UNIVERSITY OF CALIFORNIA PUBLICATIONS 
 
 COLLEGE OF AGRICULTURE 
 
 AGRICULTURAL EXPERIMENT STATION 
 
 BERKELEY, CALIFORNIA 
 
 A WHITE FIR VOLUME TABLE 
 
 BY 
 
 DONALD BRUCE 
 
 BULLETIN No. 329 
 
 August, 1921. 
 
 UNIVERSITY OF CALIFORNIA PRESS 
 BERKELEY, CALIFORNIA 
 
David P. Barrows, President of the University. 
 
 EXPEKIMENT STATION STAFF 
 
 HEADS OF DIVISIONS 
 
 Thomas Forsyth Hunt, Dean. 
 
 Edward J. Wickson, Horticulture (Emeritus). 
 
 , Director of Resident Instruction. 
 
 C. M. Haring, Veterinary Science, Director of Agricultural Experiment Station. 
 
 B. H. Crocheron, Director of Agricultural Extension. 
 Hubert E. Van Norman, Vice-Director; Dairy Management. 
 
 James T. Barrett, Acting Director of Citrus Experiment Station; Plant Pathology. 
 William A. Setchell, Botany. 
 Myer E. Jaffa, Nutrition. 
 Ralph E. Smith, Plant Pathology. 
 John W. Gilmore, Agronomy. 
 Charles F. Shaw, Soil Technology. 
 
 John W. Gregg, Landscape Gardening and Floriculture. 
 Frederic T. Bioletti, Viticulture and Fruit Products. 
 Warren T. Clarke, Agricultural Extension. 
 John S. Burd, Agricultural Chemistry. 
 Charles B. Lipman, Soil Chemistry and Bacteriology. 
 Ernest B. Babcock, Genetics. 
 Gordon H. True, Animal Husbandry. 
 Walter Mulford, Forestry. 
 Fritz W. Woll, Animal Nutrition. 
 W. P. Kelley, Agricultural Chemistry. 
 H. J. Quayle, Entomology. 
 Elwood Mead, Rural Institutions. 
 H. S. Reed, Plant Physiology. 
 L. D. Batchelor, Orchard Management. 
 J. C. Whitten, Pomology, 
 f Frank Adams, Irrigation Investigations. 
 
 C. L. Roadhouse, Dairy Industry. 
 
 F. L. Griffin, Agricultural Education. 
 John E. Dougherty, Poultry Husbandry. 
 W. B. Herms, Entomology and Parasitology. 
 L. J. Fletcher, Agricultural Engineering. 
 Edwin C. Voorhies, Assistant to the Dean. 
 
 Division of Forestry 
 
 Walter Mulfokd Woodbridge Metcalf 
 
 Donald Bruce Emanuel Fritz 
 
 t In cooperation with office of Public Roads and Rural Engineering, U. S. Department of 
 Agriculture. 
 
A WHITE FIR VOLUME TABLE 
 
 By DONALD BRUCE 
 
 White Fir (Abies concolor) is of increasing commercial importance. 
 A few years ago this tree was usually left standing during logging 
 operations, as the value of lumber to be secured therefrom was not 
 sufficient to repay the cost of manufacture. To-day it is usually logged, 
 and at a profit, and in the future, as timber becomes scarcer, its value 
 will increase still more. It is therefore both natural that no accurate 
 volume table for this species should have previously been prepared, and 
 important that one should be made available for future use. 
 
 By means of the three-part table herein presented, the average 
 volume in board feet of trees of given diameters and heights may be 
 accurately determined. The table will not, however, give more than 
 approximately the volume of an individual tree. As every woodsman 
 knows, trees of the same diameter and height may vary widely in 
 volume. Some trees will therefore be larger than the tabular values 
 indicate and others smaller, but in averages of many trees these dis- 
 crepancies tend to counteract each other and for large groups of trees 
 disappear. 
 
 It is worth while to emphasize this point. Many woodsmen have 
 noted that an ocular estimate of an individual tree may be more exact 
 than one made by means of a volume table, and have hence thought 
 such tables useless. It must be remembered, however, that the exact 
 volumes of single trees are rarely of use, for what the timber owner or 
 operator is interested in is the combined or total volume of all the 
 trees of a given species on some specified area. Volume tables based 
 on the averages of hundreds of accurately measured trees, will give 
 this result as exactly as it is possible to obtain it, for they reduce to a 
 minimum the factor of the personal judgment of the estimator. This 
 is true, however, only where the table is properly used, and the follow- 
 ing precautions must be observed. 
 
 The right table must be selected. It has been found impossible to 
 prepare a single table that would be accurate for the whole state of 
 California, since growing conditions differ widely, and differences in 
 the form or shape of trees of similar height and diameter result. It 
 has been established, however, that this form is essentially similar on 
 two tracts, even if quite remote from one another, if the maximum 
 
42 UNIVERSITY OF CALIFORNIA EXPERIMENT STATION 
 
 average height to which the trees grow at maturity is approximately 
 the same. To determine the "site" of any given tract, then, the aver- 
 age height of the tallest tenth of the merchantable trees should be 
 estimated. If this be over 93^ 16-foot logs, Table I should be used; 
 if 73^2 or under, Table III, and for intermediate values, Table II. 
 
 Heights should be measured (or estimated if the estimator has 
 sufficient skill) in 16-foot logs, to the point in the top where the tree is 
 8 inches in diameter inside the bark. If, in accordance with the logging 
 practice of any region, it is evident that this represents too close a 
 utilization, a deduction for unused tops should be made in connection 
 with the cull factor. 
 
 Diameters should be measured (or estimated) outside the bark at 
 43^ feet from the ground, measuring (in the case of sidehill timber) 
 from the average ground level. 
 
 A deduction should be made for cull. The table is based on trees 
 measured as if sound, unbroken, and to be completely utilized. Per- 
 centage reductions must therefore be made for 
 
 (a) Rot, if present. 
 
 (b) Breakage, if inevitable even with careful handling. 
 
 (c) Unused tops (see above). 
 
 (d) Unused stumps (if the logging practice of the region cuts 
 stumps materially higher than 18 inches). 
 
 This cull percentage for white fir commonly ranges from 15 to 35 
 per cent, including all the above items; of these only the first two, 
 however, are of much importance. 
 
Bulletin 329 
 
 A WHITE FIR VOLUME TABLE 
 
 43 
 
 TABLE I. 
 
 Site I (Tallest 10% Merchantable Trees of Stand 9.6 Logs or Over) 
 Height — Number of 16-Ft. Logs 
 
 Diameter 
 Breast- 
 High 
 Inches 
 
 10 '... 
 
 12 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 3 
 4 
 4 
 4 
 5 
 
 5 
 
 7 
 
 8 
 
 10 
 
 11 
 
 9 
 11 
 13 
 16 
 19 
 
 VOLU 
 
 12 
 15 
 19 
 23 
 
 28 
 
 ME 
 
 30 
 37 
 
 Boar 
 
 48 
 
 D FE 
 
 ET IN 
 
 Tens 
 
 
 
 
 14 
 
 16 
 
 18 
 
 
 
 
 20 
 
 
 13 
 15 
 17 
 19 
 
 23 
 
 28 
 32 
 38 
 44 
 
 34 
 
 42 
 49 
 58 
 67 
 
 45 
 56 
 66 
 
 78 
 90 
 
 57 
 70 
 82 
 97 
 113 
 
 68 
 
 83 
 
 98 
 
 117 
 
 136 
 
 97 
 114 
 136 
 159 
 
 156 
 
 182 
 
 
 
 
 22 
 
 
 24 
 
 
 26 
 
 
 28 
 
 
 
 
 30 
 
 
 
 49 
 56 
 63 
 69 
 
 75 
 
 85 
 
 95 
 
 106 
 
 117 
 
 101 
 114 
 128 
 142 
 157 
 
 128 
 144 
 161 
 179 
 198 
 
 154 
 174 
 194 
 216 
 
 238 
 
 181 
 204 
 
 227 
 253 
 279 
 
 207 
 233 
 260 
 290 
 320 
 
 234 
 263 
 294 
 327 
 360 
 
 292 
 327 
 364 
 401 
 
 
 32 
 
 34 
 
 
 36... 
 
 38 
 
 441 
 
 
 
 40 
 
 
 
 
 128 
 139 
 151 
 
 172 
 
 188 
 204 
 221 
 239 
 
 217 
 237 
 
 258 
 279 
 301 
 
 262 
 286 
 311 
 336 
 364 
 
 307 
 335 
 364 
 394 
 426 
 
 352 
 384 
 418 
 452 
 489 
 
 397 
 432 
 471 
 509 
 551 
 
 442 
 481 
 524 
 567 
 613 
 
 487 
 
 42 
 
 528 
 
 44 
 
 577 
 
 46 
 
 625 
 
 48 
 
 676 
 
 
 
 50 
 
 
 
 
 
 257 
 
 324 
 347 
 367 
 
 391 
 418 
 443 
 469 
 
 458 
 489 
 520 
 549 
 
 525 
 561 
 596 
 630 
 666 
 
 592 
 632 
 672 
 710 
 751 
 
 659 
 703 
 748 
 791 
 836 
 
 726 
 
 52 
 
 774 
 
 54 
 
 824 
 
 56 
 
 871 
 
 58 
 
 921 
 
 
 
 60 
 
 
 
 
 
 
 
 
 
 702 
 
 794 
 
 885 
 
 936 
 
 
 
 Stump height 1.5 feet. 
 
 Trees scaled in 16-foot logs with 0.3 foot trimming allowance, to 8 inches 
 diameter inside bark in top, by Scribner Decimal C. rule * 
 
 Basis, 841 tree measurements taken by U. S. Forest Service, and 27 by U. S. 
 Bureau of Plant Pathology on the Stanislaus National Forest and in the Yosemite 
 National Park. Table prepared from taper curves by frustum form factor method. 
 Aggregate check against basic trees shows error of -0.24%. 
 
 ♦This rule has been adopted as standard by the TJ. S. Forest Service. Its values multiplied by 10 are 
 essentially the same as those of the Spaulding rule, which is the legal rule for California. 
 
44 
 
 UNIVERSITY OF CALIFORNIA EXPERIMENT STATION 
 
 TABLE II. 
 
 Site II (Tallest 10% Merchantable Trees of Stand from 7.6 to 9.5 Logs.) 
 Height — Number of 16-Ft. Logs 
 
 Diameter 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Breast- 
 High 
 Inches 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 
 
 
 VOLU 
 
 ME 
 
 Boar 
 
 D FE 
 
 ET IN 
 
 Tens 
 
 
 
 
 10 
 
 4 
 
 6 
 
 12 
 
 15 
 
 
 
 
 
 
 
 
 
 12 
 
 5 
 
 8 
 
 13 
 
 18 
 
 
 
 
 
 
 
 
 
 14 
 
 5 
 
 9 
 
 15 
 
 22 
 
 
 
 
 
 
 
 
 
 16 
 
 5 
 
 11 
 
 18 
 
 25 
 
 33 
 
 
 
 
 
 
 
 
 18 
 
 5 
 
 12 
 
 20 
 
 30 
 
 39 
 
 
 
 
 
 
 
 
 20 
 
 
 13 
 15 
 
 23 
 
 28 
 
 35 
 42 
 
 46 
 55 
 
 58 
 69 
 
 
 
 
 
 
 
 22 
 
 
 24 
 
 
 16 
 
 31 
 
 48 
 
 64 
 
 80 
 
 96 
 
 112 
 
 128 
 
 
 
 
 26 
 
 
 18 
 
 36 
 
 55 
 
 75 
 
 93 
 
 112 
 
 130 
 
 148 
 
 
 
 
 28 
 
 
 
 42 
 
 63 
 
 85 
 
 107 
 
 128 
 
 150 
 
 172 
 
 
 
 
 
 
 30 
 
 
 
 46 
 
 70 
 
 94 
 
 120 
 
 144 
 
 169 
 
 194 
 
 
 
 
 32 
 
 
 
 52 
 
 58 
 
 79 
 88 
 
 106 
 118 
 131 
 
 134 
 148 
 165 
 
 162 
 179 
 197 
 
 189 
 209 
 234 
 
 216 
 239 
 266 
 
 269 
 298 
 
 
 
 34 
 
 
 36 
 
 
 38 
 
 
 
 
 
 144 
 
 181 
 
 218 
 
 256 
 
 293 
 
 330 
 
 
 
 40 
 
 
 
 
 
 158 
 
 199 
 
 240 
 
 281 
 
 323 
 
 365 
 
 
 
 42 
 
 
 
 
 
 
 218 
 237 
 
 263 
 
 286 
 
 308 
 335 
 
 353 
 385 
 
 397 
 433 
 
 482 
 
 
 44 
 
 
 46 
 
 
 
 
 
 
 
 310 
 
 338 
 
 364 
 396 
 
 418 
 454 
 
 470 
 512 
 
 524 
 569 
 
 
 48 
 
 
 50. 
 
 
 
 
 
 
 
 366 
 394 
 
 428 
 461 
 493 
 526 
 561 
 
 491 
 
 528 
 566 
 603 
 644 
 
 554 
 595 
 638 
 679 
 726 
 
 616 
 662 
 710 
 
 756 
 
 808 
 
 
 52.... 
 
 
 54... 
 
 
 56... 
 
 
 58.... 
 
 
 
 
 60 
 
 
 
 
 
 
 
 
 599 
 
 687 
 
 775 
 
 864 
 
 
 
 
 Stump height 1.5 feet. 
 
 Trees scaled in 16-foot logs with 0.3 foot trimming allowance, to 8 inches 
 diameter inside bark in top, by Scribner Decimal C. rule. 
 
 Basis: 124 tree measurements taken by U. S. Forest Service on the Plumas 
 and Tahoe National Forests, and 179 by the U. S. Bureau of Plant Pathology on the 
 Sierra National Forest. 
 
 Table prepared from taper curves by frustum form factor method. 
 
 Aggregate check against basic trees shows error of -0.42%. 
 
Bulletin 329 
 
 A WHITE FIR VOLUME TABLE 
 
 45 
 
 TABLE III. 
 
 Site III (Tallest 10% of Merchantable Trees of Stand 7.5 Logs or Under) 
 Height — Number of 16-Ft. Logs 
 
 Diameter 
 Breast- 
 High 
 Inches 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 4 
 5 
 5 
 5 
 5 
 
 7 
 
 9 
 
 10 
 
 11 
 
 11 
 
 13 
 15 
 16 
 
 18 
 20 
 
 23 
 
 26 
 29 
 
 VOLU 
 
 34 
 
 38 
 
 ME 
 
 48 
 
 Boar 
 
 D FE 
 
 ET IN 
 
 Tens 
 
 
 
 20 
 
 22 
 
 
 12 
 14 
 15 
 17 
 
 22 
 
 26 
 
 28 
 33 
 38 
 
 32 
 
 38 
 44 
 52 
 
 58 
 
 43 
 52 
 60 
 69 
 
 78 
 
 55 
 65 
 74 
 
 85 
 98 
 
 103 
 118 
 
 
 
 
 
 
 24 
 
 26 
 
 28 
 
 
 30 
 
 
 
 41 
 
 47 
 53 
 57 
 
 64 
 
 72 
 80 
 89 
 97 
 
 86 
 
 96 
 
 107 
 
 118 
 
 129 
 
 109 
 121 
 135 
 
 148 
 165 
 
 131 
 146 
 163 
 179 
 197 
 
 155 
 172 
 190 
 211 
 
 232 
 
 177 
 
 197 
 217 
 241 
 266 
 
 
 
 
 32 
 
 
 34 
 
 
 36 
 
 
 38 
 
 
 
 
 40 
 
 
 
 
 105 
 
 142 
 156 
 169 
 183 
 199 
 
 179 
 196 
 213 
 231 
 250 
 
 217 
 
 236 
 
 258 
 279 
 302 
 
 254 
 277 
 301 
 326 
 354 
 
 291 
 318 
 346 
 375 
 406 
 
 
 
 
 42 
 
 
 44 
 
 
 46 
 
 48 
 
 
 50 
 
 52 
 
 
 
 
 
 
 270 
 291 
 310 
 329 
 351 
 
 325 
 349 
 374 
 
 397 
 424 
 
 382 
 410 
 438 
 466 
 498 
 
 437 
 
 471 
 502 
 534 
 571 
 
 492 
 530 
 567 
 602 
 642 
 
 
 
 54 
 
 
 56 
 
 58 
 
 
 60 
 
 
 
 
 
 
 372 
 
 448 
 
 526 
 
 604 
 
 683 
 
 
 
 Stump height 1.5 feet. 
 
 Trees scaled in 16-ft. logs with 0.3 foot trimming allowance, to 8 inches 
 diameter inside bark in top, by Scribner Decimal C. rule. 
 
 Basis: 206 tree measurements taken by U. S. Bureau of Plant Pathology in 
 the Tahoe and Siskiyou regions. 
 
 Table prepared from taper curves by frustum form factor method. 
 
 Aggregate check against basic trees shows error of -0.17%.