measured for their contents in sawed lumber. For round i)roducts, as poles, piles or posts, or for hewn products, as hewn or " pole " ties, the number of pieces of standard sizes and shapes is the simplest method of measurement. For this group the important factor in measurement is the set of specifications which deter- mine the grades of product. The waste to be expected in manufacture under Group I is shown in Fig. 2. THE FACTOR OF WASTE IN MANUFACTURE 13 19. The Factor of Waste in Manufacture. A waste product is one for which a profitable use has not been found. It is not sufficient that the product could be used for some purpose if it could be transported to some place other than the site of its first appearance as waste. The value of the product must be such as to bear the cost of manufacture and transportation plus a profit. Unless some portion of a tree yields products which fulfill these conditions, the whole tree remains unutilized to finally die and rot, a true waste product of nature. In inaccessible places, entire stands go to waste. Waste in tops and limbs represents those portions of the tree which under the existing conditions do not yield profitable products. But little deliberate or inexcus- able waste occurs over any long period without discovery and correction. The per cent of waste for unprofitable portions of the trees is often as high as 50 per cent for staves or other special products and 25 per cent or over for lumljer. The average of 16.6 per cent shown in Fig. 2 for lumber is far too high for bulk products such as pull) wood or for trees with small limbs and boles of regular form. Bark is a typical example of a "waste" product. As fuel, it is not wasted. When tannin extract or cork is yielded it is carefully gathered. For lumber, it is entirely wasted, except as incidental fuel. The waste in sawdust, slabs, edgings and factory finishing, when reduced to the lowest possible terms by good machinery, can hardly be regarded as avoidable waste, since the product which results from this apparent waste has a value much higher and a utility much greater than before the " loss " of the extra bulk. When this sawdust and refuse is used as fuel in the mill, as is now the common practice, it replaces coal, thus not only effecting a great economy but performing an important public function in saving transportation costs on coal. The only real waste in manufacture is where methods are used which unduly increase sawdust and slab waste at the expense of finished products. Waste caused by seasoning of wood is not avoidable, and increases the value of the product in greater ratio than its loss in bulk. The per cent of actual avoidable waste in utilization of the tree is difficult to determine or to prove. It constitutes the per cent of difference between what is utilized in higher forms, and what could be utilized under the same economic condi- tions, at a profit. It is a measure of the efficiency and alertness of the operator, and will seldom exceed from 5 to 10 per cent even under exceptionally bad conditions; while under good management this avoidable waste is probably not over from 2 to 5 per cent. The utilization of small-sized pieces and bulk products not only reduces the per cent of waste in single trees, but brings entire trees of smaller dimensions into the merchantable class, thus increasing the per cent of volume in a stand of timber which is merchantable, and lowering the age at which trees can be marketed. Since the number of trees per acre rapidly diminishes with increasing size, close utilization of small diameters will very greatly increase the per cent of merchantable volume in young stands and reduce the per cent of waste by natural losses of trees before they reach the larger diameters. 20. Actual versus Superficial Contents of Sawed Lumber. The variation between actual cubic contents of sawed lumber, and the superficial contents as expressed in board measure, must not be overlooked in Forest Mensuration. Log- rules for board feet are uniformly based on the sawing of boards 1 inch thick. Mill tallies of lumber which is sawed scant, such as |-inch boxboard material, will con- sequently greatly overrun the scale of the logs, in so-called superficial feet, which is the number of square feet of surface measure regardless of thickness. On the 14 SYSTEMS AND UNITS OF MEASUREMENT other hand, hardwoods are customarily sawed to thicknesses sHghtly greater than 1 inch to allow surfacing down to full inch thickness, and this practice reduces the superficial yield in board feet as compared to softwood species which are commonly sawed scant. Either practice causes the actual output measured in board feet (§ 12) to differ from the scaled contents of the logs. The actual dimensions of board which are accepted as inch lumber and. other standard thicknesses, and the amount of difference, scanting or extra thickness, permitted, is standardized by trade prac- tice for each region and species.^ These differences in sawing affect the over-run of sawed lumber, which for the same log rule would thus be greater for softwoods than for hardwoods. 21. Round-edged Lumber. Most lumber is square edged in sawing. Close utilization by the box, match, sash and blind, woodenware, furniture and certain other industries has led to the sawing of logs " alive " or through and through into boards from which the waney edges are not removed by squaring. These boards, except when sawed from the middle of the log, have one face narrower than the other and owing to the taper of the log, the faces are not of uniform width throughout their length. As the lumber in such boards is closely utilized, its board-foot contents is computed by measuring the average wddth of the narrow face. The thickness is considered on the same basis as for square-edged lumber. Lumber of this char- acter is usually cut by portable sawmills and sold direct to factories. The scale at the factory is used to check that at the mill. This prevents taking advantage of the uncertainties of the method. The logging and sawing are paid for on the basis of the mill scale, which scale usually becomes the standard for measuring the contents of the standing timber. Round-edged lumber will yield from 10 to 20 per cent more scale than square- edged, the excess being greater, the smaller the logs sawed. For plank 2 inches or more in thickness, a loss is incurred both in utilization and in scaling by reason of the wane, which causes an excessive difference in width of the two faces. This loss is reduced by cutting 1-inch boards from the sides of the log (§ 51). Closeness of utilization of the tree and stand is increased by this method of saw- ing. Tops are sometimes taken down to 2 inches and never to greater than 4 inches. Branches which crook only in one plane are used. 22. Products Made from Bolts and Billets. Bolts are sections of logs still in the round, and less than 8 feet long, i.e., too short to be conveniently measured as logs. Billets are obtained by halving, quartering, or otherwise splitting or sawing bolts lengthwise. Bolts may be split into billets, each of which is intended to pro- duce one finished article, such as a wagon spoke or stave. These are measured by count. Billets of larger size may also be split from bolts. So-called shingle bolts are billets split or sawed from large trees, or blocks from thick slabs. Billets are also obtained by sawing bolts, and are then termed flitches, squares, slats, or blocks. Squares are used in turning out round articles, such as shuttles, spools and bobbins. On account of their regular form, squares are sold by count, or by bulk, on standards agreed on, the price being based on either the number or the board-foot contents. They may be sold by stacked cords. Bolts, and split or sawed billets of irregular form, not yet manufactured into squares, are sold by stacked cubic measure except in the case of bolts over 12 inches in diameter and over 4 feet long, which may be scaled by a log rule. The width of the stack is determined by the length of the product and may range from 22 inches to 5 feet and over. In 1 Lumber and its Uses, by R. S. Kellogg, 1914, Radford Architectural Company, Chicago, Illinois. PRODUCTS MADE FROM BOLTS AND BILLETS L5 this case a cord is a stack 4 by 8 feet but whose width is that of the given product (§ 99). Different customs prevail in different industries. Shingle bolts (split or sawed billets) are sold in lengths which allow three cuts. For 16-inch shingles, with 4 inches for trimming, the piece is 52 inches long. For 18-inch shingles, a length of 58 inches is required. The cord is 4 by 8 feet by the indicated width. Spoke manufacturers dealing in standard 30-inch spoke_ billets compute a cord as 4 by 8 by 2| feet, or 80 cubic feet. Others measure the cubic contents, using 128 feet for a cord. In the stave industry a cord measuring 4 by 11 feet by the length of the stave bolts is quite common. For 36-inch billets this gives 132 cubic stacked feet, but the rule is applied to billets of other lengths. Billets and bolts for tool handles are always measured by the rank, in cords measuring 4 by 8 feet by the required width. References Measuring and Marketing Woodlot Products, Wilbur R. Mattoon and William B. Barrows, Farmers Bulletin, 715, U. S. Forest Service, 1916, Wood Using Industries of New York, John G. Harris, U. S. Forest Service, New York State College of Forestry, Series XIV, No. 2, 1917. CHAPTER III THE MEASUREMENT OF LOGS. CUBIC CONTENTS 23. Total versus Merchantable Contents. Logs are measured to determine their total cubic contents with or without bark, or they are scaled for merchantable contents only. The total cubic con- tents is required in scientific studies of volume and growth and for such commercial purposes as make use of the entire volmiie of the log. The cubic contents is found by measuring the length and the diameter at one or more cross sections and computing the volume of the log as a whole, or by sections, from these measurements. Where the thickness of bark is measm-ed, the difference in volume of the log measured out- side and inside the bark gives the volume of bark. 24. Log Lengths. Softwood or coniferous logs are usually cut into even lengths, or multiples of 2 feet, and may be any length from 8 feet to over 60 feet, being limited only by the height and upper merchant- able diameter of the tree, the length of material demanded for manu- facture, or the convenience of transporting long versus short logs. Logs, especiallj' hardwoods, are sometimes cut to odd lengths or multi- ples of 1 foot. The standard commercial lengths for softwood logs vary from 10 to 22 feet, and average 16 feet. In hardwoods, log lengths average somewhat shorter, since utilization of shorter lengths is more common. Log lengths are marked off on the felled tree by notching with an axe. It is customary to use a wooden measuring stick 8 feet long, and divided into 2-foot lengths.^ For exact measurement of length, the steel tape, graduated to feet, and tenths instead of inches, is used. The log length is measured along the surface, which is assumed to equal the length of the axis. For commercial uses, an excess length of from 2 to 6 inches is required as a margin for trimming. For total cubic contents the logs or sections are measured to their actual lengths. ' The accidental chopping off of the top of the measuring stick sometimes results in short measurements. In some regions, notably in Southern pine, careless measure- ment of log lengths resulting in excess trimming allowance and odd lengths causes a waste in woods and mill, in trimming to standard sizes, of from 3 to 5 per cent of the total cut. This statement is based on careful measurements covering 14 years' experience in six states with eight different companies. 16 DIAMETERS AND AREAS OF CROSS SECTIONS 17 25. Diameters and Areas of Cross sections. Cross sectional areas are assumed to be circular in form, and were this assumption correct the measurement of any. average diameter would give the cross section. If B =" basal" area, or area of circle, D = Diameter of circle, 7r= Ratio, or 3.1416. Then 2?=-— = .7854D2. 4 But practically every cross section departs slightly from a true circle, and a large proportion are very eccentric, some showing a dif- ference of several inches between their longest and shortest diameters, and having an elHptical or oval form.^ No attempt is ever made to compute the actual cross sectional area of such eccentric sections. Instead, two diameter measurements are taken at right angles and the average of these is assumed to be the average diameter. A circle with corresponding diameter is assumed to have the same cross sectional area as that of the actual section. Usually the longest diameter is taken, and one at right angles to it, through the geometric center of the section.^ Abnormal cross sections are occasionally encountered in which the average diameter of the section and its area are either too large or too small to give the volume accurately owing to some distortion in form of the log as a whole or of the portion 1 The area of an ellipse is TrDd B = -, 4 when D and d represent the long and short axes. D+d The area of a circle whose diameter is calculated as ■ is 2 n = . 4(2) Then w(D+dy- irlM _Tr (D-dy 4(2) 4~"4 (2) ' which is equal to the area of a circle whose diameter equals one-half the difference between D and d. This correction which is always minus, is ignored in measuring cross-sections. 2 In determining the average diameter, no attention is paid to the growth rings or the position of the pith or growth center of the section. In eccentric cross sections the pith is always found some distance to one side of the geometric center, which is the point through which the diameter measurement must fall. 18 THE MEASUREMENT OF LOGS. CUBIC CONTENTS measured. Abnormally large sections are found at forks or at the base of limbs or are caused by swellings. Stumps cut low give a section averaging much too large to indicate the true volume of the log, due to the rapid flare of the butt. Abnormally large diameters at the top end of logs should be measured by reduc- ing the diameter to what the log would have if it held its regular form. Where flaring butts are measured, the errors incurred may be serious. It is preferable to adopt a method which does not require this butt measurement, or else to subdivide the log by caliper measurements into shorter sections. Abnormal cross sections caused by limb swellings, or knots, should be measured, if possible, by taking the diameters at equal distances above and below the swelling. When logs are cut to small diameters in the top, the log may taper rapidly in the last few feet, and the disproportionally small diameter at the top will reduce the computed volume of the log as a whole. This problem may be solved by measuring the tapering portion separately as a short piece. In commercial scaling of logs which have abnormal diameters, the scaler should apply a measurement which in his judgment will give the correct contents of the log. In ordinaiy scaling, the diameter of logs is expressed in the nearest inch with fractions entirely dropped or rounded off (§83). For accu- rate volume measurements, each diameter is secured to the nearest tenth of an inch, for which purpose the rule or cahpers used must be graduated to tenths. In commercial practice, thickness of bark is never included in measuring the diameter of a log except when the bark is to be utilized, as for fuel or tannin,^ in which case the diameter is measured outside the bark. When the diameter of the log is taken in the middle, the thickness of bark must be ascertained and deducted. For accurate volume measurements, thickness of bark on one side may be determined by notching and measuring to the nearest tenth of an inch. Double this thickness when deducted gives diameter inside bark. Or the bark may be stripped from opposite faces in order to apply the calipers directly to the wood. This latter method is laborious and is seldom used even in scientific volume determination. 26. The Form of Logs. Logs diminish in diameter from butt to top, corresponding to the form and growth of trees. This difference or loss in diameter at successive distances from the butt, is termed taper. The taper of logs gives them their characteristic foi'ms. On account of this taper, logs are never truly cylindrical no matter how closely they may approach the cylinder in form. The geometrical forms to which logs can be compared must there- fore be circular in cross section and tapering. The forms suitable for this purpose are the paraboloid, cone, and neiloid. 1 Exceptions to this practice may be found in some regions, in scaling, when the log rule in use gives a large over-run which is offset by including width of one bark (§83). FOEMUL^ FOR SOLID CONTENTS OF LOGS 19 These three sohds form a series of successively diminishing per- centages of the volume of a cjdinder of equal basal area and height." Each tapers to zero at the tip. But logs are cut with two parallel faces at the two ends. The corresponding solids are the truncated forms of these bodies, termed frustums, as shown in Fig. 3. Fig. 3. — Forms of the cylinder, paraboloid, cone and neiloid, and truncated forms or frustums of the last three solids. 27. Formulae for Solid Contents of Logs. The comparative vol- umes of these four solids are stated by formulae below; when 5 = Area of base, square feet, 6| = Area of cross-section, at | height, 6 = Area of top, /i = Height or length, in feet. 1 Each of these solids is formed by the revolution of a curve about a central axis. A true Appolonian paraboloid is derived from that form of a conic section (a symmetrical curve formed by the intersection of a plane with a cone) in which the plane is parallel with the side of the cone. For the conoid formed by the revolution of this curve about its axis, the ratio between a cross section taken at right angles with the axis at any point, and the height above this point to the apex, is constant Bh for all points on the axis. This gives a volume equal to — . Logs which taper regularly will have straight sides, and resemble a truncated cone. Logs whose taper is most rapid near the butt, diminishing towards the top, will have concave sides and resemble a truncated neiloid. The form and volume of such logs will usually fall somewhere between a neiloid and a cone. Most logs taper more rapidly at the top than at the butt and will have convex sides, and resemble in form a truncated para- boloid — -their volume usually falls between that of a paraboloid and a cone. Where most of the taper occurs close to the top, the log may exceed the paraboloid in volume, falling between it and the volume of the cylinder. 20 THE MEASUREMENT OF LOGS. CUBIC CONTENTS Form Volume of perfect solid Volume of Frustum Cylinder Paraboloid Cone Neiloid Bh Bh 2 Bh y Bh T Bh (B+b) h h, or {B-\-h) ^ . Smalian's Formula z z h\h. Huberts Formula (B+b+Vs-b)^ o h (B+Abh+b)-. Newton's Formula 6 Newton's formula will also give the volume of the cone, paraboloid and cylinder. The per cent of the volume of the cylinder which is contained in the other three forms, when of equal diameter at base and equal height, is Paraboloid 50 per cent Cone 33^ per cent Neiloid 25 per cent But each of these three solids decreases in cross section from base to tip, while that of a cylinder remains the same. The frustum of a cylinder is always a cylinder, while the frustum of a paraboloid, cone or neiloid with equal basal area tends to more nearly resemble a cyhnder as the area of its top section approaches that of its base, which results when the relative height of the frustum is shortened. The per cent of the cubic contents of a cylinder of equal base and height, which is con- tained in these frustums increases in the same manner, and the possible limits of variation in form and volume between the cylinder and each of the other three frustums correspondingly diminishes. E.g., when the height of the frustum is one-fourth that of the perfect solid, the per cent of cylindrical volume is, for Frustum of paraboloid 87 per cent Frustum of cone 77 per cent Frustum of neiloid Gl per cent When the height is one-eighth of a perfect solid, these per cents are: Frustum of paraboloid 94 per cent Frustum of cone 88 per cent Frustum of neiloid 77.5 per cent A rapidly tapering log forms a truncated section of a relatively shorter completed paraboloid or cone than a log with gradual taper. The greater the height of a com- plete paraboloid with a given basal area, the less it will taper for a given length, as 16 feet. Whether the taper is rapid or gradual, a log may exactly resemble the frustum of a paraboloid, cone, or neiloid, RELATIVE ACCURACY OF SMALIAN AND HUBER FORMULA 21 Provided it has the true form of one of these soHds, its volume can be exactly determined by employing the corresponding formula. But the true form of the log may fall anywhere between the fixed points or forms in the series, which are marked successively by paraboloid, cone and neiloid, and in this case the volume even when calculated by the formula which corresponds most nearly to its Lrue form, will still be in error by the amount of this divergence. This error may be excessive for long logs. But by taking advantage of the effect of reducing the proportional height of the frustum, the probable error from this source may be reduced to any desired limit of accuracy. This is done simply by shortening the length of the logs, or by dividing each log into several shorter sections, measured separately. It is then no longer necessary to employ two or more forms arbitrarily according to the variations in the form of the logs, but a single standard geometric form may be chosen, which most nearly resembles the average form of logs, and the same formula? applied to all logs measured. The paraboloid comes nearest to answering this requirement, and for this reason the Smalian formula and the Huber formula have been generally adopted for both scientific and practical measurements of cubic volume of logs, to the exclusion of the formula? for cone and neiloid. 28. Relative Accuracy of the Smalian and the Huber Formulae. Logs having the form of a truncated paraboloid are measured with absolute accuracy regardless of their taper by either Ruber's or Smalian's formula. But if the form of the log is more convex and lies between that of the paraboloid and the cylinder, the Smalian formula, measur- ing the two ends, gives too small a result, while the Huber formula will give too large a volume. Nearly all logs lie between the frustum of a paraboloid and the frustum of a cone in form, having slightly convex sides, but not the full form of the paraboloid, so the end area formula (Smalian's) shows an excess, while the middle area measurement (Huber's) gives too small a result. In either of the above cases, the error by Huber's formula is one-half that of Smalian's and opposite in character. Newton's or Prismoidal Formula. To check the accuracy of measure- ments made on sections of given length and to determine the maximum length of section which will secure the desired degree of accuracy, the prismoidal formula may be applied. This formula is correct for cylinder, paraboloid, cone or neiloid, and consequently for logs of regular form whose volume lies within these extremes. It will not measure accu- rately eccentric or. distorted forms resembling none of the above solids. The formula requires the measurement of both ends and the middle section, and is known as Newton's formula. When the form of logs resembles more closely the cylinder, cone or 22 THE MEASUREMENT OF LOGS. CUBIC CONTENTS neiloid than the paraboloid, the errors in the use of the Huber or the Smahan formula may easily be checked by the above formula.^ 29. The Technic of Measuring Logs. By either of the two para- boloidal formulae, Ruber's or Smalian's, the area of a single average cross-section is obtained which, multiplied by the length of log, gives the cubic contents. By the Smalian method, this area is the average of two cross-sections, while by the Huber method it is obtained directly. The volume of the frustum, or log, is thus equal to that of a cylinder of equal height, with a base equal in diameter to the average cross- section. Diameters Measured at Ends of Log. Diameter inside the bark is usually required, and is best obtained at the exposed ends of the log. But if only the small end is measured, the corresponding cylinder does not give the cubic contents of the log on account of neglect of its taper (§ 26). Although almost universally practiced in scaling for board feet, this single measurement is never used to scale cubic contents. The choice lies, therefore, between the single measurement at middle of log, or the averaging of two end areas. The volumes of cylinders vary directly as their basal areas, or as D^, and not as their diameters. Hence an accurate procedure would require first, measurement of each diameter; second, determination of each corresponding area; third, averag- ing these areas; fourth, computing the corresponding diameter. The volume of a cylinder of this diameter and length is required. Such a procedure is practical only in scientific studies; in scaling, the two end-diameters are averaged directly. The assumption is that, 1 The following formulae are cited by Guttenberg, in Lorey's Handbuch der Forstwissenschaft, 3d Ed., Chapter XII, 1913. Breymann, V=\{B+b+2,h\+hl) o Hossfeld, F=^(36i+6). 4 Simoney, V = ^(2(h\+h\)-hh). While the substitution of the Hossfeld formulae for that of Smalian on butt logs would give far more accurate results, and would be closer than the Huber formula, the point one-third from butt is not ordinarily measured in the field and is trouble- some to ascertain. Hence this formula is impractical. The same objection applies to Breymann's. Simoney's formula has no advantage over either Huber's or Smalian's, since by using the small lengths, one-fourth log, the latter formulae will secure results within 1 per cent of the true volume for the standard 16-feet length. THE TECHNIC OF MEASURING LOGS 23 This gives a slightly smaller volume than by the correct method. The error increases as the square of the difference between the top and the bottom diameters. • This error, expressed in per cent of total contents, falls below 1 per cent for logs not over 16 feet long with a taper of 2 inches or less. It also tends to offset the plus error caused by the use of the Smalian method as a whole ( § 28) . The error increases with length of log scaled as one piece. A far more serious source of error by this method is that due to the flare of butt logs. Due to the excessively large cross-section thus obtained at the butt, this error may give an excess cubic volume for the log of from 10 to 20 per cent. Chiefly for this reason, the end area method is confined in practice to scientific studies of volume, in which the length of the sections can be regulated to reduce this error, and time is not the determining factor. For such studies, the computation of average basal areas is no drawback. The volumes of the lengths into which the log is to be divided are more conveniently computed by the Smalian formula than by the Huber formula, which requires the middle diameter of each short section. Smalian's mean end formula is therefore universally adoi)ted in these studies, Diameter Measured at Middle of Log. Since it is impossible to measure the diameter at the middle of a log unless the log is exposed, logs cannot be scaled by this method if they lie in large rollways or piled one on another. The scaling for cubic contents therefore requires a time and place for the work where each log is exposed for its entire length and is less convenient than scaling for board feet ( § 83) . By measuring the middle diameter, the error due to flaring butts is avoided. But this practice requires, in addition to total length, the determination of this middle point. The use of calipers is required, since it is impossible to obtain consistent accuracy by placing a scale stick across a log and judging the diameter; the error thus incurred is always minus. This method is therefore termed a caliper scale. In applying a caliper scale, the double width of bark is subtracted either by taking off a fixed average thickness or bj^ adjusting the calipers 1 The error in use of mean diameters is shown as follows: Volume of truncated cone may be expressed as, V = ^JiiD-'+Dd+d''). Volume of cylinder having a basal area equal to the mean diameter of the log is, 4 2 Then, 12 4 2 12 2 ■ The minus error thus shown is equivalent to the volume of a cone having a basal area equal to the difference between the mean end diameters of the log. For the paraboloid, this error equals the contents of a cylinder with a basal area equal to that of the above cone. The error thus increases with the total taper of the log. 24 THE MEASUREMENT OF LOGS. CUBIC CONTENTS to read that much less in diameter for all logs alike. For more accurate scaling the width of bark is deducted separately for each log. The caliper scale is the more accurate of the two methods for commercial use. The volumes by this formula, in average logs, are slightly below the actual contents.^ Where the length of a log exceeds that which can be accurately measured as one log by the above methods, the practice is to consider it as composed of two or more shorter sections. By Smalian's method, the intermediate points measured are taken as the ends of these sec- tions. By Ruber's method, the middle point of each section is found. In either case, calipers should be used. The length of section which can be measured without subdivision depends primarily on the rapidity of taper. Logs or sections whose total taper does not exceed 2 inches may be scaled or measured as one piece regardless of length. In com- mercial scaling logs less than 18 feet long are seldom subdivided. In scientific studies 8 feet is usually the maximum length between measure- ments of diameter, and 4 feet is often required for the first or butt sections. 30. Girth as a Substitute for Diameter in Log Measurements. The circumference of tlie circle, corresponding to the girth of the log, may be used to determine the area of the cross-section.- In this case, if (7 = girth, and B = Basal or end area, 47r A tape is used in which the results are read directly in inches of diameter, each inch being equal to 3.1416 inches on the tape. A pin in the end of the tape enables one man to encircle the log. The ratio between diameter and circumference, tt, holds good only for the circle. The more eccentric the cross-section, the greater this ratio becomes, and the smaller the actual area in proportion to girth. Hence, whatever error occurs by this method tends to give a cross- sectional area greater than the actual area.'^ 1 Tests of 4398 spruce and fir logs measured in lengths up to 40 feet by this method in Maine indicated that the scale required a correction factor of 1.049 or 4.9 per cent over-run. The Measurement of Logs, Halbert S. Robinson, Bangor, Me., 1909. 2 Girth measurements are commonly used in India, and in commercial measure- ment of imported logs in England. In the United States, the girth of large logs is sometimes taken, when more convenient than the measurement of diameter, but G the result is reduced to diameter by the formula D = — = .3183G. TT ' Mensuration of Timber and Timber Crops, P. J. Carter, Office of Supt. of Gov't. Printing, Calcutta, 1893, p. 2. GIRTH AS A SUBSTITUTE FOR DIAMETER 25 One advantage of giith measurements over diameter is that two measurements taken at the same point give consistent results, while in determining the average diameter of large and irregular or eccentric logs, considerable differences may occur in two separate measurements. Owing to the difficulty of measuring the girth of a log at its middle point, the mean of the two ends may be taken. This incurs an error identical with that by the mean diameter method (§29). This error is offset by the tendency of .girth measurement to over-run. The volume of the cylinder whose basal area is obtained from girth may be found by the method of the Fifth Girth in which G is here expressed in feet. If measured in inches, divide the result by 144. Another method, known as the Quarter Girth, is expressed as F=(f)\.113. In this formula G is expressed in inches.^ 1 The Fifth Girth method will give a result which is only approximately correct. G=irD, —— n should equal I — I 2/i, therefore, and — should equal ( I X2, 4 \5/ .7854 should equal .6283= X2, .7854 should equal .7895, an error of less than 1 per cent. The Quarter Girth formula is of no particular value as it is merely a means of correcting a commercial standard ( § 35 Hoppus or Quarter Girth Log Rule) to obtain the full volume of the cylinder. CHAPTER IV LOG RULES BASED ON CUBIC CONTENTS 31. Comparison of Log Rules Based on Diameter at Middle and at Small End of Log. Log rules giving the contents of logs in cubic feet should be based on the diameter inside bark at middle of log. If, instead, the diameter is measured at the small end of the log, the indi- cated contents falls short of the true cubic volume (§ 29). But the measurement of diameters at the small end of logs rather than at the middle point is so great a convenience in log scaling ( § 83) that efforts have been made to find a converting factor, or ratio, by which the true contents of logs may be correlated with diameters at the small end, and expressed directly in a log rule based on these diam- eters. Since the true contents is assumed to be equal to the cylinder whose diameter is that of the log at its middle point, the ratio or factor desired is the multiple required for converting the volume of the smaller cylinder whose diameter is measured at the small end of the log into the true cubic volume of the log taken as equaling this large cylinder. This ratio is influenced by three factors— namely, rate of taper, length, and diameter of the log. A log rule, if based on the same conversion factor for logs of all sizes and tapers, will give correct volumes only for a log of a given diameter, length and taper and will be in error for logs of all other dimensions, A log rule based on separate conversion factors for logs of each diameter but making no further distinction for different lengths or tapers will give correct volumes only for logs of a specific length and rate of taper in each diameter class, and will be in error for all other lengths and tapers. A log rule based on separate conversion factors for each different diameter and length, can be applied accurately to obtain the average scale of logs of all diameters and lengths only in case the average taper of the logs scaled agrees with that of the logs measured in determining the factor used, and is in error when the average taper of the logs scaled is greater or less than this. While these conditions apply to log rules based on measurement at the small end of log, a log rule based on measurement at middle of log is correct for all the above conditions, incurring only the errors due to divergence in shape of log from that of a paraboloid. The ratio of volumes, and the loss in scaling legs by a rule based on the cylinder measured at small end, are illustrated in Table I. The figures in the last column represent the loss in scale expressed in per cent of the volume scaled, e.g., a 16-foot log 6 inches at the small end with 2-inch taper contains 36 per cent greater volume than shown by the scale. 26 COMPARISON OF LOG RULES BASED ON DIAMETER 27 a >j ij ■< s m < Q < a Over-run. Per cent (N CO ^ ^ t^ COi-fCOCMt^ COtI CO CM t> t^cOCMO-* COI>rH00CO CCrHr-t l>COfOt^CO t>.OOCM.-H rH i> CO CO t^ CO !>• CO C.t>.C5CDQ0 I>|>TJHC0CM Proportion of total contents scaled. Per cent Tt<(Nt^(Mt^ CO lO --1 CO 05 C0>0 --I CO c» O COO lO 05 fO>0 05(M CO t>. GO 00 0105 CO CO --no t^ k01> 00 00 00 COCOt-i lO t^ 1CI>00 00 00 CO CO t^ CO t-- COuOCOt^l^ Loss in cubic con- tents. CI O GO CO 00 CO l> lO 05 t>- i— 1 1> IC CS t>. i-H O b- O IC tH coco OOTfHCM Ttl CM T-H T-H T-H CO CD 00^ CM ■* CM T-H .-1 r-H "* CO cocoes COTjiCOCMCM Id ■* 00COt^(M ^ ^ CM C<) CO o> 00 CO ic ■* OOOCM Tt< CO »OC0 rf CM CM •^ lO CD t^ 00 t^ CO CM O 00 ^ >oo5co CO .-H(N COrtH lO CMrfcOOOO -H 05 t^ CO ^ ^ ^ CM CO '*< H <1 Q H iJ <) O m 03 H o O o m O Middle. Cubic feet C^I>iOiO00 t^rH^HOOCM >-HCM00O5I> O O .-H 05 CD lOrH © OCO lOOO t^ CO CO Tt< CD T}H oot^ rjl TjH .-(•>!*< CO tHCOiOOO i-HrtH Oit^ 00 T-H CO COi-H t^ lOt^-"* 00 Oi tH CO lO 00 t>- •* 'J^ CO T-H T-ITJH oocoo .-iCM Small end. Cubic feet CO CO lO CO 00 CM T-H iO O O .-HiOCMCMiC 00 CO lO CO 00 CMt-HOiO c COIM OOO CO coiocoot^ CM lOOiO I— 1 1-H CO CM 00 O 00' i-H CM »C t^ CO lOcO o t^ CM lO C "O Diameter at middle of log. Inches t^ CO 05 lO ^ ^ ^ CM CO 00t)< O COCM ^CM CMCO 00 --^O CD CM --H CM CM CO OCOCM OOTfH ■-I —1 CM CM CO Diameter at small end. Inches CD CM 00 ■* O -H rH CM CO CO CM 00 "*0 ^r-lCM CO CO CM 00 '^ O ^^CMCO CD CM 00-* O >-• >-i CM CO Total taper. Inches C^l 'I* '^ GO Taper per 16-foot length. Inches CM CM ■^ ■* Length of log. CO CM CO CD CM CO 28 LOG RULES BASED ON CUBIC CONTENTS Table I indicates that the per cent of error resulting from assuming that the total contents of a log is equal to that of the cylinder measured at the small end decreases with increased diameter, increases with the total number of inches of taper in the log but for logs with a given diameter and the same number of inches of total taper, the per cent of error is the same regardless of the rate of taper or length of log, and is determined by the difference in volume of the cylinders based respectively on diameter at small end and middle of log. 32. Log Rules in Use, Based on Cubic Volume. There are two classes of log rules in use, based on cubic volume. The first class gives the actual or total cubic contents of the log. The second class gives the volume of sawed lumber expressed in board feet, but these rules are based upon the use of a fixed ratio of conversion from cubic volume and not upon the volume of sawed lumber which can actually be obtained from logs of different sizes (§ 39). Cubic measure was early adopted in log measurements, but owing to the fact that logs are roughly cylindrical in shape, the custom grew up of using the contents of a cylinder of standard dimensions instead of the simpler standard of the cubic foot. There is no advantage in this substitution of new arbitrary cubic standards for the cubic foot.^ The principle used in the application of such a standard ^s that the volumes of cylinders of different sizes will vary as the square of the diameter multiplied by the length. The contents of all logs can then be expressed in a log rule in terms of the number of standards they contain. The Adirondack Standard, or Market. In the Adirondack region of New York several such standards have been used but the only one of importance is the 19-inch or Glens Falls Standard, termed also the Market.^ This is a cylinder 19 inches in diameter and 13 feet long, 1 The cubic meter is the standard of volume used in the Philippine Islands. Logs less than 8 meters (26j feet) long are measured as a cylinder whose diameter is the small end. The average diameter in centimeters is taken, the end area is obtained from tables and multiplied by the length of the log in meters to give the volume in cubic meters. For logs over 8 meters in length, the diameter at the middle is taken, or if this is impractical, the average of the diameters of the two ends is used. 2 It is assumed that one market equals 200 board feet which is 65.1 per cent of its cubic contents regarding the log as a cylinder measured at the small end of log and neglecting taper. This gives 7.8 board feet per cubic foot. Tests of actual output in board feet per market, sawed from 600 logs of each sepa- rate diameter, gave the results as shown in table on opposite page. The saws used were a band and a band resaw, both cutting i^-inch kerf. The lumber was 60 per cent 1-inch, the rest Ij-inch and 2-inch thicknesses. These ratios are therefore higher than for inch lumber sawed with j-inch kerf. The ratio is still further increased by the fact that the cubic contents measured does not include the entire log but only the cyhnder measured at small end while the sawed output is from the entire log. H. L. Churchill, Finch, Pruyn Co., Glens Falls, N. Y. Twenty-two-inch Standard, A different unit is in use to a slight extent LOG RULES IN USE, BASED ON CUBIC VOLUME 29 equivalent to 25.6 cubic feet. In application the log is measured at the small end and its contents are taken as that of the corresponding small cylinder. The taper is disregarded. * When Z) = diameter of standard log in feet or in inches; L ^ length of standard log in feet. The volume of the standard is .7854 D'^L. Let d and I equal the diameter and length of any other log, whose volume will be .7854 dH. The volume of any log is found in terms of standard units by the formula, J854dH__m_ .7854D2L~^' F = The market is still a common standard of log measure on the Hudson River watershed in the Adirondack region. Its neglect of the taper makes the Adirondack standard unsuitable for measurement of pulp wood, but were it applied at middle of log on the Saranac river drainage in New York, termed the Twenty-Two-Inch Standard. The standard log is here 22 inches at small end, and 12 feet long, containing 3L68 cubic feet. It is assumed that one standard equals 250 board feet which equals 65.8 per cent of the cubic contents of the small cylinder. There have been still other log standards, which are now obsolete. Diameter at Board feet Board feet Diameter at Board feet Board feet small end per per small end per per inside bark. market cubic foot inside bark. market cubic foot Inches Inches 5 1.35 5.3 13 228 8.9 6 155 6.0 14 236 9.2 7 168 6.6 15 243 9.5 8 179 7.0 16 248 9.7 9 190 7.4 17 252 9.8 10 200 7.8 18 255 9.9 11 210 8.2 19 . 257 10.0 12 219 8.5 20 259 10.1 In principle and practice, these standards coincide closely with the use of the cubic meter, the only difference being in the size or cubic contents of the unit. The difference in shape, or use of a cylinder instead of a cubic foot, is of no significance. Since the cubic meter contains 35.3156 cubic feet, the market is a smaller standard. The cubic volumes are convertible from one of these standards to another by using 25.6 the proper ratios; markets to cubic meters - — — - = .725; markets to cubic feet 25.6. 35.31 30 LOG RULES BASED ON CUBIC CONTENTS it would give accurate contents. This standard, in common with all other cubic rules, is unsuited to the measurement of the board foot con- tents of logs. 33. The Blodgett or New Hampshire Cubic Foot. A cylindrical unit has been adopted as the legal standard of the state of New Hamp- shire. The statute reads, " All round timber shall be measured accord- ing to the following rule. A stick of timber 16 inches in diameter and 12 inches in length shall constitute 1 cubic foot; and in the same ratio for any other size and quantity." This arbitrary cubic foot contains 1.396 or approximately 1.4 cubic feet. The contents of logs is computed in Blodgett feet by the formula, This log rule is based on the middle diameter, and is therefore more accurate in application than the Adirondack standards. The diameter is measured by calipers and double width of bark is deducted (§ 84). This rule is a rough attempt to use the cubic foot, with an allowance for waste in squaring round logs. But the per cent of waste by the rule is 28.4 per cent of the cylinder, utilizing 71.6 per cent, while the area of an inscribed square is 63.6 per cent of the circle with 36.4 per cent waste. The "squared" stick 1 foot long would therefore have considerable wane. The Blodgett Rule was an attempt to secure a standard which could be converted into board feet. The statute fixed the converting factor as, 100 Blodgett feet = 1000 board feet, or a ratio of 1 : 10 But in scaling practice it was concluded that this ratio was unsatisfactory, and gave too large a scale in board feet. So it was arbitrarily set in practice at 115 Blodgett feet = 1000 board feet, or a ratio of 1 :8.7, when the rule was applied, as intended, to the middle diameter inside bark. Though the scale in Blodgett feet in either case was the same, the converted resalt gave for the ratio of 1 : 10, 59.7 per cent of the contents of the log in board feet, and for the ratio 1 : 8.7, 51.9 per cent. Since 12 board feet = l cubic foot, 10 = 83g per cent of 1 cubic foot. 12 and Likewise, and 1 .831 .396 =.597. 8.7 12 " = 72.5 per cent. .725 = 519. 1.396 USE OF CUBIC FOOT IN LOG SCALING 31 In order to permit measurement of diameter at the small end of log instead of the middle (§31), a further modification of the rule more radical in its character was now made. The loss in cubic contents by measuring the small cylinder was offset by arbitrarily increasing the ratio of board feet to each Blodgett foot. This new ratio was set for logs of all sizes at 106 Blodgett feet = 1000 board feet. When compared with the cubic contents of the sinall cylinder this makes the ratio 1 : 9.44. For the ratio of 1 : 9.44 the per cent of the small cylinder scaled as boards is 56.2 per cent. But for the true cubic contents of the log the ratio would vary with length and taper of log ( § 31) . 9.44 12 " ■ 78f 1 396 = 56.2 per cent. From Table I, § 31, the following comparisons can be made between the volume thus expressed and the true volume. Taking 16-foot logs with 2-inch taper, Diameter of log. Inches Per cent of total con- tents of log in small cylinder Per cent of total con- tents scaled as boards by above ratio of 56.2 per cent. Per cent 6 12 18 24 30 73.4 85.2 89.7 92.2 93.7 41 2 47.8 50.4 51.8 52.6 The attempt to convert this rule to apply at small end gives values which agree with the current ratio of 115 Blodgett feet to 1000 board feet in 16-foot only when these logs are 24 inches in diameter and with 2-inch total taper, while for 6-inch logs, 41.2 tapering 2 inches the scale is or 79 . 3 per cent, incurring a loss of 20 . 7 per cent 51.9 of the true cubic scale measured at the middle point. Thus the change in point of measurement destroys the consistency of this log rule for cubic contents, while the conversion to board feet introduces still another error, discussed in § 42. The rule should either be used for Blodgett feet only, as a cubic measure, and applied only at middle diameter, or if the end diameter is used, the conversion factor should have been separately computed for logs of different diameters and lengths on basis of an average taper. 34. Use of Cubic Foot in Log Scaling. The cubic foot has been substituted for the Blodgett foot as the basis for measuring logs, by the U. S. Forest Service on the National Forests in Maine and New Hampshire. 32 LOG RULES BASED ON CUBIC CONTENTS A caliper with a long arm to the end of which is attached a measuring wheel, is used. The wheel consists of ten spokes, each tipped with a spike, and all painted black except one, which is yellow. The tips of the spokes are 6 inches apart. The yellow spoke is weighted. When the wheel is run along a log, each revolution as comited by the yellow spoke measures 5 feet, and the remaining spokes permit the length of log to be measured to the nearest 6 inches. The measuring wheel is run the length of the log, and then brought back to the center, at which point the caliper measurement is taken. Allowance for bark is made by moving the caliper jaw inward by a distance in inches equal to the estimated double width of bark on each log separately. The diameter in inches is stamped on one edge of the arm, and around the base of the arm are placed standard lengths running from 8 to 34 feet. Opi)osite each length, and below each diameter, on the arm, is stamped the cubic volume of a log of these dimensions. The lengths are also stamped on the movable arm. When the log is caUpered, the scaler reads the volume which lies opposite the proper length, Fkj. 4. — Caliper scale for measuring logs in middle, outside bark, with wheel for determining length of log. the diameter being indicated by the position of the movable arm after calipering the log and taking off the bark correction. Defects are then deducted from the gross volume, either by measuring the defective portion or by ocular estimate of the volume of the defect. J. J. Fritz, Gorham, N. H., 192L Note. In 1909 a commission of investigation recommended to the Maine Legislature the adoption of the cubic foot as the statute rule of Maine. This was not done. One lumber company, Hollingsworth & Whitney, Waterville, Maine, has since 1904 used a cubic foot standard, measuring the middle diameter with caU- pers, outside bark. The rule then allows 12^ per cent deduction for volume of bark, and gives the net cubic contents of solid wood. The per cent of volume of bark is not constant but varies with the size of tree and its age and exposure. The arbitrary figure chosen simply represented the approximate average volume for the species and region in question, namely, spruce and balsam in Maine. A converting factor for this rule has been suggested, of 185 cubic feet to 1000 feet B. M. This gives 5.4 board feet per cubic foot, or 45 per cent of the cubic con- tents when measured at the middle. Reduced to diameter at small end, for a taper of 1 inch in 8 feet, logs 18 inches in diameter would give 50 per cent of the small LOG RULES FOR CUBIC CONTENTS OF SQUARED TIMBERS 33 cylinder in board feet. This suggested ratio is therefore lower than those adopted for the New Hampshire and most other converted cubic log rules. Note. Weight as a Basis for Measuring Cubic Contents. Actual weight of logs is seldom used as a basis of measurement, as the variation in moisture contents caused by seasoning prevents standardization even for a given species. A few valuable timbers are imported by weight. The long ton of 2240 pounds is used. The ton as ordinarily used in measuring timber is a cubic measure equivalent to either 40 or to 50 cubic feet and is usually applied to squared timbers. The unit of 50 cubic feet is also termed a "load" and is used in measuring teak. Red cedar logs are sometimes purchased by weight, on account of their extreme irregularity and the difficulty of measuring them. 35. Log Rules for Cubic Contents of Squared Timbers. A definite departure from the use of total cubic contents is found in log rules giving the cubic contents of the squared timbers which may be hewn or sawed from round logs. The waste constitutes the portion hewn or slabbed off. A square inscribed in a circle occupies 63.6 per cent of its area. Rules based on this principle would give a waste factor of 36.4 per cent of the cylinder scaled. Inscribed Square Rule. The width of a square inscribed in a 24-inch circle is 17 inches.^ The width of any other inscribed s(juare is seven- teen twenty-fourths of the diameter of the log. The cubic contents of the log is that of the square so determined, measured at the small end of log. The width of a square inscribed in a 17-inch circle is 12 inches, each foot of log containing 1 cubic foot of squared timber. The cubic con- tents of anv log is --=o-^- Bv either of these rules of thumb, the so-called 17*^ Inscribed Square Rule is obtained. The latter method is termed the Seventeen- 1 rich Rule. The rule gives 63.4 per cent of the cubic contents of the small cylinder, and proportionately less of the entire log depend- ing on taper, length and diameter (§31). Big Sandy Cube Rule. Synonyms: Cube Rule, Goble Rule. This Cube Rule, used on the Ohio River, assumes that it requires a log 18 inches in diameter at small end to give a timber 1 foot square. This rule scales 56.6 per cent of the small cylinder. The volume of logs of other sizes is found by the formula, jr)2 V = — L This rule is sometimes expressed in board feet by multiplying the cubic contents by 12. 1 The side of the inscribed square is found by squaring the diameter of the log, dividing by 2 and extracting the square root, 34 LOG RULES BASED ON CUBIC CONTENTS Two-thirds Rule. By this rule, the diameter of the log is reduced one-third, the remainder squared, and multiplied by the length of the log. As diameters are in inches the formula is F = (fZ))^ L^-144. This is a caliper rule applied to the middle area, and gives 56.5 per cent of the full cubic contents of the log. It is sometimes erroneously applied to the small end. Quarter Girth or Hoppus Rule. This rule depends upon the direct use of the girth, rather than diameter. The average girth is taken in inches at middle point, or by averaging both ends. Then V "={-7) L. This formula gives 78.5 per cent of the actual total cubic contents of the log. It is a commonly used standard for measuring round logs in England and India. To express the contents in cubic feet the result is divided by 144. 36. Log Rules Expressed in Board Feet but Based Directly upon Cubic Contents. The Blodgett or New Hampshire rule is not the only log rule based on cubic contents, which attempted to express the results in terms of board feet. Any cubic rule can be converted into board- foot form, in theory, by the use of a ratio similar to those used for the Blodgett Rule. The ratio for board-foot contents of one cubic foot is 12. Twelve 1-inch boards cannot be sawed from 1 cubic foot, but a squared timber 12 by 12 inches contains 12 board feet per linear foot. For con- verting the entire log directly into board-foot contents of squared timbers, it is evident that the ratio will be less than 12 board feet per cubic foot, due to waste in squaring the log, while the conversion into contents in inch lumber requires a still lower ratio. The characteristic of all converted rules is that a fixed multiple or converting factor is used, regardless of the diameter or taper of the log. The rules differ only in the converting factor used, and in the method of measuring the log, whether at middle, or end. Constantine Log Rule. This rule is merely the expression of the cubic contents of a log regarded as a cylinder, in terms of board feet, by multiplying the cubic contents by 12. The diameter is measured at the small end of log. The formula is ,. 7rZ)2 4X144 The rule is used to measure the contents of logs used for veneers. Cuban One-fifth Rule. This Rule is based on the square of one- fifth of the girth taken in middle of log. The formula when G is in inches is FORMULA FOR BOARD-FOOT RULES 35 The rule gives just 50 per cent of the total cubic contents of logs in board feet. This is equivalent to 6 board feet per cubic foot. This rule is extensively used for imported hardwood logs. The contents of logs in cubic feet is found by dividing bv 144 instead of 12. In practice, fractional inches resulting from the fifth girth are dropped as follows, e.g., Girth, .50, 51 or 52 inches Square, 10 bj' 10 inches 53, 54 inches 11 by 10 inches 55, 56, 57 inches 11 by 11 inches 58, 59 inches 12 by 11 inches, etc. Square of Two-thirds Rule. Sj^nonyms: St. Louis Hardwood, Two-Thirds, Tennessee River, Lehigh, Miner. This rule is derived from the Two-thirds Rule by multiplying the cubic scale by 12. The rule is used for hardwood logs in the Middle States, and for pine to some extent in the South Atlantic States, and is frequently erroneously applied to the small-end diameter of the log. Cumberland River Ride. Synonyms: Evansville, Third and Fifth. This rule resembles the Square of Two-Thirds Rule, in that one-third of the diameter is deducted and the remainder squared. But it differs, in that one-fifth of the volume of the squared stick is then subtracted for saw kerf, and the remainder converted into board feet. The rule is always applied to the small end of the log except for long logs, when the diameter at middle point is taken. This rule is used on the Missis- sippi Valle}^ and its tributaries, for hardwood logs. Square of Three-fourths Rule. Synonyms: Portland, Noble & Cooley, Cook, Crooked River, Lumberman's. In this rule, one-fourth is deducted from the diameter at small end, and the squared timber expressed in board feet. The rule was formerly used in New England but is now obsolete. Vermont Rule. This rule is derived from the Inscribed Square Rule by multiplying the values by 12. It is the legal standard of the State of Vermont. The contents of a 12-foot log may be calculated by a rule of thumb, by multiplying the average diameter of the top of the log inside bark, in inches, by half such diameter in inches. The rule is not extensively used even in Vermont, being supplanted by others, notably the New Hampshire or Blodgett Rule. 37. Formula for Board-foot Rules Based on Cubic Contents. Any board-foot log rule the values for which are obtained by deducting the same per cent from the cubic contents of logs of all sizes, may be expressed by the formula Board feet = (1 - C)^ X ^ X L, 4 144 36 LOG RULES BASED ON CUBIC CONTENTS in which C = total per cent of waste deducted from the cyHnder, 1 — C = per cent of cubic contents utiHzed, — j-7 reduces D'~ from inches to square feet, and 144 ^ ' 12 converts cubic feet to board measure. The formula, simplified, becomes Board feet =(1-C)^L. 4o But the important distinction remains, that some of these log rules are meant to apply to the middle diameter and others to the small end, and while the per cent subtracted from the cylinder measured is uniform for the rule, the per cent actually subtracted from the log is uniform only for those rules using middle diameter, and varies over a wide range for rules based on diameter at small end of log. Note. Obsolete Rules. The following log rules, obsolete or unused, are based on the above formula and principles: Saco River (Maine), Derby (Mass.), Partridge (Mass.), Stillwell's Vade Mecum (Ga.), Ake (Pa.), Orange River or Ochultree (Texas). A new rule, the Calcasieu (La.), deserves the same fate. The Tatarian rule (Wis.), which is based on this principle, gives approximately correct board- foot contents for a log of a given size. It has never been adopted in practice. 38. Comparison of Scaled Cubic Contents by Different Log Rules. In Table II is shown the comparative volumes, in per cent of total cubic contents, which are scaled by different log rules based upon cubic volume. These per cents represent the converting factor used to obtain the values given in the rule from the volumes of cjdinders. Note. The values in this table were obtained by applying the ratio between the volume of two cylinders 16 feet long, IS inches and 19 inches in diameter respect- ively. This ratio is 28.27 : 31.50. Log rules based on cylinder at small end then 28.27 scale but • or 89.7 per cent of their volume, to which the reduction per cent for 31.50 ' waste is applied; e.g., the Vermont rule wastes 36.6 per cent by the inscribed square method. Then, based on the small end, the per cent scaled is 63.4, but based on middle diameter for the above size, it is 89.7X63.4 = 56.9 per cent. The table gives a correct comparison of the different log rules which are constructed by using a fixed per cent of cubic volume. The per cents given for the rule under the first column, based on the point at which the rule is applied, are consistent for all logs. But the equivalent per cents obtained by converting the scaled contents into terms of the cylinder based on the other diameter — as middle, for logs measured at the end and vice versa, will vary as the relative contents of these two cylinders varies (§ 31). This will not change the rank or order in which the rules fall. The rules are tabulated in order of the relative per cent of total contents which they scale. There is no common standard for measuring the cubic contents of squared timbers. The Quarter Girth method gives the tullest measurements, while the others more closely approximate the net contents as given by board-foot rules, COMPARISON OF SCALED CUBIC CONTENTS 37 TABLE II Comparison of Per Cents of Cubic Contents of Cylinders Scaled by Various Log Rules, for Logs 18 Inches in Diameter at Small End, with 2-inch Total Taper Cylindrical contents measured inside bark Log rule Basis of measure-i Per cent of scale! Per cent deducted ment of cylin- der, in applica- tion of rule at small end. Per cent at middle. Per cent if measured at other point at middle at small end from contents of cylinder to ob- tain contents given in rule — For rules applied at small end at middle Cuhic Standards Market or Glens Falls standard 22-inch standard Blodgett or New Hampshire. . . Cubic foot — Maine Cubic meter — Philippines: Short logs Long logs 100 100 Cubic Log Rules for Squared Timbers Quarter girth or Hoppus Inscribe;! square Two-thirds Cube rule, or Big Sandy Log Rules Expressed in Board Feet but Based on Cubic Contents Constantine 100 Tatarian 84.0 Saco River 72 . 4 Derby 72 . 1 Square of Three- Fourths'. ! 71 . 7 Partridge j 68.8 Blodgett, converted, ratio 100; tolOOOft. B.M ! 63.4 56.6 100 100 100 78.5 56.5 59.7 89.7 89.7 89.7 56 9 8 50 89 7 75 4 65 64 7 64 3 61 8 111.4 111.4 111.4 87.5 62.9 66.5 11.4^ 11.4^ 11.4^ 12.5 36.6 37.1 43.4 16.0 27.6 27.9 28.3 31.2 33.5 10. 10. 10. 21.5 43.1 43.4 49.2 10.3 24.6 35.0 35.3 35.7 38.2 40.3 * Added. 38 LOG RULES BASED ON CUBIC CONTENTS TABLE 11— Continued Basis of measure- Per cent of scale Per cent deducted ment of cylin- if measured at from contents of der, in applica- other point cylinder to ob- tion of rule tain contents given in rule — For rules applied Log rule at at at at at at small middle. middle small small middle end. end end Per Per cent cent* Log Rules. — Continued 22-inch standard, converted, ratio 1 to 250 ft. B.M 65.6 58.9 34.4 41.1 Market, or 19-inch standard. converted, ratio 1 to 200 ft. B.M 65.1 58 . 4 34 9 41.6 Vermont 63.4 63.2 56.9 56.7 36.6 36.8 43 1 Vade Mecum (Stillwell's) 43.3 Square of Two-thirds 56.5 62.9 37.1 43.5 Ake 62.4 52.2 56.0 58.2 37.6 41.8 44 French's (Los Angeles) 47.8 Calcasieu 57.8 51.9 42.2 48 1 Blodgett, converted, ratio 115 to 1000 ft. B.M 51.9 57.8 42.2 48.1 Blodgett, converted, ratio 106 to 100 ft. B.M 56.2 50.4 43.8 49.6 Cuban One-Fifth 50.1 45.7 55.9 44.1 49.1 49 9 Orange River 50.9 54.3 Maine cubic rule, converted 185 cu. ft. per 1000 ft. B.M. . 45.0 50.1 49.9 55.0 Cumberland River 45.2 40.6 54.8 59.4 Delaware or Eastern Shore . . . 42.4 38.1 57.6 61.9 Of the cubic log rules expressed in board feet, the Constantine is frankly a cubic rule, converted from the cubic foot, but based on the small end of log. The rest are suitable neither for cubic contents nor for board feet, since they do not express the former nor do they measure the latter correctly (Chapter \). These rules are all convertible into cubic units or from one to the other, when based on cylinders measured at the same point. 7rD2 The formula. Board feet = (l — C) L, can be used to obtain the values for any 48 of these rules, by substituting for C the per cent given in the last two columns of Table II, e.g. RELATION BETWEEN CUBIC MEASURE 39 To derive the Inscribed Square rule, the cubic contents of cylinders from Table II are multiplied by 1 —36.6, or 63.4 per cent. To convert the Inscribed Square rule into terms of the Cumberland River rule; since 1 —54.8 = 45.2 per cent, the volumes of the two rules are as 45.2 to 63.4. The 45.2 Cumberland River rule gives of the Inscribed Square rule, or 71.3 per cent. ^ 63.4 ^ But the Hoppus Rule cannot be converted into terms of either of the above rules, since it is measured at the middle point, unless a log of a given diameter and average taper is assumed. 39. Relation between Cubic Measure and True Board-foot Log Rules. The conversion of these log rules from cubic to board feet is based on the erroneous assumption that logs of all dimensions when sawed into lumber will yield the same ratio of board-foot contents to cubic contents. In practice, the larger the log, the greater will be the ratio or per cent of its contents which makes lumber and the less the per cent wasted. For this reason it is not possible to use the same standard for scaling both the cubic- and board-foot contents of logs, no matter what converting factor is chosen. Cubic rules, converted to board-foot contents by a fixed ratio, tend to scale small logs too high and large logs too low, as compared to the actual sawed contents. The common mistake of the authors of these rules is to assume that once the sawed contents of a log of given diameter and length is found, the ratio obtained will apply unchanged to logs of all other sizes. These rules have therefore fallen into disrepute in the scaling of board feet, because of their inconsistencies for this purpose. For products such as pulpwood, which utilizes the entire contents of the log, these so-called board-foot rules give consistent results for logs of all sizes, but do not possess any advantage over the direct use of the cubic standard upon which they are based. On the other hand, if log rules are intended for the measurement of the actual output of 1-inch lumber, they must be based on other principles (§ 54). The two quantities of measurement, cubic volume, and squared board feet obtainable, are incommensurable unless the diameter and also the taper of each log is known. The lump sum of a lot of logs measured in cubic volume therefore, cannot be converted into board-foot measure except by readjusting each individual value by the diameter of each individual log. The use of these hybrid rules should be discon- tinued in favor of cubic standards on the one hand, and board-foot log rules based on correct principles on the other. CHAPTER V THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 40. Necessity for Board-foot Log Rules. In other lines of industry- it is not customary to measure raw materials in terms of the quantity of finished product contained therein. The volume or weight of the raw product is the basis of sale. On this basis logs would be sold for theu- cubic contents. But the purchaser of raw material must know approximately the quantity of finished product he can obtain from it before he can estimate its value. If the product is to be lumber, the possible yield of boards of certain qualities and grades determines for him the value of the logs. If it had been found by experience that all logs regardless of size would yield the same per cent of their contents in lumber, if sawed by the same methods, the cubic standard might have been universally accepted, as it was in the Adirondack region. But when it developed that there was no consistent ratio of cubic to board feet the only alternative was to measure the product directly as boards. That the board-foot log rule was needed is shown by the fact that such rules were originated independently in practically every lumbering region. The contents of the log in sawed 1-inch boards was placed on the scale stick, separately for each inch-class and each standard length. These board-foot rules soon became practically the universal standard of log measure, and are only recently being superseded where the logs are used for other purposes than lumber; they will continue to be a generally accepted commercial standard of log measure for the lumber industry as a whole, until such time as the original stands of timber of the country give way to smaller second-growth and closer utilization and probably as long as a large percentage of logs are sawed into linnber. 41. Relation of Diameter of Log to Per Cent of Utilization in Sawed Lumber. The sawed output from logs in board feet shows an increasing per cent of utilization with increasing diameter of the logs. This result may be expressed by the ratio of board feet produced from each cubic foot of total volume. This tendency is illustrated in Table III. The per cent of utilization in this table is based on the total cubic contents of the log as measured by Huber's formula at middle diameter inside bark. But practically all log rules for board feet base the con- tents upon the cylinder whose diameter is taken at the small end, in 40 RELATION OF DIAMETER OF LOG 41 which case the volume of the log lying outside the cylinder is neglected. On this basis, the apparent per cent of utilization would be con- siderably increased over the figures given in the table.^ TABLE III Relation of Cubic and Boaed-foot Contents op 16-foot Logs with a Taper OF 1 Inch in 8 Feet, Based on Tiemann's Log Rule, j^-inch Saw Kerf. (§ 63) Diameter inside bark at middle of log. Inches Cubic contents. Cubic feet Sawed contents, Tiemann Log Rule. Feet B.M. Ratio feet B.M. to 1 cubic foot Volume utiHzed Per cent 3 0.79 1 1.27 10.5 4 1.40 4 2 . 85 23.8 5 2.18 9 4 13 34.4 6 3.14 15 4.77 39.5 7 4.28 23 5.37 44.8 8 5.59 32 5.71 47.7 9 7.07 43 6.08 50.7 10 8.73 55 6.30 52.5 11 10.56 69 6.53 54.4 12 12.57 84 6.68 55.7 13 14.75 101 6.85 57.0 14 17.10 119 6.96 57.9 15 19.63 139 7.08 59.0 16 22.34 160 7.16 59.7 17 25.22 183 7.26 60.5 18 28.27 207 7.32 61.0 19 31 . 50 233 7.39 61.6 25 54.54 419 7.68 64.0 31 83.86 659 7.86 65.5 37 119.47 954 7.99 66.5 43 161 . 36 1301 8.06 67.2 49 209 . 52 1703 8.13 67.7 55 263.98 2159 8.18 68.2 61 324.96 2669 8,22 68.5 1 For a 16-foot log 12 inches at middle, with 2-inch taper, and scaling diameter at end of 11 inches, the cubic contents are 10.56 cubic feet, the ratio of board feet to cubic feet is 7.95, and the apparent per cent of utilization is 665 per cent as against an actual 55.7 per cent when the entire volume including taper is taken as the basis. For logs with considerable taper, which permits more lumber to be cut from the slabs lying outside the cylinder, the apparent per cent of utilization would be still greater, while the actual per cent utilized would in reality be lower for such rapidly tapering logs than for more cylindrical forms. 42 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS It is practically impossible to secure closer utilization than 70 per cent of actual total cubic contents of logs in the form of sawed inch lumber exclusive of the utilization of slabs, edgings and sawdust when circular saws whose kerf is j inch or more are used. By using band saws which cut a |-inch kerf and by producing a large per cent of timbers and boards thicker than 1 inch, thus reducing the waste from saw kerf, the utilization may rise as high as 80 per cent for the larger logs. 42. Errors in Use of Cubic Rules for Board Feet. By comparing the per cent of possible utilization in Table III (§ 41) with the per cents given for cubic log rules in Table II (§ 38) the character and relative accuracy of these log rules can be judged. For the Blodgett Rule, with a ratio of 115 units to 1000 board feet measured at middle diameter, the ratio or per cent scaled is 51.9 for all classes and sizes of logs. By comparison with Tiemann's Rule this* rule is shown to be correct for logs between 9 and 10 inches in diameter, but over-scales smaller logs, and under-scales larger logs. The original Blodgett ratio of 100 : 1000 gives a per cent of 59.7. This is correct for 16-inch logs, too high for all logs of smaller diameter and too low for larger logs. When the point of measurement is shifted to the small end of log, the diameter measurement is correspondingly reduced. When the scale of board-foot contents thus determined is compared with this smaller cylinder, the per cent of utilization can be expressed for such log rules and applies uniformly to logs of all sizes, but only to the small cylinder thus measured (§ 81). A comparison of the Blodgett Rule applied at the small end of log, with the Tiemann rule applied at the middle of log, is shown below. The per cents will apply to logs of all lengths whose total taper is but 2 inches. TABLE IV Comparison of Blodgett and Tiemann Log Rules for Certain Logs Diam- Total taper. Per cent of Per cent of Per cent of Per cent of Error eter small cylinder total log total log total log in log. scaled by in small scaled by scaled by Blodgett Inches Inches Blodgett Rule cylinder Blodgett Rule Tiemann Rule Rule 6 2 56.2 73.4 . 41.2 44.8 - 2.6 12 2 56.2 85.2 47.9 57.0 - 9.1 18 2 56.2 89.7 50.4 61.6 -11.2 24 2 56.2 92.2 51.8 64.0 -12.2 30 2 56.2 93.7 52.6 65.5 -12.9 Cubic rules, as a class, when converted to read in terms of board feet, thus tend to over-scale small logs and under-scale large logs, whether SCALING LENGTH OF LOGS FOR BOARD-FOOT CONTENTS 43 they are applied at the middle point, or at the small end. Of the two methods the small end gives the most consistent results in board measure, since both the actual per cent utilized and the per cent of total con- tents scaled decrease with diameter of log. But the decrease in scaled contents is always at a lesser rate than that of actual sawed contents, hence the tendency to over-scale small logs remains though the size of the error is reduced. 43. Taper as a Factor in Limiting the Scaling Length of Logs for Board-foot Contents. Since board-foot contents of logs is equal to cubic contents minus waste in sawing, the character and amount of .this waste determines the net scale of the log. This waste consists of saw- dust, slabs and edgings. As lumber is commonly manufactured with parallel edges, in even widths, the custom of sawing boards whose length equals that of the log and rejecting all shorter pieces would cause a waste not only of the slabs sawed from the cross section at the small end but of the entire taper of the log, which would be discarded as edgings and slabs. When board-foot rules were first brought into use close utilization of short lengths and of wedge-shaped pieces was not practiced, and this total waste actually occurred. Under these con- ditions the correct point of diameter measurement was not the middle, but the small end of the log. Owing to their early origin, the com- mercial board-foot log rules now in use are nearly all based on measure- ment at the latter point. This waste, as measured in cubic volume, increases rapidly with increasing length of log. The shorter the logs cut from a given tree, the less will be the apparent waste from taper. Long logs, the scaled contents of which are based on cylinders measured at their small end, would give an entirely different and much smaller scale than if the same logs were cut instead into two or more shorter sections and sawed into correspondingly shorter lumber. Instead of scaling one log of a given top diameter sometimes extending the entire length of the bole, we would then have to scale a series of shorter logs, each of which has a top diam- eter larger than the preceding one by the amount of the taper between the points measured. The sum of volumes of these short logs would always exceed that of the single log measured at small end. These long logs are usually cut into two or more sections at the mill. For these reasons, logs, if their length exceeds a definite maximum are scaled as the sum of two or more shorter logs, by taking caliper measurements at arbitrary points of division; e.g., a 26-foot log scaled as two pieces would be measured at its small end, and at a point 12 feet from the end, thus scaling as a 12-foot and a 14-foot log. The scaling diameter of the larger or butt section exceeds that of the top end by the amount of the taper between the points measured. Each section is thus scaled as a 44 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS cylinder, and measured at its upper or small diameter, and the sum of volumes of these cylinders gives the scale of the long log. The shorter these scaling lengths are made, the larger the total scale of the log, but the maximum scaling length must not be shorter than the average length of the lumber sawed. In log rules, figures for lengths up to 40 feet may be given, and scaling practice often corresponds, but in selling logs the U. S. Forest Service limits the scaling length to 16 feet, which is a standard commonly accepted by timber owners. 44. The Introduction of Taper into Log Rules. With the increase in utilization, much of the lumber formerly wasted in slabs is now secured as .short lengths. All log rules in commercial use ignore this product and treat the logs as if cylindrical, up to the maximum scaling length. To overcome this drawback and include the products from slabs or taper without requiring the measurement of logs in separate very short sec- tions, the International log rule was constructed,^ based on the principle Taper, 2 inches in 16 feet. Vertical scale exaggerated. Fig. 5. — Short versus long sections in measuring log contents and in constructing a log rule. of building up the scaled volume of a log from shorter cylindrical sec- tions. These short cylinders are 4 feet long and each successive cylinder is increased by |-inch in diameter. The scaled contents of each short section is determined, and the sum of these sections gives the scale of the log as given in the log rule. The soundness of this method depends upon demonstrating that the average taper of most logs is not less than that used in the rule, namely, 2 inches in 16 feet. This holds good for most Northern and Western species, but for Southern pines the taper does not always equal this figure. To guard against excessive error from tapers differing from the rate used in the rule, the maximum scaling length is limited to 20 feet. If the log in Fig. 5 is regarded as a 64-foot log, scaled in four 16-foot lengths by any commercial log rule, the scaling diameters are taken at A, B, C and D. The gain in scale is caused by inclusion of the shaded portions. 1 The Measurement of Saw Logs, Judson F. Clark, Forestry Quarterly, Vol. IV, 1906, p. 79. THE INTRODUCTION OF TAPER INTO LOG RULES 45 Regarded as a 64-foot log scaled by middle diameter the scaUng diameter is C, and the log content is that of a cylinder 64 feet long and of size indicated by C C . Regarded as a 64-foot log scaled by end diameter, the scahng diameter is A and the log content is that of a cylinder 64 feet long and of size indicated hy A A'. Regarded as a 16-foot log scaled at small end, and not in middle, the loss in scale is indicated by the shaded portions. This loss is common to all commercial log scales based on small end of log. But if the contents of the 16-foot log as given in the scale when measured at A is built up by measuring the log as four 4-foot cylinders whose scaling diameters are A, B, C and D, this loss from taper common to all the commercial log rules, except when apphed at middle diameter, is avoided and practically full scale secured. A comparison of the results of these three methods of treating taper is brought out in Table V. TABLE V Effect of Different Methods of Scaling a Log Length of log. Diameter inside bark. Scaling diameter rounded off. Scaled as one log based on small diameter. Scaled as 16-foot logs each regarded as a cy Under. Scaled as 16-foot logs allowing ^-inch taper every 4 feet. Feet Inches Inches Board feet Board feet Board feet (1) (2) (3) (4) (5) (6) 24.5 16 20.6 21.0 328 328 355 32 19.6 20.0 590 623 675 48 17.3 17.0 618 829 900 64 14.0 14.0 531 962 1050 The final column in each of the above examples is the contents of a log 4 feet long as scaled by the International log rule. The difference in scale by the other methods is due entirely to the length of section scaled as one piece. In column 4, this cyhnder, with top diameter indicated, extends the full length of the log. In column 5, a new diameter measurement is made every 16 feet, but the cylinder of this diameter is 16 feet long. In column 6, the diameter is taken at 16-foot intervals, but the cylinder from which this 16-foot log is scaled is built up from four cylinders each 4 feet long, and each |-inch greater in diameter than the one preceding it. If the average taper of logs is 5-inch for 4 feet, and pieces 4 feet long are mer- chantable, then the scale in column 6 is correct. Based on this conclusion the loss in scale through neglect of taper is as follows : Length of Scaled as one Scaled as 16-foot log. log. logs. Feet Per cent loss Per cent loss 16 8 8 32 13 8 48 31 8 64 51 8 Thus the loss in scale is proportional to the length and total taper of the log. 46 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 45. Middle Diameter as a Basis for Board-foot Contents. In some regions no attempt is made to divide long logs in scaling. While short logs are scaled at the end, logs over a given length are measured once at the middle and the scale applied to the entire log. In cypress this measurement is sometimes taken at a point distant from the small end by one-third of the total length. This practice of substituting middle for end diameters on long logs and scaling the log as one long cylinder whose diameter is thus obtained assumes that the loss in sawing the smaller top section will be offset by gain from taper in the butt portion. The total scale by this method exceeds that obtained by scaling the log as the sum of separate cylinders. In theory this measurement of logs for board-foot contents at the middle diameter should possess the same advantage over measurement at the small end as for cubic contents. But for the former purpose, the factor of waste exercises a definite influ- ence on the method of scaling adopted, where for cubic contents it does not. With very close utilization of short lengths, it may be assumed that the sawed output of two logs of the same middle diameter, one of which tapers rapidly, the other gradually, would be nearly equal, since what is lost at the small end of the rapidly tapering log would be saved at the larger end. That this is approximately true is the premise on which Tiemann based his board-foot log rule ( § 63) on middle diameter. If, on the other hand, the minimum length of board corresponds with the ordinary length of log sawed, the log with rapid taper loses a far greater percent than that with small taper, and two logs whose diameters at their small end are the same would give equal sawed contents regardless of differences in taper. Since the latter condition held when the log rules in common use were invented, this fact, and not the difficulty of scaling logs at the middle point, explains the general adoption of the custom of basing the contents upon the diameter at the small end. 46. Definition and Basis of Over-run. The purpose of all log rules is to furnish a standard of measurement for logs, fair alike to buyer and seller. For board-foot log rules this is best accomplished when the rule measures accurately the amount of lumber that may be sawed from straight, sound logs. It was the intention and the claim that each of the fifty or more log rules extant should perform this service under the con- ditions for which it was made; yet in spite of this fact, the contents of sound logs of the same dimensions, as measured by different rules, may differ more than 100 per cent. While some rules based on incorrect premises never were accurate, most of the rules as checked by actual mill tests were probably satisfactory when first employed. But these rules were not changed to keep pace with the closer utilization brought about by the improvements in machinery, methods and markets. Although obso- lete as a measure of actual product, they have been retained through custom. It is difficult to supplant or alter a commonly accepted standard of measure, even if grossly inconsistent and inaccurate. Antiquated log rules thus cease to perform the true function for which they INFLUENCES AFFECTING OVER-RUN 47 were intended, of measuring in the log the possible output of lumber. The sawed product tends to over-run the scale of contents shown by the log rule. An excess of sawed over scaled contents of logs is termed the over-run. The over-run is always stated as a per cent of the log scale. The log rule, whether accurate or defective, is accepted as the fixed standard, giving the same contents for all straight and sound logs of the same dimensions. Over-run, on the contrary, will vary with several factors. A knowledge of the average per cent of over-run which may be expected over the scale enables both buyer and seller of logs to gage their value more accurately. As value is dependent on the price of lumber, the dealer in logs must know whether for every 1000 board feet of lumber scaled by the log rule, there will be obtained say 1250 board feet of sawed lumber,' or only the 1000 board feet scaled, for in the former case the logs are worth 25 per cent more per 1000 board feet of scaled contents than in the latter. 47. Influences Affecting Over-run. The Log Rule Itself. Two log rules giving different scaled contents for logs of the same sizes will yield correspondingly different per cents of over-run. Each rule is arbitrarily assumed to represent a standard of 100 per cent, the over-run being computed in terms of the rule employed. For instance, a given quantity of logs when scaled by the Doyle rule may measure 67,000, and saw out 100,000 board feet. Instead of stating that the log scale gives 67 per cent of the actual product, with an "over-run" of 33 per cent, the scale is taken as the standard or 100 per cent, and the correct over-run in this case is 49 per cent. When scaled by the Scribner rule, these same logs may give 85,000 board feet. In this case the over-run will be 17.6 per cent since 15,000 board feet is 17.6 per cent of 85,000 board feet scaled in the log. Since the quantity of sound lumber contained in logs can be measured with only approximate accuracy, due to hidden defects and other factors, the buyer demands a certain margin of safety. A reasonable over-run of from 5 to 10 per cent is usually expected. With a properly constructed log rule, the over-run should be about the same for large as for small logs. The worst defect which a log rule can possess is inconsistency in scale between logs of different sizes (§39). Slight irregularities in scale of individual diameter classes may average out in the general run of logs. But when the per cent of board-foot contents scaled by a log rule increases or decreases in proportion to size of log, there is no way of adjusting it. The over-run will then vary with the average size of the logs scaled. Such a rule can never give permanent satisfaction to both the buyer and the seller of logs. 48. Influences Affecting Over-run. Methods of Manufacture. With a fixed standard set by a log rule, the greater the economy of man- ufacture, the greater will be the over-run. Any factor which reduces the waste in manufacture increases the output. The waste in straight, sound logs consists of slabs, edgings, trimmings and sawdust. In addi- tion, there may be a loss or gain in the scale of lumber due to fractional thicknesses not measured in board feet (§ 20). 48 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS Saw Kerf. The fewer the number of saw cuts required, the less the waste. Lumber sawed and measured to standard thicknesses greater than 1 inch therefore increases the total output in board feet. A dimin- ished thickness of the saw has a similar influence. Log rules, correct when adapted to a j-inch saw kerf, give an over-run of more than 10 per cent when a |-inch saw kerf i's cut. The use of circular saws cutting a j^-inch kerf partially accounts for the small scaled contents given by some of the old log rules. Slabs. Waste in slabs is reduced by sawing narrow and thin boards and short lengths. The short lengths serve to fully utilize the taper in long logs, increasing the over-run on this class of material. The method of sawing a log also affects the per ceril of utilization of slabs. Slash sawing, or sawing alive, as practiced for round-edged boards (§ 21) would result in waste where the boards are to be used in their full length, and trimmed to square parallel edges. By this method, short boards would be secured from but two sides of the log. The usual custom in manufacturing lumber of standard lengths is to turn and square the log, slabbing all four sides. The gain in sawed product, by sawing around, in comparison with slash sawing, for square-edged boards, was shown to equal the following per cents, as determined by H. D. Tiemann. TABLE VI Gain in Output Securei) by Sawing Around, Compared with Slash Sawing, IN Per Cent of Latter Output Diameter of log. Length 10 feet. Length 20 feet. Inches Per cent saved Per cent saved 6 15 22 7 14 18 8 13 15 9 12 13 10 11 11 11 9 10 12 G 7 13 : 4 6 Above 13 inches the difference is less perceptible. Where round-edged boards are fully utilized and not reduced to square parallel edges, not only does sawing around give place to slash sawing, but the per cent of utilization is much greater than by either method of sawing for square-edged lumber, due to the shorter lengths utilized in working up the round-edged lumber in the factory. STANDARDIZATION OF VARIABLES IN LOG RULE 49 Full and Scant Thicknesses of Boards. Boards not cut to exact dimensions, if cut full lose the excess when measured, and if too scant are either rejected, or reduced in grade. If cut scant but within pre- scribed limits, they are scaled by superficial measure, and increase the over-run (§ 20). In either case the sawyer to secure full scale of lumber must pro- duce boards measuring within j^-inch of the required thickness. This is impossible without good machinery. In local custom mills, much lumber is manufactured in uneven thicknesses causing a loss in scale and reducing the over-run. 49. Standardization of Variables in Construction of a Log Rule. The over-run in sawing logs will depend for a given log rule upon thick- ness of saw kerf, average dimensions of lumber, closeness of utilization of slabs and of taper, and the exactness of manufactured dimensions. All four of these factors are variables. For a given mill, the saw kerf alone is constant and even then the waste will vary if two or more saws of different kerfs are used. The other factors are variable. For different mills, one or more conditions are certain to differ radically, giving a corresponding increase or decrease in over-run. Standardization of output and methods, possible in mills of the same class serving the same markets, may secure a similar degree of slab utilization and of efficiency in sawing to exact dimensions, but this still leaves the fourth variable, differences in thickness of lumber sawed, to affect the over-run. Where the sawed output is in thicknesses less than 1 inch, and expressed in superficial feet, the product is not comparable with l-inch lumber and must be reduced to terms of 1-inch boards for a true comparison with the log scale. Arbitrary Standards. The essentials of any standard of measure are fixed qualities and common acceptance. Even a poor or faulty standard which is universally used would be better than a number of different rules, or a rule which may be changed to suit conditions or the preference of the user. These four variables must therefore be arbitrarily fixed in adopting values for a standard or common log rule, and in the case of most rules which have found wide use this was done. The thickness of lumber was fixed at 1 inch, permitting an over-run whenever thicker dimensions are sawed. The width of saw kerf adopted by the rule was that used at the time and place of constructing the rule, and was usually j-inch or larger. Local custom determined the width of the narrowest 1-inch board sawed and this fixed the amount of waste allowed for slabbing and edging. Taper was disregarded. Boards were usually measured only to the nearest full inch of width and fractional inches disregarded. SkUl in manufacture was considered by checking the results of the rule with the actual sawed output, by means of mill tallies. 50 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS Variable Sta^idards. As contrasted with these fixed standard rules, comes the suggestion ^ for a log rule in which average thickness of lumber, saw kerf and degree of utilization of slabs and taper shall be represented by variable quantities, and adjusted by each mill owner to suit the conditions of manufacture prevailing at the time or for the past few months. Such a rule, when adjusted, would eliminate over-run as long as the variables in manufacture on which it was computed remained unchanged. But as a standard of measurement it could never have any general or legal status unless its values were fixed, when it would at once be open to the same objections which by its flexibility it sought to avoid. 50. The Need for More Accurate Log Rules. The great question with log rules is whether conditions have changed so permanently that new rules adjusted to these factors should replace those now in use. The j-inch circular saw is still retained in small custom mills, and there is a tendency, in regions that have been cut over by big operators, to revert to these primitive methods. The operator of a band saw mill is probably entitled to the over-run resulting from the use of thinner saws and closer utilization. A log rule made to scale closely the out- put of such up-to-date plants would exceed the product of the small mill. Provided the rule is consistent, a conservative log rule which will give an over-run varying in per cent with closeness of utilization is probably better for commercial uses than one which aims at securing the maximum product from modern mills. Log rules based on correct mathematical principles are the only rules from which consistent and satisfactory results can be expected, and this is a far more important factor than the elimination of over- run. If, in addition, such log rules conform to the present conditions of manufacture, they have a use in scientific measurements of logs and standing timber, as a basis for estimates of volume and growth expressed in the board-foot unit. This use of such a rule would justify its exist- ence, entirely aside from the question of its possible universal adoption as a legal standard of log measure. 51. The Waste from Slabs and Edgings. The total waste in sawing straight sound logs is the sum of the two factors, sawdust, and slabs plus edgings. For lumber of a given thickness, such as 1-inch boards, the portion of the cross section of the log wasted in slabs and edgings may be shown graphically by plotting on diagrams, allowing the proper space between each board for saw kerf. From these diagrams it is possible to compute the area of this waste, in square inches, and the thickness of a ring or collar which will have the same area and thus represent the waste from slabbing and edging. 1 H. E. McKenzie, Bui. 5, California State Board of Forestry, 1915. THE WASTE FROM CROOK OR SWEEP 51 When this is done for logs of all sizes it is found that except for the smaller logs the width of these collars is practically the same regardless of diameter. This law does not hold for small logs, because the width of the minimum boards remains the same for all logs and as the diameter of the log approaches this minimum width of board, the proportional waste in slabs and edgings rapidly increases until utilization becomes zero and waste 100 per cent for a diameter of log just too small to saw out the smallest board or piece that is merchantable. The waste in slabbing and edging varies, for any log, with the aver- age thickness of the lumber sawed. Logs sawed entirely into 2j-inch plank would show considerably greater waste in edging than where 1-inch boards are sawed (§ 21). The results shown by diagram are confirmed by tests in the mill. From these investigations it is evident that the waste from slabs and edgings is proportional, approx- imately, to the surface of the log inside the bark. The surface of a log is equal to the circumference or girth, multiplied by the length. As circumference equals irD for all logs, the waste from slabs and edging p ^ is then proportional to the diameter of the log multiplied by its length. But the volume of the log in- creases as the cross sectional area, which is proportional to the square of the diameter (§ 27). The amount of waste in slabs and edgings from a log 20 inches in diameter is just twice that for a 10-inch log, since the diameter and the surface are doubled. But the 20-inch log contains four times the volume of the smaller piece, and this reduces the per cent of waste from slabs and edgings based on the volume of the larger log to one-half that for the 10-inch log. 52. The Waste from Crook or Sweep. Log rules apply only to straight logs. But the standard as to what constitutes straight logs requires definition. For all commercial log rules, this standard permits of " normal " crook (§ 93). This is best defined as crook averaging not over 1| inches in 12 feet, and including no log which crooks more than 4 inches in 12 feet. Crook or sweep in long logs is reduced by cutting them into two or more short sections before sawing. Where Relative waste in slabs and edgings from sawing 2j-inch plank and 1-inch boards. If 1-inch boards are sawed, the waste is reduced by the amount of the shaded portion. The greater proportion of waste in sawing thick boards comes from the side cuts, hence the practice is to cut 1-inch lumber from the sides. 52 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS very short material such as box boards is used, crook does not cause abnormal waste in logs. Care in laying off log lengths in the woods to secure the maximum length of straight sections by dividing the tree at the points of greatest crook reduces this source of waste to small proportions. Waste from crook is deducted in scaling on the assumption that the merchantable portion of the log must cut boards extending its whole length. The influence of length of log upon the waste due to crook is very pronounced, and where long logs are divided into shorter lengths in the mill they should never be discounted for crook except to the extent that this crook will affect the sawed contents of the shorter pieces. For lumber longer than 12 feet the influence of crook rapidly increases. The relation of normal crook to taper is shown in Fig. 7 in which the line DE is the axis of the cylinder corresponding to a straight log. The line AB is parallel to this axis and tangent to the margin at the small Fig. 7. — Method of measuring amount of crook in a log, in inches. The line JM represents the proper measurement, coinciding with the shaded portion J A or waste in the circle representing small end of log. end. The line AC is a straight line connecting the margins of both ends of the log. Were the log cylindrical, the line HJ under these circum- stances would represent the amount of crook. But the taper gives a larger cross-section at JL than at AK. Unless crook exceeds the taper for half the log, the cross-section JL when projected upon AK would, completely cover it, permitting as much lumber to be sawed as if the log were straight. In the diagram the crook exceeds this taper and the upper shaded portion of the cross section which represents the small end must be wasted in slabs, in addition to the normal slabbing of a round log. But this waste is incorrectly measured by any other method than that shown by the line JM, which is the distance to the surface of the log from a line parallel to the axis, and tangent to the margin of the small end. This distance gives the crook in inches. * For a 16-foot log tapering 2 inches, a crook of 1 to 1^ inches at the middle point has no appreciable effect on the output. THE WASTE FROM SAW KERF 53 By slabbing in the direction of KN this waste may be still further reduced, since the cylinder sawed is not parallel with the axis but follows the crook at the small end, and takes maximum advantage of taper at butt. Logs so crooked that their sawed contents is materially reduced are not scaled " straight and sound " or full. Deductions for crook are discussed in § 93. The waste from normal crook is included with that for slabbing and edging and is in proportion to surface, and hence to diameter. 53. The Waste from Saw Kerf. The total waste in sawdust, unlike that in slabs and edgings, takes approximately the same per cent of the cubic volume of all logs, regardless of their size. If a log is sawed by the method called slash sawing, in parallel saw cuts without squaring it, then, after the first slab is removed, there will be one saw kerf to each 41 w Fig. 8. — Waste incurred as slabs and sawdust in sawing round, straight logs. board. The initial saw kerf, and the sawdust wasted in edging, and in ripping wide boards into narrower boards, forms an additional percentage of waste not exactly proportional to volume. Disregarding this dis- crepancy, the fixed per cent of waste from saw kerf for the log is the same as the per cent wasted in sawing one board. If the thickness of board plus that of the saw is taken as 100 per cent, this waste, for a 1-inch board with j-inch saw kerf is as j to 1^ or 20 per cent, while for a |-inch saw kerf the proportion is | to 1| or 11.1 per cent. A general formula applicable to saws of all thicknesses is as follows: Let 1^= width of saw kerf; T = thickness of lumber. Then 7"+^ = total volume of board plus kerf, 54 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS K T-\-K T T-\-K = per cent deduction for saw kerf, = per cent of log utilized as lumber. Efforts to account for the exact per cent of waste in sawdust have been made, by including, first the saw kerf required for ripping or edging one edge, as shown in Fig. 8,' and second, the additional saw kerf for the first slab. But neither method is complete, since boards are edged when necessary on both edges. The best method is probably to include this extra saw kerf, together with the edgings, in the waste due to slabbing, leaving the sawdust as a straight per cent of volume. Shrinkage. Where shrinkage is considered, or where lumber must be sawed a trifle full, the extra thickness which is not measured in the green lumber constitutes a waste exactly similar to saw kerf, and can be added to the latter factor in the formula before calculating the per cent of reduction. For instance, if a log rule is intended to measure the output of 1-inch lumber after seasoning, and the average shrinkage on inch boards is Y6-inch, and saw kerf |-inch, the per cent of waste in small logs is ¥+i - -^^^^ = 15.8 per cent. 1+1 + 1^ 1-1875 ^ By the inclusion of one edge, the formula for sawdust would be: Volume of unit (W+K){T+K), Saw kerf K{W+T+K), K{W+T-\-K) Per cent of waste ^^_^^^^y,_^-. H. E. McKenzie, Bui. 5, California State Board of Forestry, Sacramento, Cal., 1915. By inclusion of the extra saw kerf but not of the cut for edging. Number of cuts = N, Average saw kerf per board = if -|-t;, K Volume of unit = T+K + -, K Per cent of waste K' T+K+- C. M. Hilton, Bangor, Me., 1920. TOTAL PER CENT OF WASTE IN LOG 55 Corrections for Saw Kerfs of Different Widths. Since the per cent of waste caused by saw kerf applies directly to the residual volume of logs after subtracting the waste for slabbing and edging, the effect of using a saw of greater or lesser width than that used in constructing the rule can be found in terms of a per cent of the values of the log rule. This flat correction can then be applied if desired, to correct timber estimates, convert the log rule into one which eliminates over-run from saw kerf, or correct the scale of logs to coincide more closely with sawed output. For instance, the above rule would utilize 1— .158 or 84.2 per cent of the net cubic contents of the cylinder. A saw cutting a j-ineh kerf, with the same allowance for shrinkage, calls for the formula, i+T& -3125 = 23.8 per cent, l + i+^ 1.3125 giving 72.6 per cent utilized. The values expressed by the log rule made for the 1-inch kerf must now be taken as 100 per cent to which the correction will apply. 76.2 Then gives 90.5 per cent. The second rule requires values equaling 90.5 per 84 . 2 cent of the first, or a straight reduction of 9.5 per cent. That this conversion can be accurately made was demonstrated on diagrams by H. D. Tiemann, who found that the possible error was less than one-half of one per cent.i 54. Total Per Cent of Waste in a Log. The total per cent of waste in a log is the sum of the waste from slabbing and edging, or surface waste, and from saw kerf. The proportion of this total waste represented respectively by slabbing and by sawdust will depend upon which of these deductions is made first, and whether the sawdust made in slabbing and edging is included as part of the waste in slabs and edgings, or is counted as part of the waste in sawdust. If the deduction for sawdust is made first, it will include a fixed per cent of the cubic volume of the log. If on the other hand, the slab waste is first deducted as a ring or collar of a given thickness, the subsequent deduction for saw kerf, although the per cent is the same, applies only to the residual volume of the log. The total per cent of waste, and its distribution between these two factors is illustrated in table VII. Let slab waste equal a ring f-inch in thickness or a reduction of 1.5 inches in diameter. Sawdust, for j-inch kerf, equals 20 per cent. The per cent of waste will vary with diameter of logs, as shown : In column 2 the per cent of waste is seen to be approximately one-half as great for 20-inch logs as for 10-inch logs. 1 Proc. Soc. of Am. Foresters, Vol. V, 1909, p. 29. 56 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS TABLE VII Distribution of Waste between Slabbing and Sawdust 1 2 3 4 5 6 7 8 Diameter at small end of log. Inches Waste in slabbing. Per cent Waste in sawdust 20 per cent of remainder of log. Per cent Total waste Columns 2+3. Per cent Waste saw kerf in slabs. Per cent Total waste saw kerf, Columns 3+5. Per cent Waste in slabs less saw kerf in slabs. Per cent Utiliza- tion.* Per cent 10 20 40 27.75 14.44 7.27 14.45 17.11 18.54 42.20 31.55 25.81 5.55 2.89 1.45 20 20 20 22.20 11.55 5.82 57.80 68.45 74.19 * Of the small cylinder not including taper. The waste in slabbing would be exactly proportional to diameter except for the fact that the volume of the hollow cylinders representing the collar deducted for slabs is not directly proportional to the outer surface of the respective cylinders in logs of different sizes. The same relation is seen to hold whether or not the slab waste is deducted before or after the sawdust. (Columns 2 and 7.) Since the per cent of slab waste is roughly proportional to D, while that from sawdust is as £)-, the sum of these two factors causes the total per cent of waste to decrease as shown in column 4, instead of remaining constant as in column 6. The rate of decrease is less rapid than in columns 2 or 7 since only a portion of the waste decreases in per cent with increasing diameter of log. Were the total waste in logs proportional to D^ as is the waste from saw kerf, log rules could be converted from cubic to board feet by a single ratio. But since the part of this waste due to slabbing is pro- portional to D, the per cent of total waste decreases with increasing diameter by a rate which is the sum of these two factors and is therefore directly proportional to neither D nor D^. This explains the increasing per cent of utilization secured in sawing larger logs and the need for log rules based directly upon the board-foot unit and not derived by conversion of cubic units. To derive an accurate log rule, not only must the waste from slabs and edgings be deducted separately from the waste from saw kerf, but the correct amount must be deducted for each source of waste. A rule which deducts too much for slabs and too little for saw kerf will deduct TOTAL PER CENT OF WASTE IN LOG 57 too much on small logs, where the slab waste is normally high, and too little on large logs, where the greater portion of the deduction is for saw kerf. Such a rule can be correct only for a single diameter class where the two errors happen to balance. On the other hand, if too small a deduction is made for slabs, and too large for sawdust, small logs may be overscaled, while the increasing per cent of utilization possible in larger logs will not be shown in the scale (Column 8), and the rule therefore tends to under-scale large sizes. CHAPTER VI THE CONSTRUCTION OF LOG RULES FOR BOARD-FOOT CONTENTS 55. Methods Used in Constructing Log Rules for Board Feet. The great variation in the contents of different log rules for board feet, and the variation in accuracy and consistency of these rules is due to the methods used in their construction as well as to the factor of over-run resulting from closer utilization. Four general methods have been used in constructing such rules. These are: 1. By mathematical formulae. A formula is used, which derives the board-foot contents of the log directly from its diameter and length, by allowing for reductions from D"XL for cubic volume, waste in saw kerf, waste in slabs, and reduction of residual volume to board feet. If the principles used in making these reductions (§ 54) are correct and the amounts used are also correct, such log rules are superior to diagram rules, but if errors in either principles or amounts of deduction are introduced into the formula, the rule is worse than useless. 2. By diagrams. Full-sized circles of all diameters are drawn on large sheets of paper, representing the top ends of the logs. On these cross sections of the log the ends or cross sections of the boards which could be sawed from these logs are drawn, leaving between each board a space equal to the width of the saw kerf. The area of boards in square inches is then reduced to board feet by the factor -^ X length in feet, for logs of a standard length, and from this, for logs of all lengths. 3. By tallying the actual sawed contents of logs at the mill for differ- ent diameters and lengths. Owing to the variables introduced by the thickness of lumber sawed, and by taper, this method has seldom been accepted as the sole basis for a log rule, but has been extensively used to check the accuracy of rules made by the preceding two methods. 4. By conversion of the cubic contents of logs into board feet, after deducting a fixed per cent of this total cubic contents for waste in saw- ing and slabbing. As shown in Chapter V, all board-foot log rules constructed on this basis are fundamentally wrong. A fifth method has been used, which is a combination of methods 1 and 2 or 3, namely, to alter or correct the values of an existing log rule, by means of mill tallies obtained in sawing. The author of such cor- 58 THE CONSTRUCTION OF LOG RULES 59 rections may give a new name to such a rule, or may state that it is an old rule corrected. Such corrected rules while undoubtedly better than the originals have so far failed of adoption in place of the rules from which they were made, owing to the force of custom in perpetuating established standards even if in error. 56. The Construction of Rules Based on Mathematical Formulae. Many efforts have been made to evolve a formula which will give an accurate basis for a board-foot log rule. Of these the erroneous formulae, or rules of thumb, based on a fixed conversion factor are most common. Of those which recognize the fundamental difference between waste from slabs, and waste from saw kerf, we have two groups, distinguished not by principle, but by the method of procedure dependent on whether the deduction for saw kerf is made first, from the total contents of the log, or whether that for slabs and edgings is first deducted, and the waste from saw kerf then taken from the residual volume. Method of Deducting Slabs First. When the first plan is used, a constant, a, representing in inches the double width or thickness of the hollow cylinder or sur- face layer wasted in slabs, edgings and crook, is first deducted from the diameter of the log at small end. From the area of the smaller circle thus obtained, the required per cent is subtracted for saw kerf, shrinkage or surplus thickness of board required in sawing. The residual area of the circle in square inches is converted into board feet for logs 1 foot long, by dividing by the factor 12. Disregarding the taper, the volume of a log of any length is found by multiplying the contents by length in feet. D = diameter of log in inches; a = inches subtracted from diameter, a constant ; D—o = reduced diameter of log after subtracting waste from slabs and edgings; = reduced area of small end of log in square inches; 4 b—per cent of volume deducted for saw kerf; 1 — 6=per cent remaining after deduction for saw kerf; L = length of log in feet ; B.M. = volume of log in board feet; then 7r(D-a)2 L B.M. = (l-i,)-4-A - 48 Illustration Let a = 1 .5 inches, representing a collar of .75 inch thickness deducted for slabs, etc. b = 20 per cent representing a j-inch saw kerf. 60 THE CONSTRUCTION OF LOG RULES Then for any log, B.M. = (l-.20)^— — ^L. 4o For a 12-inch log IG feet long, /3. 1416(12- -.„, ,,^ B.M. = .80 ^ 16 \ 48 = 92 board feet. ±^y Method of Deducting Sawdust First. — By the second method, the per cent of waste in saw kerf is first deducted from the entire volume of the log. From the residual volume the amount to be further subtracted for slabs, edging and crook is taken. This is a smaller per cent than by the first method, as shown in Table VII, column 7 since the sawdust used in slabbing is not included, and it is for convenience computed in the form of a plank of width and length equal to the log, and whose thickness is varied to give the required volume of waste. Let A equal the width of this plank in inches. This is taken as a constant. Then, / ttD'- \ L Illustration Let b = 20 per cent — sawdust allowance, A = 1.767 inches, the thickness of a plank whose width is equal to D, and length to L — for slabbing allowance. Then for any log. B.M.= rD2 .80( ■ — )-1.767D For a 12-inch log 16 feet long, B.M. =[.80(. 7854 X 122) -1. 767 Xl2]|f, B.M.=92 board feet. This result shows that for 12-inch logs, after subtracting 20 per cent from log for sawdust, a plank 1.767 inches by 12 inches gives a deduction from the net volume, equal to method 1 when a collar .75 inch thick is first deducted and 20 per cent for sawdust taken from the remainder. The two methods are not absolutely interchangeable. Their relation may be shown by algebraical means. Substitute C for (1-6). Then C = per cent left after subtracting saw kerf. Since D is in inches, and L exerts no influence on the relative values, the areas of the small end of log, left after subtracting total waste, should be equal, and can be expressed in square inches for each formula as: CniD-ay CirD^ ^^ = AD. 4 4 Then, C(1.5708aD-.7854a2) A=- D COMPARISON OF LOG RULES BASED ON FORMULA The results, for certain diameters are shown below: 61 TABLE VIII Thickness of Plank to be Deducted for Slab Waste to Coincide with a Collar 1.5 Inches Thick. Sawdust Allowance 20 Per Cent Double thicknes.sof col Corresponding thick- Ratio of thickness of Diameter of kir deducted for slab ness of plank to be of plank to collar log. waste previous to de- deducted after de- ducting .sawdust. ducting sawdust. Inches Inches Inches 3 1.5 1.414 0.940 6 15 1.649 1.099 9 1.5 1.728 1.152 12 15 1.767 1.178 18 1.5 1.800 1.200 40 1.5 1.849 1.233 The use of these ratios would give identical results by both methods. But in application the second method usually stipulates that the thickness of plank shall be constant for all logs. This results in a greater proportionate deduction for slabs on small logs than by the first method. This deduction is more in accordance with the actual results of sawing, owing to the increasing effect of minimum widths of board on per cent of loss in slabbing (§51). The best application is to adopt a ratio which applies to medium-sized logs, and use this for all logs, large and small. If a log rule is constructed to deduct the waste which actually occurs in sawing, it must be based on one or the other of these two formulae. If the waste allowances are correct for the conditions assumed, there will still be over-run when other condi- tions apply, but the per cent of over-run will be practically the same for all sizes, the rule is consistent, and the results are subject to correction by a fixed ratio or per cent. If the waste allowance for either slabbing or sawing, or both, are incorrect for the conditions assumed, the rule will not only give over- or under-run, but will also be inconsistent, the per cent will differ with diameter, and the rule will not be subject to correction by a fixed ratio, and will lack the basic requirements of a standard of measure. 57. Comparison of Log Rules Based on Formulae. In constructing a formula log rule, the correct application of tlie deduction for saw kerf presents no great difficulty. In the International rule, an extra deduc- tion of Ye-inch was made for shrinkage. Other rules neglect all factors but the actual width of saw kerf (§ 53). The deduction for slabs, edging and normal crook requires determination not only from diagrams but from practical tests. The following amoimts are deducted by the log rules given below, expressed both as a "collar" deduction from diameter, (a), and as a thickness of plank {A), to correspond with the two methods described (§ 56). 62 THE CONSTRUCTION OF LOG RULES TABLE IX Deductions for Slabbing and for Saw Iverf, for 12-inch Logs, in Ten Log Rules Based on Formul.«. The Basis Used in the Rule is Shown in Heavy Type. Log Rule. Deduction from diameter for slabbing. Inches Equivalent deduction in form of a plank thickness. Inches Saw kerf plus shrinkage. Inches Deduction for saw kerf. Per cent International Universal Preston : Large logs Small logs British Columbia. . Click Clement Wilson Thomas Baughman * Champlain Doyle Baxter 1.73 1.66 1 75 1 50 1.50 1 25 1.18 1.00 1.00 0.87 0.83 4 00 1.00 12 00 04 8 P 16 1.77 77 42 32 17 17 05 00 GO GO 15.8 20.0 20.0 20.0 27.3 23.6 25.0 22.2 22.0 20.0 20.0 4.5 33.8 * Diagram rule. Of the rules above cited, the British Columbia and Doyle are the only ones used extensively at present. The table is instructive as an indication of the proper allow- ances to make for slabbing. The test of a formula is actual comparison with sawed output. The deductions in the International rule were determined by careful measurement on logs actually sawed. The Champlain rule is known to be too close a rule, with too small an allowance for slabs. The British Columbia rule neglects shrinkage and is a good standard. The Click rule was carefully checked by sawed output. These results indicate that for 1-inch lumber sawed to exact dimensions, an allowance for slabbing of 1 .5 to 1 .75 inches subtracted from diameter, or one-half this deduction as the single thickness of the collar, is a fair allowance for slabbing. This allowance would be too small for lumber of greater average thickness than 1 inch or for very small logs. When the deduction is made in the form of a plank whose width equals the diameter, D, of the log, the thickness of plank required to make it equivalent to the collar deduction is from 1.75 to 2 inches for 12-inch logs, slightly more for larger logs, and decreasing in thickness for smaller logs. But where the deduction is made in this form, as in the International and Champlain rules, it is used as a constant for all dimensions (§ 59 and § 62) with results corresponding more closely to actual waste than by the first method. The allowance for saw kerf, on all log rules in commercial use, is j-inch or over. The International rule in its original form gives values for a |-inch saw kerf, which, with the other allowances, gives a rule intended to measure the output of modern band mills. McKENZIE LOG RULE, 1915 63 58. McKenzie Log Rule, 1915. This log rule is a universal formula and not a commercial standard or true log rule. It is intended to reduce all the variable factors in the production of sawed lumber to elements in a formula, which will permit the determination of a local rule that will accurately measure the sawed output in the log for any condition, and eliminate over-run. The factor of taper is treated by building up the log in 8-foot sections, permitting the use of whatever actual average taper coincides with that of the logs sawed. The allowance for slabs, edging and crook is made by the first method, that of deduction from the diameter previous to sub- tracting saw kerf. Shrinkage could be included with saw kerf, if neces- sary, but the author does not mention it. The formula is the one already shown to be correct and universal for board-foot log rules, L B.M. = (l-fe).7854(I>-a)2— . The saw kerf allowance, h, is computed to include width as well as thickness of lumber sawed (§ 53). To this general formula the author adds a constant, c, to offset excessive taper on small logs. The principal utility of this log rule will be found in determining, in advance of sawing, the amount of over-run which may be obtained from logs scaled by a com- mercial rule, or to test the results in over-run to be expected by the use of different log rules and different methods of manufacture. The objections to adopting it as a standard of measure are stated in § 49. Reference Bui. 5, California State Board of Forestry, by H. E. McKenzie. 59. International Log Rule for |-inch Kerf, Judson F. Clark, 1900. In constructing this rule, modern conditions of manufacture in large mills were presupposed. The values of the rule as published are for a band saw cutting a |-inch kerf and are rounded off to 5 and 10 board feet, thus approaching the principle of a decimal rule. Saw kerf is first subtracted, allowing j^-inch for shrinkage, or a total of -j^ inch. The deduction for slabs and edging, including a normal crook of from 1 to \\ inches is then made in the form of a plank measuring 2.12D. The forrpula reads: B.M. = (.66D2-2.12D)— . 12 The rule was constructed as follows: Since the per cent of waste in saw kerf plus K ^ shrinkage is — this becomes for inch boards or 3 parts in 19, which gives 1+A 16-1-3 ' ^ .158, and the factor for residual volume is .842. Then, .842(.7854Z)2) = .66Z)2. 64 THE CONSTRUCTION OF LOG RULES The deduction 2.12D was determined from tests of sawed logs, including all crook of 4 inches or less. Since the log is divided into 4-foot lengths, the sum of which gives the scale, the formula reads for each length, B.M. = (.66D2-2.12D)y*2 = .22D^-.71D. A taper of ^-inch in 4 feet is allowed. D is thus increased by ^-inch for each succes- sive section and the sum of the scale of the separate 4-foot cylinders gives the scale of the log (§ 43). On account of the allowance for shrinkage the rule is based in reality on the production of Irg-i^ch boards measured as inch boards. A minimum width of 3 inches, and a minimum length of 2 feet are adopted as standard, no piece to contain less than 2 board feet. Standard values were published, it being the inten- tion of the author to furnish a commercial log rule that could be accepted as a com- mon standard for the measurement of logs as sawed in modern mills using a band saw cutting a j-inch kerf. 60. International Log Rule for ^-inch Kerf, Judson F. Clark, 1917. For general adoption as a standard commercial log rule, the |-inch rule is open to the objection that it over-scales the product of most small mills, since it is seldom that such mills use saws cutting less than j-inch kerf, or make close use of the taper of the log. A log rule which gives a safe margin, and which permits mills using thin band saws and up-to- date equipment to secure an over-run of about 10 per cent is more acceptable as a commercial standard than one which scales for the closest possible standard of utilization. For this reason, Mr. Clark has computed values for the International rule, for j-inch saw kerf. This form of the rule is here published for the first time from values furnished by its author (Appendix C, Table LXXX). To obtain this rule, the original values for the |-inch rule were reduced by 9.5 per cent and then rounded off to the nearest 5 or 10 board feet. The rule is recommended as a standard for scientific measurements of volume and growth in terms of board feet, for regions where the product is manufac- tured ])y small mills using circular saws cutting a j-inch kerf. 61. British Columbia Log Rule, 1902. This is the only case of the legal adoption and application in commercial scaling of a new log rule based on sound scientific principles, as the direct result of a thorough investigation. In 1902 a commission of three men prepared from dia- grams a rule to suceed the Doyle Rule for the province, which was adopted in 1909 as the Statute rule. Their results were embodied in a formula reading: "For logs up to 40 feet in length deduct H inches from the diameter of the small end inside the bark; square the result and multiply by the decimal .7854; from OTHER FORMULA RULES . 65 the product deduct three-elevenths; multiply the remainder by the length of the log and divide by twelve." Or, B.M. = (1 -fV).7854(Z)-1.5)2- 12 = .727^ -—. 4 12 The minimum width of board used was 3 inches. For logs over 40 feet in length, an increase in diameter is allowed on half the length of the log amounting to 1 inch on the diameter at the small end, for each 10 feet in length over 40 feet. Thus for logs from 41 to 50 feet long the contents of the butt cylinder is scaled by a diameter 1 inch larger than the top end; for logs from 51 to 60 feet long, the rise allowed is 2 inches, etc. This allowance for taper is absurdly small and constitutes the only weak point in the rule. It is a concession to the low standards of utilization practiced in the province at the time. 62. Other Formula Rules, Approximately Accurate, Both in Princi- ples and Quantities. When a log rule is constructed by using the prin- ciples embodied in the standard formula, and when in addition, the amount of deduction for both saw kerf and slabbing is approximately correct, the resultant log rule will be far more accurate and consistent than any of the commercial rules in common use except the last men- tioned. Several rules have been constfucted, whose values differ only because of slightly different allowances for waste, as shown in Table IX. Seven such rules are given below. This completes the list of log rules known to the author, and based on diameter at small end of log, which deserve to be classed as fundamentally correct standards for board-foot contents of saw logs. Champlain Log Rule, A. L. Daniels, 1902. This log rule, intended as a perfect rule for 1-inch boards, is based on j-inch saw kerf and neglects taper. It is for perfect logs. The deduction for slabs and edging, without normal crook, is made equal to a 1-inch plank or ID. No shrinkage is considered. The diameter is taken at small end. Were it not for an over-run secured from taper or the methods of sawing used, logs would never saw out what this rule calls for. The quantities given are above normal in cylindrical contents for short logs. This error is offset by neglect of taper, so that in long logs the rule falls below the International. This rule has not been used commercially, except in a few instances in Vermont. The formula is : L B.M. = (.62832D-D)^— . 12 The author of the Champlain log rule realized that the slab allowance was too small for actual conditions. By increasing the width of plank deducted for slabbing to 2D, a modification, termed the Universal log rule was computed, using the formula, L B. M. = (.62832D2-2Z))— . 12 66 THE CONSTRUCTION OF LOG RULES This rule compares favorably with other theoretically accurate rules except that it shares the common fault of neglecting taper. Mr. Daniels states (1917), that he favors the use of the Champ lain rule as the more accurate of the two . Wilson Log Rule, 1825. B.M. = .807-^ — . 4 12 By Clark Wilson, Swanzey, N. H. Originated in 1825, and computed for j-inch boards. Now obsolete. This was unquestionably the first formula rule. The author was a mathematician, and "estimated the difference in yield in gain of the large logs over the small ones, and then calculated the intermediate spaces by nearly regular integral differences as logs increase in size. The author intended it for |-inch boards. It is recorded that E. A. Parks later used it for 1-inch boards, which use resulted in a lawsuit." (John Humphrey, Keene, N. H.) Preston Log Rule, An Old Rule. Large logs, B.M. = .80^ Small logs: B.M. = .80 1 12 w{D-1.5yL_ 1 12' Still used in Florida. Known locally as a seller's rule. Sold in Jacksonville, Fla., by H. & W. B. Drew Co. Thomas' Accurate Log Rule. ■K(D-\yL B.M. = .78- — 12 For j-inch saw kerf. Also computed for |-inch kerf. Click's. Log Rule, 1909. 7r(D-1.25)2L B.M. = .764-^ . 4 12 By A. C. Click, Elkin, N. C, 1909. This rule was based on 1-inch boards averaging 6 inches in width and makes reduction for saw kerf of j-inch as per the formula (§ 58), used by McKenzie. Other rules for different widths of saw kerf were worked out by the author. (Forestry Quarterly, Vol. VII, 1909, p. 145.) Carey Rule, Date Unknown. This was a caliper rule to be applied to middle diameter, and was used for round edge boards^-inch thick. The values given are almost identical with the Wilson ruie. Former^ used in Massachusetts. Clement's Log Rule, 1904. 12 B.M.: .75 -1.18D \ 4 ; J This log rule illustrates the use of a rule of thumb, based on correct mathematics. The above formula is expressed thus: Multiply half the diameter by half the circum- ference, then subtract half the circumference. The remainder will be the total amount of feet board measure, in a 16-foot log. This becomes : B.M. = (.7854D2-1.57D)— , 16 from which the above formula is derived. With the exception of the Preston, none of these rules is in commercial use. TIEMANN LOG RULE 1910 67 63. Tiemann Log Rule, H. D. Tiemann, 1910. All of the com- mercial log rules in use are open to the criticism that the taper is dis- regarded, thus causing the over-run to vary according to the length and amount of total taper of the log. The International rule, in which taper is included, is not in commercial use to any extent. But one attempt has been made to take proper cognizance of taper by the method of applying a log rule for board feet to the middle diameter instead of the small end. Most rules employing this method are cubic-foot rules or based on cubic contents. The Tiemann log rule on the other hand is a true board-foot rule based on a j^-inch saw kerf. The rule was made from actual mill tallies accurately adjusted for saw kerf and for exact thicknesses and the results worked out graphically by curves. Quite remarkably the curves were found to correspond very closely to the exceedingly simple formula B.M. = (.751)2 -2D)^, which equals (.IIQ^^-Ldo) 7rD2 . _\L_ 12' The application of the rule is limited by its author to lengths not exceeding 24 feet. This log rule applies to logs scaled in the middle. When this is possible, the rule is more accurate than any other board foot log rule, since neither the variation in taper nor length of log affects it. It can be adjusted to apply to the small end just as well as any other rule can, but it is intended primarily for middle diameter as this largely elimi- nates errors in estimates of taper. For scientific records it is of distinct value. It is superior to the International rule as it eliminates taper as a variable instead of averaging it. The obstacles to converting this rule or any other rule into equivalent values at small end are discussed in § 31. The rule is given in Appendix C, Table LXXXIV. 64. Formula Rules Inaccurately Constructed. Baxter Rule. If the allowance for slabbing in a formula rule is excessive, and that for sawdust too small, the resultant volumes will be too small for logs of small diameters and too large for large logs, thus giving not only an inaccurate but an inconsistent rule. If these errors in deducting waste are reversed, slabbing allowance being too small, and that for sawdust too large, the reverse is true, and the large logs will be under-scaled. Baxter Log Rule. In adopting a rule of thumb for the construction of a log rule, the author may have in mind a certain result, but the rule when expressed in a formula may give quite a different result. The Baxter Log Rule was constructed by the rule "Subtract 1 from the diameter inside bark at the small end, square the remainder, and multiply by .52. The result 68 THE CONSTRUCTION OF LOG RULES is the contents of a 12-foot log" (hence — gives the contents of any log). This squar- ing and subsequent subtraction of one-half the square was intended to give suffi- cient deduction for both slabs and saw kerf. But it actually gives, 7r(D-l)L B.M. = .662- '—. 4 12 The factor 1, for ^4, is insufficient for slabs and the factor .338 for C is far too great for sawdu.st, corresponding in fact to a kerf of -i.inch. The rule therefore greatly underscales large logs. Its inconsistency makes it worthless. 65. Doyle Log Rule. Synonyms: Connecticut River, St. Croix, Thurber, Vannoy, Moore-Beeman (in part), Ontario, Scribner (erro- neously) . This rule is used almost to the exclusion of all other rules for hard- woods in parts of the Ohio Valley, and for Southern yellow pine. Its use is extensive in every eastern state outside of New England and Minnesota. In the West, it is not used to any extent. The Doyle rule reverses the error of the Baxter rule by deducting too large a per cent for slabbing and not enough for sawdust. The wide use of this rule has caused losses of millions of dollars to owners selling logs and standing timber, by improper and defective measurement of contents. The prevalence of its use is due first to the simplicity of its application as a rule of thumb. The rule reads: 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. The result is the contents in board feet. Timber cruisers estimate logs in 16-foot lengths. For this length of log the rule would read: Deduct 4 inches from the diameter of the log inside bark, and square the remainder. The result is the contents of the log in board feet, by the Doyle rule. A rule as easily applied as this was sure to be popular. The second reason for its wide use was its substitution for the old Scribner rule in Scribner's Log and Lumber Book, after this publication had already attained a large circulation. As this book was widely accepted as a standard and almost the only publication on log rules, the impetus given to the use of this inaccurate rule by this substitution was tremendous. The third reason for the continued use of the Doyle rule is the same which operates to prevent reform in the use of log rules in general. Custom, or habit of using it, is fixed. So far has this gone that the States of Arkansas, Florida and Mississippi prescribe its use by statute. Added to this is the fact that a rule favoring the buyer will be advocated by this class to its own advantage. DOYLE LOG RULE 69 The seller can defend himself against the use of a short measure if the latter is consistent and its per cent of error is known. But with a log rule like the Doyle, the per cent of error differs with every scale of logs or stand of timber and it is practically impossible to determine the actual loss without remeasuring the logs by a correct log rule or tally- ing the sawed contents. Since it will be impossible to displace this log rule by better standards unless its vicious character is fully understood, the exact nature of the error should be made clear. The original form of this rule read "Deduct 4 inches from the diameter for slabs, then squaring the remainder, subtract one-fourth for saw kerf and the balance will be the contents of a log 12 feet long." The sawdust allowance as intended, would have corresponded to a i^-inch saw kerf. The author evidently figured that 4 inches of slab would square the log sufficiently so that the sawdust rT Fig. 9. — Actual deductions for slabs and for saw kerf made by the formula of the Doyle rule, for logs 6 inches, and 28 inches in diameter respectively. The square ABCD is the supposed residue after deduction for slabs, while the outer inscribed circle represents the actual residue. The inner inscribed circle represents the residual percentage shown as board feet by the rule. The sawdust allowance is, therefore, the difference between the outer and inner inscribed circles, whose area is but 4.5 per cent of the contents of the cylinder. allowance could be applied in this manner to the squared or partially squared stick. His fundamental error lay in his method of deducting for slabbing and edging. As shown, the waste from slabs and edging does not amount to a reduction of 4 inches in the diameter, but to about 1.75 inches, and instead of being slabbed from four sides, it is distributed evenly over the entire surface as a collar. The assumption made resulted in an actual deduction for slab far in excess of what was intended, this excess in turn reducing the sawdust allowance from an assumed 25 per cent to negligible proportions. The above diagrams (Fig. 9) will explain the reason for this inconsistency. The diagram for the larger log shows that the squaring of the timber would not The standard formula -(D— 4)^ gives the volume 4 require a 4-inch slab allowance .7854(D— 4)- as the actual net result of deducting 4 inches from the diameter of the 70 THE CONSTRUCTION OF LOG RULES log. This was the point overlooked in constructing the rule. The deduction so made is in its eiTect "a deduction for slabbing and edging although not so intended. That it was not intended is shown by the instructions for next deducting one- fourth of (/)— 4)^ "for saw kerf." But this leaves .75(D— 4)- for all logs, instead of .7854(D— 4)2, which is a further reduction of but .0354(0—4)^, the actual reduc- .0354 tion for saw kerf = . 045 or 4 .5 per cent of the cylindrical contents for saw kerf instead of the 20 per cent of the same cylinder required by a j-inch saw kerf. The remaining 21.5 per cent of the supposed saw kerf is a true slab deduction of 4 inches from diameter. Thus the amounts and proportions of slab deductions are grossly out of balance and this ruins the rule. This early form was not known as the Doyle rule. The present form, first published in the decade 1870-80 was advertised as a new rule. The scale is identical with the older form but the change in the wording of the rule to its present form still further concealed the flaw in its construction. The formula for the Doyle rule is: /D-4^ B.M.= — \ ^ corresponding to the standard formula: B.M. = .955-^ -—. 4 12 The true sawdust allowance can be shown by the following comparison: 'D-4\2 j L=.0625(D-4)2L. The area contents of the cylinder D— 4, ■K L -(D-4)2— = .06547(D-4)2L. Since the cylinder D— 4 represents the log minus true slab deduction, = •^ '.06547 95.5 per cent or the log minus both slabs and sawdust. ^ 66. Effect of Errors in Doyle Rule upon Scaling and Over-run. The effect of this overbalancing of the respective allowances is to cause this rule to give zero for the contents of logs 5 inches in diameter while for logs above 47 inches, the scale yields more than 80 per cent of the cubic contents, thus, for ^-inch kerf, eliminating slab waste altogether. The over-run would thus vary with increasing diameter, from infinity to zero. When the Doyle rule Is applied to long logs, with a small top or scaling diameter, the over-run becomes proportionally greater. A careful test, under direction of the courts in Texas where logs of given sizes were actually sawed (Extending a Log Rule, E. A. Braniff, Forestry Quarterly, Vol. VI, 1908, p. 47), showed that for 24-foot logs sawed by circular saw,, the Doyle rule gave an over-run for different diameters, as shown in Table X. ^ The author is indebted to material published by H. E. McKenzie in Bui. 5, CaUfornia State Board of Forestry, for this discussion of the error in the Doyle rule. EFFECT OF ERRORS IN DOYLE RULE 71 TABLE X Over-run, Doyle Rule. Texas Diameter at small end. Sawed product. Scale Doyle Rule Per cent of over-run Inches Board feet &- 6f 35 6 483 7- 7f 49 14 250 8- 8i 61 24 150 9- 91 76 37 105 lO-lOf 95 54 76 11-llf 112 74 51 The over-run steadily diminishes with increasing diameter until at from 36 to 40 inches the rule gives practically full scale for j-inch kerf and normal allowance for slab, disregarding taper. An investigation made in 1904 for the Province of Ontario by Judson F. Clark, showed that the volume of the average log cut in the Province had decreased in 25 years by 63 per cent and at that time averaged 61 board feet and 12 inches in diameter. From mill tests of pine logs sawed with i^-inch kerf, the per cent of over-run was as follows, for 12-foot logs: TABLE XI Over-run, Doyle Rule. Ontario Diameter of log at small end. Scale by Doyle rule. Actual output of inch lumber. Per cent of over-run Inches Board feet Board feet 6 3 14 366 8 12 30 150 10 27 50 85 12 48 76 58 14 75 108 44 16 108 144 33 18 147 186 26 20 192 234 22 When the average log ran between 18 and 31 inches, the defects of this rule were not so apparent, and the over-run was not excessive. But as the size of the logs cut grows less with the advent of second-growth and closer utilization, the rule becomes impossible. Its continued use in many regions is due largely to the fact that logs are not often bought and sold, but the timber is purchased on the stump and the owner is unaware of his losses. This rule must eventually be superseded either by a more consistent standard or by the rejection of board-foot measure 72 THE CONSTRUCTION OF LOG. RULES altogether. No owner of small logs or of young standing timber can afford to sell on the basis of a scale or estimate made by the Doyle rule. As it stands, this rule is a serious obstacle to the profitable marketing of second-growth timber, hence to the practice of forestry. 67. The Construction of Log Rules Based on Diagrams. In con- structing log rules based on diagrams (§ 55), tiie quantity of 1-inch boards contained within a given diagram may vary, due to four different factors. The first is whether a 1-inch board or a saw kerf is placed on the center line. For some diameters the one method gives the most lumber, for others the alternate plan, depending upon the relation of the total diameter to the sum of the diameters of boards plus saw kerf. The second factor is the minimum width of the boards to be sawed. The narrower the board, the greater will be the product from circles of a given diameter. The third source of variation lies in the choice of plotting all boards as if slash sawed, or else arbitrarily choosing a given method of sawing around or squaring the log on the diagram, with boards taken from the slabs. The fourth factor is the acceptance or rejection of fractional inches in the boards inscribed in the circle. When all boards are read to the nearest full inch in width, dropping all frac- tions, some diagrams will lose a much larger per cent than others— while in actual sawing, these variations tend to even up. For circles of the same diameter and with the same minimum width of board and saw kerf, the board-foot contents will evidently vary con- siderably according to the treatment of these four factors in construction of the diagram. In a well-constructed consistent set of diagrams, the values in board feet should increase by a regular progression. This can be shown by plotting the original quantities on cross-section paper and connecting the consecutive points by straight lines. Irregularities are revealed by sharp angles in this continuous line. Most diagram log rules show considerable irregularity, which the authors made no attempt to smooth out, as could have been done by means of this graphic plotting. A wholly inexcusable variation of such rules is caused by increasing the average width of slab allowed on large logs. This increase does not conform to the actual practice in sawing and results in a larger over-run on large logs. It is the principal defect in both the Scribner and the Spaulding diagram log rules. The Maine or Holland rule, by avoiding this error, secured a more consistent result. Diagram log rules tend to give the scale of perfect logs under a given standard for saw kerf and width of slab. The waste for normal crook and irregular form cannot be shown. Since the commercial rules have ordinarily allowed too thick a slab or too wide a minimum board or have rejected fractions, this loss is compen- sated, but formula rules if accurate are more practical and convenient. Baughman Log Rules. As an example of a diagram rule which is too perfect for commercial use, since it neglects shrinkage and normal crook and includes frac- SCRIBNER LOG RULE, 1846 73 tional inches, can be cited the Baughman log rules for j-inch and |-inch saw kerfs respectively. The results obtained from these diagrams are so consistent that they conform to the tjqjical formula for a perfect log rule. B.M. = .si "" ~' — — for i-inch kerf, 4 12 and 7r(D-l)2L B.M. = .90 for 1-inch kerf. 4 12 In practice the use of these rules would give an under-run: i.e., the logs would not saw out the scale. In these diagrams the minimum board was 4 inches, the lumber exactly 1 inch. The 1-inch board was always placed in middle of diagram. Taper was neglected. H. R. A. Baughman, Indianapolis, Ind. 68. Scribner Log Rule, 1846. Synonym: Old Scribner. The Scribner log rule is the oldest diagram rule now in general use. But for the unfortunate substitution of the Doyle rule for this rule in Scribner's Log and Lumber Book, its use would now be practically universal. The rule held its own in the North and West, and is the legal standard for Minnesota, Wisconsin, West Virginia, Oregon, Idaho, and Nevada. It is the standard prescribed in timber sales on National Forests through- out the West and by the Dominion Forestry Branch of Canada. The rule was published previous to 1846. The diagrams are for 1-inch lumber, and \ inch saw kerf. The width of the minimum board was not stated but the author modified an earlier edition of his rule by increasing the allowance for slab on larger logs. As a result of this unfortunate error, the rule gives a larger over-run on logs above 28 inches than on smaller logs. The products of the diagrams were evidently not evened off. The values, when plotted, show great irregularities, but except for the factor just noted, the general tendency of the rule is consistent. The original values were for logs from 12 to 44 inches in diameter in sections 15 feet long, " the fractions of an inch inside the bark not taken into the measurement." Taper is not considered on logs of the lengths used. These factors the author intended to offset normal crook and concealed defects. Values were then given for logs from 10 to 24 feet in length. Modification to a Decimal Rule. Two important changes in this rule have been made to meet the demands for a universal log rule. It has been changed to a decimal rule, and values for logs below 12 inches, and above 44 inches have been added. The practice of modifying a log rule in scaling by reducing it to even tens, in order to eliminate the col- umn of unit feet in adding, is found in connection with several rules. With the Scribner, instead of dropping odd feet, thus reducing the scale, 74 THE CONSTRUCTION OF LOG RULES the odd feet were rounded off to the nearest ten, values over 5 feet being raised, while 5 feet and under are dropped. The average scale of even a few logs by this method is practically identical with that obtained by the original rule as the errors are compensating. This modi- fied rule is known as the Scribner decimal rule. Extension below 12 Inches. For values below 12 inches, the original rule pro- vided no figures. The lack of a formula permitted individuals to supply their own values for these sizes. As early as 1900, the Lufkin Rule Company tabulated the decimal values then in use, under three schedules, termed A, B and C, shown below. To read in board feet, add a cipher to each figure. TABLE XII Decimal Values Below 12 inches for Scribner Log Rule Decimal A Decimal B Decimal C Length. Diameter — inches 6 7 8 9 10 11 6 7 8 9 10 11 6 7 8 9 10 11 Feet Board feet, in tens 12 14 16 18 20 22 24 112 3 112 3 12 3 4 12 3 4 12 3 4 12 3 5 13 4 5 4 4 5 5 6 7 7 5 6 6 7 8 9 10 12 2 3 4 4 12 3 3 4 6 2 3 3 4 5 7 2 3 4 5 6 8 2 3 4 6 7 8 3 4 5 7 8 9 4 5 6 7 9 10 1 2 1 2 2 3 2 3 2 3 3 4 3 4 2 3 2 3 3 4 3 4 3 4 4 5 4 6 3 4 6 6 7 8 9 4 5 7 8 8 9 10 Still other values resulted from the use of the full scale, rather than the decimal form. In the Woodsman's Handbook, (1910 Forest Service), values for 16-foot logs used by a company in New York (Santa Clara Lumber Co.) were pubhshed. These values were adopted by the Canadian Forestry Branch in 1914. The State of Minne- sota adopted standard values differing slightly from these figures. Wisconsin adopted definite values by law for these sizes, conforming exactly to the Decimal "C" scale given above. Idaho prescribes that the Scribner Decimal Scale be used with- out specifying values and both "A" and "C" scales are in use in the state. In Oregon and West Virginia the "Scribner Scale" is called for by statute, leaving the question open for values below 12 inches. The weight of custom is at present in favor of the use of the Decimal "C" values for this rule, and the utihty of the Scribner Decimal Rule would be improved by a universal adoption of this standard. Extension above 44- inches. With the adoption of the rule by the Forest Service, its use on the Pacific coast required an extension from 44 to 120 inches. In this SPAULDING LOG RULE, 1868 75 instance a similar but worse confusion might have resulted, but was avoided by the adoption of a single standard of values prepared by the U. S. Forest Service about 1905, and published in the Woodsman's Handbook, 1910 edition. The extension (made by E. A. Ziegler) was based on a comparison of the curve formed by the plotted values of the rule with similar curves for the formula rules such as the International, and for the Spaulding rule. Ziegler states, "It might be described as an extension built on an old rule by graphic methods checked with the correct mathematical formula in which the slab waste varies with D and the kerf with D-, and compared with the accepted rules in the Northwest, notably the Spaulding." The extension was built up on a r2-foot log, and applied to lengths of from 8 to 16 feet. As a concession to logging methods in the Northwest, logs up to 32 feet were scaled without taper by this rule. No such difficulties in extension are encountered with rules constructed by the use of correct formulae, since the values of logs of all sizes are in this way determined. Attempt to Improve the Rule. Further efforts to modify this log rule have been made in order to even off the irregularities of value between contiguous sizes. Examples of this are the Hanna log rule, 1885 (John S. Hanna, Lock Haven, Pa.), the White rule, 1898 (J. A. White, Augusta, Mont.) and a local rule used by M. E. Ballou & Son, Becket, Mass., 1888, adopted from Scribner rule, for small logs. Such modifications unquestionably improve the rule, but the minor irregidarities do not appreciably modify the scale of a large number of logs of different sizes. The con- fusion which would result in attempting to secure universal agreement on any change in accepted values for this rule has prevented their adoption, and the values still stand as they were originally determined, subject only to the conversion to decimal form. The Scribner Decimal " C " log rule in spite of its imperfections comes the nearest at present to fulfilling the demand for a universal commercial log rule, because of its present wide acceptance and use (§ 13), and reasonable consistency in over-run. The latter reason alone makes it preferable to the Doyle rule. Not even this rule, however, does justice to logs below 12 inches in diameter; and in regions of second growth and small logs, a closer and more accurate rule is preferable. 69. Spaulding Log Rule, 1868. Synonym: California Rule. The Spaulding Log Rule was adopted by statute in 1878 as the standard for California, and the values were given. It was constructed by N. W. Spaulding of San Francisco in 1868 from diagrams of logs from 10 to 96 inches in diameter, using an y|-inch saw kerf, and 1-inch lumber, and afterwards tested by sawing logs of each size in two mills. The size of the slab (width of minimum board) was varied according to the size of the log. This error of construction tends to increase the over-run in large logs. The values were given for lengths from 12 to 24 feet. The author directed that longer logs be scaled by doubling the values in the table, and this practice was incorporated in the statute. Thus the rule neglects taper altogether. In scaling, this principle is not applied to logs longer than 40 feet. It constitutes the most serious defect of the rule at present. Owing to the large saw kerf considerable over-run is 76 THE CONSTRUCTION OF LOG RULES secured by modern band saws but the rule is fairly consistent, as are all well-constructed diagram rules. 70. Maine or Holland Rule, 1856. Synonym: Fabian's. This is the most accurate and consistent diagram rule in common use (§ 55). It was constructed in 1856 by Chas. T. Holland for 1-inch boards, allowing for a j-inch saw kerf and for a minimum width of board of 6 inches. Fractional parts of a foot amounting to over .5 are reckoned as a whole foot, those less than .5 are rejected. This resulted in a more consistent rule from the diagrams. The rule is applied at the small end of log and disregards taper, so cannot be applied to the scaling of long logs without considering them as sections. The best practice now limits the length of these sections to 16 feet (§ 43). 71. Canadian Log Rules. The practice of adopting standard log rules by statute has been followed by New Brunswick, Quebec, Ontario and British Columbia. Their use is practically universal in the pro- vinces. The New Brunswick Rule, 1854. This rule is the statute rule of the Province and is probably based on diagrams. Values for from 5 to 10 inches were added by later regulations. Logs 26 feet and over are measured in two lengths. The small end is used and the rule is based on 1-inch lumber. Quebec Log Rule, 1889. To construct this rule, diagrams of logs from 6 to 40 inches in diameter were divided into 1-inch boards. A second set was divided into 3-inch deals, using |-inch kerf. The mean of the two resultant contents was taken, and from this an arbitrary deduction was made, ranging from to 17 feet. Taper was neglected. This scale is applied at the small end for logs up to 18 feet in length, above which the average diameter of the two ends is taken. The rule is the statute rule of the Province.^ The British Columbia Rule is discussed in § 61. 72. Hybrid or Combination Log Rules. The inconsistency of the Doyle rule by which small logs are under-scaled and large logs over- scaled has led to its combination with the Scribner rule. The values of the latter rule drop below the Doyle rule at 28 inches. Low values in the log rule favor the buyer of logs. In purchasing large logs, especially hardwoods, the Doyle rule was considered unsafe. The combined rule, termed the Doyle-Scribner, retains the low values of * The statute rule of the province of Ontario is the Doyle Rule which was adopted in 1879. In spite of the facts brought out in an investigation in 1904, that in that one year the Province lost 134 million board feet on the scale, equiv- alent to 23 per cent of the contents of the logs cut, by reason of this rule, the influences in favor of its retention were too strong to be overcome and it is still the standard rule of the Province. GENERAL FORMULA FOR ALL LOG RULES 77 the Doyle rule up to 28 inches, and substitutes the low values of the Scribner rule above that point. The reverse of this process was adopted by the State of Louisiana in 1914. The values of the Scribner rule below 28 inches were combined with those of the Doyle rule for 29 inches and over, and the resultant hybrid rule, known as the Scribner-Doyle rule is the official rule of the state. The Doyle and Baxter rules were also combined, using the Doyle values up to 19 inches, with those of the Baxter rule for the remaining diameters. Both the Doyle-Scribner and the Doyle-Baxter are cut- throat rules calculated to give the buyer the maximum advantage of the -defects of both rules. The Scribner-Doyle rule has no advantage over the straight Scribner rule since most logs are below 28 inches in diameter. 73. General Formulae for All Log Rules. When log rules have not been constructed by a formula, but from diagrams or mill tallies, no formula can be found which will give the exact values of the rule. But, consciously or not, the authors of log rules have attempted to deduct the waste from saw kerf and from slabbing and edging and the average results which they obtained, or the actual treatment of these two fac- tors is revealed by reducing these rules to the nearest approximate formula. The general form of such a formula is: BM. = iaD^-+bD+C)— in which aD^ covers the per cent reduction of volume for sawdust after reducing the square to a circle, bD gives the reduction of diameter or surface for slabbing and edg- ing, while C is a constant added in an effort to correct irregularities in the rule itself. L The factor — reduces square inches to board feet. 12 Cubic rules converted to board feet correspond exactly to the formula, B.M. = (aD2)— 12 or to 7rD2 B.M. = (l-6) L. 4X12 Perfect formula rules correspond to the formula, BM. = {aD^+bD)— or to B.M. = (l-&)-^ -L. 4X12 78 THE CONSTRUCTION OF LOG RULES But imperfect or irregular diagram or formula rules require the formula, BM. = {aD^+bD+C)— or B.M. = ((l-6)-^^^-CML. \ 4X12 / The first of these sets of formula? was originated by A. L. Daniels, the second by H. E. McKenzie. By Daniels' formula, the values of logs of three sizes will give the formula. For the following rules, the formula; read: Doyle, B.M. = (.75D-'-6D + 12)— , Scribner, B.M. = (.555D2- .55D-23)— ; 12' Maine, B.M. = (.635D2-1 .45D+2) — ; 12' Champlain, B.M. = (.62832D2-D)— ; L Vermont, B . M . = ( . SOD^)— . 12 By the McKenzie formula, adding the constant C gives the following for: Spaulding, B.M. = ( (1 - .266)-^'^ 2)L; Scribner, B.M. = I (1 - .266)^"^^ -3 |L; ' 4X12 / ' Maine, B.M. = ( (1 - .222)-^^ - .67 |L. \ 4X12 / These formulaj permit of analysis and comparison of different log rules. 74. The Construction of Log Rules from Mill Tallies. Graded Log Rules. A log rule based directly on mill tallies or the measured product of sawing logs into lumber will have no over-run provided the variable conditions of manufacture coincide with those which determined the contents of the logs from which the rule was made. But this is never the case. Standard log rules made for 1-inch boards do not con- form to mill tally of lumber sawed partly into 2-inch plank, or even if sawed full or Ijig-inch in thickness. Standard rules for square-edged lumber fall far short of measuring the product of small logs sawed and tallied as round-edged boards. The board foot as a cubic measure will not indicate the quantity of surface or superficial feet of lumber pro- duced in sawing f-inch boards. Where it is desired to obtain, in the log, the probable actual contents in boards, and existing rules are unsatisfactory, a new rule may be worked THE MASSACHUSETTS LOG RULE 79 out based directly on mill tallies. Unfortunately, most of the rules so obtained are not standardized for lumber of a given width, as 1-inch boards, but include the mill run, with varying per cents of thicker plank. This requires a statement as to the basis of the rule. Even when based on arbitrary per cents of 1-inch and thicker lumber such a rule may be superior, for local use, to one of the older commercial rules. A mill tally, upon which a local log rule can be based, will also serve two other purposes if rightly conducted, namely, a check on the amount of over-run to be obtained from logs of different sizes if scaled by an existing log rule (Doyle rule, § 65), and an analysis of the product of the log by grades of lumber, leading to the construction of graded log rules. For the single purpose of constructing a log rule for sound logs with normal crook (§ 52) but two operations are required. Each log is meas- ured, preferably at both the small end, inside bark, and the middle diameter outside bark, and its length recorded. The contents of each board sawed from the log is then tallied, and the total found, from which, by averaging for logs of the same dimensions, and the use of graphic plotting (§ 138) the log rule may be obtained. When mill-scale studies are made to check a given log rule, and to determine contents of logs by grades, from which a graded log rule is constructed (§87), the work is planned as follows: Each log is given a number, and is scaled as it enters the mill. A second man stationed at the edger places this number on the first and last board sawed from the log. A lumber grader at the grading table indicates the grade of each board, while a fourth man tallies the board-foot contents of the piece on a ruled blank which contains columns for each standard grade. As the scaler and grader are usually employees of the mill the work requires two extra men in the mill. The study is usually extended to include defective logs, which are kept separate in the final averages, since the original scale of such logs is a matter of judgment subject to wide errors. (Appendix A, § 361 .) By a proper system of numbering the logs in the woods, a mill scale study may be applied to determine the graded contents of entire trees for the construction of graded volume tables (§ 165). Reference A Mill-scale Study of Western Yellow Pine, H. E. McKenzie, Bui. 6, Cali- fornia State Board of Forestry, Sacramento, Cal , 1915. 75. The Massachusetts Log Rule for Round-edged Lumber. This log rule is constructed for round-edged and square-edged boards as sawed from small logs for close utilization of second-growth timber. The per cent of square-edged lumber sawed varies from to 50 per cent, increas- ing with diameter of log. The rest of the cut was round-edged. The rule is for J-inch saw kerf, varying in the per cent of round- or square-edged boards included. It is based on mill taUies of 1200 logs down to 4 inches at small end. The rule is 80 THE CONSTRUCTION OF LOG RULES expressed in two forms, one for application to diameter at small end, inside bark, the other to diameter outside bark at middle of log. The latter form would apply only to species with bark of similar average thickness to the second-growth white pine on which the latter is based. The utility of this rule as a standard is inter- fered with by the fact that a certain per cent, not stated, of 1 5-inch and 2|-inch lumber was included with 1-inch boards in its construction. The results are there- fore somewhat too high for 1-inch lumber. This log rule indicates that the contents of logs measuring from 4 to 10 inches in diameter at small end are from 20 to 50 per cent greater when scaled by this rule than by the International |-inch rule. Above 12 inches, the excess is not over 10 per cent. Since these boards are measured at their average face, taper is fully utiUzed, while waste from slabs and edging is reduced to a minimum. The result- ant per cent of utilization is very consistent for logs of all sizes; hence it shows a marked gain in the small sizes over the per cents utilized in square-edged boards as shown in Table III. The importance of a log rule of this character in scaling the board-foot contents of second-growth timber in regions utilizing round-edged boards is obvious. Rules of this character are nearly as satisfactory as the cubic foot in measuring small timber. For complete accuracy in applying this rule to other species, the average taper must be known, or the average thickness of bark. Similar local log rules have been made for loblolly or old field pine in the Atlantic Coast States. 76. Conversion of Values of a Standard Rule to Apply to Different Widths of Saw Kerf and Thickness of Lumber. Where over-run or under-run is caused by a difference in the width of saw kerf used, or in the thickness of hunber sawed, from the standards used in the log rule, the per cent of this difference between scaled and sawed contents due to these factors may be easily determined, and applied, if desired, to the scale; or it may be incorporated in a new set of values or local log rule similar to those made from mill tallies. For saws of different widths. Let isr = width of saw kerf in standard rule; K' = width of saw kerf used in sawing. Then 1 -— — - =per cent of lumber, minus saw kerf by standard rule; l-\-K J , 1 - =per cent of lumber using different saw kerf. 1+K The correction to apply to the standard rule in terms of per cent is: Per cent correction = 100 X , 1+A' e.g., the International rule, 3-inch kerf plus j^g-inch shrinkage = ^-inch = . 3 125, 1 100 X =76. 3 per cent. 1.3125 ^ CONVERSION OF VALUES OF A STANDARD RULE 81 For a i^-inch saw kerf plus re-inch shrinkage = i\- = . 25, Then, 1 100 X =80 per cent. 1.25 ^ 80 100 X = 104 . 8 = +4 . 8 per cent. 76.3 The following table will convert values for the International j-inch log rule to products of saw kerfs of other widths, allowing i^-inch shrinkage in each case as for the original rule. TABLE XIII Conversion of International Rule j-inch Saw Iverf for Other Widths of Kerf Width of saw kerf. Inches Per cent utihzed* Per cent correc- tion to obtain product for desired kerf 7 64 1 8 3 16 1 1 3 g 7 16 85.4 84.3 80.0 76.3 72.7 69.6 66.7 + 11.9 + 10.5 + 4.8 - 4.7 - 8.8 -12.6 * This per cent applies only to the residual portion of the log after deducting the waste for slabbing and edging. The ratio between the per cents utilized is the basis for correcting for saw kerf. Log rules which make no allowance for shrinkage may be adjusted in the same manner by omitting this factor. Table XIV, Page 82. Correction for lumber thicker than the standard. For this jjurpose the same formula as for saw kerf is used, substituting the actual thickness of lumber {t) for 1 inch, and using X as a constant representing saw kerf. Let 1 = standard thickness of lumber; <= actual thickness of lumber. Then, =per cent of lumber, minus saw kerf by standard rule; 1+K ^ ' J , t =per cent of lumber, with thickness of t; t-^K and 1+K =per cent correction. t+K For j-inch saw kerf the results obtained are given in Table XV, Page 82 (§ 48) : 82 THE CONSTRUCTION OF LOG RULES TABLE XIV Conversion of Log Rules with |-inch Saw Kerf and No Shrinkage Allowance to Other Widths of Saw Kerf Width of saw kerf. Inches * Per cent Utilized Per cent correc- tion to obtain product for de- desired saw kerf 7 64 1 8 1 4 f 90.2 88.8 84.3 80.0 76.2 72.7 69.6 -t-12.7 4-11.1 + 5.4 - 4.8 - 9 1 -13.0 * Rules made by first subtracting slabbing and edging may evidently be altered for different widths of saw kerf, as these deductions are directly proportional to volume, and are applied to the reduced cylinder only. Where, as with the International rule, the deduction for saw kerf is made before subtracting AD for slabs and edging, this rule still holds good, since the per cent of cor- rection is not applied to the entire log, but to the values in the rule, which already exclude AD. If worked out for the log, independent of the rule, the sawdust in the slabs is deducted before the factor AD is found, and for larger saw kerfs this factor AD would be proportionally smaller, so that the total net product in lumber is the same as if computed by the above correction. TABLE XV Per Cent of Increase in Sawed Lumber Caused by Sawing Lumber of Different Thicknesses j Increase in sawed Thickness of himber. product over 1 inch lumber. Inches Per cent u 4.1 H 7.1 If 9.4 2 11.1 21 12.5 3 13.6 t In preparing tables of volume for Connecticut hardwoods (Bui. 96, Forest Service), Frothing- ham used the International rule, reduced for a J-inch saw kerf by subtracting the required 9.5 per cent of volume from-values for i-inch saw kerf. Complaint was later made that in applying these tables to logs sawed in mills using j-inch saw kerf, the output over-ran the tables. This was due not to error in the tables, but to the production of a large proportion of thick planks, thus reducing the sawdust waste. These per cents are applied to the scale of 1-inch lumber. When 50 per cent of the output is in 2-inch plank, the correction would be 50 per cent of 11.1 per cent, LIMITATIONS TO CONVERSION OF BOARD-FOOT LOG RULES 83 or 5.55 per cent. As the increase in per cent of correction in the total scale becomes less with increasing thickness of boards sawed, this method is more accurate than that of computing the average dimensions of the products sawed. In the above case the latter would have been I5 inches, calling for a correction of 7.1 per ceftt instead of 5.55 per cent. Correction for thin lumber based on superficial contents. In a similar way, log rules for 1-inch lumber may be corrected to give the product in superficial board feet for lumber sawed to thicknesses less than 1 inch. Since the board, of whatever thickness, measures 1 superficial foot, the "per cent of utilization" will be ;, ( being t-\-K thickness of board, K, saw kerf. For ^-inch kerf and 1-inch lumber, the standard 1 1 t I K per cent is =80 per cent. Then the correction per cent is . 1+K TABLE XVI Correction Per Cents for Contents of Logs in Superficial Board Feet FOR Lumber Sawed Less than 1 Inch in Thickness Thickness of lumber. Inches Saw kerf. Inches Per cent of utilization Per cent for inch lumber Correction per cent to add to log rule for 1-inch boards Per cent s 8 f i 1 133.3 114.3 100.0 88.8 80 80 80 80 66.6 42.9 25.0 11.1 77. Limitations to Conversion of Board-foot Log Rules. It is thus seen that a correction of the total scale of logs regardless of diameter or length can be made whenever thid correction takes the form of a straight per cent of the volume of the scale. In addition to the effect of saw kerf and thickness of boards, this principle applies to cubic rules erroneously- used for board feet (§ 38). But no true board-foot log rule can be con- verted by a constant or flat per cent into the values of any other log rule, unless the deduction for waste from slabs and edgings is identical for both rules, and the difference is wholly due to the use of different per cents of waste for saw kerf. Otherwise, the conversion factor will vary with diameter of log. Since tables of tree volumes and the scale of a number of logs include logs of different sizes, such volume tables or scale totals must be remeasured in the log in order to determine the values for any other than the log rule originally used. 84 THE CONSTRUCTION OF LOG RULES 78. Choice of a Board-foot Log Rule for a Universal Standard. As long as opinions and customs differ with regard to tlie measurement of taper, scaling length, saw-kerf allowance and amount of waste in slabbing which should be expressed in log rules, it will be impossible to reach an agreement on a common standard. Meanwhile, custom is working towards the elimination of rules which have not found favor and all but about ten log rules in the United States can already be classed as obsolete. A log rule becomes obsolete when it ceases to be used, regardless of the reasons for its disuse. Poor rules should, and sometimes do, become obsolete because they do not give satisfaction. But good and con- sistent rules may also become obsolete or may never be taken up, because the use of other and inferior rules is so firmly intrenched that a substitu- tion is impractical. Rules which scale so closely as to permit no over- run will be very difficult to bring into common use, owing to the opposi- tion of buyers who prefer lower standards even if inaccurate. The log rules whose use is sufficiently extensive to justify their con- sideration, on this basis alone, for universal adoption include only the following: Basis of Rule United States Canada Formula Doyle Doyle British Columbia Diagram Scribner Quebec Scribner Decimal C New Brunswick Spaulding Maine Hybrid Doyle-Scribiier Mill Tallies Massachusetts Of these, the Doyle must be rejected because of its glaring inconsis- tencies and the Doyle-Scribner because it combines the worst features of both rules. The use of the Maine and the Spaulding rules is confined to single states, and the Massachusetts rule is for a special form of product; i.e., round-edged timber. This leaves the Scribner, preferably in Decimal C form, as the only logical rule now in wide use, which is applicable to the measurement of square-edged lumber. If the admitted irregularities of the Scribner rule are deemed so seri- ous as to justify its rejection, its successor should not be chosen from among the other rules in common use, but should rather be a rule based on a formula and tested to conform to actual conditions of sawing. For such a purpose, the International {-inch Rule is probably as perfect a UNUSED AND OBSOLETE LOG RULES 85 rule as will ever be required in commerce. This rule is especially valu- able for logs below 12 inches and above 28 inches, in which classes the Scribner rule is defective. There is nothing to be gained by further efforts to construct new " perfect " log rules. 79. Unused and Obsolete Log Rules. In addition to the rules described in this chapter we may mention the following rule.s, all of which are now obsolete. Bangor Rule. Synonyms: Miller, Penobscot. The Bangor Rule was constructed from diagrams, and gives slightly higher and more consistent values than the Maine rule. It shows more care in construction and is probably the best of the diagram rules. Owing to the more extensive use of the Maine rule, this rule is almost obsolete. Parson's Rule. This rule is of similar construction to the Bangor and Maine rules and its values are almost identical but a little below the Maine rule. The difference is about 2 per cent. It is a local rule, still used to some extent. Boynton Rule, 1899 (Vermont, local). Made up from values taken from Scrib- ner and Vermont rules .checked by mill tallies. A fair rule but of no general value.. D. J. Bo3aiton, of Springfield, Vermont. Brubaker Rule. No detailed knowledge. Chapiii Rule, 1883. The most erratic of all log rules, made up apparently by selecting values from existing rules to suit the author. Dreiv Rule, 1896. The Drew rule has been the statute log rule of the State of Washington since 1898 but is used practically nowhere in the state. Instead, the Scribner rule is universally used, except along the Columbia River, where the Spauld- ing rule is in use. This rule (by Fred Drew, Port Gamble, Wash.) was made from diagrams checked by tallies of logs as sawed. The values are given for diameters from 12 to 60 inches and lengths of from 20 to 48 feet. Taper is not considered. The values are said to have been reduced to allow for hidden defects. The rule is inconsistent in scale, resembling the Doyle in tendency on large logs. Its use is practically discontinued. Dusenherry Rule, 18.3.5. This nilo was made in 1835 by a Mr. May, and adopted by Dusenberry-Wheeler Co., of Portville, N. Y. It was probably constructed from mill tallies, and was intended to measure the output of pine sawed If inches thick with some 1^- and 2-inch pieces. The saw kerf was j^ inch. The rule is very consistent and was generally adopted in the Alleghany Waters in Penn- sylvania. It is still used in that and adjoming states. Owing to the wide saw kerf used, this rule under-scales Scribner from 15 to 20 per cent and is not suited to present conditions. Favorite Rule. Synonym: Lumberman's Favorite A diagram rule, made by W. B. Judson in 1877 and published in Lumberman's Handbook, 1880. The values for small logs are lower by 15 per cent than Scribner's. The rule is now practically obsolete. Finch and Apgar Rule. Date unknown. A diagram rule, erratic, for i^-inch saw kerf. Gives low values. Forty Five Rule. About 1870. Based on an inaccurate rule of thumb formula which gives high values for small and large logs and low values between these extremes. Herring Rule, 1871. Synonym: Beaumont. The values in the Herring rule as originally made, to include from 12- to 44-inch logs, are practically identical with the Dusenberry rule. The rule was applied at the small end to logs up to 20 feet in length. Above 20 feet a rise of 1 inch was added, and was applied at middle point of logs up to 40 feet in length. Here another inch was added, and the 86 THE CONSTRUCTION OF LOG RULES scale carried to 60-foot logs. The taper allowed in this was is about half of the average taper. The rule is used extensively in the pine regions of Texas and gives a large over- run. The same trouble was ex-perienced with this rule as with the Scribner^ in agreeing upon an extension of values to cover logs less than 12 inches in diameter. The values most commonly used are the so-called Devant extension, based upon the Orange River rule, and agreeing closely with the Scribner extension. Licking River Rule. No detailed knowledge. Northwestern Rule. A diagram rule for |-inch saw kerf. Erratic, and similar to Scribner's. Ropp's Rule. A rule published by C. Ropp & Sons, Chicago. Based originally on diagrams of 1-inch lumber for a j-inch saw kerf, it was reduced to a rule of thumb which gives erroneous results especially for small logs, which are severely under-scaled. The rule is therefore of no value. Warner Rule. A diagram rule with excessive allowance of f inch for saw kerf. Worthless. Wheeler Rule. No detailed knowledge. Wilcox Rule. A diagram rule for f-inch saw kerf. Irregular. Low values. Younglove Rule.^ Fitchburg, Mass., 1840. A cahper rule resembling the Baxter in values. References General Treatises on Log Rules Relative Value of Round and Sawn Timber, James Rait, p. 114, Wm. Blackwood Sons, London, 1862. The Measurement of Saw Logs (Universal Rule), A. L. Daniels, Bui. 102 Vermont Exp. Sta., 1903. The Measurement of Saw Logs and Roimd Timber (Champlain Rule), A. L. Daniels, Forestry Quarterly, Vol. Ill, 1905, p. 339. The Measurement of Saw Logs (International Rule), Judson F. Clark, Forestry Quarterly, Vol. IV, 1906, p. 79. The Standardizing of Log Measures, E. A. Ziegler, Proc. Soc. Am. Foresters, Vol. IV, 1909, p. 172. The Log Scale in Theory and Practice (Tiemann Log Rule), H. D. Tiemann, Proc. Soc. Am. Foresters, Vol. V, 1910, p. 18. A Discussion of Log Rules, H. E. McKenzie, Bui. 5, California State Board of Forestry, 1915. Review of Bui. 5, California State Board of Forestry, by H. D. Tiemann. Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 93. Specific Log Rules Scribner's Log and Lumber Book (Cubic Measure, Two-thirds Rule, Doyle Rule), S. E. Fisher, Rochester, N. Y., 1900. Extending a Log Rule (Devant Extension of Herring Rule vs. Doyle Rule), E. A. BranifT, Forestry Quarterly, Vol. VI, 1908, p. 47. Report of Commission to Investigate Methods of Scaling Logs in Maine (Holland Rule, Blodgett Rule, HoUingsworth & Whitney Rule), House Document No. 43, 74th Legislature, Maine, 1909. 1 Reference, Forestry Quarterly, Vol. XII, 1914, p. 395. UNUSED AND OBSOLETE LOG RULES 87 A Comparison of the Maine and Blodgett Log Rules, Irving G. Stetson, Forestry Quarterly, Vol. VIII, 1910, p. 427. Woodsman's Handbook, Henry S. Graves and E. A. Ziegler (Scribner Decimal C, Doyle, Inscribed Square Log Rules, and Table of Comparisons of 44 log rules for 16-foot logs), Bui. 36, U. S. Dept. Agr. Forest Service, 1910. Comparative Study of Log Rules (Champ lain, Vermont and Doyle Rules), Austin F. Hawes, Bull. 161, Vermont Agr. Exp. Sta., Fart II, 1912. Log Rules Based on Mill Tallies Log Rules for Second-growth Hardwood from Mill Tallies, j-inch Saw Kerf, Round-edged Boards cut 1^ indies thick. Based on Small End, Inside Bark, and on Middle Diameter Outside Bark, C. A. Lyford, Reports of Forestry Commission, N. H., 1905 and 1907. Log Rule for White Pine, from Mill Tallies, J-inch Saw Kerf, for 60 per cent Roimd- edged, 40 per cent Square-edged Boards, 70 per cent l-inch Lumber, remainder 2|-mch Plank, C. A. Lyford, Reports of Forestry Commission, New Hampshire, 1905 and 1907. Log Rules for r2-ft. logs from Mill Tallies of Round and Square Edge Lumber, separately for White Pine, and Hardwoods, L. Margolin, Proc. Soc. Am. Foresters, Vol. IV, 1909, p. 182. Comparison of Round-edged and Square-edged Sawing for 2g-Lnch planks, H. O. Cook, Forest Mensuration of White Pme in Mass., 1908, pp. 38-43. Contrast of Output by Different Methods of Sawing, H. D. Tiemann, Proc. Soc. Am. Foresters, Vol. IV, 1909, p. 173. Log Rule for Hickories, in Cubic Feet, Bui. 80, Forest Service, 1910, p. 39. Log Rule for Hardwood Logs from Mill Tally, Yellow Birch, Maple, Beech, I. W. Bailey and P. C. Heald, Forestry Quarterly, Vol. XII, 1914, p. 17. Log Rule for Loblolly Pine, based on Mill Tallies, Logs with less than 2-inch Crook, i-inch Kerf. W. W. Ashe, Table 23a. Bui. 24, North CaroUna Geological Survey, 1915, p. 76. CHAPTER VII LOG SCALING FOR BOARD MEASURE 80. The Log Scale. The scale of a given quantity of logs is their total contents expressed in the unit of measurement employed. The term " scale " also refers to the general rules or customs of scaling adopted in a given region or locality, upon which depend the liJ)erality or closeness of the measurement (§ 83). Differences in the method of scaling may make from 5 to 50 per cent difference in the scaled contents of the same logs (Table XVII). To determine the contents of logs in board feet, the diameter of the log is measured with a stick marked in inches, the length in feet is deter- mined by measuring it with the above stick or by a tape or wheel (§ 34), and the volume corresponding to these dimensions looked up in the log rule.^ This process is simplified by placing upon the sides and edges of this stick, opposite each diameter, rows of figures giving the values of the rule for each of several standard lengths. The volume in board feet is then read directly from the stick, and recorded. A stick so graduated is termed a scale stick or scale rule. Scale sticks are made of hickory or maple about 1 by J inch in cross section, graduated in inches, with the figures burnt into the wood (Fig. 10). Metal sticks are also in use and in some regions caliper rules are used. The inch scale is on one or both edges and the stick easily accommodates six or seven other rows of figures corresponding to the contents in board feet of logs of as many different standard 2-foot lengths. A metal tip aids in measuring the diameter inside the bark. Other forms are made for scaling logs in water, or logs with ends rounded or sniped. Lengths of scale sticks in inches correspond to the maximum diameters of the logs to be scaled. Hexagonal scale sticks are sometimes used. Scale sticks have been made. which are graduated at points giving volumes to exact tens or hundreds of units, but these rules have never become popular as the basis of the rule is not indicated (§ 111). The purpose of a log scale depends upon the ownership of the timber or logs. Where the logs are to be sold the scale is the basis of settle- ment and must be far more carefully made than when the timber is 1 Experienced scalers sometimes substitute ocular or paced lengths on short logs. The scale of logs shorter than the minimum length given in the rule is taken as equaling one- half the scale of a log twice as long as the one in question, i.e., when the shortest length given on the scale is 10 feet, an 8-foot log is scaled as one-half of a 16-foot log. 88 THE LOG SCALE 89 owned, logged and manufactured by the same firm. In the latter case, the purpose of the scale is merel.y to provide a basis for the payment of contractors for logging or sawyers for felling, or for checking the com- -— ■ 8 SCRIBNE8 SCALE -28 _ Fig. 10. — Forms of scale sticks in use. parative efficiency of crews or camps. Finally, the woods scale deter- mines the quantity of timber felled, thus keeping track of the operation, while a re-scale at the mill permits the keeping of costs and credits separately, on the basis of the volume of logs delivered, between the 90 LOG SCALING FOR BOARD MEASURE logging and milling ends of the business, as if they were under separate management. Woods scaling also checks the accuracy of timber esti- mates, whenever the timber from given areas is scaled separately in logging. When the purpose is to determine the basis for paying saw crews, logs are scaled in the woods before skidding. When standing timber is sold on the basis of the log scale, the scaling is done at the skidways or landings before removal from the tract or vicinity. The mi.xing of logs cut from two or more tracts must be avoided by any necessary measure such as sawyers' marks, or scahng in the woods. Where no question of sale is involved, the logs are scaled wherever it is most convenient. Logs are usually re-scaled on the log deck. Where logs are rafted and sold, they usually are scaled in the water. 81. The Cylinder as the Standard of Scaling. A log rule does not give an exact scale of lumber which will be or can be sawed from logs (§ 46). The log rule is an arbitrary standard fixing the quantity of 1-inch lumber said to be contained in logs of given diameters and lengths. When the top or small end of the log inside the bark deter- mines the diameter, as it does for all board- foot log rules in common use, these rules do not include any boards or pieces sawed from the taper or swell of the log. The scaler must therefore pay no attention to that portion of the contents of the log which lies outside of this cylinder, no matter whether this portion be sound or defective. On the butt end of a log, the contents to be scaled lies within a smaller circle representing the area of the top end of the log, or the cross-section of the cylinder whose diameter is this top end. This cylinder must coincide in position with the axis of the log, so that the center of the cross-section or area to be scaled coincides with the center of the butt or larger end of the log. Common errors in scaling are the shifting of the scaled cylinder towards one side to avoid defects, and the offsetting of defects within the cylinder against sound short lumber which may be scaled from the taper. 82. Deductions from Sound Scale versus Over-run. Log rules give the scale of this cylinder in sound lumber and do not allow for defects. The standard scaling practice is to make deductions from Fig. 11. — Projection of area of top end of log on butt section, showing portion of butt to be scaled. The circle A represents the area to be scaled. The presence of defect in area C does not justify the shifting of this circle to position B but de- ductions for defect must be made from A. D is the geometric center of the log and of the scaled area A . SCALING PRACTICE 91 the scale for all visible defects which lie within the cylinder in each log separately, of the amount of lumber which would be lost because of the defect. This rule is not always observed. In many species, certain defects may exist without visible external indications either on the surface or at the exposed ends. When the logs are in water it is difficult to detect defects. There has been a tendency on the part of makers of log rules to reduce the standard volumes of the log rule in order to offset these invisible defects (Scribner rule, § 68). Log rules, like the Cumberland River rule which gives but 45 per cent of the cubic contents, permit the buyer to ignore most defects with perfect safety. The use of a log rule which is known to give a large over-run (§ 47) usually gives rise to the practice of scaling "sound" and ignoring defects. The buyer can afford to be lenient, and the seller objects to any further discounts than those inherent in the rule itself. Except for a few species and regions, defects may usually be seen and deducted. Where the opposite is true, custom sometimes permits a reduction of the final scale by a straight per cent to allow for such invisible defects. Over-run (§ 46) is therefore an element which should not influence in any way the practice of log scaling. Where an admittedly defective rule is offset by lenient but inaccurate scaling practice, the entire technique and standard of scaling suffers, and such conditions should sooner or later yield to accurate standards, both in the rule used and in its application. 83. Scaling Practice, Based on Measurement of Diameter at Small End of Log. The advantages of measurement of the log at the small end, which have made this custom practically universal in scaling, are that the scaling diameter inside the bark can be directly measured without guessing at bark thickness, and no matter how high a skidway or rollway is piled, the ends of the logs are usually visible for scaling. By contrast, logs to be calipered at the middle point can be measured only when lying separately or before being placed on rollways, and the bark thickness is usually guessed at. The per cent of over-run on the log scale is affected by three main factors. Two of these, namely, the elements affecting manufacture of lumber and the character of the log rule itself, have been discussed in Chapter V. The third is the practice of scaling, and the customs which govern it, collectively termed the " scale." This practice affects, first, the method of determining scaling diameters and lengths, for when these are once ascertained the rule permits no variation in contents for sound logs; and second, the deductions from this scale for defects, as interpreted by the scaler. Scaling Lengths. The total length of a log must be accurately deter- mined. For log rules which are based on diameter at the small end, 92 LOG SCALING FOR BOARD MEASURE logs whose length exceeds a given maximum are scaled as two or more sections or shorter logs (§ 43). Custom or " scale " determines the maximum length to be scaled as one section and the method of deter- mining the taper or diameter of the second or remaining sections to be scaled. Short sections scaled to full or actual top diameter give the maximum scale, while the loss from scaling long logs as one piece based on diameter at top end may be very large, due to the increasing per cent of volume in long logs which lies outside the cylinder and is thrown into the over-run. The standard lengths of softwood or coniferous logs are multiples of 2 feet, to which is added an allowance for trimming. Where long logs are divided into two or more lengths for scaling, this rule is still adhered to; e.g., a 26-foot log is scaled as a 14- and a 12-foot. Usually the longer length is scaled as the butt log. The tremendous variations in scale which may result from different treatment of scaling lengths and taper in long logs is illustrated in Table V (§ 44). In order to secure a consistent scale between long and short logs, the scaling length should be limited to not over 16 feet, and the actual diameter of each section taken as the scaling diameter. Trimming Allowance. The trimming allowance varies according to the method of transportation used. For logs hauled by rail or driven down sluggish streams, from 2 to 3 inches is allowed for each 16 feet of length. Large logs require the greater allowance, to guard against slanting cross cuts which might give a short length on one side. Where logs are driven down swift rocky streams the trimming length must be sufficient to allow for the brooming of the ends. In very bad waters, the exact length of a log is immaterial and the loss from brooming a heavy item. Odd lengths, i.e., lengths measured in odd feet as 13 feet, are permitted in hard- woods and to a limited extent in softwoods. In ordinary scaling, trimming lengths in excess of standard 2-foot gradations are not scaled. But sellers of logs, to reduce loss from careless cutting of log lengths, may stipulate that when trimming lengths are in excess of the margin agreed upon, the log shall be scaled as if cut from 1 to 2 feet longer. The U. S. Forest Service adopts this practice as a penalty scale. Scaling Diameters. In the apparently simple process of measuring the diameter inside the bark at the top end of the log, there are two ways in which the buyer may be given the advantage of a smaller scale. Owing to the irregular cross sections of logs, an average diameter should be found by taking two measurements at right angles. Instead, the practice of scaling the smallest diameter is common. The difference, in large logs, sometimes amounts to 2 or 3 inches. The second choice lies in the treatment of fractional inches. These fractions should be rounded off to the nearest inch; e.g., the 18-inch log class should include diameters from 17.6 inches to 18.5 inches. Instead, all fractions may SCALING PRACTICE 93 be dropped, throwing logs from 17.6 inches to 17.9 inches into the 17- inch instead of the 18-inch class. ^ The variations in scaling practice or local "scale" for the different regions in the United States and Canada are shown in Table XVII, p. 94. It is seen that the standard set by the U. S. Forest Service is almost nowhere complied with m private operations, and that the departures from this standard work uniformly in favor of the buyer. Except for hardwoods, there is no vaUd reason for rejecting fractional inches, since these are in most instances already rejected in the construction of the log rule itself (Scribner, § 68), and in any case, the contents of logs of exact inch diameters represent a fair average for logs varying up to J inch larger or smaller. In the same way, it is unfair to measure the smallest diameter instead of the average, for the sawed contents of logs with eccentric cross-sections is little if any less than for round logs, and certainly does not diminish in proportion to the ratio between smallest and average diameter.^ Fig. 12. — Effect of rapid taper at small end upon scaling diameter and scaled contents of a log. ' The adoption of these two buyers' practices in the scale will result in a loss to the seller which, l^^y the Scribner log rule, amounts to from 5 to 15 per cent, averaging 8 per cent for logs rmining 10 to the thousand board feet, and 13 per cent for logs running 20 per thousand. The use of the average diameter, and the rounding off of fractional inches are practices fair alike to buyer and seller, and are required by the U. S. Forest Service in selling public timber. The practice of reducing unit feet in a log rule to tens, or converting the rule into a "decimal" rule gives a third opportunity for discrimination in favor of the buyer. The correct method is that employed in the Scribner Decimal rule where all fractions above 5 feet are thrown to the 10-foot value above, while those less than 5 feet are dropped. But in one section of Maine it is the custom to drop all unit feet scaled by the Maine rule. Thus a log scaling 19 feet would be entered as 10 feet. The effect of such a custom on the scale is self evident. ^ In a contract for sale of logs, the log rule to be used must be mentioned. The practice regarding scahng length, trimming allowance, method of measuring taper or rise on logs of greater than scaling lengths, measurement of diameter and treatment fractional inches should be specified. Otherwise, common custom or scale in the locality will determine what constitutes a proper method. The method of deducting for defects whether by each log separately or by a straight per cent should be agreed upon, and if possible, standard instructions adopted for culling defects. The minimum dimensions of a merchantable log should be defined, both as to length and diameter, and as to per cent of total scale which must be obtained after deducting for defects. 94 LOG SCALING FOR BOARD MEASURE o o o « ^ Q X g 1 k 4^ enob- with meter s bi c •4J fl 41 o •« CL| -0 OS P. 00 bc (U C •"* 03 e a 3 bC J3 i 3 8 ■d a> ■3 « bC be •^ 03 3 a S "3 "3 9 ^ .s ° g - 3 ^m 2 _5j CI t. 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The practice of basing the scaling diameter on that of the small end of the log, with its consequent disregard of taper, gives rise to diffi- culties on logs which taper rapidly at the small end, as for instance, rough or limby logs on the basis of their top diameters may result in loss of scale when in reality a greater volume of the tree has been utilized. Fig. 12, p. 93. By the International j-inch rule this log would scale, in actual diameter Length. Scaling diameter. Scale. Feet Inches Feet B.M. 12 12 70 14 9 45 IG 6 20 Rigid adherence to the scaling practice on such logs results in the refusal of contractors to cut them. There are two possible modifications of the end diameter rule which will meet this condition: First, to scale the log as a shorter log, at the point which will give the largest total scale, in the above instance at 12 feet giving a scale of 70 board feet; second, to scale it as two logs, including the short tapering portion as a separate piece from the main portion. In the above case, the 6-inch top, with a length of 4 feet would add one-fourth of the scale of a 16-foot log of that diameter, or 5 board feet, giving a total scale of 75 board feet. The latter method is the most equitable, otherwise there is no object to the contractor in going into the top to secure closer utilization. Abnormally large diameters, occurring at the small ends of logs are the result of cross cutting through crotches or swellings caused by limbs, or by defects or cankers. Such diameters must always be reduced to a size representing the normal diameter of the cross section as determined by average taper. For slight swellings this is judged by eye. For crotches, the diameter at butt end is sometimes taken and average taper deducted. ' 84. Scaling Practice Based on Measurement of Diameter at Middle, of Log or Caliper Scale. None of the true board-foot log rules in common use are applied at the middle of the log. By the Blodgett Rule, a cubic rule expressed in board feet (§ 33) the log is usually measured in the middle, outside the bark. When taper is taken on long logs by the ordi- nary rules, the scaler depends upon his scale stick and ocular judgment for the measurement of the upper diameters. But if logs are customarily cut long, and must be scaled by getting actual taper rather than assumed 1 The following court decisions are important as defining the bearing of the "scale" on agreements: "In the absence of any agreed standard of measure in a contract, that of the place where a commodity is purchased will govern the contract." Supreme Court of New York, Dunberic vs. Spaubenberg, 121 N. Y. 299. "Where a contract involves the measurement of logs by specified rule, but does not indicate the manner of measuring whether by end, average or middle diameter, local custom shall determine such manner." Supreme Court of Louisiana, 13 So. 230. 98 LOG SCALING FOR BOARD MEASURE standard tapers, calipers must be brought into use in scaling. The calipers employed in scaling logs by the Blodgett rule are equipped with a wheel of 10 spokes, one revolution measuring 5 feet in length (§ 34). The greatest drawback to a caliper scale is the necessity of determin- ing the width of bark, doubling this, and subtracting to get the scaling diameter of the log. When all logs are calipered, it is a common prac- tice to determine the average width of bark of the species and region, and deduct twice this fixed amount on all logs regardless of variations in actual bark thickness, relying on the law of averages to secure a true scale. For the Blodgett rule, f-inch for each bark is allowed and the calipers are adjusted to read the diameter inside bark direct. On the Big Sandy River in Kentucky (Big Sandy Cube Rule) the allowance is 1 inch for each bark.^ 85. Scale Records. The tally is the record kept of the logs by the scaler or his assistant, the tally man.^ The tally may consist merely of a record of diameter and length of each log. From this the full scale is easily computed at camp. But the system prevents deductions for defects from each log separately, and is used only where such discounts are not made, or are made either as a per cent of total scale, or by reducing the length or diameter of the log. This primitive method of scahng has been largely replaced by the plan of recording the board-foot contents of each log when scaled. From the full scale, deduction is made for defect, and the net or sound scale recorded. For long logs scaled in two or more sections, only the sum of these volumes is set down, giving the total scale for the log as one piece and thus keeping the count intact. The purpose in this is to obtain a tally of the exact number of pieces scaled as well as their total contents. To still further insure an accurate record, logs are numbered serially, with crayon, coinciding with printed numbers in the scale-book. This enables a check scaler to re-scale and compare individual logs, or any number of logs, with the original scale to determine the per cent of error and the specific faults in practice. Without such enumeration, the entire number must be re-scaled to obtain a check, and specific errors are not shown. The method of numbering is cumbersome where large quantities of very small logs are handled, but it is the only plan by which a uniform standard of scaling may be attained by a force of several scalers. 1 A second method, employed in Maine in scaling cubic contents, is to assume that the volume of bark is I25 per cent of the total volume of the tree with bark. The diameter outside bark is measured direct, and the volumes given on the rule are computed to express the contents of wood alone. Bark is never removed, in scaling, to permit the calipering of the direct measure- ment inside bark, as this process is too time consuming. The Tiemann log rule (§ 63) which applie.s to middle diameter inside bark, if used commercially, would probably be applied by the common method of deducting fixed widths of bark, to be regulated by measurements taken of the species and locality. This practice permits of an additional source of variation in measuring diameters (§ 29) through the bark on individual logs being thicker or thinner than the arbitrary measure- ment. 2 Scalers usually work alone, preferring the extra labor to the risk of errors made in the record by incompetent tally men. SCALE RECORDS 99 The scaler marks the logs with crayon as he scales them. If not numbered, they are check marked. Where logs are piled in rollways, unevenly, and cut different lengths, the count must be checked carefully to see that none is missed. This is best done by making a recount after scahng a rollway, and check marking the butts of the logs, the tops having been marked in the scaling. Logs piled in high rollways can best be scaled by two men, one working at each side of the rollway. Cull logs which are not scaled are given a distinguishing mark. If already skidded, they should be counted and recorded as culls. The scaling of logs in the woods eliminates the culls from the scale altogether and saves the expense of logging them. Log Brands, Termed Stamps and Bark Marks. When the practice is necessary the scaler must see that the logs have been properly stamped and bark marked. A stamp is a pattern or die stamped into the end of a log with a marking hammer. A bark mark is a pattern cut into the bark, usually near an end, with an axe. Stamps and bark marks are used to distinguish logs when driven with those of other owners down a common stream. These marks are recorded by scalers and determine the ownership of the logs. The Scale Book. A form of scale book is shown on p. 100 containing 100 printed numbers on a page with spaces for entering the contents of logs, and for totaling each column separately and adding these totals for the page. The scale record shown in this sample page is for the Scribner Decimal C Scale. The original records give the scale in tens of feet. At the foot of each column, the total is entered parallel to the base, and the zero added to obtain full scale. Logs whose scale has been culled show the net scale, and also the amount culled enclosed in a circle as, (e), which permits checking the cull. Other forms of scale records are in use following these general principles.^ 86. The Determination of What Constitutes a Merchantable Log. A merchantable log is one which it is profitable to log. Logs whose con- tents will not return the cost of logging and manufacture are unmer- chantable. This may be due either to small size, to defects which reduce the scaled contents of the log, or to high cost of logging. Minimum Size. The costs of producing lumber are separated into logging cost and milling cost. Both depend on the cubic volume of the log. But both are modified by the time required in handling separate pieces. This causes the cost per cubic foot to increase for small logs. In logging, and in small mills, the cost also increases per cubic foot when logs reach large sizes difficult to handle. The value of the product depends not upon the cubic contents of the log, but on the quantity of sawed lumber which it contains, and 1 The following court decisions are of interest: "When record of scale is kept on temporary paper and transferred every evening to permanent record, this record holds in court as original evidence." Court of Appeals, Alabama, 68 South. 698. The U. S. Forest Service instructs its scalers to make the original and final record of scale in the field because of the HabiUty of error in copying figures. "Parties must abide by the official scaler's report except that fraud or gross mistake can be shown." Supreme Court, Michigan, Brook vs. Bellows, 146 N. W. 311. A. . 7S70 100 LOG SCALING FOR BOARD MEASURE ^ ? D a H ^^ ® © ® . ® \%%:^ S6SO X\\^^'^\^h'^%k'^^^^'^t'ts.%\ ll \\ V N- i S;^si:}SS;ii^3:3SSS3SS!S ? i N<^OJ ^ ^ Q ^ N» Q> cj4 Nj VQ^ <^< (jj cb Qi C3 0; c^ i r < V) t)> z «= PI "S 5 PI a. <^ « I c 3 2 6960 l^l;S^S^!S^^Sl^^H^^^^^ ^ 36440 f"*"- "» •■*''^ ^ ^ § S 5^ //O 7SO """"''"^ FORWARD. N^. ^" ^ N, ^ y^ "7/00 TOTAL SINCE LAST REPORT. . n? <^ ^ sV) S REPORTED TO^^.^^t:?^^? ^^S^^ P TOTAL TO ^^^.-..a?£.^/

> 1^ C3 a CD a i-H C -^ S) H CO J3 P. OJ CO o £1 ^ O o -0 ^J & _ M T3l3 ^ 3 a; «CQ r~ t~ 00 lO •* '0 iC •-D » —I •* m 00 00 X 00 t^ ■* lO ■o b- CO ■* 00 u,l O 00 o O) ■* '— ' CO •o in lO •<*< CD •^,1 o ^ ro ^^ o 73 1 & fi 3 1 ^ ^ a o '■+-> o o ■>^ > ^ o bUXt 'S3 ^ 1'° 3 cS om 25'm Q x: a i-hP5 Q o c -5 W _§ o ^ ' S o -- o c, S m-:^ coincide with the portion of the tree which is actually used, and the average top diameter with that which is actually cut. But the variable practice of sawing and the arbitrary standards set by saw crews as to waste in the tops, differing with different crews, logging jobs, regions and seasons, is a strong argument for adopting a fixed standard for top diameters for saw timber. This stand- ard may either conform to the average diameter utilized, or may depart from it and be smaller; e.g., as at By. Where a fixed top diameter is chosen, instead of the variable one coinciding with utilization practice, the last taper measure- ment will usually fall above or below this diameter, as before. Here the same rule of give and take can be applied; but if the diameter limit is small the top tapers rap- idly and it may be preferable to take no measurement of less than the minimum top diameter. The last top measurements will then fall always either at or below the point. Where 16-foot measurements only are made, it is necessary to take an 8-foot length at the top whenever the last cut falls more than 4 feet distant from the last 16-foot taper. This is another reason for taking 8-foot tapers throughout. 156. Defective Trees, Measurement. Frequently one or two top logs in certain trees will not be utilized because of defects in the upper portion of the bole. Where the table is based on actual utilization, such trees should be rejected for measure- ment or else the defective logs should be measured, since the cull is not due to form but to defect. Where the top diameter is fixed independent of the last cut, these defective trees should be measured. All trees are suitable for volume measurements except forked-topped trees, those with abnormal D.B.H. dimensions due to butt swelling and frequently caused by fire scars, and trees deformed in such a manner that a series of normal taper measure- ments cannot be obtained. Abnormalities at a given taper point ii- 5 ^ S ^ =? O fcH C t- " " c3 /i7^ \,^ X -4^ V \ \ "^^ \, ^ ^ N, \ 1 ( t '/ •% 1 N \ 1, "^ ^^N ^ \ <\ \ ^^ C\^ \ \, \"« n\ ^ ^-\ \\ ^s ^: V: "^"^ k ^ ^V \ \ V s^ 24 32 40 48 56 04 Height above Stump, Feet 80 88 96 Fig. 32. — Actual upi)cr dianiotors or tapers of four loblolly pine trees, inside bark, based on height above stump, plotted to show form of trees. 90-foot trees. 200 THE FORM OF TREES AND TAPER TABLES From these plotted forms of trees the diameters at any desired point or height on the boles can be read. The nature of these original averages is shown in Fig. 32 in which four single trees of different D.B.H., 14.4 inches, 17.7 inches, 19.4 inches, and 21 inches, but falling in the same height class, 90 feet, are plotted. The eccentricities of form in this table are partly due to branches, partly to failure to obtain the true average diameter at each point, and partly to the natural variations in form for individual trees. As in the preparation of volume tables, the averages obtained from a number of trees are more consistent than the forms of single trees. A graph plotted in this manner from averaged upper diameters instead of single trees, will be fairly regular in the relation of the curves for successive D.B.H. classes and will resemble Fig. 35, p. 204. When, as is sometimes the case, the upper diameters are measured on logs as cut by the saw crews, in irregular lengths, and hence fall at different heights above the stump, only the measurements falling at the same height can be averaged, as at 12, 14, 16, 18 and 20 feet. This will be done, and all of the resultant upper diameters for trees of a given D.B.H. and height class will ])e plotted, to obtain the curve of average form. From this curve, the desired upper diameters at regular inter- vals of 8 or 10 feet can be read. These curves of form are not in final shape for a standard table of form. Although the averages are improved by the use of larger numbers of trees, the values will be slightly irregular for two reasons. The average D.B.H. may be larger or smaller than the e.xact inch class desired, and the forms of the average trees of the consecutive D.B.H. classes may vary in fullness. These two sources of variation are well shown in Fig. 32. There is no reason why average 21-inch and 18-inch trees should have a fuller form than 19-inch trees. Values required are based on exact D.B.H. classes, and vary regularly with D.B.H., as would be the case were sufficient trees included in the mechanical average. Second Set of Curves, Tapers Based on D.B.H. For trees of each successive D.B.H. class which have the same total height and the same general form, the diameters at each given height on the boles will diminish in direct proportion with diminishing D.B.H. If D.B.H. is then taken as the independent variable in a second set of curves, and upper diameters plotted on D.B.H. as the dependent . variable, the form of these new curves approaches straight lines as did those of volume based on height (§ 141), and the irregularities between the forms or upper diameters of different average trees are easily reduced. In this second operation as in the first, the trees of a given height class form the basis for a set of curves; e.g., 90-foot trees only are included in the one set of taper curves, separate sets being rc(iuired for 70-foot or 80-foot trees. For this set of curves the same scale can be used for both vari- ables, e.g., 2 inches =1 inch. METHODS OF CONSTRUCTING TAPER TABLES 201 To plot this second set of curves the values for a given tree, or set of tapers, are transferred to this new sheet, in which process the strip method described in § 141 is most convenient. The diameter of upper tapers diminishes with in- creasing height ; each tree is plotted in a single vertical column, with the D.B.H. at the top. The D.B.H. column must be that of the actual average D.B.H., e.g., 14.4 inches, not 14 inches. When each set of values has been transferred and plotted above its respective D.B.H., the points rep- resenting equal heights above stump are con- nected by lines. The guide line for this set of curves is a line drawn at 45° angle whoso value would be D.I.B. = D.B.H. For any tree, the D.I.B. at D.B.H. is less than the D.O.B., and at upper points, D'l.B. is still less; hence all points above D.B.H. will fall below this line. Regular forms such as are shown in Fig. 35 could be drawn directly on Fig. 32 guided by the original averages, which will usually be far more regular in themselves than those shown in the diagram. But the desired shifting of the basis to exact D.B.H., e.g., 14 inches instead of 14.4 inches, and the far greater ac- curacy in harmonizing tapers secured by plot- ting (Fig. 33) makes the method of plotting a second set of curves almost obligatory. 16 17 18 19 D.B.H., Inches 20 21 22 Fig. 33. — Tapers of the four trees shown m Fig. 32, plot- ted on basis of D.B.H. for each 8-foot point, and results evened off by curves. Separate curves are made for each height above stump. Effect is to reduce the irregularities of form in Fig. 32. 202 THE FORM OF TREES AND TAPER TABLES With more regular original averages, the curves will coincide very closely with the original data, instead of showing the wide variations indicated in this figure, caused by the great irregularity of the original unharmonized values of Fig. 32. The effect of this second plotting upon the irregular forms shown in Fig. 32 is illustrated in Fig. 35, in which the curved or harmonized tapers from Fig. 33 are replotted in the original form.^ The values when read from the curves are taken from the ordinates repre- senting exact diameter classes. This set of curves therefore is evened off for values of the diameter classes, and progresses regularly by 1-inch or 2-inch diameters. • Third Set of Curves, Tapers Based on Total Heights of Trees. We now have, first, true averages of the original form of each separate class, second, true averages for exact diameter classes instead of for average diameters larger or smaller than these exact classes. Both £ 9 1 % — -. ! , 1 - 16 24 ■ ' . 'it 10 — -' „,— — ^^ ^.^^^ " ^ . ^^ "^ ^-"-^^ „.,---' ■" 56' ^ ^^^ "^^ . — '^ ,. — -—"^ 64' ^ "-^ ,^ ^^ __^ -^ _^„^ -^ 72 ^,y^ ^ -^ ^,„.^^ "^ y ^^ ^ ^ ^^ ^ y y > X ^ ' 60 70 Total height of Tree, feet 90 Fig. 34. — Tapers based on total heights of trees. For trees of the same D.B.H. class. 14-inch trees. sets of curves deal, however, only with one separate height class. It may happen that the trees of the 80-foot class are all slender, tapering trees, while those of the 70-foot or 90-foot class are more cylindrical. There is no reason why in a general tabje which seeks average form, the accidental departure of form from the average, by a set of trees in one height class, should be accepted if this deviation can be easily shown and corrected. To do this, it is necessary to compare the upper diameters of the trees of different height classes, at the same points on the stem. D.B.H. must therefore be eliminated as a variable, and height substituted. * Since height above stump is the basis of curves in Figs. 32 and 35, the tree form is shown as if lying on its side. The diameter, instead of being plotted sym- metrically on both sides of an axis, is plotted on the vertical scale above the base of the figure. But by holding this figure at right angles, the form of the bole is suggested. METHODS OF CONSTRUCTING TAPER TABLES 203 A set of curves (the third) will therefore be made from all trees of the same D.B.H., such as the 14-inch class. In this set the independent variable which is plotted on the horizontal scale is the total height of the tree in feet. The dependent variable is diameter or taper at upper points, as in all the graphs used in this method. The set of points, which is transferred from curves in Fig. 33 and falls in the vertical column above the height of the tree, is the diameter of a 14-inch tree, 90 feet high, at each taper measurement, the larger diameters, beginning with D.B.H., falling highest in the column. After each series of points for 14-inch trees, representing trees of different total heights as 80, 70, 60 and 50 feet, has been taken from the sejiarate sets of curves prepared in step 2, for each of these height classes, and plotted successively on Fig. 34, the points representing diameters at the same height, e.g., at 8 feet from stump, are connected. Irregularities in the resultant curves show departure in form for one height class as compared with others. By smoothing out these curves, the tapers of trees of different height classes are harmonized. The scale used in this set is 5 feet per inch for the horizontal scale, 2 inches per inch for the vertical scale. In Fig. 34 only the resultant harmonized values are shown Fourth Set of Curves, Tapers Replotted on Basis of D.B. H. To utilize the data from Fig. 34 the values may be read off direct, forming tables, but it is customary to have these tables classified by height classes, as in Fig. 33 instead of by diameter classes. To bring together these values, the curved values for the separate diameters may again be assem- bled on one sheet as in Fig. 33 with a separate sheet for each height, diameters on the horizontal scale, upper diameters on the vertical scale, and a curve for each fixed height above the stump. This replotting should still further iron out any irregularities in taper values. The taper table can be read from this set direct, but only for the fixed heights given in the table, e.g., for 8, 16, 24 feet, etc. Final Set of Curves, Tapers Replotted on Basis of Height above Stump. One further step completes the curves of form, by restoring them to the shape of the separate trees as shown in Fig. 32. In this final step the values are plotted as for Fig. 35, with separate graphs for height classes, height above ground on the horizontal scale, upper diameter or tapers on the vertical scale and a curve for each diameter class. The form of such a set of tapei^ for universal use should be graphic, thus showing the upper diameter at every point on the stem. From this set of graphs, board-foot volume tables for any log rule, length of log, upper diameter limit or stump height, cubic volume, number and dimensions of ties, poles or other piece products, can be determined. It is apparently a universal basis for the construction of volume tables, and while the number and diversity of such tables would remain as great as ever, the field work of gathering data on form or volume would 204 THE FORM OF TREES AND TAPER TABLES be obviated by the printing and general distribution of the graphs giving the average form, from which tables could be prepared in the office for whatever use was desired. 169. Limitations of Taper Tables. The real weakness in this apparently sound method of preparing the basis for volume tables lies in the fact that the result obtained does not differentiate form classes of trees, but averages them on exactly the same basis as do the standard volume tables. Its only merit therefore is in the transferring of records 20 10 IS ir ^v^.^^^ \ ■ ■^^.^^^ "^-^.v.^ ^^•^-., 1.1 £12 S'll ^o (5 8 ■-..^ *-w ^8n ■*^ •-««...4_^^ i^^'^^-^/ ^^"--«^ ----...^ ^^=^£g&7^ ■^ "^"■^^v..^ ^/D/jl?"'"^ ^^^ •V^^ "\^^ ■^ "'"^-- ...^^^ ^^.^^^^j^ \ --....^^ ^"""^ rC^ . \, "■---^ J^'^^ sN^ k^^ """"^ ^N: v\ \\\ 5 4 3 2 1 \Nx^ \ ^^^^^ ^ ^ ^^^ S 1 21 32 40 48 56 64 Height above Stump, Feet 88 Fig. 35. — Tapers read from Fig. 33 for four diameter classes, showing effect of har- monized curves in smoothing out the irregularities of form shown in Fig. 32. Similar curves are obtained from tapers rei)lotted inform of Fig. 33 from curves shown in Fig. 34. Such tapers will be harmonized by diameter and height classes. of average tree forms to the office as a basis for future volume tables. The form of the tables is bulky and does not lend itself to the further extension necessary to show the form of trees of several different form classes for each diameter and height class, though in the preparation of standard volume tables by the U. S. Forest Service, such taper tables have been extensively employed. The use of taper tables in connec- tion with standard form classes as a basis for universal volume tables is discussed in Chapter XVI. By preparing separate sets of taper tables for each form class based on absolute or normal form of trees (§ 174) a permanent basic standard of tree form is obtained which will fill all possible future requirements. CHAPTER XVI FORM CLASSES AND FORM FACTORS 170. The Need for Form Classes in Volume Tables. Trees which have the same D.B.H. and total height may vary in form, as shown, according as the tree is full boled, with " good " form, or concave boled, with " bad " form. These gradations of form correspond with differences in cubic volume. In order to further classify the volumes of trees of the same D.B.H. and height, tliis range of volume due solely to form must be separated into arbitrary classes or divisions. Such a series is based on measurable differences in form, and the classes thus established are termed fonn classes. The adoption of form classes as a third variable in constructing volume tables has been retarded in this country by the necessity for expressing volumes in terms of board feet, by the labor of constructing even the simpler tables based on diameter and height, and by the belief that the vari- ations due to form could be more simply overcome by averaging them. A second difficulty lay in the application of such form-class tables in timber estimating, since cruisers were unaccustomed to judging upper diameters by eye with the accuracy needed to distinguish between the form classes. Differences in taper were readily recognized, but differences in form were further obscured by the method of using merchantable top diameter limits instead of total height. Practical cruising did not seem to require such tables. But with the increasing use of the cubic foot and the cord for pulpwood and in second-growth timber, and the need for closer estimating, the desirability of distinguish- ing form classes in volume tables is increasing. Such efforts as have been made so far in this country follow standards prevailing in Europe, where the universal use of the cubic unit, close utilization and high values have made it necessary and possible to obtain more accurate measurements of the standing timber. One great possibility in this field is the demonstration that when form classes are distinguished and the true form of the tree inside the bark is made the basis, all species of trees will be shown to have practi- cally the same forms and total volumes for the same form classes; hence a single general table so classified would suffice for all field work. Were this fact established, a basic table might then be constructed for each 205 206 FORM CLASSES AND FORM FACTORS of various units of measure in addition to cubic feet. Once the average form class of the trees or stand were determined, then volumes could be obtained from these basic tables. Recent research in Sweden tends to show that this generalization holds true for certain species already investigated, namely spruce, fir, larch and Scotch pine. 171. Form Quotient as the Basis of Form Classes. The first real step towards a solution of this problem was made by Schiffel in 1899, who developed a method of expressing differences in form, previously used (Schuberg, 1891) and known as the form quotient, which is the percentage relation that the diameter at one-half the height bears to the D.B.H. The differences in form of the entire boles of trees (Chapter III) are expressed by their divergence from a cylindrical form through a series marked at definite stages by the complete paraboloid, cone, and neiloid. Each of these solids can be measured by Newton's formula: F=(B+46.+6)| The middle point on the stem of a tree, regarding the entire bole as a single complete solid, is evidently the point of greatest weight in deter- mining its form and volume with respect to the cylinder whose base is B and height h. By a complicated calculation, - Schiffei derives tne formula for obtaining at one operation the true cubic contents of an entire stem as, F=(.165+.666,.)/i. This is known as Schiffel's formula. Newton's formula, regarding the tree as a perfect, i.e., complete conoid, and the diameter at top as zero would be, F=(.16fB+.66|6.)/i. The " universal " character of Schiffel's formula failed to make the headway expected when it was first introduced in the United States for the reasons that, to apply it, one must measure the diameters of trees at one-half the stem height, and that the cubic unit of volume was little in demand. The really valuable part of Schiffel's work was not the formula, which was nothing new, but the form quotient. This was his demon- stration that the true form, and consequently the variation in form of 1 "New Method of Measuring Conifers," Review by B. E. Fernow of Article by SchifTel, "tjber die Kubirung und Sortierung Stehender Nadelholz Schafter," Centralblatt flir das gosammte Forstwesen, Dec, 1906, pp. 493-505, Forestry Quar- terly, Vol. V, 1907, p 29. FORM QUOTIENT AS THE BASIS OF FORM CLASSES 207 different trees, could be indicated by the relation between diameter at one-half height and D.B.H. (not diameter at stump). In its standard form of expression: Form quotient = — . In 1908 Tor Jonson corrected a slight inconsistency in Schiffel's method by insisting that the middle diameter be taken not at the middle point of the stem but at the middle point measuring from B.H. This he termed the absolute form quotient. This improvement finally secured a consistent basis for expressing tree forms, eliminated height as a varia- ble, and got rid of the great drawback of butt swelling. The absolute form quotients of trees were now found to vary between .575 and .825, i.e., the diameter at the middle point above B.H. bore this relation to the D.B.H., whether both measurements were taken out- side or inside the bark. It was also discovered that in most cases the form quotient if reduced by a constant would give the form factor for cubic contents of the tree. For instance, J. F. Clark found that the reduction factor for the form quotients for balsam in the Adirondacks was 0.21. This fact is of minor importance since it aids only in obtaining the cubic contents of trees. This standard of measuring form permitted the classification or differentiation of the third variable of volume, namely, form independ- ent of diameter or of height. Trees could be grouped into form classes expressed by form quotients. Seven main form classes were formed, namely, .50, .55, .60, .65, .70, .75, .80. Five sub-classes were also inter- polated as .575, 625, .675, .725, .775. The extreme lower and upper classes shown will be found only in individual trees. The average form class for a given stand will fall usually between .575 and .75 and may be correlated with the density of the stand as shown below. Character of stand Form class, based on form quotient * Poor density Fairly good density Good density 0.575-0,625 .65 .675- .70 .725- .75 Overcrowded * Tor Jonson, 1918. But most important of all, the question as to whether the form of trees was independent of species, site and region and dependent on gen- eral laws, could now be determined. 208 FORM CLASSES AND FORM FACTORS 172. Resistance to Wind Pressure as the Determining Factor of Tree Form. The theory cxphiiniiig the form of the boles of trees, v/hich is now generally accepted, was first advanced by Prof. C. Metzger, a German. This was, that the stem or bole is constructed as a girder to withstand the pressure of wind. Based on this theory, A. G. Hoejer, a civil engineer of Stockholm, devised the general formula for tree form discussed in § 173. Prof. Tor Jonson applied this formula first to spruce and then to Scotch pine, and demonstrated its correctness; as a consequence, developing the basis for tables of abso- lute form and volume for trees, and a new method of estimating thnber (§ 203). Jonson's conclusions, based on these investigations, are that tree form depends entirely on the mechanical stresses to which the tree is exposed, and is therefore independent of diameter, and height, and also of species, age, site or any other factor, except as these factors in- fluence the form of the crown. The force of the wind operates on the crown of the tree and is focused or centered on a point representing the geometric center of the crown. The pressure of the wind on the tree crown constitutes a force which compels the tree to construct its stem in such a manner that the same relative resistance to strain is found at all points, the smallest possil)le amount of material being used. As the concentrated force of the wind strikes a point situated lower or higher on the tree, dependent on the crown area presented, we get larger or smaller taper respectively, which means bad or good form class. As the location of the point of attack of the bend- ing force is determinative of form, this point is called the form point, and can be expressed as a per cent of total height. Here is a natural law, to which growth of trees, as mechanical struc- tures designed to stand up against wind, corresponds. The full bole of the forest-grown tree in a crowded stand, coinciding with a small crown and high form point, meant that this location of the strain required nearly equal strength along the total length of bole, which could be attained by rapid growth of the upper bole. If the tree were open-grown with a consequent long crown and a low form point, this would permit of smaller upper diameters and require greater strength lower down on the bole. Since the form of the crown, especially its length, with relation to the length of bole, determines this form point, this relation of crown to bole, expressed by form point serves as an index to classify trees as to their relative form classes or form quotients. Any variation in average form, such as the admitted fact that the average form quotient increases with age, is explained by a coincident change in this crown and form point relationship. Open-grown trees A GENERAL FORMULA FOR TREE FORM 209 possess a low form quotient, not because they are open-grown but because the crowns of such trees are long and the form point low. Trees with long clear length and high crowns possess a high form quotient, whether they stand alone or in a crowded stand. Short trees may be full-boled or the reverse — the rapidity of taper as a whole has no effect, but the distribution of the taper, which alone affects the form quotient, will vary with short trees as much as with tall, and on poor soils equally with good. 173. A General Formula for Tree Form. On this basis, if the actual form of trees with the same form quotient is similar, it would be possil)le to construct taper tables based on each of the three variables, diameter, height and form class, which would apply to all species of trees. To apply this principle there was required a general formula which would give the diameter of a tree of given form quotient, at any point on the stem, and second, a demonstration that the actual measurements taken on trees of this form quotient coincided with the results of the formula. Once this was shown, the formula would permit of the construction of a set of taper tables of universal application from which in turn any manner of volume table could be derived. This is a more ambitious program than the mere determination of form factors for cubic con- tents, and promises permanent results. The formula devised by A. G. Hoejer is based on the portion of the tree above B.H.: D = D.B.H. inside bark; Z = distance from top of tree to section; d = diameter of section. Then d c+l D c C and c are constants whose value depends upon the form quotient of the tree; d i.e., upon ■- when d is measured at one-half height above D. Their value must be found separately for each form class, and will then hold good for diameters at any point on the bole of trees within this class, independent of total height of tree. Absolute heights are not used in the formula, but percentage or relative heights, regarding the height of any tree above B.H. as 100, and the distance below the tip, of any other section as its per cent of this length, including sections below B.H., whose per cent of height would exceed 100. In the same way, absolute diameters are not used, but the D.B.H. is taken as d 100, and the relative diameter — expressed as its proportion of 100. These upper diameters are then measured at distances equaling tenths of this total height above D.B.H, — thus falUng at the same proportional height on each 210 FORM CLASSES AND FORM FACTORS tree; e.g., for the form class 0.70 with diameter at 0.5 of height above B.H., asJ 0.7 of D.B.H., the values in the formula are: For upper section, For D.B.H. section, 70 ^, c+50 = Clog-^- 1) 100 ^ c ^ ^ 100 c + 100 =Clog-^ (2) 100 ^ c ^ ^ If equation (2) is divided into equation (1), then 0.70 log (f + 100)=log (r+50) + (0.70-l) log C. The value of this constant c is then found by trial. Inserting this value in equa- tion (2) the value for constant C is found for the form class. Values for the remain- ing form classes are found in a similar manner. With the numerical value of the constants C and c determined, the normal diam- eter of a perfectly formed tree can be found by this formula at any point on the stem above B.H., and this normal diameter can also be calculated for stump height, thus disregarding the stump taper. By determining these normal diameters for trees of each D.B.H. and height class, at intervals of one-tenth of the total height, and plotting these diameters graphically, a set of taper curves is constructed (§ 167), for normal tree forms, from which volume tables or form factors can be constructed which will have universal application. 174. Applicability of Hoejer's Formula in Determining Tree Forms. There remained to test accuracy of these results by comparing them with measurements on felled trees. The tests showed that for the conifers measured, spruce, fir, larch and pine, the formula expressed the form of the living tree, when applied inside the bark at all points including D.B.H., and that for species with thin bark such as spruce, the same relations applied when measured outside bark. For Norway Spruce the volumes of individual trees fall within =b 3 per cent of those derived by the formula. But for thick-barked species such as Scotch pine, a poorer form, less cylindrical, was obtained outside bark, which changed the form class, but did not seriously interfere with the application of the method. Claughton- Wallin has since shown that this formula holds good for Norway or red pine {Pinus resinosa) and white pine (Pinus strobtis). As with all attempts to study the laws of tree form, this formula depends on measuring a diameter which is not affected by the abnormal flare at the butt; hence any tree or species whose butt swelling extends above B.H. will not corre- spond in form to the diameters in the formula based on this abnormal D.B.H. It was found impossible to use the formula for western conifers since the form d quotient — was too low for this reason. For general application, the second difficulty is the factor of bark thickness, whose effect upon the form quotient and form class must be worked out for different species with variable thicknesses of bark, so as to correlate the method with D.B.H. measurements outside the bark, which must continue to be used in practical estimating. FORM FACTORS 211 Can these two variables be eliminated for American trees, and taper and volume tables constructed for trees of each form class, thus attaining the goal of universal volume tables? For second-growth, or young timber, in which the factor of butt swelling will not affect D.B.H., this can be done. Taper tables should be constructed from this normal formula based on diameter inside bark at B.H. The average thickness of bark at B.H. must be determined for the species, and by graphic interpolation these D.I.B.^aper tables can be drawn for trees of each D.B.H. outside bark, from which volume tables can be constructed in any desired miit. For the larger trees or species with butt swelling extending above B.H., as for instance, virgin stands of timber on the Pacific Coast, or Southern cypress, the present practice of adhering to D.B.H. will probably be continued, and trees with variable amoimts of stump taper averaged together in volume tables regardless of true form. The only alternative is to attempt a standard measurement of diameter at a higher point on the bole, which will be difficult to adhere to in practice. Approx- imate rather than absolute accuracy will continue in the preparation and use of these tables for such timber. When the variable influence of butt swelling is further aggravated by the obsolete practice of basing volume tables on diameter at the stump, no consistent volumes can be obtained to serve as standards for estimating. 175. Form Factors. The form of a tree is a variable independent of diameter or height, while the form of a cylinder does not vary at all. That of a cone is a constant, equal to one-thii'd of the volume of a cylinder of similar height. Taking the volume of a cylinder as the unit of comparison, and dividing the volume of a cone by that of the cylinder of equal diameter and height, the quotient is always .333 or one-third. This can be termed the form factor of this cone, i.e., the factor by which the volume of the cone is derived from that of the cylin- der. It expresses the volume of the cone, but not its form. In the same way the form factor of the paraboloid is .5. Form factors of trees can thus be found by dividing their cubic volume by that of a cylinder of equal diameter and height. 5 = Basal area of cylinder equivalent to that of tree; /i = height of cylinder and of tree; Bh = volume of cylinder; /=form factor or multiple expressing the relative volume of the tree; V = volume of tree. Then Bh J y , and V=Bhf. 212 FORM CLASSES AND FORM FACTORS Volumes of trees can thus be obtained from the vokuiies of cyHnders, when once the average form factor is known. The form factor is therefore, in theory, a direct expression of the relative volume of a tree compared with a standard or constant volume, and tables of such factors were expected to give the key to universal volume tables showing form classes. But the diameter of the cylinder which is to serve as the unit or basic volume must first be obtained and must equal that of the tree. If this diameter is taken at the stump or at ground, the butt swelling gives an abnormally large irregular vari- ation in the cylindrical volume. This method is known as the Absolute Form Factor. But the diameter can be shifted to B. H. with the cylinder equaling the total height of tree as before. Form factors so calculated give uniform or consistent results from which cubic volumes can be calculated, and are termed Breast-high Form Factors. These form factors in turn vary not only with the form of the tree, but with the total height as well, hence could not be used to indicate absolute form. The reason is that the diameter of the basic cylinder is taken, not at a height pro- portional to the total height of the tree, but at the fixed height of 4^ feet. For short trees this point falls proportionally nearer the tip, with relatively smaller cjdinder, than for tall trees of identical form. The breast-high form factor therefore decreases as height of tree increases. In an effort to overcome this drawback and express form directly by means of form factors, the so-called Normal Form Factor was devised, in which the basal area is measured at a point on each tree represent- ing a fixed ratio to the height of the tree. This plan has not proved pi'actical, owing to the difficulty of determining this point rapidly and accm-ately. By comparing only the portion of the tree above B.H. with the volume of a cylinder of equal height, the form factor for this portion alone corresponds dii'ectly with variations in form for the tree. This is known as Riniker^s Absolute Form Factor. The Riniker form factor of trees of each form class was calculated by Jonson from the normal form or tapers of trees of each D.B.H. and height class, taking the diameters at points representing one-tenth of the stem above B.H. Then V f = — for the bole above B.H. only. ■' Bh Since form quotients indicate correctly the relative forms of trees, absolute form factors of trees whose form quotients are equal should also be equal. That this is true is indicated by the following test, e.g., from investigations of Claughton- Wallin and F. McVicker: STANDARD BREAST-HIGH FORM FACTORS 213 Species Form quotient Cubic form factor Basis trees Red pine, Ontario, Can Scotch pine, Sweden Red pine, Ontario, Can .■ Scotch pine, Sweden Red pine, Ontario, Can Scotch pine, Sweden White i)ino, Ontario, Can Scotch pine, Sweden White spruce, Ontario, Can Scotch pine, Sweden 65 65 70.3 70.3 74.4 74.4 70.8 70.8 65.2 65.2 0.439 .441 .480 .484 . 515 .524 .482 .489 .441 .444 11 30 40 9 6 176. The Derivation of Standard Breast-high Form Factors. The two possible uses for form factors are seen to be, first, an expression of relative forms of trees, second, a means of computing their total vol- umes from that of cylinders. It is not possible to combine these two functions in the same table of form factors. The absolute form factors for total tree volume can- not be correlated with D.B.H. nor with any other point on the bole, while the form factors which are based upon D.B.H. and total volume are not absolute but vary with height. But these Riniker's absolute form factors can be used to obtain a set of breast-high form factors which represent the relative volumes of normally formed trees of all diameters and heights when compared with the corresponding cylinders. The steps in this calculation are: 1 . Compute the Riniker form factor for trees of each form class. 2. Obtain the normal stump diameter from Hoejer's formula. Stumps were taken as 1 per cent of the height of the tree. The actual stump diameter is always too large, due to butt swelling. The conception of a normal stump diameter is the diameter which the stump would have if the normal curve of the stem from top to D.B.H. were prolonged downward to stump height. 3. Find the diameter at one-half the distance from stump to top, by Hoejer's formula. 4. Express both the stump diameter and the diameter at one-half height in per cent of D.B.H. and compute the new form quotient, this time based on height above stump. If diameter at ^t =67.7 per cent of D.B.H. Stump diameter =103.0 per cent of D.B.H. 67.7 Form quotient 103.0 = 0.657. 214 FORM CLASSES AND FORM FACTORS 5. From the table of absolute form factors interpolate for the form factor required to coincide with this form quotient.' 6. The basal area corres{)onding to the normal diameter at the stump is found as follows: Do = normal stump diameter; Z) = D.B.H.; Bo = normal basal area at stump; B = basal area at D.B.H. If Do ^l.OpD, Do= = 1.0lf-D^, Bo ttDo^ 4 xD2 4 = 1.0pW. 7. Total volume of the stem is then V = BJ,f, = B l.OpVifo. 8. Breast-high form factor is ^^Bh = 1.0p%. This series of breast-high form factors shows the diminution with increased height, the cause of which is set forth in § 175. These form factors are given in Table LXXXII, Appendix C, p. 497. Since form is best shown by taper tables, and volume is best obtained directly from volume tables, the use of form factors in America has but little practical application and has been adopted to a very limited extent. Were the breast-high form factors more regular they would serve as a means of constructing volume tables by graphic methods (§ 138) in which the curves being comparatively straight could be extended and interpolated with less chance for error than by the ordi- nary methods. 177. Merchantable Form Factors. Form factors based on the merchantable contents of the tree in cubic feet, or upon the net cubic 1 These absolute form factors are for the entire tree, but are based on the theoretical stump diameter, hence are inapplicable for practical use. FORM CLASSES AND UNIVERSAL VOLUME TABLES 215 volume utilized as board feet or in any other unit, can be computed by first ascertaining this net volume. The form factor is /= Bh V These form factors serve no useful purpose. 178. Form Height. Form height is the product of form times height. Since V=Bhf, tables of form height simply eliminate one of the two multiplications necessary in deriving cubic volumes. 0.710 0.G90 0.G70 0.G50 0.630 O.GIO 5 0.590 I 0.570 g 0.550 o ^ 0.530 u I 0.490 0,470 0.450 0.430 0.410 0.390 0.370 n 0.350 \ s\ v\~ ^ \ ^ ^ For Ik lass ^N fx V -«.. .^ -~\ ■ — — — ^ :n \ ^ —■ — — . ojrhj .^^ ^N^ \ r^ ^ Qjl |;^\: \ ^ k — . 0.725 — N ^ ■ 0.7f ■ — — N\ \ ^ "^ . O.pf fl^ ' 1 — s '^ ■ 1 -J - ^ ^^ K "^ ^ >^ ■^1 . ^ '^ \ ^ >> ^ ^ 0,60^ ■^ <^ V ^ ^ 2:575 X "^ 0^ 0r52 2i5C 1 __^ ■ . ^ . ^ -r ■ — — 1 20 25 30 35 40 15 50 55 60 05 70 75 80 Heiglit in Feet 85 90 »5 100105110115120 Fig. 36. — Curves of breast-high form factors for form classes from .50 to .80 inclu- sive, showing effect of height ui)on the form factor. From Tor Jonson. 179. Form Classes and Universal Volume Tables as Applied to Conditions in America. The standard form classes, when applied to trees of different diameter and height, thus distinguish three variables just as did the universal volume tables based on diameter, merchant- able length and rate of taper. Universal volume tables if based on total heights would show volumes for the given unit in three instead of two dimensions; D.B.H., Height, Form Class. But to derive universal volume tables by form classes to be based on merchantable length instead of total height would not be so simple, for the following reasons: 216 FORM CLASSES AND FORM FACTORS 72 ft. If taken to a uniform or fixed top diameter, trees with a high form quotient would be cut higher in the top and fall into a different merchant- able height class than trees with a low form quotient. Therefore, for trees of different form quotients, to attain the same merchantable top diameter, trees with the lower quotients must be taller than those whose form quotient is high. Hence total and merchantable heights are not interchangeable for trees whose form quotients differ. If taken to variable top diameters, this second variable will make it practically impossible to distinguish form classes based on total height in the volumes given, for these tops would not vary in any definite relation to total height or form. As long as mer- chantable rather than total heights arc used in volume tables and timber estimating, form classes based on actual form of the tree cannot be used to construct volume Fig. 37. — Effect of cutting to a fixed top diameter, upon foKlgg \i^ which trees merchantable height of trees having different form . ,.™ . „ ,. , . r ^- ,. e rn .n ot dmereut iorm are quotients. A form quotient ot .60 requires either a shorter merchantable length or a taller tree than one separated, and tne of .80. principle of averaging the differences in vol- ume due to form must continue to be used for such tables. But for cubic feet, basic volume tables may be made up giving the volume of each diameter, height and form class. Similar tables can be constructed in any unit of volume, or for any log rule, from tables of normal taper. In applying these tables, the method would be not to attempt to tally each tree in its proper form class, but to determine average form classes (§ 171) for stands or other subdivisions of the forest, the volumes for which can be taken from this basic table to form a standard volume table for the trees to which it applies. Not over three such tables would be apt to be needed for any tract, however large and varied. Methods of rapidly determining the form class of sample trees, in order to apply such a system, are given in § 201, § 202 and § 203. REFERENCES 217 References New Method of Measuring Volumes of Conifers, Review of Schiffel's method by B. E. Fernow, Forestry Quarterly, Vol. V, 1907, p. 29. Das Gesetz des Inholts der Baum Stiimme. Forstwissenschaftliches Centralblatt, Aug., 1912, pp. 397-419. Massatabellar fiir Traduppskattnung, Tor Jonson, Stockholm, Sweden, 1918. Review, Forestry Quarterly, Vol. XI, 1913, p. 399. Article by L. Mattson-Marne,Skogsverdsf6reningensTidskirft, Feb., 1917, pp. 201-36. Form Variations of Larch, L. Mattson-Marne, Meddelanden frau Statens Skogsfor- soksanstalt, 1917, pp. 843-922; Review, Journal of Forestry, Vol. XVI, 1918, p. 725. The Absolute Form Quotient, H. Claughton-Wallin, Journal of Forestry, Vol. XVI, 1918, p. 523. Tor Jonson, "Absolute Form Quotient" as an Expression of Taper, H. Claughton- • Wallin and F. McVicker, Journal of Forestry, Vol. XVIII, 1920, p. 346. Die Formausbildung der Baumstamme, Von Guttenberg, Oesterreichische Viertel- jahrschrift fiir Forstwesen, 1915, p. 217; Review, Forestry Quarterly, Vol. XIV, 1916, p. 114. CHAPTER XVII FRUSTUM FORM FACTORS FOR MERCHANTABLE CONTENTS IN BOARD FEET 180. The Principle of the Frustum Form Factor. In an effort to simplify the construction and improve the accuracy of volume tables for board feet based upon merchantable heights and top diameters, a merchantable form factor has been devised by Donald Bruce. Timber cruisers in the Pacific Northwest had already made use of the similarity in form of the merchantable portion of the tree to that of the frustum of a cone, but had neglected the possible differences in form and volume between the cone and the merchantable bole. The new method adopts the frustum of the cone as the basic volume, instead of the cylinder as for the form factors discussed in Chapter XVI, and then compares this volume with that of the tree, to determine their true relation. This relation is expressed as a form factor in the usual manner. y = volume in tree; y' = volume in frustum of cone; /=form factor. Then and The contents of this frustum were measured as the scaled board- foot contents of cylindc^-s representing the logs into which the bole would be cut. The length of these sections was fixed at IG feet, and their upper diameters were determined by the diameter of the frustum at the required point. The form factor obtained by comparing the total scaled volume of the merchantable bole with that of the frustum so measured is termed the Frustiun Form Factor and is a merchantable form factor having values close to 1, since the deductions from full cubic contents of bole have been made both in the frustum and in the tree. The merits of the frustum form factor method for constructing volume tables are that it applies directly to the merchantable portion 21S BASIS OF DETERMINING DIMENSIONS OF THE FRUSTUM 219 of the tree, on the same basis as used in timber estimating to top diameters, and that the vahies of the form factors tend to vary but httle from a straight hne, thus permitting the construction of curves of board- foot volume with greater accuracy than when volumes are plotted directly (§ 138). This advantage permits of constructing such tables on the basis of fewer measurements of felled trees. 181. Basis of Determining Dimensions of the Frustum. The top diameter of the frustum is supposed to coincide with the top diameter inside bark of the merchantable length of each tree class. The diam- eter at its base, which is at stump height is arbitrarily fixed as equal to D.B.H. outside bark. No pretense is made that this form factor is a scientific basis for studying tree form. Actual D.I.B. at stump may or may not coincide with D.B.H. outside bark. The base of the cone must be correlated with D.B.H. rather than with stump diam- eters (§ 175) and this assumption is satisfactory. Since the sides of a cone are straight, the upper diameters of each " log," or standard length into which this frustum is divided, are determined by proportion, to the nearest iV inch. In calculating the volumes of the frustums of cones the determination of the diameter at the top of each successive 16-foot log for cones of different top and base dimensions is best per- formed by plotting the form of the cone on cross-section paper, on which the vertical scale shows diameters and the horizontal scale shows heights in feet. Plot, first, D.I.B. equals D.B.H. at zero or stump height; next, top diam- eter inside bark at the mer- chantable height. Connect these two points by a straight line representing the side of Fig- 38.— Method of plotting a frustum from the frustum. The diameters which to determine the top diameters of the inside bark at top of each log l"gs which it contains, are then read at 16 feet, 32 feet, etc., to the nearest yo inch. The log rule should be tabulated to show the values for each ro inch. 182. Character and Utility of Frustum Form Factors. That the frustum form factor is a practical rather than a scientific basis of measurement is shown by the following facts: The absolute form factor of the total contents of the bole (§ 175) would be 0.5 when the tree has the form of a paraboloid. A truncated portion of the bole, with the rapidly tapering top eliminated, when compared with a trun- cated cone having the same top diameter, represents the lower portion of a cone of considerably greater height than that of the tree or paraboloid. For cone and paraboloid (or tree) of equal total height, the form factor of the 5 tree, compared with the cone is — or 1.50, since 0.5 and 0.33 are the respective 20 /•■' B. atb ise=D .B.H.2 0" ~~~" ^-^ ^^ "" ^^ ^ 8Top 16 32 40 Feet 220 FRUSTUM FORM FACTORS volume form factors of the paraboloid and cone when compared with a cy Under of equal dimensions. The nearer the top of the tree this upper diameter falls, or the closer the degree of utilization, the shorter will the completed cone become, until it coincides with the paraboloid in height. In the same manner the frustum form factor will increase, until it reaches a maximum of 1.50 for the completed cone. Chandler, 1 in an extensive investigation of the frustum form factor of northern hardwoods, birch, beech and maple, determined that this factor was independent of species, site or other influences, and independent of diameter and height, but was dependent on the two factors, form quotient, and taper ratio. The form quotient agrees in principle with that of Tor Jonson. Based on D.B.H., instead of stump, it was computed for merchantable rather than total height, by first subtracting diameter at top or d from both diameter at B.H. and at middle of merchantable length. Then d-i — d The taper ratio is the ratio between top diameter of merchantable bole, and D.B.H. Merchantable cubic frustum form factors were found to diminish as form quotient diminished and as taper ratio increased. The first result is obvious. The second confirm^ the conclusions set forth above as to the effect of close utiliza- tion in increasing the frustum form factor. These researches have definitely proved, on an empirical basis, the fact that, other things being equal, frustum form factors based on a fixed top diameter do not express a scientific relation between the form and volume, but will vary with the relation between cone and paraboloid. In its final analysis, the frustum form factor is an endeavor to express the paraboloidal forms of trees by the use of frustums of cones and the application of a correction or form factor. Although a great improvement over older methods if intelligently applied, it is not a universal method, since its results vary with taper ratio, butt swelling, bark thickness, and the top diameter utilized. On the other hand, the natural divergence in the total form and cubic volume of trees which gives rise to the variation m form quotients of from 0.575 to 0.8 is overcome in a marked degree by the substitution of the merchantable frustum form factor since, first, trees with a high-form quotient and of the same total height will be cut higher in the tops than those with a low-form quotient (§ 179). The merchantable form factor in itself coincides with this greater utilization and there- fore approaches closer to vmity, for both forms. If all trees are utilized to a fixed top diameter, a cylindrical tree, being cut nearer to its tip than a conical tree, would have fallen into a larger total height class than the conical tree, hence its per cent of cylindrical contents would have been much greater for merchantable form factor than that of the conical tree — a difference not appearing in the frustum form factor. Second, where the actual top diameter is made to coincide with the point at which the tree is commonly utilized instead of with a fixed top, there is apt to be still closer approach to unity in the form factors. The length and character of the crown usually determines the amoimt of taper from the base of the crown to the tip of the tree and consequently its distribution on the stem (§ 172). In rough utilization, the last saw cut tends to bear a direct relation to the length of crown and to fall nearer to the base of the crown than to its tip. This is especially 1 Bui. 210, Vermont Agr. Exp. Sta. 1918. CALCULATION OF THE FRUSTUM FORM FACTOR 221 true of hardwoods with branching crowns. Measured from this point, the frustum of the tree will not differ greatly from that of either a cone or a paraboloid. A great source of irregularity in frustum form factors, as in absolute form factors for cubic contents, is found to be the influence of butt swelling extending above B.H. and second, the influence of thickness of bark. Both of these factors reduce the proportion of woody contents to the dimensions and consequently reduce the form factor. 183. Calculation of the True Frustum Form Factor. A far more serious difficulty in the use of the frustum form factor hes in securing the exact coincidence of the top diameters of the frustums, used as the unit or standard for volume, and the average top diameters of the trees whose volumes are to be compared for the determination of the form factors. There is but one exact method, namely to compute the form factors of a given height separately for each tree whose D.B.H. and top diameter differ even by yVinch, by using a frustum whose three dimensions exactly coincide with those of the tree frustum. This method gives the most consistent form factors. The results for long- leaf pine given in the table on p. 222 were obtained by this method. This method can be simplified by first averaging together for all the trees in a diameter and height class the four factors, volume, D.B.H. , height, and top diameter. The frustum of a cone having these aver- age dimensions is then used to determine the frustum form factor of the class, by comparing its volume with that of the average tree of the class. While less accurate, this method reduces the computations considerably and is within the required limits of accuracy of the method. By this method, the computation of the frustum form factors is the first step in the construction of the volume table for which they are intended. 184. Calculation of the Volumes of Frustums. Influence of Fixed versus Variable Top Diameters. The purpose of the frustum form factors thus obtained is to make possible the construction of a volume table in board feet, by applying these factors to the volumes of frustums of cones. This may be done in the office, once the factors are known and the dimensions of the frustums determined. The second step is therefore to determine these dimensions of frus- tums of cones. The base is fixed, being equal to D.B.H., in 1- or 2-inch classes. But the top diameter of these cones is a source of trouble. As seen in the construction of volume tables (§§ 157-158) the top diam- eters to which trees are actually utilized tends to decrease as height increases, and to increase with D.B.H. The table will be based on one of two plans, a fixed top diameter, or variable top diameters coin- ciding with actual utilization. Whichever basis is adopted, the top diameters of the frustums must coincide with the average top diameter of the merchantable boles, 222 FRUSTUM FORM FACTORS whose volume is sought. If frustums having a fixed top diameter Hmit are used, the form factors should have been computed from trees measured to this same top diameter. If on the other hand, an attempt is made to base the table on variable or actual used top diameters, then the average actual top diameter for each diameter and height class should first be found and the frustum having the requisite top dimen- sion for each class computed. TABLE XXXV True Frustum Form Factors for Longleaf Pine, from Frustums Whose Top Diameters Coincide Exactly with the Average Top Diameter of Trees of Each D.B.H. and Height Class Merchantable Length in 16-foot Logs D.B.H. 2 2\ 3 31 4 4i 4. Averaged by diameter, Weighted Inches Frustum Form Factors 12 0.98 0.98 0.980 13 .97 1.21 0.99 .992 14 .96 .87 .97 1.03 .952 15 .90 1.01 1.03 1.05 .958 16 .92 .94- 1.04 0.94 1.10 .953 17 .89 .95 .91 .99 .99 .932 18 .89 .98 .90 .96 1.13 1.00 .934 19 .96 .90 .94 .98 .99 .954 20 1.05 .95 .88 .97 .94 .99 .937 21 .90 .88 .94 .92 .902 22 .92 .89 .94 .96 .99 .938 23 .93 .97 .94 .88 1.00 .91 .926 24 .93 .94 .87 .95 .921 25 .96 .94 .98 1.04 1.000 26 .94 .90 1.07 .90 .934 27 .93 .96 .95 .93 .95 .941 28 .93 .80 .101 .913 29 1.01 .93 .970 30 .98 .85 .96 .948 31 .94 .80 .84 1.13 .927 32 .94 .89 .915 33 34 .92 .85 .80 .817 Av'g'd by height, Weighted weighted 0.939 0.961 0.932 0.958 0.966 0.962 average 0.9468 It is possible, of course, to prepare a table of frustum volumes using fixed top diameters, and compute the form factors of trees for those classes whose top diameters are larger or smaller, but in this case the CALCULATION OF THE VOLUMES OF FRUSTUMS 223 form factors vary not with form alone but also with difference in volume due to difference in top diameter independent of form. The results are shown in Table XXXVI where an average top of 13.2 inches was used on all frustums. TABLE XXXVI Frustum Form Factors for 555 Longleaf Pines, Coosa County, Alabama, Based on Average Top Diameter of 13.2 Inches for Frustums Merchantable Length in 16-foot Logs 2 2h 3 3§ 4 ^ D.B.H Inches Frustum Form Factors 14 0.53 0.53 0.54 15 .57 .59 .50 .55 16 .71 .51 .56 0.53 0.57 17 .67 .76 .65 .69 .60 18 .88 .55 .72 .74 .77 .69 19 1.03 .81 .84 .81 .78 20 1.13 1.00 .87 .96 .87 .86 21 1.31 .98 .85 .79 22 1.39 1.00 .99 1.01 .88 23 1.54 1.39 1.19 .98 1.09 24 1.40 1.40 1.13 1.26 25 1.37 1.34 1.33 1.06 26 2.60 .95 1.85 1.21 1 47 .97 27 1.97 1.52 1.22 1.23 1.14 28 1.26 .97 1.27 29 1.67 1.35 30 1.98 1 37 1.17 31 2.36 1.04 1 18 1.68 1.51 32 1.76 .... 1.43 Such a table serves no useful purpose. The variation of top diameters actually utilized is shown in Table XXXVII. The values in this table, evened off by curves, would give proper dimensions for frustums for the volume table desired. The two steps described mean a double calculation of frustum volumes, first, as a basis of regular form factors, second as a basis of regular volumes. The second set of frustums also serves the purpose of obtaining the volumes for exact diameter and height classes, instead of for the actual average diameters and heights of the trees measured (§ 137). 224 FRUSTUM FORM FACTORS TABLE XXXVII Actual Average Top Diameters of Merchantable Lengths, Longleaf Pine, Coosa Co., Ala. Basis 555 Trees; Average of All Top Diameters 13.2 Inches Merchantable Length in 16-foot Logs D.B.H. 2 2^ 3 31 ' 4^ 5 Inches Top Diameters, Inside Bark — Inches 10 11 12 9.5 8.5 13 9.7 7.5 8.8 14 9.9 9.2 9.3 8.7 15 10.4 10.3 8.9 9.1 16 11.5 10.4 9.3 8.6 7.8 17 11.3 11.5 10.4 10.2 9.1 18 13 1 12.7 11.5 10.7 9.7 9.6 19 13.8 12.3 12.1 11.3 10.9 9.2 20 13.7 13.5 13.1 13.1 12.3 11.6 21 16.7 14.1 13.2 12.1 11.4 22 17.4 14.2 13.7 13.5 11.7 11.0 23 18.0 17.0 15.8 14.2 14.1 13.8 24 17.4 17.7 16.2 15.9 14.1 25 17.2 17.5 16.7 13.3 26 21.3 15.4 19.7 16.9 17.7 14 1 27 21.6 19.4 16.3 17.1 16.0 28 17.4 16.2 16.6 29 20.5 18.8 30 24.0 20.8 16.2 17.3 31 25.3 16.4 18.3 14.6 17.8 32 23.2 21.2 33 34 26.8 21.0 22.4 Of the two methods, the use of a fixed top diameter is preferable wherever utiHzation does not depart too far from this standard. If necessary, such a table of volumes could be corrected for actual utili- zation, by subtracting the per cent of volume lost by cutting to a lower point and larger diameter. In this case the same method must be used in estimating the standing timber, namely, to tally the heights of the trees to the fixed top diameter used, and then discount for waste. 185. Construction of the Volume Table from Frustum Form Factors. A Short Method. The third and final step is to construct the volume table by multiplying the volumes of the frustums by the form factors for each class, FORM FACTORS FOR BOARD FEET 225 Frustum form factors can be computed if desired, in cubic feet. For board feet, any log rule may be used as desired. A shorter but less satisfactory method is to first determine the top diameters of the frustums to be used in the base table and prepare the table of frustum volumes; second, to compute the arbitrary form factors which are obtained by dividing the average volumes of the trees in each class by the volume of the proper frustum, disregarding the possible difference in top diameter and average height for the class; and from these factors, to construct the volume table. This method works best when fixed top diameters are used in logging and the dif- ferences in top diameters between frustums and trees is small. The method of frustum form factors has resulted in such a marked increase in accuracy and economy in preparation of standard volume tables based on merchantable board-foot contents that it has practically superseded the standard methods of preparing these volume tables, and until total height and tables based on form classes supersede the use of mercha-ntable heights in timber estimating, this method will continue to be used extensively. 186. Other Merchantable Form Factors for Board Feet. Merchant- able form factors based on the volume of a cylinder whose height equals the merchantable length in the tree have been proposed by E. I. Terry. Merchantable volume tables based on the contents of frustums of paraboloids whose top diameters equal one-half D.B.H., scaled in 16- foot logs, have been computed by the Forest Service. These correspond in principle to the basic volumes of frustums of cones, and can be used for calculating form factors in the same manner, but offer no special advantage over the frustums of cones for the purpose required. References A New Method of Constructing Volume Tables, Donald Bruce, Forestry Quarterly, Vol. X, 1912, p. 21.5. The Use of Frustum Form Factors in Constructing Volume Tables, Donald Bruce, Proc. Soc. Am. Foresters, Vol. VIII, 1913, p. 278. Further Notes on Frustum Form Factor Volume Tables, Donald Bruce, Proc. Soc. Am. Foresters, Vol. X, 1915, p. 315. The Use of Frustum Form Factors in Constructing Volume Tables for Western Yellow Pine in the Southwest, Clarence F. Korstian, Proc. Soc. Am. Foresters, Vol. X, 1915, p. 301. Top Diameters as Affecting the Frustum Form Factor for Longleaf Pine, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 185. Frustum Form Factors of Hard Maple and Yellow Birch, B. A. Chandler, Bui. 210, Vermont Agr. Exp. Sta., May, 1918. A Formula Method for Estimating Timber, E. I. Terry, Journal of Forestry, Vol. XVII, 1919, p. 413. Comment on Above, Donald Bruce, Journal, Vol. XVII, 1919, p. 691. Further Comment, E. I. Terry, Journal, Vol. XVIII, 1920, p. 160, CHAPTER XVIII THE MEASUREMENT OF STANDING TREES 187. The Problem of Measuring Standing Timber for Volume. Standing trees are measured to determine their contents in cubic feet or in terms of manufactured products such as board feet or cross-ties. Trees are measured as a means of determining the contents of entire stands. These may be either average or sample trees, of which only a few are measured, or all of the trees in a stand or part of a stand may be tallied. The volumes contained in standing trees cannot be measured directly. Even the volume of the logs in the felled tree is computed from the measurement of their diameters and lengths. These computations, tabulated as log rules and as volume tables reduce the problem of esti- mating the volume of standing trees to that of measuring their merchant- able lengths and diameters. The cruiser must determine the height of trees either by instruments based on geometric principles of similar triangles, at considerable expenditure of time or by the eye, which is the only practical method where all or a large portion of the stand is to be so measured. Still more difficult is the actual measurement of diameters at the top of each log in the standing tree, which must be known when log rules are substituted for volume tables in timber estimating. Instead, the cruiser measures the diameter within reach, that at B.H. or stump, and judges the rate of taper as well as height, by eye, thus arriving at these upper diameters by calculation from a known measurement. Diameter breast high (D.B.H) is the only actual and accurate measurement which it is practicable to take upon all or a large per cent of the timber. All upper points are either measured on a few trees only, to obtain averages, or else are judged solely by eye; and since such ocular measurements are confined to dimensions, heights or log lengths, and diameters at upper points on the bole, the cruiser is depend- ent entirely on the computed volumes for these dimensions shown in log rules or volume tables. He may by experience correlate these volumes with their respective dimensions, just as stock buyers learn to guess the weights of animals, and may arrive directly at the volume 226 THE MEASUREMENT OF TREE DIAMETERS 227 of the tree or stand, but the method is far more uncertain than if depend- ence is placed on the computed vohimes of the logs or trees as shown in tables. In the use of volume tables, then, the accepted standards of volumes set by these tables are substituted for guessing as to the contents. The measurements required may be : 1. Diameter at base. a. Standardized at D.B.H., outside bark. h. Stump diameter inside bark, still in use by old time cruisers. 2. Height of tree. a. Total height to tip. h. Merchantable height. 1'. To a fixed top diameter. 2'. To a variable top diameter. 3. Actual measurement of an upper diameter to determine form (when form classes are distinguished). a. At middle of stem above D.B.H. (Jonson). h. At middle of stem above stump (Schiffel). c. At top of last log. 188. The Measurement of Tree Diameters — Diameter Classes. Stand Tables. Diameters will be averaged in either 1-inch or 2-inch classes. In the East and with species of a small total range of diameters, 1-inch classes are preferable. Especially with such species as spruce and white pine, 1-inch diameter classes are necessary to give a proper basis for determination of the rate of growth, and the number of such classes is not great enough to act as a drawback in estimating. A stand table is a tabular statement of the number of trees, in each diameter class standing on a given area. By dividing the total stand table by the area in acres, the stand per acre is shown, in which case the trees in each diameter class are usually expressed in decimals to two places, e.g., 12-inch class, 4.63 trees, etc. On the Pacific Coast, with a wide range of diameters running up to 60 inches or over, it is unnecessary and inadvisable to make smaller than 2-inch diameter classes.^ 189. Instruments for Measuring Diameter. Calipers, Description and Method of Use. Calipers have been the standard instrument 1 In French forest practice, 5 centimeters is the division used. This corresponds to 1.97 inches. The centimeter divisions were evidently too small and the next convenient division point was 5 centimeters. This is not an argument against the use of 1-inch diameter classes for Eastern species. 228 THE MEASUREMENT OF STANDING TREES for measuring the diameter of standing trees and their use is necessary in taking taper measurements on down timber which cannot be meas- ured with diameter tape. The standard type of cahpers for eastern n --. [\ i»ipif}f«ig««5 kjjIJIiB^^ Fig. .39. — Calipers used in measuring the diameters of standing trees. hardwoods has a beam 36 inches long with arms one-half that length. A smaller type may be used for trees whose diameter does not exceed 2 feet as in spruce or second-growth timber. The standard calipers have a beam graduated on both sides to inches and tenths, and two arms, one of which is bolted to the end of the beam, the other a sliding arm, the beam passing through a slot. Fig. 40 indicates the construction of this arm. The essential feature is that when not pressed against the tree, the arm -Construction of calipers, to secure adjustment of jg easily moved Fig. 40. movable arm at right angles to bar. along the beam but when in use it takes a position at right angles with the beam and parallel to the other arm. The position of this arm is adjustable by the movement of the screw (a) which sets a movable plate. In use the arms must be at right angles to the beam. If warped or out of adjustment, corresponding errors in measuring diameters will occur. The correct diameter can be obtained only by holding the cali- THE DIAMETER TAPE 229 pers horizontally, with the beam in contact with the tree at the point desired, usually at B.H. If measured with the tips of the calipers, the errors resulting from false adjustment or warping are exaggerated. If measured with the calipers held at an angle, the point measured is probably above D.B.H. and correspondingly too small. If measured below D.B.H., a large error results from the rapidly increasing diameter of the tree due to stump taper. An average measurement 6 inches below the desired point or at 4 feet will incur from 5 to 8 per cent excess volume, depending upon the rapidity of the taper. Where the exact average diameter of a tree is desired, two measure- ments must be taken at right angles and the mean recorded to to inch. In timber estimating, where large numbers of trees are measured, but one diameter is taken, with no efforts made to determine the average even on trees of eccentric cross sections since it is assumed that errors incurred in this way are compensating. A precaution sometimes used is to measure half of the trees in one cardinal du'ection, and the remainder in the other (French). 190. The Diameter Tape. The irregularity in the form of trees, both as to cross section and bark, makes it practically impossible to obtain consistent results in two successive measurements of diameter of the same tree with calipers even when the mean diameter is taken as above indicated. For permanent records on plots to be subsequently measured for deter- mination of growth, consistency in diameter measure- ment is absolutely required. For this purpose it has been found that the diameter tape must be substituted for calipers. The graduations on the diameter tape are in inches of diameter, each inch equal to 3.1416 inches in girth. In theory, the measurement of the circumference of a tree gives a plus error when compared with the actual mean diameter. Actual tests at the Fort Valley Experiment Station by Scherer on one hundred trees showed that the excess in diameter from tape over caliper measurement was 2 per cent, but the consistency of two successive tape measurements as compared with successive caliper measiu-ements showed that the Fig. 41. — Tape for measuring girths and diameters. 230 THE MEASUREMENT OF STANDING TREES total error of calipers over tape was in the proportion of 21 to 1. The diameter tape should therefore be adopted for all measurements of permanent sample plots. 191. The Biltmore Stick. Although calipers can be taken apart for travel and packing, they are cumbersome to carry in timber esti- mating especially through brush and over rough ground. When in addition a beam of 60 inches in length is required, their use becomes extremely burdensome. The Biltmore Stick, devised by Dr. C. A. Schenck, substitutes a straight stick for calipers and has been widely adopted by foresters for practical timber cruising. The principle of the Biltmore Stick is as follows : A straight stick, if held horizontally, tangent to or in contact with the bole of the tree, and at arm's length from the eye, forms the far side of a triangle whose other two sides are lines of sight from eye to each side of the tree, and which intersect the stick at definite points. When the stick is held so that one of these lines of sight intersects one end, a scale can be placed upon the stick starting at zero at this end, and the point of in- tersection of the other line of sight, if the eye is held in its original position without turning the head, will indicate on the scale the diameter of the tree at this point. Since this intercepted distance on the stick is evidently less than the diameter of the tree, which is at a greater distance and cannot even be seen correctly, the distances corresponding to the diameters wanted will be less than these diameters and this difference increases with diameter of tree, so that the graduations on the stick for successive diameters fall closer together for the larger diameters. The values of the graduations on the stick are directly dependent on the dimensions of the triangle which is determined by the length of the arm or reach. This ranges from 23 to 27 inches with an average of 25 inches. Fig. 42. -Principle upon which the Biltmore stick is constructed. The formula for computing the values of this scale is a = length of reach in inches; D = D.B.H. THE BILTMORE STICK 231 Scale = Va{a+D) 'a+D The derivation of this formula is as follows : AB AB' BC B'C AB = = a inches, an( Substituting these va lues, a BC' AB' D ' 2 aU 2 = AB'XBC. (I) SC- aD 2 AB" D 2' {AB'Y = {AC'Y-{B'C')\ By substitution, {AB'y=la+-\ -(-) ={ay+aD = a{a-\-D). 2/ \ 2j (II) AB' = yya{a+D). Substituting this value for AB' in equation (1), aD BC. ^ Vaia+D)' Since BC is the scale for ^ of the diameter of the circle, the formula for the scale for the whole circle is ^ „ , aD laD'^ Scale =- ~\^+D Vaia+D) yla+D' The Biltmore stick is less accurate than the caHpers or diameter tape and should therefore never be used for scientific measurements or permanent records. To insure complete accuracy in the use of a prop- erly graduated stick, the following conditions are necessary: The tree must be circular in cross-section. The stick must be held against the tree at a point 4| feet from the ground. aD VaVaD VaD foD^ VaVaD VaD ja^ VaVa+D Va^ >«" Vaia+D) VaVa+D Va+D \a+£> 282 THE MEASUREMENT OF STANDING TREES The eye must be on a level with the stick (assuming that the tree is erect). The eye must be at the proper distance from the tree. The stick must be held horizontal (assuming again that the tree is erect). The stick must be held perpendicular to the line of sight from the eye to the center of the tree at the point of measurement. Errors of 1 per cent in the measurement of diameter are incurred under the following conditions : The figures given represent the distances by which the position of stick or eye departs from the above conditions. TABLE XXXVIII Errors in Using Biltmore Stick * Sign Resulting in Error of 1 Per Cent in Diameter D.B.H. of trees 10 30 Inches Inches 9.2 7.3 4.6 4.2 4.9 4.9 1.4 0.65 60 Inches + + ± Usually Eye above or below stick by Stick not horizontal — one end higher than other by Stick not perpendicular to hnc of sight — one end nearer the eye than the other by Eye too near to or too far from tree by Measurement at wrong height Tree irregular in shape 7.1 4.1 5.1 0.45 (Variable) (Very variable — consider- ably greater than with calipers) * Donald Bruce, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 46. A still more serious error is incurred through the inevitable tendency of the cruiser to raise the stick to the level of the eye, rather than lower the eye to the level of the stick. If the stick is held at 4^ feet and the eye remains at 5 feet 3 inches, with a difference of 7 inches in height, the error is but 1 per cent of the diameter, but if the stick is raised to the level of the eye, the diameter at the point measured is appreciably less than D.B.H. The resultant average error varies from 3 to 6 per cent, dependent upon the rapidity of taper, and increases consequently with the diameter of the tree. The following table gives the graduations which should be placed upon Biltmore sticks for a reach of from 23 to 27 inches respectively: THE BILTMORE STICK 233 TABLE XXXIX Figures to be Used in Graduating a Biltmore Stick * Distance from Eye to Tree — Incites Diameter of 23 24 25 26 27 tree. Inches Distance to be marked on stick — Inches 3 2.82 2.83 2.83 2.84 2.85 5 4.53 4.55 4.56 4.58 4.59 7 6.13 6.16 6.19 6.21 6.24 9 7.63 7.68 7.72 7.76 7.79 11 9.05 9.11 9.17 9.22 9.27 13 10.39 10.47 10.54 10.61 ■ 10.68 15 11.67 11.77 11.86 11.94 12.03 17 12.89 13.01 13 . 12 13.22 13.32 19 14.06 14.19 14.32 14.44 14.56 21 15.18 15.34 15.48 15.62 15.75 23 16.26 16.44 16.60 16.75 16.90 25 17.31 17.50 17.68 17.85 18.01 27 18.31 18.52 18.72 18.91 19.09 29 19.29 19.51 19.73 19.94 20.14 31 20.23 20.48 20.71 20.94 21.15 33 21.15 21.41 21.67 21.91 22.14 35 22.04 22.32 22.59 22.85 23.10 37 22.91 23.21 23.50 23.77 24.03 39 23.75 24.07 24.37 24.67 24.94 41 24.58 24.91 25.23 25.54 25.84 43 25.38 • 25.74 26.07 26.40 26.71 45 26.17 26.54 26.89 27.23 27.56 47 26.94 27.33 27.70 28.05 28.39 49 27.69 28.10 28.48 28.85 29.21 51 28.43 28.85 29.25 29.64 30.01 53 29.16 29.59 30.01 30.41 30.79 55 29.87 30.31 30.75 31.16 31.56 57 30.56 31.03 31.47 31.90 32.32 59 31.25 31.73 32.19 32.63 33.06 61 31.92 32.41 32.89 33.35 33.79 63 32.58 33.09 33.58 34.05 34.51 65 33.23 33.75 34.26 34.74 35.21 *W. B. Barrows, Journal of Forestry, Vol. XVI, 1918, p. 747 In this table, the graduations are given for odd diameters instead of even ones. For instance, when diameters are taUied in 2-inch classes, every tree larger than 13 inches and smaller than 15 inches in diameter is tallied as a 14-inch tree. These graduations thus mark the upper and lower limits of size of each 2-inch 234 THE MEASUREMENT OF STANDING TREES D.B.H. class, instead of the average size, as 14 inches, enabhng the cruiser to classify accurately all trees on the border line between two diameter classes. In measuring trees of eccentric or irregular cross section, the errors incident to caliper measurement are exaggerated by the use of the Biltmore stick, but as before, these errors tend to compensate and can be neglected. Bruce has suggested that the volume tables standardized at D.B.H. should be converted to values for diameter at the height of the eye, or D.E.H., standardized at 5 feet 3 inches. To do this, taper measurements are taken to establish the D.E.H. of trees of given D.B.H. By interpolation, the volumes corresponding to given even D.E.H. inches can easily be obtained. In the ordinary use of the Biltmore stick, it is necessary to bevel the edge opposite the figures so that the measurement may be taken in contact with the bole. Otherwise the thickness of the stick reduces the distance from the eye and incurs an error whose magnitude is determined by this thickness. By deducting this thickness (t) from the distance (a) in the formula, so that this formula reads, Scale = Va{a+D) the resulting values are correct for the face of the stick. 192. Ocular Estimation of Tree Dimensions. Where the diameter of every tree on a given area must be recorded, the time consumed in actually measuring the diameters is a considerable item of expense. Except when scientific measurements or permanent plot records are required, estimators plan to educate the eye to read as large a percent- age as possible of the diameters directly without measurement, using the calipers, diameter tape or Biltmore stick merely as a check. This is especially desirable when the cruiser is doing his own tallying. While the eye can be trained with considerable rapidity to a sufficient degree of accuracy for estimating, it is constantly liable to error and must never be relied upon for even a single day without instrumental checks. These should be made on starting work and at intervals during the day. The eye may be trained to judge diameters at different distances equally well. Some men develop this faculty more rapidly and to greater degree than others. It is the general tendency in ocular estimation to favor a tree of a given size, diameters of trees of lesser size being over-estimated while larger diameters are under-estimated. The use of 2-inch diameter classes greatly facilitates ocular estimating. In training the eye to estimate diameters, the greatest progress is made by repeated guesses followed immediately by the measurement of the tree which is then closely observed to fix the known diameter and correct the faulty observation. Since ocular estimating is not a matter of reasoning but of impression, the decision as to the dimensions of the tree should be made instantly. Otherwise fatigue and consequent inaccuracy ensue. THE MEASUREMENT OF HEIGHTS 235 193. The Measurement of Heights. While in measuring diameters it is possible to use the instrument upon every tree as a practical measure when necessary, the greater difficulty and time required in measuring heights makes the general use of an instrument for even a large per cent of the trees impossible. Only on small, permanent sample plots will the height of each tree be actually measured. Height measures, or so-called hypsometers, are commonly used to obtain the height of average trees from which the average height of the remaining trees is determined, or to check the eye when the merchantable heights of all trees are recorded. In the latter case, ocular estimation of the number of merchantable logs in each tree, or total merchantable height, is the only practical means possible. It takes no longer to estimate the height of a tree by eye than its diameter, but the measurement of height by hypsometer takes about ten times as long as to caliper the tree. The eye is slightly more unreliable in measuring heights than diam- eters. The height scale is more difficult to fix in the mind. Con- sequently the tendency is to arrive at the height of trees by comparison with other trees. The result is that the standard of height for all trees tends to shift from day to day unless heights are carefully checked at the beginning of each day's work in order to maintain this mental basis or standard. In no other feature of ocular timber estimating are such serious errors made even by experienced cruisers as in estimat- ing heights, and the novice should never trust his judgment over- night. 194. Methods Based on the Similarity of Isoceles Triangles. Measurement of heights is based on the principles of similar triangles. From the observer's eye, the tree forms one side of a large triangle, the other two sides of which are the lines of sight to the top and base of the tree. The base of this triangle can be measured. The length of the vertical side which is the height of the tree is the dimension sought. To determine this inaccessible dimension, a smaller, measure- able, similar triangle is used. Similar triangles must have their three sides proportional and the three angles equal. This is secured when either two sides are propor- tional and one angle equal, or one side is proportional and two angles equal. The isosceles triangle with two sides of equal length forms the simplest method of measuring the height of a standing tree. In this triangle the base from the eye to the foot of the tree is equal to the height of the tree and may be directly measured. The small triangle in this case is used to find the point on the ground at which this base will be equal to tree height. A triangle which has its own base and 236 THE MEASUREMENT OF STANDING TREES / y hy X height equal and whose Hne of sight from eye to top coincides with that from eye to tip of tree gives this result. A straight stick or short pole may be grasped by the thumb and first finger at a distance from its top exactly equal to the distance from the eye to the point thus marked. Holding this stick vertically, which is best accomplished by having the greatest weight below the hand to act as a pendulum, the observer moves backward or forward until the line of sight ^6 in Fig. 43 cuts the desired upper point on the tree, and at the same time the line of sight '.Ac cuts the tree at its base. At this point the triangle Ahc has become similar to the triangle ABC, and AC is equal to BC. The measured distance from eye to base of tree is then equal to the height of the tree. This distance can be measured along the ground to the point below the eye with sufficient accuracy, pro- vided the slope is even. Thismeasurementof height can be taken from any point of elevation, either on a level with, above, or below the base of the tree without affecting its accuracy. 195. The Principle of the Klaussner Hypsom- eter. For height meas- urements which require greater accuracy than is obtainable by such ocular methods as the one just described, the small triangle is constructed in the form of an instrument called a hypsometer, on which two of the sides corresponding respectively to the lines AC and BC, or distance to tree and height of tree, are graduated to units of distance. This enables the observer to first adjust the scale AC for distance, to equal in feet the known distance from the tree, hence to determine what this distance shall be. The line of sight from the eye, beginning at the zero point of this scale or apex of the small triangle is now brought into line with the point on the tree whose height is to be measured, which makes the small and large triangles similar. The point at which this line of sight cuts the scale BC, whose graduations are equal to those on the scale AC indicates the height of the tree. These graduations may be of any size so long as both scales are graduated equally. They ;.i^Jc Fig. 43. — Similar isosceles triangles formed by use of pole, for measuring height of trees. THE PRINCIPLE OF THE KLAUSSNER HYPSOMETER 237 will serve to read height in feet, or in any other unit of distance, as meters, since whatever unit is used to measure the distance from the tree applies as well to its height. The Klaussner Hypsonieter. In hypsometers based upon similar triangles as shown in Fig. 43 the vertical scale represents tree height, the scale at base, distance to the tree. If the scale fee is on a movable arm, it may be set on the scale Ac at any required distance. By sight- ing along Ac towards C and by rais- ing the sight or bar Ah to intersect the line of sight AB, the total height of tree is read directly from the scale fee. The standard hyp- sonieter of this make is known as the Klaussner, Fig. 44. The verti- cal scale is weighted to insure its vertical position. As is seen, two lines of sight must be adjusted for this reading. The instrument is therefore used with a tripod and is rather slow in execution.^ Fig. 44. — The Klaussner hypsometer. "^f^ L Fig. 44o. — Method of application of the Klaussner hypsometer. -■'-ni,''~ . > In Forestry Quarterly, Vol. XHI, 1915, p. 442, S. B. Detwiler has suggested a simple hypsometer based upon this principle, which for practical work does away with the tripod apparently without sacrificing accuracy. 238 THE MEASUREMENT OF STANDING TREES The Klaussner principle differs from that shown in Fig. 43 only in that the height is measured on the vertical scale be, the measure- ment may be taken at any point from the tree by adjusting the scale Ac to correspond with this distance, and the triangles may be of any form, provided one side is vertical. Merritt Hypsometer. The Merritt hypsometer is a scale placed on the reverse side of the Biltmore stick (§ 191) and is read by holding the stick in a vertical position at arm's length, when standing at a given dis- tance from the tree. Six inches on the stick will give the height of a 16.3-foot log under the following conditions: Arm length, inches 23 24 25 26 27 Distance from eye to tree, feet 62 , 5 65 . 2 67 . 9 70 . 6 73 . 3 The similar triangles used here correspond in principle with those of the Klaussner hypsometer. For accurate results the stick must be held vertically and not raised or lowered during the reading. Only approximate accuracy can be secured, but the method serves as a ready check on ocular measure- ments of log lengths. 196. Methods Based on the Similarity of Right Triangles. The second general method for measuring heights is the use of the right triangle. This method is based on securing a horizontal line of sight from the eye to a point on the bole of the tree, and requires two readings, one above, the other below this point of intersection, the sum of which gives the height of the tree. This disadvantage is offset by the fact that these instruments may be held in the hand, thus eliminating the tripod, and making them compact and portable. The horizontal line of sight may be secured by using either a bubble or a plumb-bob. The simplest application of this method is that of a right isosceles triangle, for which purpose a clinometer is used. This is an instrument with bubble mounted on a graduated arc reading in per cents, or in degrees. In the latter case the graduations must be reduced to per cents. When the arc on this clinometer is set at an angle of 45°, the line of sight Ab coincides with the line AB at a, definite distance from the tree, from which a horizontal line of sight, which can then be taken by setting the arc at zero, gives a distance to the tree equal to the height of the tree above the intersection of this line with the bole. If used on fairly level ground, the distance below this point is within reach and can be measured on the tree and added to the distance to the tree to get its total height. This instrument can also be used to measure heights from any dis- tance from the bole, by taking two readings or angles, one to the upper HYPSOMETERS BASED ON PENDULUM OR PLUMB-BOB 239 point, and one to the base. In this case the actual angle from station to point on tree is read, and indicates the height in per cent of the hori- zontal distance. At 100 feet distance, an 80 per cent angle to tip equals a height of 80 feet above the eye. If the lower angle to base is Fig. 45. — The Abney hand level and clinometer. now 5 per cent, the additional height is 5 feet, total height 85 feet. At 50-foot distance these per cents applied to 50 feet give a total height of 42| feet. It is convenient therefore to read heights by this method from distances easily converted into equivalent heights. Fig. 46. — Goulier's Clinometer. 197. Hypsometers Based on the Pendulum or Plumb-bob. These angles can be read as easily from a pendulum, with graduated arc placed below. A clinometer constructed on this principle, and used as a hypsometer, is illustrated in Fig. 46. 240 THE MEASUREMENT OF STANDING TREES The Fauslmann Hypsometer. Instead of graduating a circular arc in per cents, which requires a decreasing scale with increasing per cent (since the tangents of the angles increase faster than the angle), the height scale corresponding with this arc may be placed on a straight arm as in other hypsometers (§ 195) and graduated evenly. The Faustmann hypsometer employs this principle of the pendulum, using a plumb-bob to determine the angles BAD and CAD, and indicat- ing the height of the tree above and below the point D by the intersec- tion of this plumb-bob string with the " height "scale on the base of the hypsometer. This instrument is illustrated in Fig. 47. Its method of use is shown in Fig. 48. Fig. 47. — The Faustmann hypsometer. The slide is first moved upwards until the number of units on the vertical scale, from zero, thus set off, equals the distance to the tree in feet (or in yards). When sighted at the upper point on the tree, the plumb-bob falls to the near side towards the eye, and the number of units or height is read in the mirror. The second reading is shown in Fig. 48, the plumb-bob falling to the far side. The horizontal scale thus extends in both directions from zero. On fairly level ground, this second reading is sometimes omitted, providing the height of the eye above the base of tree is regarded as a constant and added for total height. For accurate measurements both readings must be taken. Practice has demonstrated that the use of a plumb-bob and weight reduces the serviceable character of the instrument, since the seweights are easily lost and the strings broken. The mirrors also are easily damaged. Weise Hypsometer. The Weise hypsometer (Fig. 49) is the same in principle as the Faustmann but substitutes a metal pendulum for HYPSOMETERS BASED ON PENDULUM OR PLUMB-BOB 241 the string and plumb-bob. The two arms when not in use can be placed within the cylinder. The instrument is more durable than the Faust- mann but slightly less accurate. Forest Service Hypsometer. A more durable type of hypsometer based upon this principle is known as the Forest Service hypsometer. The distance at which this instrument reads the heights BD and DC is fixed at 100 feet. The scale showing these heights is computed from the tangents of the angles read at this distance and expressed in terms of feet in height. This scale is placed on a circular pendulum which Fig. 48. — Method of application of the Faustmann hypsometer. is released by pressing a small knob with the thumb while sighting through a peep-hole along the line of sight AB or AC. This scale is enclosed in a metal frame in the form of a disk, and the instrument is practically indestructible and can be operated with one hand. If read at 50 feet, the readings shown must be divided by two. If at 200 feet, they must be multiplied by two, and proportionately for other distances. As in the case of other clinometers this hypsometer may be used to read per cents of grade. The Winkler Hypsometer. The same principle may be used in constructing a hypsometer in the form of a square or rectangular board or cardboard. In this instrument the line of sight, AB, coin- cides with the top edge of the board. A board whose top and bottom edges are parallel is laid off with a 242 THE MEASUREMENT OF STANDING TREES horizontal scale at base and a vertical scale ad intersecting the scale at base at right angles, at a point to permit this horizontal scale to extend in both directions as in the Faustmann Hypsometer. Both scales are marked off in the number of equal units or graduations desired, to cor- respond with the distance from the tree at which the hypsometer is to be used. A plumb-bob is suspended from point a, and the heights above and below the eye read as usual. If but one fixed distance is desired this is represented by a scale reproduced on the line at base of card. Fig. 49. — The Weise hypsometer. This board may be graduated to read at lesser distances from the tree, by placing other horizontal scales upon the board intersecting the vertical or " distance " scale ad at the point below the apex a, representing the distances desired, and graduating these horizontal lines to the same scale as the base. This home-made hypsometer is described in Farmers' Bulletin 715, U. S. Dept. of Agriculture, 1916, p. 18. The original instrument from which this type of hypsometer was derived is known as the Winkler hypsometer, shown in Fig. 50. This instrument is also used as a dendrometer (§ 200). THE PRINCIPLE OF THE CHRISTEN HYPSOMETER 243 198. The Principle of the Christen Hypsometer. Many hypsom- eters have been invented, principally by Continental foresters, using one or the other of these general principles. The Christen hypsometer introduces a different principle but has no special merit except the simplicity of its operation. Description of this instrument, taken from Graves' Mensuration is as follows : This instrument consists of a metal strip 16 inches long, of the shape shown in Fig. 51. The instrument is made of two pieces hinged together, which are folded Fig. 50. — Winkler Hypsometer. when it is not in use. A hole is pierced in the upper end, from which it is suspended between the fingers. Along the inner edge is a notched scale which gives directly the readings for heights. The instrument is used as follows: A 10-foot pole is set against the tree. The observer stands at a convenient station whence he can see the tip and base of the tree and also the top of the 10-foot pole. The instrument is .suspended before the eye and moved back and forth until the edge b is in line of vision to the top of the tree and the edge c in line of vision with the base. The point where the line of vision from the eye to the top of the 10-foot pole intersects the inner edge of the instrument indicates on the scale the height of the tree. 244 THE MEASUREMENT OF STANDING TREES O Each instrument is constructed for use with a specified length of pole. The instrument described above is one designed by the author for convenience with the use of English units. It was constructed in the following way: The distance be on the instrument was chosen arbitrarily as 15 inches and the length of the pole as 10 feet. It would, of course, be possible to construct an instrument for a pole 12 feet or any other length and on a basis of any desired length of instrument. The theory of the construction of Christen's instrument may be shown by Fig, 52. When used as above described, two pairs of similar triangles are formed: ABC, bcXDC bcXDC and Abe; ADC, and Adc, in which BC = and dc = . de BC With a known value of DC and be, dc may be determined for all different heights which are Ukely to be required. Thus it may be assumed that it would not be necessary to measure trees less than 20 feet high, so that the lowest graduation on the instrument is made for that height. To find the proper point for the 20-foot graduation on the scale, the following formula was used: BC be 20 15 zi or = =: DC dc 10 de or de = - = 5.7 inches FiQ. 51.— The Christen hyp- someter. Fig. 52. — Method of application of the Christen hypsometer. THE TECHNIQUE OF MEASURING HEIGHTS 245 This same method was used to determine the value of dc for a 25-, 30-, 35-, 40-foot tree, etc., up to 150 feet, and the proper graduations made on the scale. The scale is somewhat more easily read when a notch is made at each graduation. The instrument is light and compact, and with practice can be used very rapidly, provided one has an assistant to manage the 10-foot pole. It requires no measure- ment of distance from the tree, and the height is obtained by one observation. It is more rapid than either the Faustmann or Weise instrument. Its disadvantages are that it requires a very steady and practiced hand to secure accuracy, that it cannot be used accurately for tall trees, and that it is not adapted for steady work because it is extremely tiresome to hold the arm in the position required. This last objection may be overcome by using a staff to support the hand. 199. The Technique of Measuring Heights. In rough checks for timber cruising, the distances used in obtaining heights are usually paced. Care must of course be taken to carefully check the paced distance desired to avoid incurring a cumulative error. For the measure- ment of average trees, depended upon to secure the heights of stands, the distance should, if possible, be measured with the tape. This latter method is the only one permissible in measuring the heights of trees on permanent sample plots. By the method illustrated by the Klaussner hypsometer, this dis- tance is measured along the ground whether the slope be leVel, gradual or steep. By the method of right triangles the distance must be meas- ured horizontally to the bole of the tree, and a considerable error would be incurred in measuring it along the surface on very sloping ground. Since the entire basis of the similar triangles used assumes that the tree which forms one side of the larger triangle stands in a vertical position, the consequences of measuring a tree which leans either towards or away from the observer are very serious (Fig. 53) . From the position A, the distance to the base of the tree is AC. But if the observer sights at the tip of the tree Bi which leans towards him, its height, when compared to the distance AC will be read as B'lC, an error of +16 per cent. If the distance is measured instead to the point directly below the tip Bi the height is read as BiCi, with an error of — 2 per cent. Again, if the tree Bo leans away from the observer, and its distance is measured as AC, its height will be read as B'iC with an error of — 16 per cent, but if this distance is measured to the point C2, the height will be read as B2C2 with an error of —2 per cent as before.^ If it is necessary to measure leaning trees, this can be done by taking a position at right angles with the line AC in Fig. 53, or at right angles with the vertical plane in which the tree lies. The ocular measure- ' Some New Aspects Regarding the Use of the Forest Service Standard Hyp- someter, Hermann Krauch, Journal of Forestry, Vol. XVI, 1918, p. 772. 246 THE MEASUREMENT OF STANDING TREES ment of heights largely avoids this specific error since the eye allows for the leaning position of the tree while the instrument does not. Where total heights are measured to the tip of the crown, the greatest accuracy is obtained in the measurement of conical-crowned conifers. Broad- or deliquescent-crowned trees are difficult to measure accurately. The source of error is the same as that which applies to leaning trees. A line of sight AB, in order to be directed at the tip B, must penetrate the foliage of the crown while if directed tangential- ly to the edge of this crown, it will take the position of ABi. The error from the meas- urement of broad- crowned trees, unless this pre- caution is ob- served, is cumu- lative and tends to over-estimate their heights. Merchantable Fig. 53. — Errors which may be incurred in measuring the heights are meas- height of a leaning tree. To avoid error the measurement ured by exactly should be taken at right angles to the plane in which the the same princi- tree falls. pjgg ^^g g^j.^ g^p_ plied to total heights, and upon broad-crowned trees may be obtained more exactly. The element of uncertainty in the measurement of mer- chantable bole is not height, but the determination of the point on the bole at which the used length will terminate, that is, the merchantable top diameter of the bole. Merchantable heights may be measured in 16-foot log lengths by the use of the principle in Fig. 43. (Merritt hypsometer, § 195.) This same principle may be more accu- rately applied by leaning a pole of known length against the tree and then noting the length of a pencil required to take up this given length at the distance of the observer. This pencil length may then be measured off by eye on the remainder of the tree to divide it up into logs. It is common practice amongst timber cruisers to measure the total or merchantable height of windfalls as a check on ocular timber estimating. MEASUREMENT OF UPPER DIAMETERS. ^ DENDROMETERS 247 200. The Measurement of Upper Diameters. Dendrometers. Upper diameters of standing trees must be measured, first, in estimating timber to a merchantable top diameter; second, to determine the form quotient of the tree, where form classes are to be distinguished. In timber estimating, ocular methods are used entirely, and the probable upper diameters approximated by knowledge of rates of taper checked by the measurement of diameters on the boles of down trees. But for the measurements required to determine form quotients, it is not safe to depend altogether on chance windfalls, nor can cutting sample trees be resorted to on account of the time and expense involved. The eye is not sufficiently accurate to gage diameters at upper points, hence these measurements for form quotient must be taken on standing trees by instrumental means. An instrument intended to measure the upper diameters of stand- ing trees is termed a dendrometer. The principle of the dendrometer is that of similar triangles; but in this case two sets of triangles are used, first, those required in determining the height to the point to be measured, and second, those used to measure the diameter at this point by comparison with the side of a smaller triangle on the dendrometer. These principles are illus- trated in Fig. 54. In determining the form quotient for standing timber, either according to Jonson's or Schiffel's methods, the diam- eter at the middle point, either above D.B.H. or above the stump respectively, is sought . As point- ed out, the absolute form quotient cannot be determined with scientific accuracy from measurements taken outside the bark or on standing timber, but approximate results can be obtained. The triangles whose bases are respectively B, 6i and 62 are similar, and the relation between B and either bi or bo determines the diameter at B. But the points 61 and 62 are not the same, and this difference distinguishes two different principles used in constructing dendrometers. When the distance Ac to the horizontal scale on which will be read the upper diameter B, is fixed, so that on sighting at point B this distance coincides with 62, jif III y^ 'i /III A^^ ± / I !c| Fig. 54. — Principles underlying construction of dendrom- eters, as illustrated by the Biltmore pachymeter. 248 THE MEASUREMENT OF STANDING TREES as it does on most dendrometers, the proportion between the upper diameter B and its equivalent C, corresponding to c on the instrument, is aUered since the side Ab remains of the same length and coincides with ^4^2 in the figure. This discrepancy increases in proportion to the cotangent of the angle A and the distance read on the dendrometer scale at 62, which is graduated for inches, will be less than the true diameter B by just the amount of this error. The use of all dendrometers built on these j)rinciples requires correction by a table, to obtain true upper diameter. This difficulty is illustrated by a dendrometer attached to the Barbow cruising compass, used to some extent on the Pacific Coast. The dendrometer on this compass was a brass scale 1 inch long, finely graduated to read the apparent diameter m inches at the upper end of the i equal to the diameter B, thus substituting two parallel lines of sight for the horizontal triangles shown, and reading the diameter of the lower side of a l)arallelogram directly in terms of inches of diameter at B. In an instrument invented by Judson F. Clark and C. A. Lyford, a telescopic sight moves on a bar. In one invented by Donald Bruce, both lines of sight are brought into the same plane by means of two reflecting mirrors, set at exact angles of 45 degrees. 201. The Biltmore Pachymeter.' By employing the second principle, in which the side of the small triangle biC remains vertical, the diameter indicated at 61 on the hypsometer remains in the same proportion to that desired at B, as when the reading is taken at position C. Since the point opposite c may be taken at the base of the tree, regardless of whether this point is horizontally opposite the eye or above or below it, a projection of the diameter B upon the base of the tree enables it to be directly measured on the tree, or on a scale c upon the instru- ment, graduated for the distance Ac. This principle is employed by an instrument termed the "Biltmore Pachymeter.'' (Ref. Forestry Quarterly, Vol. IV, 1906, p. 8.) A slot, the two edges of which are absolutely parallel, or a stick or cane of which the same is true is suspended in a vertical position in front of the eye. A scale marked in inches is held by an assistant tangentially to the tree trunk at D.B.H. The diameter at any desired point on the stem is obtained by finding the distance from the tree at which the diameter of the slot or stick exactly obscures that of the tree at the desired point, when the width corresponding to this diam- eter will be indicated by the intersections of these edges on the scale below. The instrument and its projection upon the tree trunk are shown in Fig. 54. 202. The d'Aboville Method for Determining Form Quotients. This method depends on the measurement afb;, but is simplified by using a horizontal line of sight from eye to tree, and an angle of 45 degrees at point A, in which case the proportion between the lines AC and AB in Fig. 54 becomes 1.4, and the diameter at B becomes 1.4^2. To make this measurement, a distance is found which is just equal to the length of the bole between the point horizontally opposite the eye, as in Fig. 54, and the upper point to be measured. Substituting d and D for diameter at 5 height and D.B.H. respectively, the form quotient of a tree, as read on the dendrometer, is d / = -Xl.4. D 1 Pachyineter — an instrument for measuring small thicknesses. — Century Dic- tionary. / THE JONSON FORM POINT METHOD 249 The instrument consists of a graduated scale or straight-edge. For determining merely the form quotient the actual diameters need not be as^rtained but only their proportion or relation. The two measurements are taken by eye, holding the horizontal scale at arm's length {Ac and ^62) for each reading. The principal error to be guarded against is failure to secure the horizontal line of sight and the corresponding distance, which will residt in correspondingly large errors in reading the proportional diameters. Failure to select the right point on the tree, provided a definite point is selected and the method otherwise properly applied, incurs only the error due to difference in taper between the point measured and the point desired, which depends on rapidity of taper. This simple method should be of great assistance both to practical woodsmen in determining upper diameters, and to foresters desirous of testing the form quotient of trees in order to ascertain the applicability of volume tables based upon principle of form factors. 203. The Jonson Form Point Method of Determining Form Classes. In con- nection with his studies of the form of trees and form quotients, Tor Jonson has evolved a method for determining the form class of standing trees without the necessity of measuring the upper diameter or the form quotient. This method consists in locating a point on the stem of the tree, which he terms the form point. The percentage relation which the height of this point from the stump bears to the total height of the tree, he claims, bears a consistent relation to the form quotient, and by means of a table showing these relations the form quotient and form class of the tree may be determined. Mr. Jonson describes the method as follows: The shape and position of the crown has been found to be the most dependable and useful indication of different tapers and form classes. This is connected with the bole's function to carry and steady the crown, especially against the breaking forces of the wind, and it has been found that in the building of the bole only enough material is used to make it equal in strength to the force of the winds. It may therefore be said that it is the strength of the winds that determines the necessary dimensions of the trunk, and as the force of the wind is generally applied to the crown of the tree, it will be found that its weight, shape and position indirectly influence the size and taper of the trunk. While estimating, the D.B.H. is measured with caliper and the taper is then determined through finding by ocular means the form point, i.e., the point where the pressure of the wind is apparently concentrated which is usually the geomet- rical center of the crown. By sighting at this point and at the same time at the base and tip of the tree over a stick, approximately 30 cm. long, divided into 10 equal parts (Christen's hypsometer), the height of the form point can be easily fovmd expressed in per cent of the total height. This form point can then be looked up in the table giving the form point heights which are characteristic for each form class. The higher the crown is placed, the less the taper and the more cyhndrical the form, and conversely, the lower the crown extends, the more rapid will be the taper and the poorer the form. When, as is often the case, the estimating is based on diameter outside bark, the difference which is caused by variable thickness of the bark must be taken into consideration. The spruce, fir and other species with thin even bark show no difference in form when measured inside or outside bark, for which reason the given normal form point heights give the form with, as well as without, the bark for these trees. White birch, larch and others, but especially the pine, show great reduction in form when measured with bark, for which reason the form quotient outside bark 250 THE MEASUREMENT OF STANDING TREES is different from what the crown normally signifies. On this account special tables have been made up for use with outside bark measurements, but, as the Scotch pine shows many different types of bark, four tables have been compiled for trees whose bark is thin, medium, thick and very thick. When judging the location of the form point, it should be remembered that it is at the base of the branches where the acting forces of the wind are transferred to the bole, for which reason deciduous trees with branches pointing up will have the form point not in the center of the crown contour but as much lower as the bases of the branches he lower than the foliage on which the wind is acting. In estimating trees which have quickly cleared themselves of branches, a better result will be obtained, if the newly shed crown be imagined reconstructed before the position of the form point is determined. Finally, should the butt swelHng extend so high as to influence the D.B.H., and consequently make the final result inaccurate, it will be satisfactory for prac- tical work either to roimd the diameter off downward or measure the diameter above the swelhng; for scientific work, however, the form class should be lowered as much as is made necessary by the butt swelling, which can be easily found through a number of measurements taken above and below B.H. In extensive timber estimating the density is a good indication of the general form which the trees ought to possess, as the tree grown up in dense stands will have a clean bole and high crown, while on the contrary the tree grown in the open will have a heavy, low crown and consequently a poor bole form. TABLE XL Table for Determination of Form Class of Trees by Means of Position of Form Point ^ Height Form Class of 1 1 tree in 0.50 0.525 0.550.575 0.60 0.625 0.65 0.675 0.70 0.725 0.75 0.7750.80 feet Form point height in per cent of height of tree 10 37.5 43.5 47 52 57 62 69 73 79 85 92 98 20 35.5 40 44 49 54 59 65 70.5 76.5 82.5 89 95.5 30 34.5 38 43.5 47.5 52.5 58 63.5 69 75 81 87 94 40 34 38 43 47 52 57 62 68 74.5 80 86 93 50 34 38 42.5 47 52 57 62 68 74 80 86 93 60 34 38 42 47 52 57 62 68 73.5 80 86 92.5 70 34 38 42 47 52 57 62 68 73.5 79.5 86 92 80 34 38 42 47 52 57 62 68 73 79 86 92 " For spruce and fir in Norway, either inside or outside bark. Adapted from Massatabeller for Traduppskatnung. Tor Jonson, Stockholm, 1918. The prevailing density of a stand causes the greater number of the trees to acquire a certain similarity as to form, and only a very small number, usually the smallest and largest trees, differ from this average form class. Accordingly it is often 1 RULES OF THUMB 251 204. Rules of Thumb for Estimating the Contents of Standing Trees. A rule of thumb represents an attempt to formulate a simple rule which can be memorized and by the use of which the contents of trees of any diameter and height may be found. Such a rule would enable the cruiser mentally to compute the volume of average trees without looking them up in a table. It is also desired as a substitute for a universal volume table because of the difficulty of finding volume tables for the different species. The factors of variation in tree form are exaggerated by application of units of product and the variation in board-foot log rules, and the further differences in the per cent of total contents utilized in trees of different sizes make it impossible to devise rules of thumb w^hich are as accurate as good volume tables; but since their use in ocular timber estimating frequently accompanies methods of cruising by which a close degree of accuracy is not attained, a slight possibility of error in application is not considered a sufficient drawback to offset the advantage of simplicity. They are especially desired in judging by eye the contents of single trees. Rules of thumb must be based upon either the cubic or board-foot unit. The simplest forms ignore the influence of height and are therefore inaccurate except when applied to trees within a given range of heights. The effort is always made to devise rules which may be applied to the dimensions measured by the eye; that is, to diameter and height. Rules which require the use of basal area call for tables. For cubic contents, the following rules of thumb will serve as illustrations: 1. To obtain cubic feet multiply the basal area in square feet by the height and divide by 2. This is based on the theory that the cubic form factor of trees will average 0.5 which is the form factor for a paraboloid. 2. For trees averaging 80 to 100 feet in height, with a form factor of 0.49, the contents in cubic feet equals the radius in inches squared (B. E. Fernow). For "average" trees, volume in cubic feet equals one-fifth of the diameter squared (C. A. Schenck). Both of these rules of thumb are good only for trees of a given height and form factor. They are similar to the European rule of thumb — volume in cubic meters equals the diameter squared divided by 1000. In this rule, D is measured breast- high in centimeters. This rule applies to pine 30 meters high, beech, oak and spruce, 26 meters high, and correction factors are indicated as follows: for each additional meter of length above or below these heights, for pine, a 3 per cent correction; for beech, 5 per cent; for spruce and fir, 3§ per cent. Hersche's rule (h \ of thumb reads, cubic meters = 1)2 1 --[-1 1, using meters. This applies to trees 50 to 115 feet in height. \^ I possible to estimate the whole stand in the same form class, the smaller dimensions a little higher and the larger dimensions somewhat lower than the average, e.g., 0.70 for overtopped trees, 0.675 for intermediate and co-dominant trees, and 0.65 for dominant trees (§ 171). The highest and lowest form classes will never occur as an average, but only for single trees. 252 THE MEASUREMENT OF STANDING TREES Graves gives the following cubic rule of thumb for white pine; Square the breast-high diameter in feet and multiply by 30. The rule gives approximately correct 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. Other heights require a correction varying between 5 and 6 per cent, for each 5 feet of length. It can thus be seen that both simplicity and accuracy in these rules of thumb are seldom obtained in the same formula without considerable cumbersome modification and it would seem that a volume table could be referred to almost as easily and give as accurate results. The use of rules of thumb based on board feet is primarily caused by lack of suitable volume tables. This is illustrated by the development of rules of thumb based upon the Doyle log rule. These board-foot rules are efforts to obtain the total board-foot contents of the trees from the sum of the contents of the logs which they contain and were usually formulated before volume tables had come into use. The simplicity of the formula for obtaining the contents of a given log in the Doyle rule, namely, "subtract 4 inches from the upper diameter inside bark, square the remainder, and the result is the scaled contents of a log 16 feet long" (the length used in estimating), was an inducement to supplement this rule so as to obtain the contents of the average log in a given tree. There are two rules for this. 1. Take the average diameter of the top and stump inside the bark for the diameter of the average log. Scale this and multiply by the number of 16-foot logs in the tree. 2. Multiply the diameter at breast-height inside the bark by the same diameter minus 12. Multiply by the number of logs in the tree. This gives the scale of the tree (C. A. Schenck). Schenck also gives a rule which ignores height, as follows: For "tall" trees, volume = iy diameter squared, measured at breast-height. Efforts to formulate general rules of thumb, not based on the Doyle rule are illustrated by the following examples: 1. 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. (Graves' Mensuration, p. 153.) 2. Average the base diameter of the tree and the top diameter of its merchant- able timber. Get the scale of a log of that diameter, 32 feet long. Multiply by the number of 32-foot logs less | log. (Gary's Manual of Northern Woodsmen.) 3. Board f eet ^ 60 when D = inches and L = feet. (A formula method of estimating timber, E. I. Terry, Journal of Forestry, Vol. XVII, No. 4, p. 413.) This formula, according to author, requires modification by substitution of a divisor of 70 for trees from 12 to 19 inches D.B.H. 60 for trees from 20 to 29 inches D.B.H. 55 for trees from 30 to 35 inches D.B.H. 50 for all trees above 35 inches. 4. To base diameter, add one-half of base diameter and divide by 2; multiply by 0.8, square and divide by 12. The result is the number of feet in the stick per foot of its length. Three to 5 per cent may sometimes be added for contents above the point stated. • RULES OF THUMB 253 There are two steps involved in these rules of thumb for board feet: First, a rule or formula is required, which gives an approximation of actual board-foot contents of logs of different sizes. This can only be obtained by rules based on cubic instead of board-foot contents (§ 39). Taking a fixed per cent of the contents of all logs, the last rule above quoted reduces to ( The second step is to get the dimensions of an average log in a tree, thus averaging large and small, or top, butt and middle logs together. Empirical results rather than mathematical soundness has usually been the basis of all such rules of thumb. Practically all these rules of thumb for board feet are based upon the log unit, as might be expected. A more scientific application of a universal rule of thumb is that devised by F. R. Mason (Ref. Rules of Thumb for Volume Determination, Forestry Quarterly, Vol. XIII, 1915, p. 333). This rule is as follows: 5. The volume of a tree of each diameter and height class will correspond closely with the volume as obtained by averaging the scale of the butt and top logs and multiplying by the number of logs, using 16 feet as the standard log length. Mason states that this rule has been in use by Minnesota cruisers. Its superior accuracy is based upon the fact that it conforms to the form quotient of the tree as well as to its diameter and height, by introducing upper diameters at two points. For Douglas fir this rule was 3 per cent below actual scale; for cedar, above 24 inches, 10 to 15 per cent high. For white pine, spruce, yellow pine, larch, lodgepole pine and fir, average results were within 5 or 6 per cent of actual volume for individual trees of all sizes, a result which is closer than may be expected in the use of average volume tables for single trees. The only difference between this rule and the tally and computation of each log in the tree is elimination of the need for tallying logs lying between butt and top. The size of the top log is constant where a fixed top diameter is used. Mason states that 3R^ is the approximate board-foot contents for 16-foot logs over 24 inches in diameter. 6. A rule given by J. W. Girard is, "add 6 inches to the D.B.H., divided by 2 and use this result as the diameter for the average log in the tree. Multiply the scaled volume of this log by number of logs for the tree volume." This rule holds good for white pine and spruce cut to 6-inch top and for larch cut to 8-inch top. For Douglas fir cut to 8-inch top, add 4 instead of 6 inches. For lodgepole cut to 6-inch top, add 5 inches. For yellow pine under 20 inches, add 6 inches; 20 to 25 inches, add 8 inches; 26 inches and over, add 10 inches. Any rule of thumb should be based upon the log rule and standard of utilization in use. Such rules are largely worked out as a matter of personal efficiency by individuals and should be tested carefully before placing too much reliance upon them. References The Biltmore Stick and Its Use on National Forests, A. G. Jackson, Forestry Quarterly, Vol. IX, 1911, p. 406. Notes on the Biltmore Stick, Donald Bruce, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 46. The Biltmore Stick and the Point of Diameter Measurements, Donald Bruce, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 226. A Folding Biltmore Stick, W. B. Barrows, Journal of Forestry, Vol. XVI, 1918, p. 747. Relative Accuracy of Cahpers and Steel Tape, Normal W. Sherer, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 102, 254 THE MEASUREMENT OF STANDING TREES Another Caliper (Swedish pole and hook for measuring diameters at considerable height). S. T. Dana, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 337. Saving Labor in Measuring Heights, S. B. Detwiler, Forestry Quarterly, Vol. XIII, 1915, p. 442. A New Hypsometer, H. D. Tiemann, Forestry Quarterly, Vol. II, 1904, p. 145. Comparative Test of the Klaussner and Forest Service Standard Hypsometers, Douglas K. Noyes, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 417. Some New Aspects Regarding the Use of the Forest Service Standard Hypsometer, Hermann Krauch, Journal of Forestry, Vol. XVI, 1918, p. 772. A Simple Hypsometer, Vorkampff Laue, Forestry Quarterly, \'ol. Ill, 1905, p. 195. A New Dendrometer, Donald Bruce, University of California Publications, Vol. Ill, No. 4, Nov., 1917, pp. 55-61. Review, Journal of Forestry, Vol. XVI, 1918, p. 724. A New Dendrometer or Timber Scale, Judson F. Clark, Forestry Quarterly, Vol. XI, 1913, p. 467. The Biltmore Pachymeter, Ralph G. Burton, Forestry Quarterly, Vol. IV, 1906, p. 8. Determination of the Middle Diameter of Standing Trees, P. d'Aboville. Trans- lation, Journal of Forestry, Vol. XVII, 1919, p. 802. Rules of Thumb for Volume Determination, F. R. Mason, Forestry Quarterly, Vol. XIII, 1915, p. 333. A Home Made Hypsometer (Winkler t>7)c). Construction described in Farmers Bulletin 715, 1916, p. 18. CHAPTER XIX PRINCIPLES UNDERLYING THE ESTIMATION OF STANDING TIMBER 205. Factors Determining the Methods Used in Timber Estimating. There are five basic considerations which determine the conditions and methods to be used in estimating timber. These are: 1. The form of product in wliich the vohmie of the timber is to be estimated. This determines tlie unit of volume to be used, as the piece (poles, railroad ties), the board foot for saw timber, and the cord for bulk products (§§ 9-12). 2. The economic conditions, customs and usages governing thr> business of logging and lumbering. These determine the basis on which standing timber is to be sold and the place and form in which it is to be measured. The three considerations which affect the work are, whether the basis of volume measurements is to be the contents of logs or the sawed output in the form of lumber, what log rule is to be used in scaling the logs, and the practice of scaling as to log lengths, diameters and cull as affecting the scaled contents of the timber (§§81-83). 3. The character of the demand for timber products and the result- ant closeness of utilization of the trees in the stand. This will determine the top diameters and stump heights to which the timber must be esti- mated, and the minimum D.B.H. (diameter limit) of trees to be esti- mated as part of the merchantable stand, and consequently the per cent of the total cubic volume of the stand which is estimated as merchant- able (§23). 4. The available volume tables, their reliability and basis of numbers, their method of construction, their basis of diameter, height and mer- chantable top diameters (§ 124). This will determine, (a) Whether to dispense with a volume table and substitute a log rule, tallying the contents of the trees in the form of separate logs or to depend upon a volume table for entire trees. (6) The point at which diameter must be measured in timber estimated, as stump, D.B.H. , or top of first log inside bark. 255 256 ESTIMATION OF STANDING TIMBER (c) The point at which heights are taken — total height o r merchantable log length. (d) The top diameters to which tree must be estimated. Diver- gence in these conditions from those used in the volume table will make it impossible to apply the same. 5. The local characteristics of the timber to be estimated as to full- ness of form or " form quotient," quality and defects. This determines, (a) For sound trees, the applicability of existing volume tables without modification or their need of local percentage corrections, (fe) For the defective trees, the amount of deduction for defects and losses in scale to be made from the standard volume table. The object of any estimate of standing timber is to obtain the total volume as indicated by the above five conditions upon the entire area of a specific tract of land. This may be done in one of three ways: By direct ocular guess or appraisal. By actual estimate or measurement of the volume of every tree of merchantable size. By measuring or estimating a part of the timber as an average .of the whole. 206. Direct Ocular Estimate of Total Volume in Stand. The direct estimation or guess of the total volume of a tract of timber can have but one basis, that of experience in cutting tracts of similar character. This eliminates all doubtful factors, and the experience thus gained is invaluable as a standard of estimating. Skill and accuracy in this method depend upon the uniformity of the stand, and the ability of the estimator to compare this uniform stand with those of similar character whose yield he has ascertained. As the area of timber so estimated incr ases, its variability of stand becomes greater; yet the necessity for obtaining a true average of these variable conditions persists. Even in stands as large as 40 acres it becomes very difficult even with the closest inspection to arrive at the average stand on the tract, no matter how skillful the cruiser is for smaller and more uniform areas. With increasing size of area, accuracy soon becomes utterly impossible. For this reason, in spite of the simplicity of the plan in theory, in practice cruisers who depend solely upon this principle are apt to be unreliable and inaccurate. Under no circumstances can this method be applied to timber with which the cruiser is unfamiliar. It therefore limits his field of activity to a narrow basis. ESTIMATING A PART OF THE TIMBER 257 207. Actual Estimate or Measurement of the Dimensions of Every Tree of Merchantable Size. This is known as a 100 per cent estimate and differs radically from the total ocular estimate of stand just described. It consists of recording the dimensions of each log on the tract in case no volume table is used, or with a volume table, the dimen- sions of every tree of merchantable size. The total volume is then simply a matter of computation. The trees are tallied by dots and lines, in blocks of ten, as indicated in the following table, which shows the marks corresponding to dif- ferent numbers: 1 3. 3d 5 6 7 8 9 10 • ••'::: r. n n n H H When diameter alone is being tallied, a single column giving diameter classes suffices for each species. Where the height, either total or merchantable is also recorded for each tree tallied, each species will require a tally similar to that shown below. Where several species are tallied by both diameter and height, it is not cus- tomary to make half-log divisions, since too many columns would be involved. Where the top diameter of logs, instead of D.B.H., is Fig. 55. — Method of tallying trees by diameters the point talhed, the same ^^^^ log lengths. system of diameter classes or tallies is used. It is possible to combine this tally of D.B.H. for one species with top diameter of logs inside the bark for others, using the same horizontal columns for diameter in each case. 208. Estimating a Part of the Timber as an Average of the Whole. Where the greatest possible accuracy .is demanded, it is obvious that 100 per cent of the trees should be measured. Only in extreme cases can this be done, owing to the excessive cost. The process of measure- ment accomplishes no constructive change in the form of the forest (§ 6) as does logging or silviculture, but is of use merely in the orderly management of the business of regulating these operations as to location, quantity and time. Efficiency then demands the reduction of the cost of obtaining these statistics to the lowest figure which will suffice for the proper conduct of the business and avoid loss through errors in appraisals of quantities and values. With timber whose average value per tree is small, the cost of meas- Spec ies-Pine D.B.H. Hog 2 logs 2! 2 logs Slogs etc. 12 13 14 n 15 16 : I r etc. 258 ESTIMATION OF STANDING TIMBER uring each tree is far too great to be undertaken. It is often physically impossible to obtain the necessary force and personnel to perform the work on this scale. Finally, the time I'equired is too long since the results of estimates, especially for the purpose of sale are usually required within a limited period. For these reasons, the third of the above methods, by which the principle of averages is utilized as a means of reducing expense, diminishing the number of persons required and shortening the time demanded for completing the work, is almost universally used in estimating timber. The use of this principle in timber estimating does not differ from that applied in the commercial process of sampling employed in mines or in grad'ng wheat. If the product is uniform, a single sample suffices, as in wheat, but if variable, as in ore, far greater care is required in order that the samples may represent the average value for the entire body to be tested. The advantage in timber estimating is that all of the timber is actually visible and only the handicap of costs and time prevent it from being seen and measured. 209. The Six Classes of Averages Employed in Timber Estimating. There are six classes of averages employed in estimating timber. The first three differ in regard to the methods of recording the dimensions of trees. These methods are as follows: 1. The average height of the trees of each separate diameter class is obtained For this purpose, only a few sample heights for each separate diameter are measured. The heights so measured are plotted on cross-section paper on which diameter is the determinate variable plotted on the horizontal scale, while height is the indeterminate vari- able plotted on the vertical scale. An illustration of a curve to obtain average heights based on diameter is shown in Fig. 56. The trees to be measured for height must be selected in such a manner that the resultant curve will give the true average heights for each diameter class for the entire area to which it is to be applied. When a very few trees are taken, these must be carefully chosen from those whose crowns are of average height compared with the remaining stand. This is best accomplished in even-aged stands. On large areas and in many-aged stands, a mechanical distribution of trees measured for height is best, in order to secure a weighted average of differences caused by variation of site and of growth. In plotting the data, two methods are shown. By the first, all heights are plotted above their respective diameters. A height curve may thus be sketched by eye through the band of points shown. This eliminates mechanical averaging. By the second method, the average height is calculated for the trees in each diameter class, and this point is plotted 0. The points are then connected by straight lines, their weight in numbers shown, and the curve drawn, as before, guided by the original data.' 1 In the first system, when two heights fall on the same point, the number is indicated as ^. AVERAGES EMPLOYED IN TIMBER ESTIMATING 259 A combination of these two systems may be used as follows: First plot the points, then compute the mechanical averages from the plotted data by using the scale as follows: For the 9-inch trees, assume the 40-foot point as 0. The trees are then entered as having the weights 0, 3, 8, 8; total 19; average 4.8 plotted as 5 above the 40-foot point, or an average height of 45 feet. This method com- bines the advantage of visuahzing the data to indicate abnormally high or low trees, with a slight reduction in the work of mechanical averages. 2. Instead of tallying the diameters of all the trees, they are merely counted, but a certain fixed percentage of the total number is tallied for diameter (the heights are either tallied individually or the method 70 I 50 tt 40 30 / K j 9 / ^ / i^ r\ f ^ ^ ^ r 4j tJJ' ^ 2 -s A s / >* /A / / . " 3' h 10 11 12 13 D.B.H. Inches 15 IS IT 18 19 Fig. 56. — Method of constructing a curve of height based on diameter at B.H. White Pine, Milford, Pike Co., Pa. of averages described above is applied). The volume of the average tree of the per cent tallied is used to find the average volume cf the numbers counted but not measured. In Southern longleaf pine, it is possible to count all of the trees on a tract, and to tally the diameter and merchantable height of one tree in every three in such a way that the trees tallied represent the mechanical average of those counted. When the volume of the tallied trees is computed, it represents one-third of the volume of the stand. The work of tallying has been reduced one-third and the accuracy greatly increased, when considered with reference to the time required to complete the work. 3. None of the trees in the stand is tallied for either diameter or height. The trees are merely counted and the cruiser then decides upon the volume which will be contained in the average tree of the stand. He may obtain this either through a direct guess as to volume or through 260 ESTIMATION O-F STANDING TIMBER the selection of what he beheves to be a tree of average diameter and height whose volume he then ascertains. There are two modifications of this system, dependent upon whether the unit used is the log or the tree. When the log unit is used, the cruiser estimates the number of logs in the average tree and the contents of the average log or log run (§ 120). In the above three methods of averaging, nothing has been said about the question of area covered. The averages apply to that portion of the area on which the timber is either counted or in addition is tallied for dimensions. This may be 100 per cent or the total area. Although it may not be possible to measure, by diameter and total height, each tree on the entire area, yet by the employment of one of these three methods of averaging the contents, all of the trees may actually be accounted for. The remaining three of the six methods of employing averages apply to tracts whose area is too large to permit of 100 per cent esti- mates, even by the simplest plan of counting and obtaining the average tree. The principle here is to estimate the stand on a portion of the area in an effort to derive the volume of the stand upon the remainder. The systems used are as follows: 4. The stand per acre is guessed at or estimated by eye. This stand multiplied by the area in acres presumably gives the total stand on the tract. This is merely a modification of the method of total ocular estimate, in which the problem of arriving at the average is approached in a different manner. It is possible for a skilled estimator to guess closely the stand on a given acre, but the difficulty lies in either finding a specific stand whose volume per acre happens to agree with the aver- age on the entire tract or else to decide from the inspection of given stands how much the actual stand per acre observed on specific plots must be modified in order to obtain the true average for the entire tract estimated. The probabilities of error in estimates made on this basis increase with the size and diversity of the stand to be estimated. 5. The dimensions and volume of the trees on a given per cent of the total area are obtained b}^ one of the first three methods and the stand thus found is assumed to represent the average stand per acre for the entire tract. This requires, fii'st, the accurate determination of the area of the tract and of the area covered by the estimate, and second, the location of this latter area in such a way that the assumption that it represents the average of the remainder can be accepted as approximately correct. 6. The same principle is employed as described under 5, but the assumption that the per cent of area so measured will give an accurate mechanical average applicable to the remaining tract is not accepted. Instead, the remainder of the area is inspected by the method of ocular THE CHOICE OF A SYSTEM FOR TIMBER ESTIMATING 261 comparison. None of the trees is actually measured except on the per cent estimated. Using this estimated strip as a standard, the estimate upon the remainder is taken as equaling, exceeding or falling short of the stand per acre upon the estimated strip, and its volume is obtained by applying a correction to this estimated stand per acre. 210. The Choice of a System for Timbej Estimating, with Relation to Accuracy of Results. All systems of timber estimating involve the choice, first, of one of the three methods for determining the contents of the trees and second, of one of the three methods of covering the area. There are many different systems of timber cruising, involving the possibility of an endless combination of these six elements Each of these systems represents a decision as to the per cent of area required to get the average stand per acre for the total area, the method of cover- ing the area to obtain this per cent, and the question as to acceptance or modification of the stand per acre as applicable to the whole tract; it also involves the further reduction in the work of measuring dimen- sions to get the volume of trees by substituting averages for height, a per cent of total tallies for total tallies and average volumes for individual volumes. These two groups of factors are closely inter- related. For instance, where the per cent of area covered is reduced to a low figure, the area which is actually estimated must be covered thoroughly by careful measurement of distances and widths of strips, the diameter of every tree should be measured or tallied, and each tree may be tallied for height, especially if merchantable heights are used. Where, on the other hand, all of the area is covered, it may be sufficient merely to count the trees, substituting the method of an average tree or log for the more detailed and time-consuming method of measuring each diameter. The gain in accuracy in one of these factors may be offset against possible inaccuracy in another, the sum of the factors being determined by the total cost of the method. These points may be briefly summed up as follows: Area — Full estimate, 100 per cent. As modified by averages. Sample plots taken as the average. A given per cent accepted as the average. A given per cent estimated as a basis for obtaining the remainder by compari- son and correction. Trees — Full estimate, 100 per cent tallied for both diameters and height. As modified by averages. Average height obtained from sample measurements. Volume of average tree obtained from tally of dimensions of a fixed per cent of the total stand. Volume of average tree obtained by inspection, from s.-miplc tree, or average tree on sample plots. 262 ESTIMATION OF STANDING TIMBER Both the degree of accuracy obtained and the expense of estimating the timber are reduced: By the reduction of the per cent of area covered. By substituting tree counts for measurements of dimensions and averages for totals. By substituting ocular measurements of dimensions for instru- mental measurements. By substituting pacing for chained or measured distances. As an offset to the loss of absolute accuracy by the substitution of these laws of averages and reduction of detail, the relative accuracy or efficiency of the application of the cheaper methods can be enormously increased by the development of technical skill, experience and judg- ment, so much so that the old-time timber cruiser depended upon these factors both for his reputation and the reliability of his estimates. This relative accuracy is increased: By the choice of methods and care in location by which partial areas are secured in such a manner as to insure the highest probability of average volumes. This is similar to the methods used in sampling ore. By the development of skill and accuracy in the use of pacing and in the use of the eye for measuring diameters, heights and width of strips or plots. By the ability to apply the methods of tallying a fixed per cent of the stands or selecting average trees in such a manner that the true average volume of the total number or count is obtained. By painstaking observance of obtainable standards of accuracy in the use of instruments for measuring distances, diameters and heights, and in proper record or tally. By individual training and ability to make the proper discounts for defects. By the careful checking of the reliability of volume tables used, and the correlation of field methods with the conditions for which they were constructed. Finally, by correlating all of the above factors with the actual con- ditions of the tract or stand to be estimated, which in themselves will determined the degree of accuracy required in each step as above outlined. 211. Relation between Size of Area Units and Per Cent of Area to be Estimated. There are two elements to be considered in arriving at accurate averages in estimating a given tract. First, the problem of distributing the samples throughout the area in order to obtain the greatest probability of true average; second, the uniformity of the stand SIZE OF AREA AND PER CENT OF AREA ESTIMATED 263 itself as increasing or decreasing the probability of accuracy for a given method of sampling. The first of these problems is influenced by the size of the tract. In any method of estimating based upon measuring a part of the area, the system employed must be that of strips or plots spaced at regular intervals. Otherwise the element of judgment in selection introduces a difficult factor which will improve the average obtained only when accompanied by considerable individual skill. With plots or strips at fixed intervals, the number of such strips depends upon the dimensions of the tract. The choice between plots and strips does not affect this principle. Plots, when substituted for strips and taken along compass courses at regular mechanical intervals, serve to reduce the per cent of total area covered. Since the distribution of the sample areas is more evenly diffused on the basis of the per cent covered, by plots, than it is by strips, the loss in accuracy by substituting plots for strips is not in proportion to the reduction in per cent of area covered, but is consider- ably less, thus resulting in a material saving where the use of plots permits of the reduction in size of crew (§ 224). The size of the separate units of area on which accurate estimates are desired — as for instance, when owners require the estimates sepa- rately by '' forties " (§8), is the basis for determining the effect of the spacing of these strips. If the estimate must be accurate only for the entire tract, a quite different problem is presented from that when the same degree of accuracy is required for smaller subdivisions. Assuming that the tract is in the form of a square, the coefficient of accuracy bears a close relation to the number of strips run across this area, rather than to the distance between these strips. This may be expressed as follows: The per cent covered by strips will be the product of the number of strips and width of each strip, divided by width of the area. With strips of a uniform width, e.g., 8 rods or 132 feet, run at intervals of I mile, the per cent of area covered is -^ or 10 per cent, whether the tract be 40 acres, 1 square mile or 25 square miles. But the probability of accuracy in securing an average stand is not in the same proportion for each tract, but increases with the size of the tract. The reason is that, regarded as a unit, the larger tract is more uniformly sampled, and with reference to its total area, the strips or plots are more thoroughly distributed than on the smaller areas. The relative accu- racy is in proportion to the distribution of the sampled or estimated strips with respect to this total unit, which for large tracts tends to reduce the per cent of area required to obtain a given standard of accu- racy. 264 ESTIMATION OF STANDING TIMBER Standard distances between strips or plots are 80 rods, or once across a forty for very extensive work of low accuracy; 40 rods, or twice across a forty for work of average accuracy; 20 rods, or four times across a forty for work approaching a 50 per cent estimate; 10 rods, or eight times across a forty, which with a 10-rod strip permits 100 per cent of the timber is to be measured. The first problem then, in estimating a tract, is to decide upon the proper per cent of the area which must be covered to secure the desired standard of accuracy, and this per cent will be a direct function of the size of the smallest unit of area upon which a separate estimate is required (Fig. 57). 25 Sqviare Miles 1 Square Mile Va Sq.Mile 1 r I I J L tr^ ^ t-rH-r I ! ! •^ Mile Fig. 57. — Influence of size of tract upon probable error in obtaining average volume per acre, by running strips 40 rods apart in each instance. Dotted lines indicate location of strips. Narrow strips spaced at one of these standard intervals are commonly used for large tracts. Upon small tracts, the necessity for increasing the per cent of area covered, as a substitute for increasing the number of strips run, takes the form of widening the strip. This is usually accompanied by a modification of the method of tallying the trees and the substitution of a count for the measurement of every diameter. For small areas as low as 40 acres, this frequently takes the form of a 100 per cent estimate, the strips being so arranged that they cover the entire area, and where the value of the timber and its size is such that accuracy is desired for each forty, 100 per cent of the entire tract is covered, no matter what its total size. The relations between the distance apart of strips or plots, width or size of these strips or plots, and resultant per cent of area covered, to the size of the unit of area to be estimated, is the most practical UNIFORMITY OF STAND AS AFFECTING METHODS 265 problem of timber cruising upon whose solution depends the attain- ment of the desired standard of efficiency secured by properly relating costs to accuracy of results. 212. Degree of Uniformity of Stand as Affecting Methods Employed. The second factor affecting the probability of accuracy in obtaining the average stand per acre is the character of the stand as affecting its uniformity. Uniformity depends, first, upon the range of sizes both, as to diameter and height of the trees which compose the stand; second, on the regularity or evenness of their distribution or the variation in the density of the stand over the area. The greater the extremes, both in sizes and density, the more difficult the attainment of a correct average stand by a measurement of a part of the area, and the greater the necessity of increasing either the number of strips or the per cent of area covered in each strip to get a larger total per cent of area in obtaining the average. Age of timber increases both the range of sizes and the variation in density. Old timber is never as evenly distributed as a young stand, owing to the progressive losses from natural causes. Mixed forests, composed of several species, are more difficult to average than pure forests of a single or of two or three similar species. There is greater irregularity both in size and distribution in the mixed forest. The greatest irregularities for a given tract are caused by differences in topography and soil, or site conditions, which are reflected in the char- acter of the stand. In mountainous topography, the entire forest changes from bottom to lower slope and from lower slope to upper slope. In more level topography, the type changes as abruptly and completely on the basis of the moisture content of the soil from swamp to drained bottom, from drained bottom to dry upland. Any system of timber estimating must be planned to secure: 1. The separation of areas which differ radically from each other, but which within themselves are fairly uniform. These areas conform with the types of forest cover. 2. An arrangement of the strips such as to secure the greatest pos- sible accuracy in sampling, which is done by crossing these variations of density, type and form, at right angles with their longest dimen- sions of area, as far as possible (§§ 219 and 228) The degree of detail and cost of the work as reflected either in an increased per cent of area or number of strips or an increased per cent of trees tallied for dimensions, either diameter or height, will thus be increased in proportion as The size of the unit diminishes. The size of the timber increases. 266 ESTIMATION OF STANDING TIMBER The variety of the timber increases. The topography is more mountainous or varied, resulting in a greater diversity of types. The number of products required increases. Finally the degree of accuracy required, other things being equal, will depend upon the stumpage value of the products to be estimated, as influenced, first, by the character of the timber itself, and second, by the unit price of the product. In the earlier days crude and inaccu- rate methods of timber estimating were justified by the low price per acre and per thousand feet at which stumpage changed hands. With record stumpage prices running up to S27 per thousand feet for white pine in state auctions in Minnesota, in 1920, a degree of accuracy is justified which would not be thought of by old-time timber cruisers. CHAPTER XX METHODS OF TIMBER ESTIMATING 213. The Importance of Area Determination in Timber Estimating. Except in a few instances where every tree on a tract is separately measured, all methods of timber estimating depend upon the principle of applying the results obtained on part of an area to the entire area, or on small portions of an area to larger subdivisions. Any error in determining the total area included within the boundaries of a tract, or the correct area of any subdivision made within it, will incur a cor- responding error in applying the results of the estimated portion to the whole. The separation of timbered from non-timbered areas is an example. If the average stand of the timbered portion is correctly found, but its area is estimated to be 10 per cent greater than it actually is, an error of plus 10 per cent is incurred in the estimate. Correct determination of areas of the tract and its timbered subdivisions is the first consideration in the field work of timber estimating and counts for fully half in the total scale of accuracy. The first essential is to locate and determine definitely the boundaries of the area to be estimated. Where the tract lies in regions subdivided by a rectangular system of government surveys this is not ordinarily difficult. The area may be approximately located with sufficient exactness for the work. Even here it is necessary to identify the section corners and sometimes to re-run the lines if time permits. In other regions where the land surveys follow an irregular pattern, the identification of the corners and lines is best accomplished by the aid of some local resident who is familiar with these bounds. The retrac- ing and mapping of the boundaries of a property is an essential step in management, but its cost is not properly chargeable against the item of timber estimating alone. If methods are used by which 100 per cent of the timber is estimated, the total stand can be obtained independent of the actual area or shape of the tract provided only that all of the trees upon it are counted and their contents determined. When for a 100 per cent estimate is sub- stituted an estimate covering only a part of the tract, the cruiser requires a knowledge of its shape and size. In the rectangular system of surveys most of the subdivisions are square and the smallest unit commonly 267 268 METHODS OF TIMBER ESTIMATING used contains 40 acres. Even here fractional lots lying along the north and west boundaries of a township or adjoining meandered streams and lakes call for a plot which shows their dimensions. With these rectangular areas it is a simple matter to obtain a definite per cent of the total by running strips of a given width. On irregular tracts, a map showing the boundaries and area is required to enable the cruiser to determine, first, in what direction and relation to lay out his lines or strips, and second, to compute the exact per cent of the total. This desired per cent is approximated and the exact relation secured is determined after the lines are run. 214. The Forest Survey as Distinguished from Timber Estimating. Timber estimating may be undertaken for the sole purpose of determin- ing the volume of timber on a tract, but as commonly carried out, this requires the running of numerous definitely located compass courses, gridironing the area, which gives an opportunity for the collection of a large amount of additional data required in its permanent manage- ment and in the logging of the area. The collection of this additional data, together with the timber estimate, constitute what is termed a fored survey. Even the crudest work of timber cruisers embraces some elements of a forest survey. The features of such a survey are: 1. A map showing the topography of the area either by hachures or contours, giving streams and ridges and other important features which influence logging and management. 2. A map showing the character of the forest cover, classified as to (a) Timber types, corresponding with divisions made in the stand in timber estimating and showing blank areas, such as ^yater, barren, cultivated or grass-land. (6) Divisions due to age of the timber such as burns, re-stocked or l)arren, reproduction or immature timber, older age classes. 3. Soil maps, locating land of agricultural value and land fit only for forest purposes. Under timber estimating proper, the forest survey makes an inven- tory showing both the quantity and quality of timber by different products, grades and sizes as required for the purpose of valuing the tract as follows: 1. Quantity or vohmie. (a) Separately by species, (6) Separately by units of merchantable volume, as board feet, poles, cords, (c) Separately by character, as live or dead timber, sound or cull, and giving the net volume after deductions for cull. TIMBER APPRAISAL 269 2. A statement of amount and character of damage present due to rot and other defects such as shake, fire damage to standing timber, the presence of insect damage, windfall. 3. The quality and sizes of the timber under the items; average diameters, average merchantable length in logs, form of bole as to straightness, taper and clearness and finally the grades present, classi- fied either as log grades or as grades of lumber. The third class of data is that needed for permanent forest manage- ment for the production of timber by growth. These data are fre- quently omitted or overlooked in a timber survey, first, by old cruisers who have not been trained to collect them; second, by foresters who have failed to formulate a definite plan for their proper collection in anticipation of the need for its use. These data fall under: 1. Age classes in the merchantable timber, either by area (maps), or by size or diameter (stand tables of diameter classes), or both. 2. Age classes in immature timber either by areas as mapped, by per cent of area occupied or by tree counts; the ages and sizes of these age classes, their condition, thrift and the chances of survival. In addition, a forest survey may include data on all other resources of the forest such as forage for grazing, while under timber it should determine the areas included within different site classes (§ 227). Forest surveys include all data of every kind necessary for the making of a working plan for the management of the area for permanent forest production. 215. Timber Appraisal as Distinguished from Forest Survey. The forest survey as described above is the preliminary step in the appraisal of the value of timber stumpage. This appraisal constitutes a separate operation, although the survey and the appraisal are so closely bound together that the}^ are frequently performed by the same man. They must not be confused, however, for a timber appraisal is not a part of Forest Mensuration, but belongs under the separate subject, Forest Valuation (§5). It may begin where the timber survey leaves off, using the data acquired by this survey. Separate parties may conduct the timber survey and the timber appraisal with satisfactory results. A timber appraisal covers the following points: 1. Logging conditions summarized for each logging unit, under topogiaphy, slopes, surface, rock, brush and character of bottom as affecting logging. Transportation possibilities, availability of streams for log driving, routes for roads, flume or railroads, methods best adapted for skidding and hauling the timber and the costs of these processes. 2. Costs of forestry such as the per cent of the stand to leave for seed or second cut. the cost of brush disposal and other protective measures. 270 METHODS OF TIMBER ESTIMATING 3. Economic conditions, markets and prices for lumber. 4. General appraisal, cost of milling, cost of logging, cost of trans- portation, profits requii-ed. 5. Specific appraisal, the direct cost of logging the specific body of timber and the resultant stumpage value of this unit. A clear-cut distinction between the work of timber estimating and of timber appraisal will prevent the mistake so often made of burden- ing the timber estimating crew with the work of recording in great detail items of cover, surface, brush, etc., which instead should he sum- marized for an entire unit by the person who appraises the value of the timber and sizes up logging conditions. It is seldom that the two jobs can be effectively combined in the same party or individual. The work of timber estimating requires routine and concentration on the details of the job. The actual appraisal, even if the same party makes it, should follow rather than accompany the estimate and should be based first, upon the data on topography as shown by the map and second, upon the data on volumes as shown in the estimate. 216. Forest Surveying as a Part of the Forest Survey. A forest survey as above outlined includes the work of forest surveying or the determination of the boundaries and area and the mapping of the topog- raphy of a forest tract. This subject is not a part of Forest Mensu- ration, but must be treated separately. Since the gridironing of the tract requires the measurement of distance and direction and the plotting of these lines will give the framework of a map, it follows that the work of making a topographic map which may employ the same general methods of examination for the area, can he advantageously combined with the work of timber estimating. Timber cruisers usually prepare a crude map showing the intersection of streams and the position of ridges and other topographic features of importance. The prepara- tion of a map based upon basal elevations and giving contours is a development of the timber survey introduced by foresters and adds greatly to the efficiency of the survey. By combining this map-making with the entirely separate operation of estimating, a crew of two men can complete both operations with a very slight increase in expense, not comparable with the cost of doing each piece of work separately. At the same time the preparation of the type or timber-cover map can proceed, and upon this in many instances depends the accuracy of the timber estimate itself (§ 225).^ 1 The detailed methods of Forest Surveying employed in a forest survey cannot be discussed in a text on Forest Mensuration without exceeding the limits of the volume. Any summary of a system of forest survey must include a description of the methods of surveying and topographic mapping which are to be used. The various methods of survey must be co-ordinated with the methods of cruising and with the cost and relative accuracy of the work desired, both for the survey and the estimate. THE CULL FACTOR, OR DEDUCTIONS FOR DEFECTS 271 217. The Cull Factor, or Deductions for Defects. Most timber estimating for board-foot contents of stands is based on the amount which the logs will scale (§ 116). Since a sound scale of logs requires deductions for defects which will not make sound boards, the timber estimator must make the same deductions in the standing trees. This deduction from total sound scale is independent of any separation of the timber into grades or quality, which calls for additional special attention. Deductions from full sound scale of standing timber are made either by the log unit or by the tree unit on the basis of the judg- ment and experience of the cruiser. Where the estimate is made by logs, only sound logs are tallied. Culled logs are dropped from the tally altogether and trees which contain defective portions are scaled by shortening the length or decreasing the size of the logs tallied so as to represent only their net sound volume. Where it is impossible or inaccurate to use this method of omission, a straight percentage deduction for cull is either substituted for the method of dropping or reducing logs or is subtracted after all of the clearly visible defect has been deducted. Tree units are handled in the same manner. Trees so defective that they are practically cull are not tallied at all, but in species where few, if any, trees are cull and the defect constitutes a portion of a large per cent of the logs and is not easily deducted, cruisers deduct a straight per cent from the total sound scale of the trees tallied. Usually a com- bination of these methods is necessary since the per cent deducted represents more accurately the loss in the sound scale of logs actually sawed and taken to the mill, while a considerable additional cull is found in logs and trees not utilized at all. Foresters, in making a tally of diameters and heights, customarily tally all trees, regardless of their condition, omitting only dead timber which is unmerchantable, and then apply to the total volume a per- centage deduction for total cull, which will cover both that portion left in the woods and that lost in sawing. 218. Total, or 100 Per Cent Estimates. To completely cover a small area, it is only necessary to avoid duplicating the count or measure- ment of the individual trees. This may be done by the use of a bark blazer or scratcher, or by tagging the trees, a method employed in India where labor is cheap. Trees may be given a light bark blaze. In working over a tract in this manner, the blaze is placed upon the same side of all trees, facing the direction towards which the measurement is proceeding. Where topographic features are present on small areas, duplication may be avoided by covering sections bounded by these natural features without the necessity of spotting the trees. 272 METHODS OF TIMBER ESTIMATING On larger areas, where it would be impossible to keep track of the individual trees, parallel strips may be run. The trees on the outer edge of a strip 'can be blazed facing the strip which has not yet been measured, and in this way the entire tract covered with a minimum of effort. In dense swamps men may be employed to hew parallel lanes through the underbrush; the cruiser then estimates all trees between these lanes. It is possible to dispense with all methods of marking the trees provided sufficient care is taken, first, in running the strips accurately as to direction so that they lie parallel and at fixed distances apart, and second, by estimating or measuring the trees on strips so placed that they cover the entu'e area; i.e., strips whose borders are contiguous. There is danger of overlapping or duplication by this method, and if it is the intention to run a 100 per cent estimate, a slightly greater accuracy can be insured by blazing. This ocular method, however, is commonly employed as a substitute for blazing. A modification of this method of completely covering the area by strips, is the laying out of rectangular plots whose dimensions are such as to cover the area without overlapping. These plots are estimated consecutively and may be of any convenient width and length. As an example, a method given in Graves' Mensuration, page 196, consists in laying out two tiers of plots, each 40 rods wide and 16 rods across. Ten of these plots give the area of 40 acres. The cruiser proceeds 20 rods from the corner of the forty, and then crosses the center of the first tier of five plots, returning through the center of the second tier. To get the contents of the trees on areas 100 per cent of which is estimated, the following systems may be used : 1. Tally the merchantable contents of each tree directly. This is estimated by eye, or from a universal volume table which may be printed on a Biltmore stick, or any other convenient form. 2. Tally the upper diameter, inside bark, of eiich log in the tree, or tally the upper diameter of the butt log and top log (see Rule of Thumb by F. R. Mason, § 204). The contents are then computed from a log rule. 3. Tally the diameter and merchantable height in 16- or 32-foot logs or half -logs of every tree. The contents are then computed from a volume table based on similar dimensions. 4. Tally the diameter only, of every tree, either by eye or by the use of calipers. Measure, by a hypsometer, several sample trees of each diameter to give a curve of average height on diameter. The contents of the trees are then computed from a volume table based on diameter and height. The heights measured maj^ be either merchant- able or total, but are usually the latter. In this method, types or areas ESTIMATES COVERING PART OF TOTAL AREA 273 which differ in average height and diameter must be estimated sepa- rately. 5. Count all the trees on the area and tally a fixed percentage such as 1 in either 3, 4 or 5, whose volumes are found as by method 4 above. 6. Count all the trees on the area and determine their volume by arriving at the contents of an average tree. This may be done: By guessing at the average contents. By selecting a tree of average diameter and height and determin- ing its contents by the use of volume table. By determining the number of logs per tree or average mer- chantable height expressed in logs, thus getting the total number of logs on the area and then guessing at the con- tents of the average log or number of logs per thousand. Method 6 may be applied to all of the timber considered as one class, or the timber may be separated into two or possibly three dif- ferent classes, corresponding with marked differences in size and char- acter. 219. Estimates Covering a Part of the Total Area. The Strip Method. There are two methods generally employed to estimate a portion of the area, the strip method and the plot method. The strip method adopts the principle of endeavoring to obtain the average stand per acre for the whole area, from the portion estimated by the running of strips parallel or in a given direction and spaced at mechanic- ally regular intervals. By this means it is sought to eliminate judg- ment or choice in the obtaining of the required average. This average is still further improved by the choice of direction of running these strips. The effect of differences in elevation and in drain- age or soil moisture is to produce differences in the density and character of the forest corresponding with these changes. The belts of forest which have comparatively uniform stands usually run parallel with contour lines and at right angles to the direction of slope. A basic principle of strip estimating is therefore to cross these belts at right angles or proceed directly up and down slopes or directly across the larger stream or drainage bottoms as far as possible, and to avoid traveling along contour lines or bottoms and in general along the long axis of belts of timber. If this fundamental principle is neglected, very large errors may be incurred in applying the average estimate so obtained to the larger area. In rectangular surveys, it is customary to run the strips in one of two cardinal directions, and the choice is therefore narrowed down to either north and south, or east and west. In irregular surveys, or where the topography is so mountainous that the estimate will be made 274 METHODS OF TIMBER ESTIMATING by topographic blocks and units, rather than by forties or legal sub- divisions, the system of strips will be planned with reference to base lines run along the main bottoms and streams, from which, at regular intervals, the strips will be run directly up the slopes and as nearly parallel to each other as possible. The strips in each separate unit may, therefore, have a different direction. 220. Factors Determining the Width of Strips. The standard widths of strips used in timber estimating are six in number and their dimen- sions are given in the following table; TABLE XLI Relation of Width and Number of Strips to Area Covered Width of Strips Area covered by one strip per forty acres or four per mile. Per cent Strips per \ mile to cover entire Feet Rods Chains area. Number 33 66 110 132 165 330 2 4 61 8 10 20 1 2 1 2 2^ 5 91 5 8§ 10 12i 25 40 20 12 10 8 4 On rectangular siu'vej'S, to compute this per cent of total area covered by the strips, multiply the number of strips run per forty or one-fourth mile square, by the width of the strip in rods, and divide by 80 rods. These two factors, number and width of strips, are not reciprocals since each has a distinct function to perform. The number of strips per forty increases directly the probability of accuracy in securing an average stand or proper sampling of the timber on the area (§ 211). The width of the strip affects this average to a lesser degree. Its principal function is to enable the cruiser to determine accurately the dimensions and volume of the trees which stand upon the strip estimated, and the factors which affect his ability to obtain this accuracy will determine the width of strip without respect to its effect upon the total area covered. If narrow strips must be run in order to get accurate estimates of timber on the strip, and it is necessary to increase the per cent of area, the number of strips will have to be increased rather than the width of the strip. An example of the relations between these two factors is cited by Austin Cary, Manual for Northern Woodsmen, where a system on the Pacific Coast of using two FACTORS DETERMINING WIDTH OF STRIPS 275 strips per forty, each 10 rods wide, covering 25 per cent of the area was abandoned in favor of the use of a narrower strip 6f rods wide to increase the accuracy of the estimate on the strip. The nuinber of strips was then doubled, or four strips run per forty, and the total per cent of the area estimated was thus increased from 25 per cent to 33| per cent. If, instead, the number of strips had been kept the same, but the width of each strip increased to 20 rods, a lesser degree of accuracy would have been attained in spite of an increase to 50 per cent of the area covered. In determining the number of strips required for a forest survey, the character of the topographic map desired must be considered with reference to the topography. Lines run ^-mile apart will give only a rough scale map in bold mountainous topography. Lines placed at j-mile intervals in mountainous slopes with large features, are sufficient for an accurate topographic map with a large contour interval of from 50 to 100 feet. On all flat or gently rolling forested slopes with no outlook, cut up by drainage or interspersed with swamps, it is impos- sible to make an accurate topographic map with proper contour interval of from 10 to 20 feet and show all details of drainage and slope, unless lines are run at |-mile intervals, but this interval is sufficient for all maps on the ordinary scale of from 2 to 4 inches per mile. Only for a much greater detail will lines be required at less than this interval. The influence of the forest cover upon the number of strips required for accuracy increases with the two factors, density of the forest cover and variation of the timber, whether caused either by age, size or diver- sity of species. Finally, the increasing value of the timber from any cause, whether through quality or unit price, will require an increase in the per cent of area covered, which means a greater number and more closely spaced strips. These conditions frequently require a full or 100 per cent estimate by forties, the best examples of which are the heavy stands of rapidly increasing value in the Pacific Coast States, or stands of large mature hardwoods with great variety in size and value. The width of strips is determined by the accuracy with which this width can be measured by the eye and the dimensions of all the trees standing thereon ascertained, or the timber upon it measured and counted. This width is diminished directly by the amount of brush and undergrowth which obstructs the vision. In brushy country, strips seldom exceed from 4 to 6f rods. The width of a strip is also diminished by decreasing size and increasing number of trees on the strip. In young timber, with many stems per acre, a greater degree of accuracy is obtained on a 4-rod strip accurately measured and counted than upon a strip of twice the width. Conversely, open and large timber with fewer and more scattered trees and an unobstructed view not only permits a wider strip to be measured accurately, but requires an 276 METHODS OF TIMBER ESTIMATING increase in the per cent of area, which is easily obtained by increasing the width of the strip without an appreciable increase in the cost. This is independent of the need for running more strips per acre, by which the per cent is still further increased. With unobstructed vision, a wide strip may be estimated with almost as great accuracy as a narrow strip, since the error may be in proportion to the total width without affecting the percentage of error in the estimate. With increasing openness and irregularity of timber, strips may give way altogether to a total count of timber on an entire forty, since no system of partial or sample estimates can be depended upon to secure an average oi- a correct total. The method of determining the volume of the trees on the strip affects the width of strip which can be used accurately. Where trees are counted, without measuring the diameter of each tree, nearly double the width of strip can be used because trees can be seen for this additional distance while it is less possible to judge their diameters accurately. Upon a calipered strip, the additional width sometimes slows up the work and introduces a greater per cent of error. The counting of trees in open country is so simple a matter that cruisers accustomed to estimating such species as longleaf pine in the South have usually abandoned the strip method altogether. Guided by the compassman, they cross a forty about twice, pursuing a snake's course back and forth, and attempting to see and roughly to count all of the trees on the forty. 221. Method of Rumiing Strip Surveys. Record of Timber. Strips are universally run with the compass. A hand compass is com- monly used by cruisers working in dense, swampy or brushy country, as it is more quickly read and increases the number of sights possible without delaying the work. For ordinary accurate surveying, in which a topographic map is made, the use of a staff compass adds to the accu- racy of the direction of the strips, and is commonly employed (Fig. 58). In the use of either hand or staff compasses, it is a great advan- tage to be able to turn off the declination of the needle on a movable arc with a vernier so that a cardinal direction is indicated by the sights. This is especially true in the Pacific Northwest, where variations up to 25 degrees are encountered. The size of the field party for strip estimating depends upon the methods used in measuring and recording the timber. Wliere the diameters of each tree are measured either with the calipers or Bilt- more stick, the party will consist of three or four men to best advantage. One man runs the compass and makes the topographic and type maps. A second man tallies the diameters; the third and fourth work, one on each side, calipering trees. Heights are usually taken at regular METHOD OF RUNNING STRIP SURVEYS 277 intervals so as to be distributed uniformly over the area. Consider- able errors may be incurred in bunching sample heights in timber which may be too tall or too short for the average of the stand. Where diameters and mer- chantable heights are meas- ured by the eye, the party is usually reduced to two men, one for the compass and map, the other to record the dimen- sions of the trees which he estimates. It was a common practice in the Lake States in earlier days, for timber cruisers to work alone without the assistance of a compass- man. The system of counting timber and recording merely the average dimensions and volume enabled a man to run his own compass, keep track of his paces, and at the same time count the trees. The record kept by cruis- ers on strip estimating con- sists primarily of a tally of the trees by diameter, height, or volumes direct; second, of the cull, per cent; third, notes on damage to the stand; fourth, quality of timber and grades; fifth, young timber and reproduction; sixth, soil and ground cover. A report or summary sheet for each sepa- rate unit, usually by forties, is worked out. The following headings are submitted as samples (p. 278) : In the Appalachian region upwards of twenty species and a variety of products may be estimated. For the hardwoods, volume tables based upon diameter and merchantable log lengths are used. It has been found necessary to have available a table for one- and two-log trees to avoid errors in inaccurately applying small top diameters for these trees rather than the actual merchantable top. Cull is deducted from each tree by reducing the D.B.H. or number of logs. An additional per cent is deducted for unseen defects. The tally is coordinated with existing volume tables to secure a record of lumber, cordwood (principally acid wood), poles, ties, posts, or other products. An example of the tally form used is shown on p. 279. Fig. 58. — Staff compass. 278 METHODS OF TIMBER ESTIMATING c p o O W '.B < -2 ^ pq w O ■^ o pj Q w CO H H s H Pi < oi 00 oo o [14 i p-i w o ^ P ^'-,' ^CQ 2m s O « 1 ^ 1 : ^ >> o s M 1 - 1 o3 "a PL, ■^ 1 CO 1 \ ^ 1 ^ - 1 1 1 03 3 a J3 e^siX 1 ^ 1 ^ CO 1 1 ^ 1 - 1 1 a 4) U SMOd 1 s<'!X 1 CO , ■^ ^ 1 a> - 1 a 1 3 pa Q CI 3 OC C 5 C -t r -1 >- H « 5 a 3 C 1 4 C 5 ce c 5 C 5 C 3 C< 3 P 3 5 9 !^\ -7! 280 METHODS OF TIMBER ESTIMATING REVERSE SIDE OF BLANK Forest types, Lower slope Age classes, 1-60 Condition of timber, Immature Thrifty 95 per cent Mature 2 per cent Decadent 3 per cent Fire killed per cent; damaged, 5 per cent Insect killed per cent; damaged, - per cent Other killed per cent; damaged, 2 per cent Name of disease. Bark disease Species affected. Chestnut Quality of timber {give by log grade; percentage of tall, medium or short clear boles; or number of clear logs of stated minimum length and diameter) : 80% tall; 15% medium; 5% short Logging factors: Undergrowth; light-medium-dense. Light Windfall; light-medium-dense. None Bowlders and broken rock; numerous; occasional; absent. Absent Other factors, Easy gradient. Logging conditions ideal as skid and wagon roads can be constructed anywhere Replacement: Species ■ Per cent No replacement, Ground one-third stocked, Ground two-thirds stocked, Ground fully stocked. Chestnut, 50%; white, 5%, red, 5%, black, 20%, and chestnut oaks, 10%; white, 1%, pitch, 2%, and scrub pines, 2%; gum, 2%; sourwood, 1%, and maple, 2% 100% The stand shows an absence of poplar due to grazing Additional Notes: This is a stand which was cut over for charcoal during the war and since then was culled for chestnut ties and poles. Bark infested chestnuts should be cut as well as suppressed chestnut for extractwood. The few mature "wolf" trees left from former cuttings should be removed as well as some of the scarlet and black oaks where the stand is too dense. Removal of the latter can be made for ties. The dead and down timber from the laps in the tie and pole cuttings should be removed for extractwood TYING IN THE STRIPS. THE BASE LINE 281 Explanation of Blank, by Supervisor J. H.Fahrenbach. All saw timber is tallied by the number of 16-foot logs in each tree. If a tree happens to have odd lengths " we give and take." Under chestnut all trees to be removed for extract wood are tallied in the " " column. All trees to be left are tallied in the one-log column, even though they are not large enough to make one 16-foot log as is the case in trees imder 10 inches D.B.H. Street railway ties (6 by 6 inches by 8 feet) are taUied in trees which have reached their maximum value for hewn ties. Standard gage ties are usually sawed in saw timber operations, and are tallied as saw timber. Poles are tallied by diameter class. In this way we are able to approximate the number of 25-foot, 30-foot, 35-foot, etc., poles. Chestnut oak and hemlock trees, suitable for bark alone, are tallied in the " " column. In figuring the estimate for bark the number of trees tallied as saw timber must also be included. It sometimes happens that we also have a market for black oak bark, and in this event a " " column must be entered under mixed oak. Poplar and scrub pine pulp wood are entered in the "0 " column. We class black, scarlet, pin and Spanish oak under mixed oak. If a " " column is added, it is understood that black-oak bark is to be entered. Under mixed-oak ties red-oak ties are included. Pitch, short-leaf and table-mountain pine are tallied under yellow pine. If there is a market for locust-tree nails they are tallied in the one- and two-log columns for the larger locust trees and the smaller trees are tallied as posts, using as a basis a post 4 inches in diameter and 7 5 feet long. Under others are tallied beech, birch, gum, maple, sourwood and sycamore. If there should be other valuable species for which provision has not been made in the headings the diameter and number of logs in each tree are given at the bottom of the Form. This includes walnut, ash and wild cherry. If there is a market for fuel wood, provision must be made for a " " column for all those species which cannot be utilized for either bark, pulp or extract wood. All the oaks can be thrown together in one heading, the pine in one heading and the remainder of the species, except hickory, in another heading. 222. Tying in the Strips. The Base Line. In laying out and recording the strips run in estimating, independent of the question of topographic mapping, it is necessary to tie in each strip to a known point at each end, so that its position and the error incurred in running it in both distance and direction may be determined. For this purpose, and also to form the basis of a map when one is constructed, a base line is first surveyed along the route from which the strip will be later laid out. The strip, whether rectangular or irregular areas are being estimated, will start as nearly at right angles as possible from points on this base line, and will either be tied in to a second base line approximately parallel to the first, or by offsets will be run back at the proper interval and tied in to the original base line. In laying out this base line, therefore, stations or measurements are established at the exact points and intervals from which these strips must later be initiated and tied in. Methods of survey and establish- ment of base lines fall under the subject of Forest Surveying. The 282 METHODS OF TIMBER ESTIMATING base line is a primary feature of the forest survey. Where a land survey exists which is accurate and easily traced, or where such a survey is retraced, it may serve as a base line. Where the area is small, and a survey and map exists, the corners and known or located points on the boundaries of the tract are sub- stituted for a base line as points from which to initiate strip surveys. The same rules apply as to the necessity of tying in each strip on its completion to some known point on the map, in order to check errors in the survey which would affect the areas determined. In running the strip, the estimator is dependent upon the compass- man for the distances from which the areas are determined and the estimate separated by 40-acre tracts. Errors in measuring this dis- tance will cause the cruiser to misplace timber, thus altering the accuracy of the individual estimates per forty. Where types or differences in stand are separated in estimating, the distance across each separate type, as kept by the compassman, will determine the area and con- sequently the accuracy of the estimate within the type. If errors are incurred, their character and extent is revealed by tying in to known points, which enables the construction of a correct map and the correc- tion of the estimates. In running estimates over separate forties, it is customary to run strips 1 mile in length, cruising a tier of 4 forties before returning. Where one strip per forty is run, the estimate for the forty is completed at the end of 80 rods. Where two or more strips are run per forty, the tally of the timber on each forty is separated for each strip as indi- cated to the cruiser by the compassman, and is not completed until the last strip on each forty is run. The results for each strip on the same forty are usually tallied together on the same sheet, and care must be exercised not to misplace or mix up these tallies. 223. Systems of Strip Estimating in Use. Examples of systems of estimating in which the various factors itemized above are harmonized to meet a given set of conditions, are given below: Forest Service Standard Valuation Survey. This system was used almost uni- versally by the Forest Service and with minor modifications is still a standard method used on national forests. Its characteristics are: Width of strip 4 rods or 1 chain Number of strips per forty 1 to 2 Per cent of area estimated 5 to 10 Measurement of distances By chain or tape Measurement of trees, diameters By calipers or Biltmore stick or ocular Heights Sample heights by hypsometer Forest types Separated and coordinated with aveiaj^c- heights Cull factor Estimated by a total per cent Corrections from strip estimate for average stand None SYSTEMS OF STRIP ESTIMATING IN USE 283 In this system, as indicated in the last item, no effort was made to modify the average stand per acre obtained from the strip in order to get a more correct total for the area. The employment of inexperienced men made necessary the use of instru- ments for diameter and height measurement, and the rigid elimination of the element of judgment on every point possible. Where the unit of area was large, from 1 square mile up, this method gave excellent results, since the mechanical average for areas of this size is quite dependable on the basis of a 5 to 10 per cent estimate. The errors possible could be easily avoided by conscientious effort. These errors consisted of too wide or narrow a strip, diameters measured too low, average heights measured too high, dead trees calipered for live ones. When applied to large timber in units of 40 acres or less, these mechanical results cannot be depended upon. Lake States Cruisers' Method Width of strip 8 to 10 rods — 2 to 2^ chains Number of strips per forty ... 1 to 2 Per cent of area estimated 10 to 25 Measurement of distances By pacing Measurement of trees Counted Heights Average number of 16-foot logs per tree Volume From number of logs on tract and log run, or contents of average log Forest types Timber of different age classes and quality separated Cull factor Usually by per cent deduction from total esti- mate Corrections from strip estimate for average stand Close inspection of remaining area and modifi- cation of average whenever necessary to obtain correct total Of late, timber cruisers in these states have been adopting the use of volume tables, but in many instances these tables are based upon stump diameter inside the bark which makes them less consistent and accurate than if based on D.B.H. The more modern cruisers are adopting the use of standard volume tables constructed by regular methods and differentiated by D.B.H. and height. Southern Timber Cruisers' Methods Width of strip A strong tendency to substitute ocular esti- mate, based on the stand per acre, for the running of strips. Great carelessness in methods until recently Measurement of distances Paced by a compassman, the cruiser usually riding a horse. Consequently estimates fre- quently stopped at the edges of swamps Measurement of trees Cruiser gets located by compassman, but does not follow the strip. Trees are counted on acre plots Volume of average tree Guessed at, using rule of thumb based on Doyle rule. Trees on entire forty may be counted to check results of plots and get reduction factor 284 METHODS OF TIMBER ESTIMATING Forest types Accuracy of the better class of cruisers greatly increased by careful elimination of blank areas and containing net area of timber to which reduction factor from stand per acre is applied for total Cull factor Usually neglected on account of deficiencies in Doyle scale Corrections from strip estimate for average stand This is based on general inspection and count- ing since no. systematic strips are run Many Southern cruisers have adopted more systematic methods of late. Yale Forest School Method in Southern Pine. Width of strip 10 rods — 2^ chains Number of strips per forty 2 Per cent of area estimated 25 Measurement of distances By pacing Measurement of trees Count of the trees on the strip, tally of one- third to one-fifth of the timber by mechan- ical selection to avoid choice. Diameters Tallied by eye Merchantable height Tallied by eye in 16-foot logs and half-logs of all trees whose diameters are tallied Volume on strip From volume table for trees tallied multiplied by 3, 4 or 5, according to per cent tallied Forest tyjjes Areas not stocked with merchantable timber eliminated by mapping. Net area of timber obtained. Types not usually separate within a forty except on the map Cull factor By per cent of total estimate Correction from strip estimate for aver- age stand Careful inspection at stated intervals of stand on remainder of forty. Comparison by weighted volumes with stand estimated. Weighted correction factor applied to area estimated to obtain proper stand per forty Horseshoe Method. This is a modification of the strip method, by which two strips are practically combined in one by running a horseshoe or angular course through the forty as shown in Fig. 59. This results, first, in a saving of time, cut- ting down a certain amount of travel from one strip to another; second, in a better inspection of the timber and, it is thought, in a better average, since the strips run in both cardinal directions. This method was employed extensively by a firm of Southern timber cruisers, who used a 10-rod strip, thus running 25 per cent of the area. Pacific Coast Method. Width of strip 10 rods, or 2| chains Number of strips per forty 4 Per cent of area estimated 50 Measurement of distances By pacing METHODS DEPENDENT ON THE USE OF PLOTS 285 Measurement of trees The volume of each tree recorded directly, based upon the universal volume tables Forest types Not necessary to regard them Cull factor Deductions made for each tree when its volume is ascertained Correction from strip estimate for aver- age stand By running 50 per cent, corrections are usually avoided. Where inspection reveals the necessity, modifications are made in the total estimate Separate record under this system may be made of the board-foot contents and of other products, such as poles. The estimate is fre- quently increased to 100 per cent. These examples are cited merely to show the various combinations of ele- ments which go to make up a system of timber estimat- ing. The securing of accuracy consists •- in adapting the Fig number and width of strips to the local conditions described as, first, character of timber estimated and, second, size of the smallest unit of area estimated. The details of measurement, whether by eye or r "H r "1 1 1 1 1 1 1 l_ _j L 1^ Mile 59. Horseshoe method of strip estimating. Route of compassman shown by dotted line. to be to be instru- ment, for distance or for tree dimensions, must be coordinated with the volume table and with the skill and personal ability of the individ- uals employed in the work. The saving in time by the substitution of the eye and of ocular judgment requires dependence upon personal skill. Where cruisers with sufficient experience are unobtainable, accurate results may still be obtained by mechanical measurements, carefully supervised and conscientiously applied. 224. Methods Dependent on the Use of Plots Systematically Spaced. In the use of plots in timber estimating, the method employed depends upon whether the principle of mechanical arrangement or spacing is to be observed, in order to obtain an average stand, free from the element of personal judgment, or whether instead, plots are to be selected by the use of judgment in an effort to obtain thereby an average stand which will apply to the area as a whole. By the first principle, the plot method, so-called, is merely a modification of 286 METHODS OF TIMBER ESTIMATING the strip method. Compass strips are run at the usual intervals, but instead of a continuous belt or ribbon of area being covered, this is broken or separated into plots at fixed or stated intervals along the line. These plots may be rectangular, but the use of such plots is not common. In the measurement of rectangular plots, a crew is usually- employed, and this same crew can probably run out the entire strip with better results. Rectangular plots for the measurement of young growth and reproduction, which is desired only on a small per cent of the area, are frequently used in conjunction with a strip for the merchantable timber. The common form of plots is circular to enable one man to work to advantage without the assistance of a compassman. By dividing the functions of pacing and compass work from those of estimating and recording the diameters and heights of timber, the mind is kept free for concentration on each task in turn. A crew of two men is sometimes used for circular plot estimating with the same advantage to the timber cruiser, who can inspect the stand for defect and quality between the estimation of the volumes of his plots. The common size of plots is as follows : TABLE XLII Sizes of Circular Plots Size of plot. Acres Radius. Feet Diameter Feet Rods 1 4 1 2 1 59 83 118 118 166 236 7.15 10.0 14.3 The relation of these plots to the per cent of area covered is given below. TABLE XLIII Relation between Plots and Area Covered Size of plot. Shortest distance between centers. Rods Plots for i mile of strip Total area included in plots. Acres Per Cent of 40 Acres Included in Running Acres 1 strip 2 strips 1 4 h 1 8 10 16 10 8 5 21 4 5 6i 10 m 12^ 20 25 METHODS DEPENDENT ON THE USE OF PLOTS 287 Great care must be taken in the use of circular plots to obtain the width of the plot correctly. An error in this factor is more serious than that on a strip, since it affects the entire boundary. The same principle as to size and number of plots and per cent of area covered applies to these methods as to strip estimating. In dense brush and with small timber, the common size is one-fourth acre, while plots 1 acre in size are required for old and large trees. The amount of timber on each plot is obtained by the use of the same variety of methods as for strips. Examples. Spruce in the Northeast on large tracts. Size of plot J acre Number of strips per forty 1 Distance between plots on strip 20 rods — 5 chains Per cent of area covered 2§ Measurement of distances By pacing Measurement of trees D.B.H., cahpered or tallied by eye Heights A few sample heights taken on each plot for curve of height on diameter Types Separated in mapping Cull By per cent applied to total estimate Correction of estimates to get average . None Large Timber on the Pacific Coast. Number of strips per forty 1 to 2 Size of plots 1 acre Number of plots per strip 5 Per cent of area 12^ to 25 Measurement of distance By pacing Measurement of trees on plot Average tree selected for each species. Diam- eter at stump inside bark and at top measured. Average of these diameters taken as diameter of the average log Volume Obtained by rule of thumb (§ 214). (Any of the three standard methods for obtaining the contents of trees on a plot or area apply to this method.) Tj^es Blank areas eUminated and stand obtained for average acre Cull By a per cent of the total estimate Correction factor to the estimate Obtained by general observation and com- parison with stands on the plots CHAPTER XXI METHODS OF IMPROVING THE ACCURACY OF TIMBER ESTIMATES 225. The Use of Forest Types in Estimating. When only a part of the area of a tract is covered in estimating, the accuracy of the resultant estimate depends upon the success with which the actual average stand per acre has been obtained. Although the per cent of area taken has been properly chosen to fit the topographic conditions and character of the timber and although the measurement of the timber upon this area and the width of the strips has been accurately carried out, so that no avoidable error remains in the work done, yet the esti- mate may still be in error by the failure to secure the same proportion of the different types and variations of stand on the strips as exist on the area as a whole. On account of the prohibitive expense of running a sufficient per cent of the area to get this average mechanically, a margin of error in timber estimating is permitted, and is gaged by the value of the timber and the purpose of the estimate. Any modification which will secure the required degree of accuracy and at the same time avoid incurring an unreasonable expense will necessarily become a part of the system employed. The more uniform the stand as to sizes and density of stocking, the better the averages. This applies to the use of all six of the classes of averages cited in § 209. For the purpose of securing a greater degree of uniformity in the stand on those subdivisions of total area to which the estimates obtained on strips or plots are applied, the distinction of forest cover types is indispensable. A forest type includes all stands of similar character as regards composition and development due to given physical and biological factors, by which they may be differentiated from other groups of stands. A cover type is the forest type now occupying the ground, whether this be temporary or permanent. Timber estimating concerns itself only with the existing forest cover. The factors which are reduced to greater uniformity by the sepa- ration of forest types in estimating are composition of stand as to species, and consequent relative per cent of total volume of stand represented by the different species, a vital consideration in timber estimating. This 288 THE USE OF FOREST TYPES IN ESTIMATING 289 factor has an influence upon the total vokime of the stand, as well as its average height, though both of these are influenced even more pro- foundly by differences in quality of site within the same cover type. These differences in type may be caused by altitude, slope, moist- ure and depth of soU. By separating the total into sub-areas, a far greater uniformity of size and density of the timber in these sub- divisions may be obtained, first by securing a more uniform mixture of species in the per cents of the different species represented in the stand ; second, by reducing differences in the density of stocking per acre; third, by securing more uniform sizes both in height and diameter, and* a smaller range. The subdivision of an area into a number of smaller units is a means of avoiding the necessity for securing a weighted average of these factors in order to get the average acre. Doubling the number of strips would probably secure the same result, but the expense of separation of the estimate into two or more types is much less than this increase in field work. The only increased expense of separating types consists of the increase in computations required by separating the areas and the precaution required in changing the tally sheet on entering the type. Proper coordination between the compassman who maps the area and the estimator who records the timber is necessary. Where areas as small as 40 acres are mapped and a large per cent taken, distinctions between the two types of timber are not often made by old woodsmen. The total volume of each species is obtained with- out separate computations of area. But the principle of type separations is universally applied in sepa- rating areas which do not contain merchantable timber from those which do. Blank areas caused by cultivation, burns, swamps, or uimierchant- able reproduction must be subtracted from the total timbered area under any system which permits the completion of a cover map. The arbitrary inclusion of these unstocked areas makes it practically impos- sible to obtain an average stand on the remainder. In theory the same law of averages applies even in this case and with a sufficient number of strips which cross blank areas in such a way that a per cent of the blanks is taken as the merchantable stand, no error would be incurred in the average. But the extreme danger of obtaining a different per cent from that on the whole tract, and the comparative simplicity of mapping out these blanks to obtain net timbered area, makes this method universal wherever the number of strips per forty or |-mile amounts to at least two, and possible even when but one strip is run. This correction requires, first, the area of the type whether timbered or blank, from a map; second, the area covered by the strip in esti- mating. The latter expressed in acres is computed by multiplying 290 IMPROVING THE ACCURACY OF TIMBER ESTIMATES Fig. 60. — Polar planimeter. length of strip by its width. The most convenient units are rods, since 160 square rods equals 1 acre, or chains, 10 square chains to 1 acre. Distance in chains on strip required for 1 acre may be computed for each width of strip and the area of the strip obtained by dividing its length by this factor. 226. Method of Separating Areas of Different Types. To determine the total area of the type accurately from a map, a 'plan- imeter may be used. By the use of this instrument a direct reading on the map is obtained in square inches of the area whose boundary is traced by the needle, moving clockwise. The stationary pin is placed outside of the area to.be traced. When placed within the area so that the movable pin finally encircles the pivot before returning to its point of origin, a deduction or correction must be made in the indicated area, the size of which depends upon the make of instrument used. The equivalent in acres for square inches, as determined by scale of the map, gives the acreage. Lacking a planimeter, the area of types can be computed by the method of approximation through triangles or the sum of small squares. For the latter purpose a map should be plotted on fine cross-section paper. The area of these types is required only to a reasonable degree of accuracy since the determination of their field boundaries is a matter of inspection and sketching and the total area of the tract is not involved. i Type 1 n ---. Type II As an illustration of the effect of using type areas in estimating, the follow- ing example may be cited: Area of tract, 200 acres, divided into two types containing 100 acres each. The stand on the first type is 30,000 board feet per acre, and on the second 10,000 board feet. The total stand is therefore 4 million board feet. Twenty-five per cent of this area or 50 acres is to be covered by strips. The result of the cruise is shown in Fig. 61. Fig. 61. — Relation of areas of types to strips in timber estimating. SITE CLASSES AND AVERAGE HEIGHTS OF TIMBER 291 The result of running the five strips at regular intervals is to include within type I, 30 acres, which at 30,000 board feet per acre would give 900,000 board feet. In type II, 20 acres was included which at 10,000 board feet gives 200,000 board feet, a total for the 50 acres run, of 1,100,000 board feet. As this is 25 per cent of the area, the required factor for the tract without subdivision into types would be a multiple of 4, giving an estimate of 4,400,000 board feet, an error of +10 per cent caused not by errors in the strip but by failure to get the weighted average stand from the strips run. But if while running these same strips the tally sheet had been changed wherever the strip passed from one of these types to the other, and both the map of the area and the corresponding estimate of the timber, or tally, had thus been separated into two areas, corresponding with each of the two types, the computed estimate would show that while on 30 acres 900,000 board feet was tallied the average acre for type I is 30,000 board feet, but instead of this applying to three-fifths of the total area, it applies only to the actual area shown to be in the type, or one-half of the total, which is 100 acres, totaling 3,000,000 board feet. The less fully-stocked type in the same way is shown to contain 1,000,000 board feet or a correct total for the tract of 4,000,000 board feet. The 10 per cent error incurred in the first method is elimi- nated. The accuracy of this area correction obviously depends first upon ability to obtain by sketch a correct map of the actual areas of the different types, and second, to convert this area from the map into acres by use of the proper methods of map reading as explained in this paragraph. This system of type divisions is of especial value in mountainous regions where sharp distinctions can be drawn between types coinciding with great differences in the average density, volume, size and value of the timber. Under such circum- stances the more valuable types would require a greater per cent of the total area to be estimated, to obtain the same basis of accuracy as could be secured for the less densely stocked and less valuable tracts with a smaller per cent. The type ■ divisions also are more conveniently made in large or irregular areas than where estimates are separated by rectangular tracts of 40 acres. 227. Site Classes and Average Heights of Timber, bifferences in the quality of the site on which timber is growing cause very great differences in total volume per acre, and in the total heights of the trees and stands. To quite an extent these differences are closely correlated with changes in cover types, different types being found on wet soils, fresh well-drained soils, and dry, shallow soils. But it often happens that the same type of forest cover will extend without appreciable changes in composition over a range of site quality so great that it becomes necessary to subdivide the area within the type into from two to three site classes, ranging from good to poor. This is made necessary by the effect of site upon the height of the trees in the stand, on account of the methods usually required, of selecting sample trees to measure for height. Heights constitute an extremely variable factor in timber estimating. Not only do total heights range through limits of at least 100 per cent for the same diameter, but merchantable heights, especially in old hard- woods, vary still more widely. Just as, in a 100 per cent estimate, the necessity for averages is eliminated, so when the height of every 292 IMPROVING THE ACCURACY OF TIMBER ESTIMATES tree in a stand is tallied there is no necessity for average heights. Only when merchantable log lengths are used as the basis for height will the height of every tree measured for diameter be tallied. Where total height is used, far greater accuracy can be obtained by the measure- ment of a few trees with a hypsometer than by attempting to guess by eye the height of each tree. In a large tract with varying site qualities, the securing of the average height for each diameter class from a range of heights of 100 per cent would require the selection of heights on the basis of the principle of a weighted average. If exactly the same proportion, as for instance, 1 per cent, of the heights for each diameter were obtained from large, medium and short trees as existed in the original stand on the entire tract, the height curve could then be applied to the tract as a whole. Any failure to secure this weighted average would result in a curve giving too high or too low an average for the timber as a whole. The difficulty of securing a weighted average is eliminated if the tract can be divided into two or three site qualities, separated as dis- tinct units in the field in estimating. On each of these separate sites the heights conform to a much closer range for the same diameter than for the entire area, and a few selected trees for each class will give a dependable height curve (§ 209) from which the volumes in each diameter class may be acciu-ately computed. 228. Methods of Estimating which Utilize Types and Site Classes ; Corrections for Area. An example of the application of these principles is found in the standard methods of timber cruising adopted by the Forest Service in the Appalachian region. Four types are used, termed cove, lower slope, upper slope and ridge. The variations in the per cent of estimate required are shown in the following table: TABLE XLIV Per Cent of Total Area Required in Estimating Total Area Estimated { Area of estimate Average Heavily Lightly unit. of all types. timbered timbered types. types. Acres. Per cent Per cent Per cent 0- 100 50-100 50-100 50 -100 100- .500 25- 50 25-100 10 - 25 500-1000 10- 15 20- 50 5-10 1000-5000 5- 10 15- 25 2i- 5 5000 + 3- 5 10- 25 i¥- 2§ THE USE OF CORRECTION FACTORS FOR VOLUME 293 The problem of combining a large per cent of area on a heavily timbered type, as the cove type, with a small per cent elsewhere, has been solved here by running strips across the entire area, embracing the minimmn per cent. Where these strips cross the cove types, points are marked on the ground which serve to tie in the strips run through the coves. Where 100 per cent is not estimated, a plan of running strips in a zigzag course from one boundary to the others of the type through these Qoves has been adopted. The more acute the angle between two courses and the more nearly parallel the result- ^^_^^.jn::^=^-'''^'^~'^'^'~T^' ant strips, the greater the per cent of the type included. 229. The Use of Correction Factors for Volume. The pur- pose of all estimates is to secure the actual volume of timber on the entire tract as accurately and inexpensively as possible. In systems of covering partial areas, even after the probable error has been reduced by adopt- ing subdivisions based on type or forest cover and site, there remains a final possibility that the average stand per acre within the type differs from that secured by the methods employed.^ The older and more diversified a stand, the greater will be its irregularity of stocking, and the greater the necessity for accuracy. Can this accuracy be still further improved? A correction of an average, mechanically obtained, rests upon the assumption of definite knowledge that this average is wrong, and the ability to determine approximately how much it is in error. Since the timber on the area lying outside the measured and estimated strips is neither counted nor measured, the impression that the average is wrong depends upon the ability of the cruiser to estimate or size up timber by the eye and to compare it ocularly as a whole with the stand upon the strip which he has measured. This comparison is useless unless enough of the remaining timber can be seen so that it is practically certain that the average stand on the whole remaining area is greater or less than that measured on the strips. Where strips are narrow and run at wide intervals, it is impossible to arrive at this judgment and no reliable correction can be made by eye. 1 Errors in Estimating Timber, Louis Margolin, Forestry Quarterly, Vol. XII, 1914, p. 167. Fig. 62. — Method of running strips to cover an additional 20 per cent of area in heavily timbered tj'pe, on basis of original 5 per cent estimate for entire area. Strips 8 rods wide. 294 IMPROVING THE ACCURACY OF TIMBER ESTIMATES But where strips are run at intervals of | mile and the timber is open and large, and especially in coniferous stands which have a fair degree of uniformity of sizes, although varying materially in density, it is possible to view the remaining timber without counting it or caliper- ing. If there were time for additional measurements, these would be made. The application of a correction factor is based on the assumption that the per cent actually measured is the maximum possible under the limiting conditions. Where an error would evidently be incuried unless the mechanical average is corrected, this correction should alwa} is be made. The method of applying this sort of a correction in the past has been as unsystematic as the ocular estimation of timber itself. The estimate from sample plots or strips was arbitrarily raised or lowered according to impressions obtained by the cruiser. This system may be greatly improved and a much higher per cent of accuracy obtained by observing the following principles: 1. The comparison sought is not an absolute estimate of the volume per acre on the remaining area, but a percentage relation between this stand and the strip which is measured, by which the estimate on this remaining area may be obtained by increasing or duninishing that on the strip. 2. The correction is an average for the whole area to be corrected, in the form of a per cent of total volume. Single observations must therefore be carefully weighted to obtain average results. 3. The correction actually applies only to the area lying outside the strip and not measured. If applied to the entire area of the unit, the estimate on the strip itself is arbitarily raised by the same per- centage as applied to the residual area and this factor cannot be neglected in arriving at the proper per cent. To illustrate the last point, assume that 50 per cent of a tract has been estimated. By observation, the correction factor on the remainder is assumed as + 10 per cent. The estimate is 100,000 board feet on the strip. The correct estimate on the remaining area is therefore 110,000 board feet and the total, 210,000 board feet. If 10 per cent is applied to the results obtained for the forty, the process would be, 100,000 times 2 gives the uncorrected estimate for the area, or 200,000 board feet. A correction of 10 per cent gives 220,000 board feet, which is an error of 4.8 per cent in the estimate.^ 1 This multiple, which in this illustration is 2, is sometimes termed the correction factor, but assumes no correction. It is merely the extension of the mechanical average over the entire area. For a 25 per cent estimate, the multiple is 4; for 20 per cent, it is 5, etc. A method of applying the correction factor is in use, by which this multiple is raised or lowered. Where the multiple is 4, a +25 per cent correc- tion calls for 5; +12| per cent requires 4§, etc. THE USE OF CORRECTION FACTORS FOR VOLUME 295 Since this error consists in applying the per cent erroneously to the area estimated within the strip, it diminishes with the per cent covered by the strip; e.g., should 25 per cent of the above tract be estimated and found to contain 50,000 board feet, and the correction factor be actually 10 per cent, the remaining area, which if uncorrected would have a stand of 150,000 board feet, has actually 10 per cent more than this or 165,000 board feet or a total for the tract, of 215,000 board feet. But applying 10 per cent to the entire tract indicates a total stand of 220,000 board feet or an error of + 2.4 per cent. But with the decrease in the per cent tallied, the probability of obtaining a close observation of the remainder and applying a correct per cent also diminishes so that if a correction factor is used at all, there is less need for modifying the per cent. The conclusion is that when, on account of measuring a large per cent of the area, it is possible successfully to use a correction factor as applied to the remainder, there is all the greater necessity for making a correct application of this factor. To determine the actual correction from a per cent obtained by weighted observations, two methods may be used. The first of these methods applies to irregular areas where the per cent estimated is not uniform, that is, in areas estimated by the separation of types. The steps are as follows: 1. Reduce the stand on strip to stand per acre. 2. Apply the per cent correction to this stand per acre. 3. Calculate the stand separately for the area not estimated, using the corrected average stand. 4. Add together the estimates on and off the strip for the total; e.g., on 100 acres, 17 per cent is estimated and the remaining 83 acres is judged to run 10 per cent heavier than the strip. The tally on the strip is 170,000 board feet, averaging 10,000 board feet per acre. The 10 per cent correction gives 11,000 board feet per acre off the strip, or a total estimate off strip of 913,000 board feet. The total, both on and off strip is 1,083,000 board feet. The second procedure may be applied when the per cent estimated is uniform and type or area correction seldom applied. The rule is, reduce the correction per cent by the proportion which the area estimated in the strip hears to the total area. E.g., where the strips cover one-half the area or 50 per cent, a correction factor of 10 per cent applies to the other 50 per cent or one-half. Then, .50X.10= .05. A 5 per cent cor- rection can be applied to the total normal estimate. Where 25 per cent is estimated and a 10 per cent correction is found, this applies only to three-quarters of the area; .75X.10 is .075. The correction factor of 7^ per cent may then be applied to the total area. It makes no dif- ference whether a correction of 10 per cent is applied to 75 per cent 296 IMPROVING THE ACCURACY OF TIMBER ESTIMATES of the area or 75 per cent of a correction of 10 per cent is applied to the whole area. Since the greatest danger in applying corrections to mechanical averages lies in failure to obtain a proper weighted average, and since it is better to let these mechanical averages stand rather than to intro- duce an unknown factor, dependent merely upon a guess, observations intended to demonstrate the need for a correction factor must be made as systematically as the strips themselves are run. Fixed points should be chosen at definite intervals along the strips at which to take these observations. These may be taken for instance at points 20 rods apart on the strip. At these points, the areas on either side of the strip should be compared with the stand upon the strip. The final result is expressed in terms of a per cent, but if each sepa- rate observation of a series is so expressed, the resultant per cent will not be weighted by the volumes to which its components apply; e.g., two successive observations may give the following result: Stand on strip Correction per cent Weighted volume correction 10,000 5,000 Average of 2 plots + 10 -10 + 1000 - 500 + 250 The actual correction factor is +2^ per cent instead of zero. This principle of weighting the observations by volume is very simply applied. It consists of entering for each observation, not the per cent of comparison, but a comparison based on an ocular estimate of the stand per acre. The estimator puts down in two parallel columns, first the stand per acre estunated to be on the strip at that point, second, the stand per acre estimated to be on the remaining area. In arriving at this he includes as large an area as comes under his observation both on and off the strip. For double observations, i.e., taken on both sides of the strip, it is necessary to record the stand on the strip twice, once for each observation off strip. On the completion of the unit, these stands on and off strip are totaled. By dividing the total off strip by the total on strip, the true weighted volume correction factor is obtained. This factor is a percentage relation and therefore does not require that the ocular estimates per acre on which it is based be correct, pro- vided they are in the proper proportion. Each ocular guess may be 25 per cent too low, yet the resultant correction factor will be, identical METHODS DEPENDENT ON USE OF PLOTS 297 with that obtained if the ocular guess in each case were correct. This increases the probabihty of accuracy in applying the method. Actual tests of this principle have shown that where the average stand per acre off the strip differs as much as from 10 to 15 per cent from that on the the strip, under conditions permitting the inspection or actual seeing of the greater part of the timber, it is possible to reduce the error incurred by the mechanical average by at least one-half, provided the cruisers have some training and skill in application of the principle of ocular estimating. 230. Methods Dependent on the Use of Plots Arbitrarily Located. In discussing the methods of estimating by means of sample plots, only the systematic or strip method of arrangement has been described. A second plan is to locate these plots arbitrarily by selection based upon individual judgment, the purpose being to get the total estimate by means of a few typical plots and greatly cut down the work required in systematic measurements. As in the strip systems, one of two things is done; either the plots which are measured are taken to represent the average stand per acre for the larger area of which they are a sample, or these plots are merely the basis of arriving at the stand by sub- sequent application of a correction factor. The first plan can be used only in conjunction with the area or type method in order to eliminate, as far as possible, variations in the stand by separating uniform and comparatively small areas. In this case, sample plots selected with care after a thorough inspection may be relied upon within reasonable limits of accuracy. By the second method, the plots chosen are seldom relied upon without further close inspec- tion of the stand. Cruisers using this method employ these plot measurements in order to establish in their minds the volume of typical stands having a definite density and appearance. Once fixed, this standard is used as a basis with which to compare the average stand on the area by exactly the same methods as were described under the correction factor in the strip method. The plots are merely much smaller and have more definite standards than the strips, and their application to the larger area is more difficult. The use of these plots is still further restricted, with improved accuracy, when they are intended merely to determine the volume of the average tree of certain classes of timber, and the estimate on the remaining area is determined by a tree count covering practically 100 per cent. Various combinations of the above plans are used, especially in the South, by cruisers working in pine in an effort to cover the ground accurately with a minimum of time and expense. 231. Estimating the Quality of Standing Timber. An estimate of standing timber is in effect an inventory of raw materials intended 298 IMPROVING THE ACCURACY OF TIMBER ESTIMATES to establish the total value of the stock on hand. It is not sufficient to know the quantity of wood in the forest in terms of board feet or cubic feet. The estimation of poles, ties and other piece products by sizes and grades illustrates this need. An inventory requires a statement of the total quantity of each class of product, and of each grade or quality within that class, which has a different unit price or value. Lumber grades differ enormously in value (§ 352), and the quantity of separate grades of lumber which may be sawed from trees of different ages and sizes differs as widely as their values. The estimation of the amount of the different standard grades of lumber in standing timber is as essential in determining its value as the measurement of the total quantity in board feet. The neglect or inability of many foresters, whose training was along lines of mechanical estimating (§ 223) to determine the amount of the product by grades has done much to withhold a recognition among practical cruisers of the great services rendered the profession of cruising by foresters in contributing volume tables and in systematizing the making of topographic maps. What is wanted is the estimation of the total quantity of timber on a tract, separated into the amount of each of several standard grades, covering the range of the products and sufficient to include practically the enthe cut and to determine its average value on the stump. This problem is closely related to that of discounting for defects in that both require a close observation of the character of the standing timber rather than its mere dimensions. All defects which reduce the value of sawed lumber reduce its grade. When these defects are of a character to reduce the grade below a certain standard (§ 358, Appendix A), the material is no longer scaled under the rule of sound scale. It may still be sawed and sold as lumber. But when it ceases to hold together as boards it is cull. The deduction of a per cent of the total estimate for defects brings the estimate into conformity with the quantitative " sound " scale. The further separation into grades of the sound portion of the timber which will be scaled and estimated, recognizes the influence of defects, chiefly knots, but including other classes, such as wormholes, sound stain, and twisted grain, which lower the grades and nature of the log contents (§ 352, Appendix A), To determine grades, a knowledge of the results of sawing and the study of logs as they are opened up and graded into products on the sorting table is far more valuable than the experience gained in studying the apparent defects of standing timber. This knowledge must then be supplemented by a knowledge of the growth of trees in stands. Open-grown trees, although large, are of low quality due to the presence METHOD OF MILL RUN APPLIED TO THE STAND 299 of knots, while trees grown in dense stands have a higher per cent of upper grades due to the history of their development. The skill required in judging the per cent of grades in standing timber is based directly on these two sources of information and is not a matter of guess work. 232. Method of Mill Run Applied to the Stand. Data on grades produced in sawing takes two forms; the total output by grades for mills sawing in a given region and character of timber, and the specific contents of logs of different sizes and quality, as determined by mill- scale studies (§361, Appendix A). This corresponds with two dif- ferent methods of applying the information on grades to the standing timber, namely, application to the stand as a unit, and application to the tree or log units. In applying mill-run grade per cents to the stand, the total estimate in board feet is arbitrarily divided into the different grades which it will probably yield, by per cents of this total. This method corresponds with that of ocular estimate of a stand (§ 206) and its results are about equally um-eliable. The basis is the sawed output by grades from mills in the vicinity. These per cents so obtained will apply to the timber in question, only if it happens to average the same in quality as that sawed, which assumption, considering the great variation in standing timber, is wholly untrustworthy. This means that the per cents of grade must be modified as the timber is better or poorer than that sawed, which requires a knowledge of the standing timber previous to sawing. 233. Method of Graded Volume Tables Applied to the Tree. Evi- dently, a better basis is required and, just as in timber estimating for volume, this must be found in the use of the tree unit or the log unit, by which the varying quality of the timber can be standardized. The tree unit has not proved a satisfactory basis for grading, though it is possible to use it. The basis is graded volume tables (§ 165) which show the per cent of standard grades in trees of different diameters, preferably in the form of per cents of contents. These per cents could be applied to the trees in each diameter class and the total estimate divided in this way into the component grades. The objection to this method is that it is not sufficiently elastic to take care of the great range of quality in trees of the same diameters. A given graded table will hold good only for timber of a certain character; if more open-grown, shorter boiled or limbier, or otherwise different, the volume table is not applicable. The method is probably better than the ocular guess, but is equally subject to large corrections in the field. 234. Method of Graded Log Rules Applied to the Log. The third method employs the log as the basis of grades, and applies this basis 300 IMPROVING THE ACCURACY OF TIMBER ESTIMATES to the standing timber. The graded log table (§ 74) appears to satisfy the requirements of the problem. Log grades are such as can be recognized in standing trees, on the basis of diameter, surface appear- ance, presence of knots or limbs, and character of the tree and the stand in which it is growing. In turn, these log grades can be analyzed by mill-scale studies, so that the average per cent of grades of timber in each log grade is known. Since three grades are usually made in valu- able species, and at least two for the less valuable, trees of the same D.B.H. can easily be thrown into the lumber grades corresponding with differences in their character, by recording the logs which they contain as grades No. 1, 2 or 3. By contrast, if graded volume tables are used, ordinarily only one classification is available for the tree — that corresponding with the table. The final problem is the application of these graded log tables to the standing timber, in a manner to conform to the methods used in timber estimating. Cruisers who use the method of selecting an aver- age tree (§ 209) usually analyze this tree by the use of the log gi'ades, or directly by per cents, into the grades of lumber which they believe it will cut, and apply these per cents to the remainder of the stand. This is a crude method. Where the method of tallying the diameter of every log (§ 119) is used, each log can be tallied under its proper log grade. The total volume in each log grade is thus obtained directly. Where timber is sold as logs, it is unnecessary to go beyond this point. But where the sawed product determines stumpage value, these log grades are merely the basis of application to the standing trees of the grades of lumber which they probably contain, and the contents of the log grades, in lumber of each grade, will be computed for the estimate. 235. Combination Method Based on Sample Plots and Log Tally, Where the tree tally and volume tables are used in estimating (§ 121), the application of the log-grade unit to each tree is not possible, since it would mean a shift to the tally of logs and not trees. Here a com- bination method is necessitated, based on the principle that grades or quality of timber can be determined by the measurement of a much smaller per cent of the total volume than is required for volume estimate. The method is to lay out sample or representative areas in the form of strips crossing the types as for timber estimating (§ 209) and com- prising a per cent of the area estimated, sufficient in the judgment of the cruiser to obtain the average quality sought. On these areas, every log in each tree is totaled by upper diameter, in the log grade in which it belongs. Instead of guessing at these upper diameters, taper tables based on D.B.H. (§ 167) and total, or merchantable, heights, LIMITS OF ACCURACY IN TIMBER ESTIMATING 301 possible if the latter are cut to a fixed diameter, or if made to conform to average utilization, are used to get these diameters; e.g., for a tree 38 inches D.B.H. containing eight logs, the upper diameters are respectively, from the table, 32, 30, 28, 25, 22, 18, 14, and 10 inches, and are so recorded, each log under its proper log grade. (See § 207 for form of tally.) The determination of the number of board feet of each standard grade in logs of each diameter and grade, and the total scale for each lumber grade, is based on the contents given for these log grades from mill-scale studies of log contents. The purpose is to obtain the per cent of each grade, regarding the total contents of the logs tallied as 100 per cent, and then to apply these per cents to the volume estimated for the tract. These per cents can be obtained more accurately if over- run is included in logs of each separate size (§46). The mill-scale study will show the amount of over-run in logs of different diameters and standard lengths. The scaled volume of these logs should then be increased by this per cent of over-run, before the division into lumber grades is made. On the total sawed contents thus obtained, the per cent of each grade is based. ^ Even if considerably in error, the value of an estimate expressed by grades of lumber is much greater than one which entirely ignores the quality and consequently the relative stumpage value of the tract. In the absence of specific information on grades, a record of the sizes of the trees, their clearness of bole, and the density of the stand may furnish a basis for approximating the probable grades. 236. Limits of Accuracy in Timber Estimating. Purely ocular estimates vary in accuracy up to errors of 100 per cent, dependent upon how far the method is stretched from its original limitations. This does not include errors due to inexperience, inefficiency or careless- ness. In mechanical methods of measurements, serious errors may occur in computations. Such errors, of course, are inexcusable, but their avoidance requires careful checking. The mechanical errors due to the operation of the law of averages have been pointed out as a function of the factors influencing these averages, the chief of which is the size of the area unit. The degree of accuracy must be based upon the standard of utiliz- ation. It is entirely unfair to judge the accuracy of estimates based upon one standard against the results of sawing attained by the appli- cation of an entirely different standard. Wliere the standard is the same in both cases, the present demands of timber estimating require 1 The details of this method are taken from the article by Swift Berry, Journal of Forestry, Vol. XV, 1917, p. 438. 302 IMPROVING THE ACCURACY OF TIMBER ESTIMATES an accuracy of within 10 per cent. The error should be conservative rather than an over-estimate if possible. Greater errors than 10 per cent may be caused by differences in scahng practice alone, or in the length of logs cut, or the thickness of lumber sawed. 237. The Cost of Estimating Timber. No figures will be given for the costs of various methods of timber estimating. These must be determined locally. The elements of cost are: 1. The size of the crew and the wages paid each member; the character of supervision, such as the combining of several crews under one supervisor; and the employment of a cook. 2. Accessibility of the tract as affecting transportation of men and of supplies, especially of food. The means of transportation, such as pack versus wagon haul. 3. Cost of location of boundaries and surveys and cost of establish- ment of base lines from which strip surveys are to be run. This is a function of the size of the tract and the character of the boundary survey and monuments already established. 4. The number of strips or miles of line to be run per unit of area. The cost is not exactly proportional to the miles run since certain items such as travel to and from work and from one strip to another, cost of computing the estimate, and cost of mapping in the office, increase in a lesser ratio. Doubling the number of strips increases the cost from 50 to 80 per cent, dependent upon the saving in these items. 5. The rapidity of traverse or number of miles of line which may be run per day. A standard day's work varies directly with topography and brush, and with the amount of detailed work required in the actual estimate along the strip, as determined by the number of products, the number of species, the number of trees and the details of record required. In very brushy and mountainous or precipitous country with a variety of species, 1 mile per day may be all that is possible, varying up to 2 miles. An average day's work in fairly open country varies from 2 to 4 miles; on level open land with sparse timber and no brush, 4 to 8 miles may be made. 6. The character of the topographic map required. To a certain extent, a detailed topographic map appreciably slows up the work. It is the object of a forest survey to requu-e only that degree of accuracy and detail which will not add appreciably to the cost by delaying the party. 7. Computation or office work required. By practical cruisers, this is almost eliminated through the methods employed. Methods of tallying dimensions and the use of volume tables increase this addi- tional expense. 8. Holidays, sickness and lost time. Only the number of hours TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 303 on the actual work of running lines and estimating can be considered as the basis of costs. All lost time ,for any other cause adds to the costs per hour of work. 9. Personal efficiency. The training and personal efficiency of the men employed may make from 25 to 50 per cent difference in the actual cost of the work, but its principal effect is in greatly increasing the relative accuracy of the estimate. Cost of estimating should be computed as follows: Total cost itemized under salaries, and cost of supplies, transporta- tion and subsistence. Cost reduced to the cost per hour of actual work by dividing this total by the number of hours employed in estimating. These costs can be separated into field work and office work, including mapping. The costs can then be expressed as cost per unit of area or per acre and finally as cost per unit of product, as per thousand feet or per cord. This is the final test of cost. The cost should then be compared with the stumpage value per unit. If possible it should not exceed 1 per cent of this value. 238. Methods of Training Required to Produce Efficient Timber Cruisers. Mechanical methods of timber estimating, dependent upon the measurement of diameters and heights with instruments, and secur- ing the mechanical average stand per acre by strips, do not require anything more than conscientious work and care in details. Skill and training enter with the application of the laws of averages, even for the construction of height curves. The demand for training is increased by the use of ocular methods of measurement and reaches its maximum in the application of cull for defects and in judging the quality of timber. Aside from Tamiliarity with cull and grades, there are no principles of timl^er estimating that cannot be learned in a month's intensive train- ing. The common impression that it takes several years to develop ability as a timber cruiser is based upon the unscientific methods employed in training these men. They usually acquire their skill by a maximum of hard work in the woods, with a minimum of accurate comparisons of the estimated volumes with an actual cut. Even in the matter of judging defect, the basic training should not be in the woods, but in the mill and in scaling. It is comparatively easy to recog- nize the signs of defect in standing timber, but much more difficult to judge of the amount of cull which it causes. In actual training of timber cruisers it has been found that ability to secure accurate esti- mates is greatest in men who have best developed their mental faculties by education, close observation, memory and systematic coordination. This same combination of qualities is desirable for success in any line. Many cruisers lack this ability and remain permanently inefficient tO 304 IMPROVING THE ACCURACY OF TIMBER ESTIMATES a marked degree. The only reason that such individuals have in the past continued to practice timber cruising as a profession is the almost complete absence of a reliable check on their results for years at a stretch, and the comparative indifference of purchasers to the accuracy of estimates due to a rising market and a plentiful lumber supply. Standing timber cannot be " measured." There is always a residual error in the closest work. Hence the use of the term " estimates." Although the only basic check on estimates is the measurement of the timber after it is cut, yet it is possible, by the use of intensive methods, to measure plots of standing timber so closely that they will serve as checks on individual estimators. An example of this check is cited below in the case of a Minnesota lumber com- pany, which in 1907 required each of its timber cruisers to estimate an area which had previously been carefully calipered and measured with a volume table and was afterwards cut and checked out with these measurements. The results speak for themselves. These men were given all the time they desired to make this estimate. TABLE XLV Comparative Estimates on a Tract of 40 Acres Board Feet Calipered, and measured by volume table. Defects deducted Estimators, by Individual Methods No. 1* No. 2 No. 3 No. 4 White pine Norway pine Spruce Tamarack Jack pine Balsam Hardwoods 2.50,800 4,120 9,870 35,480 730 2,220 9,910 220,000 23,000 300,000 45,000 400,000 35,000 3,000 130,000 10,000 10,000 15,000 Total 313,130 243,000 345,000 438,000 165,000 White pine f No. 5 No. 6 No. 7 No. 8 199,000 175,000 125,000 115,000 ♦ Number of cruiser. t No other species estimated by these four cruisers. TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 305 The tract, when cut, scaled by Scribner Decimal C log rule 314,350 board feet, an error of tV of 1 per cent. The best system of training men for timber estimating is by the use of sample plots on which the diameter and merchantable heights in log lengths of each tree are estimated by the eye and checked against the records. On these same plots, each of the six classes of averages (§ 209) can then be tested and their application mastered. Each day's training can be checked against the measured volume of the plot that night and not only the total error in per cent but the exact cause of this error ascertained. On this basis, the progress of training is rapid and the cruiser is advanced in a short time more than would be possible in several years of estimating without these checks. The following outline will illustrate the possi- bilities : 1. Plots of 20 acres, 40 by 80 rods, are laid out with compass. The boundaries are marked by blazing the trees facing each of the four sides on the face towards the plot. Stakes are set on all four sides at distances of 20 rods apart. Two plots are laid out adjoining each other, together comprising 40 acres. 2. Every tree on the plot is calipered at B.H. in two directions, the average being taken to the nearest even inch and the bark blazed to prevent duplication. The blazes are made facing the portion or strip not yet measured. A crew of one tally man and two caliper men are used and all trees above a fixed diameter are taken, corresponding Avith the minimum exploitable diameter class. 3. The merchantable heights to the nearest 8-foot length or half-log are measured by two or three additional men with Faustmann hypsometers. From 30 to 40 per cent of all heights can be measured during calipering in this way. Height men work mth the diameter crew taking the diameter as measured, pacing for distance from the tree and recording heights based on diameter. Forty to sixty heights per hour can be recorded by each man. Upper diameters or merchantable lengths are based upon the practice of sawing as applied to the species measured, provided this is the basis on which the voliune table was constructed. 4. The determination of the merchantable height of every tree from that of 30 to 40 per cent of the trees is made separately for each diameter class. The heights tallied within the diameter class are taken to indicate the percentage or proportion of the different height classes existing in this diameter class and the total number of trees are then distributed according to the same proportion. As the result required is a proper distribution for the plot as a whole, and not for each diameter separately, this method gives a sufficient degree of accuracy. 5. The record for the plot will show the following data : total estimate in board feet, total number of trees, average stand per acre, volume of average tree, volume of average log or log run per thousand board feet, exact number of trees in each diameter class, exact number of trees in each log and half -log height class independent of diameter. The exact number of trees in each separate diameter and height class is the basis for the last two summaries ; but the summaries rather than the detailed class- ification are made the basis of the estimating, i.e., the tally is totaled for each diameter class, and in turn, is totaled for each height class irrespective of diameter. For each day's work the cruiser hands in a report on the first five of the above seven items and brings in his notebook In which he has totaled the number of trees for each diameter class and each height class separately. His accuracy is computed as a per cent of the total stand on the plot. The error in per cent is recorded. The sources of error are then examined. These are four in number. 1. The width of the strip may be too great or too small. This is shown by an error in the number of trees tallied. 306 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 2. The trees may not be counted accurately. This error is identical with the first, but usually shows up as a deficiency of small timber near the minimum diameter tallied. 3. The diameter of the trees may be over- or under-estimated either as a whole, or in certain classes. There is a strong tendency to bunch diameters towards a tree whose size seems to be the standard in the cruiser's mind. This results in over- estimate of small trees and under-estimate of trees of larger diameters. 4. The heights may be over- or under-estimated. When this happens it shows up consistently for the whole tract, the standard of height apparently being tem- porarily distorted in the mind of the cruiser. A fifth source of error, the volume table and the failure to coordinate upper diameters and merchantable lengths with the standard used in this table, serves to exaggerate the per cent of error in the judgment of heights, but is always indi- cated when the average heights are too high or too low to agree with the measure- ments. When the volume of the average tree is high or low, it usually means an over- or under-estimate of diameters or heights. The exact character of the error in diameter and height is ascertained by a simple check as follows: the cruiser com- pares the number of trees in each diameter class with that of the standard record and sets down his difference plus or minus. If he is over-estimating, but has the right number of trees, the minus sign -mil appear opposite the smaller diameters and the larger diameters will show excess numbers. If under-estimating, the plus signs will appear opposite the small diameters. The same rule applies to heights. An over-estimate causes minus signs to appear opposite the lower height classes and corresponding plus numbers in those of greater log lengths. The size of these dis- crepancies shows the degree to which the error has been carried. It is the tendency in cruising as in scaling logs, in an effort to correct a known error, to incur immediately a still greater error in the opposite direction; but when it is possible to check against a measurement which the cruiser admits is infallible and in which he has confidence, this tendency to fluctuation is soon overcome and rapid improvement is noted, not only in the total per cent of accuracy which is sometimes merely the result of large compensating plus or minus errors, but in each of the four elements of accuracy, thus insuring a consistent degree of accuracy from day to day. The cruiser is expected to master but one detail at a time, and the schedule is as follows: 1. During the calipering of the standard plots, the eye is trained in estimating diameters which are then promptly checked by the measurements. The same is true of heights. 2. The second period is devoted to a total or 100 per cent tree by tree estimate with a tally of each diameter and merchantable length. The total area of the plot is covered by eight strips, 5 rods wide, the cruiser working not in the center, but on one side of this strip with compassman marking the opposite border. Width of strip and success in getting 100 per cent of the area is dependent absolutely upon use of eye, checked by pacing and judging distance, and the men are not permittee) to mark the boundaries of these strips to prevent overlapping. Twenty acres per day are covered by this method. 3. The third step is to increase the area covered per day to 30 acres by doubling the width of the strip to 10 rods, the cruiser taking the middle of the strip and judging 5-rod distance on each side. In all of this work, the cruiser tallies his own dimen- sions of the trees. In these preliminary 100 per cent estimates, constant repeated checks are made of the diameters and heights to continue the improvement of the eye. 4. The 100 per cent estimate is continued, but the tally of every diameter is TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 307 discontinued and a total count substituted with a tally of one tree in three. The area is increased to 60 acres per day. It is the universal testimony of cruisers that this simplification of the tally relieves the mind of a strain and improves the accuracy of the dimensions tallied and consequently of the total estimate. It has been found that an average volume is obtained through a tally of one-tlxird of the stand under the following conditions : When there are at least 500 trees per 40 acres of the species tallied and preferably 1000. When the judgment or process of selection is entirely eliminated in favor of mechanical selection of the trees to be tallied. This may be done by taking every third tree in succession or by taking the nearest tree in each case. Where there are insufficient trees to insure the mechanical average, or where the range of size is large, the count may be separated into two groups, segregating the large from the small trees, one tree in three tallied separately in each group. This adds very little to the detail required when working with a single species. 5. Only 50 per cent of the area is estimated by the above method. The area per day is nominally 120 acres. The remaining area is inspected by eye at distance of 20, 40 and 60 rods in order to apply a weighted volume correction factor as described in § 229. In this method, four strips are run, each 10 rods wide, as before, starting from points, 5, 25, 45, and 65 rods from the corner and alternating with strips not estimated as per Fig. 63. In order to check the correction factor, the alternate strips not previously estimated are now in turn estimated, keeping the record separate from the original four strips. The correction factor derived from observation is first com- puted and the corrected estimate is then com pared with the tally of the strips estimated. 6. Up to this time no effort has been made to deduct for cull which would introduce an arbitrary factor interfering with the comparison of the work of the cruiser with the measurement of the plot, both of which have been on basis of sound contents, disregarding possible cull. The cull factor is now tested by close examination of 10 acres in which every tree is individually estimated and the per cent of probable cull recorded and subtracted from the estimate. Per cent figures also are obtained from the scale of logs of similar timber in the vicinity and these per cents are used as a basis of cruising. 7. In actual cruising, the per cent of area covered is reduced to 25. The area is increased to 320 acres per day, and 4 miles of line rmi. A cull factor is used and hardwoods are added to the estimate by tallying the top diameter of each mer- chantable log, inside the bark. 8. The cruiser is then brought back to the sample plots to receive training in individual estimating. This consists of: The use of circular plots covering different per cents of the area by a systematic plot method and finally by the selection of a sample plot by eye. On these plots, he first arrives at the volume of the average tree either by direct approximation or by selection of a typical tree whose volume is ascertained from a volume table; A tally of the diameter and height of each tree on the plot and the immediate" computation of the volume to ascertain the true average tree for comparison with Fig. 63. — Method of estimating a forty by use of the correction factor. Points at which obser- vations are taken shown by dots. 308 IMPROVING THE ACCURACY OF TIMBER ESTIMATES the ocular guess. Two days of this work will greatly improve the ability of the cruiser to substitute ocular methods for measurements. An opportunity to run out strip estimates in which he does his own compass work, counting the trees ahead of him in rectangular blocks. The volume of these trees is obtained: By the log-run method of estimating the number of logs m the average tree and the average contents of the log or log run per thousand; By selecting an average tree in volume for each of eight separate strips, the total tally of which is kept separate. This principle could, after practice, be applied to the entire forty, or to separate groups. The exact details of this system as to size of sample plots, widths of strip and methods of tallying heights were worked out for Southern yellow pine, and several of these points would need modification if applied to timber of radically different type and conditions. But the general method of careful, original measurement of the control plots and of proceeding from a 100 per cent intensive estimate through various stages of less intensive work in which the six classes of averages are employed as substitutes for the full tally, can be worked out for any forest type and form the basis of rapid and practical training in the art of timber cruising. 239. Check Estimating. Just as in the training of a cruiser his greatest drawback is lack of any check on his estimates, so check esti- mating does not benefit the cruiser unless he can be told, not only what the extent of his error is, but just how he made it. Check estimating must depend either upon the infallibility of the check estimator, which may be questioned in the mind of the person checked, or by the sub- stitution of actual measurements on a basis which removes all source of doubt, leaving only cull and quality to be judged. Check estimates should therefore be made on definite areas or strips, prevously or sub- sequently estimated by the cruiser and on which a record has been kept similar to that indicated in the description of the methods of training timber cruisers. The tree count, the total volume, the average volume per tree, but most important, the tendency to over-estimate heights and diameters should all be checked separately. When this is done, one of two things will happen. Either the cruiser will rapidly acquire a much greater accuracy or he will demonstrate his complete unfitness for the job of timber cruising and can be put on other work. 240. Superficial or Extensive Estimates. The preliminary examina- tion of a tract of land for the purpose of determining roughly whether it has timber of value and approximately how much, calls for the exercise of the maximum of skill and experience in order to attain a reasonable degree of accuracy in the minimum of time allowed. A description of the estimation of a tract of 2300 acres for the Blooming Grove Hunting and Fishing Club, located in Pike County, Pennsylvania, will serve as an illustration of methods possible in such an examination. The field work on Taylor's Creek logging unit occupied two days including travel to and from the unit. Not much over one day was put on the estimate itself. The fundamental basis of the CHECK ESTIMATING 309 methods employed was the location of corners with the aid of a guide, the use of a map and the sketching of the boundaries of areas of different types by intersection, aided by rough triangulation from known points. Cardinal directions for strips were not attempted in any instance. This tract was afterwards estimated by the strip method, running 5 per cent of the area. The comparison of the two methods arid TABLE XLVI Estimate of Taylor's Creek Logging Unit, Blooming Grove Tract, Pike County, Pa., 1911 A. By extensive methods, in two days' time, one inan with guide. B. By 4-rod strip, 5 per cent of area, diameters calipered, average heights. . Error by First Method Area. Method of cruising Estimate. Type Species employed under A M feet Amount. M feet Per cent Acres B.M. B.M. Pitch pine. 375 Pitch pine j-acre circular plots A 2178 - 36 - 1.7 pure stands for sizes 8-rodrectangularplots counted, when con- venient B2214 scattered on 1275 Pitch pine 16-rod strip counted. burns when convenient White oak and 200 White oak Total count of large A 248 -197 - 47 hardwoods trees Average trees guessed at B 445 Swamps with 450 Spruce j-acre circular plots, A 750 +353 + 88 har dwoo d selected by guess for B 397 and conifers average stand per acre Hemlock A 750 B 527 +223 + 42 Yellow Some poplar coimted A 250 + 161 +181 poplar B, 89 Ash A 100 B 125 - 25 - 20 White Treetops counted A 250 - 32 - 11.3 pine from hill. Average tree guessed at Uniform old growth B 282 Total 2300 A 4526 +526 + 10.9 B4079 ' 310 IMPROVING THE ACCURACY OF TIMBER ESTIMATES their results is made on the basis of the assumption that accurate results on this area were obtained by the strip method. The cost of the original estimate was $60.00 or 2.6^ per acre, l.S^ per thousand. The cost of the subsequent strip estimate was 8^ per acre or 4«f per thousand. The results clearly show that the average stand per acre was successfully obtained for the pitch pine types in which the timber could be seen, and where the area was carefully mapped in two degrees of density of stock- ing and checked by strips and plots carefully selected there was no need of a subse- quent estimate. The method of counting every tree was successful for white pine since all of the tree tops were seen and the average tree was correctly guessed at, but for white oak, the total count apparently failed. This was due not to a defect in the method or its application, but to the fact that 123,000 feet of white oak was found later con- cealed in the swamps. This reduced the error to 23 per cent for the portion seen and counted. The estimate of spruce, hemlock and poplar broke down because of the funda- mental difficulty of applying the sample plot method when based upon selection and not on systematic arrangement. The swamp should have been crossed and all parts examined. As it was, the sample plots were selected near the boundary where the timber was one-half to two-thirds again as heavy a stand per acre as in the wetter portions. This resulted in over-estimating spruce, hemlock and poplar. An area or density correction here, or another day spent on that portion of the tract would have greatly reduced this error. In extensive mapping and estimating of large areas for purposes of classification as in the preliminary examinations for the establish- ment of national forests, rough sketch maps of the areas of timber types are made on the above principles by location of the cruiser on a map and by triangulation. The estimate must depend upon the location of occasional sample plots chosen with the best skill possible to get average stands. In State work the construction of maps showing the timber resources of the State or of various counties is usually carried on by similar methods of mapping, using roads and the principle of the wheel or odometer for distances and sample plots for average stands. In Massa- chusetts a different principle is employed. Strips 4 rods wide are run at |-mile intervals on which detailed measurements are taken of the stand. No attempt is made to complete the map of timber in the inter- vening areas, but the data are assumed to show the average for an entire town, an assumption which is probably correct owing to the large area involved. 241. Estimating by Means of Felled Sample Trees. In the absence of volume tables in earlier European practice, it was found that volume of stands could be determined by calculating the diameter of the aver- age tree, felling it and determining the cubic volume. This volume multiplied by the number of trees in the stand was supposed to give the number of cubic feet in the entire stand. Since height and form factor of individual trees both varied over a wide range, it was quite METHOD OF DETERMINING THE DIMENSIONS OF A TREE 311 difficult to get a tree which was actually an average for the stand, but when the stand was divided into diameter groups, any required degree of accuracy could be obtained, according to the number of groups made. In determining the diameter of the average tree, the arithmetical mean of diameters gave too small a result since the volumes of trees of uniform height are in proportion to D'^. With a table of the areas of circles, the total basal area or sum of the areas of the cross sections at D.B.H. for all the trees on the plot was obtained and divided by the number to obtain the average basal area. The diameter correspond- ing to this basal area was that of the tree sought. Where a tree of this exact diameter to yV-inch could not be found, a larger or smaller tree was selected and the difference found by the proportion existing between the basal areas of the tree measured and the tree desired. This method is termed the Mean Sample Tree Method. In this country the application of these methods has been confined to a few early investigations into the cubic volume of cordwood in second- growth hardwoods. The difficulty of selecting a tree of average height and form as well as basal area and the expense of felling and measuring a tree makes the use of volume tables far preferable whenever these are dependable, and their substitution is practically universal.^ 242. Method of Determining the Dimensions of a Tree Contain- ing the Average Board-foot Volume. Another use of sample trees is in connection with the determination of the age and growth of stands rather than to determine their volume. For this purpose, the volume of the stand is first found from volume tables and the average tree then determined. The volume sought is that of a tree which when multi- plied by the number of trees on the plot, will give the total volume of the plot in the unit of volume which was used in estimating. 1 A recent test, 1920, by J. Nelson Spaeth, Harvard Forest School, in second- growth hardwoods, in which mean sample trees for each 3-inch diameter group were measured, gave the following comparison of accuracy with the use of a standard volume table, although the latter was for but one species, red maple, comprising but 15 per cent of the stand : Method Yields per ^ acre. Cords Error. Per cent Actual volume cut 5.725 5.772 5.935 Standard volume table +1.70 Mean sample tree method -f-3.84 The refinements of these methods, known as Draught's, Urich's and Hartig's Methods, are set forth in Graves' Mensuration, pp. 224-242. For application to American problems that of the Mean Sample Tree is probably sufficient. 312 IMPROVING THE ACCURACY OF TIMBER ESTIMATES Wlien cubic volume is used the average tree will not be the same in diameter as when the board-foot unit is employed. The explanation for this difference is that the volume sought is a weighted average of the merchantable contents of all of the trees on the plot. Trees of different diameters do not have the same weight in this average when measured for board feet as when measured for cubic contents. The tree containing the average board-foot volume will be larger than the other. The smaller trees in the stand when measured in board feet are more immature than they are for cubic feet and the merchantable portion of the stand actually includes a lesser proportion of the whole. In stands which are not of even age, this merchantable portion would exclude many of the younger trees as being umuerchantable although they would be included in the cubic volume, and the average age as well as size of the portion merchantable for board feet is greater than that included in the cubic volume. (The increase in average age of stands due solely to the exclusion of a portion of the stand is a recog- nized fact in European practice.) To determine the size as well as volume of the average tree of a stand, we have two variables, height and diameter, one of which must be fixed or eliminated before the other can be determined. The first step is, therefore, to determine the average height of trees of each diam- eter by a height curve (§ 209). The average tree can then have but a single height and diameter and these dimensions may be found from a curve of volume based on diameter for the plot. This curve may be taken from a standard volume based on diam- eter and height (§ 143) by selecting the volumes corresponding to the average heights for each diameter interpolated if necessary to the nearest foot. At only one point on this curve will the average volume coincide with the diameter. 243. The Measurement of Permanent Sample Plots. The purpose of locating and measm-ing permanent sample plots is to determine the growth of stands. Their original measurement therefore must be made by methods which will permit of an exact scientific comparison of these with subsequent measurements. In this way, not only can the growth of individual trees be determined, but all changes which take place in the forest by decadence and by the operation of natural forces, insects, fungi and cutting and thinning, or other silvicultural measures may be noted. Permanent sample plots should be located on land under perma- nent and stable ownership and should be accessible and easily found for subsequent inspection and for a maximum of protection. The plot should be square or rectangular and marked by permanent corners, plainly labeled. Sample plots should be located in stands having THE MEASUREMENT OF PERMANENT SAMPLE PLOTS 313 uniform conditions and their size should be governed, first, by the possibility of securing this uniformity and second, by the expense of measurement which limits the size of the plot. Third, wherever possible, there should be a control strip of exactly similar timber sur- rounding the plot on all four sides in order to eliminate the influence of different conditions of density or site around the borders of the plot. The merchantable timber on these plots is measured as follows: Tree Number. Each tree should be permanently numbered either by white paint or by attaching a metal tag to the tree with a copper nail. D.B.H. The point at D.B.H. is measured and spotted with white paint or by the position of the tag. The D.B.H. is measured with a diameter tape. Crown Class. The crown class is one of the following: a: = trees standing alone; d = dominant; c = co-dominant; i = intermediate ; s = over-topped, suppressed. Height. The height is measured to the nearest even foot with a standard hypsometer. The Klaussner principle, which gives one measurement, is preferred.^ Forms are used which provide, for each tree, five vertical columns in which to record the original and four subsequent measurements which are taken at either 5- or 10-year intervals. The trees on such plots are usually numbered and measured indi- vidually down to 4 inches, although in some instances 2 inches is adopted as the basis for individual tree records. Immature timber below these sizes usually calls for smaller plots which are sometimes laid out as subdivisions of a larger permanent plot. The sizes of these plots are in proportion to the intensive ness of the problem and the age of the tunber. For determining the conditions which affect germination, plots from "10 to 20 feet square are large enough. On these plots every seedling is counted and sometimes each is marked by inserting a pin on which a tag can be attached. In this way the mortality and survival of the seedlings can be later ascertained. For the study of the development of reproduction, larger plots, up to 1 acre in size, are required. On such plots there is no effort to keep 1 Some New Aspects Respecting the Use of the Forest Service Hypsometer, Herman Krauch. Jom-nal of Forestry, Vol. XVI, No. 7, p. 772. Comparative Tests of the Klaussner and Forest Service Hypsometer, D. K. Noyes, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 417. 314 IMPROVING THE ACCURACY OF TIMBER ESTIMATES a history of each individual tree, but the total number of trees in each class is recorded in height classes as follows: Overtopped =|' in height; i' = 2' in height; 2' = 4' in height; 4'= 1" in diameter. Free, same classes. By inch classes, 1, 2 and 3 inches. In these inch classes the trees are recorded in five crown classes: x, d, c, i, and s previously indicated. References " Average Log " Cruise, W. J. Ward, Forestry Quarterly, Vol. V, 1907, p. 268. Errors in Estimating Timber, Louis Margolin, Forestry Quarterly, Vol. XII, 1914, p. 167. A Method of Timber Estimating, Clyde Leavitt, Forestry Quarterly, Vol. II, 1904, p. 161. Forest Mapping and Timber Estimating as Developed in Maryland, F. W. Besley, Proc. Soc. Am. Foresters, Vol. IV, 1909, p. 196. An Efficient System for Computing Timber Estimates, C. E. Dunstan, C. R. Gaffey, Forestry Quarterly, Vol. XIV, 1916, p. 1. Timber Estimating in the Southern Appalachians, R. C. Hall, Journal of Forestry, Vol. XV, 1917, p. 311. Some Problems in Appalachian Timber Appraisal, W. W. Ashe, Journal of Forestry, Vol. XV, 1917, p. 322. Determining the Quality of Standing Timber, Swift Berry, Journal of Forestry, Vol. XV, 1917, p. 438. Reviews Error of Strip Survey (Sweden), Journal of Forestry, Vol. XVI, 1918, p. 938. Estimating for Yield Regulation, Schubert, Forestry Quarterly, Vol. XIII, 1915, p. 399. European Methods of Estimating Compared for Accuracy, Forestry Quarterly, Vol. XIV, 1916, p. 521. Volume Tables and Felling Results, Forestry Quarterly, Vol. IX, 1911, p. 632. Results of Errors in Measuring, Schiffel, Forestry Quarterly, Vol. IX, 1911, p. 628. Methods of Estimating Compared, Prof. Zoltan Fekete (Hungary), Forestry Quar- terly, Vol. XIV, 1916, p. 521. A New Method of Cubing Standing Timber (Hungary), Forestry Quarterly, Vol. XII, 1914, p. 474. PART III THE GROWTH OF TIMBER CHAPTER XXII PRINCIPLES UNDERLYING THE STUDY OF GROWTH 244. Purpose and Character of Growth Studies. The growth of timber is studied in order to determine the rate of annual production of wood as a crop on forest land. The yield of farm products is annual and is measured at harvest. The essential difference between farm and wood crops is that the period required to produce the latter is many- years in extent, and due to this fact forest land is not the only capital involved in crop production. The growth which the trees lay on annually becomes in turn part of the capital to which future growth is added in the same manner as interest which is added to a savings account. This increase in total volume of a stand of timber does not continue indefinitely, but only up to a certain age, which marks the culmination of growth of the stand, from which time the losses occurring in the stand more than counterbalance growth, and its volume and value diminish. Forest crops therefore mature as do annual crops and one of the pur- poses of growth study is to determine the period required for maturity. The basic facts to be determined in the study of growth are, first, the total yield of stands in terms of quantity of products, quality, and money value, for the period required to grow a crop of timber from origin to maturity; second, the average annual rate of growth to which this final yield is equivalent, which is termed the mean annual growth and is comparable to sunple interest on land as capital or to annual crops; third, the actual growth or increase in volume, quality, or value, laid on during definite periods in the growth of the stand. The growth for these short periods is expressed either as current annual growth which is the growth for a single year, -periodic annual growth which is the aver- age annual growth for a short period, or periodic growth which is the 315 316 PRINCIPLES UNDERLYING THE STUDY OF GROWTH total growth for the short period. The length of these periods is com- monly a decade, but may be from 5 to 40 years. The term current annual growth is commonly used in place of the term periodic annual growth, as indicating the average annual growth for a short period instead of the separate growth for a single year, though this use of the term is technically incorrect. Finally, the relation which the increase in volume or growth bears to the volume of the tree or stand on which it is produced may be expressed as growth per cent, and indicates the rate of increase with relation to the wood capital required for its production. This growth per cent may ho comput(Hl for volume alone, for growth in (quality of wood, or for growth in the unit price of the pi-oduct (§ 334). A growth per cent figure is not an index of absolute increase in either volume, quality or price, since it is merely the exioression of a relation between capital and increment existing at a given time. Growth per cent is usually based upon a single year's growth, either current or average for a period. One year's growth is seldom measured, since a decade, or at a minimum, a five-year period is I'equired to eliminate variable factors affecting a single season's growth caused by climatic conditions. Hence periodic annual growth is commonly substituted for current annual growth as a basis for computing growth per c?nt. 245. Relation between Current and Mean Annual Growth. Growth may be studied either for an individual tree or for a stand, exi)ressed in terms of growth per acre. In either case, the current annual growth in volume increases at first slowly and then more rapidly to a maximum, after which it begins to decline and finally ceases with the death of the tree or the beginning of actual decadence of the stand. The sum of the current annual growths laid on foi- the entire period gives the total growth. The total growth or volume divided by the age in years gives the mean annual gi-owth (Fig. 64). The mean annual growth is an average rate of growth representing the total growth or yield at a given age, distributed or spread over this period. The actual productiveness of the forest is in this way compared with annual crops, which basis is otherwise obscured by the varying rate or curve of growth in volume of the trees from decade to decade. The mean annual growth at any given year is this average of past production. Current growth for the year or decade tends to increase constantly up to a given maximum. During this period the volume added each year to the total volume of the stand is greater than the average or mean annual growth up to that year. Hence this average is raised and the curve of mean annual growth increases. But it can- not increase at as rapid a rate as the current growth curve, since the CURRENT AND MEAN ANNUAL GROWTH 317 effect of this increase for the year upon the average increase is spread over all previous years. • When the current annual growth curve reaches its culmination and begins to decline, the successive average or mean annual growth figures for each year still continue to increase in spite of this fact, since the amount of growth added to the stand during the year although less than formerly is still greater than the average or mean. When the current growth for the year finally falls to an amount equal to the average or mean for the entire crop period, the curve of mean annual growth has reached its highest point. During the follow- 180 160 140 §5120 SlOO .5 80 2 .■5 60 >> 40 20 5 10 15 20 25 30 36 40 45 50 55 60 65 70 Age in Yeara Fig. 64. — Current and mean annual growth of a normal stand. Jack Pine Minnesota. r K \/ \ J \ e y \ a/ \ Year Mea of Cul 1 Add ninati al Gr< on of iWth 1 JS>^ -Vu~ ^ H - c M f ^ / -Vi f . ^ "V ing and subsequent years the current growth laid on is less than this mean, hence this average or mean begins to drop, but only to the extent that it is pulled down by the effect of this lesser current annual growth « . , XT- r X- total volume ^t 1 c- tor single years upon the traction, ■. . Hence as before, age m years this mean growth curve falls more slowly than the current growth curve. Unless these stands are cut, losses in the stand will finally exceed the growth, and the current growth curve would then become negative. But until the entire stand is destroyed, the curve of mean annual growth will still be positive. When properly computed on the basis not merely of volume, but of quality and price increment as well, the year of culmination of mean annual growth, rather than the current growth data, indicates the maturity of a stand and the age at which, if cut, it will produce the greatest average yields, when the period of production is taken into account. 318 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 246. The Character of Growth Per Cent. The growth per cent of a tree or stand cannot be compared with the per cent of interest earned annually on a fixed capital, since this growth is not separable from the wood capital on which it is laid, and thus causes this capital or base volume to increase annually. To maintain the same rate of growth per cent on this increasing volume, the amount of the annual growth must continue to increase at a geometric rate. Although the increase in volume of a stand during the period of most rapid current growth for a time does approach a geometric rate when compared to a given or fixed initial volume, yet even here the effect of the constantly and rapidly increasing volume of accumulated ivood capital upon the current annual rate of increase will cause this rate of growth per cent to drop consistently throughout the entire life of a tree or stand. The actual behavior of the growth per cent of a stand is shown by the following table: TABLE XLVII Growth of Jack Pine, Minnesota * Age. Yield per acre. Periodic Mean Periodic annual growth. annual growth. annual growth. Years Cubic feet Cubic feet Cubic feet Per cent 20 160 8 24.20 25 6.50 98 26 14.12 30 1360 142 45 9.52 35 2210 170 63 4.68 2.40 40 2800 118 70 45 3160 72 70 1.56 50 3420 52 68 1.24 55 3640 44 66 1.08 60 3840 40 • 64 0.88 65 4010 34 62 0.80 70 4180 34 60 * From Bui. 820, U. S. Dep. Agr., 1920, Table 10, p. 14. 247. The Law of Diminishing Numbers as Affecting the Growth of Trees and Stands. The growth in volume of individual trees tends at first to follow a rate of geometric increase. Were the diameter growth of trees to remain uniform for a long period, a condition characteristic of many species, notably white and sugar pine, the resultant area and volume growth would increase at a ratio similar to that of D^, rather than D (§ 270). This rate of volume growth is strengthened by height growth. With maturity, the height growth of trees falls to insignificant proportions and the diameter growth of many species falls off to a marked extent. The result is a flattening out of the curve of volume growth, LAW OF DIMINISHING NUMBERS 319 which would otherwise continue to ascend sharply. This influence of age and maturity upon individual trees which survive is due to loss of vitality, but the same effect is observed in all the remaining trees which are suppressed during the growth of the stand and ultimately die because the space needed for their normal expansion is appropriated by more vigorous trees. A forest or stand represents an area of land stocked with trees. The number of trees which can grow and thrive upon the acre is in inverse ratio to the size of crown spread- and space required by the individual tree. As trees increase in size their numbers will be reduced. The enormous number of seedlings which may spring up on an acre is merely a guarantee that a few will survive to maturity. The curve of diminishing numbers which is characteristic of all species and classes of timber, drops very rapidly in the first few years, and more gradually later on. Numbers diminish most rapidly during the period of rapid height growth and crown expansion. When trees have reached their mature heights, their numbers have been re- duced to a point where the further diminution is a much slower process. The cause of reduction is at first failure to survive the juvenile period because of un- favorable climatic or soil factors and competition with other vegetation, followed by suppression due to the competition of older trees or of trees of the same age which have attained dominance by some advantage at the start. The crown is restricted in size and spread, is finally overtopped, and the tree dies. This process is accompanied by a change in the rate of diameter growth for the trees whose crowns and growing space are restricted in the struggle. Consequently the dominant trees maintain at all times the most rapid rate of diameter and volume growth, while others which at a given period have not yet lost their dominance and still show a rapid rate of growth, will later on, with the closing of the crowns and crowding of the tree, show a falling off in growth, sometimes quite sudden in character. The prediction of the future growth of any single tree is therefore impossible without knowing whether the tree will main- 2000 ^1750 1^1500 |l250 t!iooo o 1 750 i 500 Z 250 \ \ s \ \ \ \ ■\ ^ 1 - 10 20 30 40 50 60 70 Age, years 80 90 100 Fig. 65. — Number of trees per acre at dif- ferent ages in fully stocked stands of white pine. From Table XLVIII. 320 PRINCIPLES UNDERLYING THE STUDY OF GROWTH tain its position in the stand and subdue its competitors. The net growth on an acre is the sum of the growth of the surviving trees. At any given period or year in the hfe of a stand, the number of trees is considerably less than were present and living at any previous period or decade, and is considerably greater than the number which will be alive at any given period or decade in the future. This loss in numbers, accompanied by rapidly lessening rates of growth of a portion of the surviving trees, plus the normal growth of the remainder, produces the net result or increase in the stand for the period, and any method of study of growth which does not take this natural loss and change into account will be inefTectual in predicting or measuring the growth of forests or stands. 248. Yields, Definition and Purpose of Study. The past growth of the surviving portion of stands is represented by their present volume, the measurement of which is dealt with in Part II. This present volume represents the yield of the area, provided nothing has pre- viously been removed as thinnings or otherwise. But without a knowl- edge of the period required to produce this volume, the word yield is meaningless as it cannot be expressed in terms of the rate of produc- tion per year or mean annual growth. An estimate of standing timber is merely a statement of the volume at present found on the area. A yield, on the other hand, is a statement of the volumes produced on the area within a definite period of tittie. If the total volume is to be expressed as a yield, then the total age of the stand must also be known. If the yield for a shorter period, such as a decade, is to be stated, then only that portion of the volume of the standing timber must be shown as was laid on during this period. Otherwise, the rate of growth per year is not indicated. The growth of forests is studied primarily for the purpose of pre- dicting future growth on forest land. On the basis of past records of growth of trees and stands as shown by measurements of present attained volumes and of age, predictions can be made as to the future growth of these and of similar stands. This application or prediction may be made in one of two ways: 1. B}^ projecting the rate of growth of an existing stand into the future. This is done either by assuming that the rate shown in the immediate past will continue imchanged in the immediate future, or else that this rate will change and that this tendency of future growth may be predicted by the shape of the past growth curve. Of these two assumptions the second is apparently the more accurate, but in neither case is it possible to predict the growth for more than a short period. 2. Some better method of prediction is required to cover longer YIELD TABLES 321 periods and to determine the probable yield of crops of timber, the production of which is the purpose of forestry. This is accomplished by the second general method of prediction which rests on the principle of comparison. The past growth of existing stands is taken as an indi- cation of the expected future growth of other younger stands whose prediction is desired for a similar period. It is assumed that similar stands will grow in a similar manner. The task consists of demon- strating the relation between the stands whose past growth is measured and those whose future growth is sought. 249. Yield Tables. The most practical and useful expression of growth is a yield table which shows the yields per acre for even-aged stands at different ages by five- or ten-year periods separated into different qualities of site. An example of such a yield table is shown below : TABLE XLVIII Yield Table for White Pine * Quahty II f Average Diameter Number Basal Total Yield height of breast- high of of trees area per Age. dominant average per acre trees. tree. acre Cubic feet Board feet Years Feet . Inches Square feet 10 6.0 1.4 2015 20 650 15 12.0 2.2 1834 50 1,150 20 19.5 3.2 1626 90 1,750 25 28.0 4.1 1420 131 2,420 5,400 30 36.5 •5.1 1192 169 3,250 9,600 35 44.5 6.1 950 193 4,180 15,900 40 51.5 7 1 760 209 5,130 23,500 45 58.0 8.0 633 221 6,100 30,600 50 64.0 8.9 537 232 7,000 36,600 55 69.5 9.8 460 241 7,800 42,000 60 74.5 10.7 397 248 8,500 46,900 65 79.0 11.6 348 255 9,200 51,600 70 83.0 12.4 311 261 9,840 56,100 75 86.5 13.3 277 267 10,400 60,200 80 90.0 14.1 251 272 10,930 64,000 85 93.0 14.9 229 277 11,400 67,500 90 95.5 15.7 210 282 11,850 70,900 95 98.0 16.4 195 286 12,250 74,000 100 100.0 17.1 182 290 12,630 77,000 * Taken from Tables 4 and 6 in " White Pine under Forest Management," U. S. Dept. Agr. Bui. 13, Washington, 1914, pp. 22 and 23. t Similar tables are prepared for Qualities I and III. 322 PRINCIPLES UNDERLYING THE STUDY OF GROWTH From the above table, the periodic growth for separate five-year periods may easily be obtained by subtracting the volume at one age from that of the succeeding period. 250. The Application of Yield Tables in Predicting Yields. An example of the prediction of volume growth in existing stands of timber, on the basis of periodic growth by decades is given in the following table which shows the present yield of timber over 10 inches and the future yield which may be realized upon the timber left standing below this diameter limit, and not shown in the table. TABLE XLIX Yield per Acre of Spruce Cutting to Various Diameter Limits * Based on stands containing approximately 5000 feet B.M. of timber 10 inches and over in D.B.II. per acre Am't Second Cut Second Cut Second Cut of first after Ten AFTER Twen- after Thir- cut. Years ty Years ty Years Interval required between Num- Num- Num- equal ber of ber of ber of cuts Board mer- Board mer- Board mer- Board in feet chant- able trees feet chant- able trees feet chant- able trees feet years Cutting to a 10-inch limit 5213 7.3 365 16.2 1087 26.8 2483 43 Cutting to a 12-inch limit 4341 14.3 1208 21.6 2325 30.5 4109 32 Cutting to a 14-inch limit 3382 10.3 1470 16.8 3044 40.8 6351 21 * Compiled from Yield Tables in " Practical Forestry in the Adirondacks," Bui. 26, Division of Forestry, U. S. Dept. Agr., 1899, pp. S3 and 84. To understand the use or application of a yield table in predicting growth, it must be realized that the stand or rate of growth upon a given acre or tract will seldom if ever exactly agree with that shown in a yield table even when these yields are separated by qualities into 3, 4 or 5 classes of site. In the case of bare land or very young timber, this probable difference may be ignored, the site regarded as equivalent to one of the site classes given and the yield predicted as if it would coincide with that of the table. But for most stands which have already reached a considerable age and the prediction of whose further growth is desired, a comparison with the yield table should give a more exact prediction of the growth of the stand in question. The yield table in PREDICTION OF GROWTH 323 this case, instead of predicting exact future growth, is used as a standard to express the relative increase or decrease in the yield or stand per acre. The yields may be plotted and will form curves of growth in volume per acre. The yield of any stand whose present volume and age are known represents a definite per cent of some existing yield from this table. The growth of this stand may be predicted by using the same per cent of the values in the table for the future. In Fig. G6 the present yield of a plot of white pine of fifty years is indicated and the basis of prediction for its future yield is shown. This percentage relation based upon standard yield tables is exten- sively applied in forestry to obtain the actual yields of large forest L0.O00 9,000 « 8,000 "!? 7,000 ,000 I* o 13 1, ,000 ,000 ,000 ,000 ,000 ^ QualiyI ^ ^.. .--'' < Quali ,., / y *1-^ .J / / y ^j '-^ Quali ylll / / y ^ /] /) iy^ A / / Plot X at 60 92 !i of Qual The yieia at years yields ty I standar 65 years is d. // 7 predicted as standard at For Plot o 92^ <^f the that age. Jie reliction is // 10b 5t 10 ye of Qu. rs lity i: I at / 25 30 35 40 45 50 55 60 Age in Years 65 Fig. 66. — Method of predicting yields of specific stands by comparison with standard curves of yield for different qualities of site. White Pine, Mass. areas. It is the basic idea underlying the prediction of growth by the method of comparison. 251. Prediction of Growth by Projecting the Past Growth of Trees into the Future. By either of these methods, comparison or projec- tion, it is assumed that no records exist of the past condition of the stands whose growth is to be found. Their present volume, and the age and past growth in diameter, height and volume oj the trees now standing can be studied, but there is no reliable indication of the number of trees lost during the past period, though evidences remain for a time in the form of dead and down trees.^ 1 The writer once noticed in a densely stocked stand, the stems of hundreds of small lodgepole pine which had fallen across a tamarack log and been preserved from decay, when all trace of similar dead trees on the forest floor had disappeared. 324 PRINCIPLES UNDERLYING THE STUDY OF GROWTH In using the past growth of a stand on which to base the prediction of its future growth, these records of past growth of the Hving trees in diameter, height and volume are the only data available. This prediction is based on one of two assumptions, either that the growth for a future period will continue at the sayne rate as shown for a past period, or that this future growth will be at a different rate, either increas- ing or decreasing, and that the amount of this change may be deter- mined by a study of past growth. In the use of either of these methods to predict the growth of trees, the method may be applied either to the volume of the tree or to its diameter and height instead. If a volume analysis is made for two or more past decades, it may be assumed either that this rate of volume growth will continue unchanged, an assumption which is practically never correct, or that the curve of volume growth which may be plotted from past volumes can be prolonged to indicate the growth of the next decade. But the method more commonly employed is to substitute a study of diameter and height growth for volume analysis. If future diameter growth is assumed to be at the rate shown in the past decade, future volume growth will increase (§ 270). If the past growth in diameter is plotted, and a curve projected, the future diameter so obtained is the basis of the predictetl growth in volume. 252. The Effect of Losses versus Thinnings upon Yields. The first conception in the study of growth is apt to be that it consists chiefly of measuring the growth in diameter, height and volume of individual trees. Although it is true that growth per acre is based primarily upon the rate of growth of the individual trees which make up the stand and that according as this rate of tree growth is rapid or slow, the yield per acre will be large or small, yet the total growth per acre, which is the result desired in all growth studies, is the product of the growth of individual trees and the number of trees surviving to the end of a future period plus such growth as may take place on trees which die and are removed during the period. The death of a certain number of trees in the stand during the period will have this effect, that if these trees can be removed as thinnings, their volume at the beginning of the period, augmented slightly by growth which takes place in them before they die, is part of the yield for the period, but does not appear in the volume of the standing timber alive at its end. If these trees cannot be harvested, their total volume as originally measured will disappear from the live stand, and constitute a negative growth or loss which must be deducted from the groivth on the surviving trees before the actual volume of the stand at the end of the period can be correctly ascertained from its volume at the beginning. AGE IN EVEN-AGED VERSUS MANY-AGED STANDS 325 This problem may be illustrated as follows: A stand of pine has now 10,000 board feet per acre. The growth for ten years upon the trees which will survive will be 4000 board feet. The trees which will die in ten years have now a volume of 1500 board feet. This means, first, that the growth of 4000 board feet is actually put upon a present volume of 8500 board feet; second, that the remaining 1500 board feet must either be included in or deducted from the final yield, on the basis of whether it is actually salvaged or not. There may have been some growth on these trees, but this can be neglected. On the assump- tion that no cutting of thinnings is possible, the net yield on this acre at the end of the decade is 12,500 board feet. If thinnings are harvested, the yield is 14,000 board feet. Had the growth prediction been attempted by measuring the growth of indi- vidual trees, those representing the 1500 board feet would have to be excluded from the calculation of total growth in either case. Unless salvaged, they represent an actual negative growth reducing the net gain by 1500 board feet. Unless it is possible to guess just how many and which trees are going to die, not only the volume, but the growth for ten years on some of these trees will probably be erroneously, included, instead of being subtracted from the predicted total yield in ten years. The possible error in subtracting either too few or too many trees is very large since the size of the error is doubled for stands when thinnings are impractical. It is obvious that a method depending instead on direct measurement of the result at the end of the period on older stands and the comparison of such measurements with similar younger stands furnishes a. safer basis of growth predictions on these younger stands for any considerable period than efforts to project into the next period the rate of growth of the trees now standing. Where stands are under intensive management, the trees which will die are thinned out, probably at the beginning of the period, and utilized. The loss for the succeeding ten-year period is then exceedingly small unless accidental im*oads occur from wind, insects or other destruc- tive agencies not anticipated. It is therefore safer to predict growth for short periods on stands which have been under management and have been thinned than it is on stands where thinnings and utilization of the dying material is impossible. 253. The Factor of Age in Even-aged versus Many-aged Stands. Where stands are measured as a unit to determine the production per acre, three factors are needed: first, the present volume of the stand; second, its average age or the time which it took to produce this volume; third, the area which it occupies. The age of the stand as a whole is desired. If the stand is even-aged it is sufficient to determine merely the age of one of the trees adequately to measure the period of pro- duction and the rate per year. This can be done by counting the annual rings of growth without any measurement whatever, on the assumption that the species has formed but one annual ring per year. This premise does not always hold good, since with certain species in certain localities, 326 PRINCIPLES UNDERLYING THE STUDY OF GROWTH false rings may be formed, giving two rings per season (§ 256). Pro- vided age can be determined, the study of diameter, height and volume growth of individual trees is entirely unnecessaiy for even-aged stands, as a means of determining the yields per acre. But where stands are composed of trees of different ages on the same area, it becomes practically impossible to determine the average age of the stand by any such direct method. Within certain limits, that is, if the ages of the trees composing the stand do not vary too greatly, it is possible to determine an age which may be accepted as the average period required to produce the present volume. Where the diversity of age is so great that this is impossible, it is necessary to shift the basis of age determination from the mere counting of the rings to a determination of the age of trees of a given size or diameter. To determine ages, trees must be cut down or the center reached by borings or choppings. While possible on one or two trees, it becomes out of the question to test every tree in this manner without cutting down the stand. Diameter, on the other hand, can be readily measured. For stands of mixed ages, therefore, two methods are possible. By the first, the average diameter of the trees in the stand is found, and the age of a tree of this size is determined and is assumed to indicate the average age of the stand. By the second, no attempt is made to determine the age of the stand, but instead the growth may be studied for trees of given diameters, and for a short current period, past and future. Either method requires the measurement of the diameter growth of trees to determine the number of years or period which is required to produce trees of given sizes or to grow 1 inch in diameter. 254. The Tree or Stem Analysis and the Limitations of its Use. The volume growth of an individual tree may be analyzed with almost absolute accuracy by cross-sectioning the bole and measuring the width of the annual rings at different sections by decades. This is termed stem analysis, or tree analysis. The accuracy of these results for a single tree is apt to create a false impression in the minds of investigators as to the value of the figures thus obtained. To what use will volume or total tree analyses of growth of trees be put? What question will they answer? Will they predict the growth per acre of stands or the rate of growth per year on an acre of land? The cost of a tree analysis is excessive compared with the direct measurements of yields and total age or even the measurement of diameter growth on the stump. The number of trees which may be analyzed is therefore limited. How shall these trees be selected? It has been seen in the study of volume tables that trees vary quite extensively in form. To get average growth we must be sure of obtaining average form. Average form is best obtained by averaging hundreds of trees as is done in the prepa- CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 327 ration of volume tables, but the few trees analyzed for growth may- be either cylindrical or neiloidal in form. We therefore may have a perfect record of the past growth of certain selected trees which vary in form and volume at least 10 per cent from the average desired. Even if this difficulty can be overcome by careful selection of trees of average form quotient, and a few of these average trees analyzed for past growth, how are these past results to be applied in predicting future growth? It is evident that the growth of individual trees is only a part of the problem, for the average tree in a well-stocked stand at a given age does not remain the average tree for future periods and was not the average tree at any period in the past. The trees which die in a stand are naturally the smaller, more suppressed specimens with the smallest diameters. In the lapse of a ten-year period, the loss of a number of trees from the lower diameter classes will raise the average diameter and volume of the remaining trees so that the tree which is now the average is in ten years dropped into a class below the average. There is but one way of even approximating the growth of a stand in the future by means of the analysis of volume growth of individual trees. If the number of trees which will probably survive to a given age can be predicted (which can best be ascertained by the method of comparison and yield tables), the selection of this number from a younger stand, taking trees wholly in the dominant class, will indicate the character of tree which must be cut and measured to determine the growth for the future. Yet even here it is better to take a tree which is fully mature and shows the growth for the entire period, in which case the stand, rather than the tree, is the better unit. 255. Relative Utility of Different Classes of Growth Data, and Chart of Growth Studies. To sum up these principles: past growth is measured in order to predict future growth. Growth on an area and not the growth of single trees is wanted. The three essentials of growth are volume, time and area. For even-aged stands the time element is the total age and may be determined by counting rings on one or two sample trees. This requires a minimum of investigation in addition to volume measurements. Diameter growth of trees comes next in importance and is used when size must be depended upon to determine age either for the total period or for shorter current periods of growth when diameter is sub- stituted for age. Height growth of trees comes third in importance since it is used to indicate site quality (§ 296). It may also be used together with diameter growth, to predict the volume growth of trees by a method much shorter than volume analysis (§ 288). 328 PRINCIPLES UNDERLYING THE STUDY OF GROWTH Volume-growth analysis of individual trees, although apparently the most accurate and scientific basis of growth, is in reality the least important and most inefficient when expense is compared with results. It is invaluable to determine the laws of tree growth and the changes which may take place in the form of individual trees as the result of changed conditions, as for instance, on cutover lands, and as a pre- caution against accepting general figures based on volume tables and other short methods of growth study. But ordinarily, even where volume of trees is desired, it will be obtained from diameter and height growth supplemented by use of the form quotient rather than from the stem analyses of trees. Many thousands of stem analyses have been made in the past whose results were either not worked up at all or since compilation have reposed in the archives of Government and States while investigators vainly sought an answer to the pressing problems as to what was the actual rate of growth per year on national, state and private forests. The best possible basis for growth predictions is the actual records of the growth in successive periods of specific forest stands whose history is known and whose conditions of management are fixed. The establishment of sample areas which are measured successively by ten-year periods will give a firm basis for growth predictions superior either to the method of comparison, based on past growth of older Chart of Purpose of growth study § 244 Basis Field measurements I Normal or index yields Productive capacity of different qualities of forest per acre for even-aged land— § 303 II Prediction of For even-aged stands f u t u r e — §§ 256-262 growth and yi e 1 d s on natural For total age forest areas or long per- —§§247- iods — 248 §§249-250 stands 1. Pure stands— § 304 1. Diameters B.H.— § 309 2. Mixed stands — § 314 2. Heights, total 3. Count of annual rings on average trees — §262 Comparison of stands 1. Timber estimate sepa- with normal yields at rated by age classes — same age — § 301 § 344 Counts of annual rings on average trees — § 262 CLASSES OF GROWTH DATA, CHART GRQ^'TH STUDIES 329 stands, or to the effort to predict the growth of stands from that of the trees which they contain. As a result of similar actual records of production the working plans for some European forests dispose of the subject of growth quickly, stating substantially that the growth in this class of forest is known, from past records covering (perhaps) 200 years, to be about so much. In the chart, on pages 328-333, eleven main lines of investigation of growth are listed, as a guide to the discussions in the following chap- ters. The object of a study should first be understood, and the con- dition of the stands to which it is to be applied, as indicated in the three columns under " Purpose of Growth Study." In the column under " Basis " the principles on which the solution of the problem depends are outlined. The remaining columns are seK-explanatory. Column 6 shows the steps by which the study can be applied to large areas of forest land, thus secur- ing the data for which the preceding steps are merely preliminary. By using this chart as a guide, and consulting the references to discussions of principles and methods, under each step, one may hold the purpose of growth studies clearly in mind and choose the best method of accomplishing the desired object. The relative importance and relial)ility of the methods given are indicated by the quality of type used in the table. rRowTH Studies Offif )rds Final data olitained Application to forest areas Data derived from the investigation Area of sample plots- § 308 Volumes of trees (vol ume tables) — § 131 Age of sample trees- § 255, § 257 Height of dominant trees— § 310, § 311, §312 1. Volume per acre — § 306 2. Age of stands — § 256 3. Height of stands Classification of site qual- ities—! 294, § 345 1. On basis of height growth — §§ 296-310 2. On basis of volume growth—! 295, § 312 1. Mean annual growth —§245 2. Number of trees per acre 3. Basal area per acre Maturity of stands — § 244 (rotation) 5. Maximum yields Area of stand or age class Volumes of trees (vol- ume tables )§ 131 Age of sample trees — § 256, § 257 Average volume per acre for age class Reduction per cent or relative volume de- rived from this com- parison — § 317 Empirical yield table based on this reduc- tion— §§ 304 316 j Empirical yield table to predict future growth on each age class Correction for i n - fluence of number of trees per acre at differ- ent ages— §§ 301-317 Future yields based on actual stocking — § 301, § 343 Losses due to natural agencies — § 293 Gains possible from protection and silvi- culture 330 PRINCIPLES UNDERLYING THE STUDY OF GROWTH Chart of Growth Purpose of growth study Predict! on of future growth and yields on natural for- est areas — §§ 247-248 III For large age groups- § 318, § 321 For total age or long per- iods — §§ 249-250 1. Segregation of large age groups — § 320 2. Comparison of group with normal yields at average age — § 301 IV For many-aged stands § 298. by diameter groups — § 323 For many-aged stands based on crown spacers 298 On thinned areas — § 326 Basis 1. Diameter groups substl tuted for age classes — § 270 . Comparison of diameter group with normal yields at Indicated age — § 301 1. Space required for develop ment of Individual trees— 5 300 2. Normal number of trees per acre at different ages — § 247 Same as Va Field measurements 1. Diameters B.H. 2. Heights, average based on diameter 3. Growth in diameter at stump, based on age of trees— §§ 265-269, §320 1 . Diameters B.H. Heights Counts of annual rings on trees of each diameter class — § 276 1. Diameters of crowns based on D.B.H.— § 324 2. Growth In diameter at stump based on age of trees — §§ 275-279 3. Growth In height based on age— § 284 Same as Va Mear-.ure only dominant trees — § 263 VI For even-aged stands — § 335 Same as II Same as II Predic tio n o f future growth and yields on natural for- est areas — §§ 247-248 YII For manv-aged stands §253, §299 Past growth of existing trees — § 336 For short periods or current growth — §§ 251-252 Diameters B.H. by crown classes Heights, average based on diameter 3. Growth in diameter at B.H. or stump — for given period of years — § 278 — separated into 2 or 3 periods of five to ten years — § 279 CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 331 Studies — Continued Office records Final data obtained Application to forest areas Data derived from the investigation 1. Total number of mer- chantable trees 2. Volumes of trees (vol- ume tables) (average, on diameter) 3. Age as basis of each group, from normal yield table 4. Diameter of tree of in- dicated age — § 275 5. Volume of tree of indi cated diameter — § 278 6. Number of trees in each age group — § 321 1. Areas occupied by each of two age groups —§319 2. Volumes in each age group — § 321 3. Reduction per cent- §317 4. Empirical yield table —§316 Empirical yield table applied to area and age of each group — § 322 and § 346 Correction by segrega- tion of areas occu- pied by immature age classes— §§ 341 -348, §349 Same as for II— § 301 1. stand table by diameter classes — § 188 2. Volumes of trees 3. Average ags of trees of given diameters— § 276, § 323 1. Areas occupied by each diameter group — § 319 2. Volumes In each group 3. Reduction per cent — § 317 4. Empirical yield table — §316 1. Empirical yield table ap piled to area of each diam- eter group 2. Correction by segregation of areas occupied by Immature age classes — § 341, § 348. § 350 Results only approximate due to substitution of diameter for age 1. Space occupied by circular crowns and resulting num ber per acre — § 324 2. Relation between crown spread and diameter — § 324 3. Height and volume of trees of each diameter — § 288 4. Average diameter of trees at each age — § 275 Artificial normal yield table based on number and size of trees at each age — § 324 Reduction per cent for appllca tlon of yield table deter mined by comparison of numbers of trees of each diameter on area with num- ber per acre In table — § 325 Substitute for yields based on even-aged stands when latter cannot be obtained Same as Va Same as Va Same as Va Means of predicting yields of thinned stands Most accurate basis for current growth for short periods, on even- aged stands — § 327 Growth per cent Same "s II Same as II Same as II 1. Stand table by diam eter classes — § 188 2. Growth in diameter and height of trees by diametter classes for past period — § 277 3. Volumes of trees now and at end of period. From volume tables — § 2SS. (Stem analyses only as a check on accuracy of 2 and 3) — §254 Growth in volume of trees for future period 2. Number and character of trees which will die during period — § 257 3. Net volume growth for stand— § 252 As applied to trees and stands 1. Future growth of trees by comparison with growth attained by other larger trees for- merly of same diame- ter— § 278 2. By extending into fu ture the past growth in diameter on trees whose future growth is sought — by assuming it to equal past growth — by prolonging curve based on past peri- odic diameter growth— § 279 General method for cur- rent growth of stands of any character of stocking, form or ages, and mixture of species — §§ 24,5-342 Growth per cent (§ 246) for trees or stands — This cannot in turn be substituted for growth measurements except on similar stands— §§ 331-333 For stands whose age classes cannot be deter- mined 332 PRINCIPLES UNDERLYING THE STUDY OF GROWTH Chart of Growth Purpose of growth study Basis Field measurements 1 — for last inch or half- For many-aged stands Past growth of existing inch of radius — Prediction § 253, § 299 trees— § 336 §278 of future For short 4. Growth in height growth and periods o r — by cutting back tip yields on current for required pe- natural for- growth — riod— § 294 est areas — §§ 251-252 — by substitution of §§ 247-248 relation of height to diameter — § 285 VIII Past growth of trees for 1, 2 and 4 same as VII For short For many-aged stands period since cutting, on 3. Growjth in diameter periods — —§254 formerly cut-over areas preferably at B.H.: for §336 — § 286, § 336 period since previous cutting. May be sepa- rated into five- or ten- year periods — §§ 278- Prediction oi 280 future growth and yields o n e u t V e r areas on For long periods IX 1. Proportion of total area re- Same as III or IV— 5 320 residual — § 338 For even-aged, or maining stocked after cut- stands — §2S0 large age groups or diameter groups ting, based on density equal to empirical yield tables for — § 339 forest previous to cutting 2. Residual area assumed to be clear cut 3. Growth predicted for stocked area by empirical yield table —see II— § 316 X Permanent sample plots 1. Diameters B.H. with Historical record of growth per acre — § 326 remeasured at stated intervals — § 243 diameter tape — § 190 2. Total heights, from fixed stations — § 199 3. Crown classes and condition 4. Plot description 5. Tree fags and perma- nent boundary monu- ments XI Relation between diam- 1. Diameters B.H. Effect of numerical density of stocking, and of thin- eter growth, crown 2. Heights nings on growth of individual trees and on stand — classes and number of 3. Growth in diameter § 270, § 273, § 274 trees per acre, from based on age, but rings sample plots — § 300 counted inward, per- mitting study of cur- rent growth on same trees— §§ 265-269 CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 333 Studies — Continued Office records Final data obtained Application to forest areas Data derived from the investigation 4. Tally of trees with suppressed crowns or those apt to die As applied to forest areas 1. Stand table by diam- eter classes 2. Growth from diam- eter and height growth and volume tables 3. Correction for loss in numbers of trees Source of inaccuracy is in determining mortality per cent, hence cannot be applied to long periods 1, 2, 3 and 4 same as VII 5. Partial stem analyses for current growth in volume on sample trees as check on effect of increased growth at stump — § 290 1. Probable growth in volume of trees left on cut-over areas 2. Proportion of stand showing increased growth — § 337 3. Loss in numbers and net growth in volume Future growth of trees by comparison with growth attained by trees on areas after cut- ting Growth on forest areas 1, 2 and 3 same as VII 4. Per cent of stand showing increased growth — § 337 EfTects of — expansion of areas of crowns and in- creased growing space — c o m p e t i t i o n of species left after cut- ting — degree of severity of cutting on remaining stand Same as III or IV — § 321 1. Areas In each age class lor timber left on cut-over area 2. Volumes In each age class- § 339 Same as III or IV — § 322 Minimum or conservative yields on cut-over areas No Increased growth assumed Conditions would coincide with cutting of even-aged stands Results contrasted with VIII as check on that method of prediction Safe for application to long periods 1. Individual record of : each tree on plot by number, compared for successive measure- ments at five- or ten- year intervals 2. Record of conditions 2. and of external in- fluences Permanent record of changes in volume, number of trees, and dimensions for plot Causes and extent of damage 1. Location of plots with- in control strips on areas showing typical conditions to be studied Current growth, measure- ment of all factors of change in stands under conditions selected — § 340 Yield tables for stands grown under manage- ment. Ultimate solu- tion of all growth prob- lems — § 313 Diameter growth for trees of separate classes, by diameters, and crowns — § 275, § 276, § 277 Effect of spacing or thin ning upon volume growth and upon aver age sizes and quality of individual trees — § 301 1. Stand tables by diam- eter classes 2. Ages of stands. The data are applied inten- sively to individual stands in silviculture Proper spacing for plan- tations Character, and frequency of thinnings Class of material to grow Character of initial natu- ral stocking desired Growth per cent on stand- ing trees— § 330 334 PRINCIPLES UNDERLYING THE STUDY OF GROWTH References Climatic Cycles and Tree Growth, A. E. Douglass, Carnegie Institute Pub. No. 289. Tree Growth and Climate in the United States. K. W. Woodward. Journal of Forestry, Vol. XV, 1917, p. 520. The Climatic Factor as Illustrated in Arid America, Ellsworth Huntington, Carnegie Institution of Washington, D. C, 1914, Chapter XII. Density of Stand and Rate of Growth of Arizona Yellow Pine as Influenced by Climatic Conditions, Forrest Shreve, Journal of Forestry, Vol. XV., 1917, p. 695. CHAPTER XXIII DETERMINING THE AGE OF STANDS 256. Determining the Age of Trees from Annual Rings on the Stump. The age of standing timber can only be determined from the ages of the trees which compose the stands. The age of a tree is the period elapsing from the germination of the seed or origin of the sprout to the present year. A record of the number of years of growth in a tree is made by the formation of the annual rings in which the light spring wood is sharply differentiated in color and texture from the heavier and darker band of summer wood of the year preceding. The count- ing of these annual rings determines the age of the tree. It is not always possible or easy to make this determination. Unless the growth of a tree is marked by annual seasonal changes, there are no annual rings to distinguish. This is true of most species of tropical woods, except those growing in regions marked by an annual cessation of growth due to annual recurrence of dry seasons. In some species of hardwoods there is such a slight difference between the texture of the spring and summer wood that the annual rings can be detected only with difficulty and by the aid of coloring matter and magnifying glass. This is true of such trees as basswood, hard maple and sweet gum. Many trees on dry sites grow so slowly that the annual rings are almost impossible to distinguish except by a glass. In counting rings it is usually necessary to smooth off the surface with a sharp knife or chisel in order to bring out the contrast. Where growth is affected by severe droughts, and sometimes where the trees are defoliated by insect attacks and later acquire new foliage, a false ring may be formed, giving two rings in a single year which would lead to an exaggeration in the age of the tree. This was found to be the case with Rocky Mountain juniper on dry sites. False rings may be detected if sufficient care is used, since they seldom form a complete circle, but are present on only a portion of the circum- ference and are therefore imperfect. The last annual ring of wood is not completed until after the growth for the year is finished. It must be distinguished from the ring of new bark laid down in the same season. The first two or three rings on some seedlings are difficult to distinguish. 335 336 DETERMINING THE AGE OF STANDS The increment borer (§ 277) may be used to determine the age of standing trees at breast height or at any section accessible, provided the diameter is not too great and the position of the core of the tree can be found by the instrument. This method is used with such species as spruce. 257. Correction for Age of Seedling below Stump Height. The number of rings in any cross section of a tree will indicate only the age of the tree at that cross section and not the total age. No rings can be formed at a given height above the ground until the tree reaches that height. The age of each cross section made in sectioning a tree will be less than that of the section below by just the number of years occupied in height growth between the two points. Although the total age of a tree can be determined theoretically bj^ taking a section even with the surface of the ground, this is seldom if ever done. The rings are counted at the stump, which gives the age of the tree minus the time which it took the seedling to reach this height. To get the true age of any tree, seedling ages based on height must be added to ring counts taken at stump heights. By cutting at the ground and counting the rings on a sufficient number of dominant seedlings which are sure to survive and therefore represent the average height growth of mature timber when at this age, a table is constructed showing the relation between the age of seedlings and different stump heights. In rapidly growing trees this makes from one to five years' difference in the total age, but with some species which have a long juvenile period, as much as twenty years may be required for a seedling to grow 2 feet in height. This is true of certain Western conifers. Hardwood sprouts on the other hand attain stump height in the first year. TABLE L Height of Seedlings at Different Ages, Western Yellow Pine, Colfax Co., New Mexico Age. Height. Age. Height. Years Feet Years Feet 1 7 1.7 2 0.5 8 1.9 3 0.7 9 2.2 4 0.9 10 2.4 5 1.1 11 2.7 6 1.4 12 3.0 ♦Forest Tables — Western Yellow Pine. Circular 127, U. S. Forest Service, 1908. ANNUAL WHORLS OF BRANCHES AS AN INDICATION OF AGE 337 The juvenile period for conifer seedlings is, as a rule, longer than that for hardwoods, though there are exceptions. Stump height may be separated into 6-inch height classes for determining the number of years to add for seedling heights to get total age of tree. 258. Annual Whorls of Branches as an Indication of Age. There is another method, of very limited application, for determining the age of standing trees. This is applied to conifers and is confined to those species which form but one whorl of branches per year. Species like jack pine or loblolly pine, which form two or more whorls per year, cannot be judged in this manner. The approximate age of the tree and stand is obtained by counting the number of whorls. This record holds good only when the branches or dead stubs remain visible and when the height growth continues normal. The record is lost if all traces of the lower whorls are obliterated. If this is only for a height of from 5 to 10 feet, the average age of trees of this height may be obtc,ined from a study of seedling heights and used to supplement the remaining count. When the height growth of the tree has reached its maximum, a new whorl of branches is no longer formed annually, but the leader, as well as the branches, extends its growth by prolonging a single shoot. The ages of seedlings of many species may be determined by count- ing whorls of branches, or terminal bud scars if the whorls are not all there. In such cases it is not necessary to cut the seedlings and count rings. The bud scars are distinct for many years on species such as Douglas fir, Alpine fir, and others. 259. Definition of Even-aged versus Many-aged Stands. The age of trees determines the age of stands. But unless it is known that the entire stand originated in a single year, as is the case with sprouts or with some species of conifers, such as jack pine or loblolly pine on burns, there will be a variation in age due to natural seeding for a period of reproduction which may extend to fifteen or twenty years. Stands are termed even-aged if their crowns form practically a single canopy or one-storied forest, which is true when the period of repro- duction does not exceed approximately one-fifth of the rotation or period required to reach full maturity. Where the crown cover of stands of mixed ages varies so greatly that it is composed of different stories, and must be separated into component age classes whose aver- age age is separately distinguished, the stand is termed many-aged or in some cases all-aged. The separation of such stand may be either directly into age groups, or into groups based on size or diameter with a limited range of age, whose average age is sought. 260. Average Age. Definition and Determination. The average age of a group of trees showing a range of ages must be that age which 338 DETERMINING THE AGE OF STANDS indicates or determines the rate of volume production per year at which the stand has grown; therefore, the average age must be a weighted age based on volume. The determination of average age applies only to those stands which fall under the definition of even-aged stands, yet have within the hmits of the group a sufficient range of ages so as to require a further investigation in order to fix the weighted or average age of the group. For many-aged stands, the average age of each age class must be determined separately. For a given age class or even-aged stand as thus defined, the average age is the age which would be required to produce an even-aged stand containing the same volume as that of the uneven-aged stand in ques- tion. The methods possible for determining the weighted average age of the trees comprising the age class usually involve the choice of 1. Treating the entire age class as a single group, or subdividing it into from two to three, usually not over two, sub- groups. 2. Determining the average tree, for the entire class, or sepa- rately for each sub-group. 3. Ascertaining the age of these average trees. 4. Weighting the resultant ages of average trees of sub-groups, to determine the weighted average age of the age class. 261. Determining the Volume and Diameter of Average Trees. Subdivision of a group into two or more sub-groups will be made, if at all, on the basis of diameters, by the diameter group method (§ 251). In determining the average tree for the age class, or for a sub- group, there are two reasons for basing this selection on average volume. In the first place, if these selected trees are to be felled, and their ages taken as indicating that of the stand, the larger trees must be avoided, for in aU probability they are advance growth, several years older than the rest or possibly belonging to an entirely different age class. The smaller trees would also be rejected since they may be late seedlings some years younger than the average, or in extreme cases, so badly suppressed that a certain number of rings may be lacking and the growth difficult to determine. Trees of about average size for the group or stand must then be chosen. Where two or more groups are made, an average tree for each group is separately selected. Volume is the determining factor upon which the weighted average age is to be based, hence the tree whose age is taken to indicate that of the stand must be a tree whose volume is an average of the stand. This principle applies not merely to cubic volume, but to the merchant- able volumes expressed in units of product, such as board feet. Since DETERMINING AGE OF AVERAGE TREES AND STAND 339 the purpose of the investigation is to determine the period which will produce an equal volume of material in an even-aged stand, the product in terms of which this vokuue is measured actually affects the average age (§ 260). For board-foot contents which increases more slowly at first and more rapidly later in the life of an individual tree, the average tree will be larger and older than for cubic contents, since a portion of the stand will be rejected altogether and fall in a younger age group or else will logically receive a smaller weight in the average for determin- ing the equivalent age of an even-aged stand. The first step is therefore to determine the volume of the average tree of the stand or sub-group. It is evident that the inclusion of a large number of trees of the smaller diameters in a large group will pull down the volmne of the average tree and tend to unduly lower its age. The plan of subdividing age classes into smaller diameter groups is chiefly useful in avoiding this tendency to error, and is accomplished by throwing together trees varying but little in size, to obtain the average. It is of advantage therefore to make two or more of these sub-groups where possible. When volume is measured in cubic feet, basal area may be sub- stituted for volume and the diameter of a tree of average basal area determined. To obtain this, the sum of the basal areas of the trees in the group is divided by the number of trees to obtain average basal area. The diameter of a tree of this area is found in Table LXXVIII, Appendix C, p. 490. When measured in board feet, the volume of the average tree is found directly by dividing the total volume of the stand or of the sub- group in board feet by the number of trees. As in case of basal area, the diameter of a tree of this volume is now required if sample trees are to be felled to determine age. For this purpose a local volume table based on diameter is used (§ 142) from which the D.B.H. of a tree of the given volume can be determined to within i^-inch. 262. Determining the Age of Average Trees and of the Stand. The age of these selected trees can then be obtained by felling trees of this diameter. In stands of variable age from two to three trees are pref- erable to one. As a substitute for this method, where it is extremely uncertain that the tree selected wiU have the average age, a table of diameter growth showing the ages of trees of different diameters may be prepared from similar stands in the vicinity. If the average rate of growth thus obtained applies to the stand in question, the age of a tree of the given diameter may be taken from this curve instead of from felled timber. On account of the uncertainty of the correlation between the growth figures obtained in this way and of the age of the stand in question, the method has not been widely used and the felling 340 DETERMINING THE AGE OF STANDS of the test trees or their age determination by borings or chopping^ is the standard practice in determining the age of stands. When the stand is treated as a single group, the average of the ages of the test trees, all of which will be of the same average diameter, is taken as the age of the stand. When two or more sub-groups have been separated, the age of the entire stand must be calculated by weighting the pre- determined ages of the sub-groups, in the proper proportions. The following illustration will bring out the different methods possible in doing this. An " even-aged " stand composed of 30 trees is divided into two groups as follows : Trees Average volume. Board feet Total volume of group. Board feet Average age of trees in group. Years 10 20 500 125 5000 . 2500 100 70 1. If each of these groups occupies an equal area and is given equal weight, the average age may be found by adding the ages of the sample trees and dividing by 2. This gives eighty-five years, and is known as the arithmetical mean sample tree method. This method does not conform to the basic principle of weighted ages sought. 2. When the trees are weighted by number the result is : 10X100 = 1000 20 X 70 = 1400 Total, 2400 -=- 30 = 80 years This overemphasizes the number of trees rather than their volume, hence is unsat- isfactory. 3. Trees are weighted by volume on the principle by which weighted volume averages are always obtained: 100 years X 5000 = 500,000 70 years X2500 = 175,000 Total, 675,000 -=-7500 = 90 years. This method is acceptable. 4. The sum of the mean annual growth for the groups is obtained. The total volume divided by this sum gives the average age. This method is considered by European investigators to be more accurate than the others. As applied: 5000^100 = 50 2500 -^- 70 = 35.7 Total mean annual growth for stand, 85 . 7 7500^85.7 = 87 years. By either method 3 or 4, it is seen that the average age is influenced by volume rather than by area or number of trees. AGE AS AFFECTED BY SUPPRESSION. ECONOMIC AGE 341 263. Age as Affected by Suppression. Economic Age. When stands are comparatively even-aged and the trees composing them liave grown up as dominant individuals, free from suppression, the actual age of such trees is a fair indication of the age which an even-aged stand would require to produce an equal volume. But under this same definition, the age of a tree which has been suppressed in the early period of its life does not indicate the required age but one considerably greater. The correction of the actual ages of suppressed trees to determine the age desired is known as the determination of economic age. What is wanted is the rate of growth of an average dominant tree on the same site as that occupied by the suppressed trees. Where reproduction takes place under a stand either of the same or of a different species, the problem of growth is one of having two crops of timber on the same land at the same time, and the rate of production per acre is the sum of these two successive crops divided by the total period required to produce them both. To isolate the period required for a single crop, we must determine the rate of growth of the crop as if it were in sole possession of the area. A composite growth curve may be built up for average trees by measuring the growth on these trees only down to the point at which they were evidently freed from suppression and substituting from this point on the average growth of seedlings and saplings measured on dominant specimens. For instance, if the first 2 inches of an average tree shows suppression, the average rate up to 2 inches must be taken from other dominant, younger trees, and added to the remaining years to get the total economic age of the tree in question. This factor has been neglected in American growth studies, for the reason that with such species but few attempts have been made to determine total age, investigators being content with ascertaining growth for short period based upon the diameter of the trees. CHAPTER XXIV GROWTH OF TREES IN DIAMETER 264. Purposes of Studying Diameter Growth. One purpose of studying the growth of trees in diameter is to determine the total volume of trees of given ages, or the growth in volume of trees for a short period. The volume of trees is based on D.B.H. and height. The diameter growth must always be correlated with D.B.H. for the trees measured, and height growth is usually required. A second purpose is to determine the dimensions or sizes reached by trees in a given period. 265. The Basis for Determining Diameter Growth for Trees. It is impractical to cut sections at B.H. for growth measurements. Not only is there a needless waste of timber, but the labor of felling and sec- tioning the tree may also be avoided if the measurements are taken at the stump following logging operations. Where current growth for short periods is tested with an increment borer (§ 277) the measure- ment is taken at D.B.H. The growth measurements on stumps require three steps to determine the ages of trees of given D.B.H. outside the bark; namely, 1. Diameter growth on the stvunp. 2. Correction for age of the seedling. 3. Correlation between stump diameter inside bark and D.B.H. outside bark. As diameter increases rapidly at the stump, the lower a stump is cut the greater will be the apparent rate of growth for the tree. Stump height classes differing by 6 inches may be made in growth studies, but this is not often done. Stump heights usually vary with stump diameters in a ratio of from one-third to two-thirds of the diameter, depending on the closeness of utilization. For a given region and standard, the stump heights for given diameters are fairly constant and the average rate of growth is found for stumps of each diameter with all stumji heights averaged together. 266. The Measurement of Diameter Growth on Sections. The section measured must be at right angles with the axis of the bole. In stumps this means a horizontal cross cut. Slanting cross cuts exag- gerate the length of the radius and result in a slight plus error in growth measurements. The procedure is as follows: 312 MEASUREMENT OF DIAMETER GROWTH ON SECTIONS 343 Fig. 67. — Stump sec- tion fifty years old showing eccentric growth, position of the two average radii AB and AC and rot (jn radius AB. Decades of growth are shown. The growth must be measured on radius AC. An average radius is located. Its length must equal just one-half of the average diameter inside bark (§ 25). To determine the average diameter, calipers graduated to yV-inch may be used (§ 189). In all cross sections which are not perfect circles, the lengths of the radii from the pith or center of growth vary more widely than the diameters owing to the fact that the pith is always located at one side of the geometric center of the cross section. Leaning trees grow largely on the under side and this general law accounts for the position of the pith. On an eccentric cross section there are but two radii which are average in length and can be measured for growth. It often happens that one or both of these radii (Fig. 67) are interfered with either by the undercut or by the presence of rot or deiacts which prevent growth measurement. If either one is clear, the section may be meas- ured. Otherwise, if measurement is absolutely necessary, a longer or shorter radius can be taken and the measurements reduced by proportion to the required length.^ Method of Counting Decades. The next step is to count the number of annual rings and indicate with a pencil the points at which the decades fall. Except in scientific investigations where each year's growth may be separately measured to determine the influence of climate on annual growth, the decade is ordinarily the smallest interval used in measure- ment of diameter growth. For current periodic growth a five-year period is sometimes used in order to get points for a curve in predicting the growth (§ 279). Unless the total age of the stump falls on a decade, as thirty, or forty years, there will be one fractional decade laid off, representing from one to nine years, depending on this total age. The diameter growth is always measured outivard beginning with the pith or center of growth. But in counting the annual rings to lay off these decades of growth, two distinct methods of procedure are followed. In one, the count begins at the center, laying off ten years from the pith, and throwing the fractional decade to the outside as on the right side of Fig. 68. By the other, the count begins at the cambium layer or outer ring, and this throws the fractional decade to the center as on the left side of the figure. Purpose of Counting Inward from Outer Ring to Center. The choice ^ E.g., if the average radius is 9 inches, and a radius of 10 inches is measured, each measurement must be reduced by the factor ^ or .9 344 GROWTH OF TREES IN DIAMETER of these methods is based on the purpose of the study. In all measure- ments of diameter growth, an average rate is to be found by combining the growth of a large number of trees. This means averaging together the growth by decades. The trees so averaged usually differ in age, sometimes over a v/ide range. The growth of the last decade, or current periodic growth on all trees, regardless of their total age, is represented by the outside or last ten rings. Any influence, such as cutting, fire or climate, which affects diameter growth, must be studied on the basis of current growth. In making a tree analysis, which requires the growth Inner Bark Outer Bark Fig. 68. — Alternate methods of counting and measuring annual rings on a cross section 36 years old. On left, rings are counted in decades beginning with outer ring. On right, count begins with center and odd rings fall on outside. in diameter of upper sections (§ 289) the separation of the growth in volume for each past decade requires the measurement of the same ten rings on each of the sections analyzed. This is secured by counting back from the outer ring. When growth is studied for these purposes, rings must always be counted from the outside inward. In this case the first measurement from the pith outward will be the fractional decade. The average growth for this period represents the average number of years less than 10 which were measured. This may vary from 1 to 9 years but tends to average 5 years. The second decade wall include, on different trees, the years 2 to 19, the third, 12 to 29; MEASUREMENT OF DIAMETER GROWTH ON SECTIONS 345 H >H UJ cd W ti- l—I p -o «J :3 > O ^ ta o ^ s a 3 o g K m Eh H o s o « 3 •< w < W > 2: o u Z Q to H Q O Q ■* IK » W O Z 00 lO 00 'J' 00 -*< - CO o o IN Th o OS o 00 IM ■o o o 03 C<1 00 •* lO cc CO to - O O lO o >o •* 00 ■* Tt< ■* "1 ■* ■* Tjl CO o IN o o O O O lO o O m O liO —1 "^ CO Tf< CO CO 00 CO CO 05 »0 lO »o to o lO if3 fj* 00 OJ CO (N CO IN in' o CO o CO 00 O O O O lO 00 00 o CO t^ IN --I CO (N (N o IN CO •o IN t~ O O lO lO lO (N lO -^ 05 T)H a i-H IN rH (N d O) CD o o o o >o t^ CO --i f~ o rt ^ c^ -^ c^' 00 00 t^ t- O uo lO O lO ■-1 05 o CO t^ •H C^ rt ,-1 00 O C O lO lO t> t^ t^ oc CO d -^ ' >-l o CO o TO lO lO O O lO lO lO IN ;0 O O ' ^ ' T-i OS CO OS "50000 CO CO t^ -^ ts. d ' ■ ■ ■ o •o IN o lO - O "O O o o o t~ CO CO CD d <0 'XI rt 05 o t^ O o eg IN CO Diameter, inside bark. J3 CO o ^ ^ t^ o o> O O OJ , . Width of bark, single. >o lo ira CO CO jH Til IN d J f Diameter, outside bark. o >0 IN t~ IM IN ^ o d -H d I a > 0! Height of stump. O •o >o O OO o .-1 rt rt o rt' "3 o < « ,<|>^ 40 y^. 'f / ,' /' ' / r-*^ -, „ ,J ■i 1' 5 li 1 H Diaractcrn.il. Inches and trees are shown in Fig. 76. Within a given age class, the curves indicate the somewhat slower growth in height 368 GROWTH OF TREES IN HEIGHT of Ihe suppressed trees, but the maintenance of nearly the average rate for all surviving trees. But the dotted lines indicate the greater height of suppressed trees having a given diameter, when compared with dominant trees. 284. Measurement of Height Growth. For the juvenile period of height growth of seedlings and saplings a practical method of measure- ment is to determine the total age and the total height of dominant trees (§256 and §257). Trees which will not survive should not be measured for height. For young conifers show- ing annual whorls, the exact height growth for each year may be determined by measuring the length of the whorl. This method is used in measuring the annual height growth of coniferous plan- tations (§ 258). On older trees height growth should be measured by analyzing the growth of individual trees. Total height growth for a given tree is obtained when its height and total age are known, and a composite growth cm-ve may be built up as suggested for seed- lings, by obtaining these data for a number of trees of different ages on the same site quality, plotting the heights on the basis of age and drawing an average curve of height on age. But a more accurate method is possible when each tree has .been cut into several sections, the age of which can be determined from ring counts. In this case as many points for a curve of height growth are found as there are sections cut, and these points form a true growth curve for the tree. Diameter growth begins, at a given section, in the year in which the tree reaches the height of this (1) Kings in Section (2) Height of Section Foct (3) Length of Log Feet (4) (5> Years to Years to Grow in Grow- to height height o) for Log Section 53 70 16 " 26 37 ,f \ 44 33 33 37 \ in OC \ f 7 54 17 16 8 4 68 9 12 1 J. r M \ „ 70 ^ L 1 3 1 \ " Age Age of Seedling, 3 Years ofTree] 70 Years 1 1 Fig. 77. — Method of determining the growth in height of a tree from the ages of upper sections, or ring counts. The difference in age between consecu- tive sections indicates the period re- quired to grow in height from the lower to the upper section. MEASUREMENT OF HEIGHT GROWTH 369 section. The number of rings shown by the section, when subtracted from the total age of the tree (age of stump plus seedling age) gives the years required to grow to this height. The process as shown in Fig. 77 consists of the following steps : 1. Determine age of tree from stump plus seedhng age (§ 257). 2. Count the rings at each successive upper section, and measure length of section to get height from ground. Include height of stump. ■10 Age, Years Fig. 78. — Alternate methods of averaging the heights of trees, for a curve of height based on age. Original data plotted. For curve average age at fixed heights is found. For curve © average height for each decade. The prolonged curve is made necessary by dropping out of fast-growing trees from the average by decades. 3. Subtract these counts successively from total age of tree, to obtain total height growth at each section and age. 4. Subtract the age of any section from that of the one below, to find the period required for the current growth in height for the length of section. This method may be simplified by first computing the height growth curve for the portion above the stump, on all trees, and afterwards making the average correction required for stump height and correspond- ing age of seedling, on the final curve or table. 370 GROWTH OF TREES IN HEIGHT Graphic Method. In averaging together the data for height growth on the basis of age, it is evident that few if any points will fall at the same age, even if taken at the same height above groimd. For this reason, the most convenient method of determining an average rate of height growth based on age is to plot the original data for each tree, and draw a curve based on ocular inspection of the result assisted by weighting the points or calculating the position of the average point if the data are not sufficiently abundant to dispense with this step. In this graph, age is placed on the horizontal scale and height in feet on the vertical scale. It is not practicable to determine the arithmetical average height at each separate age previous to plotting the data. This is best done from the graph. The height growth of ten trees, which were sectioned at 8-foot intervals above the stump is shown in Fig. 78. Stump height is omitted. The heights at each 8-foot section fall on the same horizontal line, i.e., have the same ordinate. The total or final heights represent the height of the tree. Two methods of averaging the data are shown. By the first, all points falling in the same decade are averaged for the points marked O. The number of points used is indicated at base of Fig. 78. This method is based on age, but in some decades the same tree enters twice while in others it does not appear. The depression of the curve at final decade is caused by the dropping out of eight of the ten trees from the average. The second method is to aver- age the age at each 8-foot point. This average, marked , is then based not on age but on height, but is plotted on age. Since all ten trees enter this average at each of three points, the curve is more regular than the first. There is not the same objection to interchanging the basis of this curve between age and height as outlined above, as there is in studying diameter growth, *" since the rate of height growth Fig. 79.— Method of correcting curve of height ^^^ ^^^^ ^^^^.^ ^^ ^^ ^^^^ ^^^_ growth based on stump, by adduig height gi^^ently a function of age and vice and age of seedling, thus givuig height ^^^^^^ j^^. ^j^^ ^^^^ ^^^^-^^ ^j ^j^.^^ growth of tree based on its total age. ^j^-^g j^j. diameter growth two or more additional variables influence the rate of growth (§ 296 and § 270). The height growth, as read from the above curve, may be shown in a table based on total age and height of tree, by adding average stump height (of 1 foot), and seed- ling age (of 2 years) to the curve, and reading the corrected values from the pro- longed curve, as shown in Fig. 79. The values, read for even decades are given in Table LVII: ' 1 The averaging of the above data to obtain the weighted average points may be simplified, after the points are plotted, by the following method. For the first decade, average heights include 7 trees, each 8 feet or points above the base of the graph, or " up " and 1 tree 16 feet " up " or a total of 72 points " up"; average for 8 trees, 9 points " up." Average age includes 3 trees 4 years or points to right of the left margin of the graph, or " over," 2 trees 5 years " over," 1 tree 6 years, 1 tree 7 years and 1 tree 8 years, a total of 43 years, average 5.4 points " over," These /. c 1 D ■ «* 2 oe ,onu y s- ,^ il §^}tt^' J- - y / O o V -^^ t- -' - -X - z .C 'LJ ■S - 5: 7' 1~ X J Heighrof / StilnllV - /" Tib 20 1 tl)()t ^ \ "p '0 Out o:§ fe -;.geof|TVee_ 1- " I'li MT 1 1 1 1 1 1 N 1 — MEASUREMENT OF HEIGHT GROWTH 371 TABLE LVn Height Growth of Chestnut Oak, Milford, Pike Co., Pa. Basis, Ten Trees Age. Height. Height. Years Feet s Feet 2 1 40 35 10 10 50 41 20 19 60 46 30 28 70 50 The total height, based on total age, of these ten trees is shown by the last ten points. It is evident that with a sufficient number of trees of all ages, a height curve based on age could be constructed without analyzing the trees above the stump sec- tion, but it is equally evident that such analyses, as shown in the figure, not only multiply the weight of each tree by the number of sections taken but substitute actual growth of given trees for composite growth by comparison of different trees. Such a history or record of growth, whether it is of diameter, height or yields per acre, (§ 266 and § 326), is the most reliable basis of growth data. Current HeigM Growth. The current or periodic height growth for the last decade or two may be required to complete the data for determining the current volume growth of trees. This should be meas- ured on felled trees by cutting back the tip until a section is found containing the requh'ed number of rings. For determining growth for short periods this is a simple process. Only on young trees should the last period of growth be determined by counting back the number of whorls from the tip In older timber and especially on standing trees, it is impossible to secure accuracy by this method. 285. The Substitution of Curves of Average Height Based on Diameter for Actual Measurement of Height Growth. In studies intended to determine the volume growth of trees, especially of seed trees and young timber left on cut-over lands, a method has been sought data are identical with the original figures, the advantage lying in the graphic classi- fication of the data for averaging. But for the next and subsequent decades the base, for age, can be shifted to the right by one decade, so that the points " over " include only the fractional decade, while for height the base can be raised to exclude that portion of the graph which includes no points. Thus, for the third decade there are 9 points, whose weights vary from 1 to 10 years or points. For age, the basis or zero is 20 years and the points " over " are 1, 2, 3, 6, 6, 7, 8, 9 and 10, or a total of 52, average 5.8 points " over " or 25.8 years. For height the base may be taken at 10 feet and the points " up " are then 6, 14, 14, 14, 22, 22, 22, 22, 30, a total of 166 points " up," average 18.4 points up, or 28.4 feet. In plotting, where two or more dots fall on the same point, a numeral miist be written in, as indicated, to show the weight of the point, 372 GROWTH OF TREES IN HEIGHT by which this volume growth can be predicted by a study of diameter growth and by the determination of the resultant volume of the tree from its average height and volume as shown in a volume table. In order to save the expense of determining the actual growth in height of these trees, recourse is had to the relation between height and diam- eter as expressed by a curve of heights based on diameter such as is illustrated in Fig. 76. The process is as fo lows: 1. The increase in diameter for a given period for a tree of a certain diameter is predicted or determined; e.g., the tree may gi'ow from a 10-inch to a 12-inch diameter. 2. The average curve of height on diameter shows the heights of a 10-inch and 12-inch tree respectively. 3. It is then erroneously assumed that the 10-inch tree will grow in height by the amount of this difference, that is, that it will have, when 12 inches in diameter, the height of a 12-inch tree. The fallacy of this reasoning is clearly evident when applied to any single tree or to any stand of a given age. If the tree or stand is young and the curve of height on diameter has been prepared for trees of this class or age in the vicinity, the tree will grow much faster than the difference in height indicated by this curve, and the same is true of the trees in an even-aged stand. But for old or mature even-aged stands, the reverse may be true and the trees may grow more slowly than the difference shown. Such a curve is not a growth curve at all, but a curve showing the average heights attained by trees which may be all of the same age. Only when the curve of height based on diameter includes trees of all ages as well as diameters, does it approach the form of a true growth curve, as shown by the dotted curves in Fig. 76. To do this it must harmonize two variables, namely, diameter and age. In general, small trees are young trees and large trees are old trees. If sufficient data have been included, covering wide enough ranges both of diameter and of age, and the measurements are taken on the same site quality, a rough average is obtained in which the height of a tree of given diam- eter is correlated with the age of tree of the same diameter. The more nearly this general result is obtained, the more reliable will be the aver- age results of applying this curve in predicting the growth in height through the medium of the growth in diameter to trees or stands of all ages, and thus avoiding a direct study of height growth. It is obvious that for special problems on specific classes, ages and stands of trees, no such generalized curve should be depended upon, but a few measure- ments of height growth on the trees in question will give results whose a(;curacy justifies the expense. The height curve of even-aged stands is determined either from the height growth of the maximum or dominant trees in the stand, or from REFERENCES 373 that of trees containing the average volume of the stand. It has been found that the relation between dominant and average trees in height growth is very consistent, and either basis furnishes an index to the growth rate, which may be used later in classifying the plots on a basis of site for the construction of yield tables. On account of its uniformity for a given site quality, average height growth may be determined from the analysis of from five to twenty- five average or dominant trees with very satisfactory results. References Relation between Spring Precipitation and Height Growth of Western Yellow Pine, G. A. Pearson, Journal of Forestry, Vol. XVI, 1918, p. 677. Relation between Height Growth of Larch Seedlings and Weather Conditions, D. R. Brewster, Journal of Forestry, Vol. XVI, 1918, p. 861. CHAPTER XXVI GROWTH OF TREES IN VOLUME 286. Relation between Volume Growth, Form and Diameter Growth. The growth of trees in volume is the product of the growth in height and the growth in area at different portions of the stem, which Is expressed in diameter growth. The exact form of the tree and the rela- tion between diameter and resulting area and volume growth at dif- ferent heights from the ground are the result of mechanical laws of resistance to stresses. The form of the tree is intended to resist wind pressure in order to maintain its upright position and not be snapped off or blown over. As was shown in Chapter XVI this pressure is directly caused by the force of the winds acting on the crown and focused in the center of area of the crown exposure (§172). Growth in diameter will be distributed in response to this strain to give the maximum resistance with the minimum of material. As the form of crown and its position with respect to the bole changes, the point of average pressure shifts and the form of the tree will be modified by a more rapid diameter growth at the points requiring strengthening. An increase in the stress to which the tree is exposed will also cause changes in the distribution of growth. Trees which have grown in a protected stand and are exposed by cutting will either blow over or will rapidly strengthen their resistance by laying on increased growth at the base or stump where the effect of this change in exposure is most evident. The upper form of the tree, being influ- enced by crown, does not change appreciably. Trees in a leaning position continually add most of the diameter growth on the under side. Where the growth in volume of a tree on cut-over areas is judged from the growth in diameter on the stump, without correction, a rate of from 50 to 100 per cent in excess of the true volume growth may be obtained. Such measurements should therefore be taken at B.H. where the effect of this increase is not felt, or else growth measurements taken on the stump must be carefully compared with measurements at upper points on the tree. 287. Tree Analysis, its Purpose and Application. The analysis of an individual tree by the measurement of diameter growth at upper sections, in order to determine its volume growth, is termed tree analysis, (synonym, stem analysis, § 254). This process enables one to determine 374 SUBSTITUTION OF VOLUME TABLES FOR TREE ANALYSIS 373 the upper dimensions and volume of trees of a smaller size than those which exist in a given stand. This is an advantage in case such smaller sizes are lacking, but where present they may be directly meas- ured. The volume which trees produce at given ages can thus be obtained in one of two ways, either by measuring trees of different ages directly for volume or by analyzing a single tree or a number of trees in order to determine the past growth in volume. The latter method alone will bring out the changes which take place in form, as described above, due to altered conditions. In applying such growth figures to answer the fundamental question of growth studies, namely, what is the rate of growth in volume per acre, annually or for a given period, not only must the growth of average rather than individual trees be determined, but the relations of these average trees to the number of trees which will survive on an acre at different ages must also be known (§ 275). Since the recording and working up of growth measurements to determine total volume growth is slow and expensive, only a few trees may be taken. It is necessary that these trees have the average form quotient for the stand to which their results will be applied. This means either a careful selection or a chance of incurring an error of from 10 to 15 per cent by the accidental selection of trees which depart from this average in form. 288. Substitution of Volume Tables for Tree Analysis. The growth of an average tree is determined by the average growth in D.B.H., the average height growth and the average growth in diameter at upper sections, of which the most important is the diameter growth at one -half of the height. The growth of upper diameters is usually accompanied by a change in form, caused by a change in the length and position of the crown. This is illustrated in Fig. 80 (§ 290) for which tree both butt swelling and upper diameters increased faster than growth at 8 feet. Relying upon the maintenance of a consistent tree form for average trees, a method is in common use as a substitute for the analysis of trees to determine their volume growth. This method depends upon the use of volume tables to determine the volume of trees whose height and diameter are known. Since a standard volume table expresses the actual volume of average trees much more accurately than it can be obtained by the analysis of a few sample trees, the substitution of a volume for the average tree taken from this table enables the investi- gator to concentrate his effort on determining average growth in D.B.H. and in height. The actual measurement of height growth involves the counting of rings for determination of age of upper sections on at least a few trees (§ 284), but dispenses with the measurement of diameter growth on these upper sections, and requires from one-fifth to one-tenth 376 GROWTH OF TREES IN VOLUME as many trees as are required for the study of average diameter growth on account of the greater consistency of height growth based on age. From a curve of growth in diameter, based on age (§ 267 and § 268), the diameters of the average trees at different ages are determined. From a second curve of height based on age (§284), the heights of the same average trees for different ages are found. Since diameter and height determine the volume as classified in these standard volume tables, the requisite volume is interpolated from the values in the table for the nearest yV-inch in diameter and foot in height. The successive volumes found in this way indicate the growth laid on by the average tree. This may be expressed in whatever unit of volume is represented by the volume table employed. This method is almost universally substituted for volume growth analysis wherever figures on average volume growth of trees are desired. This method is illustrated by Table LVIII.i ^ The method of interpolation is illustrated as follows. The 60-year-old tree is 6.6 inches in D.B.H. and 46 feet high. The values in the standard table from which to interpolate are, in cubic feet. D.B.H. Inches Heights 40 Feet 50 Feet Cubic Feet 6 7 4.2 5.7 5.0 6.6 The difference for 1 inch is 1.5 cubic feet for 40-foot trees, and for .6 inch, is .9 cubic foot, giving for 6.6 inches, 5.1 cubic feet. The average difference between 40- and 50-foot trees is .85 cubic foot. For 46-foot trees it is .6 times .85 = .51 cubic foot. Then 5.1 + .51 =5.61 roimded off to 5.6 cubic feet as the interpolated volume sought. These interpolations are more expeditiously made from graphic plotting of the values in the volume table. One drawback to the use of volume tables as a substitute for actual growth analy- sis is illustrated in the attempt to measure growth at successive decades on sample plots for scientific purposes. Even here, if a single volume table is carefully pre- pared, combining all age classes, the transition in form from young to old trees is blended with the volumes shown in the table for small and large trees, but where, as for instance with Western yellow pine, separate volume tables were made for black jack or young trees and for yellow pine or old trees which differed by about 10 per cent in the average volume due to difference in form, the application of a different volume table to trees passing from one age class to the other caused a jump of 10 per cent in the volume due apparently to growth, but in reality due to the irregular distribution of this growth by separation of form classes in these tables. MEASUREMENTS REQUIRED FOR TREE ANALYSES 377 TABLE LVIII Growth of Chestnut Oak In Cubic Volume, from Diameter and Height Growth and Use of a Standard Volume Table Corresponding * volume from Periodic Age. D.B.H. Height. table by interpolation. growth. Years Inches Feet Cubic feet Cubic feet 10 1.2 10 20 2.5 19 30 3.8 28 1.3 . 1.35 1.55 1.40 1.40 40 5.0 35 2.65 50 5.9 41 4.2 60 6.6 46 5.6 70 7.2 50 7.0 ' * Cubic volumes taken from Frothingham's table for chestnut oak in Bui. 90 Forest Service, "Second Growth Hardwoods in Connecticut." Height from Table LVII, §284. Diameter from growth of the same ten trees used in this table. 40 185 10 \ }\ 10 y ears \ \ \ 7\ 10 \ \' 1 \ 1 10 \ ,\ 24 y lars } I \ ho \. Ml Mil ^ V.N fX 5. 6 ) 10 k 10 \io\ ^-y 12 3 4 5 6 Diameter, inches Fig. 80. — Stem analysis of a tree 36 years old, by dec- ades, counting in from outer ring, based on stump. Stump is shown below point marked 0. 289. Measurements Required for Tree Analyses. The data required in a tree analysis, in addition to those taken for volume and itemized in § 134 and § 135, are, 1. Age of each section (height above stump and length given). 2. Growth on average radius from center to outer ring, by decades. 3. Where needed, width of sap and number of rings in sapwood. 290. Computation of Volume Growth for Single Trees. The method of computing the growth in volume for a given tree is best shown by graphic illustration. Fig. 80 shows the dimensions of a chestnut oak 36 years old at the stump, and the size which this tree had when 26, 16 and 6 years old. To correlate the growth of upper section for the same decades, these decades are counted from the circumference inward, as shown, with the odd rings at the center. Diameter growth for each decade is then 378 GROWTH OF TREES IN VOLUME measured from center outward, are given in the following table : The full data for this tree analysis TABLE LIX Stem Analysis of a Tree Species, Chestnut Oak. Date, 1912. Total Height, 40 feet. Width Crown, 14 feet. Tree Class, Suppressed. Locality, Milford, Pike Co., Pa. D.B.H., 4 inches. Height Stump, 1 foot. Merch. Length, 20 feet. Length Crown, 17 feet. Height Length Diameter, Width Diameter, above of outside bark. inside Age. stump. section. bark. single. bark. Feet Feet Inches Inches Inches Years Stump 1 6.05 0.5 5.05 36 1 8 8 3.95 .3 3.35 31 2 16 8 3.5 .2 3 1 24 3 24 8 2.3 .15 2.0 17 4 32 8 1.0 .05 .9 10 Tip. 39 7 Distance in inches on average radius from center to ring, by decades. The first column shows the number of years in the first fractional decade. (1) (2) (3) (4) (6) 0.5 1.3 2.1 2.5 (1) 0.05 0.65 1.25 1.7 (4) 0.25 1.05 1.55 (7) 0.55 1.0 (10) 0.45 In addition, for a group of trees analyzed, the site, density of stand, character of trees shown, conditions of cutting or other factors whose influence on growth is to be determined, are recorded. With diameter at each decade for each section recorded, the total volume of the tree and its volume at each decade in the past, e.g., for 36, 26, 16 and 6 years, is obtained by methods indicated in Chapter III, using the Smalian or the Huber formula for cubic contents. But one detail is lacking — the actual height which the tree had at the above decades, in case the former tip falls between two of the sections counted. This tip contains a very small per cent of total volume, and for merchantable contents would be ignored. But for accurate studies of total cubic contents the height is obtained by assum- ing that the height growth maintained the same rate per year as shown SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS 379 for the entire section concealing the tip; e.g., in Fig. 80 the third sec- tion took 24—17 = 7 years to grow 8 feet. The tip contains 4 rings, or 4 years' growth. Hence its height is y of 8 feet = 4.5 feet. For the second section the period required was 31 — 24 = 7 years. The tip has 1 ring, hence its height is y of 8 ft. or 1.1 ft. or / Age of tip \ Length of tip = I — 7 : -; — I Length of section, \ Years to grow length 01 section/ The age of any one tree will probably fall at an odd year instead of an even decade and the age of the average tree whose volume is calculated will fall on one of these odd years; e.g., for the chestnut oak above analyzed which took 2 years to grow to stump height, the table and figures above will show the age of a tree 8, 18, 28 and 38 years in age. To find the volume of the tree at even decades, as 10, 20, 30 years instead of odd years, the volumes as determined are now plotted on cross-section paper on which age is placed on the horizontal scale and volume on the vertical scale. From these curves the volumes for even decades can be read. By averaging these volumes on the basis of age the average growth in volume is obtained for all the trees analyzed. 291. Method of Substituting Average Growth in Form or Tapers, for Volume. The taper measurements or diameters determined from Fig. 80 thus enable one to ascertain the volume of the tree at different ages expressed in any unit. In this it does not differ from taper tables discussed in § 167 except that age is now the basis of the dimen- sions shown. The advantage of recordmg the tapers for the individual tree rather than its separate volumes at different ages applies equally to the average of a number of trees analyzed for volume growth. For this reason the method of computing volumes directly for each tree has given way entirely to the method described below by which the average tapers or dimensions of all of the trees studied are first determined. From the average tree thus plotted, the volumes can then be found for any of the desired units, such as cubic feet, board feet in any given log rule, standard ties or poles, for each age or decade. This method reduces the work of computing volumes to a single average tree for each tree class. The first requii'ement of this method is a curve of average growth in height based on age (§ 284). This establishes the year or age in the life of the tree at which the diameter growth of each upper section at a given height originates and marks the zero or origin of the curve for this section when plotted on the age of the tree (§ 269). Second, a separate curve of diameter growth based on age is constructed for 380 GROWTH OF TREES IN VOLUME all sections which fall at the same height above the ground. The sum of the age or period required for the average tree to reach this height, plus the age or period represented by the growth of the section equals the age of the tree regardless of the height of section. It is evident then that the average curve of growth in diameter for any of these sections can be plotted on a single sheet of cross section paper whose horizontal scale represents the age of the tree and whose vertical scale represents the diameter of any cross section. A cross section which does not begin to grow in diameter for 17 years will diminish to zero and the curve representing its growth will intersect the base or zero diameter at 17 on the horizontal scale representing age of tree. In Fig. 70 (§ 269) a curve of stump diameter based on the age of the tree was shown as intersecting this base at the age represented by the seedling. On this same sheet a curve representing the D.B.H. and one showing the diameter at the top of the first 16-foot log were indicated with their points of intersection. On a single vertical line the points shown were the diameters of a tree of a given age and indicated the D.B.H. , D.I.B. at stump and D.I.B. at top diameter of first log for this age. But to get a curve showing these three dimensions for trees of different ages in the illustration given, the points were not taken from the growth of one tree, but by the measurement of several trees differing in age, stump diameter and corresponding D.B.H. and upper tapers. The connection of the points for these separate trees which differ on the basis of age, gives the curves showing the increase in the upper diameters or tapers for trees of different ages. The method of plotting the upper diameters showing the growth of an average tree at the different ages of its life is identical with this previous method, with the exception that instead of these ages being represented by the final, present or outer dimensions of separate trees, they include the past, interior dimensions as well, by the measurement of past growth. Even though the growth is an average of many trees, the method still remains the same since each decade's growth is a com- posite of the actual growth or internal dimensions of a number of trees. The method of plotting the data is as follows : 1. Prepare and plot a curve of average height based on age on a separate sheet. 2. Prepare on separate sheets, curves of average diameter growth for all cross sections falling at each separate height, as for instance a curve for sections falling at 8 feet, 16 feet, etc., including one for the stump section. It is assumed that the height of seedlings based on age has been determined and that D.B.H. has been correlated with stump D.I.B. 3. After determining the initial or zero year for each of the curves SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS 381 of diameter growth, including the stump section, transfer or assemble each of these curves on a single sheet whose zero represents the zero year of the tree's age. In Fig. 81 the curve of stump growth from Table LIX is plotted with the zero at 2 years, age of seed- ling of stump height. This is usually as- sumed to be also the origin of the D.B.H. curve. For the curve of diam- eter growth at 8 feet, the period required to grow to this height by Fig. 81, or by interpolation in Table LIX is 7 years plus 2 years for seedling. The zero is placed at 9 years. Since the first fractional dec- ade averaged 6 years on these sections, the first diameter is plot- ted above 9-|-6=15 years, and subsequent decades at 25, 35 years, etc., as indicated by the points. The height growth for section 3 at 16 feet took 15-|-2=17 years. The first fractional decade was 6 years. The points are plotted above 23, 33, 43 years. In this way each upper section is plotted on the sheet representing the age of the average tree.^ To read this record for the purpose of determining the volume in any given unit for a tree of a given age, the dimensions of a tree of the required age fall in the vertical line intersecting this age. For instance, a tree 40 years old will have its diameter inside bark at the 16-foot cross section indicated in Fig. 81 as 2.4 inches. Reading upwards as the diameter increases, the next lower cross section has a diameter of 3.4 inches and D.B.H. is 4.8 inches. Since the height or distance between these cross sections cannot be shown on this diagram, but j^ > y A y / 'M A /A' .A /, / // / / A /. // // 'p/ ^ * / /. ^ 'A / / 30 40 Age, years 60 Fig. 81. — Diameters at 8-foot points, for an average tree at different ages, or growth analysis. Chestnut Oak, Milford, Pike Co., Pa. 1 In the above figure, D. B. H. outside bark exceeds D. I. B. at stump up to about 7 inches. This frequently occurs on small thick-barked trees. 382 GROWTH OF TREES IN VOLUME only diameter based on age, it is necessary to indicate upon the curves the height which each curve represents. This series of curves can be used only to determine the diameters at the definite points, as 8, 16, 24 feet, etc., for which curves have been drawn. It corresponds with Fig. 32 (§ 168) for taper curves. To obtain the growth in form for the tree at intervening points, these curves should be replotted in the form shown for a single tree, in Fig. 80. From the average tree thus shown, the growth by decades in any form or length of product can be directly computed, to any required diameter limit. ^ 292. Substitution of Taper Tables for Tree Analyses. Just as the above method" substitutes the form of the average tree at different ages for the direct calculation of the volume at these ages, so it is pos- sible to go one step further and to substitute the entire form or taper of trees of different diameters, heights and ages, just as was done in Fig. 70 on the curve of stump diameter growth, for D.B.H. and top of first log. To make this substitution, the diameter and height of average trees are first determined for each decade in age. Second, from a table of average tapers, the form or taper of trees of the cor- responding diameters and heights are taken. This may be done by interpolation in case the required diameter or height falls between inch diameter classes or 5- to 10-foot height divisions expressed in taper table. The tapers thus borrowed are assumed to be those of the tree at the different ages. This method has the same advantages and drawbacks as the sub- stitution of the volumes from a volume table for the actual volume of sample trees as described in § 242. The average tapers are taken in. most instances from a much larger number of trees than could be analyzed for form at the different decades of their growth. These tapers therefore probably represent quite closely the average form of the tree of these sizes and ages. On the other hand, this average, just as for volumes, may depart from the actual average of the trees to be measured in case the data do not coincide in origin and the trees differ in average form quotient. The best check upon the accuracy of substitution of taper tables for tree analyses is to test the form quotient both of the taper tables and of the trees desired. A considerable departure in this form quotient indicates that the tapers do not represent the average sought. 1 This method of graphic plotting of average growth in diameter at eaeh upper section was devised by A. J. Mlodjiansky (Measuring the Forest Crop, Bui. No. 20, Division of Forestry, U. S. Dept. Agr., 1898). The method of assembling all the curves on the same sheet was devised by H. S. Graves (Forest Mensura- tion, 1906, p. 295). REFERENCES 383 References Difficulties and Errors in Stem Analysis, A. S. Williams, Forestry Quarterly, Vol. I, 1903, p. 12. Pitch Pine in Pike Co., Pa., John Bentley, Jr., Forestry Quarterly, Vol. Ill, 1905, p. 14. Stem Analyses, John Bentley, Jr., Forestry Quarterly, Vol. XII, 1914, p. 158. A Simplified Method of Stem Analysis, T. W. Dwight, Journal of Forestry, Vol. XV, 1917, p. 864. Mechanical Aids in Stem Analyses, E. C. Pegg, Journal of Forestry, Vol. XVII, 1919, p. 682. CHAPTER XXVII FACTORS AFFECTING THE GROWTH OF STANDS 293. Enumeration of Factors Affecting Growth of Stands. The rate of growth per acre or total volume production of stands is the result of five classes of factors, namely, site, form, treatment, density, and composition. Under site are included all factors of local environment such as soil, exposure and altitude, which influence growth (§ 294). The term form alludes to age, and the forms of stands distinguished in yield studies are even-aged and many-aged (§ 259). Treatment refers to the silvicultural management of the stand, in the form of thinnings, and protection; untreated stands are those gi'own under natural conditions (§ 300). Density means primarily the completeness of crown cover, but this factor is also influenced by the number of trees per acre (§ 301). Under composition, pure and mixed stands are distinguished. Pure stands are those in which a single species comprises 80 per cent or more of the volume. Mixed stands are those made up of two or more species, none of which amounts to 80 per cent of the volume. Stands may be alluded to as pure if 80 per cent or more is composed of trees of the same genus, such as pure pine or pure oak stands. Natural enemies such as insects and fungi, and climatic factors such as tornadoes and ice storms reduce the density of stocking and lower the rate of growth, thereby widening the gap between average and fully stocked stands. 294. Site Factors, or Quality of Site. In estimating the volume of stands, the forest type is made a distinct unit of area for the purpose of increasing the probability of accuracy in obtaining an average stand per acre, or in securing a curve of average height on diameter (§ 225 and § 227). In the measurement of growth and yields, not only is the forest type also a fundamental factor, since it determines the species and composition of the stand, whose capacity for growth under- lies the results obtained, but these types must be further subdivided into site classes. The rate of growth per year or total yield for a given period for different species depends directly upon the combination of factors 384 VOLUME GROWTH A BASIS FOR SITE QUALITIES 385 which influence this growth, chief among which are qiiahty and depth of soil, average moisture contents, slope and exposure, altitude and climate. Site factors cause a variation in total possible yields of from 200 to 300 per cent. Hence for a given stand or area the jaeld cannot be predicted within a reasonable degree of accuracy unless the quality of site is taken into account. This difference in yield on good and on poor sites is caused by the more rapid growth in height, diameter, and volume, of the trees in the stand, when growing on more favorable sites. Fewer trees may mature on good sites than on poor, because of the larger sizes and crown spread attained, but the sum of their volumes will exceed those of the trees maturing on the poorer sites. When the period of years required to produce these yields is considered, and the mean annual growth is computed (§ 245) it will be seen that the more rapid growth on good sites produces even more striking differences in the annual rate of growth between poorer and better sites. These differences are further increased when the value of the yield is compared with the cost of production, so that it becomes of utmost importance in forestry to determine, for any large area of forest land, the acreage embraced in each of several grades or qualities of site. 295. Volume Growth a Basis for Site Qualities. Forest types some- times show abrupt transition from one to another, corresponding to sharp differences in soil moisture; but more often the change is gradual and the separation of areas in each type, as made in the field, is arbitrary. The differences in site quality within a type form an unbroken series of gradations, which must be separated, on a purely arbitrary basis, into a convenient number of site classes, whose average yields may be expressed in tables. In European practice five qualities are recog- nized when a few species occupy a wide range of conditions. In America three qualities have so far sufficed to cover the range of a single species. The problem of classifying site qualities is two-fold. First, the plots whose yields are measured to determine the average rates of growth for different sites must be separated into the predetermined site classes. Second, some convenient means must be found to apply this site classification to forest lands during a forest survey in order that the total area may be subdivided on this basis for the prediction of growth on the forest. The most direct method of classifyin,g plots measured for yield is by the rate of growth per year actually produced, i.e., the total yield based on age of the stand. This has been the basis of most of the yield tables constructed in America, and might suffice were it not for the four other factors which modify the yields per acre independent of site; namely, form of stand, treatment, degree of stocking, and composition of stand. 386 FACTORS AFFECTING THE GROWTH OF STANDS The influence of these variable factors is tremendous, and it has usually been considered necessary to eliminate them by constructing yield tables for given fixed conditions only, such as for even-aged stands, artificially grown and thinned, of normal or full stocking, and of pure species. Where these conditions do not apply, as for instance in mixed stands of broken density in forests of all ages, it has often been considered impossible to determine the rate of growth per acre. 296. Height Growth a Basis for Site Qualities. A' though it may be possible, by rigid selection, to eliminate these four variables and thus base the site qualities upon the rate of growth or the total yield per acre based on age, yet when it comes to reversing the process and applying this standard of site classes to the classification of lands on a larger area, the remaining variables are present and must be dealt with. This problem may be summed up as follows: 1. The factors of site, such as climate, and soil, are too complicated to be directly measured in the field as a means of site classification. Results expressed in forest growth, rather than causes, must be used as the indicator of site. 2. Volume as a site indicator is incomplete without the determina- tion of age. For most conditions the relative volume based on age is too variable and difficult of determination to serve as a field basis of classification of large areas. 3. Dimensions of typical dominant trees in a stand may serve as the required indicator, since the tree unit is independent of the variables of age, form, composition and density which affect the stand. 4. The dimensions which may serve for this purpose are diameter and height. Of these, height alone is a reliable index of site quality since it is affected but little by varying density or degree of stocking, or by the treatment of the stand. Height based on age is a more reliable basis than volume on age for stands of varying degrees of stock- ing, and for both wild or unmanaged forests and thinned or managed stands. This reduces or eliminates two of the five variables, namely, treatment, and density of stand. Height growth is retarded by shade to a marked degree; hence in forests of all ages, and in mixed stands of several species, height based on total age ceases to be a reliable index, since the factor of economic age is introduced. Total height or height at maturity remains, even in mixed stands, a distinguishing characteristic of different site qualities. The growth of dominant, unsuppressed trees, a few of which may be found in almost every stand, may be ascertained in a very few tests and will hold good for the stand or site. Thus the remaining two variables, form and composition, may be eliminated by selection of dominant trees or fully mature trees. OTHER POSSIBLE BASES FOR SITE QUALITIES 387 Site qualities, whether three or five in number, must be adapted to the range of actual j^ields of the species to be measured. Different species require a different range of site factors. The conifers thrive in soils too poor for hardwoods; hence quality I for pines may be quality II for oaks. The adoption of a common standard of site index for species with the same range of soil requirements is desirable. One suggestion is to classify the trees of the country into groups, based on their total growth in height at a definite age. This principle is illustrated by the follow- ing table, in which four site classes are made for each group, based on even gradations of total height for dominant trees of the same age. TABLE LX Standards of Site Classification Based on the Height of Tree at 100 Years Site Standard a. Standard h. Standard c. Feet Feet Feet I 110 90 70 II 90 75 60 III 70 60 50 IV 50 45 40 A standardization of this character serves the double purpose of coordinating the yield tables for species of similar growth habits, and furnishing the simplest basis for site classification during forest survey. 297. Other Possible Bases for Site Qualities. Medwiedew's Method. A method of site classification suggested by Medwiedew, a Russian, and appHed by Hanzhk to Douglas fir is as follows : A site factor is calculated by the formula, Site factor = cXh when c = basal area on the average acre ; h = average height of stand ; n=age of stand. These so-called site factors may then be grouped to represent different site qualities, all factors falling between certain limits indicating quality I, etc. This basis is not consistent as an indication of site, since it is nothing but the mean annual growth of the stand in a different form. If / = form factor, then, c/i/ = total cubic chj volume, and — = mean annual growth of stand. As mean annual growth varies n with age as well as site, it cannot be substituted for either volume or height as an absolute basis of classification. 388 FACTORS AFFECTING THE GROWTH OF STANDS A still more impracticable plan is to base site factors on the current annual growth of a stand. ^ 298. The Form of Stands. Even-aged versus Many-aged. There is an essential difference in the character of even-aged stands and those composed of all ages on the same area, and this difference constitutes one of the greatest difficulties in determining the rate of growth or yields. It has been shown (§ 274) that the competition between individual trees made necessary by the expansion of their crowns and growing space occurs in an even-aged stand between trees of the same age class. Except around the borders of this age class there can be no expansion of the areas occupied by the total stand belonging to this age class. The factor of area can therefore be standardized in yield tables. Since the yield of even-aged stands is composed of the volumes of trees which have remained dominant throughout the life of the stand, the rate of growth of the individual trees is a maximum both in height and diameter and the mean annual growth resulting on an acre is the maximum for the site when measured for the period required for the growth of the average tree from seedling to maturity. The conditions are entirely different in many-aged stands, the dif- ference being greatest for species which may be subjected to a long period of suppression and yet retain the power to survive and recover. In these stands several different age classes are brought into competi- tion not merely with trees of their own age, but with older and younger trees. The older trees have the advantage of the younger in appropriat- ing space vacated by the death of veterans or by the removal of trees for any cause. The young trees growing under partial shade are held back in height growth, diameter growth and consequent volume growth. The economic space occupied by the younger age classes growing under partial shade may be defined as the actual percentage of the total grow- ing space as represented by the available light, moisture and soil fer- tility which is appropriated by these young trees to the exclusion of its use by other age classes. This proportion of space so used is exceed- ingly small and may be negligible, yet the reproduction may survive as scattered individuals for many years. When old trees die, the space released is not, as in the case of even-aged stands, occupied entirely by reproduction, but is distributed among all of the trees so placed that they may avail themselves of it by expanding their crowns. A portion only of released space is taken by additional reproduction. ^ " Concerning Site," Carlos G. Bates, Journal of Forestry, XVI, 1918, p. 383. Not only is this basis impractical of measurement and classification in the field, but it varies with age of the stand to a much greater degree thkn does mean annual growth, hence is not trustworthy as a means of separating sites, though the postulate that the best sites are capable of yielding the largest current annual growth is per- fectly true. THE FORM OF STANDS. EVEN-AGED VERSUS MANY-AGED 389 The result of these two factors is that the area of an age class is at first small, its growth retarded and mortality heavy, but with advancing age, the area or per cent of total area occupied by this class increases until it reaches a maximum at a period when the stand is at maturity and before the loss of veterans begins to leave holes in the canopy. TABLE LXI Average Crown Spread of Loblolly Pine in the Forest, at Vredenburgh, Ala. Age. Diameter of crown. Per cent of increase in Per cent of increase in Trees per acre Years Feet diameter area 30 13 40 15 5 19 42 140 50 19.0 46 113 116 60 22.0 69 186 88 70 24.5 88 255 70 80 27.0 108 332 59 This law of expansion is illustrated in Fig. 82. 4 Acres I I Area occupied by Crowni ^^^ Area not occupied by Crowaa Even-aged stand. 4 Acrezi Single age-class in Many-aged forest. Fig. 82. — Possible expansion of area occupied by crowns of trees of a given age class in a many-aged forest, contrasted with limited expansion possible in crown area in an even-aged stand. Loblolly Pine, Ala. Dotted lines show possible expansion of 7 per cent in even-aged stand. Shaded area shows pos- sible expansion of stand of 332 per cent in many-aged forest. On the left, in Fig. 82 an even-aged stand occupies a square area of 4 acres, 417 feet square. During its growth, crown ex])ansion is effected by a reduction in the number of trees from 140 at 40 years, to 59 at 80 years, with much more rapid reduc- tion previous to 40 years. The only expansion of area i)ORsib]e for the age class is around the edges of the square. The trees can extend their crowns an average of 14 feet, or 7 feet on one side, in the 50-j'ear period (27-13 feet). This gives a final area in square feet of 43P or an expansion of 7 per cent. 390 FACTORS AFFECTING THE GROWTH OF STANDS By increasing the area of the stand, this possible expansion of area becomes less. By reducing the area, the per cent of expansion possible becomes greater, since a greater per cent of the total number of crowns are so placed as to be able to utilize the increased space. The maximum possible expansion occurs when there are but 59 trees per acre at 30 years, equally spaced, and unobstructed by older age classes, in which case the area actually utilized by this age class expands 332 per cent or is 432 per cent of its original area, and the stand becomes fully stocked at 80 years. This expansion of actual are is shown on the right, in Fig. 82. This second process is what takes place in a forest composed of stands of many different ages. In the case of even-aged stands, thinning or removal of trees simply permits the remainder to grow, with no change in area for the class, and the removal of the final crop is followed by reproduction which in turn occupies the entire original area. But with many-aged stands, when the final crop is removed, which takes place on any acre in several different cuttings, the area so released is reproduced only in part. The remainder is absorbed by the crown spread of the intermediate age classes which thus increase their total area in the manner shown by Fig. 82. In the illustration, this stand at 30 years occupies but one-fourth of the total area of the 4 acres. The remainder can be occupied by older timber, which in the 50-year period is removed as it matures. By assuming this 4 acres to be but a part of a larger area, and to be distributed over the area coinciding with the distribution of the single age class in question, the conditions of a many-aged forest are visualized. This factor of crown expansion and competition between different age classes is the basis of the diflerences between the increment of many-aged and even-aged stands. It explains suppression, economic age, and increased growth after cutting. The actual amount of expansion and rate of increase due to this factor will be consider- ably less in all instances than the per cents given in table LXI since only a portion of the maximum space required by each tree of the class for expansion is available at all, and but a part of this can be taken from other age classes. Summed up, this factor represents an additional rate of increment to be added to that which an even-aged stand of like volume would show, and caused by the fact that the volume of the age class in the many-aged forest, while occupying only a certain per cent of the area of the forest, is thereby distributed over a much larger area into which its crowns can expand. 299. Annual Increment of Many-aged Stands. The rate of growth per year based on a unit of area for many-aged forests does not repre- sent production of a single age class, but of the sum of all the age classes on the area, averaged for a long period. If desired for a single age class, this rate or yield per acre should not be based on the area occupied by the timber at maturity divided by the total ages of the trees com- posing this stand, for this would greatly under-estimate the rate of mean annual growth. The error can be expressed and corrected in one of three ways: (1) either the age used as a divisor must be shortened to represent the economic age of dominant trees growing in even-aged stands, or (2) the area occupied by the mature crop must be reduced to represent the average area for the stand during its life, which is practically impossible, or (3) to the yield for the period represented by the total life of the trees in the stand as actually shown by ring counts, must be added the additional yields from other crops of timber THE EFFECT OF TREATMENT ON GROWTH 391 which this same area produced during the period when the final crop was only occupying a portion of it. The latter problem may be illus- trated best by the yield or rate of growth per year of stands w^hich have come up to spruce following poplar or white birch on a burn. In the period required to produce a mature crop of spruce, a crop of poplar and birch has also been produced. The mean annual growth for the whole period must include the total yield of both species. Owing to the difficulty of adjusting these yields on one of these three bases, it is customary to employ a substitute method of determin- ing the rate of growth, not for the total period by any of these adjust- ments, but for a partial period, measuring the current periodic growth based upon trees or stands which have already reached a given diameter or average age. This will be discussed in Chapter XXXI. Its effect is to eliminate most of the uncertainty attending the adjustment of the factor of competition in many-aged stands, but it introduces the question as to whether the current growth measured represents the true mean or average for the site over a complete period of crop pro- duction. 300. The Effect of Treatment on Growth. The fact that the growth of individual trees demands expansion of their crowns influences not merely the yield per acre which may be attained, but more especi- ally the dimensions of the individual trees in the stand. Since the production of lumber and of certain piece products and the value of products grown on a given acre depend much more largely upon dimen- sions and sizes and upon quality than upon total cubic volume, yields attained in board feet are profoundly influenced by the number of trees brought to maturity in stands of equal degrees of crown density or stocking. It has been commonly assumed that a normal or fully stocked stand simply meant one which showed a complete crown density throughout its life regardless or independent of the number of trees which composed it. This conception neglects the fundamental idea of the tree as an individual. Stands which are fully stocked when young, so that crown density is early established, usually become over- stocked almost immediately. The normal number of trees, to attain best results or highest yields, is least on good sites with strong growing species, rapid height growth and correspondingly rapid diameter growth, and increases as the sites become poorer. The danger of over-stocking and stagnation of both height and diameter growth increases with poor sites, even-aged stands, and tendency to abundant reproduction. These natural tendencies are affected tremendously by artificial control. All operations such as planting, in which the initial spacing is fixed, and subsequent thinning by which the resultant number of trees per acre at each decade is determined, have a direct effect upon the diam- 392 FACTORS AFFECTING THE GROWTH OF STANDS eter growth of the remaining stand, which in stands continually under management may be maintained at an almost constant rate until the maturity of the stand. It has been found that in stands originally stocked with only part of the normal number of trees for smaller ages, as the age of such stands advances and the number of trees required in a stand of maximum or normal density decreases, the poorly stocked stand tends to approach and to equal the yield per acre of the stand which has been normally stocked throughout its life. There is therefore a universal tendency under natural conditions for stands to approach a full crown cover as well as for the more densely stocked stands to become over-stocked. This tendency must be recognized in dealing with density factors or per cents in prediction of yield and forms a conservative factor in the prediction of growth for partly stocked empirical or average stands. Ideal conditions for growth are found in stands which have been main- tained at a normal number of trees per acre as well as a normal crown density through repeated thinnings. Not only is the total volume produced per acre and the rate of growth greatly increased by a proper balance between thinnings and the remaining stand, but the maturity of the stand is hastened and its rotation may be reduced if desired. 301. Density of Stocking as Affecting Growth and Yields. In spite of the tendency of natural stands to approach normal density of stocking through the expansion of their crowns, the attainment of normality or full stocking under natural conditions of growth is seriously interfered with by many agencies. Natural spacing or stocking is largely a matter of chance and fails over extensive areas. Much of the reproduction may be destroyed during these early years by grazing, fires, frost or drought. Saplings and poles may be further destroyed by fire, insects and disease. Later on, insects, disease, fire and wind continue to make gaps in the age class and crown density. Most of these detrimental factors are reduced under protection and the average density greatly improved, yet forests covering wide areas ordinarily can not be brought to a perfect or full condition of crown cover or stock- ing, no matter how intensive the care which is bestowed upon them. The yields of forests are desired on the basis of their actual average production and not upon the small per cent of stands showing maximum or perfect conditions of density and numbers per acre. This gives rise to the problem of applying tables of yield to these conditions, first as to the selection of areas or plots for the measurement of yields, and second, as to whether the area so selected shall be an average of all conditions of stocking within the site class or shall make no attempt to attain this empirical average. It has been generally accepted that the best method of obtaining COMPOSITION OF STANDS AS TO SPECIES 393 yields is to select plots which show a fairly complete crown density, not seriously reduced by avoidable factors of damage, and to con- struct the table of yields entirely from such plots. This is supposed to give the normal relation between yields at different ages for well- stocked stands. There remain many variable factors, the chief of which is the number of trees per acre in the plots measured. It has been suggested that the age or ages at which the final yield is to be harvested shall be taken to indicate the normal number of trees per acre and that stands of lesser age having this number or more trees, while not showing the full yield for these ages may be regarded as fully stocked, if not to be cut until the final age. The only difference between such stands and stands which remain fully stocked would be found in the thinnings in the interval and in the quality and limbiness of the timber.^ Yield tables based on a given standard such as described may be discounted to predict the average degree of stocking for average areas, which are known as empirical yields. In some instances efforts have been made, by collecting data on large areas, to obtain these empirical yields or averages directly in the field instead of by discount from yield tables. In either one or the other of these forms, the empirical or actual average is the final result desired, and the normal or standard yield table is but the means to this end. The arguments in favor of obtaining a normal or standard yield table by the selection of plots are that the variables represented in the average or empirical stocking by differences in form or mixed ages, differences in density and dif- ferences in composition of the forest, are eliminated from the table, which is confined to showing differences in yield based on site qualities and age. The relations of more than two variables can not be accu- rately set forth in a single table. 302. Composition of Stands as to Species. Stands composed of a mixture of species may vary in yield from pure stands. Species may differ considerably in their capacity for growth and yields even on the same site. They vary in height growth and consequently are affected differently by the factor of suppression when in mixed stands. The rate of survival and the dimensions vary so that the composition of the stand changes with its growth. Finally, the original composition, independent of these later changes, varies greatly. For these reasons the prediction of yields in stands of mixed species has always been regarded as extremely difficult. Approximate rather. than accurate results must be accepted. Recent investigations indicate that for certain character- istic types and mixtures of species naturally growing together, yields 1 The Use of Yield Tables in Predicting Growth, E. E. Carter, Proc. Soc. Am. Foresters, Vol. IX, No. 2, p. 177. 394 FACTORS AFFECTING THE GROWTH OF STANDS determined for the mixed stands do not differ very widely from those of pure stands (§ 314). References Universal Yield Tables, Fricke (Based on height classes); Review Forestry Quarterly, Vol. XH, 1914, p. 629. Classifying Forest Sites by Height Growth, E. H. Frothingham; Journal of Forestry, Vol. XIX, 1921, p. 374. A Generalized Yield Table for Even-aged Well-stocked Stands of Southern Upland Hardwoods, W. D. Sterrett, Journal of Forestry, Vol. XIX, 1921, p. 382. Concerning Site, F. Roth, Forestry Quarterly, Vol. XIV, 1916, p. 3. Site Determination and Yield Forecasts in the Southern Appalachians, E. H. Froth- ingham, Journal of Forestry, Vol. XIX, 1921, p. 14. CHAPTER XXVIII NORMAL YIELD TABLES FOR EVEN-AGED STANDS 303. Definition and Purposes of Yield Tables. A yield table is intended to show the yields per acre which can be expected from stands of timber at given ages or for given periods, in terms of a given unit of volume or of product. A complete yield table will show yields for successive decades or five-year periods covering the range of age of a species. Ordinarity, yield tables do not show the loss in yields per acre during the decadent period in over-mature stands, but they can be constructed so as to do so. In forests under management, the maximum ages shown are those of the oldest stands before cutting. Yield tables are used primarily to predict the yield of existing stands, hence they are assumed to represent the actual development of individual or typical stands throughout their life cycle. This they do not always do, since naturally stocked areas tend constantly to pass from a condition of under-stocking to one of over-stocking. It follows that the most reliable yield tables are those constructed for stands grown under management, where thimiings have controlled the incre- ment. Yield tables are the fundamental data required for the determination of the value of forest lands and the profits of forestry, the appraisal of damages to forest property, the choice of a rotation or average age at which timber should be cut, the advisability of thinnings, the choice of species, and the relative profit from expenditures for all forestry operations on different sites. An accurate or even an approximate knowledge of yields per acre and the average rate of growth per year tends to place forestry on a business basis rather than one of blind speculation. 304. Standards for Yield Tables. Yield tables undertake to set standards in which the variables affecting yield are eliminated. The basis of all yield tables is a separation into site qualities, with separate average yields for each quality, since the fundamental variable is site quality. Form of stand requires separate yield tables for even-aged stands, and many-aged stands (§ 252). 395 396 NORMAL YIELD TABLES FOR EVEN-AGED STANDS The factor of density of stocking (§ 273) separates jaeld tables into Normal or Index tables which are based on an average full or maximum stocking, and Empirical tables, which represent the actual average density of stocking on a given area including partially stocked and unstocked portions. Composition of the forest is distinguished by constructing tables for pure stands (§314) separately from mixed stands. The most important distinction is probably that made between natural stands and those grown under management. Owing to the great influence of treatment upon growth and yields, the standard of normahty (see above) is entirely different for natural and for arti- ficially grown stands, and yield tables based on the yields of planted, thinned and managed forests must be made to replace the present normal yield tables, when the material for such measurements becomes availalile in sufficient quantity to furnish a proper basis. Normal or index yield tables serve their chief purpose as a standard of comparison, since most stands will produce either larger or smaller yields than those shown (§ 250). This function is better served if the standard of normality set by the table is not abnormally high, but is made to conform to the results possible of attainment on the average acre of the site class, with reasonably thorough protection from destructive agencies and reasonal^ly full stocking. 305. Construction of Yield Tables, Baur's Method. There are two methods possible in the preparation of yield tables. The first, known as Baur's method ^ is based on the measurement of the present volume and age of numerous plots which are then classified as to site and age and form the basis of curves of average yields based on age for from three to four site classes. This method corresponds with the defini- tion of a yield table cited in § 249 since it does not pretend to trace the past history of these individual stands; yet the use to which such a table is put is to predict from these average curves the growth of a given stand by decades. For original stands under natural conditions, this method is universally used. The second method is to re-measure established plots at stated intervals to determine the volume of growth, diminution in number of trees per acre and other changes in the stand. While more accurate, the collection of such data must await the growth of the timber and the method is best applied to stands under manage- ment. Yield tables can be constructed by Baur's method on the basis of from 50 to 200 plots dependent on the range of site qualities and condi- tions of growth. The aim is usually to get at least 100 plots. 1 Die Holzmesskunde, Franz Baur, Professor of Forestry, University of Munich, Bavaria, 1891. STANDARD FOR "NORMAL" DENSITY OF STOCKING 397 306. Standard for '* Normal " Density of Stocking. In selecting plots for a yield table, in natural stands, it is neither possible nor advis- able to seek areas which show the maximum theoretical density of stocking, either as to crown canopy or number of stems per acre. Nor should any effort be made to select plots which represent the empirical average of stocking. The standard should be to exclude from the plots all larger blanks caused by destructive agencies or failure of stocking and to select areas reasonably well stocked, with comparatively complete crown canopy. This standard of selection should be such that a suf- ficient number of plots can be readily obtained from the larger areas, without refinements either in size or in location. If too high a standard is set, the plots conforming to this standard will be found to be either located exclusively on the better portions of each site, or the area of the plots' will be too small for safe results. In natural stands this ten- dency will lead to the selection of plots containing too great a number of trees, which will result later in over-stocking. The average yield obtained from plots selected on this basis is termed the normal yield, though it may be exceeded by the best plots, or by stands grown under management. 307. Age Classes. The area of a plot should include but one age class. Where stands are actually even-aged over considerable areas, plots are easily and rapidly located. Where there is difficulty in dis- tinguishing the age classes, and in locating areas which exclude all trees but those belonging to the class desired, it may be necessary to include a few scattered trees of a different age class in order to obtain plots of a suitable size. The net area of the plot can then be found by deducting the space occupied by these trees, which can be based on the area covered by their crown spread, modified in open stands to include a proper proportion of the gaps in the crown cover. Stands whose period of reproduction is from ten to thirty years, depending on site and climatic factors, but which may still be classed as even-aged stands (§ 259) will be measured as such and their average age determined. 308. Area of Plots. The value of a single plot in indicating normal yield increases with its size, within the limit which permits of securing a uniform stocking and crown cov^r conforming with the standard sought. Since one plot represents but a single age and one shade of site quality, and the cost of measurement increases with size, it is better to limit the size of plots for a yield table and obtain a greater number more widely distributed. The size of plots should increase with the size and age of the trees to be measured. The greatest danger in measuring small plots is failure to coordinate the quantitative site factors utilized in producing 398 NORMAL YIELD TABLES FOR EVEN-AGED STANDS the yield with the area measured. This error is best illustrated by the measurement of an isolated clump of trees with wide crown and root spread. A plot laid out to include their boles will have too small an area, and an excessive yield (Fig. 83). In dry regions especially, root spread exceeds that of crowns and cannot be determined accurately. The effect of these errors is especially noticeable when the size of the plots is small, the yield per acre varying inversely with area of plots. By increasing the size of the plot, the proportional influence of a faulty location of its boundaries is lessened, and when coupled with care in making these boundaries inclusive of crown space and probable root space of the trees measured, the error is negligible. Just as for other sample plots (§ 243), it is better to have a smaller plot surrounded by a control strip of similar timber than to extend the boundaries to in- clude the whole of a stand to be measured, and it is usually possi- ble, in regions of average rainfall, to have such a control strip. The size of plots under the above principles will vary from ys- acre, for dense young stands, to 5 acres for veteran scattered timber in dry regions. Ordinary sizes run from j to 2 acres. Since these boundaries should be accurately run, plots should be square or rectangular, and since the area contributing to the growth of single trees is in theory a circle, rectangular plots should not be too narrow: their short dimension should be at least four times the average width of cro\»^ns of the trees measured. For the same reason plots should never be triangular or have sharp angles. Unless intended for permanent location and re-measurement, the corners of plots are marked tempora- rily by any convenient means, and their side lines blazed or marked so as to exclude all trees falling outside of the boundary. 309. Measurements Required on Each Plot. Dimensions of Trees. A diameter limit is determined, dependent on minimum merchantable sizes. All trees above this are measured at B.H. and recorded in diam- eter classes of 1 inch or 2 inches. Since these plots are for the purpose Fig. 83. — Relation between growing space occupied by crowns or roots of trees and size of plot measured to secure yield per acre. A — Too small an area. B — Correct for humid region or site. C — Approximately correct for arid region. MEASUREMENTS REQUIRED ON EACH PLOT 399 of measuring yields they are selected in stands which have reached merchantable sizes. Plots on which a portion only of the trees are merchantable may require the counting of the remaining stand and its classification as to size. Dead trees are recorded by diameter. Species are separately tallied. The height of trees for a yield table should be taken separately on each plot. Several tn^es of different diameters, whose heights are average for the stand should be measured and recorded together with their diameters, the number varying with the stand, from 5 to 15. Where merchantable and not total height is desired, the satisfactory determination of heights for the plot is made much more difficult by the variation in top diameters and the danger of error in judging heights. Such a yield table, while practical, is less reliable than one based on total heights. Total height should always be recorded regardless of whether merchantable height is used, since it is required for a permanent standard of site quality. Where the merchantable height unit is used it may be better to tally the merchantable length of every tree on the plot than to rely on a few trees measured by the hypsometer. This introduces the element of ocular guess. Age and Volume of Stand. The age of each plot is separately determined by methods discussed in Chapter XXIII. The common method of determining the volume on the plot is by standard volume tables, based on diameter and height. This assumes that the variation of the trees on each plot as to shape or form quotients from the average form for this species or region, is not sufficient to require separate determination. Since trees must either be felled or cut into, to deter- mine age, except when the increment borer will suffice, and since the trees selected for this purpose would be average in volume for the stand or for diameter groups within it, these sample trees are sometimes used to determine the volume of the stand. This method is useful when no reliable volume table exists, and when cubic volume is sought. The additional accuracy attained in measuring the volume of the sample trees for the plot itself is offset by the possibility that the trees cut may vary from the true average of the stand. The methods of deter- mining the size of such sample trees for felling are described in § 241. Crown Classes. Each tree on the plot is usually tallied in the crown class in which it falls, as classified in § 274. Description of Plot or Site. Since in the preparation of a yield no effort is made to classify the plots into site qualities by inspection of the site factors in the field, the description of the plot should be brief, and serve merely to explain the results obtained and check their value.. The points to be covered are the following: 400 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 1. Location of plot. Region, watershed or block, section or forty. Relocation is not contemplated from this description. 2. Density of crown cover. This has in some studies been used in an attempt to reduce the area to a fixed standard of density; e.g., a stand showing .9 crown density would be considered as the equivalent of but .9 of a full yield on the plot. The element of judgment thus introduced is dangerous and had best be omitted. 3. Altitude: Absolute — approximate. Relative — with respect to nearest stream, when it affects the quality of site. 4. Aspect — as affecting exposure. 5. Degree of slope. 6. Geological formation. 7. Soil, kind, depth, consistency and degree of moisture. 8. Origin of stand, whether from sprouts or from seed. 9. History of stand. 10. Condition of stand with respect to evidence of damage caused by fire, insects, wind or other agencies should be especially noted. 11. Exposure to winds, degree and character. 12. Amount and character of tree reproduction on the ground. 13. Herbaceous and shrubby vegetation under the timber. Record of Data for each plot. The data of permanent value for each plot are, 1. Area, in acres. 2. Age. 3. Total number of living trees, by species. 4. Number of living trees above merchantable diameter limit, by species. (This may be shown for two diameter limits, as for cordwood and saw timber units.) 5. Average diameter (from diameter of tree of average basal area, or volume) (§ 242). 6. Height of dominant trees, or dominant height of stand; total; merchantable. 7. Total basal area at B. H. of trees per acre, in square feet. This is a valuable index to density of stocking. 8. Yield per acre, in cubic feet, total. 9. Yield per acre, in merchantable units, to given top diameters and stump heights. 10. Dead standing trees, number or per cent. ■ 11. Density of crown cover. 12. Description of plot. TABLE WITH SITE CLASSES BASED ON HEIGHT GROWTH 401 310. Construction of Yield Table with Site Classes Based on Height Growth. There are two possible bases on which to sepai'ate site quality, namely yields or rate of growth, and total height or height growth. In choosing between these as the basis of site quality, not only must the construction of the table be considered but also its later application in the field. Whichever basis is used, the range of growth for a species or region must be divided arbitrarily into site classes, once its maximum and minimum limits are determined. When volume or yield is chosen as the direct basis of site classes, regular and consistent results may be obtained by eliminating most of the variables in the choice of plots. But when these results arc later used as a means of determining site qualities in the field on the basis of mean annual rate of growth per year or total yield based on age, the system breaks down. On the other hand, if the division of plots into site qualities is based on height growth as indicated in § 296 not only are the original plots apt to be separated more accurately into their true site classes since variations in volume due to over- or under-stocking as reflected in the board foot or other unit are minimized, but the division of a large area in the field into site classes for the application of the growth data in predicting yields is made possible in strict conformity with the standard used in the table itself (§ 345). While volume has been made the direct basis of many European yield tables, yet in these regulated and fully stocked stands most of the variables are reduced to reasonable proportions. Under our con- ditions of abnormal and accidental stocking, with the maximum of damage to the stands during growth, the variations from the factor of density of stocking due to variable number of trees per acre, even in stands of full crown cover, is so great as to discourage most investi- gators on first attempt. The steps in the construction of a yield table based on height are as follows: 1. On cross-section paper on which age is plotted on the horizontal scale, and height on the vertical scale, place the average height for each plot above the age of the stand. These heights may be the heights of the dominant trees (§ 296). These points will fall in a comet-shaped band increasing with age. 2. Draw a curve indicating the maximum height growth, and one for minimum height growth as in Fig. 84. 3. Decide upon the number of site classes to use. These will depend largely on the total range of heights found for trees of a given age, and the possibility of convenient subdivisions not too small to be serviceable, i.e., large enough to overcome the slight variations in height based on age which may be due to density of stand instead of site. 402 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 4. Divide the space between the maximum and minimum curves, on each ordinate, into arbitrary spaces of equal magnitude, corresponding to the number of site classes established, and connect the points so found by curves. 5. The numbered plots whose height falls in each division of the chart are assigned to the indicated site quality. Owing to variables affecting yield, some of the plots in a lower site class may exceed the growth of plots whose site class is better. 90 75 lUU ^ 90 ^ ^ .„\\^-^ • 80 ^ ^ b^- ^ / / ^ 70 / •" ^ -^ ^uaV \\ / y y — ^60 <2i / X ^ A / ^ ^• 3ua \ity uv |50 / ^ . v ■y^ >•_ . — ■ — /• ■/ '< / ^ ^- 40 ) y y.: / ^ ■^ \/ /• '/. / y 30 / / V / '■/ / /' / 20 1 f / / / 1 / / / / ao / / r / <'^ / / /' ^- 10 20 40 50 Age, years 60 70 80 90 Fig. 84. — Method of separating plots into three site quaUties based on the height attained by dominant trees in the stand, plotted on age of stand. Jack Pine, Minnesota. The height of dominant trees on 131 plots of jack pine, plotted on the basis of age, is shown in Fig. 84. By this method (Baur's), the positions of the maximum and minimum curves determine that of the curves separating the site qualities. One or two plots with abnormally rapid or slow growth must not be permitted to influence unduly the position of these outer curves. With height, the true position of the boundary curves can be found with greater certainty than if volume is used originally as the basis of classification. In this figure, the average heights of qualities I, II and III at 100 years were taken as 90, 75 and TABLE WITH SITE CLASSES BASED ON HEIGHT GROWTH 403 60 feet, following the suggestion of Roth as an example of class C in height classification (Table LV, § 296), and with these guiding points the curves limiting the three classes were drawn by Baur's method. 6. The yield of all plots in a single site class are then plotted on cross-section paper whose base or horizontal scale is age, and whose vertical scale is volume. From these data, a curve of average yield 100 no 120 130 1.40 Age. Years 160 170 180 ISO Fig. 85. — Curves of yield obtained by averaging the yields of plots whose height growth has placed them in the same site class. The final curves smooth off irregularities in these averages. Second growth Western Yellow Pine, California. S. B. Show. based on age may be drawn from which the 3delds for the site class for each decade or five-year period are read. A separate curve is plotted for each site class. The yield table finally shows the average yields based on age for each separate site class. 404 NORMAL YIELD TABLES FOR EVEN-AGED STANDS When constructed on this basis, yields for different site classes increase at a greater ratio than do the indicating heights. In drawing the curve of yield based on age for a single site class, it is best to first obtain the average yield for a given decade by arith- metical means and connect these averages by straight lines. Even if each plot were normal, the averages at different points might fall above or below the mean for the site as the plots happened to be on the better or poorer portions of this site class — and to this factor, the natural vari- ation in density or yield is added. 7. For this reason, the average curves so constructed, for each site class, should now be assembled on a single sheet, as shown in Fig. 85. The curves of yield based on age can then be harmonized for all site classes by the same principle as used for volume tables (§ 140).^ 311. Rejection of Abnormal Plots. As shown in § 304, the intent of this table is to establish a standard of yield, termed normal or index, with which the yields of any existing stand may be compared. After the separation based on height growth is effected, the yields of plots in the same site class will show great variation, due to the Natural range of site quality within the arbitrary boundaries established; Numl)er of trees per acre in the natural stocking; Completeness of the crown canopy. The eccentric behavior of the averages plotted in Fig. 85 indicates the effect of these variations in yield. The question arises as to whether all of the plots should be included in these averages or certain plots rejected as abnormally stocked. A method of correcting the yields by a factor of density of crown has been generally rejected as unsatis- factory (§ 309). The area of plots is accepted as measured. There are, then, two possibilities of rejection; first, by ocular selection in the field, which eliminates those plots which are incompletely stocked; second, by further inspection of the plotted volumes based on age. Baur's rule for rejection of plots is quoted by Graves as follows: "Stands which have the same age and average height are compared, and all are considered normal whose basal area lies within a range of 15 per cent; that is, the basal area of the best and poorest stocked stands must not differ more than 15 per cent." ^ The application of this rule rests upon the interpretation of the term " average height." Where from three to five site classes are made as in Fig. 85, and a curve of average height is found for each site class, which would fall midway of ^The yields shown in Fig. 85 are from an unpublished manuscript by S. B. Show, U. S. Forest Service, California, for second growth Western yellow pine. " Graves' Forest Mensuration, p. 319. REJECTION OF ABNORMAL PLOTS 405 the limits shown in the figure, the rule has been applied in this country to all plots whose heights classify them with a given site. The natural variation in volume for plots within one site class is greater than 15 per cent, independent of abnormalities — hence if all plots which vary 7| per cent above or below the average volume for the site at that age are rejected, about half of the plots, although noYmal, may be thrown out. If this rule is to be correctly applied as a test of normality, the arbitrary permitted variation of 15 per cent, if used at all, should first be corrected by finding what the normal yield of the particular plot should be, based on its actual height. If height for the plot is midway between quality I and II, normal yield is also midway between the averages for these qualities. The steps necessary would be as follows: 1. Draw curves of average height as shown in Fig. 84, and curves of average volume as shown in Fig. 85. 2. Determine the per cent of variation above or below average height, for each plot, and subtract or add the same per cent from the volume of the plot. This gives the corrected volume of the plot based on average height for the site. 3. Compare the corrected volume of the plot with the average volume for the site. If it falls above or below the calculated normal by more than the desired per cent of error the plot can be thrown out. 4. After testing the normality of all plots, re-compute the average, using only those plots accepted as conforming to the standard. If 15 per cent is a proper standard of variation for forests under management, it is probable that even with the above method this per cent is too small as a criterion of normality for natural stands. It should be possible, by eye, to select plots of which at least 95 per cent will be suitable for inclusion in obtaining the average results for a stand- ard yield table. With a range of basal area increased to 25 per cent for plots of the same height based on age as indicated, it is probable that only distinctly abnormal plots will be rejected. In constructing volume tables it is not customary to reject trees after they have been measured for volume, since rejection can take place in the selection of the tree. With plots for yield tables, the desire to secure a theoretically normal or uniform standard may easily lead to too rigid a rejection of plots which are entirely suitable for the aver- age sought. Maximum yields, on the basis of site alone, should never be sought by these average curves of yield, since the best portions of the site will exceed the average. Again, such tables, if made for natural stands, should show what can reasonably be expected in stands repro- duced naturally and not thinned, on the average acre for site. A con- sistent average showing the probable progress of a fully or normally stocked acre by decades, and not an abnormal maximum yield, is the 406 NORMAL YIELD TABLES FOR EVEN-AGED STANDS object sought both in field selection of plots and in their further sifting in the office for the preparation of normal yield tables for natural growth. 312. Construction of Yield Table with Site Classes Based Directly on Yields per Acre. The main objection to the direct classification of site on the basis of yield or volume on age by Baur's method is the impossibility of using this basis later as a means of classifying forest lands into site qualities from field examination. Furthermore, yield alone gives an unsatisfactory basis for correlating yield tables for given species when made for different regions, or for correlating the yields of different though similar species. It is this need of standardization that has led to the adoption of height growth rather than volume as the basic standard. A further objection to the direct use of yields lies in the method of plotting, and the testing of plots for normal density. By this method, the volumes of all plots, based on age, are entered on the same sheet as shown in Fig. 86. The drawing of the maximum and minimum curves is the next step. There is no way by which the abnormality of the plots can be first tested as with heights. So the elimination consists wholly of drawing these boundary lines to exclude certain plots whose yield is so much greater or smaller than the remainder that their inclusion would unduly influence the position of these limiting curves. The third step is to divide the space thus blocked off into equal bands by the method used for height, i.e., by dividing the distance on each ortlinate into equal parts, and connecting the points so estab- lished. Finally, a curve is drawn exactly midway of each space as described for height (§ 310), and the values are read from this curve at each decade to form the table of yield based on age. By this method yields increase with site quality by exact intervals. No averages are attempted,, and the result is entirely independent of height and is influenced principally by the maximum and minimum yields rather than the general weight of the plots studied. Using as the basis the plots which have been classed as belonging to each separate site by either of the above methods, curves showing the average at different ages can also be prepared for the following additional data: Number of trees per acre; Total, Above a minimum diameter. Average diameter. Average height of dominant trees. Total basal area. YIELD TABLES FOR STANDS GROWN UNDER MANAGEMENT 407 313. Yield Tables for Stands Grown under Management. Normal yield tables for stands grown under management may be constructed by the above methods, whenever plots are available which have been under proper management, but may in the course of time be checked and finally supplemented entirely if desirable by the yields of plots which have been measured at intervals of from five to ten vears. 4000 3500 3000 2500 2000 1500 1000 500 -^ y /f ^^- ^--" I • / m /" .-^^ • • ••/ • ^ / » / / / y • • •^.- • II / • / » » • ^^ » 1 . / / /• / \'y /• • • ^^ • • */' . / • ^^ \^ ^^ III i / 1 /• » / • .*^-- .--' ' 1 1 1 1 1 1 1 1 / / Y ,^'' y'^ • ' * 1 1 1 1 1 1 I • • • / y y^ / / ' 1 / ,'■ I / / y / / / / J / / 1 / y / <^/ • • • — y^ /- ■'^-^' 10 20 30 40 Age, Years 50 60 70 80 Fig. 86. — Curves of yield based directly on cubic volume plotted on age. Jack Pine, Minne.sota. WTiere a series of plots, differing in age by ten years, is available, the measurement a decade later on these plots will give fragments of a curve of growth which may be pieced together. The greater the period over which these re-measurements extend, the more nearly do these fragmentary curves form a complete series. It may be expected that yields on areas under treatment will exceed the so-called normal yields used as a standard for natural growth. 408 NORMAL YIELD TABLES FOR EVEN-AGED STANDS The latter tables thus become the basis or minimum from which such increased yields may be computetl for fully stocked areas. 314. Yield Tables for Stands of Mixed Species. Practically all stands are composed of more than one species, though some conifers as Western yellow pine and lodgepole pine grow in practically pure stands. So prevalent is the mixture that a stand which is composed of 80 per cent and over in volume for the given age class of a single species is termed a pure stand of that species. There may exist a large number of trees in an under-story of different species, and yet the volume of the trees of other species in the main stand may not exceed 20 per cent. In even-aged stands composed of two or more species in mixture, two methods have been proposed for the determination of yields. One is to prepare yield tables for pure stands of each species, and then to determine the per cent of these species in the mixed stand. The further yield of such a stand is predicted by applying the per cent thus indicated, to each yield table, and taking the sum of the two partial yields as the yield of the mixed stand. In applying these tables on this basis to get yields for the future from young stands, the question of survival may affect the result, in case one species tends to crowd out another. But when stands are even-aged, the association is apt to be of species which customarily grow in mixture and maintain their places in the stand. The yields, however, will be for the per cent of future, not of present mixture. Where species differ radically in their characters, and grow in a mixed stand, such as a hardwood species with conifers, there is apt to be greater variation in yields, but with trees of similar habits, such as mixed sprout hardwoods or mixtures of two or more conifers, the stand behaves much as it would for pure stands. For all such even-aged mixed stands, it is possible to prepare yield tables by disregarding the per cent of mixture, or recording it merely as a descriptive item, and proceeding as if the stand were pure. An example ^ of a yield table for mixed stands of second-growth hardwoods in New England is given below. The conclusions based on this study were, first, that in spite of wide variation in percentages of species in mixture, for a given age, site, and density, the volumes in board feet, cubic feet and cords were constant, and, second, that the volumes of trees of given height and diameter in cords and cubic feet were the same, regardless of species. 1 Bulletin of the Harvard Forest No. 1. Growth Study and Normal Yield Tables for Second-Growth Hardwood Stands in Central New England. By J. Nelson Spaeth, Cambridge, Mass., 1921. YIELD TABLES FOR STANDS OF MIXED SPECIES 409 TABLE LXII Normal Yield per Acre in Cubic Feet and Cords of Better Second-growth Hardwood Stands in Central New England site class i (All trees 2 inches in diameter and over) Age Trees Basal Height DB.H. Volume Vclume Forest in per area in in per acre. per acre. form Years acre Sq. ft. Feet Inches Cu. ft. Cords factor 20 1250 66.0 27.1 3.11 1041 15.80 0.582 25 1120 90.8 33.0 3.86 1625 23.71 .542 30 1010 107.2 37.5 4.41 2150 29.75 .501 35 900 119.9 41.5 4.94 2628 34.96 .503 40 800 130.2 45.0 5.46 3058 39.63 .520 45 700 139.7 48.2 6.05 3495 44.03 .520 50 610 148.0 50.7 6.69 3898 48.00 .520 55 525 155.7 53.1 7.37 4298 51.84 .520 60 450 162.5 55.4 8.14 4677 55.50 .520 65 390 169.0 57.8 8.91 5068 59 . 25 .520 70 340 175 1 59.8 9.72 5462 62 . 75 .522 75 300 180.9 61.9 10.51 5833 66.18 .521 80 270 186.3 64.0 11.25 6200 69.50 .520 SITE CLASS II (All trees 2 inches in diameter and over) Age Trees Basal Height DB.H. Volume Volume Forest in per area. in Ill per acre. per acre. form Years acre Sq. ft. Feet Inches Cu. ft. ■ Cords factor 25 1360 59.8 27.8 2.84 982 14.65 0.593 30 1235 77.9 31.8 3.40 1380 20.40 .557 35 1125 91.1 34.8 3.86 1798 25.48 .567 40 1030 101.6 37.4 4.25 2180 29.53 .574 45 940 110 3 39.8 4.66 2534 33.04 .577 50 855 117.9 41.5 4.94 2828 35.98 .580 55 775 124.6 42.8 5.43 3118 38.55 .584 60 700 130.7 44.2 5.85 3375 41.08 .584 65 630 136.6 45.3 6.31 3638 43.42 .587 70 565 142.2 46.3 6.79 3895 45.61 .592 75 500 147.7 47.0 7.36 4146 47.75 .598 80 440 153.0 47.6 7.78 4390 49.80 .601 The percentage of species in mixture in the stands comprising the above tables ia shown in Table LXIII. 410 NORMAL YIELD TABLES FOR EVEN-AGED STANDS TABLE LXIII Percentage of the Various Species in Mixture from Table LXII Classified AS TO Type and Site Class Oak, Red Maple Birch Beech Ch't- nut Bass- wood Pop- lar Ash, white Better Hwd Red Hard Gray Paper Yel. Misc.* Qual. I Qual. II Inf. Hwd. 27 20 2 15 12 24 3 6 2 38 2 8 3 8 10 4 2 7 6 5 1 .9 3 7 8 15 15 14 1 6 7 10 * Under miscellaneous are included all species whose combined representation in the plots of any one type or site class is less than 5 per cent of the total number of trees. These species are: white oak, black cherry, pignut hickory, white pine, hemlock, elm, butternut, hop horn- beam, black birch, flowering dogwood, and shad bush. By either of the above two methods of constructing yield tables for mixed stands, the yield of the entire stand is taken as the standard of yields.! The classification of mixed stand may be greatly simplified by group- ing together all plots in which 80 per cent or over of the merchantable volume is made up of certain species. In a study of the mixed conifer type on the Plumas National Forest in California, containing Western yellow pine, sugar pine, Douglas fir, white fir, and incense cedar, 75 per cent of 156 plots were found to contain but two principal species whose combined volume was over 80 per cent of the plot. The yields could l)e grouped as 1. Yellow pine — Douglas fir. 2. Yellow pine — Fir (Douglas or white). 3. Douglas fir — white fir. As indicating the possibilities of simplifying the problem of yields of mixed stands, it was found in this study that the average basal areas, for plots showing the same standard of height growth (§ 296) was as follows: Type Basic plots Per cents of yellow pine — Douglas fir type Yellow pine — Douglas fir 43 65 21 100.0 Douglas fir — white fir . 97 Yellow pine — fir 105.1 ^ A method by which the per cent of yields in plots of mixed species is recorded on the cross section paper, and the yield per acre expressed for different species which constitute different per cents of the total stand, is described in Graves' Forest Mensuration, Chapter XVII, p. 332. REFERENCES 411 This result strengths the conclusion that for species which form part of the same crown canopy, differences in total yield, of plots with different per cents of mixture, may not constitute a serious obstacle to the construction of yield tables based on age.^ References Rate of Growth of Conifers in the British Isles. Bui. 3, Forestry Commission, 1920. Comparison of Yields in the White Mountains and Southern Appalachians, K. W. Woodward, Forestry Quarterly, Vol. XI, 1913, p. 503. Einheitliche Schatzungstafel fur Kiefer, Zeitschrift fiir Forest- und Jagdwesen, June, 1914, p. 325. Review, Forestry Quarterly, Vol. XII, 1914, p. 629. The Use of Yield Tables in Predicting Growth, E. E. Carter, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 177. Yields of Mixed Stands, Schwappach, Untersuchungen in Mischbestanden, Zeit- schrift fiir Forest- und Jagdwesen, Aug., 1914, p. 472. Review, Forestry Quarterly, Vol. XIII, 1915, p. 98. 1 A Preliminary Study of Growth and Yield of Mixed Stands, S. B. Show and Duncan Dunning, U. S. Forest Service, San Francisco, Cal., 1921. Unpublished manuscript. CHAPTER XXIX THE USE OF YIELD TABLES IN THE PREDICTION OF GROWTH IN EVEN-AGED STANDS, WITH APPLICATION TO LARGE AGE GROUPS 315. Factors Affecting the Probable Accuracy of Yield Predictions. If the average yield on Quality I site for a species is taken as 100 per cent, and but three qualities are distinguished, the relative yields shown for Qualities II and III may be as low as 72 and 45 per cent of that on Quality I, respectively.^ This means gaps of 28 and 27 per cent in the series between the points arbitrarily marked by the average curves expressed in the yield table. The use of five qualities of site reduce these intervals to about 15 per cent. For young stands, or areas just growing up to timber, this is as close a prediction as can be expected. If the site is properly classified, its future yield if normally stocked will differ by an extreme of one-half of the above interval, either above or below the standard. Once the site is identified bj^ the use of average height based on age, the future yields can be predicted by use of the yield table, either for bare land or for partly grown young stands, provided the degree of stocking agrees with that incorporated in the table. The larger part of the area of any natural forest is not comparable with these conditions. The variables of density of stocking, form of age classes, and composition of species must all be dealt with before yields on any considerable area can be predicted within the desired mar- gin of accuracy. The degree of accuracy attainable in prediction of yields in our wild forests is not yet known even approximately since for many-aged forests and mixed stands, yield tables based on age have not been attempted untU recently (§ 314). This much can be said — the degree of accuracy attainable, and hence required, is greatest for short periods, i.e., for the current growth of a decade or two, and diminishes as the length of the period increases. But the relative importance of accuracy also diminishes with the length of the period, thus permitting the use of yield tables based on averages. 1 Norway Pine in the Lake States, U. S. Dept. Agr., 1914, Bui. 139, p. 15. ' 412 ACTUAL OR EMPIRICAL DENSITY OF STOCKING 413 316. Methods of Determining Actual or Empirical Density of Stocking. For even-aged, pure stands, but one variable is present in addition to site quality, that of the density of stocking. As this variable is the result, first, of the intrusion of small areas of unstocked land into the timbered area, which it may not pay to exclude in mapping (§ 306) and second, of the uninterrupted play of natural agencies of destruction operating on stands which are themselves originally the result of chance at the time of reproduction, the problem is to arrive at an average yield per acre which expresses not so much the capacity of the site as the accidental product of these various conditions. This average will in all cases be less than the standard or normal yields for the same area, sometimes by as much as 50 per cent. Evidently the determination of site quality is but the first step in predicting the yields of existing stands from such a standard table, and without correction these predictions may range from 50 to 100 per cent too high except on small tracts, such as plantations or managed forests, whose density factor is known to coincide closely with the yield table. Use of Empirical Yield Tables. There are two methods of over- coming this difficulty. The first is an attempt to arrive directly at the average yields based on age for the larger area, or to make an empir- ical yield table (§ 303) which will reflect the degree of stocking present. This applies the principle used in timber estimating in determining the volume of the average acre (§ 209). But the operation is more dif- ficult, as it involves the separation of the entire area into stands based on age, whose area is known, and the combining of these data into a yield table subnormal in character and representing a purely arbitrary percentage of standard yields. In the preparation of such a table, the curves of yield are affected by the varying per cents of stocking of dif- ferent age classes and areas so that practically the entire area must be analyzed to obtain the true average, and then the table will be incorrect in its prediction of yield for any specific age class or stand which differs from this arbitrary average stocking. The table will be correct only for the tract on which it is made since empirical density varies with every forest and block. Empirical yield tables on this basis have the same drawbacks as volume tables for defective trees which express the net contents only (§ 151). Use of Normal Yield Tables by Reduction. The better plan, and the one which will probably be universally used, is to depend upon a standard normal yield table (just as -upon a volume table for sound trees only) and to ascertain the relation or percentage of deduction from this table, which applies to the specific stand or larger area for which yield is desired. For even-aged stands, the application of the yield 414 THE USE OF YIELD TABLES table to the larger area involves the same steps for this area as are required in the construction of the normal yield table itself, or for the preparation of an average empirical yield table. These are as follows: 1. Determine the volume, the area occupied, and the age of each separate age class. 2. From these data in turn compute the volume per acre for the given age. 3. Determine the relative density by dividing this unit volume by the yield of an acre of the same age from the yield table; this is expressed as a per cent of the standard yield for that age. Per cent density can thus be found separately for each age class, or for each separate stand if desired. 317. Application of Density Factor in Prediction of Growth from Yield Tables. Future yield can now be predicted for all stands from the same yield table,- by applying the reduction per cent to this table which is required by the stand or age class in question. Influence of Number of Trees per Acr^. There is one valid objec- tion to this assumption that relative density as expressed at a given age in terms of volume will remain constant for future yields and that is that under the laws of growth of stands partially stocked this stand will tend to become fully stocked (§301). A knowledge of the number of trees per acre required for full stocking at the age of cutting is also obtained from a normal yield table, and this knowledge may be directly applied in determining the per cent of density in immature stands, not on the basis of crown cover existent but of the ultimate yield to be expected from the trees which will probably survive. In the same way, for older stands, when volume per acre is less than that in a nor- mal stand, but the number of trees per acre is sufficient, the reduction can be lessened as applied to these partially stocked stands as long as the trees are so distributed as to utilize the area; e.g., in one case, a 50 per cent average stocking may represent 100 per cent stocking on 50 per cent of the area, with the rest blank. No correction should be made. In another case the entire area is covered with a stand whose volume is 50 per cent of normal, but trees are well placed. In this case the yield will probably be normal at the age at which the normal num- ber of trees per acre drops to about the average number now present in the natural stand. The former or simpler method is of course extremely conservative and allows a margin for the continuance of natural losses by fire, wind, insects and diseases, while the latter may be applied to more intensively managed and better protected forests. PREDICTION OF GROWTH FROM YIELD TABLES 415 This method is illustrated below based on a standard yield table, § 314. Second-growth Habdwoods in Central New England Site Class I Prediction of Actual Standard Yield 63 Per Cent Area. Age. Yield. Yield, per Yield per Reduction. OF Standard in acre. acre. 10 Years. 20 Years. Acres Years Cords Cords Cords Per cent Cords Cords 10 25 150 15 23.71 63 22 27.7 This assumes no increase in the density factor with age and is the most conserva- tive method. Assuming that future yield will be influenced by the number of trees and their distribution, the future yields as shown may be increased as follows: Number of trees per acre now Normal number in 10 years Reduction per cent in 10 years Yield in 10 years. Cords Normal number in 20 years Reduction per cent in 20 years Yield in 20 years. Cords 600 900 66 1 23.3 700 86 37.8 This basis gives the maximum possible yields to be expected by contrast to the first method, since it does not contemplate the loss of any of the original six hundred trees, and assumes that these trees are distributed at equally spaced intervals over the area. Somewhere between these two predictions the actual future yield will be found. Use of Basal Areas. Basal area may be substituted for yields in determining the percentage relations, and as a basis for predicting yields in cubic feet. If in the above example the basal area at twenty- five years is 57.2 square feet per acre, the reduction per cent is 63 and the same prediction of future yield is obtained, which can be modified by comparing the number of trees per acre in the same way. These illustrations bring out the function of a yield table as dis- tinguished from that of merely stating the yields of stands. When the total age of any given stand is determined in addition to its volume, the rate of growth per year for that stand can then be found, or its past yield. But the whole purpose of a yield table is to predict the future yields of stands. A standard yield table gives a means of predicting this future yield, by indicating first the yield relation as to density of 416 THE USE OF YIELD TABLES the stand in question with the standard yields, the second, the rate of growth for future decades, which can be reduced to fit the existing stand. 318. Separation of the Factors of Volume, Age and Area. The difficulties surrounding the prediction of 3Melds lie in the fact that this requires for any stand the determination of three factors: volume, which can always be measured ; age, which can be determined for a given tree but is difficult to find for an entire stand of mixed ages; and area, which can be measured, provided the boundaries of the age class are known or defined. The trouble arises entirely from the mixture of trees of dif- ferent age classes on the same area, the overlapping of crowns and root spread, and the shifting of total areas occupied by each separate age class in successive periods (§ 298 and § 299). Thus two of the essential factors, age and area lose their clear definition. These two factors are interdependent in such forests. Age classes cannot be confined to stands of a single age but must include an age group. The area occupied by such a group will be influenced by the number of separate ages included in the group. It has been shown previously in this chapter that the area occupied by a given age class, when determined by mapping, determines the relative density of stands whose age is known. The yield table expresses an arbitrary standard yield on 1 acre at a given age, representing 100 per cent density at each age. (This means that the table is accepted as standard, but does not necessarily represent the maximum yields possible on any acre, which may exceed this standard, by from 15 to 20 per cent.) When both area and age are determinable for a stand, the exact relation as to density or yield when compared with the standard can be found for each stand separately. When neither can be found with accuracy, they must be found by such means as is possible, and the results, while not as accurate, will be serviceable and worth attaining. The general method of solving this problem is to work from the known to the unknown, accepting averages and approximations when exact determination is impossible. 319. Determination of Areas from Density Factor. One of the simplest and most useful applications of this principle is in the deter- mination of the area occupied by each of several age classes, whose age and volume are known but which have not been or cannot be mapped separately. The total area of the tract can always be determined. If for any reason it is impossible to map the area of each age class, these areas may still be found hy proportion if we are willing to assume that the average density of the entire stand can he applied separately to each age class. While admittedly less accurate than the separate determination of DETERMINATION OF AREAS FROM DENSITY FACTOR 41' density by classes, yet the total error is probably very small. The method is as follows: The standard densit\', or 100 per cent, as expressed in the yield table, calls for a definite volume per acre, differing with each age. The total volume and age of each age class in the forest are known. By dividing this volume by the standard volume on 1 acre of the required age from the yield table, the area which would be required by the age class if stocked at 100 per cent density is found. ' The sum of the areas found in this manner for all the age classes would be the total area of the forest if the density of stocking were 100 per cent. Since the total area actually stocked is known for this sum or total of age classes, but not for each age class separately, it follows that, Actual per cent of density for total area /Area 100 per cent stockedX = rrT — , 100, \ Total area / and, assuming this per cent for each class, . . , , / Area 100 per cent \ Area m each age class = I , , , . , 100 Vstocked in age class/ per cent of density' ILLUSTRATION Second-growth Hardwoods in Central New England Age. Volume. Cords Yield of 1 acre from table. Cords Area of 100 per cent stocked. Acres 20 30 40 50 1738 5593 3854 1008 15.80 29.75 39.63 48.00 Total 110 188 97 21 416 acres Actual area 624 acres. 416 Density per cent —- = 663 which will be assumed to apply to each of the four 024 age classes represented. To determine the area in each age class; 100 Ratio to fully stocked area — = 1.5. • 661 418 THE USE OF YIELD TABLES Age class. Years Area 100 per cent stocked. Acres Actual area in age class. Acres 20 30 40 50 110 188 97 21 165 282 145.5 31.5 Total 416 624 This method of obtaining the area of separate age classes makes possible the prediction of yields from yield tables based on age for long periods with considerable accuracy, where without such separation this would not be possible and yields could be predicted only for the current decade or two. 320. Application to Forests Having a Group Form of Age Classes. Forests composed of species which are intolerant and fire-resistant tend to form groups of approximately even age. A yield table based on age can be obtained for such species, which will serve as a 100 per cent standard. But it is very difficult to separate the forest itself into its component age classes by mapping the areas which they occupy, and equally difficult to determine in a practical manner the average actual age of the stand on such areas even if mapped. But the forest can still be separated into these age classes based on area and age, permitting the application of this yield table to predict its growth, provided proper use is made of the laws of averages. (In timber estimat- ing, it is permissible to employ averages known to be subject to error because it is not practicable to attain mathematical accuracy on account of expense.) The problem here is, 1. To determine the trees which belong to each age class so that the volume of the class may be found. 2. To determine the age of the age class. 3. To find its area. Given the first two of these elements, the method of finding the third has already been shown (§ 319). By reference to § 275 it is seen that diameter is an indicator of the age of trees, but that a given age class will include a wide range of diam- eters. Where stands are composed of trees of many difTerent ages so that it is not possible to ascertain the age of a given stand by felling one or two trees, nor to map the separate areas in the forest which are occupied by these age classes, the only alternative in obtaining age is through the use of average diameters. The diameters can be meas- VOLUME AND AREA FOR TWO AGE GROUPS 419 ured. In timber estimating, a stand table can be made giving the range and distribution of diameters in the stand. The substitution of diam- eters for ages thus furnishes a means of separating age classes in forests of mixed ages. Choice of Methods. There are tnree gradations in the possible applications of this method. 1. Diameter is used merely to determme the age of an average tree, but the forest is separated into actual age classes as nearly as possible, rather than diameter classes (§321). 2. Diameter is used as the basis of separation into classes, whose average age is then determined on the basis of these diameters (§ 323). These, as shown (§275), are not true age classes since they do not include all the trees of a given age. 3. Diameter is substituted altogether for age, and the total age of trees is not determined for these classes, but current growth is predicted merely for trees of given diameters for short periods. This method is discussed in Chapter XXXII. The use of diameter to indicate total age is most reliable when applied to large areas and numbers and to forests of many age classes, for species and stands whose actual and economic age agree, i.e., which usually do not show a period of suppression. 321. Determination of Volume and Area for Two Age Groups on Basis of Average Age. While the method to be described is limited in its application to two age groups, yet even this subdivision will be found of great value in Mensuration and Regulation. In the French many-aged forests, but two groups are made in timber above exploit- able size. In our forests, when under management, the subdivision into two groups will be equally effective. In natural stands containing decadent timber, three groups are needed instead of two, for timber above the minimum diameter. These may be termed " young merchantable," " mature " and " veteran." In the Western yellow pine stands for which this method was developed, it was possible to separate the young merchantable timber by the appearance of bark into a class termed " Blackjack," leaving the remaining yellow pine timber for separation into mature and veterans. In forests where this cannot be done, it is possible to first separate the young merchantable timber on a diameter class basis, leaving the larger mature and veteran timber for division by this method. Where the forest is cut over, and but two age classes are required, the method will separate the young merchantable from the mature timber. The three steps in this method are as follows: 1. A standard yield table based on age for even-aged stands can be made the basis of separation of the forest into two age groups. This 420 THE USE OF YIELD TABLES yield table can be constructed by standard methods from selected plots in the groups of which the forest is composed. From this yield table two ages are chosen, representing respectively the younger and the older age class. The development of the normal stand as indicated by its current and its mean annual growth is the basis for this choice of ages. 2. The ages thus chosen from the yield table must then be correlated with a given diameter since it is impossible, in the forest, to determine either the age or area of age classes directly. This requires a table of diameter growth on the basis of age, for the species and site (§ 267 to § 269) based on a sufficient number of trees to insure a reliable average. Age is the direct basis of this curve, and not diameter (§ 275). From this table, the diameter sought is indicated, for each of the two age classes. 3. The total volume on the area contained in the two age classes can be separated into the volume in each age class, by means of these two trees of average diameter, representing average age of each class. This requires: (a) That the average volume contained in a tree of this average diameter be found. For this purpose, a curve of average height based on diameter is constructed for the site (§ 209). With the height of a tree of the required diameter thus indicated, its volume is found from the standard volume table for the species and region. (b) That the number of trees with this average volume be found for each age class, which is required to make up the total volume of the combined group. This number, multiplied by the average volume will give the volume of each age class. This solution is simple, when the total number of trees and their total volume are known. Deducting a given number of trees of a given average volume from the group leaves a residual volume, which is equivalent to a fixed number of trees of the average volume for the remaining group; i.e., with total number, total volume, and the average volume of each tree of two groups fixed, there can be but one solution by which the number in each group, and consequently the sum of their volumes equals the required or existing estimate or total in the stand. If a; = number of trees in younger group; y = number of trees in older group ; a = volume of average younger tree; b = volume of average older tree. Then x-\-y = total number of trees in stand, c and ax+by = total volume of stand, d. If all the trees c had the volume a then instead of a total volume d, ax+ay = ac, APPLICATION OF RESULTS TO FOREST 421 The difference between this volume and the total actual stand is d—ac and repre- sents the surplus volume in the older trees, of which there are y. The difference in volume for each tree is b —a, and for all of the older trees is {b — a)y. Then {b — a)y = d—ac; and d—ac b — a while Having the values, or number, of each group x and y, the total volume is obtained by multiplying this number by the volume of the average tree for the group. Illustration, Western Yellow Pine. Total volume in group (d) =27,042,800 feet B.M. Total number of trees (c) =44,423. Age of older trees, veterans, chosen as 300 years. Age of younger trees, mature, chosen as 200 years. Diameter, from curve of growth, veterans, 27 inches. mature, 20.7 inches. Volume of average tree of this size, veterans 805 feet B.M. mature, 340 feet B.M. Then (1) 340x +805?/ = 27,042,800 feet B.M. (2) 340x+340y = 340f. = 15,103,820 feet B.M. Subtracting (2) from (1) 465j/ = 11,938,980 feet B.M. y = 25,675 trees; a; = 18,748 trees. Volume of younger class = 6,374,320 feet B.M. Volume of older class =20,668,375 feet B.M. 322. Application of Results to Forest by Use of Stand Table and Per Cent. It is not necessary that a 100 per cent tally of the number of trees, and total volume for the site be obtained, but only that the stand table (§ 188) from which the determination is made be representa- tive of the total area. If in the timber survey, 5 per cent of the area is covered and assumed to represent the average stand, the total count of trees on this 5 per cent and the total estimate on the strip, give the data needed. If, in turn, but 10 per cent of the strip itself or i^ of 1 per cent of the total area is tallied, and this per cent gives the run of sizes of the timber without reference to its density of stocking, the data are still sufficient. To obtain the separation of the total stand by means of the data from the smaller area counted, the volume of each age class is first expressed as a per cent of the total. These per cents are then applied to the total estimated volume on the entire area. 422 THE USE OF YIELD TABLES In the above case, the per cents are: Veterans 76.4 Mature 23 . 6 The total stand is 2,583,940,000 feet B.M. The stand of veterans is then 1,974,130,000 feet B.M. and of mature is 609,810,000 feet. B.M. To secure this division, a Uttle over 1 per cent of the total stand was tallied and estimated for the basic data, while the total estimate was secured by ocular means (§ 208) (Coconino National Forest). 323. Determination of Volume and Area for Age Groups on Basis of Diameter Groups. Where the second alternative is chosen (Method 2, § 320) to obtain the separation of age classes, namely, diameter rather than age, the following changes in procedure are necessar3^ 1. The volume of the so-called age classes is directly obtained from a stand table, in which the number of trees of each diameter class must be shown. 2. The diameter of the average tree is obtained by first finding the average volume for the group, and second, the tree of this volume from a local volume table based solely on diameter, which is obtained from a curve of average heights and a standard volume table. 3. The age of a tree of this average diameter is then found, not from the yield table as before, but from the curve of growth based on diameter, which gives directly the ages of trees of given diameters. The ages indicated will be those of the respective age groups into which the forest has been separated. As indicated, this method works back from diameters to age, while the first is based on age directly. By either of these methods, the area in each age class may now be found by following the procedure described in § 319. The age, and consequent normal yields for 1 acre at these ages, have been determined for each age class. The total normally or 100 per cent stocked area can be found, and from this the reduction per cent and the area in each age class. From the reduction per cent an empirical yield table can be computed, which will be used as the basis for predicting the yields of the forest or site class as a whole (§ 250). Since the above-described methods of determining areas of age groups are based primarily on the factor of relative density of the stands as determined by volume, they apply only to the age groups which have already grown to merchantable sizes. The problem of determin- ing the area of immature age classes is treated . in § 348, and must be considered in working out a plan for growth predictions for any large area, in connection with the above methods. 324. The Construction of Yield Tables Based on Crown Space, for Many-aged Stands. The above methods depend upon the construc- tion of yield tables from plots whose average age is determined, so that THE CONSTRUCTION OF YIELD TABLES 423 the yields are given as for even-aged stands. Since it is seldom that any species is so distributed in age classes and so free from major sources of damage as never to be found in stands of even age, plots based on age can be obtained under a greater range of conditions than is commonly admitted. But when this method is apparently impracticable, there remains one possibility for constructing a yield table based on age, which although far from being accurate, is based on a fundamental law of growth of stands. It was shown in § 274 that as trees develop, they require increased crown space, and that this expansion of crown can be attained only by the reduction of numbers of trees per acre. The diameters of crowns of trees is an index of the growing space which they require though it seldom exactly measures this space. But if it can be shown that the space occupied by trees of different diameters is proportional to the diameter of their crowns, the relative number of trees per acre of different diameters which can stand on an acre can be determined. To obtain such data, crowns can be assumed as circular in shape, (though the actual shape varies according to the light and growing space available, especially in hardwoods), and that the space occupied by each crown is in proportion to the square of its diameter or width in feet. Measurement of Width of Crowns. To determine the average width of crown for trees of different diameters, two men may work together. One stations himself behind a plumb-bob suspended from a pole so to hang clear from a height of about 8 feet. He lines in the second man at a point below the outer edge of the crown of the tree, whose width is then measured on the ground to the point intersecting the opposite edge of crown. For this purpose a pole, marked in feet, can be used. The distance measured must be at right angles to the lines of sight. A record is made of the D.B.H. and crown width. ^ Areas of Crowns. To obtain a true average of crown area, each crown width must be squared. The sum of the areas so obtained for each diameter class is divided by the number of trees in the class, to get the average area of the square for that class. The square root, or side of this square is the average width of the crown for the class. Now, if it be assumed that the space occupied by this diameter squared represents the actual growing space required by the tree, the number of trees per acre for the diameter class is found by dividing the area ■' No effort need be made to obtain the area of each crown by two or more measure- ments or by plotting the projected area of the crown. Reliance is placed on a large number of measurements of one diameter, rapidly and accurately taken, to obtain the true average diameter of crowns for each D.B.H. class. 424 THE USE OF YIELD TABLES of one acre, 43,560 square feet, by this area. This method is employed in finding the number of trees per acre required to plant an acre, if spacing is 4, 6, 8 or 10 feet apart in both directions. Density of Crown Cover. In actual stocking, the absolute number of trees cannot be so simply determined. As crowns tend to adjust themselves to light, they depart from a circular form, and the circular spacing itself may permit of more trees per acre than the square. The relation of the area of an inscribed circle to a square is .7854. That of an inscribed circle to a hexagon is .9018. If either of these relations is consistently maintained, the total number of trees per acre for full crown cover may differ, but the relative number, for trees of different diameters will remain constant. From the number so found, a curve of number of trees per acre based on diam- eter can be plotted. This is a standard, intended to show relative, not absolute, numbers. For instance, if the number per acre from such a table for a given diameter is 400 trees, a stand of 200 trees per acre of this average diameter would be 50 per cent of the standard. Two factors interfere to prevent the satisfactory application of such a table in predicting yields. First, the number of trees in fully stocked stands does not always decrease in direct proportion to their increase in crown space. In tolerant species, a great over-lapping and suppres- sion of crowns occurs, doubling the number of trees per acre over the theoretical number indicated by the spread of crown, while in over- mature stands, the increasing demand for light and moisture reduces the stand per acre below that indicated by the crowns. The relation is therefore not consistent except within rather narrow limits of age and species; and yields based on this assumption will be excessively large for over-mature age classes. The second factor tends to offset the first in stands not fully stocked — this is the tendency (§301 and § 316) to improve the degree of stocking with age. When a stand of a given age has only the number of trees required for one twice this age, its rate of mortality will be very much less since each tree has more than enough room to survive. Hence the assumption, in stands not fully stocked, that the growth of a stand can be predicted by determining the per cent which the number of trees now in the age class bears to the normal number, will not be borne out, but better results will be obtained. Method of Construction of the Yield Table. In stands which possess a full crown cover, but whose age classes are distributed in many-aged form, the rate of mortality may be assumed to hold for all classes. An illustration of the above method of constructing a yield table for yellow poplar in Tennessee is given below.^ 1 Based on data collected by W. W. Ashe. METHOD OF CONSTRUCTION OF THE YIELD TABLE 425 TABLE LXIV Trees per Acre Based on Crown Space D.B.H. Diameter of crown. Area of crown based on Trees per acre. Inches Feet Square feet Number 7 11.0 121 360 8 11 6 134 325 , 9 12.4 154 283 10 13.3 177 246 11 13.7 187 233 12 14.4 207 210 13 15.1 228 191 14 15.8 249 175 15 16.5 272 160 16 17 2 295 148 17 17.9 320 136 18 18.6 346 126 19 19.4 376 116 20 20.0 400 109 21 20.7 428 102 22 21.3 453 96 The above data must now be correlated with age. The steps are as follows: 1. From a curve of age based on diameter, the diameters at each five-year period are found, and the number of trees per acre, formerly based on diameter, are then interpolated for the fractional diameters corresponding to these exact ages. 2. From a curve of height growth based on age the height of the average tree is found. 3. From diameter and height, the volume of each tree is taken from a standard volume table (§ 288). 4. The yield per acre at each age is the product of the number of trees per acre and this average volume. The application of this method is shown in Table LXV, p. 426. 325. Application of Method to Many-aged Stands. To apply this standard table to the many-aged forest for the prediction of yield, the same principles are used as were described in § 316. But in this case, the number of trees in given diameter classes is the basis of comparison to determine the reduction per cent or density factor. It makes no material difference whether the standard table above illustrated exactly represents the true or actually possible normal yield of a pure, even-aged fully stocked stand, provided it approximately 426 THE USE OF YIELD TABLES indicates the proportional yields at different ages, correlated with the proportional falling off in numbers of trees per acre at these ages, both factors correlated with diameter of the average trees, for it is evident that in such a forest no stands will be found which are pure, even-aged or fully stocked over any large area; hence the use to which the table is put must be solely as a standard to he discounted by a reduction per cent. TABLE LXV Yields of Cordwood, for Yellow Poplak in Tennessee — Based on Crown Space and Volumes of Trees of Given Ages Age. Years D.BH Inches Average Height. Feet Volume * in cords of 160 cord feet. Cords Trees per acre Yield per acre. Long cords 40 10.5 78 0.148 237 35.1 45 11.8 83 .198 214 42.6 50 13.0 87 .254 191 48.5 55 14.2 91 .317 172 54.5 60 15.4 94 .381 155 59.0 65 16.5 97 .445 141 62.7 70 17 5 101 .511 130 66.4 75 18.4 104 .569 121 68.8 80 19.3 107 .630 114 71.8 85 20.2 110 .693 108 74.8 90 21.0 113 .755 102 77.0 95 21.8 115 .825 97 80.0 100 22.5 117 .880 94 82.7 * From volume table 5, p. 22, Bulletin 106, Yellow Poplar in Tennessee, W. W. Ashe, State Geological Survey of Tennessee, 1913. The age of stands, by this method, is assumed as the age of trees of given diameters. To determine this age, for each diameter class, a curve of growth is required in which ages are averaged on the basis of diameter (§ 276). Otherwise the ages of trees of the larger classes will be over-estimated. To apply this yield table for the prediction of yield in the forest, a large area must be considered; otherwise the assumed correlation between age and diameter will not hold good. The stand table (§ 188) for this area must show the number of trees of each diameter class in the forest. One of the principal services rendered by such a table is its indication of the probable rate of loss of numbers, which is a most difficult problem to solve by any other method. YIELD TABLES FOR STANDS GROWN UNDER MANAGEMENT 427 In applying such a table, it can be assumed that the mortality in the forest will be at the proportional rate indicated by the table. The prediction of yields will then be based on a stand table giving the number of trees in each diameter class. Several methods of applying the standard table are possible, as 1. Base the prediction upon the total number of trees in each diam- eter class or group. The per cent of reduction in numbers is obtained from the table. This per cent is applied to the stand in the forest, and the future growth obtained by computing the future volume of the remaining trees, as shown in the illustration. 2. Base the prediction upon yields. The number of trees in each diameter class is divided by the number per acre in the standard table. This gives the area normally stocked by that class, from which its future yield is taken directly from the standard yield table. This area forms, of course, but a small per cent of the forest, and is the total area occupied by trees of the diameter class. The forest can be divided into age classes, based on diameter, and the area occupied by each of these age classes obtained as described in § 316. At best, it can be seen that this substitution of standard yields based on growing space per tree is a makeshift compared with determin- ing these relations from even-aged plots in which the factors of site, tolerance and soil at different ages are directly measured. 326. Yield Tables for Stands Grown under Management. European . experience with stands grown under management has shown, first, that the best results and heaviest total yields per acre are obtained by several thinnings at frequent intervals, in which not only the trees which would otherwise die before the next cutting are removed, but the remaining crowns are freed from competition. Second, that the proportion of the total yield removed as thinnings under this system may equal one-third or more of the total yield. Third, that the diameter growth of the surviving trees can by proper thinnings be sustained at a uniform rate until the final crop is cut. The development of each tree in the stand proceeds actually at the rate of growth of a dominant tree which maintains its crown spread through- out its life. Even where second-growth stands have sprung up, in this country, and reached sizes suitable for logging, they have usually received no care in the form of thinnings. Stagnation sets in on many of these stands, especially with conifers on old fields, and the diameter growth of the whole stand suffers. This occurs even in plantations on which thinnings have been neglected. The actual yields and sizes which may be grown on such stands 428 THE USE OF YIELD TABLES under sustained management and thinnings may be roughly approxi- mated by measurements taken on natural stands not under management, by the method just discussed, of computing the number of trees per acre for given diameters. The rate of diameter growth should be that of trees now dominant in the stand. This gives the age of the diameter classes. The approximate amount of material yielded by thinnings in such a forest may also be roughly predicted by noting the number of trees which drop out of the stand at each decade, and computing their average diameter and volume. By establishing permanent plots, re-measured at intervals of 5 or 10 years, and properly thinned, data will finally become available showing not merely the yield of stands grown under management, at final cutting, but the total yield including thinnings. The absence of such stands precludes the construction of yield tables on this basis at present and justifies efforts to predict such yields by means of crown spread and number of trees per acre in normal stands. The nearest approach to such yield tables is found in tables constructed from second- growth stands, or plantations, but it is seldom that these stands have been repeatedly and properly thinned, hence the yields shown merely indicate a normal possibility for fully stocked, wild stands. References The Measurement of Increment on All-aged Stands, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 189. Yield Table Methods of Arizona and New Mexico, T. S. Woolsey, Jr., Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 207. Yield in Uneven-aged Stands, Barrington Moore, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 216. CHAPTER XXX • THE DETERMINATION OF GROWTH PER CENT 327. Definition of Growth per Cent. Growth per cent is an expres- sion of the relation between growth and volume. Current growth per cent is the relation of growth during a given year to the volume at the beginning of the year. Periodic growth per cent is the relation of the growth during a period, to a basic volume, which may be taken as the mean or average volume for the period (§ 328), but is usually that at the beginning of the period. Mean annual growth per cent is the per cent which the mean annual growth (§ 245) for a given age bears to the total volume at that age, and represents the average rate of growth per year, at which this volume has been produced. Growth per cent requires for its determination a knowledge of two factors, the growth for a period and the volume upon which this growth was laid. The primary purpose for which growth per cent is utilized is to test the maturity or ripeness of individual trees and of stands of timber. Those trees or stands which show the lowest per cent of increment on their present volume compared with other trees or stands, should be selected for cutting. The object of such selection is to withdraw from the forest the greatest possible volume of wood capital, while at the same time reducing the volume of expected growth by the smallest possible amount. If carried out, the effect is to transform the forest capital from a condition in which the ratio of growth to volume is low, to one in which this ratio is materially increased for the forest as a whole. On individual trees the difference in volume or growth for the decade may be found by analysis (§ 287 and § 288). For stands, the difference is taken from yield tables for the decade. In each case one year's growth is one-tenth of the growth for a decade. The growth per cent of average test trees is frequently assumed to be that of the stand. 328. Pressler's Formula for Volume Growth Per Cent. To deter-" mine growth per cent as a means of judging the ripeness or maturity of stands or trees, the same methods apply whether the unit is the tree or the stand. Since volume growth is measured for periods of a decade, the growth for one year is found by division. Let n equal the period representing a decade. This may be a longer or shorter period if neces- 429 430 THE DETERMINATION OF GROWTH PER CENT sary. Let V equal volume at present, and v equal volume n years ago. V — v Then growth for one year equals . If it is assumed that this n growth for n years is laid on in equal annual installments, then the growth so obtained is considered that of the current year or for any year during the period. If the growth per cent is obtained on this basis, the result will vary according to the year in which the volume of the stand is taken as the basis. If for ten years ago, then the formula is. / V — v\ Growth per cent = I — I 100. \ vn / But if the per cent is desired for the last or present year, Growth per cent= ( -r- — ) 100. For an average year midway of the period, the capital or volume is V+v 2 ' and growth per cent is V-n n ^^^^ (V-v\ 200 V-\-v \V-\-v/ n ~2~ This is known as Pressler's formula. 329. Pressler's Formula Based on Relative Diameter. Further modifications of this formula by Pressler are intended to reduce it to terms of diameter so that it may be appUed to measurements on standing trees taken at B.H. If height and form factor do not change, then _ / D'--dA 200 In this formula D is the present D.B.H. and d is the diameter Ji years ago. D—d is then designated as a and — is called the relative diameter. By making — =q, a a and substituting aq for D, and a{q — \) for d, he reduced the formula thus to ^/ q2-(q-l)2 \200 ^ W+(<7-l)V « ' for which expressions values are computed in a table. To use this table the present diameter D is divided by twice the width of the rings in the period n, thus indicating the relative diameter. The values in the table give the per cent of volume growth /or the period. This is then divided by the num- ber of years in the period to get the current annual growth per cent.i 1 This table is given in Principles of American Forestry, Samuel B. Green, John Wiley & Sons, N. Y., 1903, p. 178. SCHNEIDER'S FORMULA FOR STANDING TREES 431 Further modifications of this formula are discussed in Graves' Mensuration, pp. 306-7. 330. Schneider's Formula for Standing Trees. The most con- venient formula for testing the growth per cent of standing trees is known as Schneider's formula, developed in 1853 by Professor Schneider, Eberswalde. This formula is applied at B.H. and requires the deter- mination of diameter, D, at that point, and the number of rings in the last inch of radius, n. Then 400 The following description of the derivation of the formula is taken from Graves' Mensuration, p. 308. If n represents the number of rings in the last inch of radius at breast-height, then the periodic annual growth during n years is - inches. Let the present diameter n 2 be represented by D, then the diameter last year was D and the diameter at the n 2 end of one year from now will be D + -. n ■irD^f The present volume of the tree is — ^ — , that of one year ago was The growth for the last year is then ^D%f TT / 2y ThfUP _ 4 4 4 \ n/ 4 \ n n= The growth per cent is: TrDVlf 7rhf/4D 4\ : — = 100 : p. 4 4 \ n nV ^ 400 400 2 2 If the growth be calculated on the basis oi d+~ instead of d — , then the follow- n n ing formula will result: 400 400 The average between the two formulae is taken, namely, 400 Inasmuch as Schneider's formula assumes that there is no change in height and nor change in form factor, the results are very conservative. 432 THE DETERMINATION OF GROWTH PER CENT An attempt has been made to adapt the formula to rapid-growing trees by substituting other values for 400, but the resulting formulae have little practical value. 331. Use of Growth Per Cent to Predict Growth of Stands. Growth per cent is sometimes used to determine the growth of trees or stands, by both the standard methods, that of prediction, and of comparison. It is not well adapted to secure accurate results by either method. Owing principally to the variability of the per cent relation, and its direct dependence on and derivation from the two factors, volume and increment, the problem of reversing this process and deriving increment from growth per cent is apt to lead to error through a mistake either in choosing the basis of volume for deriving the per cent figure, or in applying this figure in turn to the wrong volume basis. The method of prediction of growth by means of growth per cent consists of determining this per cent for a stand, either from sample trees (§ 241) or by direct use of yield tables or other methods of measur- ing the past growth for a decade. Schiffel states, " If in any period of life the current annual incre- ment per cent of a tree is to be calculated, it would be contrary to nature and incorrect to relate the increment to any former dimensions or volume, but it must be related to the dimensions or volume of the previ- ous year." The formula, growth per cent = ( -tt-t— ) — when n=10 years, \ V + vj n bases growth per cent on volume five years ago, and is correct as an average per cent of the past ten-year period. If applied to the next decade, and based on V, or present volume, it assumes an increase in growth for this period. Wlien this per cent is applied only to the current year, and is based on V the per cent is more conservative. While individual trees are growing rapidly in diameter, as dominant trees, their growth per cent for a time falls less rapidly than that of slower-growing trees. In even-aged stands, growth on individual trees is proportional to their diameters. Growth per cent in area is about twice the per cent of diameter growth. If determined for the trees which will be retained under management, this relation of growth to volume may be fairly consistent in such even-aged, thinned stands. Hence sample or average trees may give a close indication of the growth per cent or present status of the stand. But the assumption that this growth per cent will continue to be laid on annually breaks down at once; hence the real assumption and the only one possible, if growth per cent is to be applied for predictions, is that the volume indicated by this per cent will continue to be laid on annually. And this in turn is inaccurate. GROWTH PER CENT TO DETERMINE GROWTH OF STANDS 433 The sources of inaccuracy in this method are: 1. Predicting the volume growth of a stand from that of one or two selected or average trees. The growth per cent of a stand is practically always less than that of the average trees which survive, due to loss of numbers and falling growth rate of the suppressed class. 2. Applying a growth per cent obtained from a past period on a smaller volume, to the present volume of tree or stand, under the assump- tion that not only will the rate of growth in volume continue the same but the per cent will remain unchanged, when, as shown, growth per cents always fall as wood capital increases. 3. Assuming that the growth per cent as derived from average trees, or even from sample plots, will apply to larger areas and to dif- ferent proportions of age classes in mixture, when in fact, so doubly sensitive is this per cent relation, that any difference in average age and volume between the forest and the sample areas will i*esult in a large error in determining the true weighted per cent by this means. The possible errors may be illustrated as follows : From a yield table for White Pine ^ the actual known yields are, . At 30 years 3750 cubic feet 40 years 6590 cubic feet 50 years 8035 cubic feet 60 years 9075 cubic feet By Pressler's formula, the current annual growth per cent for these decades is, 30 to 40 years 5.5 per cent 40 to 50 years 2.0 per cent 50 to 60 years 1.2 per cent If the growth for the decade from thirty to forty years be taken to indicate the current growth in the fortieth year, of 284 board feet, this gives a current growth per cent for that year on 6590 board feet, of 4.3 per cent. Assuming that this growth per cent will continue for the next decade, we have a total increase of 43 per cent or 2834 board feet. The actual growth is 1445 board feet. The error is 96 per cent excess. Such errors are the result of use of the growth per cent, even when the basic data are correct. The errors may be greatly increased when growth per cent is obtained from single trees and the losses in the stand are ignored, since too high a current growth per cent will be obtained. 332. Use of Growth Per Cent to Determine Growth of Stands by Comparison with Measured Plots. The only merit which growth per cent has as a method of determining growth lies in the possibility of using it as a means of comparison. Since per cent does not express ^ Forest Mensuration of the White Pine in Mass., H. O. Cook, OfRce of State Forester, 1908, p. 21. 434 THE DETERMINATION OF GROWTH PER CENT absolute quantity but a relation, the assumption is that this relation once established for a given stand will apply to other stands of a similar character but differing in area and total volume. Growth per cent on sample plots could for instance be applied to determine the annual growth on the stand within which they are located. In so far as it can be known that the relation between the volume of the larger area and the growth on this area is the same as on the stand sampled, the method is obviously correct. The error lies in applying such growth per cent figures to stands or areas on which this relation is not the same, because the average age, thrift, or other conditions, differ from the sample area. The simplicity of assuming that growth per cent for a sample tree, or for a sample plot, can be applied to large areas has led to its use as a substitute for sound growth data in many instances. No such short cut will actually measure the growth on a forest comprising many stands of different ages, site qualities, and densities of stocking. 333. Use of Growth Per Cent in Forests Composed of All Age Classes. Growth per cent is a direct expression of current growth in its relation to past or total volume. Hence it varies with the current growth curve. Current growth per cent is equal to mean annual growth per cent in the year in which the mean annual growth culmi- nates (§ 245). In a forest composed of stands of all ages, or in a stand composed of trees of all ages, equally proportioned as to area or ultimate yield, and under management, the current growth per cent for the whole forest or the whole stand, when weighted by volume of each age or tree class, will be equal to the mean annual growth per cent for every year, since there is no change from year to year in either of the two factors, total volume or increment, which determine it. For such a forest the average growth per cent can be found separately for each diameter class. By weighting each per cent according to the volume of the trees in this class for the stand, a composite per cent is obtained which shows the present status of the forest, and is applicable in predicting its growth. But accurately to determine this per cent, the growth itself must first be found on the trees or plots measured. If in determining this growth, the future factors are really considered, the numbers reduced, and the rate of diameter growth and probable suppression taken into account, the result is a quantitative statement of growth for the next decade or two instead of for the past decade. This prediction of growth, on a few acres or a small per cent of the stand, can then be reduced to the form of a per cent of present volume, and applied, in this form, to the remaining stand as a convenient means of computing growth on the total area. GROWTH PER CENT IN QUALITY AND VALUE 435 334. Growth Per Cent in Quality and Value. Growth in money value of a stand is treated in Forest Valuation.^ This depends upon the three factors mentioned in § 244, namely, increase in volume, in quality, and in unit price independent of the other two factors. The growth in quality differs from that in volume, since it tends in a measure to raise the value of the previous growth, especially when this increased quality is due to increased dimensions. Per cent increase in value is usually computed as an annual per cent found by dividing the periodic per cent by the years in the period, and is applied to the volume at the beginning of the period, thus showing simple interest on the initial value. When thus expressed, the per cent of increase is made up of the sum of the per cents due to each of the three separate factors. For young and immature timber, growth per cent in volume forms the chief element of increase, but as the trees reach maturity this diminishes, and is greatly exceeded by per cent increase in price due to quality, and to unit prices — so that the per cent of increment in value may con- tinue for a much longer time than that of volume. The growth in quality of a stand can be measured by the use of graded log tables (§74) or graded volume tables (§165) provided it is carefully ascertained that these tables apply to the trees in the stands to be measured, at the successive ages. References A Practical Application of Pressler's Formula, A. B. Recknagel, Forestry Quarterly, Vol. XIV, 1916, p. 260. Table for Determining Financial Increment Per Cent for Trees Based on their Market Values, Erling Overland, Translated by Nils B. Eckbo, Forestry Quar- terly, Vol. V, 1907, p. 36. Increment Per Cent, Schiffel, Centralblatt f. g. d. Forstwesen, Jan., 1910, p. 6. Review, Forestry Quarterly, Vol. VIII, 1910, p. 377. Hilfstafel zur Zuwachserhebung, Forstwissenschaftliches Centralblatt, Apr., 1911, p. 200. Review, Forestry Quarterly, Vol. IX, 1911, p. 321. Relative Increment of Tree Classes, Review, Forestry Quarterly, Vol. IX, 1911, p. 633. Zuwachsuntersuchungen an Tannen, AUgemeine Forst- und Jagdzeitung, Sept. 1907, p. 305. Review, Forestry Quarterly, Vol. V, 1907, p. 431. Ueber Zuwachsprocent, Centralblatt f. d. g. Forstwesen, Jan., 1910, p. 6. Review, Forestry Quarterly, Vol. VIII, 1910, p. 377. 1 Forest Valuation, H. H. Chapman. John Wiley & Sons, N. Y., 1915. CHAPTER XXXI METHODS OF MEASURING AND PREDICTING THE CURRENT OR PERIODIC GROWTH OF STANDS 335. Use of Yield Tables in Prediction of Current Growth. The current growth of stands for short periods can always be predicted with greater acciu-acy than for long periods. Not only can the present condition of the stand be gaged, as to species, numbers, crown density, form, thrift and rate of growth in immediate past, and this information applied in predicting the rate at which growth will continue, but the inevitable changes, some of them unforeseen, which will occur in the future to modify this rate of growth, take place at a rate which bears a close relation to the length of the period of prediction. Only when the net results of all the various factors which produce yields have been measured on stands after they have passed through the period is an approximate degree of accuracy obtained for long periods, hence the use of yield tables based on age. It follows that for the pre- diction of current growth for short periods on existing stands, the net current growth shown by the above yield tables, reduced on the basis of age and relative density to apply to the stand in question, is the best basis of growth prediction even for these short periods. 336. Method of Prediction Based on Growth of Trees, with Cor- rections for Losses. In endeavoring to use these yield tables for stands which differ greatly from the normal in number of trees per acre, density of crown cover, form or distribution of age classes, and com- position of species, it is often difficult to find or make a table which will apply to the stand even when corrected for density. In such cases, a direct measurement of the stand may be resorted to instead of a com- parison with a standard yield. The growth of any stand of whatever character, for the next decade, will be the sum of the growth in volume of the trees which survive till the end of this period minus the loss of the total volume of the trees which do not survive ( § 252) . The elements which give stability to this method are a knowledge of the exact pres- ent number and diameter of the trees in the stand, which may be supplemented by a classification of crowns to indicate those now domi- nant, intermediate or already suppressed, and by a tabulation of past growth in diameter, by diameter classes (§ 278). The elements of 436 PREDICTION BASED ON GROWTH OF TREES 437 uncertainty are probable loss of numbers in the next period, and future rate of diameter, height and volume growth of the survivors. At best, owing to the great difficulty of predicting for a given stand the loss in numbers and the rate at which diameter growth will be maintained, for long future periods, the method can be used only for periods of ten to twenty years, except for slow-growing or long-lived species where the factors of change are slowed down correspondingly. To apply this method of predicting tree growth to obtain current growth of stands, the steps are, 1. Prepare a stand table of the forest or area (§ 188). 2. As an aid in determining mortality, tally or estimate the number or per cent of each diameter class which is suppressed or will probably die within ten or twenty years. 3. Decide upon the method to be applied in predicting diameter growth (§ 278 and § 279) and prepare table of growth by diameter classes to conform to the requirements of the method. 4. Obtain data and construct a curve of average height growth (§ 248), which will probably be best expressed as current height growth based on height, for the last decade or two. 5. Obtain volume tables giving the volume of trees of each diameter and average height. A standard volume table classified by heights is needed for best results. 6. From present number of trees in each diameter class, deduct the per cent or number which will probably die within the period. 7. Compute the average diameter which surviving trees of each diameter class will attain at end of period. 8. Compute the increase in height for each diameter class. (The false method described in § 285 is frequently used as a substitute for a curve of height growth.) 9. The volume of the present stand is calculated from the stand table and volume table. 10. The volume of the surviving stand at end of period is obtained from the future diameter and height of the surviving trees of each diam- eter class, and volumes taken from the standard volume table. 11. The difference in volume thus found is the net growth for the period, in stands which have not been thinned and in which no salvage of dying or dead timber is possible. The volume of the trees which die is thus deducted from the growth on the survivors, and only the net growth is represented in increased volume of the stand. In stands which are thinned, this prospective loss in numbers is not lost nor deducted, but is expressed in the form of thinnings. Where thinnings are marked and will be made in such stands, they will com- monly include more trees than will actually die during the period, 438 CURRENT OR PERIODIC GROWTH OF STANDS since the suppression of diameter growth is to be avoided, and this begins considerably in advance of the death of the tree and may affect the entire stand if too crowded. By this method, neither a full volume analysis of current growth of trees is needed on the one hand, nor a yield table based on area and age on the other. Nor is it necessary to compute the average tree of the stand, and by predicting the growth of this tree for the next decade, seek to determine that of the stand ( § 275) since all the trees in the stand are given their proper weight in predicting growth. Only for very regular stands can average trees be used safely, and for such stands yield tables are better. 337. Increased Growth of Stands after Cutting. The method of predicting diameter and volume growth of trees after release by cutting is shown in § 280. The problem of predicting growth of stands left on cut-over lands is one of properly combining the growth data for the different classes of trees left on the area. That diameter growth of individual trees should increase when their crowns and roots are given increased growing space is a natural law of growth of stands. The question is, " What is the total net current growth per acre on such lands? " The first result of cutting should be to tremendously increase the growth per cent on the remaining stand, or change its status, by removing large, old and slow-growing trees with a low growth per cent, and leaving small, young and more vigorous trees with a larger growth .per cent. This change would occur even if no increased growth followed the cutting. The total growth per acre laid on after cutting is the sum of the current increments on the residual trees. In spite of change in growth per cent or status, and of possible increased growth on the trees left, the total net volume increase may be less than on the original stand. If the number of trees is greatly reduced this is usually the case. But if the stand cut over is many-aged, and only the decadent and sup- pressed trees are taken, the combination of a large number of trees left on the area, an increased rate of growth on these trees, and especially the prevention, by cutting, of a loss of volume by death of trees which would otherwise have to be deducted from current growth, may result in a larger actual net increase per acre from the cut-over stand than before it was cut, as well as a greater growth per cent. This expansion of diameter and volume growth of the residual stand after cutting, is, for even-aged stands, a response to increased light, soil, moisture and space in which to expand. In many-aged stands it may mean, as well, an expansion of the total area of the age class (§ 253). The method of determining the growth of individual trees in the REDUCED GROWTH OF STANDS AFTER CUTTING 439 stand to obtain the growth of the stand (§ 277), is favored in studies of cut-over lands, first, because such studies are usually made in many- aged stands of mixed species, second, because the difficulty of sepa- rating the age classes by area and age is even greater than on stands before cutting; hence the application to these stands of yield tables based on age is very difficult. The stimulation of growth on the trees left after logging is similar in character to the beneficial effects of repeated thinnings on stands under management. It undoubtedly increases the rate of jaeld per acre over that realized if the natural processes of selection are not interfered with. Two factors must be considered in analyzing this growth; first, to what extent have the trees left on the area been liberated or given increased growing space? — second, to what extent can they utilize or monopolize the area released by cutting? The maximum of increased growth would be found in a stand, either even- or many-aged, in which the cutting was so evenly distributed as to affect all of the remaining trees, and so light that the space released could all be absorbed by these trees. When cutting is either too light or too poorly distributed to affect all trees, the trees showing increased growth will be only a certain per cent of the total number. This per cent of each diameter class which will be released, as affected by the increased rate, will give the net actual increase over the previous rate of growth. Table LXVI illustrates the data required in a study of increased growth after cutting (p. 440). From a table of this character the average increase in growth may be computed by weighting the rate of increase by the per cent of trees affected; e.g., since 18 per cent of the trees are affected, an average increase of 18 per cent of the difference between the two classes of trees, those not affected and thus growing faster, can be added to the slower or original rate to get the new average for the forest. 338. Reduced Growth of Stands after Cutting. In heavier cuttings, even on parts of the same cut-over area, openings may easily occur from cutting even-aged or mature groups, which affect but few of the remaining trees. These clear-cut spots will result in a net reduction of current increment per acre for the forest, just as would the clear cutting of a larger area. There is no possibility of increased growth because there is no timber left on which to lay this growth. In even- aged stands cut clear, the growth for the forest occurs on separate areas of maturing timber, not on the areas cut over; the growth on cut-over areas must result from reproduction of a new crop and come along in time. Thus on heavily cut-over areas, in mixed age classes, a heavy 440 CURRENT OR PERIODIC GROWTH OF STANDS reduction of growth per acre will occur for the present regardless of in- crease on the residual trees or stand. TABLE LXVI Adieondack Spruce Average Rate of Growth in Diameter on the Stump of 1593 Trees on Cut-over Land at Santa Clara, New York Diam- eter. Inches No. of trees Current annual growth in diameter just before first cutting. Inches Current annual growth in diameter since first cutting. Inches Current annual growth in diameter since first cuttmg. Values made regular by a curve. Inches No. of years required to grow 1 inch in diameter No. of trees showing increased growth Current annual growth in diameter since first cutting. Inches 5 6 7 8 9 10 11 12 13 14 15 16 8 158 329 350 277 226 135 64 30 11 1 4 095 080 090 105 120 135 130 165 165 150 080 200 095 100 110 125 140 150 145 175 170 150 080 200 09 10 109 125 140 150 160 170 178 185 192 200 11 10 9 8 7 7 7 6 6 6 6 5 1 16 63 77 59 50 18 7 2 1 0.100 .180 .185 .205 .205 .215 .210 .240 .170 .200 Average . 0.112 0.137 0.20 No. years to grow 1 inch 9 7 5 Total number of trees, 1593. Number of trees showing increased growth, 294, or 18 per cent. The condition of such cut-over areas would be more accurately gaged if it were possible to separate the age classes in the cut-over stand on the basis of the actual area which they occupy. Thus, in a stand on which the timber cut formerly occupied 90 per cent of the growing space, it is not reasonable to expect that the trees which occupy the remaining 10 per cent of space will be able to expand sufficiently to absorb nine times their former crown space, even if properly distributed YIELD TABLES BASED ON AGE, TO CUT-OVER AREAS 441 so as to make this possible. The increment on this area for any con- siderable period into the future depends on securing reproduction to fill the gaps. The method of measuring increment on cut-over lands solely by the growth expected on the trees left after cutting is best adapted to typical many-aged or "selection"^ forests, and the more closely the conditions both as to distribution of cutting and of the residual stand resemble a many-aged forest, the better the results obtained. This method gives best results also on areas under intensive management, where if trees die or are blown over, their volume is not lost, and when the danger of reduction or loss in numbers is at a minimum. The necessity for reducing the number of trees for loss during the period remains, and applies to all stands on cut-over lands as well as elsewhere. Neglect of this factor means over-estimation of probable net growth. 339. Application of Yield Tables Based on Age, to Cut-over Areas. Where stands in the original forest can be or have been separated by area and age by any method, and a yield table based on age exists, a more conservative method of calculating growth on cut-over lands can be used, which bases this growth not on the theory of the many- aged forest and crown expansion of the age class, but on that of even- aged stands (§ 298). If age classes are on separate areas and cut clean, the cutting of one stand has no effect on the growth of another. If the forest is divided into age classes, and part is cut over, it can be assumed that this cutting removes an age class without stimulating the growth on the remainder, and that this area cut over is to be repro- duced to young timber rather than absorbed by existing age classes. To determine the area which is cut over, and that which remains stocked, the density or reduction per cent already determined for the original forest (§ 317) is assumed to apply to the residual stand. The area stocked to this degree of density can be found by dividing the volume in each age class left on the cut-over area, hy that of the empirical yield table for the given age which has been prepared for the original forest previous to cutting (§ 304). The sum of these areas, including that stocked already by young or immature age classes, subtracted from the total area, gives the area actually cut over. The actual yields of the age classes left on the cutover area will be in proportion to the per cent of the total area which they occupy, plus the degree of expansion or increased growth which they put on. The growth to be expected in the absence of any such expansion will be predicted by the empirical yield table from the net area or per cent of area stocked. This fixes 1 Selection — A term applied to forests in which the entire series of age classes is intermingled over the whole area and not separated by areas. 442 CURRENT OR PERIODIC GROWTH OF STANDS the minimum expectancy and is safe for a long future period (§ 248). Studies of growth on the individual trees and on permanent sample plots as stimulated by release will in time indicate the maximum growth possible on the same area. The actual growth will be somewhere between these two extremes, dependent on the balance between the forces tending to expand the crown area, and the destructive agencies tending to reduce the numbers in the stand, as shown in Fig. 87 by the lines; A. Based on average growth per acre in original stand, with normal ',oss of numbers. B. Based on increased growth after cutting and no loss of numbers. C. Probable rate somewhere between A and B, based on increased growth of a part of the stand and a reduced rate of loss in numbers. Probably the safest basis for growth prediction for long periods on cut- over lands is not the current growth study based on diameters, but, where possible, yields based on age, at the rate produced in the past on virgin forests, and figured for the net areas stocked, to which a percentage of in- crease may be added to represent expansion of crowns due to release and stimulus following cutting. An illustration of this principle of growth prediction is as follows: The empirical yield table for Western yellow pine, Coconino National Forest, Arizona, gives 66.2 per cent of the normal or index yield. The stand of timber left on the cut-over areas, separated into three age classes by the method given in § 321 is fovmd. By dividing the stand for each age class by the yield per acre from the empirical 3aeld table, the area which is stocked with timber, for each age class, is determined. The area reproduced to poles and saplings is estimated. The total area of cut- over land is known. The remaining area, not shown as stocked either with mature timber or young timber is the area cut clean and awaiting restocking. The results are given in Table LXVII. The prediction of growth is now made by applying the empirical yield table to the areas and ages represented in the table. With the area and age of each age class indicated, the future yields on cut-over lands may be predicted by applying the empirical yield table, increased by the per cent of expansion agreed upon. Fig. 87.— Possibilities of Growth on Cut-over Areas. PLOTS FOR MEASUREMENT OF CURRENT GROWTH 443 TABLE LXVII Areas Remaining Stocked on Cut-over Lands Class Age. Years Yield per acre. Board feet Stand, total M. Board feet Empirical area equivalent acres Per cent of 70,654 acres; also per cent of 1 acre Veteran Mature Blackjack Poles 300 200 100 50 20 12,050 16,750 7,480 Totals .... 27,900 9,702 70,908 2,315 579 9,493 6,006 17,663 34,598 3.2 0.8 13.4 8 5 Saplings Not restocked. . . 25.0 49.1 108,510 70,654 100.0 340. Permanent Sample Plots for Measurement of Current Growth. The best method of measuring the current growth of a stand is by means of permanent sample plots, established in stands which are typical of the conditions to be studied, and re-measured at intervals of from five to ten years. Methods of establishing and measuring such plots are described in § 243. In this way, just as for yield tables the actual net results of all factors which affect the current growth of the stand as a whole, such as wind, insects, disease, suppression, or increased growth, are measured, rather than either compared or predicted. The only precautions to observe on re-measurement of plots are that the diameters and heights of the trees must be taken in successive measurements in such a way as to give exact comparisons, whose difference indicates growth rather than discrepancies in re-measurements. Krauch has pointed out that the height of trees should be measured on such plots from the same position or point at each measurement, to avoid discrepancy due to the departure of the tree from the per- pendicular (§ 199). The diameter tape insures consistency in re-measure- ment of diameters (§ 190). The same volume table should be used in calculating successive volumes for trees of each size class. These pre- cautions insure the isolation of the current growth in successive measure- ments. 341. Measurement of Increment of Immature Stands as Part of the Total Increment of a Forest or Period. The increment of a forest or large area, just as in the case of a single stand, may be expressed as the total growth over a definite period, or yield, the average annual growth or mean for this period, or the actual volume laid on each year 444 CURRENT OR PERIODIC GROWTH OF STANDS or current annual growth. A forest resembles more closely a many- aged stand than one composed of a single age class. In such a stand or forest, it is not possible to separate one period which coincides with the complete cycle of production for a crop of timber, as can be done in the even-aged stand. The total production of the many-aged area or of the forest, for a period equal to that required to grow one crop from seed to maturity, may equal that of the even-aged stand, but it is laid on in many stands. In a regular many-aged forest the current growth for one year is the growth in volume of each stand, including those which are as yet unmerchantable. This is true of the forest, whatever its form. The current growth on the mature timber is but part of the total; that which represents the younger stands is equally important. Growth is not usually measured, on either trees or stands, until a size is attained which is merchantable for some form of product. Another reason for post- poning the measurement of young stands is that a very large per cent of the existing trees in such stands will never reach maturity, and the total volume at any period previous to an age at which it can be used is misleading and serves no useful purpose, while by contrast the natural selection of surviving trees in stands measured at merchantable age has already occurred and the results are accurately gaged. When the volume is finally measured on a young stand for the first time, it represents the growth for the entire preceding period. Perhaps but 10 per cent of the trees are large enough to measure at this time. After another decade, the stand is again measured. By this time 50 per cent of the trees may be merchantable. The growth for this decade now includes the current growth, for ten years, on the original 10 per cent, plus the growth since germination on the remaining 40 per cent. At the third measurement, all trees which survive may be merchantable and are measured, but a portion of them have entered the merchantable class after being missed for the two previous decades. What happens is that although current increment by decades is sought, yet for trees which mature and are measured for the first time, total growth is substituted for current growth since there is no other way to handle it. If this example is now applied to a forest composed of a series of even-aged stands, the same thing is seen to occur. For the forest, the current increment is the increase in merchantable cubic volume of stands already partly merchantable; but to this is added, in each decade, stands measured for the first time, whose volume though added as current increment is in reality the total growth of several periods instead of one. It follows that for a stand just becoming merchantable, the apparent current growth will be very rapid during this process VALUE OF CURRENT GROWTH VERSUS YIELD TABLES 445 while its actual average or mean annual growth, which takes in the true period required, is much less. But in a many-aged stand, or on a forest composed of stands of all ages, these elements counterbalance each other. As growth cannot be measured on stands below merchantable age or size, it is not meas- ured on "the areas covered by such young stands, or on the portion occupied by immature trees in mixed stands. But as soon as these stands or trees mature, the growth is measured all at once and greatly exceeds the actual current rate on the areas measured or for the trees in these age classes. Whenever the age classes are distributed evenly, the excess of current growth so caused is balanced for the area or forest by the neglect of the current growth on the younger stands. It follows, first, that in forests with well distributed age classes, the total current annual growth actually laid on in stands of all ages should be about equal to the current growth obtained by measuring only the merchant- able stands, provided the maturing volumes of young timber are included as current growth. For a single even-aged stand, or a forest devoid of younger age classes, this premise does not hold good, and the current growth for the period of early maturity will greatly exceed the real rate for the area or total period. On such stands or forests this rate will not be maintained, and the true yield must be found by dividing by age, in the form of mean annual growth. 342. Comparative Value of Current Growth versus Yield Tables and Mean Annual Growth. The relative value and utility of the methods of studying the increment on forests or large areas may be summed up as follows: Increment or growth is always desired for areas of land rather than individual trees. The rate of growth per year on an average acre is the object sought. Where forestry is a permanent land policy, the rate of growth desired is that which represents the average for the life of a crop of timber, and which can be maintained, in consequence, indefinitely. This rate can be found most accurately whenever growth can be measured directly on the basis of area and total age, as in yield tables for even-aged stands, and applied to the forest by the necessary reduc- tion per cents. The current growth on stands or forests is best obtained from these same yield tables. But where it is not possible or practicable to construct such yield tables, current growth for short periods only can be measured directly on merchantable trees, and applied in predicting growth of the stand and forest. This method gains in accuracy over yield tables, by measuring 446 CURRENT OR PERIODIC GROWTH OF STANDS directly the density of the stand, and by predicting growth on basis of actual volume and. conditions. It loses in comparison, because it measures only one current section of the growth curve for the stand or forest, which may be above or below the mean, and because the basis, the individual tree, while accurate to start with, rapidly loses its reli- ability, while by contrast, yield tables retain a fair degree of reliability over long future periods. Current growth, if it is actually measured in terms of volume, and the errors of using growth per cent are avoided, is well adapted to answer questions regarding the immediate future growth of specific stands, but is poorly adapted to growth predictions covering long periods. References Growth Rate in Selection Forest. Der Gemischte Buchen Plenterwald auf Muschel- kalk in Thiiringen, Mathes, Allgemeine Forst- u. Jagdzeitung, May 1910, p. 149. Review, Forestry Quarterly, Vol. IX, 1911. p. 129. Increment in Selection Forests. Zur Ermittlung des laufenden Zuwachses speziell im Plenterwalde, Christen, Schweizerische Zeitschrift fiir Forstwesen, Feb. 1909, p. 37. Review, Forestry Quarterly, Vol. VII, 1909, p. 206. A Method of Investigating Yields per Acre in Many-aged Stands, H. H. Chapman, Forestry Quarterly, Vol. X, 1912, p. 458. Accelerated Growth of Spruce after Cutting, in the Adirondacks, John Bentley, Jr., Journal of Forestry, Vol. XV, 1917, p. 896. Method of Regulating the Yield in Selection Forests, Walter J. Morrill, Forestry Quarterly, Vol. XI, 1913, p. 21. Determination of Stocking in Uneven-aged Stands, W. W. Ashe, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 204. The Relation of Crown Space to the Volume of Present and Future Stands of Western Yellow Pine, George A. Bright, Forestry Quarterly, Vol. XII, 1914, p. 330. Remeasurement of Permanent Sample Plots, G. A. Pearson, Forestry Quarterly, Vol. XIII, 1915, p. 60. Observations in Connection with Annual Increment of Growing Crops of Timber, Transactions of Royal Scottish Arboricultural Society, July, 1918, p. 164. CHAPTER XXXII COORDINATION OF FOREST SURVEY WITH GROWTH DETER- MINATION FOR THE FOREST 343. Factors Determining Total Growth oil a Large Area. The solution of the problem of determining the amount or volume of wood which will be grown on a forest or area of forest land in a given period depends upon six factors: 1. An analysis or classification of the forest into the areas included in each of the site quaUties present. 2. The areas occupied by stands of given type and mixture of species. 3. The actual present density of stocking, volume and number of trees, per acre, and size of diameters of the present stand on the forest. 4. The actual age classes present, and the area which each occupies. 5. The length of the period for which growth is desired, whether for a short current period, or for permanent management and a rotation. 6. The rate of growth, to be determined by whatever method can best be applied to the forest as a whole by obtaining the actual growth on the stands which compose it. 344. Data Required from the Forest Survey. The first four of these elements require the collection of data in connection with the forest survey. Studies of the rate of growth (6) for the period deter- mined (5) will not solve this problem in the absence of quantitative data to tie this growth study to the tract in question. Unless a forest is to be cleared for farms, the prediction of future growth is a basic consideration of its future management. A forest survey that is so conducted as to fail to obtain the necessary data on which growth for the forest can be determined must later be repeated to obtain this data, or supplemented in some way, while if the need were recognized at the start, the information could be obtained in final form with trivial extra cost. The character of this data depends upon the form of the forest as to its age classes. It may be itemized as, 1. Site classification. 2. Age of stands. 3. Area of stands. 4. Volume of stands. 447 448 COORDINATION OF FOREST SURVEY When these factors cannot be directly ascertained, the requisite basis must be obtained for calculating them. The most fundamental and useful basis is, 5. Diameter of trees in stand by species, or a stand tal)le. Finally, because of its inadequate handling, special emphasis must be placed on obtaining 6. The area stocked by immature age classes. 345. Site Qualities — Separation in Field. Site qualities in the forest should be separated by area. Where several types exist, such as cove, lower slope, upper slope and ridge, which correspond closely with difference in site, the division by types goes a long way toward separating the site qualities (§ 228). Where site qualities must be determined directly, there are but two methods possible of which the first is direct judgment based on obser- vation of site factors, such as soil, altitude, slope, rock, moisture (as swamps) and general character of the timber growth. This niethod is subject to serious errors (§ 226). The second method ^ is ba.sed on the height growth of dominant trees (§ 227). But to determine directly the site class indicated by trees of different heights, their age must be known. When the forest is composed of a few laige age classes of even age, direct determination of a few ages may give this basis. But where the age classes are mixed, the age of individual dominant trees, rather than age of stand, must be relied on to indicate site quality. If we could assume that diameter growth did not decrease for the average tree, on poor sites, and that average trees of a given diameter were as old on Quality I site as on Quality III, diameter could be substituted for age; but average diameter growth varies with the site quality itself, which prevents this substitution. To obtain the basis of field classification of site, the heights of dif- ferent trees based on age are plotted and divided into site qualities based on the standard chosen, as illustrated in Fig. 84 (§310) except that in this case the data are obtained by plotting individual trees, and by analysis of the height growth of trees, rather than from plots. To apply this table or set of curves, in determining the quality of a given site, a selected tree or two is measured for height. If fully matured, total height may indicate directly the site quality. If the stand is young, age must always be ascertained. The average height for the given age is then looked up on the chart. The trees chosen should preferably be dominant and must never be suppressed. The position of the height with reference to the curves or table indicates the site quality. The unit of area on which sites are separated should be that used 1 Journal of Forestry, Vol. XV, 1917, p. 552. RELATION BETWEEN VOLUME AND AGE OF STANDS 449 in separating stands or units of volume estimating, such as small legal subdivisions, e.g., 10 acres, except where, by the aid of topography, the site qualities can be mapped to conform more closely with natural boundaries. Types are commonly separated in the forest survey by mapping the areas, and the estimate is usually separated to coincide with the divisions thus made (§221) though on forties this is not always done. 346. Relation between Volume and Age of Stands. Density of stocking, as shown, is not determined by the total merchantable volume of a stand, but by a comparison of the existing volume with the index volume which stands should have at given ages. Density when deter- mined by comparison of volumes, is therefore a function not solely of area but also of age. To determine density for large areas, therefore, a basis of separation of the volume into age classes is required. This means either the direct mapping of areas of separate age classes, or a tally of diameters and a stand table for diameter classes in the stand. Methods of forest survey which utilize diameter tallies to obtain volumes (§ 207 and § 209) naturally lend themselves to the securing of such a stand table. The use of such tallies for determining age groups and average ages are shown in § 320 and § 323. In general, density of stock- ing for mature age classes will be found not in the field, but after the volumes have been computed or stand tables prepared, and by means of a comparison of volumes with the yield table, on the basis of similar ages. Age classes and their actual ages may be determined directly during timber survey only when the areas which they occupy are separate, large and eassily distinguished, and when time permits of the testing of trees for age. In intensive management, this method will l^e followed on small areas; but for large areas of mixed ages, the general method of depending upon diameters to indicate age should be relied on; hence the stand table is the basis of this age class division, both for age and area (§318 to § 323.) 347. Averaging the Site Quality for the Entire Area. Site qualities, when not correlated with type, present difficulties in classification, so much so that on large extensive projects site qualities may for the time have to be waived and an average yield table obtained for all sites. (This method was adopted in the preliminary working plan for the Coconino Nations' Forest, Arizona.) A composite stand table, including stands on all sites, is best for this purpose. Its application to the average site will depend on the average density or reduction per cent found for the area. Only when the divisions of the total area into site qualities can be coordinated with similar divisions of the esti- mate and stand can these divisions be made the basis of separate growth 450 COORDINATION OF FOREST SURVEY predictions for the forest. Wherever possible, this division must be made. 348. Growth on Areas of Immature Timber. The growth on any large area, whether the form of forest is even-aged in pure stands, or many-aged in mixed stands (§ 314) must include that of the young, unmerchantable stands. This growth is a prediction of future volume, and as such, may be obtained, not by measuring the present volume of the stand, nor by counting the number of trees in very young stands, but by the method of comparison with older stands. The yield table based on area and age gives this comparison. But to utilize the table, the one thing necessary to determine is the area which is stocked with the immature timber. Its age is more easily determined than for old timber, either by cutting or by counting whorls. Based on area and age, the future yield is a matter of density of stocking. The rate of growth per year may be taken as the mean annual growth, shown by the reduced or empirical yield table, for the age at which the stand will be cut. The density per cent for young stands is practically independent of the density of crown cover, and depends instead upon the number of trees per acre as compared with the normal number required at maturity, the distribution of these trees over the area, and the chance of survival (§ 316). Mortality in scattered stands where each tree has room to grow is much less than in crowded stands; and if the spacing of the reproduction is such that, allowing for a reasonable rate of loss from insects and causes other than suppression, the stand will reach full stocking at least a decade before maturity, it can be considered as fully stocked now. If a large area is being measured and an average density per cent is found for this area, resulting in an empirical jdeld table somewhat lower in values than the normal table, a conservative plan is to assume that the ultimate yield of young stands will not exceed this density, and to use the empirical yield table as the basis for calculating their future yields. That area and yield per acre is the only possible basis of prediction of yield for immature stands must become evident by considering the difficulties of the opposite plan, that of counting numbers of trees on snail plots. In tallying or counting reproduction or immature sizes, it is customary to lay off the plots at fixed intervals, comprising from one-tenth of the estimated strip, down to less than 1 per cent of the strip, and to count the seedlings and saplings upon these plots. The only way in which these data can be used to predict growth on such small timber is by predicting the percentage of this count which will survive. The mjethod of comparison by numbers of trees is useless, GROWTH ON AREAS OF IMMATURE TIMBER 451 first, because number of trees per acre at these ages does not in any way indicate the future yield, since this is determined by the number that survive; second, because the area rather tlian the number will determine the future yield. On a plot of 100 square feet there may be one hundred seedlings; yet if fully stocked at maturity not more than one tree would be able to survive from this number. Such counts on plots serve only to determine the extent to which reproduction is becoming established and do not give the data needed for growth predictions. Age Classes Based on Size. Immature timber may be divided into at least three classes for purposes of growth study; seedlings, saplings and poles. Seedlings are trees under 3 feet high.^ Saplings include trees from 3 feet high to 4 inches D.B.H. Poles are trees from 4 to 12 inches D.B.H. Saplings may be divided into Small — from 3 to 10 feet high. Large — from 10 feet high to 4 inches D.B.H. Poles may be divided into Small — from 4 to 8 inches D.B.H. Large — from 8 to 12 inches D.B.H. Methods for Seedlings and Saplings. In determining the quantity of reproduction and immature timber present on an area, in order to predict its growth by comparison with a yield table, the procedure will depend upon the form of the forest. In even-aged stands, areas stocked with seedlings in sufficient numbers can be entered by mapping them as fully stocked. Danger of destruction is chiefly by fire, and for this, correction can be made when fires occur. But in many-aged stands, suppression must be considered. Depending upon the silvical characteristics of the species and the behavior of the seedlings, the object should be to record only the area of mature forest which will result from the present stocking. Seedlings which are suppressed will be ignored. Those which grow in openings and are thrifty wiU be regarded as prob- able survivors. In rather open, group-selection - forests like yellow pine, the areas stocked in this manner are easily distinguished. With species such as spruce, seedlings starting under shade and not in open- ings should be disregarded altogether, both because of suppression, and because their age will be prolonged by this cause and they will not become an economic factor in the stand till a later period (§ 263). With saplings, the establishment of the stand in many-aged forests 1 Standard definitions, Society of American Foresters. ^ Group-selection, a forest composed of trees of all ages intermingled in small fairly even-aged groups. 452 COORDINATION OF FOREST SURVEY is more certain, and the area so stocked with trees which will probably survive can be better determined. For both these classes of timber, the best method of determining the area, and consequent future growth, during the forest survey, is to record on each strip the per cent of total area on the strip which is stocked with young timber, on the basis of probable survival to maturity. This per cent is then reduced to acres for the strip. The average size and age can also be noted. Seedlings and saplings can be separately noted, or thrown together, depending on the intensiveness of the work and size of area. A second method of record on the basis of area, formerly used in the Southwest, was to note the reproduction in general terms, based on whether the stocking was sufficient to replace the present stand. If so it was termed excellent. Different per cents less than this were termed good, fair, poor, and none. This system does not distinguish between the areas of mature and young timber or consider the relation which one bears to the other. To supplement the per cent method of ocular guessing at areas restocked, plots may be laid out at given intervals, on which the areas stocked can be mapped, and computed in terms of acres. The per cent of the plot thus shown as reproduced serves to correct the ocular work and to check the results. Methods for Poles. With poles, the area method can still be applied directly in even-aged stands, by mapping. In many-aged stands, a choice of two methods is offered. Either the area per cent can be used as for saplings, but separately, and the number of trees in this class ignored as before, in which case merely the average size and age of the poles on each strip is recorded with the per cent of area occupied, or instead, the poles may be counted. The purpose of the count is to obtain a second basis of comparison with the empirical yield table. The latter should show the number of trees per acre required at different ages. The yield table data may be made to include pole sizes, by including plots of this age in construct- ing the normal tables of yield. In case this has been done, the area occupied by poles can be very roughly determined by means of the numerical comparison with the empirical table. For instance, if poles, averaging sixty years old and 7 inches in diameter run 120 per acre in the normal table, and the reduction per cent is 66|, the empirical stocking is 80 poles per acre. A count of 8000 poles on the area indicates an area of 100 acres stocked with pole sizes. A definite plan for the determination of the stocking with poles must be made preliminary to undertaking the timber survey. Trees which are part of an even-aged mature stand, but which are not yet merchant- SEPARATION OF AREAS OF IMMATURE TIMBER 453 able or are suppressed, are not considered, since the yield table for the stand takes care of them. Only in many-aged stands must poles be counted, or their area determined by per cent of the total, the former method to be used if the yield table permits of direct comparison of numbers, the later, if only the mature classes are shown in the table. 349. Efifect of Separation of Areas of Immature Timber on the Density Factor for Mature Stands. The separation by area of the immature age classes accomplishes more than the determination of future jaeld for these age classes. In the many-aged forest, the mature timber is not segregated as it is in even-aged stands, but is intermingled with areas of reproduction, saplings, and poles. In the attempt to separate this mature timber into two or more age classes, either based on diameter classes, or by age groups (§ 320 and § 323) it is necessary to begin with a knowledge of the total area occupied by all the mature age classes. If the area actually stocked with seedlings, saplings and poles to the exclusion of mature timber is neglected, then the area appar- ently required by the mature timber is greater than that actually required, by just the amount of this error. In the even-aged forest no such mistake is possible, and by analogy, its correction for the many- aged forest must be undertaken. The effect of not separating the area of immature stands is to lower the reduction per cent or apparent density factor for the mature age class. E.g., a reduction per cent of 40 is found for mature timber when it is assumed to occupy the entire area. Segregation of young timber shows that one-half or 50 per cent of the area is occupied by these age classes. The total area is 10,000 acres. The actual area occupied by mature timber is now 5000 acres, which doubles its density, and gives a density per cent of 80 instead of 40. At first glance it would appear that no difference is made in the cal- culation of yield of these mature age classes by either assumption since reduced area and increased density are reciprocal and refer to the same actual stocking and volume and presumably the same future yield. The benefit lies in the fact that the corrected density factor more nearly indicates the rate of growth per year for the forest or on the average acre, which is the information most needed in permanent management. By separating the yield and area of the young timber, it is possible to predict the total actual yield of the forest over a long period, instead of for the shorter period required to harvest timber now mature. Instead of an extremely low per cent of density for mature timber and for the forest, which would indicate the need of considerable reduction in yields from the standard table (§ 316), the true conditions are revealed. Finally, it gives the same data as to age classes for the many-aged forests as are obtained by mapping for even-aged stands. 454 COORDINATION OF FOREST SURVEY 350. Stand Table by Diameters for Poles and Saplings: When Required. When diameter is definitely substituted for age and area, the growth of the forest for a period of from ten to twenty years into the future will include not only the increase on existing merchantable trees, but the volume of all young trees which grow during the period to a size which brings them into the merchantable class (§ 277). The number of diameter classes which will become merchantable will be determined by the length of the period and the rate of growth in diameter. At a rate of 1 inch in five years, trees now 4 inches below the minimum diameter will reach the required size in 20 years. In order to predict the growth of the stand for this period, the number of trees of each diameter class included in the group which will mature within the period must be recorded during the forest survey. Either all of the trees of these sizes must be calipered or counted, and the average diameter approximated, or these sizes may be calipered on a part of the area, distributed mechanically to obtain an average for the whole. This again indicates the need for correlation of the method to be used in predicting growth with the timber survey, before the latter is undertaken. References Coordination of Growth Studies, Reconnaissance and Regulation of Yield on National Forests, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. VIII, 1913, p. 317. APPENDIX A A. LUMBER GRADES AND LOG GRADES 351. Purpose of Log Grades. The most useful purpose of timber estimating and log scaling is to determine the value of the bgs and standing timber. This value depends upon the amount or per cent of lumber of different qualities which can be obtained from the logs or timber to be valued. In § 87 it was shown that for this purpose logs are separated into grades, usually three m number, but that the specifications for and value of each log grade depend upon the contents of logs as expressed in grades of lumber, and in resultant average value or price per 1000 board feet. 352. Grades of Lumber. Wood varies in texture or closeness of grain, difference between heart- and sapwood, uniformity of texture and freedom from knots, number, size, placement and character of knots, and presence of or freedom from various defects which lower the value of the piece by altering its appearance, strength, surface or suitability for the purposes for which it may be used. Pieces which are entirely free from all defects are suitable for the highest uses and possess the greatest value. At the opposite extreme are found pieces with defects so numerous or serious that they are unfitted for any useful purpose, hence possess no market value and are disposed of as refuse to the burner or as fuel. Certain " cull " grades, formerly refuse, are now generally handled as merchantable, but the practice of scaling has not been altered and such grades are still excluded from the scale as unsound. The output of a mill in lumber, if separated according to the quality and value of each board, would form an unbroken series from the most perfect pieces descend- ing through an increasing per cent of more and more serious defects until the poorest merchantable boards are passed, and refuse only is left. For practical purposes, this series must be separated by arbitrary standards into groups termed lumber grades, so defined that any piece may be assigned by its appearance to its proper classification or grade. These grades are then made the basis of lumber prices and lumber trade. The specifications for a grade are intended to defuie the poorest piece which will be accepted in the grade, thus excluding all lumber whose quality and defects are such as to unfit it for this grade. The average quality of lumber in any grade will therefore be better than the minimum specifications. Lumber which would qualify for a given grade is sometimes included in a lower grade, but this is not in the interest of the seller and tends to destroy the standards of grading. 353. Basis of Lumber Grades. The requirements of a lumber grade are, that it be generally adopted in a region or for the trade which handles the lumber from this species or region; that it be consistently applied throughout this region; that it be capable of definition and application in grading; and that it conform to the require- ments for certain definite uses of lumber. To use lumber for a given purpose, when it is better than is necessary and is suitable for a higher use, is wasteful, but to admit 455 456 APPENDIX A lumber to a grade intended for a given use, when it possesses defects which unfit it for this use, destroys the basis of sound business. Again, a grade, as apphed to the lumber of a given species or region, must be so defined as to permit of securing a sufficient volume of output qualifying for the grade to make it a commercial or market product. No purpose is served in making grades for clear lumber, to apply to second-growth stands which produce little if any lumber of this grade. Defects characteristic of one species but absent or rare in others call for modi- fications of grading rules to suit the species in order to prevent the rejection of too large a percentage of the output for grades for which it is otherwise suited. To secure uniformity in both definition and application, grades of lumber are established by regional associations of lumber manufacturers and dealers, which frequently employ a corps of grading inspectors acting under a central head. These grading rules are modified from time to time as market conditions change. The latest specifications for any region or species should be obtained from the local associations. Not only do specifications change, but there is considerable fluctua- tion in their application as a whole, and in individual mills, which it is the purpose of inspection and standardization to avoid as far as possible. 354. Grades for Remanufactured and Finished versus Rough Lumber. For the }niri)ose of valuing logs and standing timber, only those grades of lumber are serviceable which can be applied with some degree of accuracy directly to the log. Lumber is finally sold on the basis of its grade when finished or remanufactured. But these final grades are made the basis of the grading of the rough boards on the sorting table, with the modification that the better grades of rough lumber may be split up into several special grades, including lumber intended for specific uses. In all such cases, the general grade of the rough lumber is the basis of log grading. Structural and dimension lumber calls for a difi'erent basis of grading, as do sawed cross ties. Where a considerable proportion of the output is in these forms, the basis of log grading is affected. While a system based on this form of products could be worked out for logs, it has not been attempted, but the basis of log grades has been confined to 1-inch rough lumber. The average value of each standard grade of lumber may be obtained from that of the gi'ades of remanufactured lumber which it produces. It is always possible to recognize and estimate separately the quantity and value of trees containing unusual or special dimensions, in the nature of piece products. 355. General Factors which Serve to Distinguish Lumber Grades. Face. Lum- ber is graded on the appearance of the poorest face for certain uses and in certain regions. For other uses and in other regions, the appearance of the best face deter- mines the grade. The specific practice is in each case determined by the local grad- ing rules. Defects. With respect to perfect pieces, all departures from standard as defined in § 352 constitute defects. With regard to each specific grade, the defects which disqualify the piece and throw it into lower grade are defined. Defects which dis- qualify in one grade may be accepted in the grade below. The principal defects are caused by, 1. Knots, sound or unsound, encased, firm or loose, and knot holes. 2. Rot. 3. Shake, season checks, seams and cracks. 4. Pitch. 5. Worm holes. 6. Stain, either as blue sap or red heart. LUMBER GRADES AND LOG GRADES 457 7. Mechanical defects, as splits, torn grain. 8. Wane, or round edges. These defects or any combination of them may reduce grade by affecting the utility and value of the piece through its appearance, surface, texture, or strength. 356. Grouping of Grades of Rough Lumber. Even when standard grades of rough lumber only are considered, it is best not to attempt to base log grades or quality of standing timber on the determination of given per cents of each of these standard grades supposed to be contained in the logs. Instead, these grades should be com- bined into a few groups with similar characteristics conforming to the grading rules for the species and region. Three such groups may be distinguished in softwoods, namely, finishing grades, factory or shop grades, and common grades. Based on the practice of " sound " scaling, a fourth group may be made to include grades which contain rot or other defects in sufficient quantity to cause their rejection in scaling logs. Finishing grades include all of the so-called upper grades of lumber, characterized by freedom from all but a few small defects. These grades are suitable for use with- out being cut up, for purposes requiring appearance as the prime factor, combined with definite and sometimes considerable width and length. These grades are used for outside and inside finish and for many purposes of manufacture. The entire piece is graded as a unit, any defect serving to reduce its grade as a whole. Factory or Shop Grades. Boards suitable for factory or shop grades are such as will yield smaller pieces of upper grade material when ripped or cut up as to exclude or cull out disqualifying defects. In these grades, therefore, the piece is not graded as a unit but on the basis of the per cent of its volume that can be utilized. The remainder is rejected as refuse and may therefore contain defects of any character without affecting the grade of the piece. Common Grades. As applied to lumber cut from conifers or " softwoods," com- mon lumber is distinguished from the other two groups by a general coarseness of appearance caused by various defects or combinations of defects, such as nu- merous large or small knots, which not only render it unsuitable for the ujiper grades but prevent cuttings being made from it which would qualify it for factory grades. Common lumber of this class is graded for the entire piece and finds its principal use in construction. Owing to the large volume of common lumber, in conifers, which constitutes from 60 to 95 per cent of the total output, this group may be subdivided in each given region. These specific common grades are not always given identical names any more than are the grades in the other two groups. The most widely accepted nomenclature is, No. 1 Common, No. 2 Common, No. 3 Common. 357. Example of Grading Rulss. Southern Yelloio Pine. — Finishing, or Upper Grades. " A " Finishing, inch, IJ, I5 and 2-inch, dressed one or two sides, up to and including 12 inches in width, must show one face practically clear of all defects, except that it may have such wane as would dress off if surfaced four sides. 13-inch and wider " A " finishing will admit two small defects or their equivalent. " B " Finishing, inch, Ij, I5 and 2-inch, dressed one or two sides, up to and including 10 inches in width, in addition to the equivalent of one split in end which should not exceed in length the width of the piece, will admit any two of the following or their equivalent of combined defects: slight t«rn grain, three pin knots, one standard knot, three small pitch pockets, one standard pitch pocket, one standard 458 APPENDIX A pitch streak, 5 per cent of sap stain, or firm red heart; wane not to exceed 1 inch in width, J-inch in depth and I the length of the piece; small seasoning checks. 11-inch and wider " B " Finishing will admit three of the above defects or their equivalent, but sap stain or firm red heart shall not exceed 10 per cent. Select Common Finishing, up to and including 10-inch in width will admit, in addition to the equivalent of one split in end which should not exceed in length the width of the piece, any two of the following, or their equivalent of combined defects: 25 per cent of sap stain, 25 per cent firm red heart, two standard pitch streaks, medium torn grain in three places, slight shake, seasoning checks that do not show an opening through, two standard pitch pockets, six small pitch pockets, two stand- ard knots, six pin knots, wane 1 inch in width, ^ inch in depth and one-third the length of the piece. Defective dressing or slight skips in dressing will also be allowed that do not prevent its use as finish without waste. 11 and r2-inch " C " Finishing will admit one additional defect or its equivalent. Pieces wider than 12 inches will admit two additional defects to those admitted in 10-inch or their equivalent, except sap stain, which shall not be increased. Pieces otherwise as good as " B "' will admit of twenty pin-worm holes. Common Grades. No. 1 Common boards, dressed one or two sides, will admit any number of sound knots. The mean or average diameter of any one knot should not be more than 2 inches in stock 8 inches wide, nor more than 2§ inches in stock 10 and 12 inches wide; two pith knots; the equivalent of one spht, not to exceed in length the width of the piece; torn grain, pitch, pitch pockets, slight shake, sap stain, seasoning checks, firm redheart; wane I inch deep on the edge not exceeding 1 inch in width and one-third the length of the piece, or its equivalent; and a limited num- ber of pin-worm holes well scattered; or defects equivalent to the above. No. 2 Common boards, dressed one or two sides; No. 2 Shijjlaii, Grooved Roof- ing, D. & M. and Barn Siding will admit knots not necessarily soimd; but the mean or average diameter of any one knot shall not be more than one-third of the cross section if located on the edge, and shall not be more than one-half of the cross section if located away from the edge; if sound may extend one-half the cross section if located on the edge, except that no knot, the mean or average diameter of which exceeds 4 inches should be admitted; worm holes, splits one-fourth the length of the piece, wane 2 inches wide or through heart shakes, one-half the length of the piece; through rotten streaks ^ inch wide one-fourth the length of the piece, or its equivalent of unsound red heart; or defects equivalent to the above. A knot hole 2 inches in diameter will be admitted, i)rovided the piece is otherwise as good as No. 1 Common. Miscut 1-inch common boards which do not fall below f-inch in thickness shall be admitted in No. 2 Common, provided the grade of such thin stock is otherwise as good as No. 1 Common. No. 3 Common boards, No. 3 Common Shiplap, D. & M. and Barn Siding is defect- ive lumber, and will admit of coarse knots, knot holes, very wormy pieces, red rot, and other defects that will not prevent its use as a whole for cheap sheathing, or which will cut 75 per cent of lumber as good as No. 2 Common. 358. Relation between Grades of Lumber and Cull in Log Scaling. From the standpoint of the lumber trade, lumber which is merchantable, no matter what the extent and character of defects it contains, is placed in a recognized grade, while cull lumber is lumber which is not merchantable. Grades of common lumber below No. 3 are sawed from unsound or defective portions of logs, which would be culled in scaling. In mill-scale studies and in determining log grades, it is proper, there- fore, to throw all grades under No. 3 Common into the group termed cull. In addi- LUMBER (illADES AND LOG GRADES 459 tion, the grade designated as No. 3 Common may in certain regions contain unsound material which would not be scaled on the basis of sound scale. Hence a portion of the No. 3 grade, if so constituted, plus all of the cull grades of lumber, when utilized, go to increase the amount of over-run secured in manufacture. From one to three grades of lumber below No. 3 Common may be recognized, according to the species and region. Common Grades Culled in Sound Scale of Logs. Southern Yelloiv Pine. No. 4 Common boards shall include all pieces that fall below the grade of No. 3 Common, excluding such pieces as will not be held in place by nailing, after wasting one-fourth the length of the piece by cutting into two or three pieces ; mill inspection to be final. 359. Log Grades. Determination. The purpose of defining log grades is to furnish a basis for separating the logs into groups whose average value or price per 1000 board feet can be determined, instead of attempting to arrive at an average price for the entire run of logs. Three such groups permit of a sufficient differentia- tion for this purpose. Where logs are not bought or sold, but standing timber is manufactured by the purchaser, log grades (§87) form the best basis for appraising the value of this timber. The specification for determining the grade of logs must apjily to the external appearance and dimensions of the log. In application, logs on the border line between two grades are usually thrown to the grade below, since a part of the surface is invis- ible. Log grades are based on 1. Minimum diameters and lengths. 2. Surface appearance, and presence of knots or visible defects. 3. Judgment of scaler, based on 1 and 2 as to the minimum per cent of upper or better grades of lumber contained therein. The specifications for log grades are more elastic than for lumber grades, since the presence of a small per cent of high grade lumber may serve to offset serious defects and give the log the value of a grade from which it would be excluded if based solely on quantity or scale. These specifications should be drawn in such a manner as to furnish the most serviceable basis of subdivision of the existing range of quality found for the species and region, which object may be secured by modifying the requirements as to size and per cent of upper grades required for logs of first and second grades. Log grades should be established only after thorough mill-scale studies, and by some agency similar to that of the United States Forest Service or a Lumber Manu- facturers' Association, so as to secure uniformity over as wide an area as possible. Within the limits of a log grade a certain variation in average quality will occur in different quantities of logs, owing to the preponderance of higher or lower grades of lumber within the limits set. The quality of the logs which form the basis of the mill-scale study may be better or poorer than the average, even after classification into grades. But as logs and timber stumpage are worth considerably less than lumber, it is unnecessary to attempt a greater refinement; nor could it be practically applied. Diameter For logs of the best grade, diameter is a reliable guide. Up to a certain size, trees retain the branches, either alive or dead, and the central bole of the tree is filled with these knots. Stunted, slow-growing, and consequently small trees still have these knots, and during their growth, have made very little clear lumber. Large trees, on the other hand, even if no older, have laid on much clear wood outside of the knots. The minimum diameter for the highest grade can be fixed to include jiractically 460 APPENDIX A all logs of this class, not barred by knots or defects. This diameter will vary with the same species in different regions, and for different species. Effect of Defect upon Grades of Logs. The defect most easily seen, both in logs and standing timber, is a knot. In grading hardwood logs, one somid, bright knot, with a maximum diameter of 4 inches is taken as a standard defect. Other defects are compared with this knot, on the basis of an equal amount of damage to quality. These may be worm holes, smaller or larger knots, shake, rot, cat faces or fire scars. The maximum number of standard defects, or their equivalent, is prescribed for each grade of logs. For conifers, a different system is employed, and the specifications lay stress on the possible percentage of yield of certain grades, with indication as to the general appearance and character of defect in logs which will yield this ratio. Defects are of two classes, those which cause loss of grade, but no discount in total scale, i.e., sound defects, and those which require elimination from the scale of the defective part. To the first class belong sound knots, stain, firm red heart and pitch. In the second class fall rot, shake, fire scars, cat faces, and crook or sweep. Worm holes may be in either class, according to size and frequency. In the grading of hardwood logs, no distinction is made, and the presence of more than two " standard " defects serves to throw the log into the lowest class, or No. 2, except when over 24 inches in diameter, when it must cut at least 75 per cent of No. 1 common and better lumber. With conifers, the presence of either class of defect will not reduce the grade of a log as long as the minimum percentage of upper grades can still be secured. But in reality, the value of the log is greatly lessened by such defects. With increasing amounts of defect, the log is de-graded cither to second or third grade, and finally is rejected as cull. 360. Examples of Log Grades. Hardwoods — National Hardwood Lumber Association, 1916 Oak, White and Red. No. 1 logs. 2 inches of bright sap is no defect. Sap in excess of 2 inches is one standard defect. No. 1 logs must be 24 inches and over in diameter. 24 to 29 inches inclusive will admit of one standard defect or its equivalent. 30 inch and over will admit of two standard defects or their equivalent. Select. Select logs must be 18 inches and over in diameter. 2 inches of bright sap is no defect. Sap in excess of 2 inches is one standard defect. 18 to 21 inches wide inclusive must have ends and surface clear. 22 and 23 inches will admit of one standard defect or its equivalent. 24 inches and over will admit of one more standard defect than is admitted in No. 1 logs of same size. No. 2 logs. No. 2 logs must be 16 inches and over in diameter. Bright sa]) is not a defect in this grade. 16- and 17-inch will admit of one standard defect or its equivalent. 18 to 23 inches inclusive will admit of two standard defects or their equivalent. 24 inches and over must cut 75 per cent or more into No. 1 common and better lumber. The grades for other species arc similar. Softwoods — Columbia River Log Scaling and Grading Bureau, Washington and Oregon, 1920. No. 1 Logs. No. 1 logs shall be logs which, in the judgment of the scaler, will be suitable for the manufacture of lumber in the grades of No. 2 clear or better to an amount of not less than 50 per cent of the scaled contents. LUMBER GRADES AND LOG GRADES 461 No. 1 logs shall contain not less than six annual rings to the inch in the outer portion of the log equal to one-half of the log content; and No. 1 logs shall be straight grained to the extent of a variation of not more than 2 inches to the lineal foot for a space of 2 lineal feet equidistant from each end of the log. Rings, rot, or any defect that may be eliminated in the scale, are permitted in a No. 1 log, providing their size and location do not prevent the log producing the required amount of No. 2 clear or better lumber. A No. 1 log may contain a few small knots or well scattered pitch pockets as per- mitted in grades of No. 2 clear or better lumber; or may contain a very few grade defects so located that they do not prevent the production of the required amount of clear lumber. No. 2 Logs. No. 2 logs shall be not less than 12 feet in length, having defects which prevent their grading No. 1, but which, in the judgment of the scaler, will be suitable for the manufacture of lumber, principally in the grades of No. 1 common or better. No. 3 Logs. No. 3 logs shall be not less than 12 feet in length, having defects which prevent their grading No. 2 but which, in the judgment of the scaler, will be suitable for the manufacture of inferior grades of lumber. Cull Logs. Cull logs shall be any logs which do not contain 335 per cent of sound lumber. Logs which contain considerable clear lumber but not sufficient to grade No. 1, and contain also large coarse knots or other grade defects of No. 3 quality, will be classed as No. 2 if the average value of the lumber falls in this class, regardless of its actual grade. Logs which are on the border line between two grades should be graded alternately or in equal amount in the upper and the lower grade. 361. Mill-Grade or Mill-scale Studies. In §81 and §82 it was shown that the log scale should make no attempt to measure the actual sawed contents, which is the sum of the scale, plus this over-run. It is equally impossible for the scaler to separate his scale into grades, for in doing so he w^ould be compelled to substitute judgment for facts; yet the actual value of logs can be determined onl}' by a knowl- edge of both of these factors. When the sawed output of a run of logs has been tallied and totaled separately by grades, its comparison with the log scale shows for the entire qv.antity scaled, the average over-run per thousand board feet of scale, and the per cent represented by each grade produced. The value of the product of an average thousand feet B. M. log scale in terms of sawed lumber is determined by first multiplying the price of each grade of lumber sawed by the per cent of the grade in one thousand board feet, adding the by-products, and multiplying by the total per cent of over-run. This general check, applied to an average run of logs, and termed the mill run, will serve to determine the value of similar average sizes and quality. But for timber averaging larger or better, or smaller, knottier and poorer, the true value can be obtained, by this method, only after sawing. But individual logs of similar sizes possessing certain distinctive features, as shown by surface indications such as clearness, knots and other defects, will cut out about the same per cent of grades and values wherever found. By using the log as the standard, it is possible to apply the results of mill-scale studies of separate logs to stands whose average quality may be entirely different from that which is being sawed, provided only that some logs of all qualities are analyzed. For this reason, mill-scale studies should be based on the separate analy- sis of the product of individual logs, by grades of lumber. Such studies determine, for logs of each diameter, length and grade, first, the over-run in sound lumber, and 462 APPENDIX A in all merchantable grades; second, the amount of each standard grade of rough boards, expressed in per cent of the total scale of the log, net and gross. 362. Method of Conducting Mill-scale Studies. A tabulation, classification and summary of the logs so analyzed permits, first, a correlation between logs of given sizes, appearance and defects, and the actual sawed contents in grades which these logs will produce, hence their actual value; second, the adoption of arbitrary specifications for separating the logs themselves into log classes or grades; third, a comparison of the value of logs of each size and grade with the cost of logging them, enabling both owner of stumpage and operator to determine both the lower limits of merchantability as to minimum size and per cent of sound lumber in a log which warrants its removal and manufacture, and in case only a portion of the merchant- able stand is removed, to know the relative value and profit of removing certain definite classes and sizes of material and leaving others (§ 96). The steps in a mill-scale study are : 1 . Decision as to the exact number and designation of the grades of rough lumber to be tallied. 2. Scale and record of each log, on the deck. If log grades have already been adopted, the scaler assigns each log to its apparent grade. A full record would embrace the following items: number of log (serial); length, in feet and inches; position in tree, as butt, middle, top; species; average diameter inside bark at small end ; at large end ; width of sapwood ; thickness of bark ; scale, by standard log rule, full and net after deductions for cull defects; estimated log grade; description of defects, preferably graphic, on a diagram showing large and small ends, and both sides of logs. This record requires one man, an experienced log scaler, who will place a number on each log to coincide with his record. Logs scaled sound are given a special mark, and separated in the final tables. 3. Identification of this product of separate logs. A marker standing behind the head saw marks with crayon each piece sawed from a log. The number of the log is placed on the first few pieces. Different-colored crayons are used for alternate logs. A count may be made of the total number of pieces from a log, as a check on the tally. This work is made quite difficult by a resaw, which tends to mix the products of con- secutive logs on the chains and requires the marking of both sides of the piece. Gang saws further complicate the study. The marker can also check logs scaled as sound for unseen defects appearing in sawing, and make final record of the logs which saw up sound. 4. Record of grades and sizes. An expert grader, familiar with the standard for the species and locality, will grade each piece. The record, kept on a separate sheet for each log, and given the log number, will show length, width, and grade, by pieces, and a recapitulation or summary for the log, giving in addition to the data copied from the scales, the total board-foot contents in each grade, and the per cent of the sound scale which this equals. This tally requires the services of a tallyman, mak- ing a crew of four men. 5. Additional data needed, (a) Data on per cent of total contents utilized embrace the measurement of the cubic contents of a log, and the analysis of the volume which goes into slabs, edgings, and sawdust. (h) Data on sawing practice include gage of saws, actual widths and lengths of lumber sawed, efficiency of sawyers, methods of sawing, and the output or per- formance of mill. (r) Data, on the character of the timber and logs measured, to indicate the comparison with other tracts, whether of higher or lower quality. 6. Tables or compilation of results. The logs can be classified, first, into sound LUMBER GRADES AND LOG GRADES 463 and defective. Where log grades are used, these grades are also separated. Next, the logs in each separate class are sorted into diameter classes, 1-inch or 2- inch (volume based on differences of 100 board feet was used in the studies conducted in District 1, Missoula, Montana). As a result of this tabulation, the logs when orig- inally classed by the scaler into grades by judgment, can be re-graded in accordance with actual specifications for the grades. A sample form of tabulation would be, by columns: Diameter class. Number of logs as a basis. Average lengths of logs. Per cent and value per 1000 board feet of each grade, represented in the prod- uct obtained. Total lumber tally, excluding cull lumber-sawed. Over-run, excluding cull lumber sawed. Tally of cull lumber sawed. Over-run, including cull lumber sawed. Net scale. Per cent of total net scale in each class of logs. Value per 1000 board feet, based on net tally. Value per 1000 board feet, based on net scale. Gross scale. Per cent deducted for defect. These data, shown thus for each class of logs, can be totaled for all logs, and averaged. 7. Deductions or summaries. Irregularities are sure to occur in the final sum- maries. These can frequently be evened off by means of curves. The final curves and tables should show, for each separate log grade, the per cent of each grade of lumber obtained for logs of each diameter class, and the value of the average log for the class. Effect of Waste or Cull. Such studies indicate the effect of increasing amounts of waste or cull upon the value of the gross scale or log. Cull lumber may not reduce the sale value of the residual lumber cut from the log, but the cost of log- ging is based upon the actual size of the log, which is best measured by its gross scale. The value of the product divided by this total scale gives a more correct gage of the value of the whole log in terms of price per 1000 board feet, for the purpose of determining whether the log is merchantable. A crew of five men can usually tally two hundred logs per day of average sizes. A single mill-scale study requires from one thousand to two thousand logs for best results. Instructions for Recording Data, U. S. Forest Service. Logs should be lettered A, B, C, etc., A being the butt log. The species may be written out or the atlas number may be used, thus: " Loblolly pine " or " P76." The log length should be measured to the nearest tenth of a foot. The crook may be measured by noting the distance in inches between a straight line connecting the ends of the log on the concave side and the log itself. If relative terms such as " V " (very crooked), " M " (moderately crooked), and " S " (slightly crooked) are used, they should be carefully defined. Thus, if the crook is more than one-half the diameter of the log the term " V '' might be applied; if one-quarter to one-half the diameter it would be '' M'"; while less than one-quarter it would be " S." If practically straight indicate this by " O " after heading "' Crook." , 464 APPENDIX A Form of Record for Mill-scale Studies, U. S. Forest Service Form 234 Revised July 1, 1912 Large END. Small END. Tree Log (Number.) (Letter.) D. i. b„ 1 Width of bark, Log length Crook . .Knots D. o. b.. 1 2 3 Width of sap, Rings, Cubic ) Peeled, feet \ \ With bark, Full scale. Net scale. Sawad out. 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 8 9 10 11 12 Remarks: Date. ., 191 LUMBER GRADES AND LOG GRADES 465 Knottiness may not always be of importance, but if it is recorded letters may be used, as for crook. Two diameters inside bark at right angles should be measured and the average recorded to the nearest tenth inch. The average width of bark, measured on a radius, should be recorded, care being taken to make the measurements where bark is not partly worn off. The width of sap, in case desired, should be measured along an average radius. In case the age at either end of the log is found it can be inserted opposite " Rings." If the cubic content of a log is found in the office it may be entered opposite " Cubic feet." " Full scale " means the number of board feet that would be tallied by the log scaler if the log were straight and sound. " Net scale " is the number of board feet tallied by the scaler after deducting for defects of any kind. " Sawed out " is the number of board feet of lumber actually sawed out. The large spaces are for the dimensions of boards sawed out, each space being for a separate grade. The name of the grade may be written or stamped in at the head of the column. The total number of board feet of each grade sawed out should be entered opposite the proper grade number in the small spaces under " Sawed out," which is the grand total of these gi'ade totals. The boards may be tallied thus: " 1X3X16," meaning a board 1 inch thick, 3 inches wide, and 16 feet long. Frac- tions may be indicated thus: 3iX3-Xl2 (3|"X3|"Xl2'). As a rule the thickness should be recorded to the nearest even quarter inch below, the width to the nearest inch below, and the length to the nea^'est foot below the actual measurement. In some cases it may be preferable to tally the number of board feet direct. This means that the number of board feet in a board is read from a rule and entered at once. Thus for a board 1"X3"X12', the figure 3 would be tallied. APPENDIX B THE MEASUREMENT. OF PIECE PRODUCTS 363. Basis of Measurement. Any finished products of uniform or standard dimen- sions, manufactured or cut from trees or logs may be measured by tallying or count- ing the pieces. The size or contents of the standard piece determines its value, either directly or by conversion to cubic or board-foot contents. The relative value of pieces of different sizes is seldom directly proportional to their cubic volume, though for such products as mining timbers this may be true. But for piling and poles, value per cubic foot increases with increased length. The contents of sawed or hewn pieces of rectangular shape is easily computed in board feet. Finished pieces may be classed as round, hewn, or manufactured products. Squares and bolts intended for further manufacture may be sold by count (§ 9). 364. Round Products. Roum,' products include poles, piling, posts, mine timber, and certain lesser products such as hop poles and converter poles. Prac- tically all round pieces are intended for uses requiring durability against atmospheric and soil moisture, and strength to support weight or strains. Peeling reduces weight for transportation. Durability differs markedly with different species; hence whenever two or more species are available, at least two classes of product are recognized, the first con- taining the more durable or resistant species, the second, those which decay more rapidly or require preservative treatment. Round products are classed by length and diameter. Both minimum and maxi- mum specifications are quoted for length. For diameter, the minimum is given for each grade, since an excess adds to strength of piece. Prices are fixed by grades. Straightness is a quality necessary to strength, in poles and especially in piling. The degree of crook or sweep permitted in such products is always specified. A minimum taper is desired in poles and piles, especially when long, in order to diminish weight in handling. The diameter or circumference at both ends of poles and piling is specified, and both minimum and maximum limits given, corresponding to specified top diameters. Such limitations must coirespond to the average shape of the material available, both to insure strength and prevent rejection of too large' a percentage of pieces. Defects which wUl weaken the piece or decrease its durability serve to reject products of this character. The specifications are remarkably similar whether for poles, piles, mining timbers or cross ties. Such defects are shake, checks, splits, large coarse or rotten knots which weaken the piece, and rot. When the qualities of the piece for the use for which it is intended permit of knots, or of a certain amount of center or pipe rot, these defects may be permitted, especially if their exclusion would cause the rejection of a large percentage of the output. For poles, the presence of center rot requires an increased diameter at the butt, for acceptance of piece. Round products as a class give almost complete utilization of the bolt or log, and of the tree. The ends of piling, cross ties, and butts of poles are cut square with a saw, and the only waste is the bark. Where there is a market for posts or small 466 THE MEASUREMENT OF PIECE PRODUCTS 467 mine props, the tops are also utiUzed down to 3 or 4 inches. These small round prod- ucts also permit the utilization of suppressed trees and small timber, thus reducing total per cent of waste in a stand to a minimum. 365. Poles. Standard poles are 20 feet or more in length, and are used prin- cipally for telegraph or telephone lines. Specifications are based usually on circumference rat' er than diameter. Since the ratio between the two measure- ments for a circle is 3.1416 to 1, and this is exceeded for eccentric cress sections, specifications, especially for large sizes, call for I to 1 inch greater circumference than the proportion of 3 to 1 for dry poles and an extra 5 to f inch for green or water- soaked poles. Whit'i cedar, which furnishes the larger part of the poles utilized, is measured either by circumference or diameter. The specified relation of these measurements for peeled poles is, TABLE LXVIII Relation between Circumference and Diameter for White Cedar Poles Seasoned poles, Top diameter. Inches Seasoned poles. Circumference at top. Inches Green or water-soaked poles, Circumference at top. Inches 4 5 6 7 12 15 22 16 19i 22| An excess of 6 inches in length is permitted, or 1 half-inch scant for every 5 feet in length. 1 The standard specifications for Eastern white cedar poles, (American Telephone and Telegraph Company), are given below: All poles shall be reasonably straight, well proportioned from butt to top, shall have both ends squared, the bark peeled, and all knots and limbs closely trimmed. The dimensions of the poles shall be in accordance with the following table, the " top " measurement being the circumference at the top of the pole and the " butt " rasasurement the circumference, six (6) feet from the butt. The dimensions given are the minimum allowable circumferences at the points specified for measurement and are not intended to preclude the acceptance of poles of larger dimensions. When the dimension at the butt is not given, the poles shall be reasonably well proportioned throughout their entire length. No pole shall be over six (6) inches longer or three (3) inches shorter than the length for which it is accepted. If any pole is more than six (6) inches longer than is required, it shall be cut back. Quality and Defects of Timber. The wood of a dead pole is grayish in color. The presence of a black line on the edge of the sapwood (as seen on the butt) also shows that a pole is dead. No dead poles, and no poles having dead streaks covering more than one-quarter of their surface, shall be accepted under these specifications. Poles having dead streaks covering less than one-quarter of their surface shall have a cir- cumference greater than otherwise required. The increase in the circumference shall be sufficient to afford a cross-sectional area of sound wood equivalent to that of sound pieces of the same class. ^ Northwestern Cedarmen's Association. 468 APPENDIX B TABLE LXIX Minimum Dimensions of White Cedae Poles in Inches A B C i D E F G Length 1 6 feet 6 feet 6 feet 6 feet of Top j from 1 Top from Top from Top from Top Top Top poles j butt butt butt butt (Feet) 1 1 20 22 25 30 35 40 45 50 55 60 Circumference, Inches 231 33 2U 30 18f 28^ 18i 26 17 151 23^ 34 2U 31 18f 29^ 18i 27 17 15i 23^ 36 2U 33 18i 31| 18i 28^ 17 15^ 23 § 40 21i 36 ISf 34^ 18i 3U 17 151 23^ 43 2U 40 ISf 37i 18i 3^ 17 15^ 23i 47 2U 43 ISf 40 181 37i 17 151 23^ 50 2U 46 18-J 43 18i 40 23i 53 2U 49 18f 46 18i 43 23 i 56 21i 52 23i 59 2U 54 12* No dark red or copper-colored poles, which when scraped do not show good live timber, shall be accepted under these specifications. No poles having more than one complete twist for every twenty (20) feet in length, no cracked poles and no poles containing large season checks shall be accepted under these specifications. No poles having " cat faces," unless they are small and perfectly sound and the poles have an increased diameter at the " cat face," and no poles having " cat faces " near the six (6) foot mark or within ten (10) feet of their tops, shall be accepted under these specifications. No shaved poles shall be accepted under these specifications. No poles containing sap rot, evidence of internal rot as disclosed by a careful examination of all black knots, hollow knots, woodpeckers' holes, or plugged holes; and no poles showing evidences of having been eaten by ants, worms or grubs shall be accepted under these specifications except that poles containing worm or grub marks below the six (6) foot mark will be accepted. No poles having a short crook or bend, a crook or bend in two planes or a reversed curve shall be accepted under these specifications. The amount of sweep, measured between the (6) foot mark and the top of the pole, that may be present in poles accept- able under these specifications, is shown in the following tables : 35-foot poles shall not have a sweep of over lOf inches. 40-foot poles shall not have a sweep of over 12 inches. 45-foot poles shall not have a sweep of over 9 inches. 50-foot poles shall not have a sweep of over 10 inches. 55-foot poles shall not have a sweep of over 11 inches. 60-foot poles shall not have a sweep of over 12 inches. THE MEASUREMENT OF PIECE PRODUCTS 469 Poles having tops of the required dimensions must have sound tops. Poles having tops one (1) inch or more above the requirements in circumference may have one (1) pipe rot not more than one-half (^) inch in diameter. Poles with double tops or double hearts shall be free from rot where the two parts or hearts join. No poles containing ring rot (rot in the form of a complete or partial ring) shall be accepted under these specifications. Poles having hollow hearts may be accepted under the conditions shown in the following table : Average diameter Add TO Butt Requirements or rot of 25 and 30-foot of 35-, 40- and 45- of 50-, 55-, 60- and poles foot poles 65-foot poles 2 mches Nothing Nothing Nothing 3 inches 1 inch Nothing Nothing 4 inches 2 inches Nothing Nothing 5 inches 3 inches 1 inch Nothing 6 inches 4 inches 2 inches 1 inch 7 inches Reject 4 inches 2 inches 8 inches Reject 6 inches 3 inches 9 inches Reject Reject 4 inches 10 inches Reject Reject 5 inches 11 inches Reject Reject 7 inches 12 inches Reject Reject 9 inches 13 inches Reject Reject Reject Scattered rot, unless it is near the outside of the pole, may be estimated as being the same as heart rot of equal area. Poles with cup shakes (checks in the form of rings) which also have heart or star checks may be considered as equal to poles having hollow hearts of the average diameter of the cup shakes. Western Red Cedar forms the main source of supply of poles in the West. The specifications for these poles permit a much smaller taper than for Eastern timber since the tree form is more cylindrical. The specifications (American Telephone and Telegraph Company) are given in Table LXX, p. 470. For Southern Yellow Pine poles for creosoting, the required dimensions are given in Table LXXI, p. 471. Chestnut has been a standard pole timber but is rapidly disappearing in Eastern states because of the ravages of the chestnut blight. The specifications differ only slightly from those for white cedar, and are as follows: Dimensions. Length. Poles shall not be over six (6) inc;hes shorter or twenty- four (24) inches longer than the length specified in the order. Circumference. Poles shall be classified with respect to their circumferences at six (6) feet above the butt and at their top in accordance with Table LXXII, p. 472. This table gives the minimum allowable circumference at six (6) feet above the butt and at the top for poles of each class and length listed and shall not preclude the acceptance of poles having greater circumferences at those points of measure- ment than those given in the table. 470 APPENDIX B TABLE LXX (MiNiMnM Dimensions op Western Red Cedar Poles in Inches) CLASSES A B C D E F (Minimum (Minimum (Minimum (Minirrium Length of poles (Feet) top circum- ference 28). Circumfer- top circum- ference 25). Circumfer- top circum- ference 22). Circumfer- top circum- ference 18i). Circumfer- (Minimum top circum- ference 15) (Minimum top circum- ference 12) ence 6 feet ence 6 feet ence 6 feet ence 6 feet from butt from butt from butt from butt Inches 20 30 28 26 24 No butt No butt 22 32 30 27 25 require- require- 25 34 31 28 26 ment ment 30 37 34 30 28 35 40 36 32 30 40 43 38 34 32 45 45 40 36 34 50 47 42 38 36 55 49 44 40 38 60 52 46 41 39 65 54 48 43 (Chestnut poles, continued) Shape. No poles shall contain short crooks. With respect to other deviations from straightness, poles required in the order to be of the " town " class, shall be free from all deviations from straightness except sweep in one plane only. The amount of sweep between the top and the butt of these poles shall not be greater than that specified for their length in the Table LXXIII, p. 472. Poles required by the order to be of " country " class may have sweep in two planes or sweep in two directions in one plane provided that a straight line con- necting the center of the butt with the center of the top does not, at any intermediate point, pass through the external surfaces of the pole. Where sweep is in one plane and one direction only, the amount between the top and the butt shall not be greater than that specified for the length of the pole in Table LXXIV, p. 473. 366. Piling. All piles are peeled before measuring. Piling should show close grain or slow growth, and be straight, with a minimum taper. If a straight line drawn between the centers of the butt and top falls outside the peeled pile at any point the piece is usually rejected. Hence long piling brings a proportionally higher price. Specifications for piling prescribe minimum and maximum diameters for the butt, and a minimum top diameter. Examples of such specifications are shown in Table LXXV, p. 473. Piling is sold by the linear foot, but the price per foot increases with length of stick. In Southern pine, piling is frequently measured by log scale, by taking the diameter at the middle of the log. THE MEASUREMENT OF PIECE PRODUCTS 471 TABLE LXXI Minimum Dimensions of Southern Yellow Pine Poles in Inches- Classes A B C D E Length of 6 feet 6 feet 6 feet 6 feet 6 feet poles Top from Top from Top from Top from Top from (Feet) butt butt butt butt butt Circumference, Inches 20 22 291 20 27 18 26 16 24 14 21 22 22 30i 20 28 18 27 16 25 14 22 25 22 32 i 20 29 § 18 28^ 16 26 14 23 30 22 35 20 32 18 30i 16 28^ 14 241 35 22 38 20 34 18 32i 16 30 14 26 40 22 40 20 36 18 34| 16 32 14 27i 45 24 421 22 38 20 36 18 33 f 50 24 44i 22 40 20 38 18 35 55 24 47 22 42i 20 40 60 24 49 22 44 i 20 42 65 24 51 22 47 70 24 53 22 49 75 24 55 22 51 80 24 57 85 24 59 90 24 61 Defects. Defects in piling are rot, loose or rotten knots, wind shake, twisted grain, checks or other defects which interfere with driving or durability. 367. Posts, Large Posts and Small Poles. Standard fence posts are cut, 7, 7^ or 8 feet long. Dimensions up to 10 feet are termed large posts, while lengths of 12 to 18 feet inclusive are small poles; the distinction being based partly on the uses to which they are put. Standard cedar posts may be 2 inches short, and j inch scant in diameter when seasoned, but rtiust be full if green or water-soaked. Posts are graded by inch classes measured at top or small end. They will permit knots and other defects which will not weaken the piece for the purpose of a post. Cedar may contain a certain amount of center or pipe rot. White cedar posts may have a sweep of 4 inches. Western juniper and red cedar posts may have much greater sweep, provided it lies in one plane or " crooks one way." Post material in round bolts whose diameter exceeds 6 to 7 inches, when not needed for corner or gate posts, is usually split into two or more fence posts whose cross-sectional area will equal or exceed that of round posts of the standard dimen- sions. Posts must be cut from live timber and, in white cedar, rot or other defects are permitted which do not impair the strength of the post for uses of a fence post. 472 APPENDIX B TABLE LXXII Minimum Circumferenc-cs of Chestnut Poles in Inches Classes A B C D E F G Length (Feet) 6 feet 6 feet 6 feet 6 feet 6 feet 6 feet Top from butt Top from butt Top from butt Top from butt Top from butt Top from Top butt 1 Inches 20 24 34 22 31 20 29 18 27 16 24 15 1 22 ! 15 25 24 37 22 34 20 32 18 29 16 27 15 24 '■ 15 30 24 40 22 37 20 35 18 32 16 29 15 27 1 15 35 24 43 22 40 20 37 18 35 16 32 15 29 15 40 24 46 22 43 20 40 18 37 16 35 15 32 15 45 24 49 22 46 20 43 18 40 16 37 50 24 52 22 49 20 46 18 43 55 24 55 22 52 20 49 60 24 58 22 55 65 26 60 22 58 70 26 62 22 60 75 26 64 22 62 80 26 66 22 64 85 26 68 22 66 90 26 70 22 68 TABLE LXXIII Maximum Sweep, Poles, Standard Length Maximum Length Maximum Length Maximum of pole. sweep. of pole. sweep. of pole. sweep. Feet Inches Feet Inches Feet Inches 20 4 45 9 70 14 25 5 50 10 75 15 30 6 55 11 80 16 35 7 60 12 85 17 40 8 65 13 90 18 Small cedar poles up to and including 18 feet in length may have a sweep of 4 inches, which for lengths of 16 to 18 feet is measured from a point 4 feet from the butt, in the manner jjrescribed for long poles. Fire-killed lodgepole pine is accepted for jjoles and posts in the Rocky Mountains. THE MEASUREMENT OF PIECE PRODUCTS 473 TABLE LXXIV Maximum Sweep, Poles, Country Length Maximum Length Maximum Length Maximum of pole. sweep . of pole. sweep . of pole. sweep. Feet Inches Feet Inches Feet Inches 20 6 45 13i 70 21 25 n 50 15 75 22i 30 9 55 16i 80 24 35 10^ 60 18 85 25i 40 12 65 19i 90 27 TABLE LXXV Dimensions for Piling Species, region or purchaser Length. Feet Minimum top diameter — Inches Not less than Diameter limits, butt- Inches Hardwoods — Eastern 20-35 40-50 Under 30 30-50 Under 60 Over 60 Under 30 30-^0 40-69 70 and over 6 6 6 6 9 9 9 9 8 8 12 and over 14 and over 12 to 16 California 12 to 18 13 to 17 Southern Pacific R.R A., T. &S. F. R.R 13 to 20 13 to 18 14 to 18 14 to 18 16 to 18 All classes of poles and posts are usually seasoned to decrease weight for trans- portation. Fence stays are round or split pieces about 2 inches in diameter and 5 to 6 feet long. They are used between posts for wire fences as upright pieces not set in the ground, to which the wires are stapled to prevent their being spread apart by stock, and to reduce the number of posts required. Converter poles, called also furnace poles and brands, are consumed in the process of refinmg copper. The Montana specifications call for poles with a top diameter of 3 to 4 inches and length of 24 feet. They should have as little taper as possible. Eastern brass mills use poles 25 to 40 feet long, 2 inches and over at top, and 5 inches and over at butt. The bark is not removed and poles must be green. Standard California hop poles are made from split pieces 2 by 2 inches by 8 feet. In the East hop poles are usually made from round pieces of approximately the same dimensions. 368. Mine Timbers. Mine timber can be classed as stuUs and props, lagging, shaft timbers and lumber, and mine ties. StuUs include round props used as posts, caps to connect pairs of opposite posts, and girts to connect posts lengthwise of the 474 APPENDIX B gallery. Their dimensions depend on size of galleries. Diameters vary from 5| to 24 inches. Square props are used for similar purposes. Small round props used principally in coal mines are termed mine props and run from 4 inches up in diam- eter and from 4 to 10 feet in length. These timbers are used to support the ground and must be straight, sound and free from knots that will impair the strength of the piece, or from defects affecting strength or durability. Mine timber is bought by the linear foot, by classes based on top diameter. Split props must have a cross-sectional area in square inches equal to that of a round post of minimum specified diameter. Pole lagging varies from I5 to 5 inches in diameter at small end and averages 16 feet in length. Four- to five-inch poles may be split. Lodgepole pine is the principal species used. Lagging is bought by the piece. Mine Ties. Cross ties for mine tramways are usually 5 to 5^ feet long but may be from 3 feet to 6 feet in length, and vary for individual mines, from 3 by 4 inches to 5 by 6 inches in diameter. Their small size makes a market for very small timber, which can be grown in 20 to 30 years. Ties are bought by count, and on basis of specifications. Round mine timber of these classes and mine ties not only utilize the entire stick, but permit the almost complete utilization of the felled tree and of the stand. In fact, the tendency is to exploit young second-growth stands while still too small to bear seed, and under private management forests in mining regions are rapidly destroyed. The same conditions permit of thinnings in dense stands, the removal of small diseased trees and a short rotation, and under forest management offer very favorable conditions for profitable production of timber. 369. Cross Ties. Standard railroad cross ties are either hewn, with two parallel faces, or sawed to specified dimensions. Switch ties are sawed in sets of graduated lengths. Hewn ties, termed also pole ties, are made from round bolts hewn on two sides to produce parallel faces. Bolts 14 inches and over in diameter are usually split into two or more ties, hewn on four sides. Hewn ties are preferred to sawed ties as they are said to be more durable. The standard specifications for cross ties of the U. S. Railroad Administration have since March, 1920, been adopted with slight changes by over two-thirds of the railroad mileage of the country. These specifications are shown graphically in Fig. 88. The specifications of the Pennsylvania Railroad System, based on the above, are as follows: All ties shall be free from any defects that may imi)air their strength or durability as cross ties, such as decay,' splits, shakes, large or numerous holes - or knots, ^ or oblique fiber with slope greater than one in fifteen. Ties from needle-leaved trees shall be of compact wood with not less than one- 1 Ties must be rejected when decayed in the slightest degree, except that the following may be allowed: in cedar, " pipe or stump rot " up to I5 inches diameter and 15 inches deep; in cypress, " peck " up to the limitations as to holes; and, in pine, " blue sap stain." 2 A large hole in woods other than cedar is one more than \ inch in diameter and 3 inches deep within, or one more than 1 inch in diameter and 3 inches deep outside the sections of the tie between 20 and 40 inches from its middle. Numerous holes are any number equaling a large hole in damaging effect. ' A large knot is one exceeding in width more than \ of the width of the surface on which it appears; but such a knot may be allowed if it occurs outside the sections of the tie between 20 and 40 inches from its middle. Numerous knots are any number equaling a large knot in damaging effect. , i THE MEASUREMENT OF PIECE PRODUCTS 475 third summerwood when averaging five or more rings of annual growth per inch, or with not less than one-half summerwood in fewer rings, measured along any radius from the pith to the top of the tie. Ties of coarse wood, with fewer rings or less summerwood, will be accepted when specially ordered. ^i -S- ^^Xo>i 1 1 D 1 ^J ^Tl L,^ ^i ^.i\ L^ 1 kiy lo I 11 a t o .1 . < k-i Ties for use without preservative treatment shall not have sapwood wider than one-fourth the width of the top of the tie between 20 and 40 inches from the middle, and will be designated as " heart " ties. Those with more sapwood will be desig- nated as " sap " ties. Manufacture. Ties should be made from trees which have been felled not longer than one month. 476 APPENDIX B All ties shall be straight, well manufactured, ^ cut square at the ends, have bottom and top parallel, and have bark entirely removed. Dimensions. Before manufacturing ties, producers should ascertain which of the following grades will be accepted. All ties shall be eight (8) feet six (6) inches long. All ties shall measure as follows throughout both sections between 20 and 40 inches from the middle of the tie. Grade Sawed or hewn top, bottom and sides Sawed or hewn top and bottom 1 2 3 4 5 None accepted 6" thick X7" wide on top 6" thick X_8" wide on top 7" thick X8" wide on top 7" thick X9" wide on top 6" thick X6" wide on top 6" thick X7" wide on top 7" thick X6" wide on top 7" thick X7" wide on top 6" thick X8" wide on top 7" thick X8" wide on top 7" thick X9" wide on top The above are minimum dimensions. Ties over one (1) inch more in thickness, over three (3) inches more in width, or over two (2) inches more in length will be degraded or rejected. The top of the tie is the plane farthest from the pith of the tree, whether or not the pith is present in the tie. Class U — Ties which May Be Used Untreated Group Va Group Vb Group Vc Group Vd "Heart" Black Locust "Heart" White Oaks "Heart" Black Walnut "Heart" Douglas Fir " Heart" Pines " Heart" Cedars " Heart" Cypress "Heart" Redwood " Heart" Catalpa "Heart" Chestnut "Heart" Red Mulberry "Heart" Sassafras Class T — Ties which Should Be Treated Group Ta Group T6 Group Tc Group Td Ashes "Sap" Cedars Beech "Sap" Catalpa Hickories "Sap" Cypress Birches "Sap" Chestnut "Sap" Black Locust "Sap" Douglas Fir Cherries Elms Honey Locust Hemlock Gums Hackberry Red Oaks Larches Hard Maples Soft Maples "Sap" White Oaks "Sap" Pines "Sap" Mulberries "Sap" Black Walnut "Sap" Redwood "Sap" Sassafras Spruces Sycamore White Walnut 1 A tie is not well manufactured when its surfaces are cut into with score-marks more than § inch deep or when its surfaces are not even. . THE MEASUREMENT OF PIECE PRODUCTS 477 370. Inspection and Measurement of Piece Products. Piece products, while graded on basis of dimensions, may be rejected either because of scant length, thick- ness or width, below requirements for lowest grade, or because of disqualifying defects. As these products are usually hauled to track or landing before being graded, considerable losses are occasioned by failure to conform to these specifi- cations. Although the character and amount of defect disqualifying a piece is usually pre- scribed as exactly as possible in the specifications, yet there is always considerable latitude exercised by the inspector, and the closeness or laxity of inspection may vary under instructions according to the demand for the product. This method of regulating supply supplements price adjustments and is open to serious objec- tions. Good inspectors are thoroughly familiar with the qualities required of product and display a certain leniency in judging pieces which almost conform to specifications, provided the general run of the product is of good quality and work- manship. An inspector must command respect for his integrity and reputation for giving both parties a square deal. The contents of various classes of piece products may be desired in terms of either cubic feet or board feet, in order to reduce different kinds of products to terms of a common standard or to simplify terms of payment or of record. Since most of these products are exposed to decay, and their value is measured by their resistance to fungus attacks, wood preservation is becoming more prevalent. Creosoting plants base their charges upon the cubic contents of such pieces as are treated as a whole. The volume in cubic feet of poles of different dimensions is obtained by the for- mula; given in § 27 by applying the values for cubic volumes of cylinders shown in Table LXXVII, Appendix C. The middle diameter measurement is the most accurate method for long poles, owing to the errors resulting from large butts. For short poles, piling or mining stulls, the middle diameter measurement is probably the most satisfactory, and the table of cylindrical contents, or Humphrey caliper cordwood rule will suffice as a standard. Prices for mining stulls of different lengths and diameters sold by the U. S. Forest Service in Montana, are based upon the cubic contents of pieces of each standard size. Smaller material such as fence posts or other round pieces may be converted to cubic feet by the same means. Cross ties, on account of uniformity of size, are converted into their equivalent in board feet, and expressed either by average contents per tie, or by the number of ties per 1000 feet B. M. The average contents of hewn ties may be obtained by scaling a large number as logs 8 feet long. Or their cubic contents may be cal- culated from the thickness and face and reduced to board feet. The first method deducts for sawdust, and the second for squaring the tie. By either method a 6- by 8- inch tie scales about 32 board feet, or 30 ties per 1000 feet B.M. Ties 8^ feet long, 7 inches thick by 9- inch face may average 40 to 44 board feet, or 25 to 23 per 1000 board feet. Ratios are easily worked out on the basis of specifications and actual scale, and, once determined, may be substituted for measurement and applied to the count of ties, separately for each size class or grade of tie. To reduce piling to board feet, pieces are sometimes scaled directly by a log rule. For small poles, posts or mining timbers the best method of conversion is to apply a converting factor to the cubic contents of pieces of given dimensions. Where total or actual cubic contents is measured, the best ratio is probably 5.5 board feet per cubic foot. If cubic contents includes only the cylinder measured at small end, a larger ratio is required. 478 APPENDIX B The following table gives converting factors adopted by the U. S. Forest Service for products of various classes and dimensions : TABLE LXXVI Converting Factors, Piece Products to Board Feet Product Long cord (acid wood, pulpwood, and dis- tillation wood) Cord (spruce pulp- wood) Cord (shingle bolts) . . . Cord (fuel material averaging 5 inches or less in middle diame- ter) Cord (fuel material averaging 6 inches or more in middle diam- eter) Load (in the rough)*. . Pole (telephone) Pole (telephone) Pile ' StuU Tie (standard) Tie (2d class) Tie (narrow gauge) . . . Tie (narrow gauge) . . . Tie (narrow gauge) . . . Tie Tie Derrick pole Derrick set (II pieces) Assumed dimensions 4' X5' X8' 4' X4' X8' 4' X4' X8' 4' X4' X8' 4' X4' X8' 4' X4' X8' 1 cord 7"X30' 9"X30' 7"X30' 10"X16' 6"X8"X8' 6"X7"X8' 6"X7"X6' 7"X8"X6r 6"X7"X6J' 7"X8"X8' 7"X9"X8' 7"X30' Equiv- alent in board feet 625 560 600 333 J 333J 60 100 60 60 30 20 15 25 15 30 35 60 480 Product Trestle timber Trestle timber House log House log House log Mining timber Prop Converter pole Pole (fence) Pole (fence) Lagging (6 pieces) . . . Cubic foot (round) . . . Rail (split) Piece Stick Slab Post Post (circumference, 18 inches) Post Linear foot Brace Stay (fence) Stay Shake (roof) Shake (fruit tray) .... Picket Stake (fence) Assumed dimensions 10"X20' 7"X12' 8"X16' X16' XIO' XIO' XIO' X20' 7'' 7" 6'' 6'' 4" 16' 4"X20' 3"X6' i pole 6"X7' 6"X7' 2"X6"X16' 6"X7' 5.7"xr 5" XT 10" XI' 4"X6' 2"X6' 4"X6' 'X6"X2' 'X5"X32" 'X5' 'X5' Equiv- alent in board feet 70 20 30 30 15 10 10 10 8 10 10 6 5 7 7 2 7 6 5 3 2 * This refers to small irregular pieces of wood and not to material that can be ricked for measurement. APPENDIX C TABLES USED IN FOREST MENSURATION TABLE LXXVII Cubic Contents of Cylinders and Multiple Table of Basal Area This table serves a double purpose. It shows, in the first place, the contents of cylinders of different diameters and lengths. It may be used to determine the contents of logs whose diameters are measured at the middle. The table shows also the sums of the basal areas of different numbers of trees. Thus the total basal area of fifty-one trees 9 inches in diameter is 22.53 square feet. This table will be found very useful in computing the total basal area of different diameter classes in forest surveys. The values given in this table are practically identical with those of the Humphrey Caliper Cordwood Rule (§ 121) for which it may be substituted. By multiplying the values in the table by 1.28 the contents of logs will be found in terms of stacked cubic feet of cord- wood, p. 480. TABLE LXXX The International Log Rule for Saws Cutting a j inch Kerf This log rule is derived from the values of the International log rule for saws cutting a |-inch kerf, by applying the factor .904762 to the values in the former rule, computing to the third decimal place, and then rounding off the resultant values to the nearest 5 board feet. The values were computed and checked by Judson F. Clark in 1917, p. 493. TABLE LXXXIi Values in square feet for .16 and for .66 of the area of circles of dif- ferent diameters, for computing the cubic volume of trees by the Schiffel formula, F=(.16 B-\-Mb) h, p. 494. 1 Computed by the U. S. Forest Service. 479 480 APPENDIX C TABLE LXXVII Cubic Contents of Cylinders and Multiple Table op Basal Areas Diameter in In :hes. Length, Feet, or '4 3 4 5 ! 6 7 8 Number 1 of Trees. Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet. I 0.02 0.05 0.09 0.14 0. 20 0.27 0.35 2 0.04 0. 10 0.17 0.27 0.39 0.53 0. 70 3 0.07 0.15 0.26 0,41 0.59 0.80 I 05 4 0.09 0.20 0.35 0.55 0.79 1.07 I .40 5 0. II 0.25 0.44 0.68 98 1-34 1-75 6 0. I,^ 0. 29 0.52 0.82 I. 18 1 .60 2.09 7 0.15 0-34 0.61 0.95 1-37 . 1.87 2.44 8 0. 17 0-39 0. 70 •I .09 1-57 2.14 2,79 9 0. 20 0.44 0.79 1.23 1-77 2.41 314 ID 0. 22 0.49 0.87 1.36 I .96 2.67 3-49 II 0.24 0.54 0.96 1.50 2.16 2.94 3.84 12 0. 26 0.59 1.05 1.64 2.36 3-21 4.19 13 0.28 0.64 I-I3 1.77 2-55 3-47 4-54 14 0.31 0.69 1 .22 I. 91 2-75 3-74 4.89 15 0.33 074 1.31 2.05 2-95 4.01 5 24 i6 . 35 0.79 1 .40 2.18 3-14 4.28 5-59 17 0.37 0.83 1.48 2 32 3 • 34 4-54 5.93 18 0.39 0.88 1-57 2.45 3-53 4.81 6.28 19 0.41 0.93 1.66 2.59 3-73 5.08 6.63 20 0.44 0.98 1-75 2-73 3-93 5-35 6.98 21 0.46 I 03 1.83 2.86 4.12 5-6i 7-33 22 0.4S 1 .08 1.92 3.00 4 32 5.88 7.68 23 0.50 113 2 .01 314 4-52 6.15 8.03 24 0.52 1. 18 2.09 3-27 471 6.4 8.38 25 0.55 1-23 2.18 3-41 4.91 6.68 8.73 26 0.57 1.28 2.27 3-55 5 II 6.95 9.08 27 0.59 I • 33 2.36 3.68 5 • 30 7.22 9.42 28 0.61 1-37 2.44 3.82 5 50 7.48 9-77 29 . 63 1.42 2.53 3-95 5.69 7-75 10. 12 30 0.65 1-47 2.62 4.09 5-89 8.02 10.47 31 ■ 0.68 1.52 2.71 4-23 6.09 8. 28 10.82 32 0. 70 1-57 2.79 4 36 6.28 8.55 II. 17 33 0.72 1.62 2.88 4 50 6.48 8.82 11-52 34 0.74 1.67 2.97 4.64 6.68 0.09 II .87 35 0. 76 I .72 3 05 4 77 6.87 9-35 12 . 22 36 0.79 I -77 3- 14 491 7.07 9.62 • 2 57 37 0.81 I .82 3-23 5.05 7 . 26 9. 89 12.92 TABLES USED IN FOREST MENSURATION 481 TABLE LXXYU—Continued Diameter in Inches. Length, Feet, or 3 3 4 5 6 7 8 Number of Trees. Contents of Cylir ders in Cubic Feet, or Basal Areas in Square Fe.t. 38 0.83 1.87 3-32 5.18 7.46 10. 16 13.26 39 0.85 I. 91 3 40 5-32 7.66 10.42 13.61 40 0.87 1 .96 3-49 5-45 7.85 10.69 1 3 - 96 41 0.89 2.01 3.58 5 • 59 8.05 10.96 14-31 42 0.92 2.06 3.67 5-73 8.25 11.22 14.66 43 0.94 2.11 3-75 5.86 8.44 II .49 15.01 44 0.96 2.16 3-84 6.00 8.64 11.76 15-36 45 0.98 2.21 3 • 93 6.14 8.84 12.03 15-71 46 I .00 2.26 4.01 6.27 903 12.29 16.06 47 1.03 231 4. 10 6.41 9-23 12.56 16.41 48 1.05 2.36 4.19 6.54 9.42 12.83 16.76 49 1.07 2-4I 4.28 6 . 68 9.62 13.10 17 . 10 50 1.09 2-45 4.36 6.82 9.82 13.36 17.45 51 I . 1 1 2.50 4-45 6.95 10.01 13.63 17.80 52 113 2.55 4-5 + 7.09 10.21 13.90 18.15 53 I. 16 2.60 4.63 7-23 10.41 14.16 /8.50 54 I. 18 2.65 . 4-71 7.36 10.60 14.43 18.85 55 I . 20 2.70 4.80 7 -50 10.80 14.70 19. 20 56 I .22 ■ 2-75 4.89 7.64 1 1 .00 14.97 19.55 57 1.24 2.80 4-97 7-77 1 1 . 19 15.23 19.90 58 1.27 2.85 5.06 7-91 1 1 • 39 15.50 20.25 59 1.29 2.90 515 8.04 11.58 15-77 20.60 60 1 31 2-95 5 24 8. 18 II .78 16.04 20.94 61 1-33 2.99 5 • 32 8.32 11.98 16. :(0 21 .29 62 1-35 304 541 8.45 12.17 16.57 2i .64 63 1-37 3 09 5 50 8.59 12.37 16.84 21 .99 64 1.40 3-14 5-59 8.73 12.57 17.10 2 . M 65 1.42 3- 19 5 67 8.86 12.76 17-37 2 .69 66 1.44 3-24 576 9.00 12 .96 17.64 23.04 67 1.46 3 29 5.85 914 13.16 17.91 2 3 -,^9 68 1.48 3 • 34 5 93 9.27 13.35 18.17 23-74 69 1-51 3 • 39 6.02 9.41 13.55 18.44 24.09 70 I 53 3-44 6. II 9-54 13.74 18.71 24-43 71 I 55 3-49 6. 20 9 . 68 13-94 18.97 24.78 72 1-57 3-54 6.28 9.82 14. 14 19.24 25-13 73 1-59 3-58 6.37 9-95 14.33 19.51 25-48 74 1. 61 3.63 6.46 10.09 14.53 19.78 25 ■ 83 75 1.64 3.68 6.54 10. 23 14.73 20.04 26.18 482 APPENDIX C TABLE LXXYU— Continued Diameter in Inches. Length. Feet, or 9 10 11 12 13 14 15 Number of Trees. Conte nts of Cylinders in Cubic Feet, or Basal Areas in Square Feet. I 0.44 0-55 0.66 0.79 0.92 1.07 1-23 2 0.88 1 .09 1-32 1-57 1.84 2.14 2-45 3 1-33 , I .64 1.98 2.36 2.77 3-21 3-68 4 1-77 2.18 2.64 3-14 3-69 4.28 4.91 5 2.21 2.73 3-30 3-93 4.61 5-35 6. 14 6 2.65 3-27 3-96 4-71 5-53 6.41 7.36 7 3 09 3-82 4.62 5-50 6-45 7-48 8-59 8 3-53 4-36 5.28 6.28 7-37 8-55 9.82 9 3 98 4.91 5-94 7.07 8.30 9.62 11 .04 lO 4.42 5-45 6.60 7-85 9.22 10.69 12.27 II 4.86 6.00 7.26 8.64 10. 14 11 . 76 13-50 12 5.30 6.55 7.92 9-42 1 1 .06 1 2 . 83 14-73 13 5-74 7.09 8.58 10.21 11.98 13.90 15-95 14 6. 19 7.64 9-24 1 1 .00 12.90 14-97 17.18 15 6.63 8.18 9.90 11.78 13-83 16.04 18.41 i6 7.07 8-73 10.56 12.57 14-75 17 . 10 19.63 17 751 9.27 II .22 13-35 15-67 18. 17 20.86 i8 7-95 9.82 11.88 14.14 16.59 19.24 22 .09 19 8.39 10.36 12.54 14.92 1751 20.31 23-32 20 8.84 10.91 13.20 15-71 18.44 21.38 24-54 21 9.28 11-45 13-86 16.49 19-36 22.45 25-77 22 972 12 .00 14-52 17.28 20.28 23-52 27.00 23 10. 16 12.54 15.18 18.06 21 .20 24-59 28.23 24 10.60 13-09 15-84 18.85 22. 12 25 - 66 29-45 25 II .04 13-64 16.50 19.64 23.04 26.73 30.68 26 11.49 14.18 17 . 16 20.42 23-97 27.79 31-91 27 11-93 14-73 17-82 21.21 24-89 28.86 33-13 28 12.37 15-27 18.48 21.99 25.81 29-93 34-36 29 12.81 15.82 19. 14 22.78 26.73 31.00 35-59 30 1325 16.36 19.80 23-56 27.65 32-07 36.82 31 13- 70 16.91 20.46 24-35 28.57 33-14 38.04 32 14.14 17-45 21.12 25-13 29.50 34-21 39-27 33 14-58 18.00 21.78 25.92 30.42 35 - 28 40.50 34 15.02 18.54 22.44 26.70 31-34 36 - 35 41.72 35 15-46 19.09 23.10 27-49 32.26 37-42 42.95 36 15 90 19.64 23.76 28.27 33-18 38 . 48 44-18 37 16.35 20.18 24.42 29.06 34-10 39-55 45 41 TABLES USED IN FOREST MENSURATION 483 TABLE LXXYII— Continued Diameter in Inches. Length, Feet, or 9 10 11 13 13 14 15 Number of Trees. Contents of Cylinders in Cubic 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 1944 24.00 29.04 34 - 56 40.56 47.04 54.00 45 19.88 24-54 29.70 35 - 34 41.48 48.11 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 47.01 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 30 . 48 37.63 45-54 .S4 ■ rg 63.60 7376 84.68 70 30.93 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 58.12 68.2 1 79- II 90.81 75 33-13 40.91 49 50 58.91 69 - 1 3 80. 18 92.04 484 APPENDIX C TABLE LXXYIl^Continued Diameter in Inches. Length, Feet, or 16 17 18 19 20 21 22 Number of Trees. Contents of CyHnders in Cubic Feet, or Basal Areas in Square Feet. I 1.40 I . 5S 1.77 I -97 2.18 2.41 2.64 2 2.79 3.15 3 . 53 3.94 4., 36 4.81 5.28 3 4.19 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 12.03 1 3 . 20 6 8 . 3-'^ 9.46 1 . 60 1 1. 81 1 3 • 09 14.43 15.84 7 9-77 1 1 . 03 1 2 . 37 13-78 15.27 16.84 18.48 8 II. 17 12.61 14.14 1575 17.45 19.24 21.12 9 12.57 14.19 1 5 . 90 17.72 19-63 2 1 . 65 23.76 lO 13-96 15.76 17.67 19.69 21 .82 2405 26.40 II 15-36 1 7 . 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 19-55 22.07 2474 27.57 30.54 33 . 67 36 . 96 15 20 . 94 23.64 26.51 29-53 32.72 36.08 39 ■ 60 i6 22.34 25-22 28.27 31.50 ,34.91 38.48 42.24 17 23.74 26.80 30 . 04 ^V47 37 09 40.89 44.88 i8 25-13 28.37 SI . 81 .^ =i ■ 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 50.51 55-44 22 30.72 34.68 38 . 88 4332 48.00 52.92 58.08 23 32.11 36.25 io.64 45 29 50.18 55 . 32 60.72 24 33-51 37 -'^^ 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 .^9- 10 44.14 49.48 55.13 61 .09 67.35 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 6 1 . 04 67.63 74 ■ 56 81.83 32 44.68 50 -44 56 . 55 6s. 01 69.81 76.97 84.47 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 . 1 8 92.39 36 50.27 56.75 63.62 70.88 78.54 86 . 59 95-03 37 51.66 58 . 32 65 - 38 72.85 •80.72 89.00 97-67 TABLES USED IN FOREST MENSURATION TABLE LXXYII— Continued 485 " Diameter in Inches. Length, Feet, or 16 17 18 19 20 31 33 Number of Trees. Contents of Cylinders in Cu Ac 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 80.73 89 -45 98.62 108.23 42 58 . 64 66. 20 74.22 82. 70 91-63 101 .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 86.61 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 I 00 . 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 94-51 104.72 115.45 126.71 49 68.42 77-24 86.59 96.48 I 06 . 90 117.86 129.35 50 69.81 78.81 88.36 98.45 109.08 120.26 131.90 51 71.21 80 . 39 90. 12 100.42 III .26 122.67 134.63 52 72.61 81.97 91.89 102.39 "3-45 125.07 137.27 53 74.00 83-54 93.66 104-35 "563 127.48 139.91 54 7540 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 no. 26 122.17 1 34 - 70 14/. 83 57 79 • 59 89.85 100.73 112.23 124-35 137- 10 150.47 58 80.98 91.42 102.49 114.20 126.54 1 39 - 5 1 153." 59 82.^8 93.00 104. 26 116.17 128.72 141 -91 155.75 60 83.78 94.58 1 06 . 03 118.14 1 30 . 90 144.32 158.39 61 85.17 96 . 1 5 107 .80 120. II 133 08 146.72 161.03 62 86.57 97.73 109.56 122.07 135-26 149.13 163.67 63 87.96 99 . ,30 1 1 1 ■ 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 1 1 4. .86 1 27. 98 141 -81 156.34 171.59 66 92.15 104.03 1 16.63 129-95 143-99 158.75 174.23 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 .93 135-86 150.53 165.96 182.15 70 97-74 110.34 123.70 137.83 152.72 168.37 184.79 71 99 - 1 3 I II .91 125.47 1 39 . 80 1 54 ■ 90 170.77 187-43 72 100.53 1 1 3 . 49 127.23 141.76 157.08 173.18 1 90 . 07 73 101.93 115.07 129.00 143.73 159.26 175.59 192.71 74 103.32 1 16 ,64 1,^0.77 145.70 161.44 177.99 195-35 75 104.72 I I 8.22 132.54 147.67 163.62 1 80 . 40 197-99 486 APPENDIX C TABLE LXXYII— Continued Diameter in Inches. Length, Feet, or Number 33 24 25 36 37 38 39 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 II .06 "-93 12.83 13-76 4 11-54 12.57 13-64 14-75 15-90 17. 10 18.35 5 14-43 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 25-97 28.27 30.68 33-18 35-78 38.48 41.28 lO 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 51-3' 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 i6 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 i8 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. 8i 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 III. 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 1 1 1 - 33 119-73 128.43 29 83-67 91 . II 98.86 106.92 "5-31 124.01 133-02 30 86.56 94.25 102.27 no. 61 119.28 128.28 137-61 31 89.44 97.39 105.67 114.30 123.26 132.56 142.20 32 92.33 100.53 109.08 117.98 127.23 136-83 146.78 33 95-21 103.67 112.49 121 .67 131-21 141 . 1 1 151-37 34 98. 10 106.81 115-90 125-36 135-19 145-39 155.96 35 100.98 109.96 119. 31 129.05 139.16 149.66 160.54 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. II 158.21 169.72 TABLES USED IN FOREST MENSURATION TABLE LXXYII— Continued 487 Diameter in Inches. Length, Feet, or Number 23 34 35 36 37 38 29 of Trees. Contents of Cyhnders in Cubic Feet, or Basal Areas in Square Feet. 38 109.64 119.38 129-54 1 40 . II 151.09 162.49 174-30 39 112.52 122.52 132.94 143-79 155-07 166.77 178.89 40 115.41 125.66 136.35 147.48 159-04 171-04 183-48 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 46 132.72 144-51 156.8- 169.60 182.90 196.70 2 I I . 00 47 135-61 147-65 1 60 . 2 2 173-29 186.88 200.97 215.59 48 138.49 I 50 . 80 163.62 176.98 190.85 205.25 220. 17 49 141.38 1 53 - 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 1 60 . 2 2 173-85 188.04 202.78 218.08 233-93 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 . 90 206.47 222.66 239-46 256.87 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 . I 2 217-53 234-59 252.29 270.63 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 1 96 . 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 73 210.62 229.34 248.85 269.15 290.25 312.15 334.85 74 213-51 232-48 252.25 272.84 294.23 316.42 339.43 75 216.39 235-62 255-66 276.53 298.21 320.70 344-02 488 APPENDIX C TABLE LXXYIl—Conlinued Diameter in Inches. Length, Feet, or 30 31 32 33 34 35 36 Number of Trees. Contents of Cylir ders in CuDic Fe^t, or Basal Areas in Square Feet. I 4.91 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 15-72 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 24-54 26.21 27-93 29.70 31-53 33-41 35-34 6 29-45 31-45 33-51 35 64 37-83 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 4752 50.44 53-45 56.55 9 44.18 47-17 50.27 53-46 56-75 60.13 63.62 lO 49.09 52.41 55-85 59-40 63-05 66.81 70.69 II 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 94-58 100.22 106.03 16 78.54 83.86 89 . 36 95 03 100.88 I 06 . 9c 113.10 17 83-45 89. 10 94-95 100.97 107 . ]8 113-58 120. 17 18 88 . 36 94-35 100.53 1 06 . 9 1 113-49 120.26 '27.23 19 93 27 99-59 106. 12 112.85 119.80 126.95 1 34 - 30 20 98.17 104.83 III .70 118.79 126. 10 133-63 141-37 21 1 03 . 08 1 10.07 117.29 124-73 132.41 140.31 148.44 22 107.99 115-31 122 .87 1 30 . 67 138.71 146.99 155-51 23 1 1 2 . 90 120.55 128.46 136.61 145.02 153-67 162.58 24 117.81 1 25 -79 134-04 142.55 151-32 160.35 169.65 25 122.72 1 3 1 . 04 139-63 .48.49 157 63 167.03 176.71 26 127.63 136.28 145-21 154.43 163-93 173-71 183.78 27 132.54 141-52 1 50 . 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 1 5 2 . 00 161 .97 172.25 182.85 193-76 104.99 30 147.26 157-24 167 -55 178. 19 189-15 200.44 2 1 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 2 r 3 . 80 226. 19 33 161 .99 172.97 184.31 196.01 208 . 06 2 20 . 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 36 176.71 188.69 201 .06 213.82 226.98 240.53 254.47 37 181 .62 193-93 206.65 219.76 233-28 247-21 261.54 TABLES USED IN FOREST MENSURATION 489 TABLE LXXVII— Continued Diameter in In :hes. Length , Feet, or 30 31 32 33 34 35 36 Number of Trees. Contents of Cylin ders in Cubic Feet, or Basal Areas in Square Feet. 38 186.53 1 99 . I 7 212.2^ 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 2S9.81 42 206 . I 7 220.14 234.57 249.46 264.81 2S0.62 296.88 43 2 I I . 08 225.38 240. 16 255-40 271 . I I 287.30 303-95 44 215. 9S 2 ^0.62 245-74 261.34 277-42 293-98 311.02 45 220.89 235.86 251-33 267.28 283.72 300 . 66 3 1 8 . 09 46 225. So 241. II 256.^^1 273.22 290.03 307 ■ 34 325-15 47 2 ",o . 7 1 246.35 262.50 279.16 296-33 314.02 332-22 48 -^35.62 251-59 268.08 285.10 302.64 320.70 339 . 29 49 2 p. 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 53 260. 16 277.80 296.01 3 I 4 . 80 334-16 354-11 374.63 54 265.07 283.04 301.59 320.74 340.47 360.79 381.70 55 269.98 288.28 307.18 326.68 ,m6.77 367-47 388.77 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 ^80.84 402.91 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 • 3 \- 324.97 346.27 368.28 390.91 414.22 438.28 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 65 319.07 340 . 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 71 348.52 372.14 396.54 421-74 447-66 474.35 501.90 72 353-43 377.38 402 . 12 427.68 453-96 481-03 508.97 73 358-34 ^82.62 470.71 433-62 460.27 487-61 516.04 74 363-25 387.87 413.29 439-56 466.57 494-39 523.11 75 368.16 393.11 418.88 445.47 472.87 501.10 530.14 490 APPENDIX C TABLE LXXVIII Areas of Circles or Table of Basal Areas for Diameters to Nearest TTf Inch •M J! 01 V V fa fa ^ fa ^ fa fa fa s« 4) In' , 0) trt a ■4-* Oi t 1- . 4-» Qj g iS ^ Oj £ II 0) ^1 .J 1—1 El Q .006 5 2.0 .022 S 3-0 < 5 it is found that the areas corresponding ot these diameters are 0.094 and 0.236, respectively. Their sum, 0.330, multiplied by the height, 62.5, equals the volume, 20.6 cubic feet. 0. 16 OF THE Area of A Circle at Breast H eight (0 .165) Diameter. 1 0.0 0.1 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Inches Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. 1 0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.003 0.003 0.003 2 .003 .004 .004 .005 .005 !005 .006 .006 .007 .007 3 .008 .008 .009 .010 .010 .011 .011 .012 .013 .013 4 .014 .015 .015 .016 .017 .018 .018 .019 .020 .021 5 .022 .023 .024 .025 .025 .026 .027 .028 .029 .030 6 .031 .032 .034 .035 .036 .037 .038 .039 .040 .042 7 .043 .044 .045 .047 .048 .049 .050 .052 .053 .054 8 .056 .057 .059 .060 .062 .063 .065 .066 .068 .069 9 .071 .072 .074 .075 .077 .079 .080 .082 .084 .086 10 .087 .089 .091 .093. .094 .096 .098 .100 .102 .104 11 .106 .108 .109 .111 .113 .115 .117 .119 .122 .124 12 .126 .128 .130 .132 .134 .136 .139 .141 .143 .145 13 .147 .150 .152 .154 .157 .159 .161 .164 .166 .169 14 .171 .173 .176 .178 .181 .183 .186 .189 .191 .194 15 .196 .199 .202 .204 .207 .210 .212 .215 .218 .221 16 .223 .226 .229 .232 .235 .238 .240 .243 .246 249 17 .252 .255 .258 .261 .264 .267 .270 .273 .276 .280 18 .283 .286 .289 .292 .295 .299 .302 .305 .308 .312 19 .315 .318 .322 .325 .328 .332 .335 .339 .342 .346 20 .349 .353 .356 .360 .363 .367 .370 .374 .378 .381 21 .385 .389 .392 .396 .400 .403 .407 .411 .415 .419 22 .422 .426 .430 .434 .438 .442 .446 .450 .454 .458 23 .462 .466 .470 .474 .478 .482 .486 .490 .494 .498 24 .503 .507 .511 .515 .520 .524 .528 .532 .537 .541 25 .545 .550 .554 .559 .563 .567 .572 .576 .581 .585 26 .590 .594 .599 .604 .608 .613 .617 .622 .627 .631 27 .636 .641 .646 .650 .655 .660 .665 .670 .674 .679 28 .684 .689 .694 .699 .704 .709 .714 .719 .724 .729 29 .734 .7.39 .744 .749 .754 .759 .765 .770 .775 .780 30 .785 .791 .796 .801 .806 .812 .817 .822 .828 .833 31 .839 .844 .849 .855 .860 .866 .871 .877 .882 .888 32 .894 .899 .905 .910 .916 .922 .927 .933 .939 .945 33 .950 .956 .962 .968 .974 .979 .985 .991 .997 1.003 34 1.009 1.015 1.021 1.027 1.033 1.039 1.045 1.051 1.057 1.063 35 1.069 1.075 1.081 1.087 1.094 1.100 1.106 1.112 1.118 1 1.125 TABLES USED IN FOREST MENSURATION TABLE LXXXl—Continued 495 0.16 OF THE \rea of A Circle at Breast H EIGHT (C .16B) Diameter. 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 0.8 0.9 Inches Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. 36 1.131 1.137 1.144 1.150 1.150 1.163 1.109 1.175 1.182 1.188 37 1.195 1.201 1.208 1.214 1.221 1.227 1.234 1.240 1.247 1.254 38 1.260 1.267 1.273 1.280 1.287 1.294 1.300 1.307 1.314 1.321 39 1.327 1.334 1.341 1.348 1.355 1.302 1.308 1.375 1.382 1.389 40 1.396 1.403 1.410 1.417 1.424 1.431 1.438 1.440 1.453 1.460 41 1.467 1.474 1.481 1.488 1.496 1.503 1.510 1.517 1.525 1.532 42 1.539 1.547 1.554 1.561 1.569 1.576 1 . 584 1.591 1.599 1.606 43 1.614 1.621 1 . 629 1.636 1.644 1.651 1 . 059 1.667 1.674 1.682 44 1.689 1.697 1.705 1.713 1.720 '1.728 1 . 730 1.744 1.751 1.759 45 1.767 1.775 1.783 1.791 1.799 1.807 1.815 1.823 1.831 1.839 46 1.847 1.855 1.803 1.871 1.879 1.887 1 . 895 1.903 1.911 1.920 47 1.928 1.936 1.944 1.952 1.961 1.969 1.977 1.986 1.994 2.002 48 2.011 2.019 2.027 2.037 2.044 2 . 053 2.001 2.070 2.078 2.087 49 2.095 2.104 2.112 2.121 2.130 2.138 2.147 2.156 2.164 2.173 50 2 . 182 2.190 '2.199 2.208 2.217 2.226 2.234 2.243 2.252 2.261 51 2.270 2.279 2.288 2.297 2.306 2.315 2.324 2.333 2.342 2.351 52 2.360 2 . 309 2.378 2.387 2.396 2.405 2.414 2.424 2.433 2.442 53 2.451 2.461 2.470 2.479 2.488 2.498 2.507 2.510 2.520 2.535 54 2.545 2.554 2.564 2.573 2.583 2.592 2.002 2.611 2.021 2.030 55 2 . 640 2.649 2.659 2.669 2.678 2.088 2 . 098 2.707 2.717 2.727 56 2.737 2.746 2.756 2.700 2.776 2.786 2.790 2.800 2.815 2.825 57 2.835 2.845 2.855 2.805 2.875 2.885 2.895 2.905 2.915 2.926 58 2.936 2.946 2.956 2.966 2.976 2.986 2.997 3.007 3.017 3.027 59 3.038 3.048 3 . 0,58 3.069 3.079 3.089 3.100 3.110 3.121 3.131 60 3.142 3.152 3 . 163 3.173 3.184 3.194 3.205 3.215 3.226 3.237 61 3.247 3.258 3.269 3.279 3 . 290 3.301 3.311 3.322 3.333 3.344 62 3.355 3.305 3.376 3.387 3 . 398 3.409 3.420 3.431 3.442 3.453 63 3.464 3.475 3.486 3.497 3 . 508 3.519 3.530 3.541 3.552 3.503 64 3.574 3.586 3.597 3.008 3 . 019 3.630 3.642 3 . 653 3.664 3.676 65 3 . 687 3.698 3.710 3.721 3.733 3.744 3.755 3.767 3.778 3.790 66 3.801 3.813 3.824 3.836 3.848 3.859 3.871 3.882 3.894 3.906 67 3.917 3.929 3.941 3.953 3.904 3.976 3.988 4.000 4.012 4.023 68 4 . 035 4.047 4.059 4.071 4.083 4.095 4.107 4.119 4.131 4.143 69 4.155 4.107 4.179 4.191 4.203 4.215 4.227 4 . 239 4.252 4.264 70 4.276 4.288 4.301 4.313 4.325 4.337 4.350 4.362 4.374 4.387 71 4 . 399 4.412 4.424 4.436 4 . 449 4.461 4.474 4.480 4.499 4.511 72 4.524 4.530 4.549 4.502 4.574 4.587 4.600 4.012 4.625 4.638 73 4.050 4.663 4.670 4.089 4.702 4.714 4.727 4.740 4.753 4.766 74 4.779 4.792 4 . 805 4.818 4.831 4.844 4.857 4.870 4.883 4.896 75 4.909 4.922 4.935 4.948 4.901 4.975 4.988 5.001 5.014 5.027 76 5.041 5 . 054 5.067 5.080 5.094 5.107 5.120 5.134 5.147 5.161 77 5.174 5.187 5.201 5.214 5 . 228 5.241 5.255 5.209 5.282 5.296 78 5 . 309 5.323 5.337 5.350 5 . 304 5.378 5.391 5.405 5.419 5.433 79 5.440 5.400 5.474 5 . 488 5.502 5.515 5.529 5.543 5.557 5.571 80 5.585 5.599 5.013 5.027 5.041 5.655 5.669 5.683 5.097 5.711 496 APPENDIX C TABLE LXXXI— Continued ( Diameter. 3.66 OF THE Abe A, OF A Circle at the Middle Height of the Thee (0.66B) Inches 0.0 Sq. ft. 0.1 Sq. ft. 0,2 Sq. ft. 0,3 Sq. ft. 0.4 Sq. ft. 0.5 Sq. ft. 0,6 Sq. ft. 0.7 Sq. ft. 0,8 Sq, ft. 0.9 Sq. ft. 1 . 004 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0,012 0.013 2 .014 .010 ,017 ,019 .021 .023 .024 . 026 ,028 .030 3 . 032 .035 .037 ,039 .042 .044 .047 .049 .052 .055 4 .058 .061 .004 ,067 .070 .073 .076 .080 .083 .086 5 .090 .094 .097 .101 .105 .109 .113 .117 .121 .125 6 .130 .134 .138 .143 .147 .152 .157 .162 ,166 .171 7 .176 .182 .187 ,192 .197 .202 .208 ,213 ,219 .225 8 .230 ,230 .242 ,248 .254 .260 .266 .273 .279 .285 9 .292 .298 .305 ,311 .318 .325 .332 .339 .346 .353 10 . 360 . 367 .375 .382 .389 .397 .405 .412 .420 .428 11 .430 .444 .452 .460 .468 .476 .484 .493 .501 .510 12 .518 . 527 .536 . 545 .554 .563 .572 .581 .590 .599 13 .608 .618 .627 .637 .646 .656 .666 .676 .686 .696 14 .706 .716 .726 .736 .746 .757 .767 .778 .788 .799 15 .810 .821 .832 .843 .854 .865 .870 .887 .899 .910 1(1 .922 .933 .945 .956 .968 .980 .992 1.004 1.016 1.028 17 1.040 1.053 1.065 1.077 1.090 1.102 1.115 1 . 128 1,140 1.153 18 1.166 1.179 1.192 1.205 1.219 1.232 1,245 1 . 259 1,272 1.286 19 1.299 1.313 1.327 1.341 1.355 1.369 1,383 1,397 1.441 1.426 20 1.440 1.454 1.469 1.483 1.498 1.513 1,528 1 , .542 1.557 1.572 21 1 . 587 1 . 003 1.618 1 . 033 1 . 649 1.664 1.680 1.695 1.711 1.726 22 1.742 1 . 758 1.774 1.790 1.806 1.822 1,839 1,855 1.871 1.888 23 1 . 904 1.921 1.937 1.954 1.971 1.988 2.005 2,022 2,039 2.056 24 2.073 2.091 2.108 2.126 2.143 2.161 2.178 2,190 2,214 2.232 25 2.250 2.268 2.286 2.304 2.322 2.341 2.359 2,378 2,396 2.415 26 2.433 2.452 2.471 2.490 2.. 509 2.528 2.547 2 . 566 2,585 2.605 27 2.624 2.644 2.603 2 . 683 2.703 2,722 2 . 742 2.762 2.782 2,802 28 2.822 2.842 2 . 863 2 . 883 2.903 2,924 2,944 2,965 2 . 986 3,006 29 3.027 3.048 3.069 3 . 090 3.111 3,133 3,154 3.175 3.197 3,218 30 3.240 3.261 3.283 3.305 3.327 3,349 3.371 3.393 3.415 3.437 31 3.459 3.482 3.504 3.527 3.549 3.572 3.595 3.617 3.640 3.663 32 3.686 3.709 3.732 3.750 3.779 3.802 3.826 3.849 3,873 3.896 33 3.920 3.944 3.968 3.992 4.010 4.040 4,064 4.088 4,112 4.137 34 4.161 4.186 4.210 4.235 4.200 4 . 285 4.309 4.334 4.359 4.385 35 4.410 4.435 4.460 4.486 4.511 4.537 4.562 4.588 4.614 4.639 36 4.665 4.691 4.717 4.743 4.769 4 . 796 4.822 4.848 4 , 875 4.901 37 4.928 4.955 4.981 5.008 5.035 5.062 5.089 5.116 5,143 5.171 38 5.198 5.225 5.2,53 5 . 280 5.308 5.336 5 . 363 5.391 5.419 5.447 39 5.475 5..^)03 5.532 5 . 500 5.588 5.616 5.645 5.673 5.702 5.731 40 5.760 5.788 5.G17 5,846 5.875 5.904 5.934 5.963 5,992 6.022 41 6.051 6.081 0.110 0,140 0.170 6.200 6,230 6 . 260 0,290 6.320 42 6.350 6.380 6.411 6.441 6.471 6,. 502 0,533 6.563 6,594 6.625 43 6.656 6.687 6.718 6.74y 6.780 0,812 6,843 6.874 6 , 906 6.937 44 6.969 7.001 7.033 7.064 7.096 7.128 7.160 7.193 7.225 7.257 45 7.290 1 7.322 7.354 7.387 7.420 7.452 7.485 7.518 7.551 7.584 46 [ 7.617 7 . 650 7.683 7.717 7.750 7.784 7.817 7.851 7.884 7.918 47 7.952 7,986 8.020 8.054 8.088 8.122 8.156 8.190 8.225 8.259 48 8.294 8.328 8.363 8.404 8.433 8,467 8.502 8.537 8.573 8.608 49 8.643 8,678 8.714 8.749 8.785 8,820 8.856 8 . 892 8.927 8.963 50 8.999 9,035 9,072 1 9.108 ! 9.144 9.180 1 9,217 9,253 9,290 9,326 TABLES USED IN FOREST MENSURATION 497 TABLE LXXXII Breast-high Form Factors For Various Heights and Form Classes Total Cubic Volume of Stem Form Class Height Height in in feet 0.50 0.525 0.55 0.575 0.60 0.625 0.65 0.675 0.70 0.725 0.75 0.775 0.80 feet (5-foot (5-foot classes) classes) Bre.\st-high Form Fa CTOR 20 0.524 0.532 0.541 0.548 0.559 0.569 0.581 0.592 0.607 0.620 0.641 0.661 0.683 20 25 472 482 494 504 517 530 545 560 577 595 614 635 657 25 30 443 454 466 478 494 508 524 541 559 579 598 621 643 30 35 424 436 449 464 478 494 511 528 547 568 588 611 635 35 40 409 422 437 452 408 483 501 518 537 559 580 603 628 40 45 398 412 427 442 459 474 493 510 530 552 574 597 623 45 50 389 404 420 435 451 ' 468 487 504 524 546 569 592 619 50 55 583 397 414 429 445 463 482 499 519 542 565 588 615 55 60 378 392 409 424 441 459 477 495 515 538 562 584 612 60 65 373 388 405 420 437 455 473 492 512 535 559 581 609 65 70 369 385 401 417 434 452 470 489 509 532 556 579 606 70 75 366 382 398 415 431 449 467 487 507 529 553 577 604 75 80 364 380 395 412 429 446 465 485 505 527 550 575 603 80 85 361 378 393 410 427 444 463 483 503 525 548 573 601 85 90 359 370 392 409 425 442 401 481 501 523 546 571 600 90 95 357 374 390 407 424 441 460 479 500 622 545 570 598 95 100 356 373 389 405 423 440 459 478 499 521 544 569 597 100 105 354 371 387 404 421 439 457 477 498 520 543 568 596 105 110 353 370 386 403 420 437 456 476 497 519 542 567 595 110 115 352 368 385 402 419 436 455 475 495 518 541 566 594 115 120 350 367 384 401 417 434 453 474 494 516 540 565 593 120 * From table, Massatabeller fiir Traduppskattning. Tor Jonson, Stockholm, Sweden, 1918, p. 66, by conversion of height in meters to height in feet. 498 APPENDIX C TABLE LXXXIII* Weights per Cord of Timber of Various Species — 7- to 8-inch Wood Hardwoods Species Alder, red Ash, Biltmore Ash, black Ash, blue Ash, green Ash, Oregon Ash, pumpkin Ash, white (forest growth) Ash, white (second growth) Aspen Aspen, large tooth . . . Basswood Beech Birch, paper Birch, sweet Birch, yellow Bird's eye, yellow. . . . Buckthorn, cascara. . Butternut Cherry, black Cherry, wild red Chestnut Chinquapin, Western Cottonwood, black.. . Cucumber tree Dogwood, flowering. Dogwood, Western . . Elder, pale Elm, cork Elm, slippery Elm, white Gum, black Gum, blue Gum, cotton Gum, red Pounds, green 4150 4050 4700 4150 4300 4150 4150 4150 4600 • 4250 3850 3700 4950 4600 5300 5200 4400 4500 4150 4150 2950 4850 5500 4150 4500 5850 4950 5850 4750 5050 4700 4050 6300 5950 4150 Pounds, seasoned: 2600 365 D 3300 3800 3800 3600 3450 3750 4300 2500 2500 2450 4050 3550 4400 4100 2350 3350 2500 3350 2600 2850 3000 2250 3200 5050 4400 3450 4250 3500 3250 3350 4900 3450 3250 Species Hackberry Haw, pear Hickory, big shell bark Hickory, butternut.. . Hickory, mockernut.. Hickory, nutmeg .... Hickory, pig nut Hickory, shagbark. . . Hickory, water Holly, American Hornbeam Laurel, California.. . . Laurel, mountain .... Locust, black Locust, honey Madrona Magnolia, evergreen . Maple, Oregon Maple, red Maple, silver Maple, sugar Oak, burr Oak, C a 1 i f or n i a, black Oak, canyon live . . . . Oak, chestnut Oak, cow Oak, laurel Oak, Pacific post Oak, post Oak, red Oak, Spanish highland Oak, Spanish lowland Oak, water Oak, white Oak, willow Oak, yellow Pounds, green 4500 5650 5650 5750 5750 5500 5750 5750 6200 5150 5400 4850 5600 5200 5850 5400 5600 4250 4600 4150 5050 5600 5900 6400 5600 5850 5850 6100 5650 5750 5600 6050 5650 5600 6050 5650 Pounds, seasoned 3500 4550 4800 4550 4900 4000 5050 4850 4300 3750 4900 3650 4550 4550 4750 4000 3250 3200 3450 3200 4100 4200 3650 5200 4300 4650 4400 4500 4100 3900 4600 4200 4500 4300 4100 ♦From General Orders No. 63, War Department, p. 4. TABLES USED IN FOREST MENSURATION 499 TABLE LXXXIII— Continued Haedwoods — Continued Species Poplar, yellow 3400 2600 Rhododendron, great. 5600 3750 Sassafras 3950 3000 Service berry 5500 4900 Silver-bell tree 3950 3000 Sourwood 4750 3750 Pounds, 1 Pounds, green , seasoned |j Species Pounds, I Pounds, green ! seasoned Sumach, staghorn . . . i 3700 Sycamore | 4700 Umbrella, Eraser. . . . Willow, black Willow, Western black Witch hazel 3200 3400 4250 2900 4600 2400 4600 j 2900 5300 I 4300 Conifers Cedar, incense Cedar, Port Orford. . . Cedar, Western red . . Cedar, white Cypress, bald Cypress, yellow Douglas fir. Pacific Northwest Douglas fir, mountain type Fir, Alpine Fir, amabilis Fir, balsam Fir, Noble Fir, white Hemlock, black Hemlock, Eastern . . . Hemlock, Western . . . Larch, Western Pine, Cuban 4150 2400 3500 2900 2450 2100 2500 1950 4300 3200 3150 i 3400 3250 3100 2900 2500 2050 4250 2700 4050 2350 2800 2600 5050 2400 4050 3000 4350 3100 4200 2900 4300 3500 4750 4200 Pine, jack Pine, Jeffrey Pine, loblolly Pine, lodgepole Pine, longleaf Pine, Norway Pine, pitch Pine, pond Pine, shortleaf Pine, sugar Pine, Table Mountain Pine, Western white. . Pine, Western yellow . Pine, white Spruce, Englemann . . Spruce, Sitka Spruce, white Tamarack Yew, Western 4500 4250 4750 3500 4550 3800 4850 4400 4500 4500 4850 3500 4150 3500 3500 3250 3300 4250 4850 2800 2600 3600 2700 3950 3200 3200 3750 3500 2500 3450 2800 2650 2500 2200 2400 2650 3550 4200 Two pounds of air-dried wood are equivalent to 1 pound of average hard coal. The above table indicates the comparative fuel value of different species of wood compared with coal. For anthracite, the equivalent is 2.5 pounds of dry wood to 1 pound of coal, or 3y pounds green wood to 1 pound coal. 500 APPENDIX C TABLE The Tiemann Log Rule for Saws This log rule is applied to the diameter inside bark at middle of on mill tallies, for 1-inch boards, but conforms to the formula, TABLE Tiemann Middle diameter, Inches 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Length of 5 6 7 8 9 10 11 12 13 Contents- 1 1 1 1 2 2 2 2 2 3 3 2 3 3 4 4 5 5 6 7 4 5 6 7 8 8 9 10 11 6 7 9 10 11 13 14 16 17 8 10 12 14 16 18 20 22 24 11 13 16 19 21 24 27 29 32 14 17 21 24 28 31 34 38 41 17 21 26 30 34 39 43 47 52 21 26 32 37 42 47 52 58 63 25 31 38 44 50 57 63 69 76 30 37 45' 52 60 67 74 82 89 35 43 52 61 69 78 87 95 104 40 50 60 70 80 90 100 110 120 46 57 69 80 91 103 114 126 137 52 65 78 91 104 116 129 142 155 58 73 87 102 116 131 145 160 175 65 81 98 114 130 146 162 179 195 72 90 108 126 144 162 180 199 217 80 100 120 140 160 179 199 219 239 88 110 132 153 175 197 219 241 263 96 120 144 168 192 216 240 264 288 105 131 157 183 209 236 262 288 314 114 142 171 199 228 256 284 313 341 123 154 185 216 246 277 308 339 370 133 166 200 233 266 299 332 366 399 143 179 215 251 286 322 358 394 430 154 192 231 269 308 346 384 423 461 165 206 247 288 329 371 412 453 494 176 220 264 308 352 396 440 484 528 1 3 7 12 18 26 35 45 56 68 82 97 113 130 148 168 189 211 235 259 285 312 340 370 400 432 465 500 535 572 TABLES USED IN FOREST MENSURATION 501 LXXXIV Cutting a j^-inch Kerf log, by caliper scale with deduction of widths of bark. It is based L B.M. = (0.751)2 _2Z)) 16" LXXXIV Log Rule Log — Feet 14 15 16 17 18, 19 20 21 22 23 24 Board Feet 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 5 5 5 6 6 6 8 8 9 9 10 10 11 11 12 13 13 13 14 15 16 17 18 19 20 21 22 22 20 21 23 24 26 27 28 30 31 33 34 28 30 32 34 36 38 40 42 44 46 48 37 40 43 45 48 51 53 56 59 61 64 48 52 55 58 62 65 69 72 76 79 82 60 64 69 73 77 82 86 90 95 99 103 74 79 84 89 94 100 105 110 116 121 126 88 94 101 107 113 120 126 132 139 145 151 104 112 119 126 134 141 149 156 164 171 178 121 130 139 147 1.56 165 173 182 191 199 208 140 150 160 170 180 190 200 210 220 230 240 160 171 183 194 206 217 228 240 251 263 274 ISl 194 207 220 233 246 259 272 285 298 310 204 218 233 247 262 276 291 305 320 335 349 228 244 260 276 292 309 325 341 358 374 390 253 271 289 307 325 343 361 379 397 415 433 279 299 319 339 359 379 399 419 439 459 478 307 329 351 .373 395 417 438 460 482 504 526 336 360 384 408 432 456 480 504 528 552 576 366 393 419 445 471 497 523 550 576 602 628 398 427 455 483 512 540 569 597 626 654 682 431 462 493 524 554 585 616 647 678 708 739 466 499 532 565 598 632 665 698 732 765 798 501 537 .573 609 644 680 716 752 788 823 859 538 577 615 653 692 730 769 807 846 884 922 576 618 659 700 741 782 823 865 906 947 988 616 660 704 1 748 792 836 880 924 968 1012 1056 502 APPENDIX C TABLE LXXXV TiEMANN Log Rule Reduced to end measurement assuming a taper of 1 inch to 8 feet. Small Length of Log — Feet end diameter, 6 1 8 10 12 14 16 Inches Contents of Log — Board Feet 4 2 3 4 6 7 9 5 4 6 8 10 12 15 6 7 9 12 16 19 23 7 10 14 18 22 27 32 8 13 19 24 30 36 43 9 18 24 31 39 47 55 10 22 31 40 49 59 69 11 28 38 49 60 72 84 12 34 46 59 72 86 101 13 40 55 70 86 102 119 14 47 64 82 100 119 139 15 55 75 95 116 138 160 16 63 86 109 133 157 183 17 72 98 124 151 178 207 18 81 110 139 170 201 233 19 91 123 156 190 224 260 20 101 137 174 211 249 289 21 112 152 192 233 276 319 22 124 167 212 257 303 351 23 136 184 232 282 332 384 24 149 201 253 307 363 419 25 162 218 276 334 394 455 26 176 237 299 362 427 493 27 190 256 323 392 461 532 28 205 276 348 422 497 573 29 221 297 374 453 533 615 30 237 318 401 486 572 659 31 253 341 429 519 611 704 32 271 364 458 554 652 751 TABLES USED IN FOREST MENSURATION 503 TABLE LXXXVI ScRiBNER Decimal C Log Rule for Saws Cutting a j-inch Kerf This log rule disregards taper, and is applied at small end of log, inside bark. It is based on diagrams of 1-inch boards, values not made regular by curves, and deduction for slab too large above 28 inches. The Decimal form is given, with values of the original rule rounded off to the nearest 10 board feet and the cipher dropped. To read in board feet, add the cipher. Decimal C values are given, as in Table XII, § 68. Values above 44 inches adopted by the U. S. Forest Service. 504 APPENDIX C TABLE LXXXVI ScRiBNER Decimal C Log Rule Diam- Length — Feet Diam- eter, 6 1 7 1 8 1 9 10 11 12 13 14 15 16 eter, Inches Contents — Board Feet Inches 6 0.5 0.5 0.5 0.5 1 1 1 1 1 1 2 6 7 0.5 1 1 1 1 2 2 2 2 2 3 7 8 1 1 1 1 2 2 2 2 2 2 3 8 9 1 2 2 2 3 3 3 3 3 3 4 9 10 2 2 3 3 3 3 3 4 4 5 6 10 11 2 2 3 3 4 4 4 5 5 6 7 11 12 3 3 4 4 5 5 6 6 7 7 8 12 13 4 4 5 5 6 7 7 8 8 9 10 13 14 4 5 6 6 7 8 9 9 10 11 U 14 15 5 G 7 8 9 10 11 12 12 13 u 15 16 6 7 8 9 10 11 12 13 14 15 16 16 17 7 8 9 10 12 13 14 15 16 17 18 17 18 8 9 11 12 13 15 16 17 19 20 21 18 19 9 10 12 13 15 16 18 19 21 22 24 19 20 11 12 U 16 17 19 21 23 24 26 28 20 21 12 13 15 17 19 21 23 25 27 28 30 21 22 13 15 17 19 21 23 25 27 29 31 33 22 23 14 16 19 21 23 26 28 31 33 35 38 23 24 15 18 21 23 25 28 30 33 35 38 40 24 25 17 20 23 26 29 31 34 37 40 43 46 25 26 19 22 25 28 31 34 37 41 44 47 50 26 27 21 24 27 31 34 38 41 44 48 51 55 27 28 22 25 29 33 36 40 44 47 51 54 58 28 29 23 27 31 35 38 42 46 49 53 57 61 29 30 25 29 33 37 41 45 49 53 57 62 66 30 31 27 31 36 40 44 49 53 58 62 67 71 31 32 28 32 37 41 46 51 55 60 64 69 74 32 33 29 34 39 44 49 54 59 64 69 73 78 33 34 30 35 40 45 50 55 60 65 70 75 80 34 35 33 38 44 49 55 60 66 71 77 82 88 35 36 35 40 46 52 58 63 69 75 81 86 92 36 37 39 45 51 58 64 71 77 84 90 96 103 37 38 40 47 54 60 67 73 80 87 93 100 107 38 39 42 49 ,56 63 70 77 84 91 98 105 112 39 40 45 53 60 68 75 83 90 98 105 113 120 40 41 48 56 64 72 79 87 95 103 111 119 127 41 42 50 59 67 76 84 92 101 109 117 126 134 42 43 52 61 70 79 87 96 105 113 122 131 140 43 44 56 65 74 83 93 102 111 120 129 139 148 44 45 57 66 76 85 95 104 114 123 133 143 152 45 46 59 69 79 89 99 109 119 129 139 149 159 46 47 62 72 83 93 104 114 124 134 145 155 166 47 48 65 76 86 97 108 119 130 140 151 162 173 48 49 67 79 90 101 112 124 135 146 157 168 180 49 50 70 82 94 105 117 129 140 152 164 175 187 50 TABLES USED IN FOREST MENSURATION 505 TABLE LXXXVII Index to Standard Volume Tables Standard volume tables (§ 140) have been constructed by the U. S. Forest Service, by state forestry departments, by forest schools, and in some instances by private corporations, or individuals. This index is intended to include such of these tables as are of value for future timber estimating, and can be obtained in published form, or from the U. S. Forest Service. The index briefly describes each table under the standard headings to enable the estimator to decide whether or not it is suitable for his purposes. The final column gives the Forest Service designation of such tables as have not so far been published. 506 APPENDIX C Hardwoods TABLE Species Locality Tree class Unit of measure- ment Log rule Aspen . . . . Aspen . . . . Aspen . . . . Aspen . . . . Ash, black Ash, black Ash, black Ash, green . Ash, green Ash, green Ash, gieen Ash, green Ash, green Ash, white Ash, white Ash, white Ash, white Ash, white Ash, white Ash, white Ash, white Ash, white Basswood. . . Beech . . . . Beech Beech Beech Beech Beech Beech Birch, paper . Birch, paper. Birch, paper. Birch, paper . Birch, paper. Birch, paper . Birch, paper. Birch, yellow Birch, yellow Birch, yellow Birch, yellow Chestnut . . . . Chestnut . . . . Chestnut. . . . Cottonwood . Cottonwood . New Hampshire Maine Maine Utah General General General General General General General General General General General General General General General Eastern U. S. Vermont Vermont Lake States Vermont Vermont Michigan Pennsylvania New Hampshire Pennsylvania Michigan New Hampshire New Hampshire Maine, N. Hamp. Maine, N. Hamp. Maine, N. Hamp. Maine, N. Hamp. Maine, N. Hamp. Vermont Vermont New Hampshire Lake States Connecticut Connecticut Connecticut Mississippi Valley Mississippi Valley 25-50 yrs. Over 75 yrs. Over 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Second growth Second growth 45-60 yrs. 45-60 yrs. Second growth Second growth Second growth Second growth Second growth Second giowth Second growth Cubic ft. peeled merch. Cubic ft. peeled merch. Cords Board ft. Cu. ft., peeled total Cords Board feet Cu. ft., peeled total Cu. ft., peeled total Cords Cords Board feet Board feet Cu. ft., peeled total Cu. ft., peeled total Cords Cords Board feet Board feet Cu. ft. of branch wood Cu. ft., with limbs Bd. ft. and cu. ft. in tops Board feet Cu. ft., with limbs Bd. ft. and cu. ft. in tops Cubic feet Cubic feet Board feet Board feet Board feet Cubic ft., merch. Board feet Cu. ft., total Cubic ft., merch. Board feet Cubic ft., merch. Board feet Cu. ft., total with limbs Board feet Board feet Board feet Cu. ft., merch. O.B. Board feet Cubic feet merch. Cu. ft., peeled total Board feet Scribner Dec C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Mill tally New Hampshire New Hampshire Scribner Dec. C. Scribner Dec. C. International i" kerf Scribner Dec. C. TABLES USED IN FOREST MENSURATION 507 LXXXVII Hardwoods D.B.H. Height. Top diameter. Basis. Date Publication U. S. F. S. (Inches) (Feet) (Inches) Trees designation 5-13 50- 80 289 1905 Bui. 36, U. S. Forest Service 5-20 30- 90 4 362 1911 Bui. 93, U. S. Forest Service 5-20 30- 90 4 362 1911 •• 10-27 1-4 log 9 675 1913 W5-V10 6-30 60-110 116 1915 Bui. 299. U. S. Dept. Agr. 6-30 60-110 116 1915 " 8-30 2- 6 log 6-12 116 1915 " 4-24 40-100 278 1915 *' 8-44 60-130 918 1915 '• 4-24 40-100 278 1915 " 8-44 . 60-130 918 1915 " 40-100 6-10 223 1915 •' 8-44 60-130 6-10 918 1915 " 2-22 20- 90 806 1915 " 6-36 50-150 488 1915 " 4-22 20- 90 696 1915 " 6-32 50-120 487 1915 " 8-24 U-5 1og 6-18 .2 423 475 1915 1915 1915 " 3-21 40- 90 285 1914 Bui. 176, Vt. Agr. Exp. Sta. 3-20 40- 90 285 1914 8-40 2-4i 6-24 319 1915 Bui. 285, U. S. Dept. Agr. 3-14 30- 70 102 1914 Bui. 176, Vt. Agr. Exp. Sta. 3-14 30- 70 102 1914 4-26 40-100 6-15 289 1915 Bui. 285, U. S. Dept. Agr. 8-30 70-110 6-21 120 1909 ' ' 7-24 ^3^ log 6-17 376 1915 ' ' 10-30 2-4 log 6-21 118 1915 ' ' 1-4 i log 6-15 285 1915 ' ' 10-50 used 4-10 427 1905 Bui. 36, U. S. Forest Service 6-16 10-50 used 4-10 ■ 427 1905 4-16 50- 90 443 1909 Circ. 163, U. S. Forest Service 5-14 12-60 used 396 1909 5-14 12-60 used 396 1909 " 5-18 50 - 90 5-18 50- 90 3.3-6.1 396 1909 Circ. 163, U. S. Forest Service 3-15 40- 70 1914 3-14 40- 70 1914 ■• 7-32 ^3^ log 6-21 651 1915 Bui, 285, U. S. Dept. Agr. 8-30 U-3^ log 6-17 237 1915 ' ' 2-25 20- 90 2 218 1912 Bui. 96, U. S. Forest Service 9-25 50- 90 7-12 118 1912 7-20 50- 90 517 1905 N. H. Forestry Com. Report 5 30 50-150 80-150 7-19 409 267 1910 1910 W94-V8 11 30 W94-V8 508 APPENDIX C TABLE LXXXVII H ARDWOODS — Contin ued Species Eucalyptus (Blue gum) Eucalyptus (Blue gum) Gum, red Gum, red Gum, red Hickories Hickories Maple, red . . Maple, red . . Maple, sugar. Maple, sugar Maple, sugar . Maple, sugar Maple, sugar Maple, sugar Maple, sugar .... Maple, sugar Maple, sugar Oixk, chestnut Oak, chestnut . . Oak, red Oak, red Oak, red Oak, red Oak, red Oak, red, scarlet and black Oak, red, scarlet and black Oak, white Oak, white Oak, white New York Locality California California Southern States Southern States Southern States Eastern States Eastern States Massachusetts Massachusetts Vermont Vermont Lake States Pennsylvania Pennsylvania New Hampshire Lake States Lake States Lake States S. Appalachians S. Appalachians New Hampshire New Hampshire S. Appalachians S. Appalachians S. Appalachians Connecticut Connecticut Connecticut Connecticut Oak, w Poplar, Poplar, Poplar, Poplar, Poplar, Poplar, hite yellow . yellow . yellow . yellow . yellow . yellow . S. Appalachians S. Appalachians S. Appalachians S. Apiialachians S. Appalachians Virginia Virginia Tree class Unit of measure- ment Plantations Plantations Under 75 yrs. Over 75 yrs. Over 75 yrs. Second growth Second growth Second growth Second growth Over 75 yrs Over 75 yrs. Second growth Second growth Under 75 yrs. Over 75 yis. Over 75 yrs. Second growth Second growth Second growth Second growth Second growth 1-.50 yrs. 51-100 yrs. Under 100 yrs. Over 100 yrs. Second growth Second growth Cubic feet Board feet Board feet Board feet Board feet Cubic ft., merch. Cubic ft., total Cubic ft., merch. Cords Cu. ft., with limbs Bd. ft., cu. ft. in tops Cu. ft., merch. O.B. Cu. ft., merch. O.B. cu. ft. in tops Board feet Board feet Board feet Board feet Board feet ■ Board feet Board feet Cubic ft., merch. Board feet Boaid feet Board feet Board feet Cubic ft., merch. Board feet Cu. ft., merch. O.B. Board feet Cu. ft., merch. O.B. Board feet Board feet Board feet Board feet Board feet Cubic feet, total Board feet Log rule Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Mill tallies Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. International t" kerf International kerf Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Mill tallies Mill tallies Scribner Dec. C. TABLES USED IN FOREST MENSURATION 509 -Continued Hardwoods — Continued Height. (Feet) 30-160 50-160 1-6 log 1-7 log 80-140 5-65 used 40- 90 20- 80 20- 80 40 -80 40- 80 50-100 70-110 2i-4 log i-4 log' U-4 log 2-5 log 1-U log 1-5 log 40-110 10-50 used 10-50 used 40-100 1-5 log 40-130 20- 80 50- 80 20- 80 50- 70 20- 60 1-5 log 1-5 log 1-6 log 1-5 log 2-6 log 50-100 40-100 Top diameter. (Inches) 6-13 6-23 6-23 4-20 Trees Date 6-17 6-16 6-16 6-21 6-17 6-13 7-22 6-20 6-20 5- 9 5- 9 6-13 6-22 6-22 2 7-10 2 6 6- 8 6-14 6-17 5.9-7.2 2611 1906 685 332 1740 1740 630 365 397 397 222 222 305 41 41 360 278 278 278 2232 2232 683 683 198 1300 1300 441 175 293 26 349 1436 489 102 489 407 491 480 1906 1904 1904 1904 1910 1910 1915 1915 1914 1914 1915 1915 1915 i915 1915 1915 1915 1913 1913 1905 1905 1914 1914 1914 1913 1913 1913 1913 1905 1903 1913 1913 1913 1913 1907 1907 Publication Bui. 80, U. S. Forest Service Bui. 80 Bui. 285, U. S. Dept. Agr. Bui. 176, Vt. Agr. Exp. Sta. Bui. 285, U. S. Dept. Agr. Bui. 285, U. S. Dept. Agr N.H. Forestry Com. Report " and Bui. 36, U. S. For. Serv. Bui. 96, U. S. Forest Service Bui. 36, U. S. Forest Service U. S. F. S. designation Bui. 36, U. S. Forest Service G93-V2-3 G93-V1 G71-V5 G71-V7 G71-V8 Q68-V19 Q68-V20 Q61-V18 Q61-V15 Q61-V16 Q82-V1 W82-V24 W82-V25 W82-V26 W82-V28 510 APPENDIX C TABLE LXXXVII Conifers Species Cedar, incense Cedar, incense Cedar, incense Cedar, western red. Cedar, western red. . Cedar, western red. . Cypress Cypress Douglas fir Douglas fir Douglas fir Douglas fir Douglas fir Douglas fir Douglas fir Douglas fir Fir, Amabilis Fir, balsam Fir, balsam Fir, balsam Fir, balsam Fir, balsam Fir, balsam Fir, balsam Fir, balsam Fir, balsam Fir, balsam, western Fir, red Fir, red Fir, red Fir, red Fir, white Fir, white Fir, white Fir, white Fir, white Hemlock Hemlock Hemlock Hemlock Hemlock Hemlock Hemlock Hemlock Hemlock, western. . Hemlock, western. . Juniper Jumper Larch, western Locality California California California Puget Sd., Wash Idaho Idaho South Carolina South Carolina Washington, Oregon Washington, Oregon Oregon California California New Mexico Montana, Idaho Montana, Idaho Washington, Oregon New York, Maine New York Maine New Hampshire New York, Maine New Hampshire Northeast Northeast Quebec Idaho, Montana California California California California California California California California California New Hampshire Mich., Wis. New Hampshire Wis., Mich. Wis., Mich. Wis., Mich. Wis., Mich. Wis., Mich. Washington Washington Utah, Arizona Utah, Arizona Montana Tree class Second growth Unit of measure- ment Cubic feet, total Board feet Board feet Board feet Board feet Board feet Board feet Board feet Cu. ft., peeled total Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Cubic feet, total Cubic feet, peeled merch. Cubic feet, peeled merch. Cubic feet, peeled merch. Cords Cords Board feet Board feet Board feet Board feet Cubic feet, total Cubic feet, cords Board feet Board feet Cubic feet Board feet Board feet Board feet Board feet Cubic feet, merch. Cu. ft., merch. O.B. Board feet Board feet Board feet Board feet Board feet Board feet Board feet Cubic feet, total Cubic feet, total Cords with branches Cubic feet, total Log rule Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Scribner Scribner Scribner Scribner Scribner Scribner Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Scribner Dec. C. Scribner Dec. C. Maine Quebec Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Mill tally Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Vermont Scribner Dec. C. TABLES USED IN FOREST MENSURATION 511 — Continued CoNIifERS D.B.H. (Inches)' Height. (Feet) 60-150 2-9 log 40^200 Short, me- dium, tall 1-6 log 1-9 log 1 5 log 1 6 log 20-220 2-10 log 2-15 log 40-200 1-10 log 1-9 log 1-7 log 1-9 log 1-51 log 20- 80 40- 80 50- 90 40- 60 20- 80 40- 60 40- 80 40- 90 39- 91 1-9 log 40-150 40-150 40-150 1-8 log 40-170 40-180 3-10 logs 90-220 2-8 logs 30- 70 30-100 30- 70 30-100 1-5 log 50-120 1-7 log 4-100 2-11 log 50-200 10- 20 10- 20 80-160 I Top diameter.] ! Date I (Inches)! Trees 8 11 8-11 6-7 6-24 6-25 10 7-11 7-11 7 6 4 6 5.8-6 5.9-6.4 4 5.7-6, 5.7-14, 9-15 4.4-6.5 4 4.4-6.5 6-12 6-12 7-26 6-17 1054 1054 1890 186 441 437 1747 967 1394 1048 855 372 2173 947 330 100 2171 100 1866 33 677 750 752 800 597 639 366 1114 322 317 317 542 542 1402 1370 320 1440 335 495 495 1324 1910 1914 1915 1915 1911 1911 1905 1913 1913 1917 1914 1917 1904 1914 1914 1914 1914 1914 1914 1914 1911 1914 1909 1912 1912 1912 1905 1905 1913 1913 1905 1915 1905 1915 1915 1915 1915 1910 1912 1900 1900 1900 1907 Manual for Timber Reconnaisance, Dist. 1, U. S. Forest Service Bui. 272, U. S. Dept. Agr. Circ. 175, U. S. Forest Service Circ. 175, V. S. Forest Service M^anual for Timber Reconnaisance, Dist. 1, U. S. Forest Service Bui. 55, U. S. Dept. Agr. T6-V3 T6-V3 D1-V18 D4-V32 D4-V31 D1-V35-36 D1-V29 A8-V2 A-35-V2 For Quar., IX, 593 Manual for Timber Reconnaissance, Dist. 1, U. S. Forest Service For. Quar., XI, 362 For. Com. N. H., 1905; Bui. 152 U. S. Dept. Agr. Bui. 152, U. S, Dept. Agr. Bui. 161, Vt. Agr. Exp. Sta. Circ. 197, U. S. Forest Service A1-V4 A1-V6-7 A1-V2 A1-V3 A2-V3 A2-V2 A2-V5 A2-V15 A2-V17 H65-V20 H6-V5 H6-V4 L7-V3 512 APPENDIX C TABLE LXXXVII Conifers — Continued Species Larch, western . Larch, western. Larch, western. Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine, Pine Pine Pine, Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Jack . . . . Jack . . . . Jack . . . . Jack . . . . Jeffrey. . . loblolly . . loblolly. . loblolly. . loblolly . . loblolly . . loblolly . . loblolly . . loblolly . . loblolly . . loblolly. . loblolly. . lodgepcle lodgepolc lodgepole lodgepole lodgepole lodgepole lodgepole lodgepole lodgepole lodgepole longleaf . . red red red red red red scrub . . . . scrub . . . . scrub . . . . shortleaf . shortleaf . shortleaf.. shortleaf . sugar . . . . sugar . . . sugar . . . white . . . . white . . . . white . . . . white . . . . white . . . . white . . . . white . . . . white . . . . white . . . . white . . . . Locality Montana Montana Montana Minnesota Minnesota Minnesota Minnesota California Maryland, Virginia Maryland, Virginia Maryland, Virginia Maryland, Virginia North Carolina North Carolina North Carolina North Carolina North Carolina North Carolina North Carolina Montana Montana Montana Montana ' Montana Oregon Oregon Oregon Oregon Colorado, Wyoming Alabama Minnesota Minnesota Minnesota Minnesota Minnesota Minnesota Maryland Maryland Maryland North Carolina North Carolina Arkansas Arkansas California California California New Hampshire Massachusetts Massachusetts New Hampshire Massachusetts Minnesota Minnesota Minnesota New Hampshire 8. Appalachians Tree class Unit i>f measure- ment Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 75 yrs. Over 75 yrs. Under 130 yrs. Over 200 yrs. Second growth Second growth Second growth Second growth Second growth Second growth Second growth Second growth Original Original Original Second growth Under 75 yrs. Board feet Board feet Board feet Cu. ft., pesled total Cu. ft., merch. O.B. Board feet Board feet Board feet Cu. ft., merch. O.B. Peeled Board feet Board feet Cu. ft., peeled merch. Boaid feet Board feet Board feet Board feet Board feet Board feet Cubic feet, merch. Board feet Board feet Cubic ft., total O.B. Board feet Board feet Poles Ties Board feet Board feet Board feet Cu. ft., peeled total Board feet Board feet Cubic feet, total Board feet Board feet Cords O.B. Cords, peeled Cu. ft., total O.B. Cubic feet, merch. Board feet Board feet Board feet Board feet Board feet Cubic feet, merch. Cu. ft., total O.B. Cu. ft., merch O. B, Cords Board feet Board feet Board feet Board feet Board feet Cubic feet, merch. Board feet Log rule Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Mill tallies Mill tallies Mill tallies Scribner Dec. C. Scribner Dec. C. Tiemann Tiemann Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Scribner Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Mill tallies Mill tallies Scribner Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. TABLES USED IN FOREST MENSURATION 513 -Continued Conifers — Continued D.B.H. Height. Top diameter. Basis. ^ ^ Date Publication U. S. F. S. designation (Inches) (Feet) finches) Trees 12-42 80-160 7.3-10.8 1388 1907 Bui. 36, U. S. Forest Service L7-V2 12-42 3-8 log 7.3-10.8 1394 1907 L7-V4 8-40 1-9 log 233 1914 Manual for Timber Reconnaissance, Dist. 1, U, S. Forest Service 2-20 20- 80 658 1920 Bui. 820, U. S. Dept. Agr. 4-20 20- 80 3 615 1920 " 8-20 20- 80 5.5 288 1920 " 8-20 1-4 log 5.5 288 1920 " 14-54 40-130 15- 80 6-16.4 U 413 1907 372 1914 P7-V1 3-20 Bui. 11, U. S. Dept. Agr. 3-20 15- 80 U 372 1914 7-20 40- 80 5.5 372 1914 4- 8 30- 70 2.5 Tapers 1914 6-30 20-120 3-5 1915 Bui. 24, N. Car. Geol. Survey 7-22 40-120 5 11 .... 1915 P76-V24 14-36 90-140 7-15 1915 P76-V28 8-22 40-120 5-11 .... 1915 P76-V23 14-36 90-140 7-15 1915 " P76-V27 7-22 40-120 5-11 .... 1915 " P76-V21 14 36 90-140 7-15 1915 " P76-V25 3-20 30-100 2 -3 1915 Bui. 234, U. S. Dept. Agr. 7-24 1-5 log 6 555 1915 10 + 1-5 log 6.2-6.6 1808 1915 4-22 30- 90 644 1907 Circ. 126, U. S. Forest Service 10-24 50-100 6 1817 1907 " 7-22 h-^i log 30- 70 0-6 log 6 3-4 9 549 1913 255 1913 2000 .... P0-V13 P0-V14 8-18 P0^V12 9-18 i-S^ log ^5 log 40-120 8 8 6-18 .... 1913 1971 1915 614 1904 PO-VU 8-25 PO-V28 7-36 Bui. 36, U. S. Forest Service 5-20 40-100 303 1914 Bui. 139, U. S. Dept. Agr. 8-34 30-120 6 4282 1914 * ' 8-34 1-7 log 6 4282 1914 ' ' 7-30 40-120 60-100 6 613 1905 259 1909 P31-V11 7-18 Bui. 36, U. S. Forest Service 10-27 70-100 964 1909 ' ' 2-12 10- 75 228 1911 Bui. 94, U. S. Forest Service 4r-12 30- 75 228 1911 2-12 20- 70 228 1905 Bui. 36, U. S. Forest Service 6-20 40- 90 6-8 317 1915 Bui. 308, U. S. Dept. Agr. 6-20 40- 90 6-8 317 1915 " 8-34 40-120 6-13 3206 1915 8-34 U-6 log 6-13 3206 1915 " 10-80 40-220 8-16 910 1917 Bui 426, U. S. Dept. Agr. 10-80 1-12 log 8-16 910 1917 10-80 60-240 30-120 8-16 5 773 1913 1578 1905 P3-V13 5-20 Bui. 13, U. S. Dept. Agr. 5-25 30- 90 4 2000 1908 5-27 30- 90 4 2000 1908 5-26 30-120 5 1578 ! 1905 " and Bui. 820, U. S. Dept. Agr. 5-27 30- 90 4 2000 1 1908 Bui. 13, U. S. Dept. Agr. 8-40 40-140 6-14 3899 1910 8-42 40-110 n-7 log 6 6 1834 1913 1834 1913 P32-V40 8-42 P32-V39 5-26 30-120 40- 90 ! I 1578 1905 260 ' 1913 P32-V25 8-20 P32-V42 514 APPENDIX C TABLE LXXXVII Conifers — Continued Species Locality Tree class Unit of measure- ment Log rule Pine, white S. Appalachians Under 75 yrs. Pine, western white . Pine, western white . Pine, western white . Pine, western white Pine, western yellow Pine, western yellow- Pine, western yellow Pine, western yellow Pine, western yellow Pine, western yellow Pine, western yellow Pine, western yellow- Pine, western yellow- Pine, western yellow- Pine, western yellow- Pine, western yellow Pine, western yellow Pine, western yellow! Pine, western yellow Pine, western yellow- Redwood Redwood Redwood Spruce, black Spruce, black Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, red Spruce, Englemann. Spruce, Englemann, Spruce, Englemann, Spruce, Englemann, Spruce, Englemann, Spruce, white Spruce, white Tamarack Idaho Idaho Idaho Idaho Black Hills, S. Dak, California Black Hills, S. Dak, Klamath, Ore. Blue Mts., Ore. Arizona Arizona Arizona Arizona California S. Dakota, Idaho Montana Montana Montana Montana Colorado California California California Quebec Quebec Maine New Hampshire New Hampshire New Hampshire New Hampshire New York West Virginia New York New York Maine Maine Maine Maine New Hampshire New Hampshire New Hampshire New Hampshire New York New York West Virginia West Virginia Colorado, Utah Colorado, Utah Colorado, Utah Colorado, Utah Idaho, Montana Quebec Quebec Minnesota Sprouts Sprouts Original Old field Old field Original Original Original Original Original Original Board feet Board feet Board feet Board feet Cubic feet Cubic feet, total Cubic feet, total Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Cu. ft., total O.B. Board feet Board feet Cubic feet Board feet Cubic feet, merch. Cubic ft. total O.B. Cu. ft., merch. O.B. Cu. ft., merch. O.B. Cubic feet, peeled Cu. ft., merch. O.B. Cu. ft., merch. O.B. Standards Standards Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Board feet Cubic feet, merch. peeled Board feet Board feet Board feet Board feet Cubic feet, merch. Board feet Cubic feet, total Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner DeX;. C. Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Scribner Dec. C. Dec. C. Dec. C. Deo. C. Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Dec. C. Scribner Dec. C. Spaulding Quebec Dimick Dimick Maine Maine Scribner Dec. C Scribner Dec. C. New Hampshire New Hampshire Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. C. Scribner Dec. 0. Scribner Scribner Dec. C. Quebec TABLES USED IN FOREST MENSURATION 515 -Continued CONIFERS- —Continued Diam- eter. Height. Top diameter. Basis. Date Publication U. S. F. S. designation (Inches) (Feet) (Inches) Trees 8-20 li-3i log 6 260 1913 P32-V41 8-36 30- 160 6-8 1791 1908 Bui. 36, U. S. Forest Service P2-V3 8-36 2-10 log 6-8 1791 1908 P2-V4 8-60 1-9 log 306 1914 Manual of Timber Reconnaissance, Dist. 1, U. S. Forest Service 8-44 80-190 1790 1914 Bui. 36, U. S. Forest Service P2-V5 8-25 30- 90 1004 1908 Giro. 127, U. S. Forest Service 12-48 50-160 710 1908 " 8-25 40-100 2- 8i log 6-14 1419 823 1910 1917 P4-V31 12-50 Bui. 418, U. S. Dept. Agr. 10-42 2-8i log 6-16 1536 1917 10-50 30-150 1-8 log 8 8 6099 6099 P4- V43 10-50 P4-V41 12-40 40-120 8.3-17 1822 1911 Bui. 101, U. S. Forest Service 12-40 1-6 log 8.3-17 1822 1911 " 12-70 60-220 2-10 log 1-8 log 30-140 U-8 log 30-140 l-6i log 8-14 8 6-10 6-10 6-18 6.1-10.6 2396 1193 427 427 2822 2438 2167 1911 1913 1913 1913 1916 1916 1916 P4-V39 12-50 P4- V42 10-40 P4 V5 10-40 P4-V36 8-40 P4-V37 8-40 P4-V38 12-43 P4-V61 6-24 30- 90 30- 90 55-180 6-7 883 763 503 1900 1900 1917 R1-V3 7-24 R1-V2 20-112 Timberman, Dec, 1917, p. 38 7-20 46- 89 4 317 1911 For. Quar., Vol. IX, p. 591 6-20 13- 84 4 317 1911 6-25 40- 90 4.5 246 1920 Bui. 544, U. S. Dept. Agr. 6-14 40- 70 711 1920 ' ' 6-18 40- 80 5 711 1920 ' ' 5-28 40- 90 4 1226 1920 ' ' 6-14 40- 70 4-6 711 1920 ' ' 6-26 30-100 4.5 1591 1920 6-34 50-100 4.5 417 1920 " 8-26 1-5 log 6 1507 1920 8-26 30-100 6 1507 1920 " 7-25 40- 90 6 241 1920 7-25 1-4 J log 6 241 1920 " 7-25 40- 90 6-9 241 1920 7-25 1-5 log 6-9 241 1920 8-26 30- 80 6 668 1920 8-26 1-4 log 6 668 1920 " 8-26 30- 80 6 668 1920 8-26 1-4 log 6 668 1920 ' ' 8-26 30-100 6 1507 1920 8-26 1-5 log 6 1507 1920 ' ' 8-34 50-110 6 416 1920 8-34 l§-6 log 6 416 1920 " 7-36 40-120 6-8 676 1910 Circ. 170, U. S. Forest Service S2-V4 8-30 40-120 6-8 676 1910 .. S2-V1 8-30 1-6 log 6-8 671 1910 " S2-V5 7-26 35-115 1-9 log 6 2380 189 1915 1914 S2-V10 8-40 Manual for Timber Reconnaissance, Dist. 1, U. S. Forest Service 7-25 51-100 4 441 1911 For. Quart., Vol. IX, p. 590 6-25 44-112 4 1351 1911 p. 592 7-15 60-100 246 1905 I-35-V4 516 APPENDIX C 03 03 no ^ & > > fo CO ro oj 0) ., 5r *- >. >H ;>^ aj CO J g bH bH bCi ,^ -^ ^J. 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(/■ "c C t c >> c c !> > C c_ r ^ =3 .*^ ■^ ■« "k -c -c o C c: o; '^ 03 o3 c Ih e ■1 o; _ c c 03 tH CA & ft p, P. 0? ■ u c t c L, -^ t: r c; 03 cc c; ->-i 03 M ^ a a a a o < < 5 a C oj a; r-i 03 CO a C o: rr < < X. e ;: ^ ^ C O o: a o: 5 e c a: C a: ^ ^ ^ ^ S < §1 ^ ^ ^ 1 c J i "« CO .2 _> ■^> ■> > ^1 cc _c Ol ^ Q-* a. -^ 'a! 0. 1 (- 3 a 1 o: ^ ^ _c ^ J t4 to CO ^ & ^ s- cc ci o c ii? a a c a a c c a .3 .2 a c a, c c - C c - C C c E § c c p. (i fa fa fa fa fa fa fa fa fa fa fa fa fa OS H ^ APPENDIX D BIBLIOGRAPHY List of the most important works dealing with Forest Mensuration, in English: Carter, P. J. Mensuration of Timber and Timber Crops. Calcutta, Ind., 1893. Gary, A. Manual for Northern Woodsmen. Harvard University, Cambridge, 1918. Cook, H. O. Forest Mensuration of the White Pine in Massachusetts. Boston, 1908. Office of State Forester. D'Arcy, W. E. Preparation of Forest Working Plans in India. Calcutta, 1898. Graves, H. S. Forest Mensuration, John Wiley & Sons. New York, 1908. Graves, H. S. • Woodsman's Handbook. Bui. 36, U. S. Forest Service, 1910. Mattoon, W. R., and Barrows, W. B. Measuring and Marketing Woodlot Products. Farmers' Bui. 715, U. S. Dept. Agr., 1916. McGregor, J. L. L. Organization and Valuation of Forests. London, 1883. Mlodziansky, a. K. Measuring the Forest Crop. Bui. No. 20, Div. of Forestry, U. S. Dept. Agr., 1898. PiNCHOT, Gifi^ord. The Adirondack Spruce. New York, 1898. PiNCHOT, G., and Graves, H. S. The White Pine. New York, 1896. ScHENCK, C. A. Forest Mensuration. Sewanee, Tenn., 1905. ScHLicH, Wm. Manual of Forestry, Vol. III. London, 1911. \^''iNKENWERDER, H. Manual of Exercises in Forest Mensuration. John Wiley &Sons. New York, 1921. List of the most important works dealing with Forest Mensuration, in German. Selected from bibliography published in "Forest Mensuration," by H. S. Graves, with some additions : Special Works on Forest Mensuration Baur, Franz. Die Holzmesskunde. Berlin, 4th ed., 1891. Brehmann, Karl. Anleitung zur Aufnahme der Holzmasse. Berlin, 1857. Anleitung zur Holzmesskunst. Berlin, 1868. Fankhauser, F. Praktische Anleitung zur Holzmassen-Aufnahme, 3d edition, Bern, 1909. Heyer, Gust. Ueber die Ermittelungen der Masse, des Alters und des Zuwachses der Holzbestiinde. Dessau, 1852. Heyer, Karl. Anleitung zu forststatischen Untersuchungen. Giessen, 1846. Klauprecht. Die Holzmesskunst. Karlsruhe, 1842 and 1846. Konig, G. Die Forst-Mathematik mit Anweisung zur Forstvermessung. Gotha, 1835. Revised by Dr. Grebe, 1864. Kunze, M. F. Lehrbuch der Holzmesskunst. Berlin, 1873. Langenbacher, Ferd. Forstmathematik. Berlin, 1875. Lamgenbacher, F. L., und Nossek, E. A. Lehr- und Handbuch der Holzmess- kunde. Leipzig, 1889. MtJLLER, Udo. Lehrbuch der Holzmesskunde. Leipzig, 2d edition, 1915. ScHWAPPACH, Adam. Leitfaden der Holzmesskunde. Berlin, 1903. 521 522 APPENDIX D Smalian, L. Beitrag zur Holzmesskunst . Stralsund, 1837. Anleitung zur Untersuchung des Waldzustandes. Berlin, 1840. Statz, Paul. Die Abstandszahl, ihre Bedeutung fur die Forsttaxation, Bestandes- erziehung und Bestandespflege, Freiburg, 1909. Tkachenko, M. Das Gesetz des Inhalts der Baumstamme una seine Bedeutung fiir die Massen- und Sortimentstafeln. Berlin, 1912. Works on Forest Management Containing Chapters on Forest Mensuration Borggreve, B. Die Forstabschatzung. Berlin, 1888. VON FiscHBACH, C. Lehrbuch der Forstwissenschaft. Berlin, 1886. Graner, F. Die Forstbetriebseinrichtung. Tiibingen, 1889. VON Guttenberg, a. F. Forstbetriebsienrichtung. Wien and Leipzig, 1903. Hess, R. Encyclopedic und Methodologie der Forstwissenschaft. Nordlingen, 1885. Heyer, Gust. Waldertragsregelung. Leipzig, 1893. JuDEicH, F. Die Forsteinrichtung. Dresden, 1893. LoREY, TuisKO. Handbuch der Forstwissenschaft. 3d edition, Tubingen, 1913. Stotzer, H. Die Forsteinrichtung. Frankfurt, 1898. Weber, Rudolf. Lehrbuch der Forsteinrichtung. Berlin, 1891. Weise, W. Ertragsregelung. Berlin, 1904. List of the most important works dealing with Forest Mensuration, in French. From bibliography published in "Studies of French Forestry," by T. S. Woolsey, Jr.: L'amenagement des forets (2d Edit.). Puton. Paris, 1874. Notice sur les dunes de la Coubre. Vasselot de Regne. Paris, 1878. Amenagement des forets-Estimation. Fallotte. Carcassonne, 1879. La methode du controle de Gurnaud. Grandjean. Paris, 1885. L'art forestier et le controle. Gurnaud. Besangon, 1887. L'amenagement des forets (V. Edit.). Tassy. Paris, 1887. Traite d'economie forestiere. Puton. Paris, 1888. Cours d'amenagement professe a I'Ecole forestiere (1885-1886) 2 cahiers. Reuss. Nancy, 1888. Diagrammes et calculs d'accroissement. Bartet. Nancy, 1889. Guide theorique et pratique de cubage des bois. Frochot. Paris, 1890. La methode du controle d I'Exposition de 1889. Gurnaud. Pans, 1890. Note sur une nouvelle methode forestiere dite du controle de Gurnaud. de Blonay. Lausanne, 1890. Traite d'economie forestiere. Amenagement. Puton. Paris, 1891. Le traitement des bois en France. Broillard. Paris, 1894. Estimations et exploitabilites forestieres. Bizot de Jontenz. Gray, 1894. Notes pour la vente et Tachat des forets. Galmiche. BesanQon, 1897. Notes forestieres— Cubage, estimation, etc. Devarenne. Chaumont, 1889. Economic forestiere. Huff el. Paris, 1904-07. Cubage des bois sur pied et abattus manuel pratique. Berger, Levrault et al. Paris, 1905. Mathematiques et Nature. Broillard. Besangon, 1906. Aide memo ire du forestier-Sylviculture. Demorlaine. Besangon, 1907. INDEX PAGE Abney clinometer 239 Abnormal cross sections 17 plots, rejection, yield tables 404 Absolute form factors 212 quotient 207 versus relative accuracy in mensuration 3 Accuracy in timber estimating, limits of 301 of results in timber estimating, choice of system for 261 of timber estimates, methods of improving 288 of volume tables, checking 189 of yield predictions 412 Accurate formula log rules 65 log rules, need for 50 Acre, area of 6 Actual density of stocking, determination of 413 estimate or measurement of the dimensions of every tree of merchant- able size 257 Adirondack standard or market 28 Adoption of a standard log length for volume tables 182 Advantages of graphic plotting of data 106 Age, as affected by suppression 341 average, definition and determination 337 classes, group form, separation 418 in yield tables 397 economic 341 from annual whorls 337 groups, yield tables for 412 in even-aged versus many-aged stands, the factor of 325 of average trees and of stand, determining 339 of seedling 336 of stand, determining 335, 339 of stands relation to volume 449 of timber, effect on methods of estimating 265 of trees, determining 335 separation of, in yields 416 Ake log rule 36 Annual increment of many-aged stands 390 whorls of branches as an indication of age 337 Applicabihty of Hoejer's formula in determining tree forms 210 523 524 INDEX PAGE Application of graphic method in constructing volume tables 169 of yield tables in predicting yields 322 Appolonian paraboloid 19 Appraisal, timber as distinguished from forest survey 269 Arbitrary standards in constructing log rules 49 Area determination, importance in timber estimating 267 for age groups on basis of diameter groups 422 for two age groups on basis of average age 419 of plots in yield tables 397 separation of in yields 416 units, size, relation to per cent of area to be estimated 262 Areas determined from density factor 416 of circles, table LXXVIII 490 of cross sections 17 of crowns 423 of different types, separation, method 290 of immature timber, growth on 451 separation of, effect on density 453 Arkansas, statute log rule 68 Average age, basis for determining volume and area of two age groups 419 definition and determination 337 Average board-foot volume, tree containing 311 diameter growth, determination 346 heights of timber and site classes 291 heights of trees based on diameter 258 log method of estimating 143 stand per acre from partial estimate 260 trees, age, determining 339 trees, volume and diameter, determination of 338 Averages employed in timber estimating, six classes of 258 Ballon log rule 75 Barbow cruising compass 248 Bark as a waste produ(!t 13 as affecting diameter in volume tables 150 marks, log 99 measurement in cords 134 volume of 163 width, measurement for volume 161 Basal area, definition 7 areas, table LXXVIII 490 use in predicting yields 415 Base line 281 Basis for board-foot volume tables 182 for cordwood converting factors , 127 of determining dimensions of the frustum 219 Baughman log rules 72 Bangor log rule 85 Baur's method of constructing yield tables 396 Baxter log rule 67 INDEX 525 PAGE Beaumont log rule 85 Big Sandy Cube rule 33 Billets, definition 14 measurement 122 products made from 14 Biltmore pachymeter 248 stick 230 errors in use of 232 Table XXXVIII 232 graduation 233 Table XXXIX 233 Blank areas, separation in estimating 289 Blodgett foot 30 or New Hampshire log rule 30 Board-feet, basis of application to standing timber 139 errors in use of cubic rules for 42 frustum form factors for merchantable contents in 218 log rules expressed in, but based directly upon cubic contents 34 merchantable form factors for 225 volume tables for 182 Board-foot contents, construction of log rules for 58 middle diameter as a basis for 46 of logs 40 rules of thumb 252 converting factors for various piece products. Table LXXVI 478 log rules, limitations to conversion of 83 necessity for 40 rules, formula based on cubic contents 35 volume tables, construction of 188 volume, tree containing average 311 measure, definition 8 log scaling for 88 Bole, in volume tables 158 Bolts, definition 14 measurement 122 products made from ^ 14 Borer, increment 358 Boundaries, determination in timber estimating 267 Boynton log rule 85 Branch wood or lapwood in volume tables 177 Breakage 116 Breast-high form factors 212 , Table LXXXII 497 Breymann's formula 22 British Columbia log rule 64 Brubaker log rule 85 Brush, effect on width of strips 275 Bulk products, forms of 11 Business, definition 2 Butt rot 110 526 INDEX PAGE Calcasieu log rule 36 Calculation of true frustum form factor 221 of volumes of frustums 221 California log rule 75 Caliper scale 97 definition 23 Calipers, description and method of use 227 Canada, Dominion forestry branch, log rule 73 Canadian log rules 76 Carey log rule 66 Cat faces 115 Cedar, western red, poles 469 white, poles 467 Center rot 108 Chain, unit of measurement, definition 6 Champlain log rule 65 Chandler, B. A 220 Chapin log rule 85 Character and utility of frustum form factors 219 of crown tree for volume tables 157 of growth per cent 318 Chart of growth studies 328 Check estimating 308 Checking the accuracy of volume tables 189 Check scaUng. .' 117 Checks, heart 112 surface 115 Chestnut oak, height growth, Milford, Pa., Table LVII 371 volume growth, cubic, Table LVIII 376 poles, minimum circumference, Table LXXII 472 Choice of a board-foot log rule for a universal standard 84 system for timber estimating with relation to accuracy of results .... 261 of units in timber estimating 140 Christen hypsometer 243 Circular plots, sizes. Table XLII 286 Classification and averaging of tree volumes according to diameter and height classes 163 of tree, measurements required in volume tables 156 of trees by diameter 151 height in volume tables 151 Clement's log rule 66 Click's log rule 66 CUnometer, Abney 239 Codominant tree, definition 158 Columbia River Log Scaling and Grading Bureau log grades 460 Combination log rules 76 volume tables for two or more products 193 Common grades of lumber 457 Comparison of growth for diameter classes 360 of log rules based on cubic contents, Table II 37 INDEX 527 PAGE Comparison of log rules based on diameter at middle and at small end of log . . 26 on formulae 61 of scaled and cubic contents by different log rules 36 Compass, hand 276 staff 277 Composition of stands as to species, effect on yield 393 Computation of volume of the tree 161 Cone 19 Connecticut River log rule 68 Constantine log rule 34 Construction and use of local volume tables 174 of board-foot volume tables 188 of a log rule, standardization of variables in 49 of log rules based on diagrams 72 mathematical formulae 59 for board-foot contents 58 for mill talUes 78 of standard volume tables for total cubic contents 154 of volume table from frustum form factors 224 of yield table with site classes based directly on yields per acre . . . 406 on height growth 401 based on crown space, for many-aged stands 422 tables, Baur's method 396 Contents of standing trees, rules of thumb for estimating 251 solid, of logs, formulae 20 Conversion of board-foot log rules, limitations to 83 of International rule j-inch saw kerf for other widths of kerf, Table XIII 81 of log rules with J-inch saw kerf to other widths of kerf. Table XIV . . 82 of values of a standard rule to apply to different widths of saw kerf and thickness of lumber 80 of volume tables for cubic foot, to cords 180 Converter poles 473 Converting factors, cordwood basis for 127 for cordwood. Table XX 129 for log rules 27 for sticks of different diameters 129 lengths 128 piece products to board-feet 478 standard cordwood 128 stacked cords to board-feet, factors for 135 Cook log rule 35 Coordination of merchantable heights with top diameters 184 Cord foot 123 , long 121 measure 121 definition 7 discounting for defects in 133 Cords, conversion of volume tables from cubic feet to 180 Cord, short 121 528 INDEX PAGE Cord, standard, definition 7 versus short cords and long cords 121 volume tables for 177 to board-feet, factors for converting 135 Cordwood converting factors, basis for 127 standard 128 log rules 132 methods of measurement 123 rule, Humphrey caliper 132 weight as a measure of 137 Correction factors for volume, use of 293 of average stand per acre 260 Cost of estimating timber 302 Count, and average tree in estimating 259 and partial tally of trees in estimating 259 Cracks, frost 1 12 Crook or sweep, deductions for. Table XVIII 116 in scaling 116 waste from 51 Crooked River log rule 35 Cross sections, abnormal 18 diameters and areas 17 Cross ties 474 volume tables for 191 Crown class and suppression as affecting height growth 366 definition 157 effect on diameter growth 353 cover, density of 424 of tree, character for volume tables 157 space, yield tables based on, for many-aged stands 422 spread of loblolly pine, Ala., Table LXI 389 Crowns, areas of 423 width of, measurement 423 Cruisers' method, Lake States estimating 283 methods. Southern estimating 283 Cuban One Fifth log rule 34 Cube Rule, Big Sandy 33 Cubic and board foot contents of logs compared. Table III 41 contents of cylinders, Table LXXVII 480 scaled by various log rules, Table II 37 log rules based directly upon, but expressed in board-feet 34 on 26 of logs, measurement 16 scaled as board feet, by different log rules, comparison . . 36 of squared timbers, log rules for . 33 of stacked wood, soUd 124 rules of thumb 251 total, construction of standard volume tables for 154 weight as a basis of measuring 33 foot, use of, in log scaling 31 INDEX 529 PAGE Cubic measure, definition 8 in log measurements 28 relation to true board-foot log rules 39 stacked, definition 7 measure as a substitute for 121 meter in log measurement 28 rules for board-feet, errors in use of 42 volume, log rules based on 28 merchantable, standard volume tables 177 Cull factor, or deductions for defects in timber estimating 271 in log scaling, relation to grades of timber 458 in volume tables 179 Cumberland River log rule 35 Current annual growth 315 growth, compared with yield tables and mean annual growth 445 loblolly pine, diameter, Table LVI 363 per cent 429 permanent sample plots for measurement of 443 spruce, Adirondacks, Table LIV 360 use of yield tables in predicting 436 height growth 371 periodic growth based on diameter classes 358 or periodic growth of stands, measurement 436 Curves, harmonized, for volumes based on height 170 for standard volume tables based on diameter 169 for taper tables, based on D. B. H 200 on total heights of tree 202 original based on height above stump 197 Cut-over areas, application of yield tables ba-sed on age to 441 growth on 438 Cylinder 19 as the standard of scaling 90 d'Aboville method for determining form quotients 248 Data required from forest survey for growth 447 which should accompany a volume table 188 D. B. H., correlation with stump growth 348 definition 150 merchantable limit at 177 Decades, method of coimting 343 Decimal C, Scribner log rule 74 rule, Scribner 73 values below 12 inches, Scribner log rule. Table XII 74 Deducting a per cent of total scale 107 Deductions by sectors 115 by slabs 114 for crook or sweep. Table XVIII 116 for defects in timber estimating 271 from scale for unsound defects 105 from sound scale versus over-run 90 530 INDEX PAGE Defect, effect upon grades of logs 460 Defective logs, merchantable 99 scaling of 105 trees, measurement for volume tables 183 Defects, deductions for, in timber estimating 271 exterior 113 in cord measure, discounting for 133 in lumber 456 interior 108 or cull in volume tables 179 sound and unsound 103 unsound, deductions from scale for 105 Degree of uniformity of stand as affecting methods employed in estimating. . . . 265 Dendrometers 247 Density factor, determination of areas from 416 factors, application in prediction of growth from yield tables 414 for mature stands, effect of separation of areas of immature timber 453 of crown area 424 of stand, effect on diameter growth 352 of stocking as aiTecting growth and yields 392 of stocking, empirical 413 of stocking, standard for normal 397 Derby log rule ' 36 Derivation of local volume table from standard volume tables 175 of standard breast-high form factors 213 Description of plot, yield tables 399 Determination of what constitutes a merchantable log 99 Determining the age of stands 335 of trees 335 Diagrams, construction of log rules based on 72 in construction of log rules 58 use of, for deductions in scaling 106 Diameter alone, versus diameter and height as basis of volume tables 152 and height classes, classification and averaging of tree volumes by ... . 163 at middle of log, scahng practice based on 97 at small end of log, scaling practice based on 91 breast high 150 in measuring standing trees 226 Classes 227 comparison of growth for 360 current periodic growth based on 358 clasification of trees by 151 groups as basis of age groups 422 growth, basis for determining 342 computation of 346 correction for seedUng age 348 effect of species on 351 in even-aged stands, laws of 354 in many-aged sliands, laws of 357 INDEX 531 PAGE Diameter growth of trees growing in stands, factors influencing 351 on sections, measurement of •. 342 purpose of study 342 relation to volume growth 374 spruce, Table LI 345 harmonized curves for volume based on 169 in determination of log grades 459 instruments for measuring 227 of average trees, determining 338 of log, relation to per cent of utilization in sawed lumber 40 tape 229 Diameters, abnormal 18 and areas of cross sections 17 bark as affecting, in volume tables 150 measured at ends of log 22 at middle of log 23 point of measurement, in volume tables 148 scaling 92 Dimensions of frustum, basis, in form factors 219 of stick, effect of, on solid contents of stacked wood 126 of tree containing average board-foot volume 311 Diminishing numbers, law of 318 Direct ocular estimate of total volume in stand 256 Discomiting for defects in cordwood measure 133 Distances between strips in estimating 264 Doyle-Baxter log rule 77 Doyle log rule 68 rule, errors in, effect upon scaling and over-run 70 -Scribner log rule 76 Dominant tree, definition 158 Drew log rule 85 Durability 466 Dusenberry log rule 85 Economic age of trees 34I Edgings, waste from 50 Effect of dimensions of stick on solid contents of stacked wood 126 of errors in Doyle rule upon scaling and over-run 70 of irregular piling on solid contents of stacked wood 124 of losses versus thimiings upon yields 324 of minimum dimensions of merchantable boards upon deductions in scaling 107 of seasoning on volume of stacked wood 123 of variation in form of sticks on solid contents 125 Empirical density of stocking 4I3 yield tables 396 use of 413 English system of measurement 6 Errors in Doyle rule, effect upon scaling and over-nm 70 in use of Biltmore stick 232 of cubic rules for board-feet 42 532 INDEX PAGE Estimate, ocular, of total volume 256 of every tree 257 Estimates covering a part of the total area 273 extensive 308 total or 100 per cent 271 Estimating a part of the timber as an average of the whole 257 by means of felled sample trees 310 by plots arbitrarily located 297 contents of standing trees, rules of thumb 251 log as the unit of 141 quality of standing timber 297 strip, systems in use 282 timber, choice of units in 140 cost 302 tree as a unit in 144 use of forest types in 288 Estimation of standing timber, principles underlying the 255 of tree dimensions, ocular. 234 Evansville log rule 35 Even-aged stands, laws of diameter growth 354 normal yield tables for 395 versus many-aged form of stands 388 stands, definition 337 Extensive estimates 308 Extension, Scribner log rule 74 Exterior defects 113 Fabian's log rule 76 Face, lumber 456 Factors affecting the growth of stands 384 determining the methods used in timber estimating 255 width of strips 274 for converting stacked cords to board-feet 135 Factory or shop grades 457 Faustmann hypsometer 240 Favorite log rule 85 Felled sample trees, methods of estimating 310 Fence stays 473 Fifth girth 25 Finance, forest, relation to mensuration 3 Finch and Apgar log rule 85 Finished lumber grades 456 Finishing grades 457 Fixed or variable limits for top diameters 183 Florida, statute log rule 68 Forest cover, map 268 finance, relation to mensuration 3 growth determination for, coordination of forest survey 447 management, relation to mensuration 3 mensuration, definition 1 INDEX 533 PAGE Forest property, definition ' 1 Service hypsometer 241 standard valuation survey 282 survey as distinguished from timber estimating 268 coordination with growth determination for forest 447 data required for growth 447 definition 5 surveying, as a part of the forest survey 270 relation to mensuration 5 survey, timber appraisal distinguished from 269 total increment of, inclusive of immature stands 443 .types, use in estimating 288 valuation, relation to timber appraisal 269 Forestry, relation to growth measurements 2 Forests composed of all age classes, growth per cent of 434 having a group form of age classes 418 Form as a third factor affecting volume 196 class, determination from form point. Table XL 250 classes and form factors 205 and universal volume tables as applied to conditions in America. . 215 based on form quotient 206 factor, Riniker's absolute 212 factors 211 absolute 212 breast-high 212 for board-feet 225 frustum, character and utility 219 merchantable 214 normal 212 standard breast-high 213 height 215 of logs, the 18 of red pine 210 of stands 388 of sticks, effect on solid cubic contents 125 of trees and taper tables 196 Hoejer's formula for 209 of white pine 210 point method of determining form classes, Jonson 249 position of, to determine form class; Table XL 250 quotient, absolute 207 as the basis of form classes 206 quotients, d'Aboville method for determining 248 of trees, wind pressure 208 relation to volume and diameter growth 374 Formula for board-foot rules based on cubic contents 35 for tree form, Hoejer's 209 Huber's 20-21 log rules 65 log rules, inaccurately constructed 67 534 INDEX PAGE Formula, Newton's 21 prismoidal 21 Schiffel's, derivation 206 use in computing volume of tree 163 Smalian's 20-21 Formulae, general, for all log rules 77 in construction of log rules 58 waste from saw kerf 53 Forties, unit of estimating 263 Forty, definition 6 Forty- five log rule 85 Frost cracks 112 Frustum, basis of determining dimensions of, in frustum form factors 219 form factor, principle of 278 true, calculation of the 221 factors, character and utility 219 construction of volume table from 224 for merchantable contents in board-feet 218 Frustums 20 volume, calculation 221 Full and scant thicknesses of boards as aflfecting over-run 49 General formula? for all log rules 77 Girth as a substitute for diameter in log measurements 24 Glens Falls standard 28 Goble log rule 33 Graded log rules 78 applied to the log, in estimating 299 tables 195 volume tables 193 applied to tree in estimating 299 Grades, finishing 457 of lumber 455 and log grades 103 in estimating, method based on sample plots and log tables . 300 in standing timber 298 relation to cull in log scaling 458 log 103 Grading rules. Southern yellow pine 457 Graduation of Biltmore stick, Table XXXIX 233 Graphic method, application in constructing volume tables 169 of determining diameter growth. .' 347 plotting of data; its advantages 166 Graves, H. S. Method of stem analysis 382 Ground rot 110 Group form of age classes, separation of areas 418 Growth and yields, density of stocking as affecting 392 by diameter classes, projection 361 correlation of stump with D. B. H 269 current annual 315 INDEX 535 PACK Growth current periodic, leased on diameter classes 358 data, relative utility of different classes of 327 determination for forest, co-ordination of forest survey with 447 diameter, purposes of study 342 effect of treatment on 391 for diameter classes, comparison of 360 increased, method of determination 363 loblolly pine, old field, diameter; Table LIII 350 mean annual 315 of stands after cutting, increased 438 reduced 439 • current or periodic, measurement 436 factors, affecting 384 prediction by growth per cent 432 of trees as basis for method of predicting current growth of stands 436 in diameter 342 in height 365 in volume 374 on areas of immature timber 450 on even-aged stands, in large age groups 412 per cent 316 character 318 definition 429 determination 429 in forests composed of all age classes 434 in quality and value 435 to determine growth of stands by comparison with measured plots 433 use to predict growth of stands 432 periodic 315 annual 315 prediction by projecting past growth of trees 323 short leaf pine, diameter, La., Table LV 362 studies, chart of 328 purpose and character 315 volume for single trees, computation 289 substitution of tapers for 379 Hand compass, use in strip surveys 276 Hanna log rule 75 Harmonized curves for standard volume tables based on diameter 169 for volume, based on height 170 Heart checks 112 Height classes, tree volumes averaged by 163 classification of trees by, in volume tables 151 growth a basis for site qualities 386 basis for site classes in construction of yield table 401 chestnut oak, Milford, Pa., Table LVH 371 current 371 influences affecting 365 536 INDEX PAGE Heiglit, growth of trees in 365 , measurement 368 relations to diameter growth 367 substitution of curves of height on diameter 371 harmonized curves for volume based on 170 of seedlings, western yellow pine, Table L 336 of stump 156 total measurement 156 Heights, measurement of 235 measuring, technique 245 of timber, average, and site classes 291 total versus merchantable 184 Herring log rule 85 Hewn ties 474 Heyer's method, xylometric for cordwood 132 Hoejer's formula for tree form 209 Holland log rule 76 Hop poles 473 Hoppus, or Quarter Ciirth log rule 25 rule 34 Horseshoe method of estimating 284 Hossfeld's formula 22 Huber's formula 20 in measuring branch wood 177 use in computing volume of tree 162 Humphrey caliper cordwood rule 132 Hybrid log rules 76 Hypsometer, Christen 243 Faustmann 240 Forest Service 241 Klaiissner 236 Merritt 238 Weise 240 Winkler 241 Hypso meters 235 based on the pendulum or plumb-bob 239 Idaho, statute log rule 73 Immature stands, increment of, as part of total increment of forest 443 timber, growth on 450 Importance of area determination in timber estimating 267 Increased growth of stands after cutting 438 method of determination 363 Increment borer 358 use • 336 Index yield tables 396 Influence of log rule on deductions for defects 107 Influences affecting height growth 365 over-run, methods of manufacture 47 the log rule itself 47 INDEX 537 PAGE Inscribed Square log rule 33 Inspection and measurement of piece products 477 Instruments for measuring diameter 227 Interior defects 108 Intermediate tree, definition 158 International log rule for i-inch kerf, Table LXXX 493 g-inch kerf log rule 63 j-inch kerf log rule 64 Introduction of taper into log rules 44 Inventory of timber 268 Isosceles triangles as basis of height measure 235 Jack Pine, growth, Minnesota, Table XLVII 318 Jonson form point method of determining form classes 249 Tor 207 Klaussncr hypsometer, principle of 235 Knots, rot entering from 112 Lagging 474 Lake states, cruisers' method of strip estimating 283 Lapwood, in volume tables 177 Large timber on the Pacific Coast, methods of estimating 287 Law of diminishing numbers as affecting growth of trees and stands 318 Laws of diameter growth in even-aged stands, based on age 354 in many-aged stands, based on diameter 357 Leaning trees, height, measurement 245 Legal status of scaler 119 Lehigh log rule 35 Lengths, log 16 scaling 91 Licking River log rule 86 Limitations of taper tables 204 to conversion of board-foot log rules 83 Limits of accuracy in timber estimating 301 Loblolly pine crown spread, Ala., Table LX 389 current growth, diameter, Table LVI 363 old field, growth in diameter. Table LIII 350 Local volume table, form, Table XXXI 175 tables, definition 153 derivation from standard tables 175 construction and use 174 Log as the imit of estimating 141 brands 99 grades 103 defect, effect upon 460 determination 459 examples, hardwoods 460 softwoods 460 purpose 455 length, standard for volume tables 182 538 INDEX PAGE Log lengths 16 merchantable, what constitutes a 99 rule, Baxter 67 British Columbia 64 Blodgett or New Hampshire 30 board-foot, choice of, for a universal standard 84 Carey 66 Champlain 65 Clements' 66 CUck's 66 Doyle 68 Doyle-Scribner 76 for round edged lumber, Massachusetts 79 influence on deductions for defects 107 International i-inch kerf 63 j-inch kerf 64 McKenzie 63 Maine 76 New Brunswick 76 New Hampshire or Blodgett 30 Preston 66 Quebec 76 Scribner 73 Scribner-Doyle 77 Spaulding 75 Tiemann 67 Thomas' accurate 66 Wilson 66 based on cubic contents 26 on diagrams, construction of 72 on diameter at middle and at small end of log, comparison .... 26 on formulae, comparison of 61 on mathematical formula, construction of 59 rules, Baughman 72 board-foot, necessity for 40 Canadian 76 comparison of scaled cubic contents by different 36 definition 8 expressed in board-feet but based directly upon cubic contents 34 for board-foot contents, construction of 58 for cubic contents of squared timber 33 formula, accurate 65 from mill tallies, construction 78 general formulae for all 77 graded 78 appUed to log, in estimating 299 in use, based on cubic volume 28 need for more accurate 50 obsolete 36, 85 taper, introduction of, into 44 INDEX 539 PAGE Log rules, true board-foot, relation to cubic measure 39 run or average log method 143 scale, the 88 scaling, cull, relation to grades of lumber 458 for board measure 88 use of cubic foot in 31 stamps 99 tables, graded 195 Logging conditions 269 Logs, board-foot contents 40 defective, scaling of 105 measurement of cubic contents 16 solid contents of, formulae 20 technique of measuring 22 the form of 18 Long cord 122 Losses of trees, correction for, in growth prediction 437' versus thinnings, effect upon yields 324 Lot, area unit, definition 6 Lumber, defects 456 grades and log grades 455 of 103 Lumbering, relation to timber estimating 2 Limberman's Favorite log rule 85 log rule 35 Lumber, thicknesses of, conversion of values of a standard rule to apply to different 80 Maine log rule 76 Management, forest, relation to mensuration 3 Manufacture, the factor of waste in 13 Manufactured products, forms of 11 Many-aged form of stands 388 stands, annual increment of 390 application of yield table based on crown space to 425 definition 337 factor of age in 325 laws of diameter growth 357 yield tables based on crown space for 422 Map, forest cover 268 soil 268 timber types 268 topographic 268 Market, cubic standard 28 Massachusetts log rule for round-edged lumber 79 Mathematical formulae, construction of log rules based on 59 Mathematics, relation to mensuration 3 McKenzie log rule 63 Mean annual growth 315 per cent 429 540 INDEX PAGE Mean diameters, error in use of 23 end formula, use in computing volume of tree 161 sample tree method. 311 Measurement of bark in cords 134 of cordwood, methods of 123 of current growth on permanent sample plots 443 of defective trees for volume tables 183 of diameter growth on sections 342 of height by a straight stick held in hand 235 growth 368 of heights 235 of log lengths 16 of permanent sample plots 312 of piece products 466 of solid contents of stacked cords 132 of stacked wood cut for special purposes 122 of standing trees 226 of tree diameters 227 of upper diameters 247 of waste 179 of width of crowns 423 systems used in forest mensuration 6 Measurements of the tree required for classification in volume tables 156 required for tree analyses 289 on each plot, in yield tables 398 to obtain the volume of the tree. Systems used 158 Measuring and predicting the current or periodic growth of stands 436 diameter, instruments for 227 heights, technique of 245 logs, technique of 22 standing timber for volume 226 stick for log lengths 16 Medwiedew's method 387 Mensuration, Forest, definition 1 Merchantable boards, minimum dimensions, effect of, in making deductions in scaling 107 Merchantable contents in board-feet, frustum form factors for 218 cubic volume, standard volume tables 177 form factors 214 for board-feet 225 heights as a basis for tree classes 184 coordination with top diameters 184 limit in tops and at D. B. H 177 log, determination of 99 versus used length 178 Merritt hypsometer 238 for merchantable heights 246 Method of constructing taper tables 197 of counting decades for growi.h 343 of deducting sawdust first, construction of log rules 59 INDEX 541 PAGE Method of deducting slabs first, construction of log rules . . . ; 59 of determining form classes, Jonson form point 249 of graded log rules applied to the log 299 volume tables applied to tree 299 of mill-run applied to stand 299 of running strip surveys 276 of separating areas of different types 290 of volume growth by use of tapers 379 Methods of estimating dependent on use of plots arbitrarily located 297 systematically spaced 285 Pacific coast 284 • plots, large timber on the Pacific coast 287 spruce in Northeast 287 strip, horseshoe 284 Lake States timber cruisers 283 southern timber cruisers 283 valuation survey 282 Yale Forest School 284 which utilize types and site classes 292 of height measurement based on similarity of isosceles triangles 235 of right triangles 238 of improving the accuracy of timber estimates 288 of making deductions for defects 105 of measurement of cordwood 123 of scaling a log, effect of. Table V 45 of timber estimating 267 of training required to produce efficient timber cruisers 303 used in constructing log rules for board-feet 58 in timber estimating, factors determining the 255 Metric system, conversion table. Table LXXIX 492 of measurement 6 Middle diameter as a basis for board-foot contents 46 Mill factor, substitution for log rules, in universal tables 146 grade or mill scale studies 461 -run as basis of grades in standing timber 299 -scale studies 461 method of conducting 462 not a check on scaling 118 tallies, construction of log rules from 78 talh^, in construction of log rules 58 Miller log rule 85 Mine ties 474 timbers 473 Miner log rule 35 Minimum dimensions of merchantable boards, effect on deductions in scaling. ... 107 size of merchantable logs 99 Minnesota, statute log rule 73 Mississippi, statute log rule 68 Mixed species, yield tables for stands of 408 stands, effect on yield 393 542 INDEX PAGE Mlodjiansky, A. J., method of stem analysis 382 Moore-Beeman log rule 68 National forests, log rule 73 Necessity for board-foot log rules 40 Need for form classes in volume tables 205 Neiloid 19 Nevada, statute log rule 73 New Brunswick log rule 76 New Hampshire or Blodgett log rule 30 Newton's formula 20-21 Noble and Cooley log rule 35 Normal density 397 form factors 212 yield tables for even-aged stands 395 use of, by reduction 413 Northwestern log rule 86 Number and width of strips, relation 274 of trees per acre, influence on yields 414 required for a volume table 155 Oak, White and Red, log grades 460 Obsolete log rules 36, 85 Ocular estimating 256 estimation of tree dimensions 234 Old Scribner log rule 73 Ontario, Doyle rule, over-run 71 log rule 68 Orange River log rule 36 Oregon, statute log rule 73 Over-run, definition and basis of 46 deductions from sound scale versus 90 effect of errors in Doyle rule upon 70 influences affecting. Methods of manufacture 47 The log rule itself 47 -topped tree, definition 158 Pace, unit of measurement, definition 6 Pachymeter, Biltmore 248 Pacific Coast method of estimating 284 Pacing, use in estimating 262 Paraboloid, appolonian, definition 19 Parson's log rule 85 Partial area estimates 273 estimates 257 Partridge cordwood rule 133 log rule 36 Peck in cypress 113 Peeled or sohd-wood contents, volume tables for 176 Pendulum, or plumb-bob, hypsometers based on the 239 Penobscot log rule 85 INDEX 543 PAGE Per cent of area to be estimated, relation to size of area 262 of total area required in estimating, Table XLIV 292 scale as a deduction in scaling 107 of waste in a log, total 55 Periodic annual growth 315 growth 315 of stands 436 per cent 429 Permanent sample plots for measurement of current growth 443 measurement 312 Personnel, scaling 1 18 Philippine Islands, log measurement 28 Piece, as a unit of timber estimating 140 measure definition 7 products, converting factors for board feet, Table LXXVI 478 inspection and measurement 477 measurement of 466 volume tables for 191 PiUng 470 dimensions. Table LXXV 473 irregular, effect on solid cubic contents of stacked wood 124 Pitch seams 112 Plots, arbitrarily located, use of in estimating 297 permanent sample, measurement 312 systematically spaced, in estimating 285 used in estimating 263 Plotting, graphic 166 Plumb-bob, hypsometers based on the 239 Point of measurement of diameters in volume tables 148 Pole lagging 474 ties 474 Poles and saplings, stand table for 454 chestnut, specifications 469 growth of 452 small 471 specifications 467 Portland log rule 35 Posts, large posts and small poles 471 Predicting future growth, methods of 320 yields, application of yield tables in 322 Prediction of current growth of stands, methods 436 of growth by projecting past growth of trees into the future 323 from yield tables, by application of density factor 414 in even-aged stands, yield tables for 412 of stands, by growth per cent 432 Pressler's formula for volume growth per cent 429 Preston log rule "" Principle of the Christian hypsometer 243 of the frustum form factor 218 of the Klaussner hypsometer 235 544 INDEX PAGE Principles underlying the estimation of standing timber 255 the study of growth 315 Prismoidal formula 21 Products, forms of, into which the contents of trees are converted 11 made from bolts and billets 14 volume tables for two or more, combination 193 Projection of growth by diameter classes 361 P*urpose and character of growth studies 315 and derivation of tables for cubic volume of trees 177 Purposes of study of height growth 365 Qualities of site, separation in field 448 volume growth a basis for 385 Quahty, growth per cent 435 of site 384 as affecting height growth 366 effect on diameter growth 352 of standing timber, estimating 297 Quarter girth 25 or Hoppus log rule 34 section, definition 6 Quebec log rule 76 Record of data on plots, j-ield tables 400 of timber 276 Records, scale 98 Reduced growth of stands after cutting 439 Reduction in diameter, in scaling defective logs 105 in length, in scaling defective logs 105 Reisig method, xylometric, for cordwood 132 Relation between cubic measure and true board-foot log rules 39 current and mean annual growth 316 plots and area covered. Table XLIII 286 size of area units and per cent of area to be estimated 262 of cubic and board-foot contents of 16-foot logs. Table III 41 of diameter of log to per cent of utilization in sawed lumber 40 Relations of height growth and diameter growth 367 Relative diameter, in determining growth per cent 430 utility of different classes of growth data 327 Re-manufacturcd lumber, grades 456 Re-plottiiig curves, strip method 173 Resistance to wind pressure as the determining factor of tree form 208 Retracing boundaries 267 Right triangles, in measuring heights 238 Ruig shake 109 Riniker's absolute form factor 212 Ropp's log rule '. 86 Rot, butt 110 center 108 entering from knots 112 INDEX 546 PAGE Rot, stump 100 Rough lumber, grades 456 Roimd products 466 -edged lumber 14 Massachusetts log rule for 79 Rules of thumb, for board-foot contents 252 for cubic contents 251 for estimating the contents' of standing trees • 251 Rimning strip surveys, method of 276 Saco River log rule 36 St. Croix log rule 68 St. Louis Hardwood log nde 35 Sample plots, permanent, measurement 312 for measurement of current growth 443 trees, methods of estimating 310 Sap, stained ■ 115 Sapwood, volume 161 Saplings, growth of 451 Saw 1-erf, and slabbing, deductions in certain log rules. Table IX 62 as affecting over-run 48 conversion of values of a standard rule to apply to different widths of 80 waste from 53 Saw kerfs of different widths, corrections for 55 Sawdust, method of deducting 60 Sawed lumber, superficial contents 13 Scale book 99 caliper • 97 definition 88 records 98 rule 88 stick 88 Scaler, legal status 119 Scalers 118 Scaling 88 check 117 cylinder as the standard of 90 diameters 92 from the stump 118 length of logs, taper as limiting 43 lengths 91 of defective logs 105 practice, based on measurement of diameter at middle of log, or caliper scale 97 practice, based on measurement of diameter at small end of log 91 in different logging regions. Table XVII 94 use of cubic foot in 28 Schiffels' formula, derivation 206 use in computing volume of tree. 163 values. Table LXXXI ,,..,.. • , • • 494 546 INDEX PAGE Schneider's formula for growth per cent on standing trees 431 Scribner decimal log rule 73 C log rule, Table LXXXVI 504 Scribner log rule 73 decimal values, Table XII 74 erroneously termed 68 extension 74 Scribner-Doyle log rule 77 Scribner's log and lumber book 68 Seams 112 pitch 112 Seasoning, effect on volume of stacked wood 123 Second growth hardwoods, yield table, Central New England, Table LXII 409 Section, definition, area unit 6 Sections, measurement of diameter growth on 342 Sectors, deduction by, for defects 115 Seedhng, age of 336 Seedlings, height, western yellow pine, Table L 336 Selection of trees for measurement in constructing volume tables 154 Separation of factors of volume, age and area 416 of site qualities in field 448 Seventeen Inch log rule 33 Shade, effect on diameter growth.. 353 Shake Ill Shingle bolts, definition 15 measurement 122 Shop grades 457 Short cord 121 Shortleaf pine, diameter growth. La., Table LV 362 Shrinkage 54 Similar triangles as basis of height measure 235 Simoney's formula 22 Site classes and average height of timber 291 based on height growth for construction of yield table 401 on yields per acre, for yield tables 406 use in estimating 292 classifications, standards based on height of tree at 100 years. Table LX . . 387 factors, or quality of site 384 qualities, height growth a basis for 386 separation in field 448 volume growth a basis for 385 Site quality, averaging for entire area 449 effect on diameter growth 352 Six classes of averages employed in timber estimating 258 Size of area units, relation to per cent of area to be estimated 262 Slabbing and sawdust deductions in 10 log rules, Table IX 62 waste, distribution, Table VII 56 Slabs and edgings, waste from 50 as affecting over-run 48 deductions by, for defects 114 INDEX 547 PAGE Slabs, method of deducting 59 Smalian's formula 20 use in computing tree volumes 161 Small poles 471 Soil map 268 Solid contents, effect of dimensions of stick on 126 of irregular piling on 124 of variation in form of sticks on 125 of logs, formulae 20 of stacked cords, measurement 132 wood 124 Table XIX 127 -wood contents, volume tables for 176 Sound scale, deductions from versus over-run 90 Southern timber cruisers' method of estimating 283 yellow pine, grading rules 457 poles, minimum dimensions, Table LXXI 471 Spaulding log rule 75 Species as affecting height growth 365 effect on diameter growth 351 Spoke billets, definition 15 Spruce, Adirondacks, current growth. Table LIV 360 growth on cut-over lands. Table LXVI 440 diameter growth of trees, Table LI 345 in Northeast, on large tracts, method of estimating 287 Square of Three-fourths log rule 35 Two-thirds log rule 35 Squared timbers, log rules for cubic contents of 33 Squares, definition 14 Stacked cords, measurement of solid contents 132 cubic measure, definition 7 measure as a substitute for cubic measure 121 or cord measure 121 wood, solid cubic contents of 124 Staff compass 277 Stained sap 115 Stamps, log 99 Stand, determining age of 339 per acre, estimated by eye 260 table, application in growth studies 421 for poles and saplings 454 tables 227 uniformity of, as affecting methods in estimating 265 Standard, Adirondack 28 breast-high form factors 213 cord 121 cordwood converting factors 128 for normal density of stocking 397 log length in volume tables 182 of scaling, cylinder as the 90 548 INDEX PAGE Standard, Twenty-two Inch 29 universal, choice of a board-foot log rule for 84 volume table, form. Table XXX 174 tables, construction, by curves 174 definition '. . .' 153 for cords 177 for merchantable cubic volume and cords 177 for total cubic contents, construction of 154 harmonized curves for, based on diameter 169 Standardization, need of, in forest measurements 10 of variables in construction of a log rule 49 Standards for yield tables 395 in constructing log rides 49 of site classification based on height of tree at 100 years. Table LX . 387 Standing timber, estimating, principles underlying 255 units of measurement for 139 trees, measurement 226 rules of thumb for estimating the contents of 251 Stands, form of 388 grown under management, yield tables for 407, 427 growth of, factors affecting 384 of mixed species, yield tables for 408 Stave bolts 15 Staves, lengths 122 Stem analysis, limitations of use 326 of a tree. Table LIX 378 purpose and application 374 Stereometric measurement of cordwood 132 Stillwell's Vade Mecum log rule 36 Strip estimating, systems in use 282 method of estimating 273 of replotting curves 173 surveys, method of running 276 Strips, relation of width and number, to area covered. Table XLI 274 tying in. The base line 281 used in estimating 263 width of, factors determining 274 Stulls 473 Stump, height of 156 heights 178 rot 110 scaling 118 tapers. Table LII 350 Stumpage value, definition. Relation to forest mensuration 3 of products as affecting accuracy sought in timber esti- mating 266 Substitution of mill factor for log rules in universal tables 146 of taper tables for tree analysis 382 Superficial board-feet, correction in per cents for lumber sawed less than one inch thick, Table XVI 274 INDEX 549 PAGE Superficial contents of lumber, correction of log rule for 83 of sawed lumber 13 estimates 308 Suppressed tree, definition . .*. 158 Suppression, age as affected by 341 as affecting height growth 366 Surface checks 115 defects 115 Survey, forest, as distinguished from timber estimating 268 definition 5 Surveying, forest, as a part of the forest survey 270 relation to mensuration 5 Sweep in scaling 116 waste from 51 System for timber estimating, choice of 261 Systems of measurement used in forest mensuration 6 of strip estimating in use 282 used in taking measurements of the tree for volume 158 Tally sheets 277 unit of measurement, definition 6 Tape, diameter 229 Taper as a factor in limiting the scaling length of logs for board-foot contents. . 43 definition 18 introduction into log rules 44 tables 196 definition and purpose 197 limitations of 204 method of constructing 197 substitution for tree analysis 382 Tapers, standard, as basis of volume tables 144 substitution for volume growth 379 Tatarian log rule 36 Technique of measuring heights 245 Tennessee River log rule 35 Texas, Doyle rule, over-rmi 71 Third and Fifth log rule 35 Thomas' Accurate log rule ... 66 Thurber log rule 68 Tiemann log rule 67 Table LXXXIV 500 comparison with Blodgett rule 42 reduced to small end diameters, Table LXXXV 502 Timber appraisal as distinguished from forest survey , 269 cruisers, training 303 estimates, accuracy, methods of imjjroving 288 estimating 9 choice of system for , 261 of vmits in MO definition 2 550 INDEX PAGE Timber estimating, factors determining the methods used in 255 forest sm-vey as distinguished from 268 importance of area determination in 267 limits of accuracy in 301 methods 267 six classes of averages employed in 258 record of 276 types, map 268 Top diameters, co-ordination of merchantable heights with 184 fixed or variable limits 183 versus variable, influence on frustum form factors 221 Topographic map 268 Topography, effect on methods of estimating 265 Tops, merchantable hmit in 177 Tor Jonson 207 Total growth on a large area, factors 447 height of tree, measurement 156 increment of a forest includes that of immature stands 443 or 100 per cent estimates 271 per cent of waste in a log 55 versus merchantable contents of logs 16 heights as a basis for tree classes 184 yield 315 Township, definition 6 Training of timber cruisers 303 Treatment, effect on growth 391 of stand, effect on diameter growth 353 Tree analysis, hmitations of use 326 measurements required for 289 purpose and application 374 substitution of taper tables for 382 substitution of volume tables for 375 as a unit in estimating 144 classes, total versus merchantable heights as a basis for 184 diameters, measurement 227 dimensions, ocular estimation of 234 form, Hoejer's formula for 209 resistance to wind pressure 208 record, in connection with volume tables 155 volume, computation 161 systems used in taking measurements of 158 Trees for measurement, selection for volume tables 154 standing, measurement 226 Trimming allowance 92 lengths, in measuring trees for volume 161 Truncated cone 19 neiloid 19 paraboloid ' 19 Twenty-two Inch standard 29 Two-thirds log rule 34, 35 INDEX 551 PAGE Tying in the strips. The base line 281 Types, forest, use in estimating 288 method of separating areas of different 290 use m estimating 292 Uniformity of stand as affecting methods in estimating 265 Units of measurement for standing timber 139 Universal standard, choice of a board-foot log rule for 84 tables, substitution of mill factor for log rules in 146 volume table 144 tables and form classes 215 Unsound defects, deductions from scale for 105 Unused log rules 85 Upper diameters, measurement 247 Use of correction factors for volume 293 of cubic rules for board feet, errors in 42 of diagrams for deductions in scaling 106 of forest types in estimating 288 Used length, versus merchantable 178 Utilization in tops 183 Valuation survey, forest service standard 282 Value growth per cent 435 Vannoy log rule 68 \'ariable standards, in constructing log rules 50 Vermont log rule 35 Volume, age and area, separation of, in yields 416 and age of stands, relation 449 and area for age groups based on diameter groups 422 for two age groups on basis of average age 419 and diameter of average trees, determining 338 correction factors for, in estimating 293 form as a third factor affecting 196 growth a basis for site qualities 385 analysis, utility 332 for single trees, computation 289 of trees in 374 per cent, Pressler's formula 429 of bark 163 of standing timber, measurement 226 of tree, computation 161 system used in taking measurements 158 table based on mill factors, Table XXVI 147 data which should accompany 188 from frustum form factors, construction of 224 tables, bark as affecting diameter in 150 based on actual volumes of trees 147 on standard tapers per log 144 board-foot, construction 188 standard or basis 182 552 INDEX PAGE Volume, tables, checking the accuracy of 189 classification of trees by height, in 151 combination for two or more products 193 construction, graphic method 169 conversion from cubic feet to cords 180 cords, standard 177 definition 144 diameter alone versus diameter and height as basis of 152 for board-feet 182 for peeled or solid-wood contents 176 for piece products 191 for railroad cross ties 191 graded 193 ajiplied to tree in estimating 299 local, construction and use 174 definition 153 derivation from standard tables 175 need for form classes in 205 point of measurement of diameters in 148 standard definition 153 for total cubic contents, construction 154 for merchantable cubic volume and cords 177 substitution for tree analysis 375 universal 144 Volumes, tree, classification by diameter and height 163 of frustums, calculation 221 of trees, actual, volume tables based on 147 Warner log rule 86 Waste, definition and measurement 179 from crook or sweep 51 from saw kerf 53 from slabs and edgings 50 in a log, total per cent of 55 in manufacture, factor of 13 in tops and limbs 13 or cull, effect, mill-scale studies 463 slabbing and sawdust, distribution. Table VII 56 Weight as a basis of measuring cubic contents 33 as a measure of cordwood 137 Weights per cord for various species. Table LXXXIII 498 Weise hjqjsometer 240 Western red cedar poles 469 minimum dimensions, Table LXX 470 West Virginia, statute log rule 73 Wheeler log rule 86 White cedar poles 467 relation between circumference and diameter, Table LXVIII 467 log rule 75 pine, yield table, Table XLVIII 321 INDEX 553 PAGE Width of strips, factors determining 274 single, of bark 161 Wilcox log rule 86 Wilson log rule 66 Wind pressure, resistance of, in tree form 208 Winkler hj^jsometer 241 Wisconsin, statute log rule 73 Worm holes 1 12 Yale Forest School method of estimating in southern pine 284 Yellow pine. Southern, grading rules 457 poplar, in Tennessee, yields of cordwood, Table LXV 426 Yield of second growth hardwoods in central New England, Table LXII 409 per acre, spruce, cutting to various diameter hmits, Table XLIX 322 predictions, accuracy of, factors affecting 412 table based on crown space, method of construction 424 construction with site classes based on height growth 401 on yields per acre 406 white pine, Table XLVIII 321 tables, age classes 397 application in predicting yields 322 area of plots 397 based on crown space for many-aged stands 422 on age, application to cut-over areas 441 construction 396 definition and purpose 395 empirical, use of 413 example 321 for stands grown under management 407, 427 of mixed species 408 measurements required on each plot 398 normal, for even-aged stands .■ 395 record of data on plot ". 400 rejection of abnormal plots 404 standards for 395 use of, in prediction of current growth 436 total 315 Yields, definition and purpose of study 320 density of stocking as affecting 392 effect of losses versus thinnings upon 324 of cordwood for yellow poplar in Tennessee, based on crown space. Table LXV 426 Youngiove log rule 86 Xylometers 132 Xylometric measurement of cordwood 132 L1BR.\RV Ol CONijKtbS DDDDfl'=]aH4b3 #